Proceedings of 2019 Chinese Intelligent Systems Conference: Volume III [1st ed. 2020] 978-981-32-9697-8, 978-981-32-9698-5

Table of contents :
Front Matter ....Pages i-xi
Hierarchical Pooling Based Extreme Learning Machine for Image Classification (Yan Liu, Zhi Liu, Zhirong Lei)....Pages 1-9
Stability Analysis of Discrete-Time Stochastic Systems with Borel-Measurable Markov Jumps (Hongji Ma, Yuechen Cui, Yongli Wang)....Pages 10-19
Estimating the Diffusion Source in Complex Networks with Sparse Modeling Method (Chaoyi Shi, Qi Zhang, Tianguang Chu)....Pages 20-26
Knowledge Graph Embedding Bi-vector Models for Symmetric Relation (Jinkui Yao, Yulong Zhao)....Pages 27-36
A Density-Based k-Means++ Algorithm for Imbalanced Datasets Clustering (Linchuan Fan, Yi Chai, Yanxia Li)....Pages 37-43
Tracking Control for Space Non-cooperative Tumbling Target (Shihao Sun, Yanjie Zhao)....Pages 44-53
Active Disturbance Rejection Control Based on a Phase Optimized Extended State Observer (Pengfei Xia, Wei Wei)....Pages 54-61
Open-Circuit Fault Diagnosis of an Inverter Based on Bayesian Network (Sumin Han, Yongsheng He, Shuqing Zheng)....Pages 62-70
A B-Spline Surface Stitching Algorithm Based on Point Cloud Data (Xuedong Jing, Yuwei Zhang)....Pages 71-79
Real-Time Recognition of Motor Vehicle Whistle with Convolutional Neural Network (Ming Yan, Chaoli Wang, Song Shen)....Pages 80-88
Analysis of Trace Surface Morphology Based on Fractal and Complexity Theory (Bingcheng Wang, Chang Jing)....Pages 89-96
Research About Abrasion Surface Morphology of Warhead by Structure Function Method (Bingcheng Wang, Chang Jing)....Pages 97-102
Accurate Image Recognition of Plant Diseases Based on Multiple Classifiers Integration (Shuang Liang, Weicun Zhang)....Pages 103-113
Adaptive Control of DC Servo Based on PID Neural Network (Xuedong Jing, Kangkai Cheng)....Pages 114-121
LQR-Based Optimal Leader-Following Consensus of Heterogeneous Multi-agent Systems (Yuling Li, Hongyong Yang, Yize Yang, Yuanshan Liu, Yujiao Sun)....Pages 122-130
Couple-Group Tracking Consensus for Non-linear Multi-agent Systems with Time-Delays (Liqiong Zhang, Weixun Li, Jia Liu)....Pages 131-141
Optimization Algorithm for Power Flow Calculation Using Graph Theory (Yicheng Xu, Yangyang Chen, Tianrun Liu, Wen Chen)....Pages 142-150
A New Approach to Developing General Manipulator Control System Application Based on ROS (Xuedong Jing, Yuquan Xue, Ya’nan Chen)....Pages 151-158
Fault-Tolerant Control Based on LPV-Robust Model Predictive Control for Hypersonic Vehicle (Xiaohe Yang, Weijie Lv, Xiaofang Wei, Chaofang Hu)....Pages 159-168
An Improvement of PWPF in Reaction Control System of Hypersonic Vehicle (Jia Song, Likun Bian)....Pages 169-178
Trajectory Tracking Control of Quadrotor Helicopters Based on Controlled Lagrangians (Jing He, Wei Huo)....Pages 179-193
Design of Object Edge Detection System Based on FPGA (Jisheng Xing, Weile Tan, Jing Bai)....Pages 194-202
Research on Location of Pulse-Diagnosis Point Based on Image Processing (Qunpo Liu, Xiulei Xi, Guanghui Liu, Lingxiao Yang, Hongqi Wang)....Pages 203-210
Bursty Topic Detection Based on Bursty Term Detection and Filtration (Qiang Zhang, Junping Du, Feifei Kou, Zhe Xue)....Pages 211-219
Formation Consistency Research of Multi-robot Systems with Leader-Following (Yujiao Sun, Hongyong Yang, Yize Yang, Yuling Li, Yuanshan Liu)....Pages 220-226
A Method of Non-line-of-Sight Measurement and Location (Haiyan Sun, Xiaobin Li, Jie Zhang, Tianyang Yu)....Pages 227-233
An Adaptive Controller for Wheeled Mobile Robot Trajectory Tracking (Xiao Shen, Wuxi Shi)....Pages 234-242
Real-Time Semantic Segmentation Network for Edge Deployment (Junfeng Zheng, Jiangyun Li, Yan Liu, Weicun Zhang)....Pages 243-249
Solution of Distributed Optimal Control Protocol for Second-Order Multi-agent Systems (Yuanshan Liu, Hongyong Yang, Yize Yang, Yuling Li, Yujiao Sun)....Pages 250-258
The Design of an Intelligent Screw Extruder Control System Based on Fuzzy Control (Yulin Li, Jin Zhou, Qiang Li, Long He, Yonglin Zhang, Shaoyun Song)....Pages 259-267
Tracking via Enhanced Context-Aware Correlation Filter (Mianlu Zou, Zhongyi Hu, Qi Wu, Changzu Chen)....Pages 268-276
Optimization and Simulation of Fuzzy Control Based on SOA (Rong Hua, Huanyu Zhao)....Pages 277-285
A New Fixed-Wing Formation Control Algorithm (Xu Zeng, Xinhua Wang, Weicheng Xu, Yu Zheng, Jiahuan Li)....Pages 286-298
Hinged Sweeper Kinematic Modeling and Path Tracking Control (Xiaohua Wang, Kangkang Xu, Lin Xu, Zhonghua Miao, Jin Zhou)....Pages 299-309
Machine Learning in Industrial Control System Security: A Survey (Dianbin Jiang, Jingling Zhao)....Pages 310-317
Study on Quick Selection Technology of Low-Orbit Spacecraft Collision-Avoidance Strategy (Xiaohong Guo, Xiaohui Xu, Haichen Lin, Xingyi Chen)....Pages 318-324
Close Relative Navigation to a Non-cooperative Maneuvering Target Using Variable Dimension Filters (Qiyang Hu, Dayi Wang)....Pages 325-333
Vision-Based Vehicle Detection in Foggy Days by Convolutional Neural Network (Guizhen Yu, Sifen Wang, Mingxing Li, Yaxin Guo, Zhangyu Wang)....Pages 334-343
An Improved Deep Q-Learning for Intelligent Transmitter Control System (Ying Zhang, Jian Cao, Leiyan Tao, Siwen Xu, Minfeng Wei, Xing Zhang)....Pages 344-351
Containment Control of Second-Order Discrete Time Multi-agent Systems with Leaders (Yize Yang, Hongyong Yang, Yuanshan Liu, Yuling Li, Yujiao Sun)....Pages 352-360
Scattering Prediction from Data of Scale Model Based on Regression Method in SPSS (Jingcheng Zhao, Zongkai Yang, Tao Tang)....Pages 361-370
Coal Mine Power Quality Assessment System Based on Improved Entropy Weight Method (Jingyan Liu, Yumei Wang, Wenliang Yang)....Pages 371-380
A Virtual Instrument of Temperature Measurement for LPG Cylinder Incinerato (Longjun Zhu, Yingchi Zhang, Xuedong Jing)....Pages 381-387
Fast Image Multi-style Transfer and Its Quality Assessment (Xianfeng Zhao, Hai Gao)....Pages 388-397
Application Research on Information System Security Situational Awareness (Houqun Yang, Juan Hu)....Pages 398-407
Research on Vehicle Motion Control Strategy Based on Machine Vision (Jianping Mo, Haijiang Lan)....Pages 408-416
Modelling and Simulation of an Electric Trimmable Horizontal Stabilizer Actuator Based on Bond Graph (Xudong Han, Junsheng Ma, Jian Fu, Liming Yu, Wensen Zhang, Yongling Fu)....Pages 417-425
3D Super-Resolution Reconstruction Based on Multi-view Representation (Yujia Du, Yanping Zheng, Haisheng Li, Li Tan)....Pages 426-434
3D Shape Classification Based on Point Convolutional Neural Network Combining Multi-geometric Features (Guang Zeng, Yujuan Wu, Haisheng Li, Li Tan)....Pages 435-442
Evolutionary Generation of Test Data Based on Reduction of Initial Population Data (Wei Gao, Yan Song, Baoying Ma)....Pages 443-451
The Design of Fuzzy Temperature Controller Based on the Spray Cooling Experiment (Longjun Zhu, Jialong Ren)....Pages 452-460
Tracking Control of Multi-motor Servo System with Input Saturation (Shuangyi Hu, Xuemei Ren, Yongfeng Lv)....Pages 461-469
Adaptive Parameter Estimation for Hammerstein Systems with Asymmetric Dead-Zone Dynamics (Haoran He, Jing Na, Guanbin Gao, Shubo Wang, Qiang Chen)....Pages 470-479
A Quantitative Analysis on Gmapping Algorithm Parameters Based on Lidar in Small Area Environment (Hongyu Wang, Mengxing Huang, Di Wu)....Pages 480-492
A Vision-Based Method for Vehicle Forward Collision Warning (Yanfei Zhang, Zhangyu Wang, Bin Zhou, Guizhen Yu, Chaowei Hu, Li Zhang)....Pages 493-502
Design and Simulation of a Self-balanced and Wheel-Legged Robot (Lufeng Zhang, Qing Guo, Xuemei Ren)....Pages 503-510
Online RPCA Background Modeling Based on Color and Depth Data (Huini Fu, Hengzhu Liu)....Pages 511-517
Research on Vehicle Forward Target Recognition Algorithm Based on Vision and MMW Radar Fusion (Guizhen Yu, Sijia Zhang, Huan Niu, Bin Zhou, Guoqiang Liu, Da Li)....Pages 518-528
Research on Vehicle Forward Pedestrian Recognition Based on Multi-line LIDAR (Chenyang Guo, Guizhen Yu, Li Zhang, Huan Niu, Bin Zhou, Zhangyu Wang et al.)....Pages 529-538
An Approach of Non-stationary Harmonics Decomposition Based on Operator Approximated by Radial Base Function (Ye Zeng, Qunjing Wang)....Pages 539-548
Boost and Ascent Trajectory Design and Guidance Approach for Rocket Launched Supersonic Aircraft (Jianhui Liu, Lansong Wang, Mingang Zhang, Xiaoli Qin, Yajie Ge)....Pages 549-557
A Multi-robot Formation Control Method Based on an Improved Leader-Following Algorithm (Jin Xiao, Mengxing Huang, Di Wu, Chenyu Zhang, Weizhe Chen, Yiyin Ding)....Pages 558-571
Data-Driven Feedback QILC Strategy for Batch Processes (Qinsheng Li, Jiafeng Yu)....Pages 572-580
Distributed Optimization Control for Active Distribution Networks with High Penetration of Distributed PV Units (Kewang Wang, Cungang Hu)....Pages 581-589
Research on the Improved Wavelet Threshold Denoising Method for Coriolis Mass Flowmeter (Dan Feng, Qite Wang, Yanjie Zhao)....Pages 590-596
Research on Localization System of a Permanent Magnet Based on Digital Magnetic Sensors Array (Jiansheng Xu, Ming Xu, Xuan Zhao, William Zhou, Xiaojian Li)....Pages 597-604
Weighted Multiple Support Vector Regression Models Based on Clustering Algorithm (Ling Wang, Kang Li, Qian Ma)....Pages 605-613
Image Reconstruction Based on Compressed Sensing Theory (Minghai Xu, Zhongyi Hu)....Pages 614-619
Four-Point Algebraic Estimation Method for First-Order Systems via Sine Responses (Ling Xu, Feng Ding, Feng Ding)....Pages 620-627
Measurement Selection for Autonomous Satellite Constellation Navigation Using Parallel Extended Kalman Filters (Kai Xiong, Yuan Zhang, Yan Xing)....Pages 628-636
UAV Target Location Based on Multi-sensor Fusion (Hao Li, Zhirong Lei, Ning Zhang)....Pages 637-644
Normal Distribution Sampling Convolutional Neural Network for Fine-Grained Image Classification (Feng Liu, Shuling Dai)....Pages 645-652
Study on the Flow Characteristics of the Slender Body at Static and Dynamic State (Qite Wang, Yafei Zhao, Zhiqiang Jia, Yanjie Zhao, Keming Cheng)....Pages 653-663
TT&C Equipment Site Selection Under Complex Constraints (Qi Tang, Maoyun Guo, Haoxiang Liang, Fei Qi, Yi Chai, Yi Wu)....Pages 664-670
A Novel Polynomial Tracking Differentiator (Jiao Jia, Shan Zhou)....Pages 671-678
Active and Passive Fault Tolerant Control for Winged Aircraft with Simultaneous Actuator and Sensor Faults (Xingguang Xu, Changrong Chen, Zhang Ren, Shusheng Li)....Pages 679-708
Optimal Design of the Flow Field Control in a Cockpit (Zhiqiang Jia, Qite Wang, A. Zeya, Zhonghao Sun, Yanjie Zhao)....Pages 709-717
Research on High Area-to-Mass Ratio Satellite Dynamics (Yafei Zhao, Dan Feng, Shihao Sun, Yanjie Zhao)....Pages 718-726
Consistency Transformation Project of Target Information in Air Defense Weapon System (Shujun Yang, Jianqiang Zheng, Qinghua Ma, Shuaiwei Wang, Yiming Liang, Haipeng Deng)....Pages 727-733
A Mobile Visual Capture Robot Based on the Optimized Adaptive Iterative Training Algorithm (Yiyin Ding, Mengxing Huang, Di Wu, Chenyu Zhang, Weizhe Chen, Jin Xiao)....Pages 734-747
Back Matter ....Pages 749-751

Citation preview

Lecture Notes in Electrical Engineering 594

Yingmin Jia Junping Du Weicun Zhang Editors

Proceedings of 2019 Chinese Intelligent Systems Conference Volume III

Lecture Notes in Electrical Engineering Volume 594

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Lab, Karlsruhe Institute for Technology, Karlsruhe, Baden-Württemberg, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martin, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, Quality and Usability Lab, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Baden-Württemberg, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Junjie James Zhang, Charlotte, NC, USA

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Yingmin Jia Junping Du Weicun Zhang •

•

Editors

Proceedings of 2019 Chinese Intelligent Systems Conference Volume III

123

Editors Yingmin Jia Beihang University Beijing, China

Junping Du Beijing University of Posts and Telecommunications Beijing, China

Weicun Zhang University of Science and Technology Beijing Beijing, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-32-9697-8 ISBN 978-981-32-9698-5 (eBook) https://doi.org/10.1007/978-981-32-9698-5 © Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Contents

Hierarchical Pooling Based Extreme Learning Machine for Image Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yan Liu, Zhi Liu, and Zhirong Lei

1

Stability Analysis of Discrete-Time Stochastic Systems with Borel-Measurable Markov Jumps . . . . . . . . . . . . . . . . . . . . . . . . . Hongji Ma, Yuechen Cui, and Yongli Wang

10

Estimating the Diffusion Source in Complex Networks with Sparse Modeling Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chaoyi Shi, Qi Zhang, and Tianguang Chu

20

Knowledge Graph Embedding Bi-vector Models for Symmetric Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jinkui Yao and Yulong Zhao

27

A Density-Based k-Means++ Algorithm for Imbalanced Datasets Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linchuan Fan, Yi Chai, and Yanxia Li

37

Tracking Control for Space Non-cooperative Tumbling Target . . . . . . . Shihao Sun and Yanjie Zhao

44

Active Disturbance Rejection Control Based on a Phase Optimized Extended State Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pengfei Xia and Wei Wei

54

Open-Circuit Fault Diagnosis of an Inverter Based on Bayesian Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sumin Han, Yongsheng He, and Shuqing Zheng

62

A B-Spline Surface Stitching Algorithm Based on Point Cloud Data . . . Xuedong Jing and Yuwei Zhang

71

v

vi

Contents

Real-Time Recognition of Motor Vehicle Whistle with Convolutional Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ming Yan, Chaoli Wang, and Song Shen

80

Analysis of Trace Surface Morphology Based on Fractal and Complexity Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bingcheng Wang and Chang Jing

89

Research About Abrasion Surface Morphology of Warhead by Structure Function Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bingcheng Wang and Chang Jing

97

Accurate Image Recognition of Plant Diseases Based on Multiple Classifiers Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Shuang Liang and Weicun Zhang Adaptive Control of DC Servo Based on PID Neural Network . . . . . . . 114 Xuedong Jing and Kangkai Cheng LQR-Based Optimal Leader-Following Consensus of Heterogeneous Multi-agent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Yuling Li, Hongyong Yang, Yize Yang, Yuanshan Liu, and Yujiao Sun Couple-Group Tracking Consensus for Non-linear Multi-agent Systems with Time-Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Liqiong Zhang, Weixun Li, and Jia Liu Optimization Algorithm for Power Flow Calculation Using Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Yicheng Xu, Yangyang Chen, Tianrun Liu, and Wen Chen A New Approach to Developing General Manipulator Control System Application Based on ROS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Xuedong Jing, Yuquan Xue, and Ya’nan Chen Fault-Tolerant Control Based on LPV-Robust Model Predictive Control for Hypersonic Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Xiaohe Yang, Weijie Lv, Xiaofang Wei, and Chaofang Hu An Improvement of PWPF in Reaction Control System of Hypersonic Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Jia Song and Likun Bian Trajectory Tracking Control of Quadrotor Helicopters Based on Controlled Lagrangians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Jing He and Wei Huo Design of Object Edge Detection System Based on FPGA . . . . . . . . . . . 194 Jisheng Xing, Weile Tan, and Jing Bai

Contents

vii

Research on Location of Pulse-Diagnosis Point Based on Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Qunpo Liu, Xiulei Xi, Guanghui Liu, Lingxiao Yang, and Hongqi Wang Bursty Topic Detection Based on Bursty Term Detection and Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Qiang Zhang, Junping Du, Feifei Kou, and Zhe Xue Formation Consistency Research of Multi-robot Systems with Leader-Following . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Yujiao Sun, Hongyong Yang, Yize Yang, Yuling Li, and Yuanshan Liu A Method of Non-line-of-Sight Measurement and Location . . . . . . . . . . 227 Haiyan Sun, Xiaobin Li, Jie Zhang, and Tianyang Yu An Adaptive Controller for Wheeled Mobile Robot Trajectory Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 Xiao Shen and Wuxi Shi Real-Time Semantic Segmentation Network for Edge Deployment . . . . 243 Junfeng Zheng, Jiangyun Li, Yan Liu, and Weicun Zhang Solution of Distributed Optimal Control Protocol for Second-Order Multi-agent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 250 Yuanshan Liu, Hongyong Yang, Yize Yang, Yuling Li, and Yujiao Sun The Design of an Intelligent Screw Extruder Control System Based on Fuzzy Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Yulin Li, Jin Zhou, Qiang Li, Long He, Yonglin Zhang, and Shaoyun Song Tracking via Enhanced Context-Aware Correlation Filter . . . . . . . . . . . 268 Mianlu Zou, Zhongyi Hu, Qi Wu, and Changzu Chen Optimization and Simulation of Fuzzy Control Based on SOA . . . . . . . 277 Rong Hua and Huanyu Zhao A New Fixed-Wing Formation Control Algorithm . . . . . . . . . . . . . . . . . 286 Xu Zeng, Xinhua Wang, Weicheng Xu, Yu Zheng, and Jiahuan Li Hinged Sweeper Kinematic Modeling and Path Tracking Control . . . . . 299 Xiaohua Wang, Kangkang Xu, Lin Xu, Zhonghua Miao, and Jin Zhou Machine Learning in Industrial Control System Security: A Survey . . . 310 Dianbin Jiang and Jingling Zhao Study on Quick Selection Technology of Low-Orbit Spacecraft Collision-Avoidance Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 Xiaohong Guo, Xiaohui Xu, Haichen Lin, and Xingyi Chen

viii

Contents

Close Relative Navigation to a Non-cooperative Maneuvering Target Using Variable Dimension Filters . . . . . . . . . . . . . . . . . . . . . . . . 325 Qiyang Hu and Dayi Wang Vision-Based Vehicle Detection in Foggy Days by Convolutional Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 Guizhen Yu, Sifen Wang, Mingxing Li, Yaxin Guo, and Zhangyu Wang An Improved Deep Q-Learning for Intelligent Transmitter Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 Ying Zhang, Jian Cao, Leiyan Tao, Siwen Xu, Minfeng Wei, and Xing Zhang Containment Control of Second-Order Discrete Time Multi-agent Systems with Leaders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Yize Yang, Hongyong Yang, Yuanshan Liu, Yuling Li, and Yujiao Sun Scattering Prediction from Data of Scale Model Based on Regression Method in SPSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Jingcheng Zhao, Zongkai Yang, and Tao Tang Coal Mine Power Quality Assessment System Based on Improved Entropy Weight Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Jingyan Liu, Yumei Wang, and Wenliang Yang A Virtual Instrument of Temperature Measurement for LPG Cylinder Incinerato . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Longjun Zhu, Yingchi Zhang, and Xuedong Jing Fast Image Multi-style Transfer and Its Quality Assessment . . . . . . . . . 388 Xianfeng Zhao and Hai Gao Application Research on Information System Security Situational Awareness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 Houqun Yang and Juan Hu Research on Vehicle Motion Control Strategy Based on Machine Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 Jianping Mo and Haijiang Lan Modelling and Simulation of an Electric Trimmable Horizontal Stabilizer Actuator Based on Bond Graph . . . . . . . . . . . . . . . . . . . . . . . 417 Xudong Han, Junsheng Ma, Jian Fu, Liming Yu, Wensen Zhang, and Yongling Fu 3D Super-Resolution Reconstruction Based on Multi-view Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 Yujia Du, Yanping Zheng, Haisheng Li, and Li Tan

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3D Shape Classification Based on Point Convolutional Neural Network Combining Multi-geometric Features . . . . . . . . . . . . . . . . . . . . 435 Guang Zeng, Yujuan Wu, Haisheng Li, and Li Tan Evolutionary Generation of Test Data Based on Reduction of Initial Population Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 Wei Gao, Yan Song, and Baoying Ma The Design of Fuzzy Temperature Controller Based on the Spray Cooling Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 Longjun Zhu and Jialong Ren Tracking Control of Multi-motor Servo System with Input Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 Shuangyi Hu, Xuemei Ren, and Yongfeng Lv Adaptive Parameter Estimation for Hammerstein Systems with Asymmetric Dead-Zone Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 470 Haoran He, Jing Na, Guanbin Gao, Shubo Wang, and Qiang Chen A Quantitative Analysis on Gmapping Algorithm Parameters Based on Lidar in Small Area Environment . . . . . . . . . . . . . . . . . . . . . 480 Hongyu Wang, Mengxing Huang, and Di Wu A Vision-Based Method for Vehicle Forward Collision Warning . . . . . . 493 Yanfei Zhang, Zhangyu Wang, Bin Zhou, Guizhen Yu, Chaowei Hu, and Li Zhang Design and Simulation of a Self-balanced and Wheel-Legged Robot . . . 503 Lufeng Zhang, Qing Guo, and Xuemei Ren Online RPCA Background Modeling Based on Color and Depth Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Huini Fu and Hengzhu Liu Research on Vehicle Forward Target Recognition Algorithm Based on Vision and MMW Radar Fusion . . . . . . . . . . . . . . . . . . . . . . . 518 Guizhen Yu, Sijia Zhang, Huan Niu, Bin Zhou, Guoqiang Liu, and Da Li Research on Vehicle Forward Pedestrian Recognition Based on Multi-line LIDAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 Chenyang Guo, Guizhen Yu, Li Zhang, Huan Niu, Bin Zhou, Zhangyu Wang, and Da Li An Approach of Non-stationary Harmonics Decomposition Based on Operator Approximated by Radial Base Function . . . . . . . . . 539 Ye Zeng and Qunjing Wang

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Boost and Ascent Trajectory Design and Guidance Approach for Rocket Launched Supersonic Aircraft . . . . . . . . . . . . . . . 549 Jianhui Liu, Lansong Wang, Mingang Zhang, Xiaoli Qin, and Yajie Ge A Multi-robot Formation Control Method Based on an Improved Leader-Following Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 Jin Xiao, Mengxing Huang, Di Wu, Chenyu Zhang, Weizhe Chen, and Yiyin Ding Data-Driven Feedback QILC Strategy for Batch Processes . . . . . . . . . . 572 Qinsheng Li and Jiafeng Yu Distributed Optimization Control for Active Distribution Networks with High Penetration of Distributed PV Units . . . . . . . . . . . 581 Kewang Wang and Cungang Hu Research on the Improved Wavelet Threshold Denoising Method for Coriolis Mass Flowmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590 Dan Feng, Qite Wang, and Yanjie Zhao Research on Localization System of a Permanent Magnet Based on Digital Magnetic Sensors Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 Jiansheng Xu, Ming Xu, Xuan Zhao, William Zhou, and Xiaojian Li Weighted Multiple Support Vector Regression Models Based on Clustering Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 Ling Wang, Kang Li, and Qian Ma Image Reconstruction Based on Compressed Sensing Theory . . . . . . . . 614 Minghai Xu and Zhongyi Hu Four-Point Algebraic Estimation Method for First-Order Systems via Sine Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 Ling Xu, Feng Ding, and Feng Ding Measurement Selection for Autonomous Satellite Constellation Navigation Using Parallel Extended Kalman Filters . . . . . . . . . . . . . . . . 628 Kai Xiong, Yuan Zhang, and Yan Xing UAV Target Location Based on Multi-sensor Fusion . . . . . . . . . . . . . . . 637 Hao Li, Zhirong Lei, and Ning Zhang Normal Distribution Sampling Convolutional Neural Network for Fine-Grained Image Classification . . . . . . . . . . . . . . . . . . . . . . . . . . 645 Feng Liu and Shuling Dai Study on the Flow Characteristics of the Slender Body at Static and Dynamic State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 Qite Wang, Yafei Zhao, Zhiqiang Jia, Yanjie Zhao, and Keming Cheng

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TT&C Equipment Site Selection Under Complex Constraints . . . . . . . . 664 Qi Tang, Maoyun Guo, Haoxiang Liang, Fei Qi, Yi Chai, and Yi Wu A Novel Polynomial Tracking Differentiator . . . . . . . . . . . . . . . . . . . . . 671 Jiao Jia and Shan Zhou Active and Passive Fault Tolerant Control for Winged Aircraft with Simultaneous Actuator and Sensor Faults . . . . . . . . . . . . . . . . . . . 679 Xingguang Xu, Changrong Chen, Zhang Ren, and Shusheng Li Optimal Design of the Flow Field Control in a Cockpit . . . . . . . . . . . . . 709 Zhiqiang Jia, Qite Wang, A. Zeya, Zhonghao Sun, and Yanjie Zhao Research on High Area-to-Mass Ratio Satellite Dynamics . . . . . . . . . . . 718 Yafei Zhao, Dan Feng, Shihao Sun, and Yanjie Zhao Consistency Transformation Project of Target Information in Air Defense Weapon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 Shujun Yang, Jianqiang Zheng, Qinghua Ma, Shuaiwei Wang, Yiming Liang, and Haipeng Deng A Mobile Visual Capture Robot Based on the Optimized Adaptive Iterative Training Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 734 Yiyin Ding, Mengxing Huang, Di Wu, Chenyu Zhang, Weizhe Chen, and Jin Xiao Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749

Hierarchical Pooling Based Extreme Learning Machine for Image Classification Yan Liu1(B) , Zhi Liu2 , and Zhirong Lei3 1

3

Hengxiang Control Technology Company Limited, Xi’an, China yan [email protected] 2 School of Artificial Intelligence, Xidian University, Xi’an, China National Key Laboratory of Science and Technology on Aircraft Control, FACRI, Xi’an, China

Abstract. In this paper, a Hierarchical Pooling based Extreme Learning Machine (HPELM) is proposed for image classification. Extreme Learning Machine based on Local Receptive Fields (ELM-LRF) has been proved to be powerful for image classification. However, ELM-LRF is a shallow network and the features extracted by ELM-LRF is low-level. To obtain better results, one need to enlarge the dimension of the hidden features. This paper extends the concept of deep learning to ELM-LRF. Random convolutional nodes and hierarchical pooling structures are constructed for capturing high level semantic features. HPELM has the ability of feature extraction and classification. It improves the classification performance of ELM-LRF without increasing the number of the neuron in the last hidden layer. Experiments on the MNIST and NORB datasets demonstrate the attractive performance of HPELM even compared with the state-of-the-art algorithms. Keywords: Local receptive field · Hierarchical pooling Image classification · Extreme Learning Machine

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·

Introduction

Image classification is an important and fundamental task of computer vision, data mining and machine learning [1]. It has an extremely large number of domains of application ranging from medicine, bioinformatics to industrial automation, robot, etc. Generally, traditional image classification methods contain two steps: (1) image feature extraction; (2) feature classification. Feature extraction is a key step in classification task. The extracted features are fed into various classifiers, such as Multi-Layer Perception (MLP) or Support Vector Machines (SVM) for classification. The classification performance is highly depends on the feature extractor [3]. Besides, these traditional Machine Learning (ML) methods mostly use shallow structures. Obviously, the generalization performance of classification will degrade when the objects have complex texture structures. c Springer Nature Singapore Pte Ltd. 2020  Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 1–9, 2020. https://doi.org/10.1007/978-981-32-9698-5_1

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In very recent years, Deep Neural Networks (DNN) based Deep Learning (DL) methods have made significant breakthroughs in various areas such as object detection, speech recognition, image classificaiton [19]. Most of the deep models such as AlexNet [16], VGGNet [18], GoogleNet [17] are based on neural networks and have the structures of convolution and pooling. The convolution structure used in deep convolution neural network (CNN) is to imitate the local receptive field of human eye. These models can extract abstract and higherorder features automatically. With the help of big data and powerful computing resources, deep learning has shown excellent performance in various tasks. The training methods of DNN are based on back propagation (BP) algorithm, which suffers from local minima and slow convergence speed etc. Extreme Learning Machine (ELM) is another model that usually be utilized for solving regression and classification problems [8]. ELM is a generalization of feedforward neural networks with single-hidden layer. ELM projects the input data to the hidden feature space by random weights. ELMs use the leastsquare solutions as the solution of the output weight and does not need iterative optimization [7]. ELMs are known for their simplicity, short training time and unusual performance [9]. Recently, more and more studies focus on DNNs with random weights [20– 22]. On the one hand, more and more DL concepts are introduced to ELM. Hierarchical or Multi-Layer ELMs have been proposed for learning deep representations [11–15]. Huang et al. [2] introduced convolution and pooling structures into ELM and proposed ELM-LRF. The Multi-Scale version of ELM-LRF (ELM-MSLRF) are proposed in [3,6]. Different from CNNs, the input weights of ELM-LRF or ELM-MSLRF are generated randomly rather than optimized by iterative training. Since the output weights of ELM-LRF or ELM-MSLRF are calculated analytically without BP learning, the training phase is very fast. However, both ELM-LRF and ELM-MSLRF are shallow networks. In [4] and [5], the structure of Hierarchical ELM-LRF by stacking convolutional and pooling layers are studied. In this paper, we proposed a Hierarchical Pooling based ELMLRF (HPELM) by stacking pooling layers. The main works of this paper are two folds. (1) We develop a novel hierarchical structure to learn rich representations. (2) HPELM can improve the performance of shallow ELM-LRF without increasing the number of the neurons in the last hidden layer. Extensive experiments conducted on the known datasets demonstrate that HPELM is effective. The rest of this paper is organized as follows. Section 2 reviews the ELM and ELM-LRF theories briefly. Section 3 describes the proposed HPELM framework in details. Experiments on known datasets are carried out in Sect. 4 to evaluate the proposed algorithm. Finally, some conclusions are summarized in Sect. 5.

2 2.1

Related Works ELM

The key idea of ELM is the random feature mapping. Denote x ∈ Rd as the input vector, ai ∈ Rd as the input weights and bi ∈ R as the bias, g as the

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nonlinear piecewise continuous function. The random features can be obtained T by u(x) = [u1 (x), u2 (x), · · · , uL (x)] , where ui (x) = g (ai , bi , x), i = 1, 2, · · · , L. L is the dimension of the features. Consider the problem of m-class classification, the outputs of ELM is f (x) =

L 

βi ui (x) = u(x)β,

(1)

i=1 T

T

where, βi = [βi1 , βi2 , · · · , βim ] , βL×m = [β1 , β2 , · · · , βL ] is the output weights between the hidden layer and the output layer. Equation 1 is a Linear regression formulation. Given a training dataset that contains Ns samples N S = {(xi , yi ) |}i=1 , the goal of ELM is to minimize min : βσp 1 + λUβ − Yσq 2 , β

(2)

where, σ1 > 0, σ2 > 0, p, q > 0 and λ is a weight factor. U is the hidden feature matrix U = [u(x1 ), u(x2 ), · · · , u(xN )]T and Y is the class label matrix Y = [y1 , y2 , · · · , yN ]T . The output weight β can be computed using many algorithms, such as singular value decomposition, orthogonal projection and so on. When σ1 = 2, σ2 = 2, p = 2, q = 2, the solution of Eq. 2 is  −1 T I UT U U Y, if N ≥ L λ + β= . (3)  −1 Y, if N < L UT λI + UUT 2.2

ELM-LRF

ELM is essentially a generalization of SLFNs [10]. Therefore, all the variants of SLFNs can be applied to ELM. CNN is an excellent model to deal with visual tasks, in particular image classification. The basic idea of CNN is to learn representation and extract feature from small region of the receptive fields. CNN mainly contains three types of layers, i.e. convolutional, pooling and nonlinear layer. However, in ELM-LRF, there is no non-linear layers and the weights of the convolutional layer is generated randomly. In order to make the network has the properties of translation invariance and frequency selective, the square-root pooling is adopted in ELM-LRF   s+e t+e    (4) c2i,j,k , s, t = 1, · · · , (d − r + 1) hs,t,k = i=s−e j=t−e

where, ci,j,k , hs,t,k represent the neuron (i, j) in the k-th convolutional feature map and the neuron (s, t) in the k-th pooling feature map respectively. d is the size of the previous layer of the convolutional layer, r × r is the size of the convolution kernel and 2e + 1 is the pooling window size. In order to keep the feature dimension unchanged before and after pooling, zeros padding are used before pooling.

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3

HPELM

3.1

HPELM Framework

Fig. 1. The framework of hierarchical pooling based extreme learning machine

The framework of our proposed Hierarchical Pooling based Extreme Learning Machine (HPELM) is shown in Fig. 1. It has just one convolutional layer and n hierarchical pooling layers. Denote K as the number of the convolutional kernels. The output convolutional feature maps of the convolutional layer can be expressed as r r   (xi+p−1,j+q−1 · ap,q,k ) , (5) ci,j,k (x) = p=1 q=1

where, i, j = 1, 2, · · · , d−r +1, K is the number of feature maps of convolutional layer. ap,q,k denotes the random weight value at (p, q) in the k-th convolutional kernel. ci,j,k is the output node (i, j) of the k-th feature map. xi+p−1,j+q−1 is the node (i + p − 1, j + q − 1) of the input layer. The hierarchical square-root pooling layers can be formulated as   s+e t+e    (l−1)2 (0) (l) , hi,j,k = ci,j,k , (6) hs,t,k = hi,j,k i=s−e j=t−e

where, s, t = 1, · · · , (d − r + 1), l = 1, 2, · · · , n, e is the size of pooling, n is the number of pooling layers. The output nodes of the last pooling layer is flattened to a layer (called flatten layer) with size of L = P × Q × K. Where, P, Q is the height and the width of the pooling layer respectively. The flatten layer is the final features nodes and are fully connected with the output layer, the corresponding weight is denoted as β. Suppose that we have m classes, then the output weight β has size of L × m and can be solved by   −1 Y, if N < L HT λI + HHT . (7) β = I −1 T T H Y, if N ≥ L λ +H H

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5

With these hierarchical pooling operations, the size of L is fixed. That is, increase the number of hierarchical pooling layers does not increase the final feature dimension L and the calculation amount of β, but increase the time for computing H. In ELM-LRF, in order to obtain better results, we must enlarge the dimension L. However, in HPELM, we can increase the number of hierarchical pooling layers instead of the dimension L. 3.2

Training of HPELM

Similar to ELM-LRF, for training HPELM, generate K convolutional kernels with random weights 

0 0 0 = a 2 , · · · , a 0K , 1 , a A

2

0k ∈ Rr , k = 1, · · · , K a

(8)

0 ∈ Rr ×K , r is the kernel size. where, A Utilize the singular value decomposition method to orthogonalize weights ˆ Denote a ˆ then a 0 and we obtain A. ˆk as the column of A, ˆk is the orthogonal A 0 basis of A . The weight matrix for the k-th kernel is ak ∈ Rr×r is reshape from 2 ˆk ∈ Rr . a After obtain the kernel weights, utilize Eqs. 5 and 6 to compute the feature maps H, and then use Eq. 7 to compute the output weight matrix β. 2

4

Experimental Results

We test our proposed HPELM method on two datasets: (1) MNIST, (2) NORB. In experiment, we compare the performances of HPELM, ELM-LRF [2] and ELM-MSLRF [3] and some deep learning based models. Denote conv(r, k) as a convolutional layer that has k number of kernels with size r × r, pool(s) as a pooling layer with pooling window size s respectively. 4.1

MNIST Dataset

The MNIST dataset contains 10 kinds (0 to 9) of digits. It contains 60000 training samples and 10000 testing samples. In this experiment, we set the net structure of ELM-LRF to conv(9, 24) − − > pool(5) and the structure of HPELM to conv(9, 24)− > pool(5) − > pool(3)− > pool(5) − > pool(3)− > pool(5) − > pool(3)− > pool(7), We evaluate the performance of HPELM and ELM-LRF with different number of training samples Ns = [1000, 10000, 20000, 30000, 40000, 50000, 60000]. For each Ns , we test the classification errors of HPELM and ELM-LRF with balance factor λ = [0.0001, 0.001, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5]. The minimum error is shown in Fig. 2. We can see that our proposed HPELM can improve the classification accuracy of ELM-LRF on MNIST datasets without increase the dimension of the hidden feature. In Table 1, the prediction results with different methods are shown. From Fig. 2 and Table 1, we can see that our proposed HPELM has competitive results.

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Fig. 2. Classification error vs number of training samples (MNIST) Table 1. Prediction error (%) of different algorithms on MNIST ELM [15] BinaryConnect [25] ELM-LRF [2] MSLRF-ELM [3] HPELM 1.90

4.2

1.01

2.61

1.43

1.07

NORB Dataset

The NORB dataset contains 24300 stereo images for testing and training respectively [2]. In this experiment, we set the net structure of ELM-LRF to conv(4, 28)−− > pool(7) and the structure of HPELM to conv(4, 28)− > pool(7) − > pool(9)− > pool(11)− > pool(9) and set Ns = [100, 1000, 10000, 20000, 24300]. The classification performances of HPELM and ELM-LRF with different factor λ = [0.0001, 0.001, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5] are evaluated. The minimum error is shown in Fig. 3. We can see that our proposed HPELM can also increase the classification accuracy of ELM-LRF on NORB datasets.

Fig. 3. Classification error vs number of training samples (NORB)

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Table 2. Classification error rate (%) of different classification methods on NORB DBN [23] RandomWeights [24] ELM-LRF [2] MSLRF-ELM [3] HPELM 6.5

4.8

3.5

2.5

3.0

Under the above experimental parameters, HPELM has 3.0% error on the NORB dataset, slightly higher than MSLRF-ELM, but perform better than DBN, RandomWeights and ELM-LRF based methods (Table 2).

5

Conclusions

This paper is devoted to introduce the concept of deep learning into extreme learning machine. We focus on making the shallow ELM-LRF network become more deeper and creating deep models that can be trained fastly. In our proposed HPELM model, hierarchical pooling structures are introduced into ELM-LRF. Various experiments are conducted and analysed and the results prove that our proposed hierarchical pooling structure can improve the performance of ELMLRF significantly. Future work will focus on studying deep ELM models for very large datasets.

References 1. Bosch A, Zisserman A, Munoz X (2007) Image classification using random forests and ferns. In: 11th International conference on computer vision. IEEE Press, Rio de Janeiro, pp 1–8. https://doi.org/10.1109/ICCV.2007.4409066 2. Huang G, Bai Z, Kasun LLC, Vong CM (2015) Local receptive fields based extreme learning machine. IEEE Comput Intell Mag 10:18–29. https://doi.org/10.1109/ MCI.2015.2405316 3. Huang J, Yu ZL, Cai Z et al (2017) Extreme learning machine with multi-scale local receptive fields for texture classification. Multidim Syst Sign 28:995–1011. https://doi.org/10.1007/s11045-016-0414-3 4. Liu H, Li F, Xu X, Sun F (2018) Active object recognition using hierarchical local-receptive-field-based extreme learning machine. Memetic Comp 10:233–241. https://doi.org/10.1007/s12293-017-0229-2 5. Lv Q, Niu X, Dou Y, Xu J, Lei Y (2016) Classification of hyperspectral remote sensing image using hierarchical local-receptive-field-based extreme learning machine. IEEE Geosci Remote Sens Lett 13:1–5. https://doi.org/10.1109/ LGRS.2016.2517178 6. Xu X, Fang J, Li Q, Xie G, Xie J, Ren M (2019) Multi-scale local receptive field based online sequential extreme learning machine for material classification. In: Sun F, Liu H, Hu D (eds) Cognitive systems and signal processing, vol 1005. Springer, Singapore, pp 37–53. https://doi.org/10.1007/978-981-13-7983-3 4 7. Ding S, Zhao H, Zhang Y, Xu X, Nie R, Ren M (2015) Extreme learning machine: algorithm, theory and applications. Artif Intell Rev 44:103–115. https://doi.org/ 10.1007/s10462-013-9405-z

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24. Saxe AM, Koh PW, Chen Z, Bhand M, Suresh B, Andrew Y (2011) On random weights and unsupervised feature learning. In: Proceedings of the 28th international conference on international conference on machine learning. Omnipress, Washington, pp 1089–1096 (2011) 25. Matthieu C, Yoshua B, Jean-Pierre D (2015) BinaryConnect: training deep neural networks with binary weights during propagations. In: Advances in neural information processing systems, vol. 28. Curran Associates, Inc., p 3131 (2015)

Stability Analysis of Discrete-Time Stochastic Systems with Borel-Measurable Markov Jumps Hongji Ma(B) , Yuechen Cui, and Yongli Wang Shandong University of Science and Technology, Qingdao 266590, China ma [email protected]

Abstract. This paper is devoted to stability analysis of discrete-time linear systems with Borel-measurable Markov jump parameters and independent multiplicative noises. The relationships are investigated among several stability concepts about the considered dynamics. Specifically, it is shown that strong exponential stability in the mean square sense can guarantee exponential stability, l2 input-output stability and stochastic stability to hold. Moreover, both exponential stability and l2 inputoutput stability give rise to stochastic stability. By a numerical example, it is demonstrated that Borel-measurable Markov jump systems must not be exponentially stable even if it is stochastically stable. Keywords: Stability Multiplicative noise

1

· Markov jump systems · Borel-measurable set ·

Introduction

As one of the most important kinds of hybrid systems, stochastic systems with Markov jump parameters have been extensively researched in recent decades. The impetus for studying Markov jump systems has its root in the potential applications around various fields, such as solar photovoltaic power generation [1], mechanical automation [10] and portfolio optimization [12]. Up to now, a fairly complete sketch of analysis and synthesis has been established for Markov jump systems with finite possible jumps. Among many others, interested readers can refer to [2] and [5] for more details about continuous- and discrete-time Markov jump systems with finite Markov jumps. A new trend on the study of Markov jump systems is to generalize the state space of Markov process from finite to infinite. For example, [6] and [8] have addressed the exponential stability of infinite Markov jump systems based on the spectrum of Lyapunov operator. Optimal control and H2 control problems have also been tackled in [7] and [11], respectively. Recently, the state space of Markov jump parameter has been further extended to the case of Borel-measurable set. The more general state space of Markov process has more potential applications in practice, and inevitably makes the related control issues more complex in the same time (c.f. [3] and [4]). c Springer Nature Singapore Pte Ltd. 2020  Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 10–19, 2020. https://doi.org/10.1007/978-981-32-9698-5_2

Borel-Measurable Markov Jump Systems

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In this paper, our objective is to address the stability of discrete-time linear systems with Borel-measurable Markov jump parameters and independent multiplicative noises. As far as we know, there is few result reported on this type of models. The notions of (strong) exponential stability and l2 input-output stability are proposed for the first time. We will focus on the intrinsic relationships among exponential stability, stochastic stability and l2 input-output stability. The proposed results will lay a solid ground for the further study of optimal and H∞ control problems about the considered models. The outline of this paper is organized as follows. In Sect. 2, some preliminaries are presented for the considered dynamical systems. A useful representation is derived to associate the system state with a Lyapunov operator. Section 3 includes the main results of this paper. Necessary and/or sufficient conditions are provided for the concerned stability properties. The relationships among them are also clarified. Finally, Sect. 4 ends this paper with a brief concluding remark. Notations. Rn : n-dimensional real Euclidean space; Rm×n : the linear space of all m by n real matrices;  · : the Euclidean norm of Rn or the operator norm of Rm×n ; A : the transpose of a matrix (or vector) A; Sn : the set of all n × n symmetric matrices; A > 0 (≥ 0): A is positive (semi-)definite; In : the n × n identity matrix; 1(·) : the indicator function; r(·): the spectral radius of an operator; Z+ = {0, 1, 2, · · · }.

2

Preliminaries

On a complete probability space (Ω, F , P), we consider the following discretetime stochastic systems with multiplicative noises: xt+1 = A0 (ηt )xt + G0 (ηt )vt +

d 

[Ak (ηt )xt + Gk (ηt )vt ]wtk ,

(1)

k=1

where xt ∈ Rn and vt ∈ Rnv represent the system state and exogenous disturbance, respectively. For notational simplicity, x0 is assumed to be deterministic. The random vectors wt = {wt = (wt1 , · · · , wtd )} are mutually independent with E(wt ) = 0 and E(wk wj ) = Id δ(k−j) . The Markov process {ηt }t∈Z+ takes values in a Borel set S with a σ-finite measure μ, and has a transition probability function G (·, ·) associated with the probability density g(·, ·) satisfying  (2) G (, B) = P(ηt+1 ∈ B|ηt = ) = g(, s)μ(ds), B

for any  ∈ S and B ∈ σ(S). In the sequel, the stochastic processes {wt }t∈Z+ are independent of x0 and {ηt }t∈Z+ . Denote by Ft the σ-algebra generated by {ηk , wj |0 ≤ k ≤ t, 0 ≤ j ≤ t − 1}. When t = 0, F0 = σ{η0 }. The initial state of Markov chain η0 has a probability distribution π which fulfills  (3) π(B) = ν()μ(d), ∀B ∈ σ(S), B

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where ν(·) is a nonnegative measurable function defined on S. {y(t, ω) : Let l2 (0, ∞; Rm ) be the space of Rm -valued stochastic processes ∞ Z+ × Ω → Rm }, which are Fk -measurable for all k ∈ Z+ and t=0 Ey(t)2 < a Banach space {H(·) : S → Rm×n |H() ∈ Rm×n ,  ∈ ∞. Denote by Hm×n 1 S} with the norm H1 := S H()μ(d) < ∞. Similarly, we can intro, where the norm is given by H∞ = duce another Banach space Hm×n ∞ will be shorten as Hn1 , and ess sup∈S H(). In the case of m = n, Hm×n 1 m×n so does H∞ . When H() ∈ Sn and H() ≥ 0 for  ∈ S, Hn1 (Hn∞ ) will be writn+ (resp., Hn+ (resp., Hn+ ten as Hn+ ∞ ). Further, the subset of H1 ∞ ) constituting 1 of all uniformly positive elements that satisfying H() ≥ In for some > 0 and ˜ n+ ). ˜ n+ (resp. H any  ∈ S will be denoted by H ∞ 1 v (0 ≤ k ≤ In (1), we assume that the coefficients Ak ∈ Hn∞ and Gk ∈ Hn×n ∞ , M ≤ N means that M () ≤ N () for all  ∈ S. In this d). For M, N ∈ Hn+ 1 case, we have M 1 ≤ N 1 . For a given Banach space X, B(X) indicates the Banach space of all bounded linear operators that map X into X. If Γ ∈ B(X), its uniform induced norm is represented by Γ ξ . To simplify the expression, we introduce the following linear operators defined on Hn∞ :  ⎧ E (U )() = g(, s)U (s)μ(ds), ⎪ ⎪ ⎪ S ⎪ ⎪ d  ⎨  g(s, )Ak (s)U (s)Ak (s) μ(ds), L (U )() = (4) k=0 S ⎪ ⎪ ⎪ d  ⎪ ⎪ ⎩ T (U )() = Ak () E (U )()Ak (). k=0

It can be verified that the operators defined in (4) all belong to B(Hn∞ ). Some fundamental definitions of stability that will be studied are presented below. Definition 1. The zero state equilibrium of discrete-time linear infinite Markov jump system d  Ak (ηt )xt wtk , t ∈ Z+ , (5) xt+1 = A0 (ηt )xt + k=1

or (A; G ) (A := (A0 , · · · , Ad )) for short, is called strongly exponentially mean square stable (SEMSS) if r(L ) < 1, where r(L ) := max{|λ||λ ∈ Λ} denotes the spectral radius of the operator L and Λ is the spectral set of L . Definition 2. (A; G ) is called exponentially mean square stable (EMSS) if there exist β ≥ 1 and α ∈ (0, 1) such that Ext 2 ≤ βαt x0 2 for all t ∈ Z+ , x0 ∈ R n and η0 ∈ S. Here, xt is the state of (5) arising from (x0 , η0 ) at t = 0. Definition 3. The perturbed system (1), or (A, G; G ) for short, is said to be l2 input-state stable if for any x0 ∈ Rn and η0 ∈ S, x ∈ l2 (0, ∞; Rn ) whenever v ∈ l2 (0, ∞; Rnv ). To study the intrinsic relationships among several different types of stability, we need the following useful representation associated with (5).

Borel-Measurable Markov Jump Systems

13

Proposition 1. Let X0 () = x0 x0 ν() and Xt () = E[xt xt g(ηt−1 , )] (t ≥ 1), then Xt+1 () = L (Xt )() for t ∈ Z+ . Proof. For any x0 ∈ Rn , we have X1 () = E[x1 x1 g(η0 , )] =  =



A(s)x0 x0 A(s) g(s, )π(ds)

S

A(s)x0 x0 A(s) g(s, )ν(s)μ(ds) = L (X0 )().

S

Next let us consider the case of t ≥ 1. Substituting the state equation of system (5) into Xt , we will get Xt+1 () = E[xt+1 xt+1 g(ηt , )] (6)     d d     = E E [A0 (ηt )xt + Ak (ηt )xt wtk ][A0 (ηt )xt + Ak (ηt )xt wtk ] g(ηt , ) Ft−1 . k=1

k=1

Taking into account that {wtk }dk=0 are independent of Ft−1 , the above equality yields that Xt+1 () = E[xt+1 xt+1 g(ηt , )] =

d 

    E E[Ak (ηt )xt xt Ak (ηt ) g(ηt , )Ft−1 ,

(7)

k=0

where the assumptions E(wt ) = 0 and E(wk wj ) = Id δ(k−j) have been used. Then, by the knowledge of stochastic analysis, it can be computed that Xt+1 () = E[xt+1 xt+1 g(ηt , )] =

d 

 E

k=0

Ak (s)xt xt Ak (s) g(s, )g(ηt−1 , s)μ(ds), (8)

S

which, via Fubini’s theorem, leads to Xt+1 () =

d  

{Ak (s)E[xt xt g(ηt−1 , s)]Ak (s) g(s, )}μ(ds)

k=0 S

=

d  

{Ak (s)Xt (s)Ak (s) g(s, )}μ(ds) = L (Xt )().

(9)

k=0 S

The desired result is obtained. Remark 1. Since the coefficients of (5) are bounded in the norm  · ∞ , it can be further shown that Xt ∈ Hn+ 1 .

14

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Stability Analysis

In this section, we will clarify the connections among the stability concepts given in the previous section. First of all, we will provide some necessary and sufficient conditions for SEMSS of (5) based on Lyapunov equation/inequality. Theorem 1. (A; G ) is SEMSS if and only if one of the following conditions holds: ˜ n+ such that ˜ n+ , there exists a S ∈ H (i) for any Y ∈ H ∞ ∞ S() −

d 

Ak () E (S)()Ak () = Y (),  ∈ S.

(10)

k=0

˜ n+ such that the following equation has a solution (ii) there exists a Y ∈ H ∞ n+ ˜ S ∈ H∞ : S() −

d 

Ak () E (S)()Ak () = In ,  ∈ S.

(11)

k=0

˜ n+ such that (iii) there exists a S ∈ H ∞ S() −

d 

Ak () E (S)()Ak () > αIn ,  ∈ S,

(12)

k=0

where α > 0 is independent of . Proof. By Definition 1, (A; G ) is SEMSS if and only if L defines an exponentially stable causal evolution. As shown by Proposition 4.2 [3], T may be regarded as the adjoint operator of L with respect to the following bilinear operation:  X, Y = T r[X() Y ()]μ(d), X ∈ Hn1 , Y ∈ Hn∞ , (13) S

where T r(·) denotes the trace of a matrix. Then, the statements (1), (2) and (3) can be drawn from Theorem 2.4 (v), (iv) and (vii) of [5], respectively. The following result reveals that SEMSS can ensure (5) to be EMSS. Theorem 2. If (A; G ) is SEMSS, then (A; G ) is EMSS.

Borel-Measurable Markov Jump Systems

15

Proof. By means of the trace, it can be obtained that Ext 2 = E[T r(xt xt )] = T r[E(xt xt )] = T r{E[E(xt xt |Ft−1 )]} =

d 

T r{E{E[Ak (ηt−1 )xt−1 xt−1 Ak (ηt−1 ) |Ft−1 ]}}

k=0

⎧ ⎫ ⎨  ⎬ = T r E Ak (ηt−1 )xt−1 xt−1 Ak (ηt−1 ) g(ηt−1 , s)μ(ds) ⎩ ⎭ k=0 S ⎧ ⎫ d ⎨ ⎬  = Tr E[Ak (ηt−1 )xt−1 xt−1 g(ηt−1 , s)Ak (ηt−1 ) ]μ(ds) ⎩ ⎭ k=0 S ⎧ ⎫ d ⎨ ⎬  = Tr E{E[Ak (ηt−1 )xt−1 xt−1 g(ηt−1 , s)Ak (ηt−1 ) |ηt−2 ]}μ(ds) ⎩ ⎭ k=0 S ⎧ ⎫  d ⎨ ⎬  = Tr E Ak ()xt−1 xt−1 g(, s)g(ηt−2 , )Ak () μ(d)μ(ds) . (14) ⎩ ⎭ d 

k=0

S

S

Applying Fubini’s theorem to (14), we will arrive at Ext 2 =

d 

⎧ ⎨  Tr

k=0

⎩

S S

⎫ ⎬ Ak ()E[xt−1 xt−1 g(ηt−2 , )]Ak () g(, s)μ(d)μ(ds) . (15) ⎭

Bearing in mind the definition of Xt , (15) turns out to be ⎫ ⎧  ⎨ d  ⎬ Ext 2 = T r Ak ()Xt−1 ()Ak () g(, s)μ(d) μ(ds) ⎭ ⎩ k=0 S S ⎫ ⎧ ⎬ ⎨ L (Xt−1 )(s)μ(ds) . = Tr ⎭ ⎩

(16)

S

Now making use of Proposition 1, it follows from (16) that Ext 2 =



 T r[L t (X0 )(s)]μ(ds) ≤ n

S

L t (X0 )(s)μ(ds) = nL t (X0 )1 . (17) S

If system (5) is SEMSS, then r(L ) < 1. According to Lemma 1 of [9], there exist β˜ ≥ 1 and α ∈ (0, 1) such that L t  ≤ βαt . Thus, (17) implies that ˜ t X0 1 ≤ nβαt x0 2 , Ext+1 2 ≤ nL t X0 1 ≤ nβα where β = nβ˜ ≥ 1. This ends the proof.

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∞ Remark 2. Recall that in [3], if t=0 E(xt 2 ) < ∞ for any (x0 , η0 ) ∈ Rn × S, then (A; G ) is called stochastically stable (SS). It is obvious that if (A; G ) is EMSS, then it must be SS. However, the following example shows that the converse implication does not stand. Example 1. Consider a one-dimensional system in the form of (5). The Markov chain {ηt }t∈Z+ takes values in S = {Bi |Bi = (i, i+1], i ∈ Z+ } and the transition probability density is given by g(, s) = 1 if  ∈ Bi and s ∈ Bi+1 (i ∈ Z+ ), or else g(, s) = 0. The coefficients of (5) are selected as A0 (ηt ) = i/(i+1) and Ak (ηt ) = 0 (1 ≤ k ≤ d) when ηt ∈ Bi (i ∈ Z+ ). Moreover, the initial state of Markov chain 1 2 for any is set to be η0 = 1. By calculation, it is got that Ext 2 = (t+1) 2 x0  n x0 ∈ R . We can derive that the considered system is stochastically stable by Remark 2.1, but not EMSS. Indeed, if there are β ≥ 1 and α ∈ (0, 1) such that 1 t Ext 2 ≤ βαt x0 2 , then (t+1) 2 ≤ βα will hold sine some t ∈ Z+ . However, it βαt 2 t→∞ 1/(t+1)

is impossible because lim

= 0.

Below, we focus on the l2 input-output stability of (A, G; G ), which characterizes the physical phenomenon that the perturbed output preserves finite energy in the case that (A, G; G ) is influenced by a finite-energy exogenous disturbance signal. This property plays a key role in the analysis of disturbance attenuation level. It will be shown that internal stability in the sense of SEMSS can ensure the external stability of (A, G; G ). Theorem 3. If (A; G ) is SEMSS, then (A, G; G ) is l2 input-output stable. Proof. If r(L ) < 1, then by the item (ii) of Theorem 1, we confirm that there exists S ∈ Hn+ ∞ with In ≤ S() < δIn (δ > 1,  ∈ S) such that S() −

d 

Ak () E (S)()Ak () = In .

(18)

k=0

Let xt be the state of (A, G; G ) corresponding to the initial state of (x0 , η0 ) ∈ Rn × S and v ∈ l2 (0, ∞; Rnv ). It may be derived that E[xt+1 S(ηt+1 )xt+1 ] − E[xt S(ηt )xt ] = −E{xt 2 +

d 

[2xt Ak (ηt )E (S)(ηt )Gk (ηt )vt + vt Gk (ηt )E (S)(ηt )Gk (ηt )vt ]}.

(19)

k=0

By the technique of completing square, we can represent (19) as follows: E[xt+1 S(ηt+1 )xt+1 ] − E[xt S(ηt )xt ] d √ 1 1 1 xt − 2 d + 1Ak (ηt ) E (S)(ηt )Gk (ηt )vt 2 ] E[ √ = − Ext 2 − 2 2 k=0 d+1

+

d  k=0

(20)

E{vt Gk (ηt ) [E (S)(ηt ) + 2(d + 1)E (S)(ηt )Ak (ηt )Ak (ηt ) E (S)(ηt )]Gk (ηt )vt }.

Borel-Measurable Markov Jump Systems

17

Since S, A and G are all bounded in the norm  · ∞ , there holds Gk (ηt ) [E (S)(ηt ) + 2(d + 1)E (S)(ηt )Ak (ηt )Ak (ηt ) E (S)(ηt )]Gk (ηt )∞ ≤ ζ for some ζ > 0. Hence, it follows from (21) that 1 E[xt+1 S(ηt+1 )xt+1 ] − E[xt S(ηt )xt ] ≤ − Ext 2 + ζ(d + 1)Evt 2 . 2

(21)

Due to In ≤ S() < δIn for  ∈ S, it is clear that −Ext 2 < −δ −1 E[xt S(ηt )xt ]. Therefore, (21) leads to E[xt+1 S(ηt+1 )xt+1 ] < ρE[xt S(ηt )xt ] + ζ(d + 1)E(vt 2 ), ρ = 1 −

1 . (22) 2δ

By induction on t in (22), it is shown that E[xt S(ηt )xt ] < ρt E[x0 S(η0 )x0 ] + ζ(d + 1)

t−1 

ρt−i−1 Evi 2 .

(23)

i=0

Taking sum on both sides of (23) over [0, ∞) and reminding S() > In , we have ∞ 

Ext 2 SDK(c) Dden (p, c) = SDK(c) (3) SDK(c) SDK(q) for SDK(p) ≤ SDK(c) We define the sum of the distances of the K nearest neighbors of an object as the SDK of this object. Definition 3. The similarity between an object p and the cluster center c is defined as (4) S(p, c) = Dtrad (p, c) + Dden (p, c) 2.2

Algorithm Description and Analysis

Algorithm 1. density-kmeans++ algorithm Input: D,k Output: labels 1: Get SDK(p), p ∈ D. 2: Get the k initial cluster centers by kmeans++. 3: Classify each object to the nearest cluster center with S(p, c). 4: Calculate cluster centers and select the nearest object as cluster centers. 5: Repeat 3, 4 until the condition is met.

The time complexity of the first step is the largest in all steps, which is O(N 2 + K ∗ N logN ) (can be reduced to O(K ∗ N logN ) by constructing the kd-tree [10], also can be reduced by r*-tree [11]), so the total time complexity is O(K ∗ N logN ). The space complexity of the first step in all steps is also the largest, which is O(KN ), so the total space complexity is O(KN ).

3

Experiments

In this section, we select state-of-the-art improved k-means [12] as compared algorithm, and we adopt NMI, ARI to evaluate the performance of densitykmeans++ on synthetic datasets and real datasets. The range of NMI is [0, 1]. The range of ARI is [−1, 1]. The higher the value, the better the clustering performance. 3.1

Synthetic Datasets

We only adopted one synthetic dataset, which is used to explain why densitykmeans++ can get better results than k-means++.

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Fig. 1. The comparison of truth labels and clustering results on synthetic dataset

It can be seen from Fig. 1 that k-means++ classifies a larger part of the object of the right cluster into a cluster with a higher density on the left side, but density-kmeans++ does not make this kind of mistake, and density-kmeans++ obtains the closest result to the real label. Density-kmeans++ recognizes the density difference between the two clusters, so the two clusters are better separated. 3.2

UCI Datasets

We adopted UCI [13] datasets to verify the performance of density-kmeans++. The distribution of datasets can be seen in Table 2. Table 2. Distribution of 8 real datasets Datasets

Distribution

Digits

90*5,∼180*5

Iris

10,30,50

Wine

59,71,48

Wholesales

298,142

Data-user-modeling 24,129,122,102,26 Landsat-satellite

461,224,397,211,237,470

Glass

70,76,17,13,9,29

Pima

268,500

As can be seen from Table 2, there are 8 imbalanced datasets. The experimental results on datasets can be seen from Fig. 2. From Fig. 2, we observe that the performance of density-kmeans++ on five datasets is significantly improved compared with k-means++. It can be inferred that density-kmeans++ has strong adaptability to imbalanced datasets.

Density-Based k-Means++

41

Fig. 2. The comparison of experiments results generated on UCI datasets

3.3

Western Reserve University Bearing Data

Western Reserve University Bearing Data [14] is a classic bearing data that is widely applied in bearing data research. The data numbers we use are Normal 2, B007 2, B0014 2, B0021 2, IR007 2, IR0014 2, IR0021 2, OR007@6 2, OR0014@6 2, OR0021@6 2. They are from 12k Drive End Bearing Fault Data. We randomly take 1024 points from the time domain data as the original information of a sample, and extract 10 features from the time domain signal, then perform FFT on the time domain signal, finally extract 10 features from the frequency domain signal. Each sample contains 20 features [15] (Tables 3 and 4). Table 3. Distribution of bearing datasets Datasets Distribution Bearing1 1000,900,800,700,600,500,400,300,200,100 Bearing2 1000*5,100*5 Bearing3 100*5,1000*5

Table 4. Quantitative comparison of experiments results on bearing data k-means++ Density-kmeans++ Bearing1 NMI 0.82 ARI 0.72

0.83 0.77

Bearing2 NMI 0.80 ARI 0.72

0.85 0.80

Bearing3 NMI 0.79 ARI 0.66

0.83 0.72

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By extracting 20 features from the bearing data and unsupervised learning of the 10 types of bearing data, we found that the density-kmeans++ have good performance and can classify most of the bearing data into the correct class. Compared with k-means++, density-kmeans++ performs better on bearing datasets.

4

Conclusion

In this study, we propose density-kmeans++, which has the ability to process imbalanced datasets. Compared with k-means++, it exhibits better performance in UCI and bearing datasets. Its time complexity is O(K ∗ N logN ), although it is acceptable, but higher than other improved k-means algorithms. In future work we will focus on improving its efficiency.

References 1. Han J, Pei J, Kamber M (2011) Data mining: concepts and techniques. Elsevier, New York 2. Macqueen J (1965) Some methods for classification and analysis of multivariate observations. In: Proceedings of berkeley symposium on mathematical statistics & probability 3. Tian Z, Ramakrishnan R, Livny M (1996) BIRCH: an efficient data clustering method for very large databases. In: ACM SIGMOD international conference on management of data. https://doi.org/10.1145/233269.233324 4. Ester M, Kriegel HP, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: International conference on knowledge discovery & data mining 5. Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905. https://doi.org/10.1109/34.868688 6. Pearson R, Goney G, Shwaber J (2003) Imbalanced clustering for microarray timeseries. In: Proceedings of the ICML, ICML, Washington DC, vol 3 7. Chen L, Cai Z, Chen L, Gu Q (2010) A novel differential evolution-clustering hybrid resampling algorithm on imbalanced datasets. In: International conference on knowledge discovery & data mining. IEEE. https://doi.org/10.1109/WKDD. 2010.48 8. Li X, Chen ZG, Yang F (2013) Exploring of clustering algorithm on classimbalanced data. https://doi.org/10.1109/ICCSE.2013.6553890 9. Fan J, Niu Z, Liang Y, Zhao Z (2016) Probability model selection and parameter evolutionary estimation for clustering imbalanced data without sampling. Neurocomputing 211:172–181. https://doi.org/10.1016/j.neucom.2015.10. 140 S092523121630577X 10. Brown RA (2014) Building a balanced k-d tree in o(kn log n) time. Computer Science 11. Beckmann N, Kriegel HP, Schneider R, Seeger B (1990) The r*-tree: an efficient and robust access method for points and rectangles. ACM SIGMOD Rec 19(2):322–331. https://doi.org/10.1145/93605.98741

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12. Arthur D (2007) k-means++: the advantages of careful seeding. In: Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, 2007. ACM. https://doi.org/10.1145/1283383.1283494 13. UCI Machine Learning Repository. http://csegroups.case.edu/bearingdatacenter/ home 14. Bearing Data Center. http://csegroups.case.edu/bearingdatacenter/home 15. Liu H, Zhou JZ, Xu YH, Zheng Y, Peng XL, Jiang W (2018) Unsupervised fault diagnosis of rolling bearings using a deep neural network based on generative adversarial networks. Neurocomputing 315:412–424. https://doi.org/10.1016/j.neucom. 2018.07.034

Tracking Control for Space Non-cooperative Tumbling Target Shihao Sun and Yanjie Zhao(B) China Academy of Electronics and Information Technology, Beijing 100041, China zhaoyj [email protected]

Abstract. As most space invalid targets are in tumbling state, it brings a great challenge to carry out on-orbit service tasks under no communication and cooperation. This paper aims at the steady observation task of tumbling target. Firstly, the design method of virtual target based on feature point image coordinates is described, and the model of tracking the virtual target are established. Secondly, an active disturbance rejection controller is designed under the parameter uncertainty and external disturbances. Finally, the simulation results show that the proposed method can achieves the stable observation for the target feature area. Keywords: Tumbling target · Feature area Active disturbance rejection control

1

· Stable observation ·

Introduction

In the on-orbit service tasks, the failure condition, external shape, capture location and other features of the invalid target are always unknown, the service spacecraft should first to carry out the stable observation for the target before implementing the capture and the follow-up repair and maintenance operation. However, most invalid targets are in tumbling state, stable observation of service spacecraft will inevitably involve synchronous control of attitude and orbit. Many researchers have carry out a large amount of researches on the attitude and orbital coupling, input constraint, optimal fuel and other issues in this process. Such as incremental saturation PID control [1], model predictive control [2], robust adaptive control [3], sliding mode control [4], etc. These methods have different performance advantages. However, these methods need to use accurate and continuous tumbling target relative attitude and orbit information as control input. Considering the non-cooperative characteristics of the target and the limitations of the spacecraft measurement means, the applicability of the above method has been affected to some extent. Therefore, this paper designs a virtual target associated with a feature point by the image information obtained from a monocular camera; and then, a dynamic model of attitude and orbit error is established to track the region of the virtual target feature point. And at the same time considers the affect c Springer Nature Singapore Pte Ltd. 2020  Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 44–53, 2020. https://doi.org/10.1007/978-981-32-9698-5_6

Tracking Tumbling Target

45

from the parameter uncertainty and external disturbances, an active disturbance rejection controller is designed, which effectively resolves the feature area stable tracking issue in the case of unknown motion state information of tumbling target. Similar research work has not been seen in the existing literature.

2

Coordinate System and Symbol Definition

In this section, gives out the basic coordinate system as required for modeling, and the symbol notation of variables as used in this paper.

Fig. 1. Coordinate of spacecrafts

2.1

Fig. 2. Camera coordinate

Basic Coordinate Systems

The whole task system involves an out-of-control tumbling target spacecraft and a controlled service spacecraft, as shown in Fig. 1. In order to describe the position and attitude of the target spacecraft and service spacecraft in space, Four coordinate systems are defined as below: – Earth equator inertial coordinate system Fe : oe − xe ye ze – Targeted spacecraft body coordinate system Ft : ot − xt yt zt – Service spacecraft body coordinate system Fs : os − xs ys zs

Fig. 3. Feature point coordinate

Aim at the stable observation task, this paper assumes the service spacecraft is just assembled with an monocular camera sensor, as shown in Fig. 2, in order to describe the imaging relationship, Three coordinate systems are defined as below:

46

S. Sun and Y. Zhao

– Imaging coordinate system Fi : oi − yi zi – Digital image coordinate system Fuv : o − uv – Camera coordinate system Fc : oc − xc yc zc In this paper, it is assumed that the target feature points which can be extracted in the observation task are five coplanar non-collinear points. In order to describe the relationship between feature points in the target spacecraft body coordinate system as shown in Fig. 3 One coordinate systems are defined as below: – Feature point coordinate Fr : or − yr zr 2.2

Basic Symbol

Considering that there are many types of vectors and coordinate systems involved in this paper, in order to avoid confusion in the representation of vectors in different coordinate systems. If there is no special description, the following notation of the middle component array, component Matrix, etc. will always be used in this paper. (l)a ˙a (l) (l)a (l)× a (J )a r ab Q ab R ab T ab (p)a [p]a ω ab f αi Mc

3

The component array of vector l in coordinate system Fa (l)a = [lxa lya lza ] The component array of vector derivative l in coordinate system Fa The derivative of the component array of the vector l in the coordinate system Fa Multiply matrix with vector lin coordinate system Fa Tensor J component matrix in coordinate system Fa vector of Point a points to point B Attitude quaternion transformed from Fb to Fa Rotating matrix transformed from Fb to Fa homogeneous transformation matrix transformed from Fb to Fa coordinates of Point p in coordinate system Fa homogeneous coordinates of Point p in coordinate system Fa Attitude angular velocity vector of Fa relative to Fb Focal length of the camera Imaging magnification factor of the camera Internal parameter matrix of the camera

Modeling of Virtual Target Tracking Control

The control target of this paper is to achieve the stable measurement for the feature point image pixel in targeted spacecraft. Assuming that the monocular camera in service spacecraft has successfully extracted the image coordinate value of the feature point, and take the image coordinate value at the initial moment of the task as the baseline, construct a virtual target corresponding to the first targeted image, and then take the initial state of the relative virtual target as the expected status, implement the attitude and orbital tracking control to achieve the stable measurement.

Tracking Tumbling Target

3.1

47

Design of Virtual Target

Assume the virtual target body coordinate system as Ftv , the position and attitude homogeneous coordinate transformation of the relative service spacecraft body coordinate system Fs at the initial moment is:   Rstv (0) (rstv (0))s (1) Tstv (0) = 01×3 1 where Rstv (0) and (rstv (0))s can be designated arbitrarily   Furthermore, based on the image coordinates um vm of the feature points pm , (m = 1, 2, . . . , 5) at the initial moment, we can get the coordinates of the feature point pm in camera coordinate at the normalized focal condition according to the principle of Monocular visual imaging: rcpm xc um − u0 = rcpm zc αi f rcpm yc vm − v 0 = rcpm zc αi f

(2)

Assume that the plane where the feature point located is parallel to the oc xc yc plane of the camera coordinate system, with a distance of (rstv (0))s , i.e. rcpm zc = (rstv (0))s , which gives the homogeneous coordinates of pm points in the camera coordinate system of Fc ⎡ um −u0 ⎤ αi f (rstv (0))s  ⎢ vm −v0 (rstv (0))s  ⎥ αi f ⎥ (3) [pm (0)]c = ⎢ ⎣ (rst (0))s  ⎦ v 1 According to the coordinate transformation relationship, the homogeneous coordinates of the feature point pm in the virtual target ontology coordinate system Ftv can be obtained −1 (0)Tsc [pm (0)]c [pm ]tv = Tst v

(4)

Further, follow the setting of the feature point reference coordinate system in Fig. 3, we can get the feature point coordinate in the virtual reference coordinate Frv , i.e.: (r tv rv )tv = (p1 )tv (orv xrv )tv =

(r p1 p2 )tv (r p1 p2 )tv 

(r p1 p2 )tv = (p2 )tv − (p1 )tv (orv zrv )tv =

(r p1 p2 )× tv (r p1 p3 )tv (r p1 p2 )× tv (r p1 p3 )tv 

  R tv rv = (orv xrv )tv (orv yrv )tv (orv zrv )tv

(r p1 p3 )tv = (p3 )tv − (p1 )tv × v

(orv yrv )tv = (orv zrv )t (orv xrv )tv T tv rv =

  R tv rv (r tv rv )tv 01×3 1

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Therefore, the homogeneous coordinates of the feature point pm in the virtual reference coordinate system Frv can be obtained using Ttv rv [pm ]tv = Tt−1 [pm ]tv v rv

(5)

Then, we get the virtual target associated with the first targeted image, and the virtual target is coincide with the real spacecraft, so the tracking of non-cooperative target is equivalent to transform to the tracking of cooperative target of the known feature point position. 3.2

Modeling of the Tracking Error

In the above section, according to the feature point image coordinate, as well as the assumed initial relative position and attitude of two spacecrafts,we construct a virtual rigid body, and calculate the position of the feature point on the virtual rigid body. Then, we can calculate the position and attitude of the relative virtual target of the service spacecraft in real time by PnP algorithm [5]: Tcrv (t) = PnP(Mc , (pm )rv , im ) Tstv (t) = Tsc Tcrv (t)Tt−1 v rv

(6)

The relative position corresponding to the first image is used as the expected position of the service spacecraft relative to the virtual target, i.e. the desired target image is guaranteed to be the first image: Tsd tv (t) = Tsc Tcrv (0)Tt−1 v rv

(7)

The error homogenization matrix between the current position and the expected position of the service spacecraft is:   Rssd (t) (rssd (t))s (8) = Tstv (t)Tsd tv (t)−1 Tssd (t) = 01×3 1 Using the Rssd (t) and the relationship between rotation matrix and quaternion, we can calculate the attitude tracking error quaternion Qssd . Moreover, the orbital tracking error (rsd s (t))e in inertial coordinate system can be calculated using (rssd (t))s : (9) (rsd s (t))e = −Res (rssd (t))s Further, set differentiated twice for the orbital tracking error and the attitude tracking error, and using the vector derivative and quaternion derivative properties, we can obtain: (rsd s )e = (rts )e − (rtsd )e

= f ((rsd s )e , (rsd s )e ) + b(fs )e + dets

(10)

Tracking Tumbling Target

49

where, vector function f ((rsd s )e , (rsd s )e ), input gain b, Uncertainty and disturbance dets can be described as

(res )e · (rts )e μ ) − (r ) 3(r f ((rsd s )e , (rsd s )e ) = es e ts e (res )e 3 (res )e 2 1 (11) b= ms dets = (dats )e − (rtsd )e q¨vssd = f (qvssd , q˙vssd ) + b(qvssd )(τ )s + dvssd

(12)

where, vector function f (qvssd , q˙vssd ) can be described as ⎧  (ωssd )s = 2(I3 − qvssd qvss )−1 B  (Qssd )q˙vssd ⎪ ⎪ d ⎪ ⎪ ⎨ 1 f (qvssd , q˙vssd ) = − qvssd (ωssd ) s (ωssd )s 4 ⎪ ⎪ ⎪ 1 ⎪ −1 × ⎩ + B(qvssd )[(ωssd )× s (ωse )s − (Js )s (ωse )s (Js )s (ωse )s ] 2 (13) vector function b(qvssd ) can be described as b(qvssd ) =

1 B(qvssd )(Js )−1 s 2

(14)

uncertainty and disturbance dvssd can be described as 1 1 dvssd = − B(Qssd )Rssd (ωsd e )sd + B(qvssd )(Js )−1 s (dτs )s 2 2

(15)

Remark 1. When calculating the quaternion vector part,due to positive and negative quaternion correspond to the same error attitude, in order to ensure the state continuity, set qvssd = sign(q0ssd )qvssd ,where sign(·) is a symbol function without zero value.

4

Active Disturbance Rejection Control Design

According to Eqs. (10) and (12), the attitude and orbit tracking of the above virtual targets are all transformed to the stable control of three input three output second order dynamic system. Dynamic system model can be written as: y¨ = f (y, y) ˙ + b(y)u + d

(16)

y = 03×1

(17)

where the control object is Compare with Eq. (12), we can obtain that y = qvssd , and compare with Eq. (10), we can obtain that y = (rsd s )e .

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Considering attitude and orbital dynamic system also exists environment interference, spacecraft inertia, incorrect quality parameters lead to the uncertainty of the model, as well as lack of speed information, model (16) is further written as: ˙ ) + δf (y, y) ˙) ˙ − f0 (y, yˆ ˙ + δb(y)u + d + b0 (y)u + f0 (y, yˆ y¨ = f0 (y, y)

(18)

˙ is the estimated value of the y. where,yˆ ˙ ˙ ), and set ω = f0 (y, y)−f ˙ )+ Do the input transfer v = b0 (y)u+f0 (y, yˆ ˙ ˆ 0 (y, y δf (y, y) ˙ + δb(y)u + d as the total disturbance of the system, set x1 = y,x2 = y˙ as the state of the system, then we can get the state space form of the Eq. (18) as x˙ 1 = x2 x˙ 2 = ω + v y = x1

(19)

Then, design a linear Active disturbance rejection controller: ˆ˙ 1 = x ˆ 2 + l1 (y − x ˆ1) x ˙x ˆ2 = x ˆ 3 + v + l2 (y − x ˆ1) ˙x ˆ 3 = l3 (y − x ˆ1)

(20)

ˆ 1 − k2 x ˆ2 − x ˆ3 v = −k1 x   is the gain of the observer, and can set as L = where, L = l1 l2 l3    3ωo 3ωo2 ωo3 usually, where ω0 is the bandwidth of the observer. The gain of the controller can be set as k1 = ωc2 , k2 = 2ωc , where ωc is the bandwidth of the controller. Based on the reference [6], the controller (20) can stabilize the system.

5 5.1

Simulation Condition

The initial parameters of service and target spacecraft:   (Jt )t = diag( 134914 608891 0528052 )kgm2 , mt = 8000 kg, ⎡ ⎤ 11236 126 158 (Js )s = ⎣ 126 41255 99 ⎦ kgm2 , ms = 2000 kg, 158 99 36528   Qte (t0 ) = −0.62 0.0097 0.281 0.73 ,   (ωte )t (t0 ) = −0.022 0.036 0.032 rad/s,   Qse (t0 ) = 0.906 −0.0158 −0.0128 −0.422 ,   (ωse )s (t0 ) = −0.0157 −0.018 0.01 rad/s,     (res )e (t0 ) = 0 5 50 m, (res )e (t0 ) = 0 1 0 m/s,

Tracking Tumbling Target

51

The position of the five feature points in the feature point reference coordinate system Fr are set as:     (rrp1 )r = 0 0 0 m (rrp2 )r = 1.5 0 0 m       (rrp3 )r = 2 1 0 m (rrp4 )r = 1 2.1 0 m (rrp5 )r = −0.4 0.8 0 m The origin position of reference coordinate system Fr in the body coordinate of the target spacecraft and the location of the camera are set as:     (rtr )t = −0.2 −0.6 −2 m, (rsc )s = 0.1 1.5 1 m and the attitude of the camera is: ⎡ ⎤ 0.9997 −0.02 −0.015 Rsc = ⎣0.0198 0.9998 −0.01 ⎦ 0.0152 0.0097 0.9998 Assuming the camera is calibrated, the focal length f = 0.1m, magnification factor if image plane is αi = 7200 pixels/m, the size of image is 640 × 480 pix2 , Pixel Coordinates of the Center Point u0 = 320 pix, v0 = 240 pix, Disturbance and uncertainty parameters Considering the uncertainty of the inertia and qualityof the service spacecraft, the estimated value is  (Js0 )s = diag( 10000 40000 30000 )kgm2 , ms0 = 2500, image measurement noise1.5 ∗ randn(1), orbital disturbance dft = mt ∗ 0.0001 ∗ randn(3, 1), dfs = ms ∗ 0.0001 ∗ randn(3, 1), attitude disturbancedτt = 0.001 ∗ randn(3, 1), dτs = 0.001 ∗ randn(3, 1), where randn(·) is a random number generation function in MATLAB, and the corresponding interval is [−1, 1] Zero mean Gaussian distribution random number of The control period and measurement period are also H = 0.1, determining the parameters in the LESO controller(20) are ωo = 0.5, ωc = 0.5. Results

450

450

400

400

350

350

300

300

250 200

P

1

P

150

2

V (pixel)

V (pixel)

5.2

250 200

p

1

p

150

2

p

P

3

100

P

3

100

p

4

4

P

50 0

5

0

100

200

300 400 U (pixel)

500

600

Fig. 4. The first image.

p

50 0

5

0

100

200

300 400 U (pixel)

500

600

Fig. 5. The image in the tracking process.

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Construct a virtual target based on the first image of the target feature point shown in Fig. 4: ⎡ ⎤ 100 0   ⎢0 1 0 Rstv (0) (rstv (0))s 0 ⎥ ⎥ =⎢ (21) Tstv (0) = ⎣ 01×3 1 0 0 1 50.0418⎦ 000 1 ⎡ ⎤ −0.0880 0.9960 −0.0150 −1.7829   ⎢−0.9961 −0.0882 −0.0100 1.3442 ⎥ Rtv rv (rtv rv )tv ⎥ Ttv rv = =⎢ (22) ⎣−0.0113 0.0141 0.9998 0.9783 ⎦ 01×3 1 0 0 0 1.0000 [p1 ]tv = [0, 0, 0], [p2 ]tv = [1.4442, 0, 0], [p3 ]tv = [1.7692, 0.6684, 0]

(23)

[p4 ]tv = [0.6750, 1.3873, 0], [p5 ]tv = [−0.4854, 0.5409, 0]

The target feature point imaging is shown in Fig. 5, the relative attitude and relative orbital curve of two spacecraft are shown in Figs. 6 and 7, from the figures we can see the target feature point in a whole stage are all in the image plane, ensure the target feature point is always observable, the relative position and attitude of two spacecrafts are keeping in the initial state of the observation task. 1.5

60 q

1

Relative Position (m)

Relative Attitude

q0 1

q2 q3

0.5

0

−0.5

0

100

200

300 Time (s)

400

500

600

Fig. 6. The curve of relative attitude

6

40

x y z

20

0

−20

0

100

200

300 Time (s)

400

500

600

Fig. 7. The curve of relative orbit

Conclusions

Aiming at the problem of characteristic region stability observation under the unknown motion state information of tumbling target, this paper only uses monocular camera as measuring device, and designs a virtual target based on the initial imaging information of feature point. A second-order dynamic formal model for tracking control of virtual target feature areas is established. At the same time, considering the influence of parameter uncertainty and external disturbance, a active disturbance reject controller is designed. The mathematical simulation results show that this method can effectively ensure that the rolling target feature area can always be observed stably. It provides a good foundation for follow-up on-orbit service tasks.

Tracking Tumbling Target

53

References 1. Yanning G, Xu H, Zengqian G et al (2015) Control system design and simulation of binocular vision-based non-cooperative target proximity mission. Aerospace Control Appl 41(5):6–11 2. Yan Z, Le X, Wang J (2016) Tube-based robust model predictive control of nonlinear systems via collective neurodynamic optimization. IEEE Trans Industr Electron 63(7):4377–4386 3. Weiss A, Baldwin M, Erwin RS et al (2015) Model predictive control for spacecraft rendezvous and docking: strategies for handling constraints and case studies. IEEE Trans Control Syst Tech 23(4):1638–1647 4. Han F, Wu H L, Hou J W, et al (2015) The 6–DOF synchronized sliding mode control for approaching to the slowly rotating satellite. 34th Chinese control conference on proceedings, pp 3269–3274. IEEE, Hangzhou 5. Lepetit V, Moreno-Noguer F, Fua P (2009) EPnP: an aDccurateO(n) solution to the PnP Problem. Int J Comput Vision 81(2):155–166 6. Han J (2009) From PID to active disturbance rejection control. IEEE Trans Industr Electron 56(3):900–906

Active Disturbance Rejection Control Based on a Phase Optimized Extended State Observer Pengfei Xia and Wei Wei(B) Beijing Technology and Business University, Beijing 100048, China [email protected]

Abstract. This paper focuses on the issue of estimating the time varying disturbances. A phase optimized law and a phase optimized extend state observer are proposed. For typical disturbances, the proposed observer is verified by theoretical analyses and numerical simulations. Results show the phase optimized active disturbance rejection control is superior to the linear active disturbance rejection control. Keywords: Active disturbance rejection control Extend state observer · Phase optimization

1

·

Introduction

Uncertainties and disturbances are eternal problems in control engineering. In order to make the system be insensitive to the uncertainties and disturbances, generally, there are two kinds of methods [1]. Firstly, a control law is designed to suppress the uncertainties and disturbances. H∞ control [2], sliding mode control [3], and adaptive control [4] are typical examples. Secondly, an observer-based control approach. Observers, such as unknown input observer (UIO) [5], disturbance and uncertainty estimation (DUE) [6], and disturbance observer (DOB) [7] are frequently utilized. Due to the less dependence on model information, simple structure, active disturbance rejection control (ADRC) has been widely used in different fields, such as nano-positioning [8], hydraulic turbine [9] and powered parafoil [10]. An extended state observer (ESO) is designed to estimate the total disturbance, consisting of internal uncertainties and external disturbances, in real time. It plays a key role in ADRC. However, an ESO is only able to estimates the constant disturbance without steady-state error. Its estimation for the time varying disturbance is not desirable. In order to estimate the time varying disturbance more effective, a phase optimization law (POL) is proposed. Based on an ESO, a phase optimized extended state observer (POESO) is established and a phase optimized active disturbance rejection control (POADRC) is presented. For typical disturbances, A POESO is verified by theoretical analyses and numerical simulations. Results show POADRC is superior to LADRC, especially in presence of the time-varying disturbances. c Springer Nature Singapore Pte Ltd. 2020  Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 54–61, 2020. https://doi.org/10.1007/978-981-32-9698-5_7

Phase Optimized Extended State Observer

2

55

Phase Optimized Extended State Observer

A single input and single output system can be described as  (n) x = f (x(n−1) (t), x(n−2) (t), · · · , x(t), d(t), t) + bu(t), y = x(t)

(1)

where x(i) (i = 1, ..., n) are system states, n is system order, f is an unknown function and it is the total disturbance in ADRC, d(t) as the external disturbances, b is the control gain, u is the control input, y is the system output, t is the time variable. Let h = df /dt, Eq. (1) can be rewritten as ⎧ x˙ 1 (t) = x2 (t), ⎪ ⎪ ⎪. ⎪ ⎪ . ⎨. (2) x˙ n−1 (t) = xn (t), ⎪ ⎪ ⎪ (t) = x (t) + bu, x ˙ ⎪ n+1 ⎪ ⎩ n x˙ n+1 (t) = h where X = [x1 , · · · , xn , xn+1 ]T = [x, · · · , x(n) , f ]T is system state. An ESO is designed as ⎧ z˙1 = z2 − β1 e1 , ⎪ ⎪ ⎪ ⎪ .. ⎪ ⎨. (3) z˙n−1 = zn − βn−1 e1 , ⎪ ⎪ ⎪ z˙ = zn+1 − βn e1 + bu, ⎪ ⎪ ⎩ n z˙n+1 = −βn+1 e1 where Z = [z1 , · · · , zn+1 ]T is the estimation of the state, β = [β1 , · · · , βn+1 ]T is the gains of the ESO, e1 = z1 −x1 is the estimation error. When ESO works well, we have Z → X. Valuable work on ESO and ADRC can be found in Refs. [11–13]. Let ωo is observer bandwidth, observer parameters can be chosen [14]. However, ESO given in (3) is unable to estimate time-varying disturbance effectively [15]. To get a desired estimation, a POL is designed 1 zn+1 P O = zn+1 + z˙n+1 c

(4)

where c is the phase-optimization factor. Generally, c = βn+1 /βn or around it. Then, a POESO is proposed as ⎧ ⎪ ⎪ z˙1 = z2 − β1 e1 , ⎪ ⎪ .. ⎪ ⎪ ⎪ ⎨. z˙n−1 = zn − βn−1 e1 , (5) ⎪ z˙n = zn+1 − βn e1 + bu, ⎪ ⎪ ⎪ ⎪ = −βn+1 e1 z˙ ⎪ ⎪ ⎩ n+1 zn+1 P O = zn+1 + 1c z˙n+1 zn+1 is replaced by zn+1P O . It is an optimized estimation of the total disturbance. By comparing Eqs. (3) and (5), one can see that a slightly change is made on an ESO. Next, the performance of POESO will be discussed.

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Analysis of a POESO

Defining estimation error of an ESO be E = [e1 , · · · , en+1 ]T = Z − X

(6)

Output of a POESO is defined as ZP O = [z1 , · · · zn , zn+1P O ]T , as the same, estimation error of a POESO is EP O = [e1 , · · · , en+1 P O ]T = ZP O − X From Eqs. (2) and (5), one has ⎧ e˙ 1 = e2 − β1 e1 , ⎪ ⎪ ⎪. ⎪ ⎪ . ⎨. e˙ n−1 = en − βn−1 e1 , ⎪ ⎪ ⎪ ⎪ e˙ n = en+1P O , ⎪ ⎩ e˙ n+1P O = ( β1 βcn+1 − βn+1 )e1 − If c = βn+1 /βn is recommended, then ⎧ e˙ 1 = e2 − β1 e1 , ⎪ ⎪ ⎪. ⎪ ⎪ ⎨ .. e˙ n−1 = en − βn−1 e1 , ⎪ ⎪ ⎪ ⎪ e˙ n = en+1P O , ⎪ ⎩ e˙ n+1P O = ( β1 βcn+1 − βn+1 )e1 −

(7)

(8) βn+1 c e2

−h

(9) βn+1 c e2

−h

Eq. (9) can be rewritten as ˙ P O = AP O EP O + Bh E ⎡

where

AP O

−β1 ⎢ −β2 ⎢ ⎢ =⎢ ⎢ ⎣0 β1 βn − βn+1

⎤ ⎡ ⎤ 0 ··· 0 0 1 ··· 0⎥ ⎢ 0 ⎥ ⎥ ⎢ ⎥ ⎥ .. , B = ⎢ .. ⎥ ⎥ . ⎥ ⎣ . ⎦ 0 ··· 0 1⎦ −1 −βn 0 · · · 0 1 0 .. .

(10)

(11)

Solving Eq. (10), one has AP O t

EP O (t) = e

AP O t

EP O (0) + e

t

e−AP O τ Bh(τ )dτ

(12)

0

Usually, β is positive and AP O is Hurwitz. The first part of the solution (12) converges to zero, i.e. (13) lim = eAP O t EP O (0) = 0 t→∞

Phase Optimized Extended State Observer

57

For the second part of Eq. (12), let

t

S(t) =

eAP O (t−τ ) Bh(τ )dτ

(14)

0

According to Ref. [11], one has Theorem 1. lim EP O (t) is bounded if at least one of the following conditions t→∞ is satisfied, (1) |h| ≤ M1 for a constant M1 . (2) |f | ≤ M2 for a constant M1 . Proof is consistent with [11] and the only difference is the matrix A. For typical disturbances, bounds of the estimation errors can be obtained. 3.1

f is a Constant

Suppose f = C (an unknown constant), and h = 0. According to Eq. (14), S(t) = 0, then lim EP O (t) = 0. It means POESO can accurately estimate t→∞ constant disturbance. 3.2

f is a Ramp Function

Suppose f = rt, where r is an unknown constant, and h = r. Then

t AP O t eAP O (t−τ ) Bdτ = rA−1 B − rA−1 S(t) = r P Oe P OB

(15)

0

For EP O (t), one has

lim EP O (t) = −rA−1 P OB

t→∞

(16)

Algebraic complement of the (n + 1) row and (n + 1) column element in matrix AP O is ⎡ ⎤ −β1 1 · · · 0 ⎢ −β2 0 · · · 0 ⎥ ⎢ ⎥ (17) AP O(n+1)×(n+1) = (−1)2n+2 ⎢ ⎥ .. ⎣ . 1⎦ 0 0 ··· 0 Obviously, the last row of AP O −1 B is zero. Therefore lim en+1P O (t) = 0

(18)

lim zn+1P O (t) = xn+1 = f

(19)

t→∞

i.e. t→∞

Therefore, the ramp disturbance can be precisely estimated by a POESO.

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3.3

f is a Sine Function

Suppose f = K sin ωt, where K is amplitude coefficient and ω is the frequency of the sine function, respectively. According to Eq. (14), one has

t eAP O (t−τ ) B cos ωτ dτ (20) S(t) = Kω 0

Then, S(t) = KB sin ωt − Since I + S(t) = and

A2P O ω2

KAP O KAP O AP O A2 B cos ωt + e B − P2O S(t) ω ω ω

(21)

is positive and invertible, one has

 −1 KAP O AP O KAP O A2 B cos ωt + e (KB sin ωt − B) I + P2O ω ω ω

   −1  −1    A2P O A2P O   K  I + + B A B lim |EP O (t)| ≤ K  I +   PO  t→∞   ω   ω2 ω2

(22)

(23)

Different from the constant and ramp disturbance, a POESO cannot estimate the sine disturbance without stead-state error. Estimation error is determined by amplitude K, frequency ω and matrix AP O .

4

Simulation

Consider a second-order system, ⎧ ⎨ x˙ 1 (t) = x2 (t), x˙ 2 (t) = f + bu, ⎩ y = x1

(24)

Initial condition is zero, and b = 1. Reference is set to be v = 2, and disturbances are ⎧ ⎨ f = 3, f = t, (25) ⎩ f = 2 sin(3t) To make a fair comparison with Ref. [11], control law of POADRC is u = −k1 (z1 − v) − k2 z2 − z3 P O

(26)

Here, let k1 = 30, k2 = 10. It is the same as Ref. [11]. A POESO is designed as ⎧ z˙1 = z2 − β1 (z1 − x1 ), ⎪ ⎪ ⎨ z˙2 = z3 − β2 (z1 − x1 ) + u, (27) z ˙3 = −β3 (z1 − x1 ), ⎪ ⎪ ⎩ 1 z3P O = z3 + c z˙3

Phase Optimized Extended State Observer

59

Also, take the same parameters as Ref. [11], i.e. β1 = 120, β2 = 4800, β3 = 64000. The step size T = 0.01 is also the same with Ref. [11]. Here, c = β3 /β2 = 13.33. Simulation results are given in Figs. 1, 2 and 3. Figure 1 shows system outputs under disturbances given in Eq. (25) by ADRC and POADRC. Figure 2 presents the estimation of ESO and POESO. It can be seen that both ESO and POESO can estimate disturbance effectively. However, a POESO can achieve better estimation. Figure 3 reveals the static tracking errors (v − y, t > 1) and observing errors (z3 − f or z3P O − f ). It is worth pointing out that a POESO can estimate ramp disturbance with no steady state error. It is consistent with the theoretical results. Root mean squared error (RMSE) of tracking errors and observing errors are listed in Table 1. 4 Reference(f=3)

ADRC

POADRC

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ADRC

POADRC

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Fig. 1. System outputs with different disturbances.

4 f=3

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f=2sin3t

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POESO

0 -5

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Fig. 2. Estimations of the observers.

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ADRC(f=3) POADRC(f=3)

0 -0.02

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Regulating errors

Time(s)

5

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0

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POESO(f=2sin3t)

4

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Fig. 3. Tracking errors and estimation errors of observers. Table 1. Errors indicator Regulating errors (t > 1) Observing errors ADRC POADRC ESO POESO

5

Constant 0.0017 0.0018

0.2908 0.1905

Ramp

0.0035 0.0019

0.0745 0.0021

Sine

0.0112 0.0030

0.3092 0.0269

Conclusions

A POADRC is proposed. In order to improve the ability to estimate the time varying disturbances, a phase optimization law is introduced. For some typical disturbances, POADRC is verified by theoretical analyses and numerical simulations. Acknowledgment. This work is supported by Key program of Beijing Municipal Education Commission (KZ201810011012), National Natural Science Foundation of China (61873005), and Support Project of High-level Teachers in Beijing Municipal Universities in the Period of 13th Five-year Plan (CIT&TCD201704044).

References 1. Kayacan E, Peschel JM, Chowdhary G (2017) A self-learning disturbance observer for nonlinear systems in feedback-error learning scheme. Eng Appl Artif Intell 62:276–285 2. Bhattacharyya SP (2017) Robust control under parametric uncertainty: an overview and recent results. Annu Rev Control 44:45–77 3. Xu JX, Guo ZQ, Lee TH (2013) Design and implementation of integral slidingmode control on an underactuated two-wheeled mobile robot. IEEE Trans Industr Electron 61(7):3671–3681

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4. Yao J, Deng W, Jiao Z (2015) Adaptive control of hydraulic actuators with LuGre model-based friction compensation. IEEE Trans Industr Electron 62(10):6469–6477 5. Basile G, Marro G (1969) On the observability of linear, time-invariant systems with unknown inputs. J Optim Theory Appl 3(6):410–415 6. Zhong QC, Kuperman A, Stobart RK (2011) Design of UDE-based controllers from their two-degree-of-freedom nature. Int J Robust Nonlinear Control 21(17):1994– 2008 7. Schrijver E, Van DJ (2002) Disturbance observers for rigid mechanical systems: equivalence, stability, and design. J Dyn Syst Meas Contr 124(4):539–548 8. Wei W, Xia PF, Zuo M (2018) Linear active disturbance rejection control of piezoelectric nanopositioning stage. Control Theory Appl 35(11):34–47 (in Chinese) 9. Zhou R, Tan W (2019) Analysis and tuning of general linear active disturbance rejection controllers. IEEE Trans Industr Electron 66(7):5497–5507 10. Tao J, Liang W, Sun QL (2017) Modeling and control of a powered parafoil in wind and rain environments. IEEE Trans Aerosp Electron Syst 53(4):1642–1659 11. Yang X, Huang Y (2009) Capabilities of extended state observer for estimating uncertainties. In: Proceedings of the 2009 American control conference. IEEE Press, Louis, pp 3700-3705 12. Yang R, Sun M, Chen ZQ (2011) Active disturbance rejection control on first-order plant. J Syst Eng Electron 22(1):95–102 13. Chen ZQ, Sun MW, Yang RG (2013) On the stability of linear active disturbance rejection control. Acta Automatica Sinica 39(5):574–580 (in Chinese) 14. Gao ZQ (2003) Scaling and bandwidth-parameterization based controller tuning. In: Proceedings of the 2003 American control conference. IEEE Press, Denver, pp 4989-4996 15. Madonski R, Herman P (2015) Survey on methods of increasing the efficiency of extended state disturbance observers. ISA Trans 56:18–27

Open-Circuit Fault Diagnosis of an Inverter Based on Bayesian Network Sumin Han, Yongsheng He(&), and Shuqing Zheng Henan Polytechnic University, Jiaozuo 454000, Henan, China [email protected]

Abstract. The paper establishes an open-circuit fault diagnosis Bayesian network (OFDBN) to diagnose the faults of inverter’s IGBTs. The topological structure of the OFDBN includes two layers, an inverter faults layer and a fault symptoms layer. The faults layer includes various IGBT open-circuit faults, and the symptoms layer includes various fault features extracted from the output line voltage of the inverter. A number of fault training data and test data are obtained by the method of changing carrier frequency and modulation ratio. The study uses the maximum likelihood algorithm to train the OFDBN parameters by the training data simulated in Matlab. The trained OFDBN is used to diagnose IGBT open-circuit faults of inverters. The results show that the proposed OFDBN has a very high accuracy for both single IGBT fault and double IGBT fault, and it can accurately locate the open-circuit fault location. Keywords: Fault diagnosis Bayesian network




Open-circuit fault




Line voltage




Inverter




1 Introduction Frequency control can not only accurately control the speed, but also save energy and reduce consumption, which is widely applied in metallurgy, machinery, mining, electric power and other industries. As the core component of frequency control, inverter can realize direct current (DC) frequency adjustable alternating current conversion. The working states of the inverter is related to the healthy and normal operation of the whole system. Due to the frequent opening, closing and thermal sensitivity of the switching device, inverter become a fragile device. Data shows [1], 38% of inverter failures are due to the damage of inverter insulated gate bipolar transistors (IGBTs), the most common faults are open-circuit fault and short-circuit fault. For short-circuit fault, there are usually protective measures in the design. Even in extreme cases, short-circuit fault will produce high power and accumulate high heat rapidly, which will eventually lead to the opening of the switch. Therefore, the open-circuit fault of switches is a common fault, which has received extensive attention and becoming a research hotspot. Quntao [2] summarized the open-circuit faults of IGBTs in three-phase inverter as current-based detection method and voltage-based detection method. These methods are to extract current and voltage signal and apply signal processing method or algorithms for comparative diagnosis. Park [3] analyzed the current features of the motor © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 62–70, 2020. https://doi.org/10.1007/978-981-32-9698-5_8

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under normal working and open-circuit states, who used the sum of the absolute values of the three-phase current as the feature quantities for fault diagnosis. Ribeiro [4] calculated the voltages of the normal operation and fault operation of the inverter, and diagnosed the faults by their differences. Literature [5, 6] calculated the mode and phase angle of average current Park vector as fault features to diagnose the open-circuit faults of IGBTs. However, this method may cause misdiagnosis when the load is light or abrupt. A number of scholars have established neural network models to classify and diagnose the open-circuit faults of IGBTs by extracting different fault feature quantities [7, 8]. Literature [7] extracted the fault signal features from the direct sampling of the output voltage waveform. In literature [8], a wind power system was built in PSCAD environment; the authors chose the current DC component and the current harmonic distortion rate as fault feature quantities to diagnose the IGBT faults. Xiaoqiong [9] built a three-layer neural network with voltage harmonic components as the feature quantities, achieved the goal that diagnose open circuit faults within 0.02 s without increasing the sensor. Moosavi [10] identified the system state by three-phase current and wavelet transform, who extracted the current waveform, and compared the four methods of multi-layer perception neural network algorithm, support vector machine, self-organizing maps and keens, which shows that multi-layer perception and support vector machine have more high precision. Wang [11] proposed a Bayesian method for chiller fault diagnosis, the author establishes Bayesian network by extracting fault features. The results show that the proposed FS method is effective for chiller fault diagnosis. In literature [12], a dynamic Bayesian network (DBN) based fault detection, root cause diagnosis, and fault propagation pathway identification scheme is proposed. The result shows it is an efficient fault detection and diagnosis tool. Fault diagnosis method based on Bayesian network (BN) is one of the most effective theoretical models in the field of knowledge representation and diagnosis. Inverter’s IGBTs are taken as the research object in the study, and a complete set of Bayesian network diagnosis model for IGBT open circuit fault is proposed. The model structure is established by extracting important fault features from the output line voltage. The paper proposes a method of acquiring large amount of fault data by changing carrier frequency and modulation ratio. The training data is used to obtain the network parameters through the maximum likelihood algorithm, and the complete OFDBN is established. Compared with the traditional model building method based on expert knowledge, the parameters of the fault model in the proposed method are extracted from the fault information, which can better reflect the fault characteristics. Verifying the OFDBN by test data.

2 The Algorithm of Bayesian Intelligent Diagnosis BN is a directed acyclic graphical model [13]. Figure 1 shows a simple Bayesian network. Node A, B, C, and D represent random variables, and arrows between nodes represent causal relationships. A and B are root nodes; C and D are leaf nodes. P(A) and P(B) are the edge probabilities of A and B, and P (C|A, B) and P(D|C) are the conditional probabilities of C and D.

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P ( A ) = 0.1

P ( B ) = 0.2

P ( C A, B ) = 0.9

( ) P ( C A, B ) = 0.5 P ( C A, B ) = 0.1 P C A, B = 0.6

P ( D C ) = 0.5

(

)

P D C = 0.2

Fig. 1. A simple Bayesian network.

According to the chain rule [14], the joint probability distribution of the four nodes in Fig. 1 is shown in Eq. (1): PðABCDÞ ¼ Pð AÞPðBj AÞPðC jABÞPð D jABC Þ

ð1Þ

According to the independence hypothesis [15], Eq. (1) convert to Eq. (2): PðABCDÞ ¼ Pð AÞPðBÞPðC jABÞPð D jC Þ

ð2Þ

After determining the joint probability distribution table of each node, BN can calculate all kinds of network probabilities in theory. According to the evidence information, using the inference equation, the causal probability relationship between the relevant nodes in the BN graph can be obtained. There are two main categories: forward propagation and backward diagnosis. Forward propagation is to infer the state probability of the underlying node based on the state of the upper node. Take Fig. 1 as an example, if B occurs, the state probability of D can be obtained by BN calculation. The probability of occurrence of D is P(D|B) = 62.76%. Backward diagnosis is to calculate the state probability of the upper node by the state of the underlying node. For example, it is known that D occurs, and the state probability of occurrence of A is P(A|D) = 7.61%. By forward propagation and backward diagnosis, the required state probability can calculate based on the existing nodes state information. If the state of the leaf nodes is given, the posterior probability of the root nodes can be calculated. Combine with the goal of fault diagnosis research, the leaf nodes represent the faults symptom or faults feature when each fault occurs, and the root nodes indicate faults of different types. Accordingly, a fault diagnosis BN can be established.

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3 The OFDBN for the Inverter In this section, a BN structure for fault diagnosis applied to inverter is proposed, which consists of an inverter fault layer and a fault symptom layer. The inverter fault layer indicates the open-circuit faults of the IGBTs in inverter, and each node represents an IGBT. The fault symptom layer composes of monitoring quantities and features, indicate the characterization information when each node of the inverter fault layer fails. 3.1

Open-Circuit Faults Classification and Fault Feature Extraction

Figure 2 shows the topology of a typical three-phase voltage source inverter, which includes DC link and electromagnetic interference filter module of three-phase bridge main circuit. The DC link keeps the DC voltage stable and buffers the passive energy. The three-phase bridge module is the main circuit and consists of six bridge arms. Each arm has an IGBT Ti (i = 1, …, 6) and an anti-parallel continuous-current diode. The angle of conduction among three phases is 120° in turn, and the angle of conduction between upper and lower arms is 180°.

g1

T5

T3

T1 g3

g5

C1

EMI filter T4 g4

T2

T6 g6

Load

g2

Fig. 2. Topology structure of a typical three-phase bridge inverter.

When an open-circuit fault occurs in an IGBT, the current waveforms and voltage waveforms of three phases distort in different ways. In the actual situation, a single IGBT open-circuit fault is more common than other faults; the simultaneous failure of two IGBTs will also occur in the high-power converter circuit, and the damage is serious; but the probability of simultaneous failure of three IGBTs is small. Therefore, the paper assumes that there are at most two IGBTs open-circuit fault in the inverter. In addition, the faults can be classified into 5 categories and 22 sub-categories according to their locations. Table 1 shows the types of faults that may occur.

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S. Han et al. Table 1. Table captions should be placed above the tables. Fault classification Normal state Single IGBT fault Double IGBT fault of the same bridge arm Double IGBT fault in one phase Double IGBT fault of cross connection

Specific location of the fault None T1, T2, T3, T4, T5, T6 T1T3, T1T5, T3T5, T2T4, T2T6, T4T6 T1T4, T3T6, T2T5 T1T2, T1T6, T2T3, T3T4, T4T5, T5T6

When inverter faults, the output voltage and current waveforms of the circuit will change, and the corresponding voltage and current waveforms of different fault types are different. The detection method based on voltage has strong ability of antiinterference and anti-false alarm. The line voltage uab and ubc can reflect the distortion of three phase voltages. Therefore, the paper extracts features and diagnoses faults by detecting line voltage waveforms. In Matlab/Simulink environment, the open-circuit fault simulation model of the inverter is built. The simulation model is to simulate various fault types of IGBT to obtain waveforms, and fault features are extracted by FFT method. After analysis, the authors find that when different types of open-circuit fault occur, the fundamental component and the second harmonic component of the line voltage associated with the open-circuit position will change significantly. The third harmonic and above are too small in amplitude, so the fundamental component and the second harmonic component are selected as two fault features. Under normal conditions, the DC components of uab and ubc are almost zero, in the case of fault, the DC component amplitude of uab and ubc increases obviously, so the DC component amplitude can act as a fault feature. However, when different bridge arms in the same phase fail, such as T1 and T4 failure respectively, the amplitude spectrum almost the same after FFT, which cannot to distinguish only by the harmonic amplitude. Through comparison, the authors find that the phase spectra of the two faults are different. In particular, the DC phase has a difference of 180°. Therefore, we extract the phase information as fault features. In summary, the extracted fault features are as follows: DC amplitude, DC phase, fundamental amplitude, fundamental phase and second harmonic amplitude of line voltage uab and ubc after FFT, adding up to 10 features totally. 3.2

Constructing the Structure of OFDBN

From the above analysis, the root node of the BN is an open-circuit fault type and the leaf node is a fault symptom. Therefore, the structure of BN for open-circuit fault diagnosis of the inverter can be obtained. As shown in Fig. 3, it consists of the inverter faults layer and the fault symptom layer. The fault layer has 6 nodes, which are T1 open-circuit, …, T6 open-circuit, respectively represented by variables X1, …, X6. The fault symptom layer has 10 nodes, which are the DC amplitude of uab, the DC phase of uab, the fundamental amplitude of uab, the fundamental phase of uab, the second harmonic amplitude of uab, the DC amplitude of ubc, the DC phase of ubc, the fundamental Amplitude of ubc, the fundamental phase of ubc and the second harmonic amplitude of ubc, respectively represented by variables X7, …, X16.

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Inverter faults layer X1:T1 OC

X2: T2 OC

X3:T3 OC

X4: T4 OC

X5:T5 OC

X6: T6 OC

Fault symptoms layer X7: DC Amplitude of uab

X8: DC phase of uab

X15: Fundamental Phase of ubc

X16: Second harmonic amplitude of ubc

Fig. 3. The structure of OFDBN.

After the OFDBN structure is established, the structure needs to obtain the prior probability and conditional probability of each node. The study uses the maximum likelihood algorithm to train the OFDBN parameters, but it requires a large number of training data. 3.3

Data Acquisition and Model Training

The method for obtaining simulation data is as follows. For each type of fault (a total of 22 types of fault), in addition to the default output voltage frequency of 15 Hz, in the case of 10 Hz, 13 Hz, 18 Hz, 20 Hz, the modulation ratio is changed from 0.70 to 0.80 (interval 0.01) to obtain waveform data, and the waveform data is processed by FFT method. The number of training data available for each type of faults are 5  11. Therefore, 22  5  11 sets of test data are available. The data is normalized (the baseline value is the corresponding eigenvalue in the case of normal state); these data are quantified to obtain samples which can be trained for OFDBN structure. The study uses the maximum likelihood algorithm to train the OFDBN parameters by the training data simulated in Matlab. The conditional probability table of the OFDBN is obtained. Combine with the OFDBN structure, the complete OFDBN model for inverter is constructed.

4 Open-Circuit Fault Diagnosis Verification of Diagnostic Results Diagnosis of the IGBT faults in inverter based on the constructed OFDBN. First, obtain the test data samples. For the 22 kinds of faults, the output voltage frequencies are 12 Hz, 16 Hz, and 18 Hz, the modulation ratios are 0.72, 0.725, 0.775, 0.78 and 0.785, fault data are obtained by simulation. The data is processed by the FFT after normalization and quantization. Remove the samples that duplicate with the training data,

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and 286 sets of test samples completely different from the training samples are obtained. Table 2 gives the quantified data of some different types of faults, which are single IGBT fault, double IGBT fault in one phase and double IGBT fault of cross connection. Those data are to test the accuracy of the OFDBN constructed in the paper. Table 2. The quantification results of partial text data. Fault Line types/Frequency/ voltage modulation ratio uab T1/12/0.725 ubc T1T4/16/0.72 uab ubc T1T6/18/0.775 uab ubc

DC DC Fundamental amplitude phase amplitude

Fundamental phase

3 4 2 4 2 9

5 2 6 2 3 5

2 1 1 2 2 2

3 4 2 4 1 3

Second harmonic amplitude 4 4 4 4 1 3

100 80 60 40 20 0 Case1

Case2 T1

T2

T3

Case3 T4

T5

T6

Fig. 4. Fault diagnosis results.

Figure 4 shows the diagnostic results of some of the test data given in Table 2, where the ordinate is the probability value of the result and the columns of different fill patterns represent different IGBTs failure. Abscissa includes different fault types, the left, middle and right positions in abscissa coordinates are the output of diagnostic results under T1, T1T4 and T1T6 faults respectively. As the Fig. 4 shows, the evidence information of T1 fault input into the OFDBN, the probability of T1 fault is 100%, and the probability of others fault are 0. The evidence information of T1T4 fault input into the OFDBN the probability of T1 and T4 fault is 100%, and the probability of others fault are 0. The evidence information of T1T6 fault input into the OFDBN, the probability of T1 and T6 fault is 100%, and the probability of others fault are 0.

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All 286 groups of training data input into OFDBN for diagnosis, and the results show that 286 cases were correct. Therefore, the OFDBN proposed in this paper has extremely high precision.

5 Conclusion The paper establishes the OFDBN to realize the accurate diagnosis of IGBT opencircuit faults of inverter. A fault simulation model is established, and a method to obtain a number of fault data by changing carrier frequency and modulation ratio is proposed. When the model is built, fault features are extracted from the output line voltage, and the correlation among nodes is obtained by parameter learning algorithm. The OFDBN is constructed in matlab. Verifying the OFDBN by test data, the results show that the OFDBN proposed in this paper is suitable for various fault modes, and has good diagnostic effect for both single IGBT fault and double IGBT fault. The comprehensive diagnostic accuracy can reach 100%. Compared with the traditional Bayesian network construction method, the structure and parameters of the paper proposed method are obtained from the fault signal, which is simple and convenient to implement. The obtained model can better reflect the fault characteristics and has high fault diagnosis accuracy. The OFDBN is not limited to the open-circuit fault of inverter, which is also applicable to other electrical equipment based on the work of the IGBT and has certain engineering practical value.

References 1. Fuchs FW (2003) Some diagnosis methods for voltage source inverter in variable speed drives with induction machines—a survey. In: Proceedings of the IEEE industrial electronics society annual conference, Roanoke, Virginia, USA, pp 1378–1385 2. Quntao A, Li S, Lizhi S, Ke Z (2011) Recent developments of fault diagnosis methods for switches in three-phase inverter. Trans China Electrotech Soc 26(04):135–144 3. Park B-G, Lee K-J, Kim R-Y et al (2011) Simple fault diagnosis based on operating characteristic of brushless direct-current motor drives. IEEE Trans Ind Electron 58(5):1586– 1593 4. de Araujo Ribeiro RL, Jacobina CB, da Silva ERC et al (2003) Fault detection of openswitch damage in voltage-fed PWM motor drive systems. IEEE Trans Power Electron 18 (2):587–593 5. Caseiro JAA, Cardoso AJM (2009) Fault diagnosis on a PWM rectifier AC drive system with fault tolerance using the average current Park’s vector approach. In: IEEE international electric machines and drives conference, Miami, FL, USA. IEEE, pp 695–701 6. Sleszynski W, Nieznanski J, Cichowski A et al (2009) Open-transistor fault diagnostics in voltage-source inverters by analyzing the load currents. IEEE Trans Ind Electron 56 (11):4681–4688 7. Han Sumin D, Yongheng CB (2018) An open-circuit fault diagnosis method of inverter based on BP neural network. J Henan Polytech Univ (Nat Sci) 37(05):122–127 8. Mei W, Yanghong T, Yiwei H, Peiwei D (2018) Open-circuit fault detection and diagnosis for converters of D-PMSG based wind power generation systems. Control Eng China 25 (01):50–56

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9. Xiaoqiang H, Huaijun R, Pengcheng H et al (2018) Open-circuit fault diagnosis of advanced Cophase traction power supply system based on neural network. In: 2018 international conference on intelligent rail transportation (ICIRT). IEEE, pp 1–5 10. Moosavi SS, Kazemi A, Akbari H (2019) A comparison of various open-circuit fault detection methods in the IGBT-based DC/AC inverter used in electric vehicle. Eng Fail Anal 96:223–235 11. Wang Z, Wang Z, Gu X et al (2018) Feature selection based on Bayesian network for chiller fault diagnosis from the perspective of field applications. Appl Therm Eng 129:674–683 12. Amin MT, Khan F, Imtiaz S (2019) Fault detection and pathway analysis using a dynamic Bayesian network. Chem Eng Sci 195:777–790 13. Lianwen Z, Haipeng G (2006) Introduction to bayesian networks. Science Press, Beijing, pp 10–12 14. Cunfen B, Wensheng G, Lei J et al (2013) Integrated diagnosis of transformer faults based on three-layer bayesian network. High Voltage Eng 39(2):330–335 15. Junli G (2015) Research on cascade multilevel inverter and control strategy. Beijing Jiaotong University, Beijing

A B-Spline Surface Stitching Algorithm Based on Point Cloud Data Xuedong Jing and Yuwei Zhang(&) School of Shanghai Institute of Technology, Shanghai 201419, China [email protected]

Abstract. An algorithm to achieve smooth stitching between curved patches is presented. The algorithm adopts the inverse of the B-spline to find the control vertices of the common boundary of two curved blocks or multiple blocks; and then, the control vertex column vector that satisfies the condition given, which is determined by application of the continuous condition of surface G1 , is applied to substituting the original control vertex. In this algorithm, the smoothness of stitched surface is higher, and smooth stitching can be achieved by modifying one set of control vertices. The conditions for smooth stitching of two surfaces are verified, and the smooth stitching degree of the algorithm under different parameters is also tested. Keywords: B-spline


Surface stitching
Geometric continuity

1 Introduction The geometric continuity condition between free-form surfaces is applied to constructing smooth surfaces on arbitrary topological regions. The article about the geometric continuity of B-spline surface is rare. More often, Bezier surface is used as the surface model. However, Bezier surface modeling has the disadvantages of poor fitting effect and more surface number. The B-spline surface can fit large surface patches with high precision and has its inherent smoothness. To achieve strict geometric continuous smooth B-spline surface modeling, we must first solve the problem of smooth splicing conditions between B-spline surfaces. In 1990, Du [1] proposed the condition of G1 splicing between two and several Bezier patches, but it did not involve the geometric continuous splicing condition of Bspline surface. In 2002, Shi and Zhao [2], two pairs of cubic B-splines. The continuous condition of G1 between surfaces is studied, and the necessary and sufficient conditions for satisfying G1 continuity of two B-spline surfaces during splicing are given, but the B-spline surface is split into multiple Bezier surfaces and then found. The relationship between the vertices and the vertices is studied. Che and Liang [3] not only pointed out the essential difference between B-spline surface and Bezier surface in splicing, but also studied the continuous and sufficient conditions of G1 satisfying NURBS surface. The algorithm is to splicing the B-spline patches and does not need to split. Based on the known necessary and sufficient conditions, the correction of the control vertices makes the splicing of the patches satisfy the smoothing condition. © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 71–79, 2020. https://doi.org/10.1007/978-981-32-9698-5_9

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2 B-Spline Curve Surface Basis 2.1

B-Spline Curve Surface Recursion Formula

The Bezier curve lacks flexibility in the application and is limited by the vertices. When the number of vertices of the feature polygon is determined, the order of the curve is determined, so the controllability is poor. When the number of vertices is large, the order of the curve will be higher. At this time, the control of the shape of the curve by the feature polygon will be significantly weakened. In addition, the Bezier curve defines that any point in the interval of (0 < t < 1) is affected by the vertices, which makes it impossible to locally modify the curve, which greatly limits the possibility of actual modeling. In order to better adapt to the needs of the actual modeling, the structural curve can be locally modified, closer to the feature polygon, lower order and easier to construct, and the B-spline curve comes into being. The mathematical expression of the B-spline curve is as follows: Pi;n ðtÞ ¼

n X

Pi þ k Nk;n ðtÞ; ð0  t  1Þ

ð1Þ

k¼0

The B-spline basis function is used as a weight, which enables the domain to be subdivided by the node. In fact, each B-spline basis function is non-zero in a nearby subinterval, so the B-spline basis function is quite “Partial.” Where Pi þ k is the control vertex and Nk;n ðtÞ is the B-spline basis function, which is determined by the node vector T: t0  t1  . . .  tn þ k . It can be seen from (1) that the B-spline curve is segmentally defined by the control vertices. If m + n + 1 vertices are given, the parameter curve of m + 1 segments n times can be defined. The expression of Nk;n ðtÞ is as follows: Nk;n ðtÞ ¼

nk 1X ð1Þ j Cnj þ i ðt þ n  k  jÞn n! j¼0

Cnj þ i ¼

ðn þ iÞ! j!ðn þ i  jÞ!

ð2Þ

ð3Þ

In formula, 0  t  1, k ¼ 0; 1; 2; . . .. . .; n When we read the i-th vertex, the polygonal polyline segment obtained by connecting the vertices with the line segments in turn is the characteristic polygon of the B-spline curve, and the vertices applied to the surface represent the control vertex mesh (Fig. 1). Due to the nature of the segmentation representation, the cubic B-spline curve is defined by four adjacent control vertices whose expression is: Pt ¼ N0;3 ðtÞP0 þ N1;3 ðtÞP1 þ N2;3 ðtÞP2 þ N3;3 ðtÞP3

ð4Þ

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Fig. 1. Cubic B-spline curve

It can be seen from Eq. (4) that a cubic B-spline curve defined by n vertices is connected by segmentation curves of n-3 segments, and the second-order continuous condition is satisfied at the joint. The B-spline surface is a point column Pi;j ði ¼ 0; 1; 2; . . .; nÞ; ðj ¼ 0; 1; 2; . . .; mÞ in space given (n + 1)  (m + 1) points; Connect the adjacent two points in the point sequence Pi;j to construct a feature mesh, constructing a B-spline curve in the u and v directions to form a parametric polynomial surface in the form of tensor product, and  þ1 þ1 set the node vector U ¼ fui gi¼1 , V ¼ vj j¼1 are the divisions of the u-axis and the v-axis of the parameter uv plane, respectively (Fig. 2). The B-spline surface definition is: Pu;v ¼

n X m X

Pi;j Ni;k ðuÞNj;h ðvÞ

i¼0 j¼0

Fig. 2. B-spline control grid surface

ð5Þ

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B-Spline Curve Back Calculation

The general process of inverse B-spline curve is as follows: (1) Construct a non-uniform node vector based on the distribution trend of the type point. (2) Apply the calculated node vector to construct a non-uniform B-spline base. (3) Construct a coefficient matrix for the inverse of the control points. (4) Establish a control point inverse equation system to solve the control point column. Among them, the evaluation of the B-spline basis function is the key. Given n + 1 data points pi ði ¼ 0; 1; . . .; nÞ, the general algorithm [4] is to use the first and last data points p0 and pn as the two endpoints of the B-spline interpolation curve, respectively. The remaining data points p1 ; p2 . . .; pn1 are sequentially used as the segment connection points of the B-spline interpolation curve.  The node of the  control point pi is ui þ k ði ¼ 0; 1; . . .; mÞ, the node vector U = u0; u1; . . .; un þ k þ 1 . m + 1 linear equations with n + 1 control vertices as unknown vectors can be given by interpolation condition: Pðui Þ ¼

n X

dj Nj;k ðui Þ ¼

i¼0

i X

dj Nj;k ðui Þ ¼ qik ; u 2 ½ui ; ui þ 1 

ð6Þ

j¼ik

The node values in the curve definition domain u 2 ½ui ; ui þ 1  are sequentially substituted into the equation to satisfy the interpolation condition, namely: i X

Pðui Þ ¼

dj Nj;3 ðui Þ ¼ qi3 ; i ¼ 3; 4; . . .; n

ð7Þ

j¼i3

Pðun þ 1 Þ ¼

n X

dj Nj;3 ðun þ 3 Þ ¼ qm

ð8Þ

j¼n3

2.3

Geometric Continuity Analysis of Curved Surfaces

For the curve, G0 continuous means that the two curve segments have a common connection point, and G1 continuous means that the two curve segments have the same unit tangent at the connection point, i.e., the tangent vector, except that the G0 continuity is satisfied [2]. The direction is the same or the tangential direction is continuous. G2 continuous means that the two curved segments have the same curvature direction at the joint except that G1 is continuous. Specific to the cubic B-spline curve, there is the following expression: two B-spline curves are provided BðuÞ ¼

n X i¼0

bi Ni;3 ðuÞ; CðvÞ ¼

m X j¼0

cj Nj;3 ðvÞ

ð9Þ

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G0 continuous means that the two curved surfaces have a common boundary line; G1 means that the two curved surfaces have continuous tangent planes on the common boundary line on the basis of G0 continuous; G2 is continuous in G1 on the basis of the two surfaces, there is a continuous principal curvature on the common boundary line. The conditions for continuity of the two surfaces are as follows:

ð

Bð0; vÞ ¼ Cð0; vÞ

ð10Þ

@B @C @B ; ; Þj @u @s @v Bð0;vÞ¼0

ð11Þ

3 Research on Bicubic B-Spline Surface Stitching Algorithm 3.1

Two Pieces of Bicubic B-Spline Surface G1 Continuous Splicing

Although the predecessors have already demonstrated the smoothing conditions of the B-spline surface splicing in detail, there may be errors in the actual measurement of the point cloud data, so that the surface splicing of the originally smooth measured object does not necessarily satisfy the smoothing condition when generating the threedimensional surface. Therefore, the algorithm is to achieve the correction of the local surface, which not only solves the problem that the complete data can be fitted in the three-dimensional scanning work, but also can correct the feature area, and is more suitable for the accurate measurement technology. The core of the algorithm is to use the back-calculation of B-spline to find the vertices of the relevant control points of the two surfaces, and on this basis, the two surfaces can be smoothly spliced. There are two bicubic B-spline surfaces Bðu; vÞ and C ðs; vÞ. Can the two bicubic Bspline patches known to be G1 continuous splicing, which only has two common boundaries? A column of control vertices on the side is easy to implement and has good interactivity when applied to engineering problems. Assuming that they have a common boundary u(v), the surfaces Bðu; vÞ and Cðs; vÞ need to satisfy the condition of reaching G1 continuously, Deduced by Eqs. (7) and (8) as follows: a

n X

ðb1j  b0j ÞNj;3 ðvÞ þ b

j¼0

n  X

 c1j  c0j Nj;3 ðvÞ þ cðvÞu0 ðvÞ ¼ 0

ð12Þ

j¼0

  In fact Hj ¼ b0j ; c0j , what we have to do is to adjust a; b; cðvÞ and b1j , c1j to make the above formula. In Eq. (12), cðvÞu0 ðvÞ is the overall cubic polynomial curve. Due to the basis function Nj;3 ðvÞ, cðvÞu0 ðvÞ can be expressed in the following form: 0

cðvÞu ðvÞ ¼

n X

Pj Nj;3 ðvÞ

j¼0 3 Among them. P0 ¼ cð0Þu0 ð0Þ ¼ cð0Þ ðv4 v ðH1  H0 Þ 3Þ

ð13Þ

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Rephrase (12) to read: n X

  ½aðb1j  b0j Þ þ b c1j  c0j þ Pj Nj;3 ðvÞ ¼ 0

ð14Þ

j¼0

  Pn If the base function is not equal to 0, then j¼0 aðb1j  b0j Þ þ b c1j  c0j þ     Pj ¼ 0, the solution is b1j ¼ b0j  a1 b c1j  c0j þ Pj . Replace the actual b1j in the original Bðu; vÞ surface patch with the solved b1j , so that the two curved slices Bðu; vÞ and Cðs; vÞ can achieve G1 continuous stitching. The specific algorithm is as follows: (1) The common boundary curve u(v) is converted into an overall cubic B-spline curve. However, we still use u(v) to represent the adjusted common boundary curve. Then we use the B-spline curve reverse method to calculate u(v) as a cubic B-spline curve, which is recorded as: u ð vÞ ¼

n X

Hj Nj;3 ðvÞ

j¼0

(2) Select the appropriate parameters, a; b; cðvÞ (3) Using the inverse of the B-spline method, find the cubic B-spline control vertex Pj of cðvÞu0 ðvÞ. (4) Find b1j from the Eq. (14) and replace the actual control vertex b1j in the original Bðu; vÞ surface patch (Fig. 3).

Fig. 3. Splicing verification experiment

3.2

Three Pieces of Bicubic B-Spline Surface G1 Continuous Splicing

With three tensor plot B-spline surface:

A B-Spline Surface Stitching Algorithm Based on Point Cloud Data

8 n1 P n2 P > > B ð u; v Þ ¼ bij Ni;3 ðuÞNj;3 ðvÞ > > > i¼0 j¼0 > > < n3 n2 P P cij Ni;3 ðvÞNj;3 ðwÞ C ðv; wÞ ¼ > i¼0 j¼0 > > n3 P n1 > P > > > cij Ni;3 ðwÞNj;3 ðuÞ : Dðw; uÞ ¼

77

ð15Þ

i¼0 j¼0

When we solved the algorithm of continuous splicing of two bicubic B-spline surfaces G1 , we continued to solve the splicing of multiple surfaces. In this problem, the problem of three-slice splicing is solved first. Obviously, the three surfaces only need to be stitched together in two or two. However, due to the contradiction between the three surfaces, the second control point (E) on the boundary curve and the closest point (G) to the off-angle point will affect whether the splicing of the surface satisfies the smoothing condition (Fig. 4).

Fig. 4. Stitching diagram

Let the three boundary curves be d1 ðuÞ d2 ðvÞ d3 ðwÞ, and the algorithm based on the two surfaces is to find the corresponding ai ; bi ; ci so that d1 ðuÞ d2 ðvÞ d3 ðwÞ is estab@C lished. Let d1 ðuÞ d2 ðvÞ d3 ðwÞ control vertices, Pi ; Qi ; Ri be c1 ðvÞ @B @u jv¼0 ; c2 ðvÞ @u jw¼0 ; c3 ðvÞ @D @w ju¼0 control vertices. The purpose of our algorithm is not to construct three smooth-joined surfaces out of thin air, but to study how to modify the control vertices of the original surface so that they reach a smooth connection, with three surfaces already. Therefore, in our splicing process, we should try to keep the original control vertices smaller. 8 3c1 > < a1 ðE3  OÞ þ b1 ðE2  OÞ þ u4 u3 ðE1  OÞ ¼ 0 a2 ðE1  OÞ þ b2 ðE3  OÞ þ v43cv2 3 ðE2  OÞ ¼ 0 > : 3 a3 ðE2  OÞ þ b3 ðE1  OÞ þ w43cw ðE3  OÞ ¼ 0 3

ð16Þ

The geometric meaning is that ðE1  OÞ, ðE2  OÞ, and ðE3  OÞ satisfy the coplanar condition, and the relevant parameters ai ; bi ; ci are calculated. Actually, there is only one degree of freedom in ai ; bi ; ci .

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8 < a1 ðG3  E1 Þ þ b1 ðG1  E1 Þ þ P1 ¼ 0 a ðG  E2 Þ þ b2 ðG2  E2 Þ þ P2 ¼ 0 : 2 1 a3 ðG2  E3 Þ þ b3 ðG3  E3 Þ þ P3 ¼ 0

ð17Þ

To solve this problem, turn it into: 2

b1 4 a2 0

0 b2 a3

32 3 2 3 G1 W1 a1 0 5 4 G 2 5 ¼ 4 W2 5 b3 G3 W3

ð18Þ

Among them 8 < W1 ¼ ða1 þ b1 ÞE1  P1 W ¼ ða2 þ b2 ÞE2  Q1 : 2 W3 ¼ ða3 þ b3 ÞE1  R1

ð19Þ

Where ai ; bi can be calculated [5], the determinant of the coefficient matrix is not equal to 0, so the equation group has a unique solution, and the solution is G1 ; G2 ; G3 , replacing the original G1 ; G2 ; G3 . The stitching algorithm for three B-spline surfaces is: (1) The common boundaries of the surfaces B, C, and D are obtained by the inverse of the B-spline curve to obtain the control vertices Hi , Ii and Ji . The condition that needs to be satisfied is H0 ¼ I0 ¼ J0 , and H1  H0 ; I1  I0 ; J1  J0 are coplanar. (2) Given the parameter ci , ai and bi are solved by ci : (3) Using the inverse B-spline curve method, the control vertices Pi ; Qi and Ri of @C @D c1 ðvÞ @B @u jv¼0 c2 ðvÞ @u jw¼0 c3 ðvÞ @w ju¼0 are solved. (4) Solved by the equations, the solution is G1 ; G2 ; G3 , replacing the original G1 ; G2 ; G3 : (5) Two-piece splicing of three curved surfaces by using a splicing algorithm of two Bspline surfaces.

4 Algorithm, Experiment and Analysis We test the feasibility of the algorithm by taking two and three surfaces as examples. Firstly, the unit sphere is evenly divided into 24 pieces according to the longitude and latitude, and the reverse processing of the B-spline surface is performed separately for each piece. The node vector is taken as: [0, 0, 0, 0, 0.25, 0.5, 0.75, 1, 1, 1, 1]. The lattice point is 5  5 dot matrix, and the obtained control points are 7  7 dot matrix. The two curved surfaces are judged by verifying the values of the three tangential determinants at the boundary of the two curved surfaces. For the two surfaces, before the splicing, calculate the three-way tangential determinant at each point on the common boundary with a step of 0.001. The maximum value is 0.01596772, and the average value is 0.0095462 (Table 1).

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Table 1. Algorithm 1 verifies test data. Parameter value Maximum value Average value a ¼ 1:25; b ¼ 1:25 0.009653846 0.001362941 cð0Þ ¼ 0:25, cð1Þ ¼ 1 a ¼ 1; b ¼ 1 0.094856112 0.018356527 cð0Þ ¼ 1, cð1Þ ¼ 1 It can be seen from the experiment that different parameter selection has a great influence on the smooth splicing of the surface. If the parameters are properly selected, the smoothness of the splicing is relatively good.

Acknowledgments. This work was supported by ‘Study on Key technologies of Parallel Robot for Minimally Invasive Spine Surgery’, Scientific Research Project of Shanghai Municipal Science and Technology Commission, (Projection No. 16090503700).

References 1. Du WH, Schmitt FJM (1990) On the G1 continuity of piecewise Bezier surface: a review with new results. Comput -Aided Des 7(1–4):165–180 2. Shi X, Zhao Y (2002) G1 continuous conditions between Bicubic B-Spline surfaces. J Comput -Aided Des Graph 14(7):676–682 3. Che XJ, Liang XZ (2002) G1 continuity conditions of B-spline surfaces. Northeast Math J 18 (4):343–352 4. Shi FZ (1994) Computer aided geometric design and non-uniform rational B-spline. Beijing University of Aeronautics and Astronautics Press 5. Shi XQ, Wang TJ, Wu PR et al (2004) Reconstruction of convergent G1 smooth B-spline surfaces. Comput Aided Geom Des 21:893–913

Real-Time Recognition of Motor Vehicle Whistle with Convolutional Neural Network Ming Yan1(&), Chaoli Wang1, and Song Shen2 1

University of Shanghai for Science and Technology, Shanghai 200093, China [email protected] 2 China Orient Institute of Noise and Vibration, Beijing 100085, China

Abstract. This paper proposes a method based on convolutional neural network (CNN) to recognition of motor vehicle whistle, which is used to monitor illegal whistle. The convolutional neural network architecture takes the spectrum as input and infers through the trained convolutional network to determine whether whistled. We achieve a recognition accuracy of 99% on the whistle data collected by China Orient Institute of Noise & Vibration. The convolutional neural network consists of two layers of convolution and two layers of full connections. The time of single inference is less than 3 ms, which can used to monitor the whistle in real time. Keywords: Whistle detection


Real-time recognition
CNN

1 Introduction Sound is an important source of human information, and it is easy to collect. Sound events are audio segments that humans mark as unique concepts in acoustic signals [1]. Applications for sound event detection include audio surveillance [2], medical surveillance [3], urban sound analysis [4], multimedia event detection [5] and bird detection [6]. Traditional methods of speech recognition are common, such as the use of the Mel Frequency Cepstral Coefficient (MFCC) as a combination of Gaussian Mixture Model (GMM) or Hidden Markov Model (HMM) [7, 8]. Some scholars also match the input sound with the template in the sound dictionary, which can be achieved by sound source separation techniques, such as non-negative matrix factorization (NMF) on the time-frequency representation of the signal. NMF has been used in [9] and [10] to pre-process signals from a single event, and then pre-process the mixture directly in [8] and [11] without learning from isolated sounds. However, when the number is not known as a priori, the NMF’s fixed constraint on the number of overlapping events to reduces its usefulness. When coupled NMF is used, the estimate of the number of overlapping events can be bypassed, as shown in [12]. In [13], spectrogram features are combined with a generalized Hough transform (GHT) voting system to detect overlapping sound events. This provides a different path rather than traditional frame-based features and achieves higher precision, evaluating combinations on five different sound events [14] et al. The sound events are classified based on the front-end features of the spectrogram combined with Support Vector Machine (SVM) and Deep Neural Network (DNN). The above research has achieved certain © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 80–88, 2020. https://doi.org/10.1007/978-981-32-9698-5_10

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results in the recognition of sound events. However, traditional SVM algorithms are difficult to implement on large-scale training samples and multi-classification problems. The DNN model has problems such as the expansion of the number of parameters and the long learning time. Recently, a CNN-based approach has been proposed for acoustic event recognition [15], which uses a network design suitable for image classification [16]. It has been shown that this method greatly exceeds the most advanced methods previously. However, the above two methods of convolutional networks have higher hardware requirements, and it is difficult to achieve real-time detection due to the large amount of computation. Therefore, this paper proposes a new method to identify whistle in real traffic environment. Compared to the previous methods, we use the spectrum directly as input and propose a new network architecture. Our recognition speed has been greatly improved. The reason why we increase our speed is that two aspects. The first one is that the data we input is relatively short, each data has only 512 points, and we only need to do the one-dimensional convolution. Another is that we propose a new network architecture, with fewer layers and fewer parameters, which allows us to achieve higher speeds. Our data set consists of two parts, one is 2054 whistle and the other is 3247 non-whistling. All data is collected in a real environment. We achieve a recognition accuracy of 99% on this data sets.

Fig. 1. Whistle spectrum of different car

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2 Data Analysis and Processing 2.1

Data Analysis

This paper mainly studies the whistle of motor vehicles. The horns of motor vehicles are mainly divided into two categories. One type is an electric horn which can be divided into single horn, two-tone horn and three-tone horn. The other type is an airhorn, which is mainly mounted on a truck. The sound characteristics of the air horn are quite different from the electric horn. For the same horn of the same car, the sound characteristics is very different under different working conditions. As shown in Fig. 1, the first two figures are the spectrum of the same car under two different working conditions. The first picture is the spectrum of the whistle while stop, the second picture is the spectrum of the whistle while driving. The third, the fourth and the fifth picture are the whistle sound spectrum of three different brands of vehicles in the same environment. The sixth picture shows the spectrum of the car whistle in the real life. There is basically no obvious regularity in the above various situations, and this is only the car whistle. There are also vehicles such as large trucks that are air horns, and rescue vehicles such as ambulances and fire engines. How to separate the sound of the rescue vehicle from the whistle sound is also a difficult problem. The universal approximation theorem shows that a feedforward neural network only needs to have a linear output layer and at least one hidden layer of an activation function with any kind of “squeeze” property. Giving a sufficient number of hidden units in the network, it can approximate any Borel measurable function from one finite dimensional space to another finite dimensional space with arbitrary precision [17]. In summary, a feedforward neural network with a single layer is sufficient to represent an arbitrary function, and thus the problem can be solved by using a convolutional neural network. 2.2

Data Processing

In order to analyze different frequency components, different sampling frequencies were used for data acquisition at the beginning of the experiment. Some sampling frequencies are 22.05 kHz, some are 44.1 kHz and some are 11.025 kHz. We need to normalize the sampling frequency. We chose to normalize the data of different sampling frequencies by using cubic spline interpolations which has been used in engineering for many years. Since our data has a large proportion of 22.05 kHz, all sampling frequencies are normalized to 22.05 kHz. Despite the sampling frequency is same, different sampling time will result in different data lengths. Therefore, it is necessary to normalize all the data to the same length. There are four methods of normalization. First one, data interception: record the number of points by finding the shortest data of all the data, and then intercept all the data as long as the shortest data. The second, zero padding: record the number of points by finding the longest data, and then zero the end of all data to the same length as the longest data point. Third, maximum peak interception: find the point with the largest absolute value in the data, then take the maximum point as the center point and intercept the fixed number of points to the left and right sides. Fourth, spectrum linear

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average: Intercept the data into a length of 1024 points and do Fast Fourier transform for every 1024 points then average them, so that we get a data length of 1024 points. Since the sound data is symmetrical about 0 point after the spectrum is obtained, we just need to take half of 1024 points.

3 CNN A convolutional neural network is a neural network designed to process data with a similar network structure [17], such as time series data (which can be recognized as a one-dimensional grid that is regularly sampled on the time axis) and images data (which can be seen as a two-dimensional pixel grid). In the convolutional layer, the input data is convolved by a learnable convolution kernel. The convolution operation formula is as shown in following: Z yðtÞ ¼

þ1

1

f ðtÞgðt  rÞ ¼ f ðtÞ  gðtÞ

ð1Þ

Where f(t) and g(t) functions are convolutional variables, r is an integral variable, t is the displacement of the function, and * is the convolution. Convolutional neural networks have the following advantages compared to traditional methods. The model is relatively easy to establish: due to the ever-changing traffic sounds, different types of sounds have very similar characteristics, and the sounds of the same category will the displacement of the function g(−t), and * is the convolution. Convolutional neural networks have the following advantages compared to traditional methods. The model is relatively easy to establish: due to the ever-changing traffic sounds, different types of sounds have very similar characteristics, and the sounds of the same category will have large differences, it is very difficult to accurately identify these typical traffic sounds. It is difficult to find a unified sound feature and it is difficult to establish a theoretical mathematical model of different sounds. Convolutional neural networks are good at data classification. It is easy to find a model to fit the data.

Fig. 2. Whistle detection with convolution network

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The traditional method is not very accurate for the braking sound of large vehicles such as buses, and such sounds are often judged as whistling sounds. Weighing the relationship between network performance and training difficulty based on the data size of the training set. We use two convolutional layers and two fully connected layers, in which the number of convolutional layer filters is 9 in the first layer and 9 in the second layer; the number of nodes in the first layer of fully connected layers is 40, the number of nodes in the second layer of fully connected layers is 2 (Fig. 2). This section briefly introduces the convolutional neural network and the specific architecture of our convolutional network model, the setting and selection of related parameters.

4 Experiment The hardware environment of this experiment CPU: Intel CORE i5, memory: 8 GB GPU-free household notebook. The software environment: tensorflow, python and vs2015. The data set is a city motor whistle data set provided by China Orient Institute of Noise & Vibration. First, the experiment tested the CNN algorithm with different convolution network layers and selected the best network model. This experiment mainly compares the effects of the algorithm from two angles. One is the recognition accuracy, and the other is the time consumed by one reasoning. Table 1 shows the performance of a convolutional neural network composed of different convolutional network layers and different fully connected layers. It can be seen from the table that the number of network layers is not as deep as possible, such as convolution layers with 5 and full connected layers with 3, which does not have a high recognition accuracy. We believe that because the model is relatively complex, the data is over-fitting, resulting in poor model performance. And the model is complex, the more time it takes for a single reasoning. The simpler corresponding model, the shorter the time spent on a single reasoning, but the simpler model, the less likely to fit the data. For example, the second to last column on Table 1 the number of conv layers is 1, and the number of fully connected layers is 2. Although the time of single reasoning is very short, the accuracy of recognition is not high due to under-fitting of the model. Through multiple experiments, the convolutional neural network consisting of twolayer convolution and two-layer full connection is best, not only it has high recognition accuracy, but also it takes less time. Table 1. Comparison of different layers of convolutional networks. Conv layers Fc layers Accuracy Time (ms)

5 2 3 0.986 0.813 6.29 6.54

4 2 3 0.933 0.873 5.21 6.52

3 2 3 0.946 0.908 4.23 4.56

2 2 3 0.991 0.986 2.47 2.73

1 2 3 0.908 0.960 1.77 2.06

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Another important parameter of the convolutional network after the model is determined by the number of the convolution kernels. If the number of convolution kernels is large, it may lead to parameter redundancy and affect the model effect. As shown in Table 2, when the number of convolution kernels is 16 convolution kernels in the first layer and 14 convolution kernels in the second column, the accuracy of identification is not good, and the time consumption is relatively high. We believe that the reason is that our data is relatively simple, and the number of convolution kernels is too large, which tends to cause a slight overfitting of the model. When the number of convolutions is relatively small, such as when the first layer of convolution kernel is 5 and the second layer of convolution kernel is 3. The recognition accuracy at this time is not high. The reason for this situation is that the number of convolution kernels is relatively small, and the features are not learned. The accuracy of recognition is not too high. Table 2. Comparison of the number of different convolution kernels. Conv1 Conv2 Accuracy Time (ms)

16 14 0.92 3.17

15 13 0.91 2.57

12 10 0.93 2.38

11 9 0.93 2.44

9 9 0.99 2.41

9 7 0.98 2.37

7 5 0.9 2.33

5 5 0.88 2.4

5 3 0.85 2.3

The normalization of data is very important for convolutional neural networks. If the data processing is not good, the impact on the results is very serious. Table 3. Comparison of four different data normalization methods. Data process Data interception Zero padding Maximum interception Spectrum linear average

Acc 0.901 0.978 0.957 0.992

Time (ms) 4.88 12.64 3.82 2.51

Table 3 compares the four different data normalization methods introduced above. For the first data interception method, this method has an obvious drawback, all data is calculated based on the shortest data. If the shortest data is short and the rest of the data is long, the intercepted data may not have reached the peak of the whistle and the information is lost. As the first one shown in Fig. 3, a time domain waveform diagram of a car whistle with a number of points of 46592 points. It can be clearly seen that the peak is at 20000 points, if the shortest number of data points is less than 20000, it is obvious that the peak cannot be intercepted. For the second data zero-padding method, all the data is used, but if the longest data length is very long (for example, the longest data sampling frequency is 22.05 kHz, the sampling time is 2 s, then the number of points of the data has 44100 points), it will increase the amount of calculation, and increase the overall calculation time. For the third the maximum peak cut method can

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be used to obtain the whistle peak of the data, and the efficiency is also high. However, the misjudgment of data such as sirens and ambulances, because the waveform of this type of data is relatively flat. The second one in Fig. 3 shows the time domain shape of the siren sound of the rescue vehicle. If the interception is based on the maximum peak, it is apparent that the interception of the waveform data of the rescue vehicle does not intercept the valid data. The method of linear averaging for the fourth spectrum is used for all points of the data, and the number of data points is relatively small and the efficiency is relatively high.

Fig. 3. Car whistle waveform and ambulance whistle waveform

We also do some comparisons with other more common methods of using convolutional network which use picture as the input.

Fig. 4. Car whistle spectral map

Compared with other convolutional networks that use pictures as input, the singletime reasoning of the network structure proposed in this paper consumes the least time under the same accuracy rate. As shown in Table 4, the first column is the method of this article, and the rest are other related methods. Not only the architectures of the convolutional network are different, but also the input is different. The input of CNNFC and CNN-c is picture. As shown in Fig. 4, the horizontal axis is time and the vertical axis is frequency.

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Table 4. Comparison of different convolution network model Ours Input Conv 5*1,1,9 Conv 5*1,1,9 fc 40 fc 2 – – – – – – Time (ms): 2.51 ms

CNN-FC Input Conv 3*3,1,64 Conv 3*3,1,64 max pool 1*2 Conv 3*3,1,128 Conv 3*3,1,128 max pool 2*2 fc 40 fc 2 – – Time (ms): 27.34 ms

CNN-C Input Conv 3*3,1,64 Conv 3*3,1,64 max pool 2*2 Conv 3*3,1,128 Conv 3*3,1,128 max pool 2*2 Conv 3*3,1,64 Conv 1*1,1,2 Conv 1*1,1,2 avg pool Time (ms): 23.16 ms

The size of the training set has a greater impact on the training results. At the beginning of the project, the size of the training set is 1066, and our test accuracy can reach 92%. In the later stage, we increased the test accuracy by a small amount after we increased the number of training sets. Our current training set number is 4770, the number of test sets is 561, and the test accuracy can reach 99%. In terms of current accuracy, our algorithm is ready for use. This section mainly introduces several experiments we have done and draws several conclusions. Correct In the motor vehicle whistle sound data, when the structure of the convolution network is 2 layers of convolution, 2 layers of fully connection, the performance of the network is best. The number of convolution kernels of the two convolutional layers both 9. For the normalization of data, it is recommended to select the spectral liner average, at this time the data is not only short but also rich in effective information.

5 Conclusion This paper introduces a new method to identify the sound of a horn in a motor vehicle. This method has a good effect on the recognition of car whistle sound, and it can also achieve real-time recognition. And through several sets of comparative experiments, this paper chooses a better data normalization method. Our method only recognizes the whistle sound, and can further capture the image and video signals with the HD camera to obtain further complete information such as the license plate number, what type of motor vehicle, and so on. In addition, this paper not only recognizes the sound of motor vehicle whistle, it also increases other sound recognition on the road, such as the recognition of modified car sound, the recognition of car crash sound and the related research of construction sound.

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References 1. Heittola T, Mesaros A, Virtanen T, Gabbouj M (2013) Supervised model training for overlapping sound events based on unsupervised source separation. In: International conference on acoustics, speech, and signal processing (ICASSP), Vancouver, Canada, pp 8677–8681 2. Foggia P et al (2015) Reliable detection of audio events in highly noisy environments. Pattern Recogn Lett 65:22–28 3. Goetze S, Schroder J, Gerlach S, Hollosi D, Appell J-E, Wallhoff F (2012) Acoustic monitoring and localization for social care. J Comput Sci Eng 6(1):40–50 4. Salamon J, Bello JP (2015) Feature learning with deep scattering for urban sound analysis. In: Proceedings of the 2015 23rd European signal processing conference, pp 724–728 5. Wang Y, Neves L, Metze L (2016) Audio-based multimedia event detection using deep recurrent neural networks. IEEE international conference on acoustics. IEEE 6. Stowell D, Clayton D (2015) Acoustic event detection for multiple overlapping similar sources. In: Procedings of the 2015 IEEE Workshop Applications of Signal Processing to Audio and Acoustics, pp 1–5 7. Mesaros A, Heittola T, Eronen A, Virtanen T (2010) Acoustic event detection in real life recordings. In: 18th European signal processing conference, pp 1267–1271 8. Heittola T, Mesaros A, Virtanen T, Gabbouj M (2013) Supervised model training for overlapping sound events based on unsupervised source separation. In: IEEE International conference on acoustics, speech and signal processing (ICASSP), pp 8677–8681 9. Innami S, Kasai H (2012) NMF-based environmental sound source separation using timevariant gain features. Comput Math Appl 64(5):1333–1342 10. Dessein A, Cont A, Lemaitre G (2013) Realtime detection of overlapping sound events with non-negative matrix factorization. In: Matrix information geometry. Springer, pp 341–371 11. Dikmen O, Mesaros A (2014) Sound event detection using non-negative dictionaries learned from annotated overlapping events. In: Applications of signal processing to audio and acoustics. IEEE 12. Dennis J, Tran HD, Chng ES (2013) Overlapping sound event recognition using local spectrogram features and the generalised hough transform. Pattern Recogn Lett 34(9):1085– 1093 13. Zhang M, Zhou Z (2006) Multi label neural networks with applications to functional genomics and text categorization. IEEE Trans Knowl Data Eng 18(10):1338–1351 14. Mcloughlin I et al (2015) Robust sound event classification using deep neural networks. IEEE/ACM Trans Audio Speech Lang Process 23(3):540–552 15. Takahashi N, Gygli M, Pfister B, Gool LV (2016) Deep convolutional neural networks and data augmentation for acoustic event recognition. In: Proceedings of the interspeech 2016, San Fransisco 16. Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. CoRR, abs/1409.1556 17. Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge

Analysis of Trace Surface Morphology Based on Fractal and Complexity Theory Bingcheng Wang(&) and Chang Jing Shenzhen University, Shenzhen 518060, China [email protected]

Abstract. Since the fractal and complexity theory can quantitatively describe the non-linear problems, the fractal and complexity theory are applied to analyze the surface topography characteristics of linear traces. Taking complexity, approximate entropy, and spectral width and peak value of singular spectrum as quantitative indicators, the surface morphology characteristics of linear traces generated by different shearing tools were analyzed, and the results of quantitative analysis and inspection were obtained. The results show that the surface morphology of the traces produced by different tools is different, and the four indices of complexity, approximate entropy, and spectral width and peak value of the singular spectrum are different. These four features can effectively measure the randomness and nonlinearity of the surface topographic features of traces. It is an active and feasible exploration to apply the non-linear theory to the field of trace inspection, which provides a new way for qualitative and quantitative analysis of trace surface topography features. Keywords: Fractal theory
Complexity theory Surface topography characteristics




Quantitative description




1 Introduction Quantitatively describing and accurately detecting the surface topography of linear traces has become an important part of the study of characteristics and mechanisms. Previous studies on various problems are mostly based on Euclidean geometry of integer dimension, which can not objectively and accurately describe these stochastic complex graphs. Previous studies on various problems are mostly based on Euclidean geometry of integer dimension, which can not objectively and accurately describe these stochastic complex graphs. Dealing with trace patterns and phenomena is even more ineffective, and cannot be applied in actual inspection work. Because fractal and complexity theory can quantitatively describe irregular and disordered complex graphics, fractal theory is used to study the surface morphology characteristics of materials and some results have been achieved [1, 2]. Taking complexity, approximate entropy, and spectral width and peak value of singular spectrum as quantitative indicators, the surface morphology characteristics of linear traces generated by different shearing tools were analyzed, and the results of quantitative analysis and inspection were obtained. It is an active and feasible exploration to apply the non-linear theory to the field of trace inspection. © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 89–96, 2020. https://doi.org/10.1007/978-981-32-9698-5_11

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2 Line Trace Production and Data Collection In order to apply fractal theory and complexity theory to analyze the surface topography characteristics of line traces, three double-edged tools, scissors, wire pliers and wire breaker, were used in the laboratory. Lead wire with a diameter of 6 mm was selected as the object of damage, and a batch of line traces samples were made. Stereo microscope, comparative microscopy and three-dimensional surface topography instrument were used to observe and compare the characteristics of line trace samples. Finally, the data of trace surface topography were collected. The contour curve which can reflect the cutting edge processing and use stable features is taken as the research object. The contour curves perpendicular to the surface of the trace are generated by scissors, pliers and wire breakers, respectively, as shown in Fig. 1.

(a)

(b)

(c)

Fig. 1. Surface profile curves of three traces

3 Complexity Theories and Computation The complexity of things has two characteristics, one is the complexity of spatial structure, and the other is the complexity of changing with time. Kolmogrov’s study of complexity suggests that complexity is the minimum number of bits of a computer program required to give a “0, 1” sequence. It is generally believed that the fewer the programming statements for the characterization system, the simpler the system. LemZiv defines the complexity of a random sequence: it reflects the rate at which a time series appears in a new pattern as its length grows, showing the degree to which the data sequence is close to random. The Lem-Ziv complexity algorithm reflects the extent to which a data sequence is close to a random sequence [3–6]. It is considered that if a sequence is completely ordered, the complexity is the lowest, and if the sequence is completely random, the complexity is the highest. This algorithm applies to symbol sequences, so the data sequence of the study is first symbolized. Setting the data sequence as fz1 ; z2 ; . . .zn g, first of all, it is coarsened. First, the  is calculated, and the rules of reconstructing the average value of the sequence Z sequence are formulated. The rule content is equal to 1 when zi is greater than the  and equal to 0 when zi is less than the average value Z.  The new average value Z,

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sequence reconstructed following such a rule is fs1 ; s2 ; s3 . . .; sn g, and the new sequence is composed of 0 and 1 and has the same length as the original sequence. For a given binary symbol sequence, let A and B be two substring sequences, then AB is a symbol string sequence formed by merging A and B substring strings, and AB1 is a symbol string formed by abandoning the last symbol of AB sequence. Specific provisions are as follows: (1) For the original string S, if the additional character B is included in A, the number of segments A and B is the same, that is, the number of segments A and B does not increase. (2) When symbol string B is not included in A, the number of segments is increased from m to m þ 1. The sequence is divided into non-repeating segments, the number of segments is the absolute value of the complexity, and that is, the unnormalized complexity cðnÞ is represented by the number of segments. (3) Dividing the complexity cðnÞ absolute value by the complexity of the random signal theoretical value bðnÞ ¼ en= loge n (n is the sequence length), the normalized complexity is obtained: CLZ ðnÞ ¼ CðnÞ=bðnÞ

ð1Þ

The calculation formula of complexity shows that if the complexity of the symbol sequence is larger, the number of sub-symbol strings that need to be different from each other to express the symbol sequence is more, indicating that the system is in a complicated state. It reflects the high degree of randomness and irregularity in the process of data sequence. At the same time, the greater the complexity of the sequence, the more new dynamic modes or spatial structures that appear in the system at a given time, and the faster the dynamic mode or spatial structure changes. On the contrary, the smaller the complexity of symbol sequence is, the lower the complexity of the system is, reflecting the slower the frequency of dynamic mode or spatial structure changes in the system is. At this point, it can be considered that the regularity of the dynamic mode or spatial structure change is stronger in a given time, that is, the periodicity of the change of the symbol sequence is more obvious. In the actual research, the complexity of the obtained measured data sequence is between 0 and 1, and the size of CLZ ðnÞ directly reflects whether the system is in a random state or in a periodic state. In this paper, the surface topographic features are analyzed by the complexity of the surface contour curve of line traces. By using the formula of complexity (1), the complexity of surface contour curves generated by three kinds of double-edged tools is obtained as shown in Table 1.

Table 1. Complexity of surface profile curves for different traces Types Sample a Sample b Sample c Complexity 14 17 51 Normalized 0.0986 0.1384 0.3877

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As can be seen from Table 1, the different trace surface profile curves have different complexity CLZ ðnÞ. The complexity of sample c is the largest, and its value is 0.3877, which indicates that the surface contour curve (measured data sequence) generated by the bolt cutter has a high degree of randomness and irregularity, and the surface morphology of the mark is relatively complicated. The complexity of sample a is the smallest, and its value is 0.0986, indicating that the surface profile curve (measured data sequence) produced by the scissors is periodic, The surface morphology of the trace is regular, reflecting the processing trace of the cutting edge of the scissors, which has periodic characteristics.

4 Approximate Entropy and Calculation in Complexity Theory The Approximate Entropy algorithm provides a feature quantity that characterizes the complexity of a data sequence. The approximate entropy calculation requires a small amount of data, and is applicable to both deterministic and random signals [7, 8]. The approximate entropy can be derived from the correlation integral Cim ðr Þ of data series. (1) Assuming that a data sequence is fy1 ; y2 ; . . .yn g and given the mode dimension m and the similar tolerance limit r, the m-dimensional vector is composed of the data sequence in serial order: YðiÞ ¼ ½yðiÞ; yði þ 1Þ; . . .; yði þ m  1Þi ¼ 1; . . .; N  m þ 1

ð2Þ

(2) If the maximum difference between the corresponding elements of vector YðiÞ and vector YðjÞ is distance d½YðiÞ; YðjÞ, then: d½YðiÞ; YðjÞ ¼ max ½jyði þ kÞ  yðj þ kÞj k¼0m1

ð3Þ

(3) Given the similar tolerance limit m > 0, the ratio is calculated. The expression is as follows: Cim ðrÞ ¼

1 f½YðiÞ; YðjÞ\rg N  mþ1

ð4Þ

That is: the ratio of the number of d½XðiÞ; XðjÞ less than r to the total number of vectors N – m + 1 is denoted as Cim ðrÞ. (4) The correlation integral Cim ðrÞ is taken as a logarithm, and then the average value of all i is calculated. Then increase the dimension m to m þ 1 and repeat the above steps to get Cim þ 1 ðrÞ and wm þ 1 ðrÞ. Among them wm ðrÞ ¼

Nm Xþ 1 1 ln Cim ðrÞ N  m þ 1 i¼1

ð5Þ

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The approximate entropy expression is: ApEnðm; rÞ ¼ ½wm  wm þ 1 

ð6Þ

The ApEnðm; rÞ value is a dimensionless scalar. Obviously, the given model dimension m and the similar tolerance r value have an effect on the calculation of the approximate entropy. The values of m and r are different, and the values of the approximate entropy are different. According to experience, m = 2, r ¼ ð0:1  0:2Þa is generally chosen, where a is the standard deviation of the original data. Using the approximate entropy calculation formula (6), the approximate entropy of the surface profile curve obtained by the three double-edged tools is shown in Table 2. Table 2. Approximate entropy of surface profile curves of different traces Type Sample a Sample b Sample c Approximate entropy 0.1574 0.1656 0.7962

As can be seen from Table 2, the different trace surface profile curves have different approximate entropy ApEnðm; rÞ. The approximate entropy of sample c is the largest, and its value is 0.7962, which indicates that the surface contour curve (measured data sequence) generated by the bolt cutter has a high degree of randomness and irregularity, and the surface morphology of the mark is relatively complicated. The approximate entropy of sample a is the smallest, and its value is 0.1574, indicating that the surface profile curve (measured data sequence) produced by the scissors is periodic, The surface morphology of the trace is regular, reflecting the processing trace of the cutting edge of the scissors, which has periodic characteristics.

5 Multi-scale Fractal Principle and Generalized Fractal Singular Spectrum Fractal theory provides a theoretical basis for the study of nonlinear system behavior. Multi-scale fractal is suitable for feature extraction and recognition of non-stationary signals [9]. For the observation data series fy1 ; y2 ; . . .yn g covered by a small box with scale e, the distribution probability of the i-th small area measured by scale ei is Pi ðeÞ, and the scale index ai is used to represent the different probabilities of different small regions, the following mathematical expressions are obtained: Pi ðei Þ ¼ eai i i ¼ 1; 2; 3;


N

ð7Þ

According to the definition of the fractal calculation formula, it can be seen that it is the fractal dimension of a small region of the fractal set, and its size reflects the probability measure of the mass distribution of the small region. It controls the singularity of probability density and is therefore called the singularity index. Customary

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called a is the Lipschitz-Holder index. When the scale ei becomes smaller, the number NðeÞ of probability measures Pi increases, then it can be concluded: NðeÞ / ef ðaÞ

ð8Þ

Where f ðaÞ represents the rate of change of the number of elements in each subset as a function of scale, obviously the function f ðaÞ changes with the singularity index a. The curve drawn by a * f ðaÞ is called singular spectrum, abbreviated as a * f ðaÞ spectrum, which is an important parameter to describe multi-scale fractal. The relationship between f ðaÞ and the fractal dimension Dq in the singular spectrum is: f ðaÞ ¼ aq  ðq  1ÞDq a¼

ð9Þ

d½ðq  1ÞDq dq

ð10Þ

Finally, the multi-scale fractal parameter extracted by singular spectrum is: Da ¼ amax  amin

ð11Þ

Df ¼ f ðamin Þ  f ðamax Þ

ð12Þ

Where Da represents the singular spectrum width, and its size reflects the state of the probability distribution of the entire fractal structure. The degree of convexity and concavity of trace surface morphology can be characterized by the size of spectral width, or the degree of height fluctuation of two-dimensional curve can be quantitatively described. The difference between the dimension of the largest and the smallest probability subset in the singular spectrum Df can be used to calculate the number ratio of the maximum height and the smallest height on the surface. By using the formula of singular spectrum, the singular spectrum of the surface contour curve generated by three kinds of double-edged tools is obtained as shown in Fig. 2, and its special positive value is shown in Table 3.

(a)

(b)

(c)

Fig. 2. Singular spectra of surface profile curves of different traces

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Table 3. Characteristic values in singular spectrum Type Da fmax Sample a 3.0490 0.2287 Sample b 2.4260 0.4833 Sample c 2.4213 0.8088

Df 0.5563 0.3046 0.1727

Discussion on the experimental results: According to the eigenvalues of Table 3, the singular spectrum of sample a has the characteristics of large spectral width value and small peak value, which indicates that the surface topography of this kind of trace has simple structure, few complicated and fine structures, and obvious convex and concave undulations. The singular spectrum of sample c has the characteristics of small spectral width and large peak value, which indicates that the structure of the contour curve of the trace surface is fine and complex. Therefore, the spectral width and spectral peak difference can be used to quantitatively divide the surface topography and scientifically express the geometric features of the linear trace surface.

6 Conclusions A method for analyzing the surface topography of traces by fractal and complexity theory is proposed. Complexity and approximate entropy characteristic value reflecting the surface topography of traces are obtained by using complexity theory, using multiscale fractal theory, the parameters reflecting the surface topography of traces, namely. singular spectral width and spectral value difference, are obtained, and these four parameters are used as characteristic quantities for describing the surface topography of traces. The analysis and calculations show that the surface features of the traces produced by different tools are different, and the four feature quantities are different, and it is also shown that these four feature quantities are effective for describing the structural complexity of the surface topography. It is an active and feasible exploration to apply fractal and complexity theory to trace inspection. A new approach is provided for the qualitative and quantitative analysis of trace surface topography. Acknowledgments. This work is supported by the Nature Science Fund of China (NSFC), No.: 61571307.

References 1. Ge S, Tonder K (1997) Fractal characterization and fractal expression of rough surfaces. J Tribol 17(1):73–80 (in Chinese) 2. Bin F, Hairong W, Zhuangde J (1998) Study on fractal characteristics of machined surfaces. J Xi’an Jiaotong Univ 32(5):83–86 (in Chinese) 3. Diqing L, Zhigang C, Xiaohong D (2015) Analysis of chaotic sequence complexity based on wavelet packet energy entropy. Acta Electronica Sinica 43(10):1971–1977 (in Chinese)

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4. Gao J, Si H, Yu X, Gu L (2017) Study of lie detection using complexity feature of multichannel EEG. J Univ Electron Sci Technol China 46:636–640 (in Chinese) 5. Shoulin Z, Lilong Q, Xiang C (2015) Digital modulation recognition based on complexity measure. Comput Eng Appl 51(4):226–231 (in Chinese) 6. Wang X, Wang F (2013) Auto classification for sleep stage based on complexity and approximate entropy of EEG. Software 34(2):97–100 (in Chinese) 7. Jianming W, Kun Z, Wang Q (2017) Identification of flaw shape in metal material based onphase space and fuzzy entropy. Chin J Sens. Actuators 30(5):721–730 (in Chinese) 8. Guo F, Li K, Chen C et al (2017) Seres arc fault identification method based on wavelet approximate entropy property. Trans China Electrotechnical Soc 31(24):164–170 (in Chinese) 9. Zhang S, Li P, Hu Y et al (2017) Research and application of multifractal approximate entropy and subtraction FCM clustering. J Vib Shock 51(10):47–52 (in Chinese)

Research About Abrasion Surface Morphology of Warhead by Structure Function Method Bingcheng Wang1(&) and Chang Jing2 1

2

Shenzhen University, Shenzhen 518060, China [email protected] Guangdong Hengzheng Judicial Appraisal Institute, Guangzhou, China

Abstract. The surface abrasion date of the warheads shot from three type guns were collected by applying collection instrument, and the abrasion topography of warhead surface was studied by application of fractal theory, its surface abrasion show the fractal characteristics. The fractal dimension of abrasion surface profile curve is calculated by structure function method. The result shows that abrasion degree of warhead surface is not same; its fractal dimension is not same when warheads are shot with different types of gun. Therefore, its fractal dimension can be defined as a characteristic quantity to characterize the wear degree of warhead surface, which can be used to analyze the characteristics of warhead surface morphology change. This may help to analyze the change characteristics of abrasion surface topography of warhead, and provide reference for judgment of the gun that shoots such warhead. It provided an identification method for quantitative examination of warhead mark. Keywords: Fractal theory Warhead surface abrasion


Fractal dimension
Structure function method


1 Introduction When the warheads move in the barrel, on the one hand, the pressure from the inside of gun barrel caused plastic deformation; on the other hand, the Warheads and the inner wall of the barrel contact with each other, so they have a relative motion and a frictional wear is generated [1]. The geometric figure reflected by the warhead surface abrasion is so complex and irregular that it’s difficult to describe it accurately. In the past, we make the research on the characteristic of warhead surface abrasion by using some parameters related to measuring instrument resolution or gage length and measure area, such as arithmetical mean deviation of the profile. These parameters have a positive effect on the understanding of friction and wear, but there are also some shortcomings. In the examination and identification of judicial evidence, the inspection of warhead surface abrasion is usually by visual comparison. That is, the identification and judgment of the abrasion shape of warhead recovered from the crime scene or the suspected guns with eyes are not quantitative examinations. Surface topography was studied by using fractal theory and the research has obtained certain achievement [2–5]. In this paper, fractal geometry theory and the literature on the application of fractal research are applied to study the characteristics of © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 97–102, 2020. https://doi.org/10.1007/978-981-32-9698-5_12

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the surface topography of warhead abrasion. The purpose of the study is to apply the fractal theory to the inspection of warhead marks, so that the modern theory and application technology can be combined to deepen the theory of trace inspection. Its practical value is the introduction of new examination techniques for the inspection of the warhead mark in the process of investigating the guns case.

2 Experimental Conditions and Data Acquisition In experimental study, the fired warheads were sampled which are two kinds of Warheads fired by three types of guns (the number of 1, 2, 3 gun) with moderate abrasion, the unit is lm. Some mark specimen of the surface abrasion was made, and the specimens were examined by the stereoscopic microscope, and the specimens reflecting the stable wear morphology were selected for digital acquisition.

(a)

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Fig. 1. Surface profile curves of three traces

Using optical 3D measurement device G4 g made in Austria, the mark of the surface abrasion is digitally collected, and a 3-D data of wear trace surface are obtained. The magnification of the objective lens of the experimental instrument is 20 times and the resolution of the sampling point is 1.1 lm. Data processing software is used to calibrate the trace position to be analyzed and the contour curve and data of the trace surface are obtained. The collected data was input to the computer to print out profile curve to perpendicular to the wear surface. As is shown in Fig. 1. The abscissa is the sampling points of the curve, the ordinate is the profile height value Z (x).

3 Calculating Fractal Dimension of Contour Curve by Structure Function Method Fractal theory provides the theoretical basis for the description of nonlinear behavior of the system, and it is used to quantitatively characterize the singularity of chaotic attractor. To a certain extent, the fractal dimension make up for the deficiency of the traditional analysis model. In order to describe the nonlinear system behavior characteristics by fractal dimension, Several different definitions and calculation methods of

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fractal dimension are proposed, for example, Hausdorff dimension, similarity dimension, spectral dimension, correlation dimension, box counting method, structure function method and correlation integral method, etc [6–10]. The research on various fractal dimension calculation methods shows that the structure function method is simple in calculation, and compared with the theoretical value, it has higher accuracy and lower error. In order to calculate fractal dimension of warhead wear surface, the structure function method is adopted in this paper. Principle of structure function method: Since the rough surface contour curve is randomly distributed, it can be regarded as a function ZðxÞ of one-dimensional variable x. So the mathematical expression of rough surface contour is: ZðxÞ ¼ GD1

1 X cosð2pcn xÞ n¼n1

cð2DÞn

ð1Þ

This function is abbreviated as W-M function, where cn1 ¼ 1=L (L = sampling length). We define the \½Zðx þ sÞ  ZðxÞ2 [ structure function, whose expression is. Z SðsÞ ¼ \½Zðx þ sÞ  ZðxÞ2 [¼

þ1 1

SðxÞðejxs  1Þdx

ð2Þ

SðxÞ is the power spectrum function of W – M, obtained from autocorrelation function of W – M through Fourier transform. The expression of autocorrelation function is: Z

l

RðsÞ ¼ lim

l!1

ZðxÞZðx þ sÞdx ¼

0 ^

SðxÞ ¼

1 G2ðD1Þ X cosð2pcn sÞ 2 n¼n1 cð42DÞn

1 G2ðD1Þ X dðx  cn Þ 2 n¼n1 cð42DÞn

ð3Þ

ð4Þ

In which: x is frequency (the reciprocal of roughness wavelength) and dðxÞ is impulse function. The discrete W * M power spectral function (3) is replaced by a continuous function whose continuous function is expressed as: G2ðD1Þ 1 2 ln c xð52DÞ

ð5Þ

SðsÞ ¼ CG2ðD1Þ sð42DÞ

ð6Þ

SðxÞ ¼ Substitute (5) into (2), then:

The curves of discrete data are drawn in logarithmic coordinates log SðsÞ  log s. According to the relationship between slope of regression straight line and fractal dimension, the expression is as follows:

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D ¼ ð4  aÞ=2

ð7Þ

When calculating the fractal dimension of warhead wear surface by formula (7), the collected data are input into the computer and the discrete structure function is calculated by formula (2). The specific calculation method is as follows: Assuming the sampling interval is DL, N points are collected on the sampling length L, then there are: Zðxi Þ ¼ Zi ði ¼ 0; 1; 2; 3; . . .N  1Þ

ð8Þ

Assume s ¼ nDLðn ¼ 0; 1; 2; 3; . . .N  1Þ in formula (2), and then the discretized structure function expression is: SðsÞ ¼ SðnDlÞ ¼

N n 1 X ðZi þ n  Zi Þ2 N  n i¼0

ð9Þ

Formula (9) is used to calculate the value of structural function SðsÞ and plot the curves of discrete data in logarithmic coordinates log SðsÞ  log s. The fractal dimension is obtained from the relationship between the slope of regression line a and the fractal dimension D. According to formula (9), logarithmic structure function graphs of the surface abrasion of the Warheads shot from three type guns can be obtained, it is shown in Fig. 2.

(a)

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(c)

Fig. 2. Structure function curves of abrasion surface on warhead from gun

The curve above shows that the structure function curve of the wear surface contour of the warheads shot from different kinds of guns has a distinct linear region in the curve of the double logarithmic coordinate system, that is, the scale-free region exists. This relationship curve shows that there is a good fractal characteristic of the abrasion surface profile of firing warhead in the range of scale-free zone. herefore, the fractal geometry theory can be used to describe the abrasion surface morphology of firing warheads. When different types of guns fire warheads, the wear surface features produced on the warhead surface are difference, so the fractal dimension D is difference. The fractal dimension of abrasion surface contour curves of warhead firing by gun No. 1 and No. 2 is 1.73615 and 1.6702658 respectively. Since the guns of type 1 and 2 have the same structural characteristics, the types of warheads emitted are also the same, so the difference in the fractal dimension between them is small. The fractal

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dimension of the abrasion surface contour curves of warhead firing by gun No. 3 is 1.578 706. The No. 1 and No. 2 guns are compared with No. 3 guns. The guns have different structural characteristics and different types of warheads. Therefore, the fractal dimension is not the same.

4 Conclusions The abrasion surface contour curve of warhead has very good fractal characteristics, so the fractal geometry theory can be used to describe the abrasion surface morphology of warhead. The fractal dimension of the worn surface profile of warhead is calculated by using structure function method. The research results show that the wear characteristics of on the warhead surface when firing warheads different guns are different, so the fractal dimension D is not the same. The size and variation of fractal dimension can reflect the irregularity and complexity of profile curve of the wear surface. Therefore, fractal dimension D can be used to characterize the characteristics of warhead surface wear degree, which is helpful to describe the characteristics of warhead surface morphology change. Combining the image comparison technology of bullet trace with the digital processing technology of fractal dimension is more advantageous to the inspection, identification and recognition of bullet trace. This new detection technology is introduced into the warhead marks inspection, which is used for investigating gun related cases. Based on the quantitative inspection of the wear marks of the warhead extracted from the scene, the wear degree of the barrel surface of the gun was analyzed and the scope of investigation was narrowed. It provides technical support for inferring gun weapon; and provides new method of quantitative inspection of warhead marks. Acknowledgments. This work is supported by the Nature Science Fund of China (NSFC), No.: 61571307.

References 1. Li D, Li G (1995) Technical Inspection of Bullet Marks. Police Education Press, Beijing (in Chinese) 2. Majudar A, Tien CL (1990) Fractal characterization and simulation of rough surfaces. Wear 116(8):35–39 3. Majumdar A, Bhushan B (1991) Fractal model of elastic-plastic contact between rough surfaces. J Tribol 113(1):1–11 4. Ge S, Zhu Z (2005) Fractal of Tribology. China Machine Press, Beijing (in Chinese) 5. Wang B-C, Ren Z-H, Hou R-T (2010) Multi-fractal method on fault diagnoses. Modern Manuf Eng (7):1–4. (in Chinese) 6. Li S, Wu J (2002) Fractal and Wavelet. Science Press, Beijing (in Chinese) 7. Zhang L (2012) Comparison study of two multifractal approaches on stock markets. In: IWCFTA 2012, p 298–302

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8. Wang BC, Jing C (2017) General fractal dimension calculation of surface curve of shearing marks based on correlation integral. In: 10th International Symposium on Computational Intelligence and Design (ISCID), p 12–15 9. Wang B, Ren Z, Wen B (2010) Chaotic parameters analysis in fault diagnoses. Mach Tool Hydraul 38(23):144–147 (in Chinese) 10. Wang B, Jing C (2018) Study on surface morphology of pliers- clippers trace by using Lyapunov index energy spectrum. In: 2018 11th International Symposium on Computational Intelligence and Design (ISCID 2018), p 49–52. IEEE Computer Society, ISBN 978-1-53868526-6

Accurate Image Recognition of Plant Diseases Based on Multiple Classifiers Integration Shuang Liang and Weicun Zhang(&) School of Automation and Electrical Engineering, University of Science and Technology Beijing, 100083 Beijing, China [email protected]

Abstract. In agriculture, early detection of plant diseases is essential to avoid irretrievable damage to crops. However, accurate plant disease diagnosis is usually performed by professionals with high precision instruments which is both expensive and time consuming. To tackle this problem, an image recognition method based on multiple classifier integration is described. The method is composed of three parts. Firstly, a public dataset of diseased and healthy plant leaves is adopted. Secondly, three types of convolutional neural network (CNN) models are fine tuned to classify different diseases of plants and evaluated separately. Finally, the three models are integrated and evaluated for accurately diagnosing plant diseases. Experiment result shows the correctness and efficiency of the approach with a best accuracy of 99.92% on split test set. Keywords: Plant disease
Convolution neural network Multiple classifiers integration


Image recognition


1 Introduction Agriculture and food security problem has been taken as one of the most severe global issues with the rapid growth of global population. It is estimated by food and agriculture organization of the united nations (FAO) that global food demand will increase by roughly 70 percent till the end of 2050 [1], which poses grave challenge for all countries. In food security, plant disease is a tremendous threat because it directly affects crop production. Therefore, it is important to recognize plants diseases accurately when the diseased plants were found to reduce farther crop loss. Traditionally, plant diseases are firstly judged by experienced farmers or agriculture experts through plants’ appearance and then analyzed in different plant physiological indicators by using sophisticated instruments. As described in the work [2], although the combination of appearance observation and chemical analysis is accurate, it will cost at least a week to provide results and could be very expensive which is not practical and economical for farmers. Deep learning, which is a branch of machine learning, is designed to extract multilevel features automatically and learn the abstract relationship between input and output by its nonlinear mapping capability. It has made great strides in many areas, such as game theory [3], nature language processing [4], and especially image recognition and analysis [5] due to the explosion of computing and the introduction of large-scale data © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 103–113, 2020. https://doi.org/10.1007/978-981-32-9698-5_13

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sets. Meanwhile, many deep neural network structures are proposed to extract useful information and features from massive data. Deep convolutional neural network (CNN), which is one of these structures, shows great superiority in characterization of images and has been widely used in the filed of computer vision. It is typically consisted of four parts, convolution layer, pooling layer, nonlinear activation function and fully-connected layer. An example of convolutional neural network structure is shown in Fig. 1.

Fig. 1. An example of convolutional neural network structure.

In 2012, AlexNet [6], which is a large and deep convolutional neural network, was proposed and achieved impressive accuracy on ImageNet [7] LSVRC-2012 contest. Since then, many structures of deep networks have been designed for improving the ability of feature extraction and representation capacity. Resnet [8] uses element-wise adding method to connect input with convolution layer’s output and transmit residual error between those layers that are not connected directly to fusion different level feature maps. WideResnet [9] is inherited from Resnet and tries to expand the network in width and reduce the network in depth to make full use of more residual module. This type of structure gives potential on a large horizon perspective. DPN [10] is a convolutional neural network that have two different paths of residual alike module and densely alike module and achieves currently best results on ImageNet dataset. However, as explained in this work [11], the average accuracy of a single network maybe high but it may behave bad on some test cases. To deal with this situation, we use a multiple models integration method to increase the robustness of the classifier. Because different models represented relationship between input and output differently, the integration will improve the robustness of the final classifier and can correct the uncertain label to some extent which bring a slightly improvement on accuracy. In order to investigate plant diseases by images, a large amount of plants pictures need to be collected in advance. As mentioned in this paper [12], many representative symptoms of plants diseases are changes of plants’ appearance, for instance, leaves. With the popularization of photographic equipment and internet, many plant diseases images are collected and well labeled of which the biggest data set is the project Plant Village [13]. It records 54,309 leaf images of 14 crop species and separates them into 38 different categories with both healthy and diseased samples. Figure 2 shows each category in the data set. We conduct experiments on this data set with our proposed multiple classifiers integration method and achieve a best accuracy score of 0.9992.

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Fig. 2. Each category in the data set.

2 Method Our plant diseases image recognition method based on multiple classifiers integration consists of the following parts: (1) augmenting image data to expand image training set and improve generalization ability of models. (2) fine tuning different convolutional neural networks and evaluating each performance. (3) integrating multiple classifiers and evaluating final performance. (4) experimental results and analysis. 2.1

Dataset Description and Image Preprocessing

As introduced in the work [14], the data set is consisted of 14 crop species and 38 different classes. Table 1 shows the details of the data structure. We can find the imbalance between different crops or different class of diseases. This may influence the intend of the network during training, which means that the model is intend to classify the test case into classes that have a large proportion in the dataset. We use the following image data augmentation method including rotation, horizon flip and vertical flip, color jittering, random scale transform, contrast transform, and gaussian noise. Outputs of these augmentations are shown in Fig. 3.

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Number 630 621 275 1645 1502 854 1052 854 513 1192 985 1162 1180 1383 1076 423 5507 2297 360 997 1478 1000 152 371 5090 1835 1109 456 2127 1000 1909 952 1771 1676 1404 5357 373 1591

Crop species Apple Apple Apple Apple Blueberry Cherry Cherry Corn Corn Corn Corn Grape Grape Grape Grape Grape Peach Peach Pepper Pepper Potato Potato Potato Raspberry Soybean Squash Strawberry Strawberry Tomato Tomato Tomato Tomato Tomato Tomato Tomato Tomato Tomato Tomato

Index 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

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Fig. 3. Image augmentations

2.2

CNN Models Description

As mentioned above, ImageNet [7] competition has played an important role in promoting the development of convolutional neural networks. And the rank board is continuously refreshed by different models. In this paper, we choose three state-of-the-art convolutional neural networks as basic models, which are Resnet50, Wideresnet50, DPN92, respectively. 2.2.1 Residual Network for Image Recognition Residual Network directly adds a linear connected path between two or more layers, which is called the residual module. The residual module can directly combine input with output, which not only protect the integrity of information but also simplify the learning problem for the gradient can be transmitted to the bottom through a linear path. A typical residual module is shown in Fig. 4.

Fig. 4. A typical residual module

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2.2.2 Wide Residual Network for Image Recognition Wide Residual Network is inherited from ResNet, the main purpose is to make full use of the most residual modules. The network structure make some improvement on ResNet by increase the number of convolution kernels in each residual block. The structure can be seen from Table 2. Where K(3,3) represent a 3  3 convolution kernel. k is a width factor, the larger k is, the wider the network is. Table 2. Wide ResNet structure Layer name Conv1 Conv2 Conv3

Output size 32 * 32 32 * 32 16 * 16

Block type = K(3,3) [3 * 3, 16] [3 * 3, 16 * k] * N [3 * 3, 32 * k] * N

Layer name Conv1 Conv2 Conv3

2.2.3 Dual Path Network for Image Recognition Dual path Network is a combination of ResNet and DenseNet [15]. As mentioned above, ResNet can reduce the redundancy of features and reuse the extracted features but can’t dig low-level features through high-level features. While DenseNet extracted useful information from outputs of all previous layers, which could effectively utilize high-level information to dig low-level information. Dual path Network adapted both advantages of ResNet and DenseNet by fusing the two network complementary structures. The structure is shown in Table 3. Table 3. DPN structure Stage Conv1 Conv2 Conv3

Output 112 * 112 56 * 56 28 * 28

Conv4 14 * 14

Conv5 7 * 7

1*1

Dpn92 (32 * 3d) 7 * 7, 96, stride 2 3 * 3 max pool, stride 2 2 3 1  1; 320 4 3  3; 320; G¼ 40 5  6 1  1; 512ðþ32Þ 2 3 1  1; 640 4 3  3; 640; G¼ 40 5  20 1  1; 1024ðþ32Þ 2 3 1  1; 1280 4 3  3; 1280; G = 40 5  3 1  1; 2048ðþ128Þ Global average pool 38 dimensions fc, softmax

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Multiple Classifier Integration

Multiple models integration method is proved to be effective in some machine learning algorithms [16]. However, in our task, we need to modify the outputs of models to accommodate the input of the integration method. We use oi to represent each model’s output, in our applications, each prediction is converted into a vector of possibility. oi is an n-dimensional vectors where n is the total number of classes and the sum of all components in the vector is 1. And the integrated output of the test case is as described below. M P 0

o ¼

i¼0

w i  oi M

ð1Þ

Where M is the number of models. wi is the weight of the ith model. And for classification task, the final label L is the index with the maximum probability in o0 , which can be described below: L ¼ arg maxðo0 Þ

ð2Þ

3 Experiments We conduct our experiments on one GPU(1080ti) Each model is trained in the following manners: (1) To avoid overfitting of CNN models, we split the whole dataset into train data set and test data set with a ratio of 70–30 (70% for training and 30% for testing) based on stratified sampling method. (2) Use validation accuracy as the indicator to choose the best model. (3) Use early stop method to stop the training before the error on test data begin to rise. 3.1

Dataset Split

The three CNN models are trained with the dataset split above with a training data set of 70% and a test data set of 30%. As shown in Table 4, The training set includes 38,016 images, and the test data includes 16,293 images. Table 4. Dataset split Data set Samples number Training set 38,016 Test set 16,293

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Base Parameters of Training CNN Model

We use the dataset mentioned above and use a same base parameter configuration to train each CNN models. All the parameters are shown in Table 5. We use GlobalAveragePooling [17] method to do pooling operation. The activation function we choose is ReLU. To Mitigating sample imbalance problem, we use FocalLoss [18] and the typical cross-entropy loss as loss functions. Optimization function is SGD with a decay of 0.001. Base learning rate is 0.01 and batch size is 32. Table 5. Training parameters Training parameters Pooling method Activation function Loss function Optimization function Base learning rate Batch_size

3.3

Setting values GlobalAveragePooling ReLU FocalLoss/Cross-Entropy SGD, decay = 0.001 0.01 32

Evaluation of the Trained CNN Model

The test set are used to evaluate each CNN model saved in different epoches to choose the best fit model for accurate image recognition task. We use the Test Accuracy metric as the evaluation index, which is defined as below: Acc ¼

Correctpredictions AllTestsamples

ð3Þ

Where Correct predictions represent the number of images that have been predicted correctly, and All Test Samples indicates the total number of the test data set. It needs to emphasize that the higher this metric is, the better performance the model achieves. Table 6 indicates the best accuracy of each model under different Loss functions.

Table 6. Best accuracy of each model under different Loss functions. Models Type Resnet50 Wideresnet50 Dpn92 Integrated Best accuracy (Focal Loss) 99.66% 99.78% 99.80% 99.92% Best accuracy (Cross-Entropy) 99.21% 99.30% 99.32% 99.40%

The training accuracy and loss values of the best single model (Dpn92) during training process are shown in Fig. 5. The best accuracy on test set of each model is demonstrated in Fig. 6.

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Fig. 5. Test accuracy and loss of Dpn92 during training process.

Fig. 6. Best accuracy of each model

4 Analysis of Experimental Results As described in the Tables 4 and 5, The three CNN models are trained with the same dataset and parameters configuration. Moreover, the experimental results are gained after 35 epochs where epochs mean number of traversing the training data.

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The experimental results demonstrate the effectiveness of the integration method. Also, some significant conclusions are acquired. (1) The Three different CNN models behave variously during the training process but have a similar accuracy on the test data set which can be seen in Fig. 5. (2) Focal Loss function works better over the typical cross-entropy loss function on the imbalanced plant diseases data set as shown in Table 6. (3) As the Fig. 6 shows, Integration method bring a direct improvement on accuracy over each single CNN network. Compared with traditional plant diseases diagnosis, the image recognition method based on multiple classifiers integrated method can diagnosis 38 different diseases with a best accuracy of 99.92% ad it also needs to be emphasized that the entire process only cost several seconds. Therefore, we believe that our method has incomparable advantages in both time-consuming and accuracy than traditional diagnosis method.

5 Summary In this paper, we have trained three different CNN models and integrated them into a model with higher accuracy to perform accurate plant diseases diagnosis. A large plant diseases dataset is adopted to evaluate our method. Several images augmentation methods are applied on the data set to enlarge the dataset. We also compare the accuracy under different loss functions, and the results show that focal loss behave better than cross-entropy on this imbalanced data set. The experimental results indicate that our integration method works well on the image recognition task. Acknowledgments. This work was supported by National Natural Science Foundation of China (No. 61520106010; 61741302).

References 1. FAO. http://www.fao.org. Accessed 23 Sep 2009 2. Michailides TJ, Morgan DP, Ma Z et al (2005) Conventional and molecular assays aid diagnosis of crop disease and fungicide resistance. Calif Agric 59(2):115–123 3. Silver D, Schrittwieser J, Simonyan K et al (2017) Mastering the game of go without human knowledge. Nature 550(7676):354 4. Graves A, Mohamed A, Hinton G (2013) Speech recognition with deep recurrent neural networks. In: 2013 IEEE international conference on acoustics, speech and signal processing. IEEE, pp 6645–6649 5. Szegedy C, Liu W, Jia Y, et al (2015) Going deeper with convolutions. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 1–9 6. Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. In: Advances in neural information processing systems, pp 1097–1105 7. Deng J, Dong W, Socher R, et al (2009) Imagenet: a large-scale hierarchical image database. In: 2009 IEEE conference on computer vision and pattern recognition. IEEE, pp 248–255 8. He K, Zhang X, Ren S et al (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 770–778

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9. Zagoruyko S, Komodakis N (2016) Wide residual networks. arXiv preprint arXiv:1605. 07146 10. Chen Y, Li J, Xiao H et al (2017) Dual path networks. In: Advances in neural information processing systems, pp 4467–4475 11. Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85– 117 12. Gavhale KR, Gawande U (2014) An overview of the research on plant leaves disease detection using image processing techniques. IOSR J Comput Engin 16(1):10–16 13. Hughes D, Salathé M (2015) An open access repository of images on plant health to enable the development of mobile disease diagnostics. arXiv preprint arXiv:1511.08060 14. Mohanty SP, Hughes DP, Salathé M (2016) Using deep learning for image-based plant disease detection. Front Plant Sci 7:1419 15. Iandola F, Moskewicz M, Karayev S et al (2014) Densenet: implementing efficient convnet descriptor pyramids. arXiv preprint arXiv:1404.1869 16. Ling X, Deng W, Gu C, et al (2017) Model ensemble for click prediction in bing search ads. In: Proceedings of the 26th international conference on world wide web companion. international world wide web conferences steering committee, pp 689–698 17. Lin M, Chen Q, Yan S (2013) Network in network. arXiv preprint arXiv:1312.4400 18. Lin TY, Goyal P, Girshick R et al (2017) Focal loss for dense object detection. In: Proceedings of the IEEE international conference on computer vision, pp 2980–2988

Adaptive Control of DC Servo Based on PID Neural Network Xuedong Jing and Kangkai Cheng(&) School of Shanghai Institute of Technology, Shanghai 201418, China [email protected]

Abstract. For the DC servos that removes the control electronics with certain load, the efficiency of establishing the controller model is improved by establishing the steering gear control model to achieve the simulated control effect on the motor. Based on Tensorflow, the control model of the DC servo is established. The input of the model is the angular state of the motor and different expected angles. The output of the model is the feedback corresponding to the motor. Then based on the control model of the servo, the controller model of the PID neural network is established. The input of the controller model is the expected angle and the angular position of the motor, and the output is the pulse width of the PWM. Adaptive control of the DC servo is confirmed by the controller model. Keywords: DC servo


Tensorflow
PID control

1 Introduction With the advancement of industrialization, industrial production has gradually developed toward large-scale, systematic and automated, which has higher requirements for motor control, and stable control of the motor is a key part of industrialization. Currently, the motor needs to adjust the motor operating parameters after determining the load [1]. When adjusting the running speed of the motor, it takes time and effort to adjust the operating parameters of the motor. In this paper, the PID neural network adaptive model designed by Tensorflow can automatically match the appropriate motor operating parameters according to the load of the motor to save energy and improve efficiency. TensorFlow runs on all types of machines, from supercomputers to embedded systems. This has very important engineering significance for controlling DC motors, so that the content of this paper can be carried out in FPGA, ARM and system on chip. TensorFlow is a deep learning framework that makes it easier for developers to build the neural network structure they need. This is why this article uses TensorFlow.

© Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 114–121, 2020. https://doi.org/10.1007/978-981-32-9698-5_14

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2 System Description 2.1

The Establishment of the Motor Model

Because the load of the motor will change, the parameters of the motor need to be updated in time [2]. But if the network model is trained by the input and output data of the motor in real time, the efficiency is too low, and the stability of the motor control will be affected. So this paper establishes the control model of the motor for the network training of the controller model [3]. In this study, a joint motor - steering machine of the robot arm was used. Analytical modeling of the steering gear. The steering gear can be regarded as an execution terminal, and its state has the position x of the current moment and the position pre_x of the previous moment. There is also the current time t. The servo needs to change the output angle of the servo by changing the pulse width of PWM. Therefore, the duty ratio of PWM is one input of the servo, and the final angle v is used as the-output. The state parameter is also taken as part of the input, and the model of the steering gear is: f ðpwm; x; pre x; tÞ ¼ v In order to make the model cover most cases to increase the credibility of the servo model, two sets of data are generated by changing the sampling time of the cyclically varying pwm duty cycle, plus a set of random pwm duty cycles, a total of three Group data, 50,000 data records per group, a total of 150,000 data records. Then read the angles of the corresponding motor outputs and save them together in the computer. Using a neural network model Tensorflow 4  5  1, as Fig. 1, where the xi input network are pwm pulse, the motor current position x, a motor position pre_x, time spent in the current cycle t (here we set t to 1000 ms). The output of the network is the output angle v of the motor.

Input layer(xi)

Hidden layer

Output layer(v)

Fig. 1. Neural network model

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Establish a model optimization function: set the angle of the network output to between 1010 and 1; Network output location 9 8 10 10 > > = < 10 ; v½i\10 10 v½i ¼ v½i; 10  v½i\1 > > ; : 1; v½i  1 The actual position of the motor y, the design optimization function is: P loss ¼  ni¼0 y½i  log v. Optimized by AdamOptimizer to find the minimum value of loss that is stable, and consider the model as a motor model [4]. The expression of this motor model is as follows: X ¼ ½ pwm

x

pre x t 

v ¼ X  w1  w2 Comparing the motor model and the output of the motor is shown in Fig. 2.

Fig. 2. Comparison of motor model and motor output curve

It was found that it almost coincided, and it can be considered that the motor model was established. 2.2

Controller Model

The controller model is to establish a single output PID neuron through Tensorflow. The neural network structure is a 2  3  1 structure. As shown in Fig. 3, During execution time, two neurons of the input layer, three neurons of the hidden layer, and one neuron of the output layer are included [5].

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Fig. 3. PID neural network

The input layer is the desired output angle (pred) and the angle of the current motor (real). The output of the input layer is xi ¼ fxi %180g. Where i = 1, 2. The three neurons of the hidden layer are proportional neurons, integral neurons and differential neurons [6]. Their input is as follows P¼

2 X

wi1  xi

ð1Þ

wi2  xi

ð2Þ

i¼1

I¼

2 X i¼1

D¼

2 X

wi3  xi

ð3Þ

i¼1

The output layer is the calculated angle result (res), and the motor model is controlled by inputting the result to the duty cycle of the PWM to the motor model. In the model training, the output layer is the input PWM of the motor, the output of the controller is taken as the PWM input of the motor model, and the output y of the motor model is taken as the output of the whole system, and the desired angle of the P controller is set to y . The model uses the minimum value of loss ¼ ð ni¼0 ðy  y Þ2 Þ=n as the optimization goal, optimized by GradientDescentOptimizer. The system block diagram of the entire system is shown in the Fig. 4.

pred

real controller

motor

Fig. 4. System block diagram

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Finally, bring Eqs. 1, 2 and 3 into the output network: res ¼ ðKP

2 X

wi1  xi þ KI

i¼1

2 X i¼1

wi2  xi þ KD

2 X

wi3  xi Þ:

i¼1

3 Prototype and Test Results The set (blue) curve in the following figure indicates that the set value curve is generated using the Sigmod function, and the real (green) curve is the angle value of the servo output. The original PIDNN controller is shown in Fig. 5. Try to use the traditional PID algorithm to adjust the PIDNN to remove the static deviation as shown in Fig. 6. Abandon the traditional PID, use the activation function to control the minimum output as shown in Fig. 7. Performance tests at 800 ms and 1600 ms, respectively, are shown in Fig. 8 and Fig. 9. As can be seen from the above picture, the error is much smaller than the traditional PID control effect.

Fig. 5. The original PIDNN controller

Adaptive Control of DC Servo Based on PID Neural Network

Fig. 6. Traditional PID adjustment PIDNN

Fig. 7. Activation function controls minimum output

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Fig. 8. Within 1600 ms

Fig. 9. Within 800 ms

4 Analysis of Experimental Results From the research in this paper, we can find that only the data of the system motor operation is needed, and the system can train the corresponding motor model through Tensorflow. According to the motor model, the single-output PID neural network model controller is trained to avoid the steps of manual parameter adjustment. Acknowledgments. This study was supported by ‘Study on Key technologies of Parallel Robot for Minimally Invasive Spine Surgery’, Scientific Research Project of Shanghai Municipal Science and Technology Commission, (Projection No. 16090503700).

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References 1. Niu G-C, Wang W, Zong G-H (2014) Hybrid control theory application of electric load simulator based on iterative learning. Control Theor Appl 31(12):1740–1747 2. Wang Y-X, Chen J-J, Huang P-Y et al (2014) Study on the electric loading technology of the new rudder load simulation system. Aerospace Control 32(2):78–86 3. Tang Y (2007) A discussion about standard parameter models of synchronous machine. Power Syst Technol 31(12):48–51 4. Minmin Z (2017) Application of Google TensorFlow machine learning framework. Inf Technol Netw Secur 36(10):58–60 5. Wang X-Y (2017) Composite control of electric load simulator based on RBF neural network and repetitive control PID. J Eiectric Power Sci Technol 32(1):71–76 6. Chen S-Y, Lin F-J (2013) Decentralized PID neural network control for five degree-offreedom active magnetic bearing. Eng Appl Artif Intell 26:962–973

LQR-Based Optimal Leader-Following Consensus of Heterogeneous Multi-agent Systems Yuling Li1,2, Hongyong Yang1,2(&), Yize Yang2,3, Yuanshan Liu1,2, and Yujiao Sun1,2 1

School of Information and Electrical Engineering, Ludong University, Yantai 264025, Shandong, China [email protected] 2 Key Laboratory of Cyber-Physical System and Intelligent Control in Universities of Shandong, Ludong University, Yantai, China 3 School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia

Abstract. This paper studies optimal leader-following consensus of multiagent systems based on linear-quadratic regulator (LQR). By applying matrix theory and linear-quadratic regulator theory, an optimal approach with the scaling factor is proposed for heterogeneous multi-agent systems which consist of first-order agents and second-order agents to reach consensus as well as minimize the cost function. Numerical simulations verify the validity of the conclusions in this paper. Keywords: Optimal control
Heterogeneous multi-agent systems Linear-quadratic regulator
Consensus




1 Introduction Recently, the study on multi-agent system control has received increasing attention. Distributed coordination promotes the rapid development of multi-agent systems research, due to its broad applications in various areas such as mobile robots cooperation control, military reconnaissance and formation control of drones. In the multi-agent systems, the followers dynamically follow the states of leaders, which can be called the cooperative control of cluster systems [1–3]. The leaderfollowing consensus problem of multi-agent systems, as an important research direction of distributed cooperative control problem, is to design a distributed control algorithm to make all agents reach an agreement through information exchange between neighbors. Xie et al. [4] investigated the global leader-following consensus problem for discretetime neutrally stable linear systems subject to actuator saturation. The consensus problem for the multi-agent systems with a smart leader was studied in [5], and a sufficient condition was provided to ensure the boundedness of the position-tracking

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error and velocity-tracking error. The above literatures considered homogeneous multiagent systems where all agents have the same dynamics. However, in practical applications, the multi-agent systems with different dynamics and abilities have more practical value than homogeneous systems. Xu et al. [6] studied consensus of a class of heterogeneous multi-agent systems composed of first-order and second-order agents with intermittent communication, and some sufficient conditions were obtained to guarantee the consensus of heterogeneous multi-agent systems. Leader-following consensus protocol was adopted to solve consensus problem of heterogeneous multi-agent systems which consist of first-order and second-order agents with time-varying communication and input delays in [7]. Cong et al. [8] have studied the containment control problem of singular heterogeneous multi-agent systems based on the output regulation method. In addition, in the engineering, the tasks often require as little time and energy as possible to accomplish. Therefore, when designing the control protocols, not only the control requirements should be satisfied, but also the specific cost functions should be optimized. Cao et al. [9] investigated the optimal consensus with the method of LQR, and proved that any symmetric Laplacian matrix was inverse optimal with respect to a properly chosen cost function. Ma et al. [10] considered the optimal topology for leader-following consensus problem of multi-agent systems based on LQR theory, and found the optimal topology was a star topology. In this paper, LQR-based optimal leader-following consensus of heterogeneous multi-agent systems is investigated. The innovation of this paper is to propose an optimal control protocol to achieve optimal consensus while minimizing the cost function. The rest of the paper is organized as follows. In Sect. 2, some preliminaries about graph theory are shown, and we recall some useful definitions and supporting lemmas. LQR-based optimal leader-following consensus of heterogeneous multi-agent systems is studied in Sect. 3. In Sect. 4, numerical simulations are used to verify the theoretical analysis. Finally, conclusions are drawn in Sect. 5.

2 Preliminaries Assume that n agents constitute a network topology graph G ¼ ðV; E; AÞ, in which V ¼ fv1 ; v2 ; . . .; vn g represents a set of n nodes,
and its edges set is E  V  V. I ¼ f1; 2; . . .; ng is the node subscripts set, A ¼ aij 2 Rnn is an adjacency matrix with elements aij  0. An edge of the graph G is denoted by eij ¼ ðvi ; vj Þ 2 E. Let the adjacency element aij [ 0 when  eij 2 E,otherwise aij ¼ 0. The neighbors’ set of node i  is denoted by Ni ¼ vj 2 V ðvi ; vj Þ 2 E . Let graph G be a weighted graph without self-loops, i.e. aii ¼ 0, and let matrix nn D ¼ diag Pn fd1 ; d2 ; . . .; dn g 2 R nn be the diagonal matrix with the diagonal elements is the Laplacian matrix of the weighted graph G. di ¼ j¼1 aij . L ¼ D  A 2 R

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3 LQR-Based Optimal Leader-Following Consensus of Heterogeneous Multi-agent Systems In this paper, the heterogeneous multi-agent systems consist of n followers and a leader. There are n  m first-order agents and m second-order agents in the follower systems. Suppose that the second-order agent dynamics is given as follows (

x_ i ðtÞ ¼ vi ðtÞ v_ i ðtÞ ¼ ui ðtÞ

i ¼ 1; . . .; m

ð1Þ

And the first-order agent dynamics is given as follows x_ i ðtÞ ¼ ui ðtÞ

i ¼ m þ 1; . . .; n

ð2Þ

where xi ðtÞ and vi ðtÞ are the position and velocity of the i-th agent, ui ðtÞ is the control input. The leader dynamics is defined as x_ n þ 1 ðtÞ ¼ 0

ð3Þ

A common control protocol is proposed as # 8 " n   > P > > > < b j¼1 aij xj ðtÞ  xi ðtÞ  ci ðxi ðtÞ  xn þ 1 ðtÞÞ " # ui ðtÞ ¼ n m >   P   P > > >b aij xj ðtÞ  xi ðtÞ þ aij vj ðtÞ  vi ðtÞ  ci ðxi ðtÞ  xn þ 1 ðtÞÞ  fi vi : j¼1

j¼1

i ¼ 1; . . .; n

ð4Þ

where b is the scaling factor, aij is a connection weight between agents i and j, ci  0, fi  0. ci [ 0 represents agent i can sense the state of leader. Let xðtÞ ¼ ½x1 ðtÞ; . . .; xm ðtÞ; xm þ 1 ðtÞ; . . .; xn ðtÞT , vðtÞ ¼ ½v1 ðtÞ; . . .; vm ðtÞT , XðtÞ ¼ ½xðtÞ; vðtÞT , UðtÞ ¼ ½u1 ðtÞ; . . .; un ðtÞT , then the systems (1) and (3) can be rewritten as _ XðtÞ ¼ AXðtÞ þ BUðtÞ ð5Þ 2 3 2 3 0 0 I 0 0 where A ¼ 4 0 0 0 5, B ¼ 4 0 I 5. I 0 0 0 0  ¼ ½x1 ðtÞ; . . .; xn ðtÞ; Denote the state error xi ðtÞ ¼ xi ðtÞ  xn þ 1 ðtÞ, and let XðtÞ T v1 ðtÞ; . . .; vm ðtÞ . Then system (5) can be rewritten as

LQR-Based Optimal Leader-Following Consensus of Heterogeneous

_  þ BUðtÞ XðtÞ ¼ AXðtÞ

125

ð6Þ

And the control protocol (4) is written as L þ C1 UðtÞ ¼ b 11 L21

L12 L22 þ C2

LV þ F  XðtÞ 0

ð7Þ

where C1 ¼ diagfc1 ; . . .; cm g, C2 ¼ diagfcm þ 1 ; . . .; cn g, F ¼ diagff1 ; . . .; fm g. LP ¼  L11 L12 and LV represents the position information exchange and the velocity L21 L22 information exchange of followers, respectively. Consider the cost function Z

1

JðtÞ ¼

(

n X i¼1

0

q1i ðxi ðtÞ  xn þ 1 ðtÞÞ2 þ q2i v2i ðtÞ þ ri u2i ðtÞ

) 

dt

ð8Þ

where q1i [ 0, q2i [ 0 are respectively the weights of position consensus error and velocity consensus error, ri [ 0 is weighting coefficient of the control input. And it can be rewritten as Z

1

JðtÞ ¼




  T ðtÞQXðtÞ  þ U T ðtÞRUðtÞ dt X

ð9Þ

0

2 where Q ¼ 4

Q1

3 Q2

  5, Q1 ¼ diagfq11 ; . . .q1m g, Q2 ¼ diag q1;m þ 1 ; . . .q1n ,

Q3 Q3 ¼ diagfq21 ; . . .q2m g, R ¼ diagfr1 ; . . .; rn g. The matrices Q and R are positive definite, and for simplicity, let R ¼ I in this paper. In this paper, the aim is to find an optimal control protocol and an optimal scaling factor to minimize the cost function, and at the same time to ensure the consistency of heterogeneous multi-agent systems. The optimization problem can be written as follows Z min JðtÞ ¼

1


T   ðtÞQXðtÞ  þ U T ðtÞRUðtÞ dt X

0

_  þ BUðtÞ ¼ AXðtÞ Subject to : XðtÞ  UðtÞ ¼ bK XðtÞ where K ¼

L11 þ C1 L21

L12 L22 þ C2

LV þ F 0

is the feedback gain matrix.

ð10Þ

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Theorem 1. Suppose that the communication topology is connected, for the heterogeneous multi-agent systems (1)–(3) and cost function (8), when 2

P11 P¼4 0 PT13

0 P22 0

3 P13 0 5[0 P33

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffiffi where P ¼ diag q11 q21 þ 2q11 q11 ; . . .; q1m q2m þ 2q1m q1m , P13 ¼ pffiffiffiffiffiffi 11 pffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi diag q11 ; . . .; q1m , P22 ¼ diag q1;m þ 1 ; . . .; q1n , P33 ¼ diag q21 þ 2 q11 ; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi . . .; q2m þ 2 q1m g. The optimal control protocol is  U  ðtÞ ¼ bK XðtÞ

where

0 pffiffiffiffiffiffi q11 B .. B . B B B K¼B B B B 0 @

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi q21 þ 2 q11 pffiffiffiffiffiffiffi q1m

0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi q1;m þ 1

..

.

pffiffiffiffiffiffi q1n

1 ..

0

.

C C pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi C C q2m þ 2 q1m C C. C C C A

The heterogeneous systems can achieve consensus and there exists an optimal scaling factor b 2 ð0; 1Þ to minimize the cost function (8). Proof.

2

3 P11 P12 P13 Assume that P ¼ 4 PT12 P22 P23 5 [ 0, and by applying algebraic Riccati equation PT13 PT23 P33 AT P þ PA þ Q  PBR1 BT P ¼ 0, it can be obtained that 2

P12 PT12 þ P13 PT13 Q ¼ 4 P22 PT12 þ P22 PT13 PT23 PT12 þ P33 PT13  P11

P12 P22 þ P13 PT23 P222 þ P23 PT23 PT23 P22 þ P33 PT23  P12

3 P12 P23 þ P13 P33  P11 P22 P23 þ P23 P33  PT12 5 PT23 P23 þ P233  P13  PT13 ð11Þ

That is (

P12 PT12 þ P13 PT13 ¼ Q1 ; P222 þ P23 PT23 ¼ Q2 ; PT23 P23 þ P233  P13  PT13 ¼ Q3 P12 P22 þ P13 PT23 ¼ 0; P12 P23 þ P13 P33  P11 ¼ 0; P22 P23 þ P23 P33  PT12 ¼ 0 ð12Þ 

PT13 PT23 P33 And K ¼ R B P ¼ , so it can be obtained that P23 ¼ 0. PT12 P22 P23 According to P22 P23 þ P23 P33  PT12 ¼ 0, we can obtain that PT12 ¼ 0. Hence, we have 1 T

LQR-Based Optimal Leader-Following Consensus of Heterogeneous

8 P PT13 ¼ Q1 > > < 13 P222 ¼ Q2 P2  P13  PT13 ¼ Q3 > > : 33 P13 P33  P11 ¼ 0

127

ð13Þ

That is pffiffiffiffiffiffi pffiffiffiffiffiffi 8 pffiffiffiffiffiffiffi P13 ¼ pQ 1ffi ¼ diag q11 ; . . .; q1m > ffiffiffiffiffi > pffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi < P ¼ Q ¼ diag q 22 2 1;m þ 1 ; . . .; q1n pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffiffi P33 ¼ Q3 þ 2P13 ¼ diag q21 þ 2 q11 ; . . .; q2m þ 2 q1m > >  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : pffiffiffiffiffiffi pffiffiffiffiffiffiffi P11 ¼ P13 P33 ¼ diag q11 q21 þ 2q11 q11 ; . . .; q1m q2m þ 2q1m q1m

ð14Þ

From this we can obtain P, and it then follows from K ¼ R1 BT P that K is obtained as shown in Theorem 1. According to (10), we can obtain _  XðtÞ ¼ ðA  bBK ÞXðtÞ

ð15Þ

2

3 0 0 I bP22 0 5. It’s known that system Denote M ¼ A  bBK ¼ 4 0 T bP13 0 bP33 (15) is asymptotically stable if and only if M is a Hurwitz matrix. The following part is the proof that M is Hurwitz. From system (15), we have 2

kI

6 detðkI  M Þ ¼ det4 0 bPT13

0

I

3

7 kI þ bP22 0 5 0 kI þ bP33  kI I ¼ detðkI þ bP22 Þ
det bPT13 kI þ bP33

ð16Þ

For detðkIþ bP22 Þ, it is easy to prove that the eigenvalues have negative real parts. kI I , that is k2i þ bgi ki þ bli ¼ 0, where gi ¼ For det bPT13 kI þ bP33 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi q2i þ 2 q1i [ 0 and li ¼ q1i [ 0 ði ¼ 1; . . .; mÞ are eigenvalues of P33 and P13 , pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffi bgi b2 g2i 4bli respectively. Then it can be obtained that ki ¼ . If gi \2 lbi , it is obvious 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffi bgi þ b2 g2i 4bli li þ i , k \0. If g [ 2 ¼ \ bgi2þ bgi ¼ 0 and that ki ¼ bg i i 2 b 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi bgi  b2 g2i 4bli \0. k i ¼ 2 Above all, we can deduce that M is Hurwitz. That is, the system (15) is asymptotically stable. Hence, the heterogeneous systems (1)–(3) can achieve consensus. From (15), we can get

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 ¼ eðAbBK Þt Xð0Þ  XðtÞ

ð17Þ

  where Xð0Þ is the initial value of XðtÞ. The cost function JðtÞ can be written as Z

1

JðtÞ ¼

n

o h i   T ð0Þ eðAbBK Þt QeðAbBK Þt þ b2 eðAbBK Þt K T KeðAbBK Þt Xð0Þ dt ð18Þ X

0

Then calculate the derivative of JðtÞ with respect to b, it can be obtained that dJðtÞ ¼ db

Z

1

(

"  T ð0Þ X

2bKteðAbBK Þt QeðAbBK Þt þ 2beðAbBK Þt K 2 eðAbBK Þt 2b2 BKteðAbBK Þt K 2 eðAbBK Þt

0

#

)  Xð0Þ dt ð19Þ

Denote yðbÞ ¼

Z

i  BKteðAbBK Þt QeðAbBK Þt dt Xð0Þ 0 Z 1 T ðAbBK Þt T ðAbBK Þt   þ 2bX ð0Þ e K Ke dt Xð0Þ 0 Z 1 2 T ðAbBK Þt T ðAbBK Þt  BKte K Ke dt Xð0Þ  2b X ð0Þ

dJðtÞ  T ð0Þ ¼  2X db

1

h

ð20Þ

0

It can be known from (20) that yð0Þ\0 and yð1Þ [ 0, and yðbÞ is a continuous function. Hence, there is an optimal scaling factor between 0 and 1 for the optimization problem (10).

4 Numerical Simulations In order to verify the effectiveness of the control protocol (4), consider the communication topology with six followers and a leader 0 shown in Fig. 1, where white circles and black circles represent the first-order agents labeled 1–3 and second-order agents label 4–6, respectively.

Fig. 1. The communication topology of multi-agent systems

LQR-Based Optimal Leader-Following Consensus of Heterogeneous

129

Assume that the initial positions and velocities of followers are respectively taken as xð0Þ ¼ ½8; 2; 0; 3; 5; 1T and vð0Þ ¼ ½2; 3; 1T . The position of the leader is 2. The parameter of the control protocol (6) is taken b ¼ 0:5, fi ¼ 10 and ci ¼ 10. From Figs. 2 and 3, we can observe that the positions of followers can track that of the leader and the velocities of followers can converge to zero. Hence, it is obtained that the heterogeneous multi-agents can achieve optimal consensus control.

3

8

Follower4

Follower1

7

Follower2

Follower6

Follower4 Follower5

5

1

Follower6

The actual values of velocities/m/s

The actual values of positions/m

Follower5

2

Follower3

6

Leader

4 3 2 1 0

0

-1

-2

-3

-1 -4

-2 0

2

4

6

8

10

12

14

16

18

20

t/s

Fig. 2. The actual position values

0

2

4

6

8

10

12

14

16

18

20

t/s

Fig. 3. The actual velocity value

5 Conclusion This paper studies LQR-based optimal leader-following consensus of heterogeneous multi-agent systems. A control protocol with scaling factor is designed to obtain the optimal scaling factor while minimizing the cost function. The numerical simulations results show that the control algorithm can achieve optimal consensus of the heterogeneous multi-agent systems. Acknowledgements. The research is supported by the National Natural Science Foundation of China (61673200, 61771231), the Major Basic Research Project of Natural Science Foundation of Shandong Province of China (ZR2018ZC0438) and the Key Research and Development Program of Yantai City of China (2019XDHZ085).

References 1. Hongyong Y, Yize Y, Fujun H et al (2019) Containment control of heterogeneous fractionalorder multi-agent systems. J Franklin Inst 356(2):752–765 2. Hongyong Y, Xunlin Z, Siying Z (2010) Consensus of second-order delayed multi-agent systems with leader-following. Eur J Control 16(2):188–199 3. Funjun H, Lei G, Hongyong Y (2016) Sampling control on collaborative flocking motion of discrete-time system with time-delays. Neurocomputing 216:242–249 4. Yijing X, Zongli L (2018) Global leader-following consensus of a group of discrete-time neutrally stable linear systems by event-triggered bounded controls. Inf Sci 459:302–316

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5. Zhengguang M, Zhongxin L, Zengqiang C (2016) Leader-following consensus of multiagent system with a smart leader. Neurocomputing 214:401–408 6. Lv X, Shuanghe M, Liang C (2017) Consensus of heterogeneous multi-agent systems with intermittent communication. J Syst Sci Inf 5:328–342 7. Pingping D, Chenglin L, Fei L (2014) Consensus problem of heterogeneous multi-agent systems with time delay under fixed and switching topologies. Int J Autom Comput 11(3): 340–346 8. Yirui C, Zhiguang F, Hongwei S et al (2018) Containment control of singular heterogeneous multi-agent systems. J Franklin Inst 355:4629–4643 9. Yongcan C, Wei R (2010) Optimal linear-consensus algorithms: An LQR perspective. IEEE Trans Syst Man Cybern B Cybern 40(3):819–830 10. Jingying M, Yuanshi Z, Long W (2015) LQR-based optimal topology of leader-following consensus. Int J Robust Nonlinear Control 15(17):3404–3421

Couple-Group Tracking Consensus for Non-linear Multi-agent Systems with Time-Delays Liqiong Zhang1, Weixun Li1(&), and Jia Liu2 1

School of Science, Tianjin University of Technology and Education, Tianjin 300222, China [email protected] 2 School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China

Abstract. In this paper, we consider couple-group consensus problems of second-order leader-following multi-agent systems with time-varying delays. Two significant components are investigated in multi-agent systems, which involve time-lags and non-linear dynamics. A sufficient condition which guarantees the couple-group consensus problems can be solved is given by Lyapunov-Razumikhin theorem and some lemmas. The validity of this result is demonstrated through the numerical simulations. Keywords: Multi-agent systems
Group consensus
Time delay Lyapunov-Razumikhin theorem
Non-linear systems




1 Introduction Over the past several decades, a great deal of significant accomplishments has been delivered about consensus problems. According to the best of our acquaintance, the main results about consensus analyses have concentrated on a network for identical agents about consensus states such as [1–7]. The last few years have caught the vision of grand achievements in order to the comprehending for networked systems in mechanics, ecology, biology, sociology and so on. Unfortunately, in actual life, the difference of conditions, collaborative assignments and time decide diverse definitive consensus states. For the sake of disposing this trouble, we should design appropriate coherence algorithms and make all agents in a network attain many consensus states. A novel notion is proposed, which is called “Group Consensus” in [8, 9]. Most of researches consider the group consensus problems in identical network, and this network are divided into multiple sub-group, the agents can reach multiple consensus states in every sub-group. The couple-group consensus problems are investigated for first-order multi-agent systems in [10]. In many multi-agent systems, time-lag maybe appear easily. On account of the motion of the agents, the congestion of the communication passageways and the restricted transfer tempo. To make a long story short, the delays should take into account in practical problems. Till now, copious

© Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 131–141, 2020. https://doi.org/10.1007/978-981-32-9698-5_16

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achievements on single linear multi-agent systems can be discovered in the exoteric literatures. However, in actual life, majority of engineering problems involve complex non-linear dynamics so that results for linear systems are not suitable for application. Consequently, the nonlinearities should been into consideration. In [11–13], consensus problems for multi-agent systems with time delays have been considered. However, they didn’t consider the non-linear. In [14, 15], Qing Cui and Jin-Liang Wang considered the situation that tracking consensus problem for second-order multi-agent systems. It is obvious that they didn’t consider time-delays. Motivated by this notion, in this paper, based on literature [14], we investigate multi-group consensus control for second-order leader-following multi-agent systems with time lags. Besides, we add the term of non-linear. Finally, we will testify theoretical results by numerical simulations.

2 Model Description and Preliminaries 2.1

Graph Theory

Algebraic graph theory is vital for reaching consensus problems. Suppose G ¼ ðI; T; C Þ is a weighted digraph which has a set of node I¼f1; . . .; n; n þ 1. . .; mg, a set
 of trajectory TI  I and a weighted adjacency matrix C ¼ cij 2 Rðn þ mÞðn þ mÞ . The node index is a finite set. A trajectory of G is denoted by ði; jÞ, it means to from j to i. If the element cij fulfills the trajectory in the digraph, then it denotes cij 6¼ 0 , ði; jÞ 2 T; otherwise, cij ¼ 0. We suppose cii ¼ 0 for all agents i 2 I. The set of neighbors of node i is denoted by Ni ¼ fj 2 I : ði; jÞ 2 T g. A digraph G is said to be strongly connected if and only if there exists a trail between arbitrary two diverse nodes. For two directed  ¼ ðI; T Þ and G ¼ ðI; T Þ, if I  I, T  T we say that G  is a subgraph of G. If graphs G  is an induced  if and only if ði; jÞ 2 T for two nodes i; j 2 I, we say that G ði; jÞ 2 T, subgroup of G. A strongly connected component of a digraph is an induced sub-graph that is maximal, owing to being strongly connected. Then Laplacian of the weighted
 digraph G is defined as L ¼ D  C ¼ lij 2 Rðn þ mÞðn þ mÞ . According to Laplacian definition, we can know the all row-sums of L are zero. Therefore, L invariably has a zero eigenvalue corresponding to a right eigenvector 1 ¼ ð1; . . .1ÞT 2 Rn þ m . Suppose nP þm D ¼ diagðd1 ; d2 ; . . .; dn þ m Þ of graph G and di ¼ degin ðiÞ ¼ cij . i¼1

~ satisfied with all followers and two In this paper, we define a generalized graph G leaders. Without lack of generality, the couple subgroups which are divided from the ~ the first subgroup G ~ 1 contains front n followers and follows their leader l1 network G, ~ and the  rest of followers belong to the second group G2 which follows l2 . Let Gj ¼ Ij ; Tj ; Cj ðj ¼ ð1; 2Þ be a subgroup of G ¼ ðI  ; T  ; C  Þ and its leader lj for

j ¼ ð1; 2Þ.

Couple-Group Tracking Consensus for Non-linear

2.2

133

Systems Description and Preliminaries

In this paper, we ponder couple groups of identical agents, and each group has a special agent which is said to be the “intra-group leader’’ and the rest of agents are referred to the “follower-agents’’. The motions of two intra-group leaders are independent respectively, but the movements of all followers are affected by the intra-group leader and other followers. We investigate systems with fixed topology. The dynamical model of the follower i can be depicted as: 

p_ i ðtÞ ¼ qi ðtÞ i 2 I :¼ f1; 2; . . .; n þ mg q_ i ðtÞ ¼ ui ðtÞ þ f ðpi ðtÞ; qi ðtÞÞ

ð1Þ

where pi ðtÞ; qi ðtÞ; ui ðtÞ and f ðpi ðtÞ; qi ðtÞÞ are position state, velocity state, control input and the inherent non-linear dynamics of agent i. A dynamics of leader of multi-agent systems as follows: 8 < p_ j ðtÞ ¼ qj ðtÞ   : q_ j ðtÞ ¼ f pj ðtÞ; qj ðtÞ

j 2 I :¼ f1; 2g

ð2Þ

where pj ðtÞ; qj ðtÞ and pj ðtÞ; qj ðtÞ delegate the position status, velocity state and the intrinsic non-linear dynamics of the intra-leader severally. In order to simplicity of presentation, we lay emphasis on one-dimensional space. However, for any high-dimensional space, we can generalize the results through applying the characteristics of the Kronrcker product, denote as . In virtue of the time delays, all agents may not promptly acquire some messages from other agents and its leader. Therefore, for agent i, we design a coupled control input which is neighbor-based as follows:    8 P
 cij a pj ðt  r ðtÞÞ  pi ðt  r ðtÞÞ þ b qj ðtÞ  qi ðtÞ > > > j2N1i > >  P
> > > þ cij apj ðt  r ðtÞÞ þ bqj ðtÞ > > > j2N2i > > > < b
ap ðt  r ðtÞÞ  p ðt  r ðtÞÞ þ bq ðtÞ  q ðtÞ8i 2 I i i i 1 1 1  ui ðtÞ ¼ P
> cij apj ðt  r ðtÞÞ þ bqj ðtÞ > > > j2N1i > >    P
 > > > þ cij a pj ðt  r ðtÞÞ  pi ðt  r ðtÞÞ þ b qj ðtÞ  qi ðtÞ > > > j2N2i > >
    : bi a pi ðt  r ðtÞÞ  p2 ðt  r ðtÞÞ þ b qi ðtÞ  q2 ðtÞ 8i 2 I2

ð3Þ

where I1 ¼ f1; 2; . . .; ng; I2 ¼ fn þ 1; . . .; n þ mg; Ni ¼ N1i [ N2i ; N1i ¼ fj 2 I1 : ði; jÞ 2 Tg; I ¼ I1 [ I2 ; N1i ¼ fj 2 I1 : ði; jÞ 2 T g; N2i ¼ fj 2 I2 : ði; jÞ 2 T g; T ¼ T1 [ T2 ; T1 I1  I1 ; T2 I2  I2 .

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The time-varying lag r ðtÞ [ 0 is a continuously differentiable function and 0\r ðtÞ\s, bi is a diagonal element of an adjacency matrix of leader tallied with G. And if agent i can receive message from leader lj , then bi [ 0; otherwise, bi ¼ 0; B ¼ diagfbi g 2 Rðn þ mÞðn þ mÞ for i 2 I. Remark 1. In order to decrease the communication cost, we assume that there does not have information exchange between leader l1 and leader l2 . Furthermore, each leader only can transfer message to its own followers. Last but not least, we assume only some agents can receive the messages from their own leader in each subgroup for decreasing the fare of information communication. Thus, we establish the assumption in the following. In the sequel, we need to introduce several lemmas to guarantee the validity of our conclusions. Lemma 1 (see in [14]). The sum of each node’s adjacent weights to the nodes in other sub-group is zero in the interconnection topology. Denote as nX þm j¼n þ 1

cij ¼ 0; 8i 2 I;

n X

cij ¼ 0; 8i 2 I2 :

j¼1

With (3) and Lemma 1, the system (1) can be substituted for a matrix format: 8 > < p_ ðtÞ ¼ qðtÞ q_ ðtÞ ¼ aðL þ BÞpðt  r ðtÞÞ  bðL þ BÞqðtÞ > : þ aBp ðt  r ðtÞÞ þ bBq ðtÞ þ F ðpðtÞ; qðtÞÞ

ð4Þ

T

where F ðpðtÞ; qðtÞÞ ¼ ðf T ðp1 ðtÞ; q1 ðtÞÞ; . . .; f T ðpn þ m ðtÞ; qn þ m ðtÞÞÞ : According to the characteristic of L, we can obtain  aðL þ BÞpðt  r ðtÞÞ þ aBp ðt  r ðtÞÞ ¼ aðL þ BÞðpðt  r ðtÞÞ  p ðt  r ðtÞÞÞ;  bðL þ BÞqðtÞ þ bBq ðtÞ ¼ bðL þ BÞðqðtÞ  q ðtÞÞ: Let ni ðtÞ ¼ pi ðtÞ  p1 ðtÞ; gi ðtÞ ¼ qi ðtÞ  q1 ðtÞ; i 2 I1 ; ni ðtÞ ¼ pi ðtÞ  p2 ðtÞ; gi ðtÞ ¼ qi   T ðtÞ  q2 ðtÞ; i 2 I2 ; nðtÞ ¼ nT1 ðtÞ; nT2 ðtÞ; . . .; nTn ðtÞ; nTn þ 1 ðtÞ; . . .; nTn þ m ðtÞ ; gðtÞ ¼ gT1  T  T  T ðtÞ; gT2 ðtÞ; . . .; gTn ðtÞ; gTn þ 1 ðtÞ; . . .gTn þ m ðtÞÞT ; p ðtÞ ¼ pT 1 ðtÞ; p2 ðtÞ ; q ðt Þ ¼ q1 ðtÞ; T qT 2 ðt ÞÞ : Hence error system can be expressed in the following format: (

n_ ðtÞ ¼ gðtÞ g_ ðtÞ ¼ aðL þ BÞnðt  r ðtÞÞ  bðL þ BÞgðtÞ þ GðtÞ

  where GðtÞ ¼ ðg1 ðtÞ; g2 ðtÞ; . . .; gn þ m ðtÞÞ; gi ðtÞ ¼ f ðpi ðtÞ; qi ðtÞÞ  f pj ðtÞ; qj ðtÞ :

ð5Þ

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 T Let fðtÞ ¼ nT ðtÞ; gT ðtÞ , then the derivative of fðtÞ as follows: ~ f_ ðtÞ ¼ A1 fðtÞ þ Ar fðt  r ðtÞÞ þ G ð6Þ





0 In þ m 0 0 ~ 0 ;G ¼ ; L þ B ¼ M: where A1 ¼ ; Ar ¼ aM 0 G ðt Þ 0 bM   Lemma 2 (See in [15]). f ðpi ðtÞ; qi ðtÞÞ and f pj ðtÞ; qj ðtÞ are continuous differentiable function vectors. The multi-group consensus problems of the multi-agent systems involving non-linear dynamic and some sufficient conditions were derived in order to reach consensus under the following assumption: kf ðp; qÞ  f ðp ; q Þk q1 kp  p k þ q2 kq  q k; 8p; q; p ; q 2 Rn ; for some non-negative constants q1 and q2 . Definition 1. The couple-group consensus of multi-agent systems can be achieved if the states of followers tend to the states of intra-group leaders in the sense of     lim pi ðtÞ  p1 ðtÞ ¼ 0; lim qi ðtÞ  q1 ðtÞ ¼ 0; 8i 2 I1 ; t!1

t!1

    lim pi ðtÞ  p2 ðtÞ ¼ 0; lim qi ðtÞ  q2 ðtÞ ¼ 0; 8i 2 I2 :

t!1

t!1


 Lemma 3 (See in [14]). Let C ¼ cij 2 Cðn þ mÞðn þ mÞ be an adjacency matrix corresponding to directed graph G, C has property SC if and only if the directed graph G is strongly connected. Lemma 4 (See in [16]). For arbitrary constant vectors a; b 2 Rn þ m and a positive defined matrix P 2 Rnn , the inequality holds:

2aT b aT Pa þ bT P1 b: Lemma 5 (See in [16]) (Schur Complement). Give a symmetric matrix S ¼

S11 S12 . ST12 S22

Thus the following conditions are equivalent. (i) S\0; (ii) S11 \0; S22  ST12 S1 11 S12 \0 T (iii) S22 \0; S11  S12 S1 22 S12 \0. Lemma 6 (Lypunov  Razumikhin theorem) (See in [12]). Let /1 ; /2 and /3 be continuous, nonnegative, non-decreasing functions with /1 ðsÞ [ 0; /2 ðsÞ [ 0; /3 ðsÞ [ 0 for s [ 0 and /1 ð0Þ ¼ 0 ¼ /2 ð0Þ. If there is a continuous function V ðt; xÞ such that /1 ð xÞ V ðt; xÞ /2 ð xÞ; t 2 R; x 2 Rn . Furthermore, there exists a continuous non-decreasing function /ðsÞ [ s; s [ 0 such that V_ ðt; xÞ  /3 ð xÞ. If

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V ðt þ h; xðt þ hÞÞ /ðV ðt; xðtÞÞÞ; h 2 ½s; 0, then the solution x ¼ 0 is uniformly asymptotically stable. Lemma 7 (See in [12]). A matrix M ¼ L þ B is positive defined if and only if the node ~ and G ~ ¼G ~1 [ G ~ 2. of the intra-leader is globally reachable in G ~ and M is positive Remark 2. Suppose a node of leaders is globally reachable in G, T~ ~ ¼ In þ m holds, if and only if defined. Then knowable by Lyapunov theorem M P þ PM ðn þ mÞðn þ mÞ ~ has a positive defined matrix P 2 R .

3 Main Results In this part, we investigate two kinds of situations for couple-group consensus of second-order lead-following multi-agent systems with time-lags. On the one hand, we investigate couple-group consensus with nonlinear dynamics; on the other hand, we also discuss couple-group consensus without nonlinear dynamics. The details are as follows. 3.1

Couple-Group Consensus with Nonlinear Dynamics

Theorem 1. Suppose the above assumptions hold. The couple-group consensus problem of tracking multi-agent systems of n þ m followers and two leaders with timevarying lags and non-linear dynamics can be solved under the control protocol (3) if and only if the following two conditions hold: 2

~ b In þ m ; a [ 0; b [ 0 P\ a

" 2qba b

In þ m 2q ~ P b

2q ~ b P

2ða þ qbÞ ~ P ab

 ba In þ m

ð7Þ # \0

ð8Þ

~ and M are both positive defined matrices if intra-group leader is globally where P ~ reachable in G. ~ then we choose Proof: On account of intragroup leader is globally reachable in G, T ~ þ PM ~ ¼ In þ m and ~ which satisfy M P two "positive defined matrices M and P # 1~ In þ m P P ¼ 1 ~ 1 b~ . Therefore, knowable by (7) P is also positive defined. P P b

a

In this article, we select a Lyapunov-Razumikhin function as shown below: V ðtÞ ¼ fT ðtÞPfðtÞ:

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Knowable by Leibniz  Newton formulary, fð t  r ð t Þ Þ ¼ fð t Þ 

Z

0 r ðtÞ

f_ ðt þ sÞds:

ð9Þ

With (6) and (9), we can obtain fðt  rðtÞÞ ¼ fðtÞ  A1

Z

0 rðtÞ

fðt þ sÞds  Ar

Z

r ðtÞ 2rðtÞ

fðt þ sÞds

ð10Þ

Owing to A2r ¼ 0 and combine (10) the delayed differentiable Eq. (6) can be substituted for Z ~ f_ ðtÞ ¼ AfðtÞ  Ar A1 0rðtÞ fðt þ sÞds þ G

ð11Þ

where A ¼ A1 þ Ar : Take the derivative of V ðtÞ and combine (11) as follows: V_ ðtÞ ¼ f_ T ðtÞPfðtÞ þ fT ðtÞPf_ ðtÞ R0 ~ ¼ fT ðtÞðAT P þ PAÞfðtÞ  2fT ðtÞPAr A1 rðtÞ fðt þ sÞds þ 2fT ðtÞPG: According to Lemmas 4 and 6 and ðV ðxðt þ hÞÞ\cV ðxðtÞÞ; 0 h sÞ,   V_ ðtÞ r ðtÞfT ðtÞ PAr A1 P1 AT1 ATr P þ cP fðtÞ   ~ þ fT ðtÞ AT P þ PA fðtÞ þ 2fT ðtÞPG

ð12Þ

According to Lemma 2, we could obtain kGðtÞk ¼

nX þm

kf ðpi ðtÞ; qi ðtÞÞ  f ðp ðtÞ; q ðtÞÞk

i¼1



¼ q1 In þ m nðtÞ þ q2 In þ m gðtÞ ¼

nX þm

ðq1 kni ðtÞk þ q2 kgi ðtÞkÞ

i¼1

q1 In þ m

0

0

q2 In þ m

fðtÞ qfðtÞ:

where q ¼ maxfq1 ; q2 g: Therefore, we can have: ~ 2qfT ðtÞPfðtÞ: 2fT ðtÞPG

ð13Þ

Apply (12) and (13), we can get   V_ ðtÞ fT ðtÞHfðtÞ þ r ðtÞfT ðtÞ PAr A1 P1 AT1 ATr P þ cP fðtÞ: " 2qba 0

where H ¼ A P þ PA þ 2qP ¼

b

In þ m 2q ~ P

2q ~ b P

#

.  ba In þ m Let u max ¼ maxfeigenvalues of H g. In the light of triangle inequality and homogeneity, PAr A1 P1 AT1 ATr P þ cP PAr A1 P1 AT1 ATr P þ ckPk. b

2ða þ qbÞ ~ P ab

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Therefore, we seek r ðtÞ\s ¼ 

umax through Lemma 5. kPAr A1 P1 AT1 ATr Pk þ ckPk Finally, according to the conditions (7) and (8), we can get V_ ðtÞ\0:. The termination of the proof of couple-group consensus for second-order multi-agent systems.

3.2

Couple-Group Consensus Without Linear Dynamics

Corollary 1. Suppose the hold. Considered a linear dynamic, when  above assumptions  f ðpi ðtÞ; qi ðtÞÞ ¼ 0 and f pj ðtÞ; qj ðtÞ ¼ 0 for all i 2 I; j 2 I  . The couple-group consensus of multi-agent systems can be achieved under the control protocol (3) if the following two conditions are satisfied: 2

~ b In þ m ; a [ 0; b [ 0; P\ a " a #  b In þ m 0 \0; 2~ P  b In þ m 0 b

ð14Þ ð15Þ

a

~ and M are both positive defined matrices if intra-group leader is globally where P ~ reachable in G. Due to its proof has many similarities to the proof of Theorem 1, we are not going to go into details about it anymore. In this paper, we considered the couple-group consensus problem. In fact we can generalize couple-group consensus to multi-group consensus, the details as follows. Remark 5. Based on the theory of couple-group consensus, we design the following control protocol for more than couple-group consensus in the complex network G: X
    ui ð t Þ ¼ cij a pj ðt  r ðtÞÞ  pi ðt  r ðtÞÞ þ b qj ðtÞ  qi ðtÞ j2NSi i

h    i  bi a pi ðt  r ðtÞÞ  pSi ðt  r ðtÞÞ þ b qi ðtÞ  qSi ðtÞ X
 þ cij apj ðt  r ðtÞÞ þ bqj ðtÞ i 2 I :¼ f1; 2; . . .; n þ mg j2N.i ;.6¼Si

where Si and . denote the subgroups which are separated many subgroups from the network G. We will put the situation into research in the follow-up work.

4 Numerical Simulations Example: We investigate couple-group consensus problems in a network which is divided to two sub-graphs with fixed topology as follows (Fig. 1). In the graph above, 1, 2, 3 present the followers of the first subgroup; 4, 5, 6 also denote the followers of the second subgroup; ● expresses the leader of the first group and the second group.

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Fig. 1. Directed topology

Let a ¼ 1:5; b ¼ 2:06; q ¼ 0:01 and 0\r ðtÞ\0:3. When r ðtÞ¼0:01, the simulation results are shown clearly in the following below:

Fig. 2. Position error

Fig. 3. Velocity error

Fig. 4. Position state

Fig. 5. Velocity state

  When f ðpi ðtÞ; qi ðtÞÞ ¼ 0 and f pj ðtÞ; qj ðtÞ ¼ 0 for all i 2 I; j 2 I.

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Fig. 6. Position error

Fig. 7. Velocity error

As can be seen from Figs. 2 and 3, the position error and the velocity error of the agents of multi-agent systems in nonlinear condition both trend to balance; as the Figs. 4 and 5, the position state and the velocity state of the agents of multi-agent in nonlinear circumstance both respectively reach each stabilization; as shown in the Figs. 6 and 7, the position error and velocity error of the agents of multi-agent systems in linear condition both can achieve consensus as well.

5 Conclusions Couple-group consensus problems for second-order non-linear tracking multi-agent systems with time-delays and fixed topology have been investigated. In this paper, based on the relative states of neighbor agents, a controller with time-varying lags is designed for every follower so that the states of followers follow the status of their own intra-group leader. In order to investigate the situation, we adopt LyapunovRazumikhin theorem. At last, numerical simulation is exhibited to indicate the validity of this theoretical outcome. Acknowledgments. This work was supported by National Science Foundation of China under Grant (61703307, 11526155) and Tianjin University of Technology and Education Innovation Research Fund (KRKC011511).

References 1. Meng DY, Jia YM, Du JP (2013) Multi-agent iterative learning control with communication topologies dynamically changing in two directions. IET Control Theory Appl 7(2):261–270 2. Ren CE, Shi ZP, Du T (2018) Distributed observer-based leader-following consensus control for second-order stochastic multi-agent systems. IEEE Access 6:20077–20084 3. Hong YG, Hu JP, Gao LX (2006) Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42(7):1177–1182

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4. Ren W, Randal WB (2005) Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50(5):655–661 5. Li WX, Chen ZQ, Liu ZX (2013) Leader-following formation control for second-order multi-agent systems with time-varying delay and nonlinear dynamics. Nonlinear Dyn 72 (4):803–812 6. Yang T, Meng ZY, Shi GD et al (2016) Network synchronization with nonlinear dynamics and switching interactions. IEEE Trans Autom Control 61(10):3103–3108 7. Chen L, Hou ZG, Tan M et al (2011) Necessary and sufficient conditions for consensus of double-integrator multi-agent systems with measurement noises. IEEE Trans Autom Control 56(8):1958–1963 8. Yu JY, Wang L (2010) Group consensus of multi-agent systems with switching topologies and communication delays. Syst Control Lett 59(6):340–348 9. Yu JY, Wang L (2012) Group consensus of multi-agent systems with directed information exchange. Int J Syst Sci 59(6):334–348 10. Tan C, Liu GP, Duan GR (2011) Coupled-group consensus of multi-agent systems with directed and fixed topology. In: 30th proceedings of Chinese control conference. Yantai, China, pp 6516–6520 11. Liu CL, Liu F (2012) Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation. Syst Control Lett 61(12):1235–1241 12. Hu JP, Hong YG (2007) Leader-following coordination of multi-agent systems with coupling time delays. Phys A 374(2):853–863 13. Chen YW, Wen GG, Peng ZX (2016) Necessary and sufficient conditions for group consensus of fractional multi-agent systems under fixed and switching topologies via pinning control. IEEE Trans Cybern 1–12 14. Cui Q, Xie DM, Jiang FC (2016) Group consensus tracking control of second-order multiagent systems with directed fixed topology. Neurocomputing 218:286–295 15. Wang JL, Wu HN (2012) Leader-following formation control of multi-agent systems under fixed and switching topologies. Int J Control 85(6):695–705 16. Lü SY, Sun HF (2008) Consensus algorithm for second-order networks with time-delays. Int J Syst Control 3:199–209

Optimization Algorithm for Power Flow Calculation Using Graph Theory Yicheng Xu, Yangyang Chen(&), Tianrun Liu, and Wen Chen School of Automation, Southeast University, Nanjing 211189, China [email protected]

Abstract. This paper considers the optimization of line loss calculation and the improvement of the rapidity of power flow analysis. A novel splitting strategy, say, decoupling the topology associated with the power gird into the main network containing the power branch and the subnet-based segmentation, is proposed to reduce the iterative matrix dimension, which makes it possible to calculate the subnet and the main net with the tools of Newton-Raphson method and the fast flow algorithm separately. The feasibility and effectiveness of the proposed scheme are proven by simulation results of the IEEE-30 Bus system. Keywords: Power flow Optimization


Graph decomposition
Cutting point
Line loss


1 Introduction Line loss is an important technical indicator for evaluating the plan, operation and management of the power grid [1]. With the liberalization of the power industry, the electricity system is gradually driven by the market [2, 3]. The transparent market requires for real-time and accurate analysis of line losses and currents. Distributed generation [4], especial the development of microgrid, makes the grid structure increasingly complex and the parameters become increasingly large, which results in the difficulty of analysis of line loss in real time. Therefore, how to optimize line loss calculation and improve the rapidity of power flow analysis becomes a must. In the line of the line loss calculation, there are several major method includes the equation squared root method of currents, the average current method, the equivalent resistance method, the forward and backward substitution method of flow, the coulometric method. As we all know, each method has its own advantages and disadvantages and is suitable the certain occasion [5]. For instance, with knowledge of the grid structure and parameters, the power flow iterative method is proved to be more accurate in the calculation of the theoretical line loss. However, the traditional methods mostly focus on finding suitable computer iterative algorithms for power flow calculations. In the case of transmission network, approximate linearization iterative method is usually used for solving nonlinear equations: Newton–Raphson method and PQ decomposition method [6]. In the case of distribution network, for its certain aspects like large r/x ratio, closed-loop structure, open-loop operation etc. researches develop methods like: forward and backward substitution method [7, 8] improved Newton–Raphson method © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 142–150, 2020. https://doi.org/10.1007/978-981-32-9698-5_17

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[9], Zbus method [10]. As the scale of the grid grows larger, the amount of computation required by iterative algorithms is exploding. Note that the distributed optimization based on network structure is widely used in bio-population performance analysis [11], social characteristics analysis [12, 13], data mining [14], machine learning [15] and the like. Some scholars start from the grid network topology to study the optimization method of line loss calculation. In [4], with the principle of proportional power distribution between nodes, a method for quickly estimating line loss and power flow distribution is given. However, it is required to give an already solved power flow distribution. In [16], a hierarchical decoupling method is proposed with the forward and backward substitution method for the radial network while P-Q decomposition method for the ring network. [17] presents a method of graph division to separate power grids from different grids to prevent cascading failures. [18] uses the min-cut method to divide the grid. However, most researches’ limitation is that either only the grid partition and cascading failure are considered, which is not suitable to flow analysis; or in other words, the power flow calculation is effective with knowledge of some or all of the network power flow information. Furthermore, the dimension of the iterative matrix is still large. Inspired by [16], this paper focuses on the optimization of the power flow algorithm by dividing the high-order matrix under certain conditions into the linearity of the loworder matrix iteration and thus accelerates. First, we decompose the original power grid into the main network containing the power branch and the subnet obtained by segmentation. Then, the simple ring existing in the subnet is de-looped. At the same time, the fast power flow algorithm [19] is used to calculate the equivalent load and power flow distribution of the boundary nodes. Next, the main network voltage and power flow distribution are obtained by using the Newton–Raphson method for the main network calculation. Finally, the voltage distribution is obtained by voltage superposition. Compared with the existing results, the contribution of this paper has the following three aspects: 1. By using the concept of cutting points in graph theory, the split calculation of graphs is extended to complex looped networks, which is more general. 2. Based on the characteristics of the distribution network node voltage around 1p.u., a simple voltage conversion is proposed, which replaces the complex forwardpushing back method and the alternate iteration of the cow-pull method in [16]. 3. This algorithm can simultaneously calculate the main network and subnet, thus improve computational efficiency through parallel computing.

2 Basic Theory Considering the power supply system of Chinese power grid, most of the network topology presents a power supply mode of multi-stage radial power distribution network, so that some characteristics of the radiated network can largely reflect the actual characteristics of the distribution network. In order to analyze and optimize line loss calculation and power flow analysis based on graph theory, root nodes, vertices, leaves,

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edges, and weights in graph theory can be respectively mapped to power plants, users, users at the end of the grid, and the Line between users, impedance. From the perspective of graph theory, the topology of radial network can be analyzed. According to the theory of cutting edges and cut points in graph theory, the network can be disassembled and disassembled into a representative radial network, ring network and ptype equivalent circuit. Then use the power flow calculation method in the power grid to calculate the line loss, voltage, active power, reactive power, phase angle, and compare with the current power line and line loss, so that we can evaluate the actual effect of our optimization algorithm. In order to make it clear, the following definition of graph should be revisited. The distribution network usually uses a radial distribution system [20]. One example is composed of main trunk, branch, distributed generator, leaf point and node. In the undirected connection graph G = (V, E), If x 2 V, after deleting node x and all edges associated with x, G splits into two or more unconnected subgraph, then x is the cutting point of G. Edge e is one of the edges. If G-e is not connected, the edge e is a cutting edge of the graph G. In this case, G-e must contain two connected branches. By cutting edge and cutting point processing, the network can be divided into main network and subnet. According to the literature [21] in a closed-loop network, the distribution of power is affected by many factors. Because the load in the closed-loop network absorbs different power from each branch, the losses on the line are also different. The power loss in each branch is related to the voltage across the line and the impedance of the line. Therefore, the power flow distribution in the closed-loop network is related to the structure, load, and power supply of the network, which is much more complicated than the power flow distribution of the radiating network. The power flow calculation method is as follows: (1) The ring network is unwound from the power point, and the computing load or computing power of each node is calculated. (2) Ignore the power loss, set the whole network voltage to the rated voltage U_ N ¼ UN \0 and then execute the distribution calculation of perform preliminary power. In our proposed algorithm, we calculate the current distribution according to the Newton-Raphson algorithm [22] and then use the formula of calculating the line loss: DPi ¼ Pi  Ui

n X

Uj ðGij cos dij þ Bij sin dij Þ

ð1Þ

Uj ðGij sin dij  Bij cos dij Þ

ð2Þ

j¼1

DQi ¼ Qi  Ui

n X j¼1

The unknowns for this system of equations are d and U. Among them, there are n nodes in the system, including a slack bus, m-1 P-Q nodes, and the number of P-V nodes is n-m. Therefore, n-1 di and n-m Ui are required. Because the Newton-Raphson

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method has better convergence and square convergence, the iteration can converge 3–7 times and a more accurate solution is obtained.

3 Optimization Algorithm Since the essence of the Newton-Raphson algorithm is an iterative method for solving nonlinear equations or systems [23], the equilibrium node power and line power are solved in the case of convergence, but due to its high Jacobian matrix order, it will make the calculation process complicated, the calculation amount is large, and the calculation speed is slow. Therefore, from the perspective of graph theory, we can simplify the network topology and reduce some nodes and edges to other nodes to reduce the number of nodes and the number of edges, thus reducing the order and sparse processing of the Jacobian matrix in the algorithm. A purpose of optimizing the power flow calculation efficiency is achieved under the condition that the power flow calculation error and the line loss have little influence. Design philosophy: 1. Traversing a distribution network, then we do power flow conversion among all leaf nodes of the PQ type until there are no leaf nodes. 2. Processing all the cutting edges and cutting points existing in the power grid, that is, simplifying the cut subnet. Subnet that can be simplified include radial networks and ring networks. 3. For a simple ring containing only PQ nodes, we disassemble it into a radiating network. 4. Using the Newton-Raphson method to calculate the power flow of the simplified grid and the line loss, and then calculate the error and compare time efficiency. Next, we will detail the optimization design of each step. The optimization criteria based on PQ type leaf nodes in a radial network are given as follows: The leaf node and its upper-level node can be regarded as a two-node ptype equivalent circuit, and then according to the calculation method of the type circuit mentioned above, the flow of the leaf node can be transformed to the upper-level node. And “delete” the leaf node and the edge connected to it. According to the above optimization criteria, the algorithm works as follows: Traverse each node in the network topology, find the node with degree 1, that is, the leaf node, and calculate the power flow of all the leaf nodes into the corresponding upper-level nodes, and then perform graph traversal to find the newly generated leaf nodes and Restore, until there are no leaf nodes in the network, end the traversal, calculate the power flow distribution of the network at this time.

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The optimization criteria based on cutting edges and cutting points are shown as follows: If there are cutting edges and cutting points in the network, the network can be divided into a main network including slack bus and a subnet without slack bus. For the subnet, we can calculate the distribution of the power flow in the subnet and transform all the power flow to the cutting points to “delete” the subnet. According to the above optimization criteria, the algorithm works as follows: First traverse the network, find the cutting point in the network, divide the total network from the cutting point into the main network and several subnets, calculate distribution of the power flow in each subnet separately and transform them to the corresponding cutting points in the main network, and then use the Newton–Raphson method to calculate the power flow of the main network.

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The optimization criteria for a simple ring containing only PQ nodes are shown as follows: As mentioned above, for a simple loop containing only PQ nodes, based on the known power flow flowing into and out of the loop, we can use the moment method to calculate the distribution of the power flow inside the loop. Then we can unloop the ring. Thus, the ring network is simplified into a typical radial network. Then we use the Forward and Backward Substitution method calculate the power flow of the simplified radial network. The result can be used to calculate the power flow of the upper node. In the literature, the direct using of the Newton-Raphson method to calculate the power flow of the ring network leads the lower efficiency rather than the calculation of the radial network under the Forward and Backward Substitution method. It can be avoided by our proposed method. According to the above optimization criteria, the algorithm works as follows: First traverse the network, find a simple ring in the network, unloop the simple ring, for the disassembled radiating network we use the Forward and Backward Substitution method, and then use the cutting-edge method to process the network, transform the power flow to the cutting point of the main network. Finally, we use the NewtonRaphson method for power flow calculation. After dividing the total network into several subnets according to the above method, separate power flow calculations are performed for each subnet, and then the calculation results are combined. The method of convertion is as follows: for a subnet, find its split point, and the voltage vector of the point in the total network is recorded as U1. Set the split point in the subnet as the slack node, that is, the voltage amplitude is 1 (p.u.) and the phase angle is 0(deg). Then, the power flow calculation is performed on the subnet to obtain the voltages of all the nodes in the subnet, and the absolute difference of the voltage between each node and the slack node is represented by a vector, and then add this vector to U1 to obtain the voltage vector of each node after the conversion.

4 Analysis of Experimental Results The power gird in this example is a 30-nodes system as used in [24, 25]. The comparison results of the line losses on the sides are shown in Table 1. It can be seen from the above table that the error of the active part and the reactive part of each side line loss are less than 2.1%. The error is small and is within an acceptable range.

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Node number From 1 1 2 3 2 2 4 5 6 6 6 6 9 9 4 12 12 12 12 14 16 15 18 19 10 10 10 10 21 15 22 23 24 25 25 28 27 27

To 2 3 4 4 5 6 6 7 7 8 9 10 11 10 12 13 14 15 16 15 17 18 19 20 20 17 21 22 22 23 24 24 25 26 27 27 29 30

Line loss of each side in total network P (MW) Q (MVAr) 0.0026 −0.2921 0.0127 −0.1485 0.0178 −0.1456 0.0018 0.0073 0.0110 −0.1524 0.0289 −0.1079 0.0066 0.0265 0.0120 −0.0662 0.0031 −0.0858 0.0128 0.0512 0.0000 0.0099 0.0000 0.0086 0.0000 0.0000 0.0000 0.0052 0.0000 0.0019 0.0000 0.2097 0.0037 0.0080 0.0066 0.0122 0.0080 0.0177 0.0003 0.0003 0.0031 0.0073 0.0097 0.0194 0.0022 0.0048 0.0009 0.0021 0.0052 0.0122 0.0023 0.0062 0.0044 0.0102 0.0062 0.0133 0.0093 0.0186 0.0109 0.0219 0.0078 0.0117 0.0066 0.0138 0.0035 0.0061 0.0046 0.0071 0.0063 0.0119 0.0000 0.0313 0.0090 0.0172 0.0171 0.0321

Line loss of each side in converted network P (MW) Q (MVAr) 0.0026 −0.2921 0.0127 −0.1485 0.0178 −0.1456 0.0018 0.0073 0.0110 −0.1524 0.0289 −0.1079 0.0066 0.0265 0.0120 −0.0662 0.0031 −0.0858 0.0128 0.0512 0.0000 0.0099 0.0000 0.0086 0.0000 0.0000 0.0000 0.0052 0.0000 0.0019 0.0000 0.2097 0.0037 0.0080 0.0066 0.0122 0.0080 0.0177 0.0003 0.0003 0.0031 0.0073 0.0097 0.0194 0.0022 0.0048 0.0009 0.0021 0.0052 0.0122 0.0023 0.0062 0.0044 0.0102 0.0062 0.0133 0.0093 0.0186 0.0109 0.0219 0.0078 0.0117 0.0066 0.0138 0.0035 0.0061 0.0045 0.0069 0.0063 0.0119 0.0000 0.0313 0.0090 0.0172 0.0171 0.0321

Error P 0.011% 0.004% 0.002% 0.004% 0.001% 0.002% 0.002% 0.001% 0.002% 0.000% / / / / / 0.000% 0.001% 0.003% 0.001% 0.002% 0.001% 0.000% 0.000% 0.000% 0.000% 0.000% 0.000% 0.000% 0.001% 0.002% 0.002% 0.005% 0.012% 2.020% 0.015% / 0.000% 0.000%

Q 0.000% 0.001% 0.001% 0.004% 0.000% 0.002% 0.002% 0.001% 0.000% 0.000% 0.005% 0.005% / 0.005% 0.006% 0.000% 0.001% 0.003% 0.001% 0.002% 0.001% 0.000% 0.000% 0.000% 0.000% 0.000% 0.000% 0.000% 0.001% 0.002% 0.002% 0.005% 0.012% 2.020% 0.015% 0.006% 0.000% 0.000% (continued)

Optimization Algorithm for Power Flow Calculation

149

Table 1. (continued) Node number From 29 8 6

To 30 28 28

Line loss of each side in total network P (MW) Q (MVAr) 0.0035 0.0065 0.0036 −0.1754 0.0001 −0.0945

Line loss of each side in converted network P (MW) Q (MVAr) 0.0035 0.0065 0.0036 −0.1754 0.0001 −0.0945 Maximum

Error P 0.000% 0.002% 0.006% 2.020%

Q 0.000% 0.000% 0.000% 2.020%

5 Conclusion and Future Recommendation In the case of grid structure and parameters given in the distribution network, the PQ type leaf nodes, cut-edge cut points and simple loops containing only PQ nodes existing in the grid can be processed by analyzing the network topology of the grid. The node voltage value and phase angle value of the power grid realize “deletion” and “deletion point” within the range of the maximum error not exceeding 1.17%, which simplifies the network topology and makes the Jacobian matrix in the bull-and-jaw method degraded and sparsely processed. To achieve the purpose of improving the efficiency of power flow calculation within a certain error limit. Through examples, it is prove that this optimization algorithm is completely feasible. Using this optimization algorithm can improve the efficiency of power flow calculation. Acknowledgement. This work was supported by the National Natural Science Foundation of China (61673106), Natural Science Foundation of Jiangsu Province (BK20171362) and the Fundamental Research Funds for the Central Universities (2242019K40024).

References 1. Chen B et al (2018) Theoretical line loss calculation of distribution network based on the integrated electricity and line loss management system. In: China international conference on electricity distribution CICED, pp 2531–2535. https://doi.org/10.1109/ciced.2018.8592309 2. Wu ZQ (2002) Loss and branch power flow allocation based on topological method. Electr Power Compon Syst 30:1179–1193 3. De M, Goswami SK (2010) A direct and simplified approach to power-flow tracing and loss allocation using graph theory. Electr Power Compon Syst 38:241–259 4. Sharma S, Abhyankar AR (2018) Deviation cost allocation of DISCOM using shapley value. Electr Power Compon Syst 46:1–13 5. Zhang Q, Gang C (2015) A study of line loss calculation method and its application in distribution network, pp 180–184. https://doi.org/10.3969/j.issn.1007-2284.2015.05.045 6. Yan C (2015) The steady state analysis of power systems, pp 109–143 7. Chen GU, Xiu-fan LE, Zhang XM (2010) Three-phase power flow method for weakly meshed distribution systems based on modified back/forward sweep method. Power Syst Prot (2010). https://doi.org/10.3969/j.issn.1674-3415.2010.19.030

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8. Haque MH (2010) A general load flow method for distribution systems. Power Syst Prot Control 38, 57–61,68 9. Goswami SK, Basu SK (1991) Direct solution of distribution systems. In: IEE proceedings C (generation, transmission and distribution), vol 138. IET, pp 78–88 10. Bortolosso C, Leborgne RC (2015) Analysis of the impact of new power sources to voltage sags using Zbus. In: 2015 IEEE PES innovative smart grid technologies Latin America (ISGT LATAM). IEEE, pp 371–375. https://doi.org/10.1109/isgt-la.2015.7381184 11. Kim S, Thapa I, Ali HH (2018) A graph-theoretic approach for identifying bacterial intercorrelations and functional pathways in microbiome data. In: 2018 IEEE international conference on bioinformatics and biomedicine (BIBM). IEEE, pp 405–411. https://doi.org/ 10.1109/bibm.2018.8621179 12. Rong H, Ma T, Tang M, Cao J (2018) A novel subgraph K+-isomorphism method in social network based on graph similarity detection. Soft Comput 22:2583–2601 13. Xia Q, Liang W, Xu Z (2017) The operational cost minimization in distributed clouds via community-aware user data placements of social networks. Comput Netw 112:263–278 14. Meysman P et al (2018) Mining the enriched subgraphs for specific vertices in a biological graph. IEEE/ACM Trans Comput Biol Bioinform 5963:1–12 15. Amali S, Faddouli NEL, Boutoulout A (2018) Machine learning and graph theory to optimize drinking water. Proc Comput Sci 127:310–319 16. Yu DC (2010) Layer-decoupled power flow algorithm for complex networks. Proc CSEE 30:56–61. https://doi.org/10.13334/j.0258-8013.pcsee.2010.07.009 17. Wang XD, Lin J (2014) The controlled splitting strategy for power system based on a decomposition algorithm. In: China international conference on electricity distribution, CICED, pp 1605–1609 18. Sen A, Ghosh P, Vittal V, Yang B (2009) A new min-cut problem with application to electric power network partitioning. Eur Trans Electr Power 19:778–797 19. Yan W, Liu F, Wang G, Xiu G, Huang S (2003) Layer-by-layer back/forward sweep method for radial distribution load flow. Proc Chin Soc Electr Eng 23(8):76–80 20. Nassar ME, Salama MMA (2017) A novel branch-based power flow algorithm for islanded AC microgrids. Electr Power Syst Res 146:51–62 21. Gonen T (2016) Modern power system analysis. CRC Press, Boca Raton 22. Gu XF (2018) Line loss calculation and loss reduction analysis of distribution network. Smart Grid 08:312–322 23. Men X, Wang Z, Cao J, Pan X (2017) Coupling analysis of gas-electric hybrid system based on Newton-Raphson method. J Eng 2017:1505–1510 24. Alsac O, Stott B (1974) Optimal load flow with steady-state security. IEEE Trans Power Appar Syst PAS 93:745–751 25. Ferrero RW, Shahidehpour SM, Ramesh VC (1997) Transaction analysis in deregulated power systems using game theory. IEEE Trans Power Syst 12:1340–1347

A New Approach to Developing General Manipulator Control System Application Based on ROS Xuedong Jing, Yuquan Xue(&), and Ya’nan Chen School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China [email protected]

Abstract. This paper proposes a new approach to developing control applications for general manipulator using the open source robot operating system (ROS) as the platform. The tool MoveIt! is used to complete the task of the motion planning and the motion data transmission between client and server is realized by setting up the relevant nodes. In combination with the experiment, this paper explains the model building of the robot with a specific manipulator and the motion data is processed by quintic polynomial interpolation algorithm to improve the stability of the manipulator. According to the above methods, it can realize the control of different types of manipulators on the market not specifically referring to certain structures and provides a new way for crossplatform control of robots. Keywords: Manipulator


ROS
MoveIt
Quintic polynomial interpolation

1 Introduction Society is becoming more automated with robots starting to perform most tasks in factories and help out in office and home environments. In this environment, one of the most important functions of robots [1] is the ability to manipulate specific objects. However, due to the closure of the traditional manipulator’s control system, it’s not conducive to conduct demonstration experiments in the university laboratories. When faced with different work tasks, the complexity of the closed control system undoubtedly increases the difficulty of programming. At the same time, algorithm migration takes a lot of time and efforts between different types of robots. Considering the above deficiencies, this paper proposes a new approach to developing general manipulator control applications using the open source robot operating system (ROS) [2] as the platform.

© Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 151–158, 2020. https://doi.org/10.1007/978-981-32-9698-5_18

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2 Design of Manipulator Control System Application This paper uses the tool MoveIt to build the motion planning layer of the robot and the most important part of whole system is to transmit the results to the corresponding controller specifically by the way of action. After the relevant trajectory controller interpolates the path points provided by the tool MoveIt, the motion data is sent to the corresponding motor drivers and the data that can be identified by motors is converted into them. Through the above operations, we can realize the control of the general manipulator. ROS manipulator control system framework is shown in Fig. 1.

MoveIt!

Rviz HMI

C++

Python

KinemaƟcs

Path Planning

Collision Checking

Trajectory Controller Follow Joint Trajectory

Socket

robot

AcƟon

Trajectory InterpolaƟon

PosiƟon Servo1

M

PosiƟon Servo2

M

PosiƟon Servo3

M

PosiƟon Servo4

M

PosiƟon Servo5

M

PosiƟon Servo6

M

Joint State Controller

Fig. 1. ROS manipulator control system framework

The above content is only for the control part. The construction of the whole manipulator control system can depend on the five-layer architecture of ROS. The fivelayer architecture of ROS consists of UI layer, ROS Layer, Interface layer, Communication layer and controller layer. ROS layer is the base of the framework and it provides the basis for communication mechanism. MoveIt! layer can provide motion planning and find the kinematic solutions. Robot controllers communicate with robot client by communication protocol of simple message. ROS manipulator software architecture is shown in Fig. 2.

A New Approach to Developing General Manipulator Control System Application

UI

Model display

Status monitor

Parameters

Motion planning

MoveIt!

153

Online/offline simulation

Jog control

Collision detection

ROS Interface

Control command

Log

Status

Simple Message (TCP/IP)

Communication

Controller & Robot

Parameters

Controller TCP Robot

IO

USB

Driver+Motor

Fig. 2. ROS manipulator software architecture

At the software level, we design the framework of the control system based on ROS. And the above four layers can be completed in ROS environment, mainly including motion planning, application processing of manipulator and sending message to the underlying controller. The controller is basically equipped with the function of trajectory interpolation, kinematic solution, system management, interface expansion, algorithm acceleration and motor control, etc. Next, we choose the Jibot-Zxs provided by the ZL-robot for example to build the model of this robot, solve the kinematics, interpolate the motion trajectory provided by the tool MoveIt! and carry out the experiments to realize the stable control of it.

3 Robot Model Building and Motion Planning 3.1

Robot Model Building

The manipulator can be seen as a kinematic chain composed of links through the joint. Each link has 4 parameters, which can be divided into two groups: the rod parameters that determine the structure of the rod and the joint parameters that determine the position of the adjacent rod. In this paper, the D-H parameter method is used to build model and analyze the manipulator. The coordinate system is established in each joint and pose between the coordinate systems is described by homogeneous transformation. Table 1 gives D-H parameter table of the manipulator linkage coordinate system.

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ai di hi ai 0 0 339 h1 p/2 0 0 h2 0 250 0 h3 p/2 70 250 h4 −p/2 0 0 h5 p/2 0 95 h6

The unified robot description model URDF is used in ROS. The URDF is used to describe the kinematic chain of the robotic arm, the inertial characteristics and the parent-child relationship diagram of each link and joint. For complicated mechanical structures such as six-DOF manipulator, the model of the robot should be created using the 3D modeling software Solidworks. The position and orientation of each joint coordinate system are determined by the link coordinate system. The manipulator linkage coordinate system is shown in Fig. 3.

Fig. 3. Manipulator linkage coordinate system

3.2

Kinematics

The kinematics [4] of the manipulator is divided into forward kinematics and inverse kinematics. Forward kinematics is known to solve the pose of the end effector at each joint angle; the solution process of inverse kinematics is the opposite of forward kinematics. For forward kinematics, the position of the mechanical arm link relative to the position can be represented by a homogeneous transformation matrix. For the inverse kinematics, if the end pose is given, it is more complicated to get the angle value of each joint limited by the constraint of the workspace. This article uses the ROS operating tool MoveIt! which provides a way for motion planning, kinematics analysis, collision detection. It uses KDL (Kinematics and Dynamics Library) to solve the inverse kinematics problem by default. This way uses numerical methods which can be applied to different types of robots. However, it requires a lot of iterative operations and the speed of its solution is a little low. At the same time, the numerical solution is sensitive to the initial value and an inappropriate initial value may result in no solution.

A New Approach to Developing General Manipulator Control System Application

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Fig. 4. Two 6-DOF solvable structure types of the IKFast analytical algorithm

In response to the above problems, the inverse kinematics problem is solved by the IKFast analytical algorithm provided by OpenRAVE [5] motion planning software. The IKFast analytical algorithm can solve the inverse kinematics problem of the two types of 6-DOF manipulators. The first type is the structure that the last three joints J3, J4, J5 axes intersect at one point; The second type is the one whose first three joints J0, J1, and J2 axes intersect at one point, as shown in Fig. 4 The manipulator used in this paper belongs to the first type and its last three joint axes intersect at one common point. The inverse kinematics of the manipulator is solved by the IKFast [6] analytical algorithm to realize the transformation between Cartesian space and joint space. 3.3

Trajectory Interpolation

There are not enough path points to meet the actual task requirements just depending on the tool MoveIt. The robot may shake from time to time if it is lack of motion trajectories, which would seriously affect the quality of the specific experiment. In order to improve the quality and precision of the manipulator during the demonstration experiment, this paper interpolates the planned motion trajectories to improve the stability of the robot. First of all, we analyze the differences between cubic and quintic polynomial interpolation [7] algorithm and provide a new interpolation algorithm to reduce the amplitude of the jitter during the experiment and meet the requirements of different tasks. Cubic Polynomial Interpolation Trajectory Planning There are 4 unknown coefficients in the cubic polynomial [8] and the joint angles at the beginning or end of the motion are known in the circumstances. At the same time, the joint speeds are all 0 and the four unknown coefficients can be solved by four known conditions. The joint angle, angular velocity, angular acceleration function equations and constraints are as follows: hðtÞ ¼ h3 t3 þ h2 t2 þ h1 t þ h0

ð1Þ

_ ¼ 3h3 t2 þ 2h2 t þ h1 hðtÞ

ð2Þ

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€hðtÞ ¼ 6h3 t þ 2h2

ð3Þ

_ 0Þ ¼ 0 hðt0 Þ ¼ h0 ; hðt _ fÞ ¼ 0 hðtf Þ ¼ hf ; hðt

ð4Þ

By simultaneous Eqs. (1), (2) and (4), we can get the coefficient expressions: (

h3 ¼

2ðhf h0 Þ ; h2 tf3

¼

3ðhf h0 Þ tf2

ð5Þ

h1 ¼ 0; h0 ¼ 0

We can conclude that the cubic polynomial interpolation algorithm can ensure that the joint angle and the angular velocity curve are smooth. There are still some problems with this algorithm. The acceleration mutation would happen if we do not set the acceleration constraint. Quintic Polynomial Interpolation Trajectory Planning Based on the cubic polynomial, the quintic polynomial algorithm [9] adds the angular acceleration constraints at the beginning and the end of the motion. It solves the six unknowns by combining the following six equations. The joint angle, angular velocity, angular acceleration function equations and constraints are as follows: hðtÞ ¼ h5 t5 þ h4 t4 þ h3 t3 þ h2 t2 þ h1 t þ h0

ð6Þ

_ ¼ 5h5 t4 þ 4h4 t3 þ 3h3 t2 þ 2h2 t þ h1 hðtÞ

ð7Þ

€hðtÞ ¼ 20h5 t3 þ 12h4 t2 þ 6h3 t þ 2h2

ð8Þ




_ 0 Þ ¼ 0; €hðt0 Þ ¼ 0 hðt0 Þ ¼ h0 ; hðt _ f Þ ¼ 0; €hðtf Þ ¼ 0 hðtf Þ ¼ hf ; hðt

ð9Þ

By simultaneous Eqs. (6), (7) and (9), we can get the coefficient expressions: 8 > pffiffiffiffi P > < v_ i ðtÞ ¼ ½ m aij ðx i ðtÞ  x i ðtÞÞ  2pn ffiffimffi x i ðtÞ j2Ni pffiffiffi pffiffiffiffi P > > > aij ðv i ðtÞ  v i ðtÞÞ  n þ2p2ffiffimffi m v i ðtÞ  d^i ðtÞ þ di ðtÞ  m : j2Ni

ð10Þ

Solution of Distributed Optimal Control Protocol

255

Let ^xi ðtÞ ¼ x i ðtÞ  x 1 ðtÞ, ^vi ðtÞ ¼ v i ðtÞ  v 1 ðtÞ, the above formula can be shown as ^y_ ðtÞ ¼ A^yðtÞ þ ^ed ðtÞ, where e_ d ðtÞ ¼ Sed ðtÞ, S ¼ diagfW2  KY2 ;


; WN  KYN g  pffiffiffiffi 0N1N1 ^¼ A ^  pn ffiffiffi IN1N1  mL 2 m

 pffiffiffi pffiffiffiffi IN1N1 n þ 2 m ^  pffiffiffi IN1N1 ;  mL 2 m

 T  T  T ^xðtÞ ¼ ^x 2 ðtÞ;


; ^x N ðtÞ 2 RN1 , ^vðtÞ ¼ ^v 2 ðtÞ;


; ^v N ðtÞ 2 RN1 , ^yðtÞ ¼ ^ xðtÞT ; ^vðtÞT ,

ed ðtÞ ¼ ½Y2 e2d ðtÞ;


; YN eNd ðtÞ, ^ed ðtÞ ¼ ½0N1N1 ; ed ðtÞ

Theorem 2. Consider a multi-agent systems (1), Suppose Assumption 1 hold. Then under the influence of the distributed control protocol (6), when w ¼ maxfkmax ðNk Þg \0, k = 1, 2, 3. Multi-agent systems (1) can achieve consensus, and cost function (2) pffiffiffiffi pffiffiffiffi ^ þ ða þ b  n= mÞIN1N1 , N2 ¼ can get the minimum. Where N1 ¼ 2 mL pffiffiffiffi pffiffiffiffi pffiffiffiffi pffiffiffiffi pffiffiffiffi ^  n=ð2 mÞIN1N1 Þ2 , ^ þ ð2 þ b  ðn þ 2 m= 2 mL mÞIN1N1 þ 1=að mL N3 ¼ S þ ST þ 2=bIN1N1 . Proof. Let the Lyapunov function be ^ yðtÞ þ ^ed ðtÞT ^ed ðtÞ VðtÞ ¼ ^yðtÞT P^ pffiffiffi  pffiffiffiffi ^  n þp2ffiffiffi m IN1N1  m L ^ 2 m where P ¼ IN1N1

IN1N1 IN1N1



^ yðtÞ þ ^e ðtÞT P^ ^T P _ ^þP ^ AÞ^ ^ yðtÞ þ ^yðtÞT P^ ^ ed ðtÞ VðtÞ ¼ ^yðtÞT ðA d þ ed ðtÞT Sed ðtÞ þ ed ðtÞT ST ed ðtÞ pffiffiffiffi pffiffiffiffi n ^  pnffiffiffiffi IN1N1 Þ^xðtÞ þ 2^xðtÞT ð mL ^ p ffiffiffiffi IN1N1 Þ^vðtÞ  ^xðtÞT ð2 mL m 2 m pffiffiffiffi pffiffiffiffi ^  n þp2ffiffiffiffi m IN1N1 Þ^vðtÞ þ ^vðtÞð2IN1N1  2 mL m þ 2^xðtÞT IN1N1 ed ðtÞ þ 2^vðtÞT IN1N1 ed ðtÞ þ ed ðtÞT ðS þ ST Þed ðtÞ pffiffiffiffi ^  pnffiffiffiffi IN1N1 Þ^xðtÞ þ a^xðtÞT ^xðtÞ + b^xðtÞT IN1N1^xðtÞ  ^xðtÞT ð2 mL m pffiffiffiffi pffiffiffiffi ^  n þp2ffiffiffiffi m IN1N1 Þ^vðtÞ þ 2 ed ðtÞT IN1N1 ed ðtÞ þ ^vðtÞð2IN1N1  2 mL b m pffiffiffiffi 1 n T 2 2 ^  pffiffiffiffi IN1N1 Þ ^vðtÞ þ b^vðtÞ IN1N1^vðtÞ þ ed ðtÞT ðS þ ST Þed ðtÞ þ ^vðtÞ ð mL a 2 m

Select the appropriate parameters a, b to make w ¼ maxfkmax ðNk Þg\0

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_ VðtÞ\w

N X  2  2  2 ð^x i ðtÞ þ ^v i ðtÞ þ Yi eid ðtÞ Þ i¼2

According to the stability theory of Lyapunov, for any initial position and velocity  _ we can obtain lim ^x i ðtÞ ¼ 0, state, If w ¼ maxfkmax ðNk Þg\0, so that VðtÞ\0.      t!1  lim ^v i ðtÞ ¼ 0, in other words lim x i ðtÞ  x 1 ðtÞ ¼ 0, lim v i ðtÞ  v 1 ðtÞ ¼ 0:

t!1

t!1

t!1

Therefore, according to Definition 1, we can know that system (1) can achieve consensus.

4 Numerical Simulation

Fig. 1. Communication topology diagram

In this part, Matlab will be used to simulate and verify the algorithm proposed in this paper. In this experiment, a multi-agent systems consisting of 4 agents is considered. The topology of the system is shown in Fig. 1. Then the Laplacian matrix is 2

1 6 1 6 6 0 L¼6 6 0 6 4 0 0

1 2 1 0 0 0

0 1 2 1 0 0

0 0 1 2 1 0

0 0 0 1 2 1

3 0 0 7 7 0 7 7 0 7 7 1 5 1

Suppose that the external disturbance signal is generated by the following external    T 0 2 1 _ system ni ðtÞ ¼ n ðtÞ, di ðtÞ ¼ ni ðtÞ. Applying a linear matrix inequality, 2 0 i 0 In order to make Wi  KYi Hurwitz, we can get the disturbance observation gain K as ½3; 3T . For the control protocol, select n ¼ 3, m ¼ 4, k ¼ 9=14. The initial state of the agent is x1 ð0Þ ¼ 6:0, x2 ð0Þ ¼ 2:0, x3 ð0Þ ¼ 13:0, x4 ð0Þ ¼ 10:0, x5 ð0Þ ¼ 2:5, x6 ð0Þ ¼ 6:17, and velocity state is v1 ð0Þ ¼ 2:5, v2 ð0Þ ¼ 1:3, v3 ð0Þ ¼ 2:2, v4 ð0Þ ¼ 3:4, v5 ð0Þ ¼ 1:0, v6 ð0Þ ¼ 0:2. In the above initial state, according to the given controller to control the system, the following multi-agent position state simulation diagram can be obtained.

Solution of Distributed Optimal Control Protocol

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Fig. 2. Position and velocity state of multi-agent systems with disturbance and without disturbance observer

Fig. 3. Position and velocity state of multi-agent systems with disturbance and disturbance observer

Figures 2 and 3 are simulation of the disturbance control active control without the disturbance suppression in the multi-agent systems and the application of the proposed disturbance control. It can be seen from the figure that the proposed algorithm has good control effect.

5 Conclusion In this paper, the optimal control problem for second-order multi-agent systems with disturbance in fixed topology is considered. Combined with the idea of LQR theory and active disturbance rejection control, a composite control protocol based on status

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feedback and disturbance estimate is presented. Through the theoretical analysis, the sufficient conditions for the consensus of multi-agent systems are obtained. Finally, the influences of the control algorithm is verified by numerical simulation. Acknowledgments. The research is supported by the National Natural Science Foundation of China (61673200, 61771231), the Major Basic Research Project of Natural Science Foundation of Shandong Province of China (ZR2018ZC0438) and the Key Research and Development Program of Yantai City of China (2019XDHZ085).

References 1. Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multiagent systems. Proc IEEE 95(1):215–233 2. Parker Dawn C, Manson Steven M, Janssen Marco A et al (2015) Multi-agent systems for the simulation of land-use and land-cover change: a review. Ann Assoc Am Geogr 93(2):314– 337 3. Yang H, Wang F, Han F (2017) Containment control of fractional order multi-agent systems with time delays. IEEE/CAA J Automatica Sinica 5:1–6 4. Yang H, Han F, Zhao M, Zhang S, Yue J (2017) Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays. Open Phys 15(1):509–516 5. Cao Y, Ren W (2010) Optimal linear-consensus algorithms: an LQR perspective. IEEE Trans Syst Man Cybern Part B Cybern Publication IEEE Syst Man Cybern Soc 40(3):819 6. Lin X, Cassandras CG (2013) An Optimal control approach to the multi-agent persistent monitoring problem in two-dimensional spaces. IEEE Trans Automatic Control 60(6):1659– 1664 7. Foderaro G, Ferrari S, Wettergren TA (2014) Distributed optimal control for multi-agent trajectory optimization. Automatica 50(1):149–154 8. Li R, Shi Y (2014) Finite-time optimal consensus control for second-order multi-agent systems. J Ind Manag Optim (JIMO) 10(3):929–943 9. Sun J, Geng Z, Liu Y (2014) Distributed optimal tracking control for second-order multiagent systems. In: Control conference. IEEE

The Design of an Intelligent Screw Extruder Control System Based on Fuzzy Control Yulin Li, Jin Zhou(&), Qiang Li, Long He, Yonglin Zhang, and Shaoyun Song Wuhan Polytechnic University, Wuhan 430023, China [email protected]

Abstract. Aiming at the problems of poor quality stability and high working intensity of workers and low degree of mechanical automation caused by the traditional control system of Screw extruder which relies on manual adjustment of feeding motor speed, this paper proposes an intelligent control system of Screw extruder based on fuzzy control algorithm. The temperature and pressure signals of oil press chamber are used as the detection method, and the expert control experience is simulated by the fuzzy control algorithm to realize automatic control of oil press motor speed. The system uses PLC as the central controller to complete the design of the control system and uses MATLAB to carry out the model and simulation tests. According to the simulation results, the intelligent Screw extruder based on fuzzy control algorithm has better control effect and stability, and better replace the manual operation of the control process relatively. Keywords: Fuzzy control Screw extruder


PLC application
Automatic control


1 Introduction China is one of the most massive oil crops producers in the world, but still challenging to meet the demand for edible oil, and need to import a large amount of oil crop from foreign countries every year, the reasons leading to this shortage are not only related to the methods and processes of edible oil producing but also the low automation degree of Screw extruder machine [1]. Therefore, the research on screw extruder technology has become a crucial subject in China. Because of its simple principle and structure, screw extruder is the broader usage equipment in the oil squeezed industry in China. At present, the most improved methods for screw extruder are to change the single squeezing axle into the multi-squeezing axle, and press it from different directions or to use high-hardness alloy as the material of Screw extruder and change the squeezing environment. However, as people demand for stability of oil product quality and reducing the labor intensity of workers, merely changing the material of the Screw extruder or changing the mechanical structure can no longer meet the needs of current production [2], the intelligent transformation of Screw extruder is extremely urgent. By intelligent transformation, this paper combines artificial intelligence, automatic control technology and screw extruder, and applies fuzzy control algorithm to oil press © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 259–267, 2020. https://doi.org/10.1007/978-981-32-9698-5_30

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production line, so that the Screw extruder can achieve the requirements of automatic control. The fuzzy control algorithm formulates the fuzzy control rules according to the expert control experience, which makes the screw extruder make the judgment according to the input information in the process of operation, and choose the appropriate operation mode automatically, solving the current situation that the screw extruder relies on human operation too much. Through the trial operation of the production line, the design of intelligent screw extruder control system not only reduces the intensity of labor, makes the industrial control more flexible, but also improves the stability of product quality.

2 Screw Extruder Control System In the process of operating, it is necessary for the traditional screw extruder that worker should monitor Current Signal of oil press motor in real time to adjust the speed of feeding motor. The improved screw extruder directly uses the fuzzy controller to replace the worker’s real-time monitoring and adjusts its motor speed by judging and calculating the input information independently. The pressure information in the chamber of the screw extruder reflects the amount of oilseeds. Pressure change rate reflects the trend of oilseeds increase or decrease. With the accumulation of oilseeds, the ambient temperature in the chamber will also increase, so the control system will take the real-time temperature and pressure signals and pressure change rate in the chamber as input information. The system has mainly two operation modes: manual and automatic. Under the manual operation, workers manually control the running of the screw extrude and accumulate control experience, and then simulates the control experience by fuzzy control, which is applied in the automatic operation mode to make the intelligent screw extruder control system meet the automation requirements. In the process of operation, the upper computer is used for real-time monitoring and remote control of the whole system. 2.1

System Hardware Design

The main hardware structure of the screw extruder control system includes PLC, power supply, variable-frequency drive, temperature and pressure signal acquisition sensor, oil press motor, HMI touch pane, upper computer and so on. Because of its high reliability and strong applicability, the PLC is widely used in the control of industrial production, but in the actual production line, it is often accompanied by many nonlinear factors and difficult to establish accurate mathematical model, so the general control method of PLC will have its limitations [3]. The PLC is selected as the controller of the screw extruder control system, and the fuzzy control rules are formulated according to expert control experience, and the fuzzy control algorithm is implemented by the PLC programming, which enables the control system to choose the best control mode, solve the control problems in the nonlinear environment, and expand the application field of the PLC [4]. The central controller in the system is Siemens CPU1215C, The computing capacity of it meets the requirements of the fuzzy control operation. Oil press motor is a Three-phase asynchronous motor with 22 KW rated power. Adopting the

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variable-frequency drive to control the speed of oil press motor in the system, this speed control method has the advantages of stability and energy saving (Fig. 1).

Fig. 1. The hardware structure of the system

2.2

Fuzzy Control Algorithm

The Principle of Fuzzy Control. Fuzzy control consists of four parts: the fuzzification of input, knowledge base, fuzzy inference and defuzzification of output. In fuzzy control system, fuzzy variable linguistic are often used to establish fuzzy subsets such as “bigger”, “big”, “medium”, “small” and “smaller”. The actual range of variable value is called the basic domain of fuzzy control. Since the data can be processed in fuzzy control system are fuzzy sets rather than exact values, the fuzzification of input is to convert the precise amounts of input into fuzzy values corresponding to fuzzy subsets through membership functions. The relevant data and fuzzy rules needed for fuzzy control algorithm are stored in the knowledge base. The fuzzy control algorithm deduces according to the fuzzy rules and outputs the control quantity. However, the output control quantity is still fuzzy and cannot be recognized by the machine at this time, it must be defuzzified and converted to an accurate value before it can be applied (Fig. 2).

Fig. 2. Schematic diagram of fuzzy control

Fuzzy Control System of Screw Extruder. The fuzzy control system of the intelligent screw extruder is a three-input and single-output system which takes the temperature, pressure and pressure change rate in the chamber as input and the speed of oil press motor as output. The system through the temperature and pressure values to determine the number of oilseeds in the chamber, through the pressure change rate to

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judge the trend of oilseeds increase or decrease. The basic domain of temperature for 0–150 °C, the basic domain of pressure value for 0–200 MPa, pressure change rate between –15 to 15, the speed range of 0–960 r/min. The precision of the fuzzy control algorithm is related to the resolution of the fuzzy subset. When the resolution of the fuzzy subset becomes higher, the control precision is improved, but the control method becomes more complicated. Compared the weights of three input signals in daily production, the following fuzzy subsets are determined. Temperature: {L M H}, corresponding to the description of temperature values in natural language respectively: “low temperature”, “middle temperature” and “high temperature”. Pressure: {NB NS ZO PS PB}, corresponding to the description of pressure values in natural language respectively: “lower pressure”, “ low pressure”, “middle pressure”, “high pressure”, “higher pressure”. Pressure change rate: {NB NS ZO PS PB}, corresponding to the natural language description about the changes of oilseeds: “rapidly reduced”, “ reduced”, “basically unchanged”, “increased”, “rapidly increased”. Speed: {NB NS ZO PS PB}, corresponding to the description of speed in natural language: “slower”, “slow”, “middle”, “fast”, “faster”. Membership function indicates the degree of membership that the exact quantity converted to the corresponding fuzzy subset, for example, when the temperature of 0 °C, it is considered that the membership degree that 0 °C converted to fuzzy subset “L” is 1 and converted to other subsets is 0. There are many methods to establish membership function, such as fuzzy statistics method, example method, expert experience method and so on. The fuzzy control system of the intelligent screw extruder uses the expert experience method to establish membership function, it is based on the operational experience accumulated in the actual control process and the specific environment of the application, it also can be further adjusted in the practice process to achieve the most suitable control effect. In the fuzzy control system, the membership functions of “temperature”, “pressure”, “pressure change rate” and “speed” are named as “T”, “P”, “PC” and “S” respectively. Their specific shape is shown in the figure below (Figs. 3, 4, 5 and 6):

Fig. 3. Temperature ‘T’ membership function

Fig. 4. Pressure ‘P’ membership function

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Fig. 6. Speed ‘S’ membership function

The control system of screw extruder is a three-input and single-output system, then the fuzzy inference rule adopts the form of IF A AND B AND C THEN D, which is interpreted as if all three conditions of A, B and C for the three input signals are satisfied at the same time, the output is D. Corresponding to inputs a, b, c, and output d, the subsets about fuzzy variable linguistic are A, B, C and D, the inner product of each subset is the total fuzzy relation ‘Y’ of the system [5]. According the actual demand to formulate inference rules, for example, when the temperature ‘T’ in the low temperature ‘L’, if the ‘P’ belongs to low pressure ‘NB’, and “PC” belongs to the “NB”, namely that at this time there aren’t many oilseeds in the chamber and the quantity of oilseeds presents the trend of reduce rapidly. Therefore, the oil press motor should run at low speed “NB” state, described with fuzzy inference rules: IF T = L AND P = NB AND PC = NB THEN S = NB. The fuzzy control system of screw extruder is determined by 75 fuzzy inference rules, and each control rules connected by logic ‘OR’. The specific fuzzy inference rules are shown in the table below (Table 1). Table 1. The fuzzy rule T=L P PC NB NB NB NS NB ZO NB PS NS PB ZO

T=M NS NB NB NS ZO ZO

ZO NB NS ZO PS PS

PS NS NS ZO PS PB

PB NS ZO PS PB PB

NB NB NB NS ZO ZO

NS NB NS ZO ZO PS

T=H ZO NS ZO PS PS PB

PS NS ZO PS PB PB

PB ZO PS PB PB PB

NB NB NS ZO ZO PS

NS NS ZO ZO PS PS

ZO ZO PS PS PB PB

PS ZO PS PB PB PB

PB PS PB PB PB PB

For accurately input information a1, b1 and c1, the fuzzy operations about outputting d1 is [5]

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d1 ¼ ðA  B  CÞ
Y

ð1Þ

‘Y’ is total fuzzy relation, ‘A’, ‘B’ and ‘C’ are the fuzzy variable subsets corresponding to the input respectively. The fuzzy controller outputs a fuzzy set after reasoning operation, and the defuzzification of output is aim to transform the fuzzy set into an accurate value which can be recognized and applied by machine. There are also many methods about defuzzification, the maximum membership degree method and weighted average method are commonly used. The maximum membership degree method is to output the value corresponding to the maximum membership degree, if multiple values are corresponding to the maximum membership degree, the average value is taken, this method is simple in calculation but prone to error, and is only applicable to environments with low control requirements [6]. For weighted average method, the output is the weighted average value of all outputs corresponding to their membership degree. When the information points are discrete, the calculation formula of the weighted average method is: Pn 1 Xi lðXi Þ Q¼ P n 1 lðXi Þ

ð2Þ

lðXi Þ is the membership degree of Xi corresponding to the membership function. Compared with the maximum membership degree method, the weighted average method has more complicated calculations and the higher control precision. In order to improve the precision of control for oil press motor, the weighted average method is chosen to complete defuzzification. 2.3

The Design of Software System

The software system of Screw extruder is mainly divided into PLC programing and the configuration of monitoring system on upper computer. The program design of PLC controller about fuzzy control algorithm is implemented by TIA Portal software. In order to simplify programming and make the control system with the character of good real-time, the calculated fuzzy control table is stored in the PLC memory. After received the real-time data which update by temperature and pressure sensors, the PLC queries the fuzzy control table based on the quantized input values to output the suitable speed value, finally, the output speed value is converted into a control signal of variable-frequency drive to adjust the speed of the oil press motor [7]. The simplified program makes the control process more efficient and straightforward, meets the realtime requirements, and improves the overall efficiency of production (Fig. 7).

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Fig. 7. The flow chart of fuzzy control algorithm program

The configuration of monitoring system on upper computer is achieved by Kingview software. TCP/IP communication protocol is adopted between Kingview software and PLC. According to data type and register address, data can be directly read or modified. Therefore, the monitoring system on upper computer can not only read realtime data such as working voltage, current, electric energy and speed of motor but also achieve the function of issuing instructions such as formula. And the database and OPC functions of Kingview are used to collect and send a large number of essential parameters of the system to facilitate the analysis and improvement of the intelligent screw extruder control system.

3 Test Results and Analysis According to the designed control system of Screw extruder, a Mamdani fuzzy controller was established in the Simulink software package. After determined the membership function of input and output information and set fuzzy reasoning rules, several simulation tests were carried out. For the convenience of observation, setting the signal quantization factor of pressure and temperature as 0.1, the temperature range of 0–1500 °C, pressure range of 0–2000 MPa (Figs. 8, 9 and 10).

Fig. 8. The simulation result of S-T

Fig. 9. The simulation result of S-P/Pc

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Fig. 10. The simulation result of S-T/P/Pc simulation

As shown in the above three figures, when only the temperature signal is input, the speed of motor increases along with the rise of temperature, after the temperature signal maintained at 1500 °C, the speed value is 480 r/min and maintain stability. When only the pressure signal is input, the value of pressure signal increases to 2000 Mpa and remains stable, the maximum speed can reach 800 r/min, when the change rate of pressure signal decreases to 0, the speed can be maintained at 780 r/min. When above signals are input into the system at the same time, the maximum speed is maintained at 900 r/min.

Fig. 11. Pressure signal of trial operation

Fig. 12. The simulation result of trial operation

Figure 11 shows the pressure information collected during a trial operation of the screw extruder. In order to verify the rationality of the control system under the actual load condition, taken a simulate test of the pressure information above. A scale-up square wave signal is used to simulate the collected information, the result is shown in Fig. 12. The control system can reasonably adjust the speed of the motor according to the change of the actual load. It can be seen from the simulation results, the speed of motor will change as the input signal changes, and the response time is within the acceptance range, indicating that the system in real-time. When the temperature and pressure signals remain constant, the motor speed will also remain unchanged, meaning that the system has a certain stability. Since the speed control of the oil press motor conforms to the fuzzy control rules, it can make the motor run at an appropriate speed and can better simulate

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the control experience of workers in practical application. According to the results of multiple simulations, the fuzzy controller shows a good applicability in different application environments.

4 Conclusion Based on the previous control experience, this paper designs a fuzzy control algorithm and applies it to the screw extruder control system. It improves the traditional screw extruder control mode which relies on manual control, and improved screw extruder can automatically adjust the oil press motor speed according to the temperature and pressure information in the chamber to achieve requirements of the automatic control. In this system, Siemens CPU1215C is selected as the central controller, the fuzzy control algorithm and the modules of system software and hardware are designed. Several simulation tests were carried out through the MATLAB software, the test results meet the actual control requirements. The improved intelligent screw extruder control system not only reduces the labor intensity, but also ensure the stability of product quality, and the production test goes well.

References 1. Gao J (2010) Present state and countermeasures for spiral oil press industry. Agric Sci Technol Equipment 4:116–118 2. Wang J, Zhang Y (2012) Current status of screw presses at home and abroad. Charming China 32:185 3. OuYang S, Zhou Q, OuYang X (2005) Study and application of fuzzy-controller based on PLC. Mach Tool Electric Apparatus 32(3):28–31 4. Perez IG, Godoy AJC, Godoy MC (2015) Fuzzy controller based on PLC S7-1200: application to a servomotor. In: International conference on informatics in control. IEEE 5. Luo J, Wang L (2010) Application of the fuzzy prediction based on PLC in variable water flow system for heat pump air-conditioning. Electric Drive 40(5):53–55 6. Tan Y, Chen C, Zeng L (2010) Program design of PLC fuzzy control. J Inf Eng Univ 11(1) 7. Bai G, Jin M (2018) Adaptive fuzzy control of DC belt conveyor system based on PLC. Coal Technol 37(12)

Tracking via Enhanced Context-Aware Correlation Filter Mianlu Zou, Zhongyi Hu(&), Qi Wu, and Changzu Chen Intelligent Information Systems Institute, Wenzhou University, Wenzhou 325035, Zhejiang, China [email protected] Abstract. The tracking method based on correlation filtering is widely used, because of its superior performance and high frame rate in large data sets. A significant amount of recent researchers focus on the incorporation of stronger features for a richer representation of the tracking target, but ignore the fitting accuracy between samples and regression target. In this paper, based on correlation filter model and context clues, more discriminant information is provided during the tracking, to solve the interference such as occlusion and inplane rotation. In addition, as the introduction of contextual clues cause unnecessary loss, this paper analyzes the regression, establishes an optimized target regression model, and inhibits it through regression parameters to reduce information loss. Extensive experiments proved the advancement of the proposed algorithm. Keywords: Correlation filter Tracking


Context-aware
Enhanced regression model


1 Introduction Visual tracking is one of core tasks in computer vision, and has many applications including video monitor, motion analysis and recognition, abnormal event monitoring and human-computer interaction. Generally speaking, the target tracking task refers to the single target tracking task, that is given an image sequence, a rectangular box is given in the first frame, and then the tracking algorithm needs to track the target in the subsequent frames [1]. Tracking algorithms can be divided into two categories: discriminant method [1–7], and generating method [8–14]. Discriminant methods learn features by using foreground and background information, such as multiple instance learning MIL [2], correlation filtering [1, 3, 6, 7]. Generative methods represent the tracking problem as searching the area most similar to the target. Typically generative methods including quantum space learning [12], sparse representation [8, 11, 14–16], probability model [13]. In many cases, the tracking results of the above methods are promising, but in complex environments, the appearance of the target is affected by multiple factors at the same time (such as occlusion interference, in-plane and put-of-plane rotation, deformation, illumination change, background clutter, etc.), and the performance of these complex situations is not good. In this paper, discriminant method based on the correlation filtering framework, combined with the context awareness model, is © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 268–276, 2020. https://doi.org/10.1007/978-981-32-9698-5_31

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introduced, to achieve fast processing speed, strong discrimination. At the same time, due to the introduction of context information, which will introduce unnecessary information loss, this paper introduces regression parameters for enhanced processing of the model. The experimental results show that the proposed algorithm has better performance in discrimination, especially the introduction of regression, which can better deal with occlusion interference and in-plane rotation.

2 Context-Aware Framework Context model has been proposed for tracking for a long time [17]. It can detect opponents and supporters, i.e., namely background and target, by using sequence random forest, online template and local feature based on appearance model. In recent years, context information of a scene has been used in multi-level clustering to detect similar targets or possible interference [18]. A global dynamic constraint is used for online learning to identify interference terms in interested objects. Partial background information of the target has a great impact on tracking performance [19]. For example, if occlusion or background clutter is severe, context cues provide important clues for successful tracking, so adding context information in the filter learning stage can help improve tracking performance. Context information can help tracking target, especially when the target is severe occlusion, drastic change or motion blur. STCL [20] uses the context model for visual tracking, and utilizes the spatio-temporal relationship between the target and its local context under the Bayesian framework. BACF [21] utilizes background aware and uniquely models the foreground and background of targets. This paper is inspired by the CACF [19], based on the correlation filtering, taking into account the global context, but it differs from CACF [19], which not only considers the context information, but also constructs a new objective function to adapt the regression target. In order to make the training sample label more reasonable and accurate, this paper analyzes the context model, regression target according to the introduction of the context information, to improve the context-aware model is shown in Fig. 1: Training sample

Context clues

Learning model

Learning model

Response score

+ Testing sample

Fig. 1. Context-aware framework for tracking

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In Fig. 1, the first row and the second row represent the training process and the detection process, respectively. In the training stage, the training image block sampled at the current frame position and the context sample cropped around the target should be considered when learns the model. In the detection stage, when the target is heavily occluded, the appearance model containing the context information will help to locate the target according to the foreground and context.

3 Regression Model 3.1

Formulation Model

First of all, Establishing a regression model (1), for constructing expected output f ðzÞ, i.e., the value of regression, to fit target model. In addition, the purpose of general regression is to minimize the error between the expected output and the actual output. f ðzÞ ¼ wT z

ð1Þ

In the above equation, z is the input data, w is the parameter matrix filter of the regression model, f ðzÞ is the result of regression, i.e., response value. The loss function of the ridge regression, which is added the norm of the parameter w as the penalty term on the basis of the Least Square, as shown in (2). X min ð f ðxi Þ  yi Þ2 þ kkwk2 ð2Þ w

i

xi denotes the input sample. Finally, yi denotes actual output. by minimizing the loss function, the solution is obtained. ^ ¼ diagð w

^x  ^y Þ ^x  ^x þ k 

ð3Þ

^x denotes the value of sample after Fourier transform, ð^ xÞ denotes the autox  ^ correlation of the signal x. 3.2

Enhanced Regression Model

After comprehensive consideration of the introduction of context and the establishment of the original objective equation, the predefined Gaussian shaped label is optimized for specific analysis. And regression parameter e is used to suppress expected output. After the introduction of context, its peak value remained unchanged, but the shape would tend to flatten, as shown in Fig. 2. The variation is from (4) to (5). yi ¼

  1 ð x2 þ y2 Þ exp  2pr2 2r2

ð4Þ

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yi ¼

 e 1 ð x2 þ y2 Þ exp  2pr2 2r2

Predefined Gaussian label

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ð5Þ

Improved regression objective

Fig. 2. Optimized regression objective

Where e denotes regression parameter. ðx; yÞ denotes the spatial location of feature vector x. r denotes spatial bandwidth. The explanation of the change from (4) to (5): This study is based on DCF_CA [19], which is based on DCF model [7], i.e., correlation filter and context framework mode. Due to the introduction of the context, the model of the original fitting regression equation further needs to be optimized. The general way to solve the loss function is to employ the Least Square method, through the derivative to find the minimum. Followup improvements are added constraints, such as spatial regularization [22], spatiotemporal regularization [23], context-aware [19], as well as the background-aware [21], etc., to optimize the model. Generally, researchers are utilizing Gaussian function to simulate the regression to adapt desired target response, the regression equation may not be optimal. Because during correlation filter, the partly context information is filled in. In fact, Gaussian shape of fitting target image is sharp. With adding context-aware, due to the model bounds the background and target region, i.e., highlighting the target area and suppressing background region in the large range, so the actual generated image should be in a state of gentle.

4 Experimental Results 4.1

Parameters Configuration

In the whole experiment, in order to achieve optimal performance, the regularization parameter k ¼ 104 in the Eqs. (2) and (3), regression parameter e ¼ 0:9 and spatial bandwidth r ¼ 0:1 in Eq. (5).

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Quantitative Analysis

In order to validate the effectiveness of the algorithm in this paper, the proposed algorithm is compared with four state-of-the-art algorithms in 10 image sequences [24, 25] in the visual tracking standard data sets. Table 1 is the information and properties of the test sequences. The four algorithms are CT [26], DCF_CA [19], TLD [4] and MOSSE_CA [19], respectively. All tracking algorithms are implemented on the same workstation, Matlab2016a, inter(R) Core(TM) i5-4590 [email protected] GHz, 8 GB. The evaluation method of visual tracking formulated in [24], obtain wide acknowledgement. So this paper adopts the success evaluation defined by [24]. And based on the definition of three methods [24], this paper utilizes them to assess initialization sensitivity of tracker. Three models are one pass estimation (OPE), spatial robustness estimation (TRE), and temporal robustness estimation (SRE). Please refer to reference [24] for more details. Table 1. The information and properties of test sequences. Where Y denotes yes, N denotes no. sequences Properties Resolution Frames Background blur

Motion blur

Illumination Rotation Occlusion Scale Deformation Fast motion

Crossing

360  240

120

Y

N

N

Y

N

Y

Y

Y

Dancer

320  246

225

N

N

N

N

Y

Y

Y

N

Freeman1

360  240

326

N

N

N

Y

N

Y

N

N

Gym

426  234

767

N

N

N

Y

N

Y

Y

N

Kitesurf

480  270

84

N

N

Y

Y

Y

N

N

N

Singer2

624  352

366

Y

N

Y

Y

Y

Y

Y

N

Rubik

640  480 1997

N

N

N

Y

Y

Y

N

N

Tiger1

640  480

N

Y

Y

Y

Y

N

Y

Y

354

Suv

320  240

945

N

N

N

Y

Y

N

N

N

Vase

320  240

271

N

Y

N

Y

N

Y

N

N

Experimental results as shown in Fig. 3, by analyzing the data, one can know that the proposed algorithm’s (DCFF) success plots in OPE, SRE, TRE three initialization conditions are 0.505, 0.492, 0.582, respectively. The overall experimental performance compared with DCF_CA [19] is improved. Figure 4 shows that under the occlusion interference, the success plots of the proposed algorithm are 0.543, 0.531, 0611, respectively. Figure 5 shows that, in-plane rotation, the success plots of proposed

Fig. 3. The overlap success plots of OPE, SRE, and TRE

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Fig. 4. The overlap success plots of OPE, SRE, and TRE under occlusion

Fig. 5. The overlap success plots of OPE, SRE, and TRE under in-plane rotation

algorithm under the three evaluation ways are 0.538, 0.521, 0.600 respectively. Overall assessment results, show that the performance of the proposed algorithm is better. Figures 4 and 5 show that the proposed tracking algorithms have better performance in dealing with occlusion and processing in-plane rotation. The proposed algorithm is based on context awareness, optimizes the regression equation of the target, and reduces the drift phenomenon in the process of tracking. DCF_CA [19] takes context information into consideration, but does not consider the reconstruction of the regression model to improve the algorithm performance. CT [26] uses compressed domain features extracted by random observation matrix, which will focus on the expression of target texture features. And under the condition of the background clutter or illumination change, CT [26] is not stable. TLD [4] will combine detection and track implementation, together with learn model, when it appears errors, the error will cycle accumulation, leading to the final tracking failure, so the tracker model is not highly robust. In this paper, proposed algorithm can achieve fast speed and high robustness, which is based on correlation filter, combines context and optimizes the regression objective equation. 4.3

Qualitative Analysis

Figure 6 shows the tracking results for 5 algorithms. The experimental results demonstrate that the impact of different degree in dealing with the interference. The visualization results are the tracking bounding box, which represents the tracking position of target, also reflect the precision of tracking. The proposed algorithm is relatively stable during the tracking, because the relationship between the context

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Dancer

Gym

Rubik

Tiger

Vase

DCFF(Ours)

MOSSE_CA

CT

DCF_CA

TLD

Fig. 6. Partial rectangle boxes of tracking results

model can increase the samples region, which makes the performance improvement. At the same time, the proposed still has improvement room to make tracker stronger robustness when the target appearance under significant appearance variation. Of course, the state-of-the-art algorithm may not address all the challenges for processing, but also in dealing with some special changes show superior performance.

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5 Conclusion Based on correlation filter model and context clues, this paper provides more discriminant information in the process of tracking, which can well overcome the interference such as occlusion and in-plane rotation. In addition, this paper analyzes regression function. Because of the introduction of context clues, it will cause unnecessary information loss. In order to deals with the problem, this paper establishes optimized regression equation through introducing regression parameter, i.e., further fitting model to reduce the information loss. Experimental results also show that the establishment of the target equation need to combine sampling of the sample space structure. Extensive experiments prove that the proposed algorithm is advanced compared with other state-of-the-art algorithms. Acknowledgement. This work is supported by the Natural Science Foundation of Zhejiang Province (project No.: LY16F020022). And Wenzhou science and technology planning project (project No.: S20180017). The author is grateful to the anonymous referee for the careful checking of the details of this paper and for helpful comments and constructive criticism.

References 1. Henriques JF, Caseiro R, Martins P, Batista J (2015) High-speed tracking with kernelized correlation filters. IEEE Trans Pattern Anal Mach Intell 37(3):583–596 2. Babenko B, Yang M-H, Belongie S (2009) Visual tracking with online multiple instance learning. In: CVPR 3. Danelljan M, Hager G, Shahbaz Khan F, Felsberg M (2015) Learning spatially regularized correlation filters for visual tracking. In: ICCV 4. Kalal Z, Mikolajczyk K, Matas J (2012) Tracking-learning-detection. IEEE TPAMI 34(7):1409–1422 5. Zhang K, Zhang L, Yang M-H (2014) Fast compressive tracking. IEEE TPAMI 36(10):2002–2015 6. Bolme DS, Beveridge JR, Draper BA et al (2010) Visual object tracking using adaptive correlation filters. In: IEEE conference on computer vision and pattern recognition, CVPR 2010, San Francisco, CA, USA, pp 13–18 7. Henriques JF, Caseiro R, Martins P et al (2012) Exploiting the circulant structure of tracking-by-detection with kernels. In: Computer vision–ECCV 2012. Springer 8. Bao C, Wu Y, Ling H, Ji H (2012) Real time robust l1 tracker using accelerated proximal gradient approach. In: CVPR 9. Fan H, Xiang J (2016) Robust visual tracking with multitask joint dictionary learning. IEEE TCSVT 27:1018–1030 10. Fan H, Xiang J, Liao H, Du X (2015) Robust tracking based on local structural cell graph. JVCIR 31:54–63 11. Mei X, Ling H (2011) Robust visual tracking and vehicle classification via sparse representation. IEEE TPAMI 33(11):2259–2272 12. Yang G, Hu Z, Tang J (2018) Robust visual tracking via incremental subspace learning and local sparse representation. Arab J Sci Eng 43(2):627–636 13. Wang D, Lu H (2014) Visual tracking via probability continuous outlier model. In: CVPR

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14. Zhang T, Bibi A, Ghanem B (2016) In defense of sparse tracking: circulant sparse tracker. In: CVPR 15. Xiao L, Xu MH, Hu ZY (2018) Real-time inland CCTV ship tracking. Math Probl Eng 1–10 16. Xiao L, Wang H, Hu Z (2018) Visual tracking via adaptive random projection based on subregions. IEEE Access 6:41955–41965 17. Dinh TB, Vo N, Medioni G (2011) Context tracker: Exploring supporters and distracters in unconstrained environments. In: 2011 IEEE conference on computer vision and pattern recognition (CVPR), pp 1177–1184 18. Xiao J, Qiao L, Stolkin R, Leonardis A (2016) Distractor-supported single target tracking in extremely cluttered scenes. Springer, pp 121–136 19. Mueller M, Smith N, Ghanem B (2017) Context-aware correlation filter tracking. In: IEEE conference on computer vision and pattern recognition (CVPR). IEEE Computer Society, pp 1387–1395 20. Zhang K, Zhang L, Liu Q, Zhang D, Yang M-H (2014) Fast visual tracking via dense spatiotemporal context learning. In: Proceedings of the European conference on computer vision, pp 127–141 21. Galoogahi HK, Fagg A, Lucey S (2017) Learning background-aware correlation filters for visual tracking. In: Proceedings of the IEEE international conference on computer vision, pp 1144–1152 22. Danelljan M, Hager G, Khan FS, Felsberg M (2015) Learning spatially regularized correlation filters for visual tracking. In: Proceedings of IEEE international conference on computer vision 23. Li F, Tian C, Zuo W et al (2018) Learning spatial-temporal regularized correlation filters for visual tracking. In: 2018 IEEE/CVF conference on computer vision and pattern recognition, Salt Lake City, UT, pp 4904–4913 24. Wu Y, Lim J, Yang M-H (2013) Online object tracking: a benchmark. In: CVPR 2013, pp 2411–2418 25. Wu Y, Lim J, Yang M-H (2015) Object tracking benchmark. TPAMI 37(9):1834–1848 26. Zhang WZ, Ji JG, Jing ZZ et al (2015) Adaptive real-time compressive tracking. International conference on network and information systems for computers. IEEE

Optimization and Simulation of Fuzzy Control Based on SOA Rong Hua and Huanyu Zhao(&) Huaiyin Institute of Technology, Huai’an 223001, Jiangsu, China [email protected]

Abstract. Fuzzy control is one of the important branches of intelligent control. And its optimization problem has become more and more important. The knowledge base formed by the experience of the researcher can often determine the performance of the fuzzy controller. Therefore, the optimization of the fuzzy control is mainly the optimization of the knowledge base. This paper will focus on using the seeker optimization algorithm (SOA) to optimize the membership function in the fuzzy controller knowledge base. Through the Matlab simulation, the original fuzzy control is compared with the SOA fuzzy control. The results show that the control effect of SOA fuzzy control is better than that of original fuzzy control. Keywords: Fuzzy control
Seeker optimization algorithm Membership function
Matlab simulation




1 Introduction Fuzzy control is a new stage of development of automatic control. It can control complex and uncertain objects, and has great significance in real production. Because of the importance of fuzzy control, it has been well applied in various fields. Its optimization problem has always been the focus of people’s research. The optimization of fuzzy control is mainly to optimize the various parameters of the control process. The direction of optimization can be roughly divided into three directions: First, it can optimize the scale factor and quantization factor of fuzzy control, such as optimizing the fuzzy control factor by uniform design method [1], which enables the control object to respond in a shorter time and has no steady-state error. Second, it can optimize the membership function of fuzzy control. For example, using harmony search algorithm to optimize fuzzy control [2], set the bottom abscissa of the fuzzy membership function of the triangle to be fixed and then optimize the vertex abscissa of the trigonometric membership function by harmony search algorithm. The feasibility of optimization is proved by comparing the optimization results. Using the golden section to optimize the triangle membership function [3, 11]. Through simulation, the membership function of the golden section optimization, the membership function of the original uniform distribution, and the membership function of the golden section optimization of the uniform fuzzy set are compared. It is found that the control performance is significantly improved after using the golden section. Using genetic algorithm to optimize membership function [4]. By using the genetic algorithm based on improved coding method © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 277–285, 2020. https://doi.org/10.1007/978-981-32-9698-5_32

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and crossover operator to optimize the fuzzy control, it gives the ability of learning and accelerates the convergence speed. Third, optimizing the fuzzy rules of fuzzy control. Various algorithms are used to increase or decrease the fuzzy rules formed by the experience of the researchers, such as the improvement of fuzzy rules by genetic algorithms [5]. Through the optimization of genetic algorithm, the useless fuzzy control rules are eliminated, and the poor fuzzy control rules are optimized to better fuzzy control rules. The feasibility and effectiveness of the method are verified by comparison with PID control. Some studies not only optimize one of the three directions, but also optimize each direction at the same time, such as using genetic algorithm to encode the membership function parameters together with the fuzzy rules and optimize them [6], The feasibility is proved by simulation, and it is found that the optimized fuzzy control still has good control performance for the unlearned desired trajectory; The immune genetic algorithm simultaneously optimizes the membership function, scale factor and quantization factor [7]. The feasibility of simultaneous optimization is proved by comparing the single parameter and multi-parameter optimization of genetic algorithm and immune genetic algorithm. Most of the above studies are optimized by genetic algorithms, and most of the optimized membership functions are triangle membership functions. Inspired by the above research, this paper proposes the optimization and simulation of fuzzy control based on seeker optimization algorithm. The triangulation membership function and the trapezoidal membership function in fuzzy control are optimized by a novel swarm intelligence algorithm to optimize the fuzzy control. The simulation results show that the method is feasible and reliable.

2 Fuzzy Control Fuzzy control is based on fuzzy theory, which has a good control effect on controlled objects that are difficult to determine their mathematical model [10]. In fuzzy theory, the relationship between an element and a set is not a vested relationship, but the degree to which the element belongs to the set represents the relationship between them. The membership function represents the degree of attribution of each element to the domain, and then transforms the control experience that is usually accumulated into multiple control rules. Through the comparison of fuzzy sets and fuzzy control rules, intelligent fuzzy control is realized through computer processing.

Knowledge base Input variable

Fuzzification

Fuzzy input

Fuzzy reasoning

Fuzzy output

Fig. 1. Fuzzy control system

Anti-fuzzification

Precise output

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A complete fuzzy control system is shown in Fig. 1. The fuzzy system is mainly divided into four parts: fuzzification, knowledge base, fuzzy reasoning and antifuzzification [14]. 2.1

Fuzzification

Fuzzification refers to the conversion of accurate input values into fuzzy input values [13]. Generally, the system error, error variation, and error change are selected as inputs. These three inputs determine that the input of the fuzzy control system can be one-dimensional, two-dimensional and three-dimensional, but the one-dimensional will result in poor control effect due to the small number of dimensions, and the threedimensional will be difficult to realize due to the excessive number of dimensions. Therefore, most fuzzy controls use two-dimensional input. In this paper, the system error and the error change are selected as fuzzy input, which are respectively set to e and ec. The process of fuzzification is to convert the exact input e and ec into fuzzy input. The fuzzified fuzzy quantity does not represent a specific number. It represents an interval, which is described by fuzzy linguistic variables. The fuzzy variable and the exact quantity can be converted by the quantization factor. 2.2

Knowledge Base

The knowledge base contains the knowledge and control objectives of the application domain, usually composed of two parts: the database and the fuzzy control rule base [8]. The database contains membership functions and fuzzy control rules. The membership function is an important part of the knowledge base. It can accurately describe the fuzzy set. There are four commonly used membership functions: triangular membership function, trapezoidal membership function, Gaussian membership function and generalized bell type membership function [8]. The formulas of the triangle membership function and the trapezoidal membership function are shown in Eqs. (1) and (2). 8 > > < 0 x  a; x  c triangleðx; a; b; cÞ ¼ xa axb > > ba : cx b xc cb

ð1Þ

where a, b, and c are the abscissas of the three vertices of the triangle, respectively, and x is the domain of the fuzzy set, requiring a < b < c.

trapezoidðx; a; b; c; dÞ ¼

8 > > > >0
> 1 > > : cx

cb

x  a; x  d axb bxc bxc

ð2Þ

where a, b, c, and d are the abscissas of the four vertices of the trapezoid, respectively, and a < b < c < d is required.

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This paper uses the seeker optimization algorithm to optimize the parameters a, b, c, d of the membership function to optimize the fuzzy control. The fuzzy control rules are formed by the experience of the control personnel, and its essence is a summary of the operational experience. There may be multiple fuzzy control rules, but too many control rules will lead to complicated calculations. Too few control rules will result in poor control performance. The fuzzy control rule can reflect the relationship between the input and output of the fuzzy control through the conditional statement of If-AndThen. 2.3

Fuzzy Reasoning and Anti-fuzzification

The fuzzified input quantity combines the control factor, the membership function and the fuzzy control rule in the knowledge base, and the fuzzy output can be obtained through fuzzy reasoning [12]. There are two methods of synthetic reasoning. One is generalized reasoning and the other is generalized refusal. In fuzzy control, generalized inference is used [8], that is, premise 1: x is A′, premise 2: if x is A then y is B, and conclusion: y is B′. Anti-fuzzification is the conversion of fuzzy output into accurate output. There are generally three methods: the maximum membership degree criterion, the median method and the center of gravity method.

3 Seeker Optimization Algorithm The seeker optimization algorithm (SOA) is a search that directly applies human intelligent search behavior to the optimal solution. Its search principle is determined by the pros and cons of the current solution. If the current solution is poor, the optimal solution is searched in a larger neighborhood. If the current solution is better, the optimal solution is searched in a smaller neighborhood. The individual’s search direction is to simulate the four behaviors of human beings. First, self-interested behavior: human beings will consider for themselves. Individuals in the seeker optimization algorithm also search for positions that are good for them and move. Second, altruistic behavior: humans want to be able to help others or get help from others. Individuals in the seeker optimization algorithm search for the best location and move through mutual help and communication between individuals. Third, pre-action: human beings can guide future events based on past experience. Individuals in the seeker optimization algorithm can also use past experience to guide the search for the best location. Fourth, uncertain behavior: human thinking is uncertain. The individual in the seeker optimization algorithm also searches for the optimal solution in the large neighborhood of the poor solution or the small neighborhood of the better solution because of the uncertainty. The seeker optimization algorithm the search direction and the step size according to the target function value of each individual and updates the position. The search step is the formula (3), and the search direction are the formulas (4) and (5) [9].

Optimization and Simulation of Fuzzy Control

aij ¼ dij

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  lnðuij Þ

281

ð3Þ

where uij is the membership degree of the objective function value i of the jdimensional search space, and dij is the Gaussian membership function parameter. 8! ! ! > < d i;ego ðtÞ ¼ p i;best ðtÞ  x i ðtÞ ! d i;alt ðtÞ ¼ ! g i;best ðtÞ  ! x i ðtÞ > : ! d i;pro ðtÞ ¼ xi ðt1 Þ  xi ðt2 Þ

ð4Þ

! ! ! ! d ij ðtÞ ¼ signðx d ij;pro þ u1 d ij;ego þ u2 d ij;alt Þ

ð5Þ

! ! ! ! where d ij ðtÞ is the search direction of the individual, d i;pro ; d i;ego ; d i;alt are the predirection, self-interest and altruism, respectively. ! p i;best is the best position of the ! ! x i ðt2 Þ are the best positions individual, g i;best is the best position of the whole, x i ðt1 Þ; !   x i ðt  1Þ; ! x i ðtÞ , respectively. signðÞ is a symbol function, x; u1 ; u2 in ! x i ðt  2Þ; ! are the weights in all directions, x is the inertia weight, u1 ; u2 are constants in [0, 1]. After the search step and search direction are determined, the location can be updated. The update formulas for the position are formulas (6) and (7). In the update process of the location, it is judged whether the condition of the search stop is satisfied. If it is satisfied, the iteration is stopped. And if it is not satisfied, the iteration is continued. Dxij ðt þ 1Þ ¼ aij ðtÞdij ðtÞ

ð6Þ

xij ðt þ 1Þ ¼ xij ðtÞ þ Dxij ðt þ 1Þ

ð7Þ

4 Algorithm and Simulation All the simulation processes in this paper are realized by MatlabR2014a. The seeker optimization algorithm is used to optimize the membership function of fuzzy control, and the control effects of original fuzzy control and SOA fuzzy control are compared. Both control approaches use the same fuzzy set, control factor and control rules. In this paper, two kinds of control method are used to simulate the control of the step response of a typical second-order system. The transfer function of a typical second-order system is set to formula (8). GðsÞ ¼

1:6s2

20 þ 4:4s þ 1

ð8Þ

The two fuzzy control inputs e and ec are set in [−6, 6], and the output u is set in [−3, 3]. The two inputs and outputs take five fuzzy subsets {NB, NS, ZR, PS, PB},

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which represent {negative big, negative small, zero, positive small, positive big}. Fuzzy control rules are shown in Table 1. Table 1. Fuzzy control rules e and ec NB NS ZR PS PB NB PB PB PS PS ZR NS PB PS PS ZR ZR ZR PS PS ZR ZR NS PS PS ZR ZR NS NS PB ZR ZR NS NB NB

The number of fuzzy control rules in this paper is 25. These fuzzy control rules express the control relationship between input and output. For example, when the fuzzy input error is negative enlargement and the error change is negative enlargement, the fuzzy control output needs to be made to be positive enlargement. The relationship among the three is obtained from the usual control experience. 4.1

SOA Fuzzy Control

The SOA fuzzy control optimizes the membership function of the original fuzzy control. There are 15 fuzzy subsets in the input and output, and each subset corresponds to a membership function. Among them, the trapezoidal membership function needs to be optimized with 4 parameters, and the triangular membership function needs to be optimized with 3 parameters. The two output fuzzy subsets are four trapezoidal membership functions and one triangular membership function, with a total of 38 parameters. An output fuzzy subset has two trapezoidal membership functions and three triangular membership functions with a total of 17 parameters. Hence the parameters of the membership function to be optimized by SOA are 55. When SOA optimizes parameters, we need to choose the appropriate fitness function to evaluate the advantages and disadvantages of individuals and the whole. In this paper, the time integral of the absolute value of the error and the square of the control output is taken as the fitness function. To reduce the overshoot, it is also introduced into the fitness function. The formula is formula (9). Z F¼

1

ðx1 jeðtÞj þ x2 u2 ðtÞ þ x3 jeðtÞjÞdt

ð9Þ

0

where x1 ; x2 ; x3 are the weights of the respective integral terms. The first two terms are the squared term of the error term and the control output, and the latter term is the penalty term introduced when overshoot occurs, requiring x3  x1 . It takes values x1 ¼ 0:999; x2 ¼ 0:001; x3 ¼ 150, respectively, in this paper. The SOA fuzzy control is as follows: First, the population size is set to 50, and the maximum number of iterations is 50. When the maximum number of iterations is reached, the search will stop. The spatial dimension is the parameter that needs to be

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optimized. It is set to be 55 in this paper. Set the maximum and minimum values of each individual, and then initialize the individual individuals so that each individual is randomly distributed in the fuzzy interval. By calculating the individual’s fitness function, it is worthwhile to get the global best and the individual best. Then update the position according to the search direction and the step size, and find the optimal solution. By using the optimization of SOA, the process of adapting its fitness function is shown in Fig. 2.

Fig. 2. Change in fitness function

The optimal fitness value is fbest ¼ 101:5839. The comparison of the membership function of the input fuzzy e of the original fuzzy control and the SOA optimized fuzzy control is shown in Fig. 3.

(a) Original membership function

(b) Optimized membership function

Fig. 3. Comparison of membership functions

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Comparison and Analysis of Results

The original fuzzy control and the SOA-optimized fuzzy control are used to simulate the step response control of Eq. (8), respectively. The simulation results are shown in Fig. 4.

Fig. 4. Comparison of original fuzzy control and SOA fuzzy control

It can be seen from Fig. 4 that the SOA fuzzy control has faster response time, smaller overshoot and smaller steady-state error than the original fuzzy control, which proves the feasibility and reliability of SOA for fuzzy control optimization.

5 Conclusion This paper has used the seeker optimization algorithm to optimize the membership function in the fuzzy controller knowledge base. The parameters of the fuzzy control triangle membership function and the trapezoid membership function have been optimized by Matlab simulation. The parameters of the two membership functions are used as the object of the seeker optimization algorithm optimization. The time integral of the absolute value of the error and the square of the control output has been set as the fitness function, and the overshoot penalty has been introduced to perform the optimal search of the parameters. By comparing the original fuzzy control with the SOA fuzzy control, it can be found that the control effect of SOA fuzzy control is better than that of the original fuzzy control.

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Acknowledgments. This work was supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. SJCX 18_0906) and the Natural Science Foundation of Huaiyin Institute of Technology (Grant No. 18HGZ002).

References 1. Zhou W, Zhu J (2002) On-line optimization of fuzzy control factor by uniform design method. Ind Control Comput (04):31–34 2. Xu W, Fei M (2012) Design and implementation of circulating fluidized bed temperature control based on harmonic optimization fuzzy controller. Instrum Technol (10):30–32+35 3. Fang Q (2003) Optimal design of fuzzy control membership function. J Electron Meas Instrum (03):42–45 4. Xia C, Guo P, Shi T, Wang M (2005) Adaptive control of brushless DC motor based on fuzzy genetic algorithm. Proc CSEE (11):129–133 5. Zhang W, Lu Y (2003) Mobile robot navigation based on improved genetic algorithm and fuzzy logic control. Robot (01):1–6 6. Jin Y, Jiang J (1996) Optimization of fuzzy control rules based on evolutionary computation. Control Decis (06):672–676 7. Huang H, Li A, Lin X (2007) Fuzzy control method based on immune genetic algorithm optimization and its application. J Comput Appl (07):1737–1740+1750 8. Yu J (2008) Advanced Control Technology in Industrial Processes, vol 8, pp 232–239. East China University of Science and Technology Press, Shanghai 9. Yu S, Cao Z (2014) Parameter optimization of PID controller based on seeker optimization algorithm. Comput Simul 31(09), 347–350+373 10. Xuewei L, Lixin Ma, Yihu Y (2019) Research on fuzzy PID vector control based on fuzzy scaling factor optimization variable universe. Electr Power Sci Eng 35(02):14–19 11. Yannian W, Hao Z, Huan Y, Yanjie C, Wenting L (2018) Application of genetic algorithm optimization fuzzy PID controller in intelligent hydraulic servo control system. Foreign Electron Meas Technol 37(12):125–128 12. Kewang P, Xuyu L, Yayun S (2018) Fuzzy PID control of bridge crane based on particle swarm optimization. Meas Control Technol 37(10):127–131 13. Yanwei X, Donghui W (2018) Weight decision grey wolf optimization algorithm based on fuzzy control. Comput Syst 27(10):202–208 14. Wei C, Qiao W (2018) Research on motion control of crawler robot based on particle swarm optimization fuzzy PID. Mod Electron Technol 41(18):49–53

A New Fixed-Wing Formation Control Algorithm Xu Zeng1(&), Xinhua Wang1, Weicheng Xu1, Yu Zheng2, and Jiahuan Li1 1

College of Automation Engineering, NUAA, Nanjing 100191, China [email protected] 2 School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Abstract. This paper proposes a novel fixed-wing UAVs formation tracking algorithm which is called the Optimal Turning Radius (OTR) algorithm. And it introduces the concept of lead tracking point and lag tracking point near the tracking desired point, and divides the tracking distance into three situations such as fur distance, medium distance and close distance. When the leader flying in a straight line, the lateral command is mainly generated by the yaw error, and the desired yaw is calculated according to different situations of fur distance, medium distance and close distance. When the leader turns, the follower’s lateral command will add real-time feedback of leader’s turning radius to ensure that the follower can also quickly track the desired point during the turning process, so that the formation can quickly converge to the desired formation. And a lot of test flight demonstrations show that it has the better performance than the L1 nonlinear guidance law and the traditional PID control law in the formation tracking base on Leader-Follower mode. The test results of two small UAVs tracking virtual leader show that the tracking error is with-in 2 m in the straight line segment. And in the turning section, the formation convergence speed is within 3 s. Keywords: Leading lag point tracking technology
Optimal Turning Radius
Fixed-wing UAV formation technology Virtual leader




1 Introduction With the rapid development of microelectronic sensors, embedded processors and communication technologies, multi-UAV formation control system has become a widely studied research field. Formation control technology has very important engineering application value in scientific research, transportation, geological survey and future defense field [1–3]. In recent years, many researchers proposed many different multi-UAV formation control algorithms and strategies. The relatively mature and common formation control methods are: (1) Leader-Follower [4]; (2) Behavior-based method [5]; (3) Virtual structure method [6]. And each control form has its own advantages and disadvantages. © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 286–298, 2020. https://doi.org/10.1007/978-981-32-9698-5_33

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In the “Leader-Follower” mode, one of the UAV in the formation is used as leader, while the other UAVs are used as a follower. Each of the followers in the formation tracks a fixed deviation relative to the leader, thus maintaining the formation. In [7], a formation control method for multi-UAV and same direction mission requirements is proposed. Using the leader-follower structure formation model to control formation flight, taking the formation trace coordinate of leader UAV as the reference coordinate system, and it realizes the relative position of follower UAVs and leader UAV. The advantage of this method is that the principle is simple and easy to implement. But the disadvantage is that the robustness and stability of the formation is too poor. If the leader fails, the entire formation will be out of control. Behavior-based method is a formation control method which simulates biological reaction behavior mechanism. It has good flexibility and robustness, but the disadvantage is that it cannot maintain the formation accurately, and it is difficult to analyze the stability of the system by mathematical methods. [8] has studied the behavior-based approach, but this research only stays at the theoretical level and has not been applied to engineering implementation. The virtual structure method (VSM) is to use the information sharing between the formations to maintain the formation accurately. However, in actual situation, it requires data transmission to support multi-point to multi-point network mode. At present, it is difficult to achieve this requirement for telemetry radio. Even with such telemetry radio, its communication distance, bandwidth and delay may not be suitable for actual needs. In order to effectively solve the problem of formation coordination control, this paper proposes an optimal turning radius (OTR) formation coordination algorithm based on virtual leader mode. Considering that the fixed-wing UAVs is different from helicopters and drones, it has the minimal stall positive speed and minimum turning radius limits. Therefore, the leading lag control model is adopted in the formation algorithm design. First, there is a leading point in the algorithm which can predict the future target of the desired point. This feature enables it to track the curve flight path closely. Secondly, the real-time turning radius of the leader UAV is added to the algorithm for feedback control. This parameter can ensure the fast synchronization of the leader behavior, and then improve the formation convergence speed. Thirdly, the algorithm adds a fixed deviation of the follower to leader in the lateral direction as feedback. This design allows the formation with lateral deviation to coordinate turns around the same center with different turning radius.

2 Virtual Leader Formation Strategy In this section, the formation control strategy of virtual leader is introduced, which is based on the secondary development of ArduPilot and Mission planner [9]. Virtual leader selects Software In The Loop (SITL) model of ArduPilot. SITL of ArduPilot allows us to run ArduPilot on PC directly, without any special hardware. It takes advantage of the fact that ArduPilot is a portable auto-pilot that can run on a very wide variety of platforms. PC is just another plat-form that ArduPilot can be built and run on. When running in SITL the sensor data comes from a flight dynamics model in a flight simulator. ArduPilot has a wide range of vehicle simulators built in, and can interface to several external simulators. The framework of SITL is shown in Fig. 1.

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Fig. 1. Framework of SITL

The running SITL is connected to the Mission planner ground station via TCP communication. The three-UAV formation information flow based on the virtual leader is shown in Fig. 2. SITL is chosen as the leader of the formation, which can achieve full-state control of the leader and provide more flexibility and scalability for the formation flight. For the centralized formation control of the ground station, the data transmission rate of the virtual leader can be increased, and a higher frequency control command transmission can be provided for the follower. This does not affect the data transmission of the actual follower flight.

Fig. 2. Three-UAV formation information flow based on the virtual leader

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3 Optimal Turning Radius Principle The fixed deviation of follower relative to leader is Offsetðx; y; zÞ, the leader’s coordinate is Leader ðlat; lng; altÞ, and the follower’s coordinate is Followðlat; lng; altÞ. The desired position Targetðlat; lng; altÞ of the follower can be calculated based on the Offsetðx; y; zÞ and Leader ðlat; lng; altÞ. A challenge in the formation tracking process is the desired path oscillation during the turning process, and the phenomenon is that the roll angle is oscillating and the heading is opposite. To solve this problem, we introduce the lead tracking point and the lag tracking point near the actual desired tracking point, and add the real-time turning radius of the leader as feedback. The design of the lead tracking point can effectively solve the lateral oscillating problem caused by the overturning of the desired point. The introduce of the lag tracking point enables the follower to maintain the tracking ability at a long distance. The lead tracking point is defined as targetleader and the lag tracking point is targettrailer, the distance between the current position of the follower and the leader is L. Defining far means that the distance is far, and close means that the distance is closer, then the calculation formula of the desired position of the follower is: 8 > < targettrailer L [ far target¼ Target close\L\far > : targetleader L\close

ð1Þ

Figure 3 shows a schematic diagram of the calculation of the desired roll angle roll when L [ far. Where L is the distance between the follower and the leader. The lag tracking point targettrailer is equal to Targetðlat; lng; altÞ minus 0:25L in the opposite direction of the leader’s heading, u¼90h. Next calculate the desired roll angle roll. 8 L R > > ¼ > > sinð180  2uÞ sin u > > > > > > v2leader > >  Offset:x > < Rleader ¼ g
tan u leader > R þ Rleader > > r¼ > > > 2 > > > > > v2 > > : roll ¼ arctanð follow Þ þ Kp
bearingerror g
r

ð2Þ

Where vleader is the ground speed of the leader, uleader is the actual roll angle of the leader, bearingerror is the bearing error of the follower, and Kp is the bearing error proportional coefficient and Rleader is the turning radius of leader.

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0. 25

L

290

ϕ

R

L

180-2ϕ

θ

ϕ

R

Fig. 3. Lag tracking diagram

When L\close and close\L\far, the expected roll angle is calculated as shown in Figs. 4 and 5, and the calculation method is similar to the method that when L [ far. The longitudinal control law uses classical PID control, and the height control equation is:

25

ϕ

0.

L

ϕ R

L

R

ϕ θ 180-2ϕ

R

Fig. 4. Lead tracking point

180-2ϕ

L

R

ϕ θ

Fig. 5. Desired tracking point

A New Fixed-Wing Formation Control Algorithm

pitch ¼ KHP
DH þ a
KHI

k X



DH þ KHd DDH

291

ð3Þ

i¼0

Where pitch is the desired pitch angle, DH¼HC  H, HC is the desired height, and H is the current height. a is the integral separation switching factor.  a¼

1 jHC j\e 0

ð4Þ

jHC j [ e

The speed and throttle control is: DV ¼ KLP
L þ a
KLI

k X



L þ KLd DL

ð5Þ

i¼0

Vdem ¼ Vleader þ DV

ð6Þ

DVdem ¼ Vfollow Vdem

ð7Þ

Dthr ¼ KTP
DVdem þ KTI

k X



DVdem þ KTd DDVdem

ð8Þ

i¼0

thrdem ¼ thrtrim þ Dthr

ð9Þ

Where L is the distance between the follower and the real target point, a is the integral separation switch coefficient, Vleader is the ground speed of the leader, Vdem is the desired speed of the follower, thrdem is the desired throttle of the follower, and thrtrim is the throttle trim of the follower. After the ground station calculates the desired roll, pitch, yaw angle and throttle, it sends the ArduPilot via the SET_ATTITUDE_TARGET message of mavlink ID 82, and run the attitude control in the flight control.

4 Simulation Analysis of Formation Tracking Control Base on SITL 4.1

Compared with Traditional PID Control Method

The input of the PID control method compared in this paper is the cross track error d, where S is the starting point of the desired path and E is the end point of the desired path. The specific calculation method is (Fig. 6): roll ¼ KDP
d þ a
KDI

k X i¼0



d þ KDd Dd

ð10Þ

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Fig. 6. Cross track error calculation

In order to achieve the formation tracking tasks, the PID algorithm also adds a lead lag model, the specific form is: 8 pidupdateðFollow; targettrailerÞ L [ fur > < roll¼ pidupdateðtargettrailer; TargetÞ close\L\fur ð11Þ > : pidupdateðtargettrailer; targetleaderÞ L\close Where Follow is the current position of the follower (latitude, longitude, altitude), pidupdateðstart; endÞ is the desired command calculation function for the PID algorithm to track the target line, start is the starting point of the target line, and end is the end point of the target line. The simulation test conditions are as follows: the leader is in auto mode, the long side of the route is 2 km, the short side is 1 km, and the cruising speed is 22 m/s. The three UAVs form an equilateral triangle formation with a side length of 60 m, and the lead tracking point targetleader is ahead 60 m of target point, far ¼ 100, close ¼ 60. The lateral direction parameter of the PID control law is KDP ¼ 0:75; KDI ¼ 0:06; KDd ¼ 0:06, and the longitudinal control law and parameters are consistent with those described in Sect. 2. Select the follower’s tracking curve located on the right side of the leader for analysis. The purple curve in the figure is the actual path of the follower, and the yellow line is the route of the leader. Figures 7 and 8 are schematic diagrams of trajectory tracking of the optimal turning radius tracking control law and the PID control law. In Fig. 9, the X-axis is the distance the UAVs flies after the turn, and the Y-axis is the horizontal distance between the current point of the UAVs and the desired trajectory. It can be seen from Figs. 7 to 9 that the PID control law has little difference with the OTR control law after the trajectory converges, but the path oscillation is severe during the turning, and the convergence is slow, and the formation is difficult to maintain for a long time after turning. The OTR control law is superior to the PID control law in tracking fastness, accuracy and stability. 4.2

Compared With L1 Control Method

The L1 algorithm is inspired by the proportional guidance method of the missile, which selects a reference point on the desired path and generates a lateral acceleration command through the reference point [10–12]. The selection of the reference point is shown in Fig. 10.

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Fig. 7. Optimal turning radius control law tracking trajectory

Fig. 8. PID control law tracking trajectory 40 35 30 25 20 15 10 5 0 -5 -10 -15 -20

0

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v η L1

ascmd R

R

2η

Fig. 10. Reference point selection

The lateral acceleration command can be calculated by the following formula: ascmd ¼ 2

v2 sing L1

ð12Þ

The next step is to calculate the desired roll angle: as roll ¼ arctanð cmd Þ g

ð13Þ

Where v is the current speed of the follower in the geodetic coordinate system. In order to achieve the formation tracking tasks, the L1 algorithm also adds a lead lag model, the specific form is: 8 > < roll¼

> :

L1updateðFollow; targettrailerÞ

L [ far

L1updateðtargettrailer; TargetÞ close\L\far L1updateðtargettrailer; targetleaderÞ L\close

ð14Þ

Where Follow is the current position of the follower (latitude, longitude, altitude), L1updateðstart; endÞ is the desired command calculation function for the L1 algorithm to track the target line, start is the starting point of the target line, and end is the end point of the target line. The simulation test conditions are as follows: the leader is in auto mode, the long side of the route is 2 km, the short side is 1 km, and the cruising speed is 22 m/s. The 3 aircrafts form an equilateral triangle formation with a side length of 60 m, and the lead tracking point targetleader is ahead 60 m of target point, far ¼ 100, close ¼ 60. The lateral direction parameter of the L1 control law: the period of L1 is 15 and the damping of L1 is 0.75. The longitudinal control law and parameters are consistent with those described in Sect. 2. Select the follower’s tracking curve located on the right side of the leader for analysis. The purple curve in the figure is the actual path of the follower, and the yellow line is the route of the leader. Figures 11 and 12 are schematic diagrams of trajectory tracking of the optimal turning radius tracking control law and the L1 control law.

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Fig. 11. Optimal turning radius control law tracking trajectory

Fig. 12. L1 control law tracking trajectory 5 4 3 2 1 0 -1 -2 -3 -4 -5

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Fig. 13. Comparison of horizontal distance between L1 and OTR during the turning

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As can be seen from Figs. 11 to 13, the L1 algorithm, as a nonlinear control law, is still outstanding in the formation tracking process, and the tracking of the curve is particularly rapid. The overall performance of the L1 algorithm and the OTR control law are not much different. However, since the optimal turning control law adds the feedback of the real-time turning radius of the leader and the lateral offset compensation, after the turning, the formation convergence speed of the optimal turning radius control law is slightly better than the L1 control law, and the trajectory overshoot is also slightly smaller than L1 control law.

5 Three-UAV Formation Flight Test and Analysis The algorithm is applied to two oil-powered target fix-wing UAVs called “change one” in the air for testing. The fix-wing UAV uses an upper single-wing, front-pull layout, and the power is matched with the Komatsu 62 engine. The wingspan is 2.2 m and weighs 12 kg. Generally, it uses a catapult method to take off, landing with glide slope, and an umbrella can be selected in an emergency. Figure 14 is a picture of the automatic take-off of the aircraft.

Fig. 14. “Change one” catapult take off

The test method is that the two fix-wing UAVs automatically take off to the scheduled route respectively. After the flight is stable, the ground station sends a formation command. The shape of the formation is “I” and the initial spacing of the formation is 100 m, which is gradually reduced to 20 m. Figure 15 is a photograph taken from the ground while flying in formation. During the formation flight, the distance between the follower and the follower’s real desired point is maintained within 2 m, and the convergence speed of the formation after the turn is less than 3 s in the breezy weather. Figure 16 is a data plot of formation flight.

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Fig. 15. Formation flight (20 m spacing)

Fig. 16. Tracking error and height error curve of a follower in formation flight

It can be seen from the figure that the height tracking is basically stable within 1 m, and the tracking distance error with the desired point is stable within 2 m.

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6 Summary In this paper, a new formation tracking algorithm based on optimal turning radius is proposed and tested by SITL simulation and flight test. The test results show better performance than traditional PID and nonlinear L1 algorithm. There are three reasons: (1) When calculating the optimal turning radius, the follower adds the real-time turning radius of the leader for feedback, which can quickly track the turning behavior of the leader at close distances. (2) Add lead and lag points near the desired point to keep track of the target at both close and far distances. (3) Adding the lateral offset of the follower that relative to the leader as compensation, which improves the convergence speed of the formation shape.

References 1. Kong X, Song X, Xia F, Guo H, Wang J, Tolba A (2018) LoTAD: Long-term traffic anomaly detection based on crowdsourced bus trajectory data. World Wide Web 21:825– 847. https://doi.org/10.1007/s11280-017-0487-4 2. Zhao S, Hu Z, Yin M et al (2017) A robust real-time vision system for autonomous cargo transfer by an unmanned helicopter. IEEE Trans Industr Electron 62(2):1210–1219 3. Wu K, Cai Z, Zhao J, Wang Y (2017) Target tracking based on a nonsingular fast terminal sliding mode guidance law by fixed-wing UAV. Appl Sci 7(4):333 4. Hu J, Gang F (2010) Distributed tracking control of leader–follower multi-agent systems under noisy measurement. Automatica 46(8):1382–1387 5. Monteiro S, Bicho E (2002) A dynamical systems approach to behavior-based formation control. In: Proceedings IEEE international conference on robotics and automation (ICRA), pp 2606–2611, May 2002 6. Mehrjerdi H, Ghommam J, Saad M (2011) Nonlinear coordination control for a group of mobile robots using a virtual structure. Mechatronics 21(7):1147–1155 7. Min Q et al (2017) Research on UAV cooperative formation flight based on 3D program control. Meas Control Technol 3:84–87 8. Campa G, Napolitano MR, Brad S et al (2004) Design of control laws for maneuvered formation flight. In: Proceedings of the American control conference, Boston, USA. IEEE 9. http://www.ardupilot.org/ 10. Park S, Deyst J, How JP (2004) A new nonlinear guidance logic for trajectory tracking. In: Proceedings of the AIAA guidance, navigation and control conference, August 2004. AIAA2004-4900 11. Mukherjee J (2000) Automatic control of an OHS aircraft, Ph.D. thesis, University of Calgary 12. Park S (2004) Avionics and control system development for mid-air rendezvous of two unmanned aerial vehicles, Ph.D. thesis, MIT, February 2004

Hinged Sweeper Kinematic Modeling and Path Tracking Control Xiaohua Wang1(&), Kangkang Xu1, Lin Xu1, Zhonghua Miao1, and Jin Zhou2 1

School of Mechanical and Electrical Engineering and Automation, Shanghai University, Shanghai 200444, China [email protected] 2 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Abstract. Intelligent cleaning vehicles are the trend of sanitation vehicles. This paper studies the modeling and control of an electrical hinged sweeper. To begin with, the structure and steering characteristics of the hinged sweeper are analyzed, and the kinematic model is established. The model and parameters are verified by the simulations and experiments. After that, based on the established sweeping vehicle model, the corresponding path tracking controller is designed. The segmented PID control strategy is adopted. The path tracking of the hinged sweeper is realized by using different PID parameters in different error bands. Finally, in the real road environments, the motion modeling and control strategy of the hinged sweeper are verified. Keywords: Hinged sweeper Segmented PID


Kinematics model
Path tracking


1 Introduction The hinged sweeper has the characteristics of small turning radius and flexible steering, and is widely used for cleaning the outdoor road of parks. Due to the special structure, its path tracking control method is different from traditional vehicles. For the path tracking problem of hinged structure vehicles, many scholars domestic and abroad have conducted the researches [1, 2]. The study of the vehicle kinematics modeling is mostly based on a four-wheeled vehicle model of front wheel steering. As described in [3–6], the vehicle was regarded as a moving rigid body, which is convenient for the research of the movement characteristics and the control law. In [7], a four-wheel steering smart car was taken as the research object, and the corresponding kinematic model was established. Based on this, a fuzzy controller was designed for path tracking. For path tracking problem, [8] used the classical PID control method to design the vehicle’s navigation controller. [9] adopted the linear quadratic control method. [10] designed a sliding mode variable structure path tracking controller according to the Ackermann formula and exponential approach law. In this paper, based on the structural characteristics of the hinged sweeper, the kinematic model of the vehicle is established and © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 299–309, 2020. https://doi.org/10.1007/978-981-32-9698-5_34

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experimentally verified. An error band control strategy is proposed and a segmented PID control algorithm is applied for the path tracking of the hinged sweeper.

2 Hinged Sweeper Modeling Hinged sweepers are low-speed. When driven normally, sweeping speed is about 1 m=s. Figure 1 shows an electrical hinged sweeper.

Fig. 1. Electrical hinged sweeper

2.1

Hinged Sweeper Kinematic Model

In order to study the movement characteristics of the hinged sweeper, the front car body and the rear car body are simplified into a rigid body of triangular structures. Two steering cylinder units Q1 and Q2 are connected to the front and rear bodies respectively. The simplified car body model is shown in Fig. 2.

a a Q1

Q2

Z

b

b

Fig. 2. Hinged sweeper simplified model

Figure 3 is a steering model of the hinged sweeper. When the hinged sweeper does not turn, the positions of the left and right steering cylinders are symmetrical about its longitudinal axis. The left and right triangles are formed by the connecting shaft axis, the front body, the rear body and the steering cylinder, which are congruent, that is, \1 ¼ \2. The left triangle is blue and the right triangle is yellow.\1 and \2 are the angle between the front and rear car bodies. When the hinged sweeper is turning, \1 and \2 changes at the same time due to the transformation in the length of the steering

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cylinder. And one of the angles increases and the other one decreases. a is the counterclockwise rotation angle of the front body relative to the initial heading which is the central axis of the hinged sweeper, as shown in the state of the vehicle in Fig. 2. b is the clockwise rotation angle of the rear body relative to the initial heading.

 Q2

Q1 β

Fig. 3. Hinged sweeper steering model

Figure 4 is a motion model of the hinged sweeper in the plane rectangular coordinate system XOY. ðxf ; yf Þ is the coordinates of the front axle pivot point of the hinged sweeper under XOY , and ðxr ; yr Þ is the coordinate of the pivot point of the rear axle under XOY. hf – the heading angle of the front body hr – the heading angle of the rear body. vr – the axis speed of the rear axle vf –the axial speed of the front axle. Y f

c r

O

l vr

P

X

Fig. 4. Motion model of the hinged sweeper

According to the angle change in the steering movement of the hinged sweeper: u ¼ aþb ¼

\2  \1 2

ð1Þ

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u ¼ hf  hr is heading deviation angle between the front and rear bodies of the hinged sweeper. From the geometric relationship, the front wheel axle speed vf is: vf ¼ vr cos u

ð2Þ

Steady steering turn radius of the front body: Rf ¼

l þ c cos u sin u

ð3Þ

c is the distance from the axis of the connecting shaft Z to the axis of the front wheel axle . l is the distance from the axis of the connecting shaft Z to the axis of the rear wheel axle. According to Eqs. (2) and (3):


hf ¼

vr cos u sin u l þ c cos u

ð4Þ

Establish a kinematic model of the front body: 2


3 2 3 xf vr cos u cos hf 6 y
7 4 v cos u sin h 5 r f 4 f5¼
vr cos u sin u l þ c cos u hf

ð5Þ

The connection between the front and rear bodies is satisfied: 

xr yr





x ¼ f yf





cos hf c sin hf





cos hr l sin hr

 ð6Þ

The kinematic model of the hinged sweeper is obtained by combining the above equations:
3 3 2 xf vr cos u cos hf 6 y
7 6 7 vr cos u sin hf 6 f7 6 7 6
7 6 vr cos u sin u 7 6 hf 7 6 7 l þ c cos u 6 7¼6 6 xr 7 6 xf  c cos hf  l cos hr 7 7 6 7 4 yf  c sin hf  l sin hr 5 4 yr 5 hf  u hr

2

ð7Þ

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Hinged Sweeper Kinematic Model Simulation

In order to verify the motion characteristics of the hinged sweeper, a motion simulation of the hinged sweeper is performed. Figure 5 is the motion trajectory obtained. p In the Fig. 5(a), the heading deviation angle of the front and rear bodies is u ¼ 10 : In the Fig. 5(b), the heading deviation angle of the front and rear bodies changes p during the movement. That is u ¼  10 ! u ¼ p6 :

(a) ϕ = π

(b) ϕ = −

10

π 10

→ϕ =

π 6

Fig. 5. Motion trajectory simulation

When the hinged sweeper is driving in an arc, the steering center of the front and rear bodies is at the same point. It is seen from Fig. 5(a) when the hinged sweeper makes a circular motion, the motion trajectories of the front and rear bodies converge to a concentric circle. In Fig. 5(b), the steering angle of the hinged sweeper changes at 4 s. After the angel changes the front and rear bodies of the hinged sweeper still converge to a concentric circle. This verifies the kinematic model.

3 Hinged Sweeper Path Tracking 3.1

Hinged Sweeper Path Tracking

The front and rear bodies are regarded as mass points. As shown in the path tracking model of Fig. 6, the front and rear bodies of the hinged sweeper are simplified to the mass points D1 and D2, which are the axle center point of the front body and the rear body respectively. Point A, point B, and point C are the three points on the target path. The hinged sweeper needs to track the path AB, and the point C is the closest point on the path AB to the hinged sweeper. The heading angles of path points A, B, and C are hA , hB and hC respectively. The heading angle of

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Fig. 6. Hinged sweeper path tracking model

the front body is hf , and the heading angle of the rear body is hr . The distance between the front of the car body and the closest point of the target path is d. The heading angle deviation between the heading angle of the hinged sweeper and the target point B is Dh ¼ hf  hB : 3.2

Path Tracking Controller’s Design Based on Segmented PID

3.2.1 PID Control Principle The conventional PID controller controls the object according to the linear combination of the deviation (P-Proportional), integral (I-Integral) and differential (D-Derivative) [11]. The control law of the PID algorithm is: 1 uðtÞ ¼ kp ½eðtÞ þ Ti

Z 0

t

eðtÞdt þ

TD deðtÞ  dt

ð8Þ

Where kp - scale factor, Ti - integral time constant, TD - derivative time constant, eðtÞdeviation. 3.2.2 Path Tracking Control Strategy There is a threshold for the steering angle during the driving of the hinged sweeper. When the distance between the hinged sweeper and the target path is large, the steering angle of the controller output is always near the threshold. In this case, it is difficult to reduce the distance error and track the target heading angel at the same time. In this study, the segmented PID method is proposed. The error band range of a path tracking is set, and the error band is segmented into two parts, inner and outer. Outside the error band, the sweeper travels at a fixed heading angle to reduce the distance between the target path and the sweeper. In the error band, the sweeper tracks the heading angle and distance error through the PID controller. Considering the size of the car body and the width of the road, the error band range is one meter. As shown in Fig. 7, the thick line segment in the middle is the target path tracked by the hinged sweeper. The dotted line portion on both sides of the path is the error band of one meter range. When d [ 1m, the hinged sweeper is outside the error

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Error out-of-band

ϕ

d

1m

(a)

Error out-of-band control strategy Error in-band

d 1m (b) Error in-band control strategy

Fig. 7. Schematic diagram of the error band internal and external control strategy

band, and the hinged sweeper travels toward the target path at a given heading angle u. When d  1m, the hinged sweeper is within the error band, the hinged sweeper’s driving direction is accurately controlled according to the PID algorithm. 3.3

Simulation and Analysis

In order to verify the path tracking control strategy, the path tracking simulation is performed. The reference trajectory is given, and the hinged sweeper performs path tracking according to the designed control algorithm. Then the system states and trajectories of the hinged sweeper are recorded. Because actual paths are composed of straight lines and curves, the reference trajectories are executed on the paths of straight lines and circles respectively. The speed is set as v ¼ 1 m=s, and get c ¼ 0:71 m, l ¼ 0:69 m according to the measured data. c is the distance from the axis of the connecting shaft Z to the axis of the front wheel axle . l is the distance from the axis of the connecting shaft Z to the axis of the rear wheel axle. The initial pose of the hinged sweeper is (0 m, 10 m, 0, −1.4 m, 10 m, 0), and performs the path tracking simulations of the straight path. Other pose of the hinged sweeper is (0 m, −2 m, −p/6, −1.2 m, −1.3 m, −p/6) and the circular path tracking simulations are performed. Figures 8 and 9 show the trajectories and the corresponding steering angle during the tracking straight and circular paths. From the perspective of the tracking effect, there is no overshoot. In the circular tracking simulations, the target path is a circular path with a center of the circle at the origin and a radius of 4 m. From the simulation results, the hinged sweeper tracks the target paths very well.

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Trajectory diagram

Steering angle

Fig. 8. Straight line tracking

Trajectory diagram

Steering angle

Fig. 9. Round tracking

Fig. 10. GPS receiving device

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4 Experiments 4.1

Kinematic Model Verification

In this study, the IMU and the GPS sensors are used to verify the hinged sweeper’s kinematic model. The RTK-GPS (Real-Time Kinematic Global Positioning System) outputs accurate global positioning information with positioning accuracy of about 5 cm. Figure 10 is the photograph of the GPS receiving device. The hinged sweeper drives along the road and maintains a constant speed of 1 m=s. A series of track points and heading angles are obtained by the IMU and the GPS.

(a) Trajectory chart

(b) Heading chart

Fig. 11. Track and heading chart

Figure 11 shows the trajectories and heading of the hinged sweeper’s front body. It is seen from the figure that the data from IMU and the GPS match the kinematic model. Through the comparative analysis of the two sets of data, the average error of the calculated trajectory and the experimental trajectory is 0.08 m, and the average error of the calculated heading angle and the experimental heading angle is 0.25°. According to the experimental results, the model reflects the kinematics of the hinged sweeper while driving. 4.2

Path Tracking Experiment

Shanghai University campus is selected to conduct the path tracking experiments of the hinged sweeper. This road has straight road sections, curved road sections and a right turn. Before performing the experiment, the position information of the road is collected by the GPS sensor, and the position information is input as the expected path for the path tracking controller.

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Fig. 12. Experimental tracking path

In the experiments, the hinged sweeper tracks the path which is shown in Fig. 12 with a total length of approximately 93 m. The hinged sweeper first tracks a segment of the arc with a small curvature and turns right after about 50 m. Then the vehicle tracks a straight segment about 15 m.

Actual path versus expected path

Position deviation

Fig. 13. Experimental results

In Fig. 13, it is shown that the hinged sweeper tracks the arc path. When the curvature of the path changes, the position tracking deviation grows large. The deviation is relatively small when tracking the straight line segments. During the tracking process, the maximum position deviation of the hinged sweeper is about 30 cm. The experimental road conditions are unstructured. The position information of the hinged sweeper is recorded and compared with the desired path. Experimental results shows that the hinged sweeper can track the expected path.

5 Conclusions In this study, the hinged sweeper’s kinematic model and the path tracking method are studied. A kinematic model of the hinged sweeper is established. The segmented PID tracking strategy is proposed. Finally, the path tracking experiments are executed, and the experimental results are analyzed. The experimental results show that proposed method of path tracking performs well. In the subsequent research work, the kinetic

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model should be further considered for the hinged sweeper, and adds dynamic constraints. For PID controllers, related algorithms should be added and the control parameters are adjusted with the state of the hinged sweeper to further improve the control accuracy.

References 1. Hajjaji AE, Bentalba S (2003) Fuzzy path tracking control for automatic steering of vehicles. Robot Auton Syst 43(4):203–213 2. Shao J, Zhao X, Yang J et al (2017) Reinforcement learning algorithm for path following control of articulated vehicle [J/OL]. Trans Chin Soc Agric Mach 48(3):376–382 3. Jianwei G, Yan J, Wei X (2016) Predictive control of unmanned vehicle model. Beijing Institute of Technology Press 4. Rajamani R (2006) Vehicle dynamics and control. Springer, Cham 5. Akeb H, Hifi M (2013) Solving the circular open dimension problem by using separate beams and look- ahead strategies. Comput Oper Res 40(5):1243–1255 6. Paden B, Čáp M, Yong SZ et al (2016) A survey of motion planning and control techniques for self-driving urban vehicles. IEEE Trans Intell Veh 1(1):33–55 7. Wang T, Tong J, Chen N et al (2018) Fractional control of an active four-wheel-steering vehicle. In: Materials science and engineering conference series. materials science and engineering conference series 8. Marino R, Scalzi S, Netto M (2011) Nested PID steering control for lane keeping in autonomous vehicles. Control Eng Prac 19(12):1459–1467 9. Netto M, Blosseville JM, Lusetti B et al (2006) A new robust control system with optimized use of the lane detection data for vehicle full lateral control under strong curvatures. In: IEEE intelligent transportation systems conference. IEEE 10. Zhao X, Yang J, Zhang W et al (2015) Sliding mode control algorithm for path tracking of articulated dump truck. Trans CSSE 31(10):198–203 11. Rivera DE, Morari M, Skogestad S (1986) Internal model control: PID controller design. Ind Eng Chem Process Des Dev 25(1):252–265

Machine Learning in Industrial Control System Security: A Survey Dianbin Jiang and Jingling Zhao(&) Beijing University of Posts and Telecommunications, Beijing 100876, China [email protected]

Abstract. Industrial control system (ICS) is becoming more and more open to the outside world for the advancement of Industrial Internet, which means people can have access to the industrial control system with traditional internetbased methods. However, the connections with outside world make ICS exposed to numerous unpredictable dangers. In addition, artificial intelligence (AI) has made great progress and applying AI to other fields is the trend in both academia and industry. This paper will introduce the basic information of ICS and review related works in anomaly detection based on AI. Based on the analysis of previous researches and the features of ICS, the prospect of anomaly detection of ICS is forecasted. Keywords: Anomaly detection
Industrial control system Machine Learning
Deep Learning


Survey


1 Introduction ICSs are widely used in various industries and play a key role in the power system, petroleum, railway, nuclear and other industries. Immeasurable losses will be caused when a security incident occurs in an industrial control network (ICN). The security of traditional ICNs mainly depends on its closedness, and some industries don’t even have any security measures. However, with the development of the industrial Internet, IT and OT technologies have gradually merged, making the enterprise control system connected to the Internet. In addition, a lot of common software and hardware are applied to the industrial control network, which brings more and more vulnerabilities to the industrial control network. In recent years, ICS security incidents has occurred constantly, each time causing very serious consequences, which makes the ICS security a major concern of many countries. Besides, AI technology is developing rapidly, the combination of Machine Learning and information security has become a hot research direction for security researchers. This paper is organized as follows: background and basic information of ICS is reviewed in Sect. 2. Anomaly detection based on Machine Learning and related datasets are discussed in Sect. 3. In Sect. 4, there are conclusion and the forecast for trends of future research in anomaly detection in ICS.

© Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 310–317, 2020. https://doi.org/10.1007/978-981-32-9698-5_35

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2 Background The traditional ICN is relatively closed, the manipulation and management of the devices is only carried out in the internal network. The security of the ICS is guaranteed by the physical isolation between the internal network and the external network. Therefore, both the academia and industry payed little attention to ICN security, and in some company, the ICNs even run without any security measures. However, with the advancement of the Industrial Internet in recent years, the ICN and information network of companies have begun to merge. As is shown in Fig. 1, there is no more physical isolation between the industrial control network and the internet, which means hackers can have access to the ICSs. On the other hand, some protocols of industrial control system lack authentication and encryption mechanism, making it easy for Manin-the-Middle (MITM) attacks and tampering the network packets. In addition, lots of general-purpose computers and other hardware and general-purpose software are applied to the industrial control network, which brings many threats and vulnerabilities to the industrial control network. Figure 2 shows the trend of vulnerability in Industrial control system. As we can see from Fig. 2, the number of vulnerabilities in ICS grows rapidly these years. Therefore, the security of ICS has become a big challenge for both the academia and industry, and intuition detection in industrial control network is getting hotter and hotter.

Fig. 1. The structure of a typical control system [1]

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Fig. 2. The trend of vulnerability in industrial control system [2]

3 Anomaly Detection in Industrial Control System Intrusion detection is divided into two categories according to detection methods, one is signature-based detection, the other is anomaly detection. Signature-based detection builds models for abnormal behaviors so it plays a very limited role in detecting unknown Attacks. Anomaly detection builds models for normal behaviors, any behavior deviates the model can be detected and treated as intrusion. Deterministic Finite Automata (DFA) and Statistical methods are the baselines of anomaly detection before Machine Learning. The traditional approach of anomaly detection in ICS is building DFAs for the ICS protocols or splitting devices into some partitions and formulating a baseline for each partition. However, it’s hard to determine the thresholds or build DFAs for non-public protocols. At present, the popular practice in academia and industry is using Machine Learning technology instead of traditional methods for modeling. The rest of this chapter will mainly introduce researches related to anomaly detection based on Machine Learning and Deep Learning. Some datasets of ICS will be introduced following with several feature extraction methods, and anomaly detection methodologies are discussed in the last section of this chapter. 3.1

Datasets of ICS for Machine Learning

Dataset plays an important role in machine learning, it determines the result of training. A good dataset is the beginning of successful machine learning. Due to the sensitive nature of industrial control system, there is little publicly available dataset for researchers to evaluate the effectiveness of the proposed solution, and most of the available datasets is generated from testbeds or simulation platforms. The most famous

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dataset for anomaly detection is KDD-CUP99 which contains 5 million records of real network activities with attacks. However, it is not so suitable for anomaly detection of ICS. So, some researchers tried to create datasets for ICS anomaly detection. Pan et al. in Oak Ridge National Laboratories [3, 4] create three datasets of electric transmission system. These datasets contain many measurements including normal behaviors, attack behaviors, data logs from Snort and relays of network. Goh et al. [5] collect data from a Water Treatment which can represents a real-world industrial water treatment plant. The dataset contains physical properties and network traffic under attacked and normal modes. Thomas et al. [6] create a new dataset in a gas pipeline, and it contains data from normal activities and more than 30 different attacks. Lemay et al. [7] use simulators to set up an electrical network and generate malicious traffic by means of real attack tools, though the dataset can’t replicate true industrial control network, it can be a good baseline to validate and evaluate models and algorithms of anomaly detection. Table 1 shows measurements and Classes of these datasets. Table 1. Datasets of ICS Datasets [3] [4] [5] [6] [7]

3.2

Measurements & protocols Relays, logs, physical properties Relays, logs, physical properties physical properties, Modbus Modbus, logs Modbus

Classes Binary Multiclass Binary Multiclass Multiclass

Feature Extraction with Machine Learning in ICS

Feature extraction is the key procedure of data preprocessing in machine learning. Principal Component Analysis (PCA) and Auto-Encoder are the main approaches of Feature extraction. To select the better feature of PROFINET which is a popular protocol in ICS. Sestito et al. [8] optimize the data extraction by assessing the correlation coefficient between all the features under evaluation by a trained Artificial neural network (ANN). The ANN works for classifying the data and events based on correlation coefficient between the extracted features and the occurrence of events. The usual way of feature extraction is selecting some fields of the protocol or some parameters of network and combining them while Hua Zhang et al. [9] train a modified RNN-RBM as a feature decoder which works with PCA to extract high-quality features from raw features. Hua Zhang et al. [10] encode every raw feature vector into a low-dimensional binary ‘word’ and removes duplicates to form a document. Then they use LDA to detect anomaly of the docs. Both decoders in [9] and [10] are used to converting MODBUS/TCP packets into forms suitable for training and evaluating of machine learning. Schneider et al. [11] train deep auto-encoders for feature extraction and they work well in Ethernet/IP and Modbus.

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Anomaly Detection Methodologies with Machine Learning in ICS

There are many protocols in ICS. There is not much research on other protocols except for Modbus. This chapter will introduce anomaly detection methods using machine learning around several common industrial control network protocols such as MODBUS IEC and so on. Modbus is a general communication protocol which has been widely used in the field of industrial control network. Controllers can communicate with each other or with other devices via networks such as ethernet through Modbus. Modbus is not so secure for lack of authentication and encryption mechanism, and it is the most studied protocol in anomaly detection of ICS. Ming et al. [12] propose an approach based on Wavelet Neural Network (WNN) which can perceive changes of abnormal function control in ICS. The result shows that the approach has a good accuracy and real-time capability in Modbus/TCP protocol anomaly detection. Kensuke et al. [13] proposed an improved method which employs regularity and similarity of packet flow. They model with Markov-chain and use word2vec for calculating packet similarity. This approach has a good performance at detecting scanning attacks. Cheng et al. [14] developed a base-line signature database for normal packets and used a Bloom filter to store the databases. Besides, they trained a Long Short-Term Memory (LSTM) to predict the packet signature which has the maximum possibility to occur by giving previous packages. The result shows their anomaly detection combining the two approaches have better performance compared to other single techniques on a dataset created from a gas pipeline control system. Zhang et al. [9] train a feature decoder based on RNN with Gaussian-Bernoulli Boltzmann Machine (GBRBM) which can extract features with high quality from raw features. Besides, they modified RNN-RBM and trained it to model feature patterns of normal behaviors. Moreover, to improve the efficiency of anomaly detection and updating the anomaly detection, they designed a semisupervised incremental algorithm. Experiments show that the approach performs better than other traditional approaches in some datasets of ICS. Hua Zhang et al. [10] propose a hybrid model which combines Latent Dirichlet Allocation (LDA) with autoencoder. In their work, they use a simple autoencoder to translate network flow packets of ICS into documents and trained a classifier based on LDA model to detect abnormal behaviors. Experiments on the dataset KDD-CUP-99 shows that the method has a better receiver operating characteristic (ROC) curve than other traditional NIDS. Class imbalance exists in most of the datasets of ICS because the proportion of abnormal flow is too small. To analyze the impact of imbalanced data in the results, Vasquez et al. [15] studied nine different Machine Learning algorithms in classification of ICS flows. The experiments show that classifier based on decision trees is superior to others and Decision Jungle has the best performance when dealing with unbalanced datasets. Dong Hao et al. [16] selected the combination of function code and start address of register of Modbus/TCP packet as feature. They trained a OSSVM classifier and evaluated it in power plant control network and the results shows the approach good in accuracy. Pin-Han Wang et al. [17] propose detection method which can cluster attacking behaviors with unsupervised learning algorithm based on similarity of log sequence. The approach works well in detecting misbehaviors of Modbus/TCP.

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Some protocols have been less studied but they are popular in ICS. Guilherme et al. [8] use sliding window in feature extraction and propose a model based on artificial neural network (ANN). Results shows that the approach is successful for detecting anomalies in PROFINET network. Alfonso Valdes et al. [18] developed a hybrid anomaly detection system which can detect anomaly packets of IEC61850 and abnormal measurements of different devices. Some researches focus not on protocols of ICS but general measurements. Host logs and network traffic are usually use for anomaly detection, while Valdes et al. [18] proposed to consider the impacts attacks have on measurements from different devices. For example, voltage and current can be useful measurements for anomaly detection in smart grid. Zhang et al. [19] designed a multi-layer intrusion detection system for ICS which could detect anomalies in network packets host logs and process data. They tried many algorithms, the results show that k-Nearest Neighbor (KNN), bagging and random forest perform well in detecting MITM and denial of service (DOS) attacks. Basumallik et al. [20] propose a filter based on Convolutional Neural Network (CNN) to detect anomalies of phasor measurement units in power systems. Results shows that the filter performed better than filters based on Recurrent Neural Networks (RNN) LSTM or SVM.

4 Conclusion In conclusion, applying machine learning to anomaly detection is a hot research direction in the field of ICS security. Anomaly detection based on Machine Learning has higher accuracy than traditional methods. However, some problems remain to be solved. Firstly, there is little publicly available data for researchers to evaluate their algorithms, most of the researchers evaluate the models or algorithms with datasets collected from simulation platform or testbed. More datasets collected from real ICS env is needed. Secondly, as we can see above, the main protocol used in researches in anomaly detection of ICN is Modbus while other protocols rarely appear in related works or datasets. But, Modbus only shares part of the market, more anomaly detection of other ICS protocols need to be researched. Thirdly, the detection method aimed at single network packet, but the context of packets has not been studied. Finally, ICN has strict requirements on delay of network but there is little research focusing on timeconsuming of anomaly detection. Anomaly detection has great progress with the application of artificial intelligence technologies. In future research, accuracy may still be one of the main objectives of researches. Besides, there are four trend: (1) More and more researches will begin to focus on efficiency of detection for time sensitivity of ICS. (2) More protocols will be studied and more datasets will be created and open to researches. More datasets will be collected from real ICN env with the application of data desensitization.

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(3) More useful features will be extracted from ICS env. For example the context of packets and periodicity of ICN may be import measurements for anomaly detection of ICS.

References 1. Yanbo D, Peng Z (2017) Jamming attacks against control systems: a survey. In: International conference on intelligent computing for sustainable energy and environment, pp 566–574 2. WINICSSEC Technologies. Statistics of ICS Vulnerability. ICS Vulnerability Database. http://ivd.winicssec.com/index.php/Home/Index/index.html. Accessed 10 May 2019 3. Pan S, Morris T, Adhikari U (2015) Developing a hybrid intrusion detection system using data mining for power systems. IEEE Trans Smart Grid 6(6):1 4. Pan S, Morris T, Adhikari U (2015) Classification of disturbances and cyber-attacks in power systems using heterogeneous time-synchronized data. 11th IEEE Trans Ind Inf 11(3):650–662 5. Goh J, Adepu S, Junejo KN (2016) A dataset to support research in the design of secure water treatment systems. In: 11th international conference on critical information infrastructures security. Springer, Cham 6. Morris T, Zach T, Ian T (2015) Industrial control system simulation and data logging for intrusion detection system research. In: 7th annual southeastern cyber security summit (2015) 7. Antoine L, José MF (2016) Providing SCADA network data sets for intrusion detection research. In: 9th USENIX workshop on security experimentation and test (2016) 8. Sestito GS (2018) A method for anomalies detection in Real Time Ethernet data traffic applied to PROFINET. IEEE Trans Ind Inf 14(5):2171–2180 9. Zhang H, Zhu S, Ma X (2017) A novel RNN-GBRBM based feature decoder for anomaly detection technology in industrial control network. IEICE Trans Inf Syst D(8):1780–1789 10. Zhang H, Zhu S, Zhao J (2016) Anomaly detection in industrial control networks using hybrid LDA-autoencoder based models. In: International conference on computer, electronic engineering and information science, vol 63(2), pp 53–58 11. Schneider P, Böttinger K (2018) High-performance unsupervised anomaly detection for cyber-physical system networks. In: Cyber-physical systems integrate computing and communication capabilities 12. Wan M, Song Y, Jing Y (2018) Function-aware anomaly detection based on wavelet neural network for industrial control communication. Secur Commun Networks 2018(5):1–11 13. Tamura K, Matsuura K (2019) Improvement of anomaly detection performance using packet flow regularity in industrial control networks. IEICE Trans Fundam Electron Commun Comput Sci E102-A(1):65–73 14. Feng C, Li TT (2017) Multi-level anomaly detection in industrial control systems via package signatures and LSTM networks. In: 47th IEEE/IFIP International Conference on Dependable Systems and Networks. IEEE, Denver 15. Gabriel V, Rodrigo SM, Bogaz Z (2017) Flow-based intrusion detection for SCADA networks using supervised learning. In: XVII Simpósio Brasileiro em Segurança da Informação e de Sistemas Computacionais, pp 167–181 16. Dong H, Peng D (2018) Research on abnormal detection of ModbusTCP/IP protocol based on one-class SVM. In: Youth Academy Annual Conference of Chinese Association of Automation

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17. Pin HW, Liao IE (2018) An intrusion detection method based on log sequence clustering of honeypot for Modbus TCP protocol. In: IEEE international conference on applied system invention, pp 255–258 18. Alfonso V, Richard M, Matthew B (2016) Anomaly detection in electrical substation circuits via unsupervised machine learning. In: 17th international conference on information reuse and integration (IRI). IEEE, Pittburgh 19. Fan Z, Hansaka ADEK (2019) Multi-layer data-driven cyber-attack detection system for industrial control systems based on network, system and process data. IEEE Trans Ind Inf 20. Sagnik B, Rui M (2019) Packet-data anomaly detection in PMU-based state estimator using convolutional neural network. Int J Electr Power Energy Syst 107:690–702

Study on Quick Selection Technology of LowOrbit Spacecraft Collision-Avoidance Strategy Xiaohong Guo(&), Xiaohui Xu, Haichen Lin, and Xingyi Chen Key Laboratory of Faults Diagnosis and Maintenance of Spacecraft in Orbit, Xi’an 710043, China [email protected]

Abstract. Considering the fact that more and more collision-warning events occur in daily management of low-orbit spacecraft, this paper investigates some key techniques of the spacecraft collision-avoidance. Radial and trajectory separation methods are analyzed emphatically. The relationship between separating effect and control quantity, control position as well as control time is revealed. The radial separation method uses relationship of velocity control quantity and the radial distance change quantity to calculate control quantity which satisfied mission requirement. New method design has guidance role for collision-avoidance realization in the practical work. Keywords: Collision-avoidance


Radial separation
Trajectory separation

1 Introduction With the development of human beings’ outer space exploration, space objects and debris are increasing sharply. In orbit collision and alarm events are rising year-to-year, which has brought serious pressure to the normal operation of spacecraft, especially those in low orbits. How to effectively isolate the spacecraft and the approaching target, and maintain the normal operation of satellites, is an important research content of spacecraft operation management. The research of spacecraft collision-avoidance technology has extensive application value, which has aroused the strong interest of researches. Paper [1] and [2] has introduced the probability of collision between satellites and space debris. Paper [3–5] describe the specific procedures and practices of the department of defense’s space monitoring network to calculate the space debris warning information and timely release the circumvention work under the cooperation of NASA. For the daily operation and management of spacecraft in orbit, collision-avoidance has some characters, such as strong suddenness, high degree of emergency, which could not be neglected. If a collision occurs, the consequences could be catastrophic. Therefore, the determination of certain basic principles of avoidance control is great significance problem. In this paper, authors give full consideration to the character of strong suddenness and high degree of emergency in collision-avoidance control process, on the base of the daily operation and management system of spacecraft. In particular, a preliminary analysis on the relationship of operation time, control location and control quantity is © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 318–324, 2020. https://doi.org/10.1007/978-981-32-9698-5_36

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given by using the information obtained from collision warning system and of avoidance control with the minimum requirements between spacecraft and approach targets for avoidance control. And then, a practical judgment method for collisionavoidance control for the daily operation and management of spacecraft is proposed. This paper is organized as follows. Section 2, two means of spacecraft collisionavoidance are introduced in detail, and a selection principle for avoidance control in practice. Section 3, results and analyzes of the application with the collision-avoidance strategy is proposed in this paper to solve the collision events in practical management work. Section 4, the work is concluded.

2 Collision Avoidance Means According to the geometrical relationship between spacecraft and approaching target, collision could be divided into four kinds, including head-on collision, rear-end collision, coplanar collision and non-coplanar collision [4]. The actual probability of headon and rear-end collisions is almost zero. At present, in practical daily operation and management of spacecraft, there are two common means to carry out collisionavoidance control, which are radial separation method and trajectory separation method. In the following discussion in this paper, it is assumed that the engine works in pulse mode with small control amount and short working time. 2.1

Radial Separation Method New Design

By changing the semi-major axis of orbit, radial separation method could achieve separation on the altitude between spacecraft and approaching target at the time of collision, so as to get the mutual isolation goal. The radial separation method is suitable for acute short-term collision or near-face collision with large approach angle. It has the advantages of quick response and high reliability, but the disadvantage is that the control quantity is larger than the normal control relatively. This new method would be described as follow. Some definitions are stated in advance. The semi-major axis, eccentricity ratio, and eccentric anomaly of spacecraft before the spacecraft’s orbit change, are defined as a1 , e1 , E10 , respectively. Then, the radial distance of the spacecraft is [5] r1 ¼ a1 ð1  e1 cos E1 Þ. If eccentric anomaly of the spacecraft is defined as E2 , the approaching radial distance would be r2 ¼ a1 ð1  e1 cos E2 Þ. After collision-avoidance control, the semi-major axis, eccentricity ratio, and eccentric anomaly angle of approaching of spacecraft at the location where it was before being controlled at the original approach time, are defined as a2 , e2 , E20 . Then, at the original of the spacecraft could be calculated as 
approach time, the radial distance r20 ¼ a2 1  e2 cos E20 [6–9]. If jDr j ¼ r20  r2  [ L, and the L is minimum safe distance, the collision-avoidance control between spacecraft and the approach target is successful. If r20 is known, a2 , e2 , E20 must to be sure firstly to calculate r20 . The semi-major axis after collision-avoidance control, a2 , could be derived from the mechanical energy just as the following formula:

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.h

a2 ¼ r 1 l

2l  r1 ðV1 þ DV Þ2

i

ð1Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Where, the velocity before control work is: V1 ¼ lð2a1  r1 Þ=r1 a1 . The eccentricity ratio after control operation e2 is gotten from the angular momentum per unit mass of spacecraft formula as follow: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  . e2 ¼ la2  r12 Vf2 la2

ð2Þ

The vertical radial component of velocity, Vf , at the original radial distance r1 after orbit changing, could be calculated by the following formula:  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 
ffi a21  a21 e21 Vf ¼ DV þ ð2a1 l  r1 lÞ=ðr1 a1 Þ 2a1 r1  r12

ð3Þ

After collision-avoidance control working of the spacecraft, the eccentric anomaly, E20 , at radial distance r2 could be calculated by the following formula step by step: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii
 2a1 r1  r12 Vr ¼ a1 e1 DV þ ð2a1 l  r1 lÞ=ðr1 a1 Þ sin E1 h

(

(

(


pffiffiffiffiffiffiffi sin E10 ¼ Vr r1 e2 a2 l qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h
 .
i. cos E10 ¼ 1  a2 l 1  e22 V f a2 e2

ð5Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffi . 1  e21 sin E1 ð1  e1 cos E1 Þ sin f1 ¼ cos f1 ¼ ðcos E1  e1 Þ=ð1  e1 cos E1 Þ

ð6Þ

. pffiffiffiffiffiffiffiffiffiffiffiffiffi 1  e21 sin E2 ð1  e1 cos E2 Þ sin f2 ¼ cos f2 ¼ ðcos E2  e1 Þ=ð1  e1 cos E2 Þ

ð7Þ

Df ¼ f2  f1 .
pffiffiffiffiffiffiffiffiffiffiffiffiffi (  sin f10 ¼ 1  e22 sin E10 1  e2 cos E10

 1  e2 cos E10 cos f10 ¼ cos E10  e2 (

ð4Þ







þ e2 cos f10 þ Df cos E20 ¼ h cos f10 þ Df þ e2 1i. pffiffiffiffiffiffiffiffiffiffiffiffiffi



 sin E20 ¼ 1  e22 cos f10 þ Df 1 þ e2 cos f10 þ Df

ð8Þ ð9Þ

ð10Þ

Where, Vr represents the velocity along r1 , the radial component at the radial distance of the spacecraft at the location after orbit changing work. And, E10 represents the eccentric anomaly of spacecraft at the end of the orbit changing work. And f1 represents the true anomaly before orbit change work. f2

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represents the true anomaly at the time of approaching time, f10 represents the true anomaly after orbit changing work. The direct expression, which is used to calculate the radial distance’s difference, could be obtained through the symbolic operation of Matlab tools. The expression is too cumbersome to be listed in this article. From the perspective of application, this article analyze mainly the relationship between the radial distance’s difference Dr and the selected position E2  E1 for control work, as well as the relationship between and the velocity control quantity DV. Since the eccentricity ratio of the low-orbit satellite is smaller than high-orbit satellite, generally less than three thousandths. Therefore, the approximate relationship between the difference of radial distance, and the selected position, E2  E1 could be given. The approximate relationship between the difference of radial distance and the velocity control quantity DV could be given too. If the velocity control quantity DV is given, the difference of radial distance Dr has the approximate relationship as following: Dr 

Drmax Drmax  cosðM2  M1 Þ 2 2

ð11Þ


 Where, Drmax ¼ r20  r2 ðE2 E1 Þ¼p . Under certain known conditions of a1 , e1 , E1 , E2 the radial maximum safe distance, Drmax , could be determined by the velocity control quality DV. Thus, the relationship between the velocity control quantity, DV, and the radial distance change quantity E2  E1 of spacecraft is established. And, in early warning information, the distance and relative position between the spacecraft and the approaching target on the radial direction could be obtained. Combined with the pre-set safety threshold, the control direction (up or down) required on the radial position r2 could be gotten. According to the change of the distance, the minimum control quantity on r1 , the radial distance before the control work, could be deduced. 2.2

Traditional Trajectory Separation Method

Trajectory separation method is the traditional method, which just is to change the spacecraft speed by adding a small velocity increment on the spacecraft trajectory direction. After a period of time accumulation, as soon as it is on the target approaching time, the spacecraft would be far away from the collision position in the trajectory. This method is suitable for the approach events which still has a long distance to the collision position. The advantage of this method is to save fuel, but the reliability of this method is weaker than the radial separation method’s. The reason is that orbit prediction error is mainly concentrated on the direction along the trajectory. And the orbit prediction error diverges rapidly with time square, and the lower the orbit is, the more serious the error diverges. The variable definition is the same as the Sect. 2.1 above. The relationship between the rate of change of the velocity of the plane angle and the rate of change of the semimajor axis is derived as follows:

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. pffiffiffiffiffiffiffiffiffiffi n ¼ zp=T ¼ 2p 2p a3 =l ¼ a3=2 l1=2 ) Dn ¼ 3Dan=2a Therefore, after the orbit change, the separation distance on the trajectory is: Z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a21 sin2 t þ b21 cos2 tdt L¼

ð12Þ

ð13Þ

H

pffiffiffiffiffiffiffiffiffiffiffiffiffi



 Where, b1 ¼ a 1  e2 , H is the integrating rage E20  jDnt0 j; E20 , or E20 ; E20 þ jDnt0 j , t0 represents the time difference between the time of orbit change and the time close to the target. Because the eccentricity ratio of the lower orbit spacecraft is generally very small, the separation distance could be approximately calculated by formula 14:

pffiffiffi  L ¼ a1 Dn1 t ¼ ð3a1 Dan1 t Þ=ð2a1 Þ ¼ 3 lða2  a1 Þt0 0

0

qffiffiffiffiffi 2 a31

ð14Þ

The value of a2 could be calculated by formula 1. The distance of trajectory separation is related to the control quantity and time of orbit change. The larger the control quantity, the earlier the orbit-change control time would be met, and the larger the separation distance would be gotten. 2.3

Indicators of Quick Collision-Avoidance Method and Innovation

At present, the early warning of space collision events is generally issued 48 h in advance to ensure the accuracy of forecast, because the orbit forecast error accumulates with the forecast time. But it is ordered to finish the avoidance operation with 15 min in real-time order working now. With the indicator of the 15 min well done the work, the engineers should select more effective and quicker method than traditional strategy. So the quick collision-avoidance method provided in the Sect. 2.1, the method uses the relationship of the velocity control quantity and the radial distance change quantity to calculate the control quantity. This method has quicker computation speed than traditional method which takes more than one hour usually. So new algorithm design could satisfy the mission requirement. For approach angle of an oncoming or near-oncoming event is near 180°, the trajectory separation method could only change the approach time with the approach target, but could not really achieve a safe separation distance, because the approach target is on different surface with our spacecraft. Considering that most spacecraft in orbit have their own trajectory maintenance requirements or network maintenance requirements, in order to avoid interfering with the normal use of users, spacecraft control maneuver could not be too large. Therefore, in the practical implementation process, the controller operates the orbital maneuver control in the near time of the relative surface generally. Then, the reliable radial avoidance effect could be obtained, at the same time the normal use of spacecraft requirements could be strengthen.

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3 Analysis of Example According to the analysis of Sect. 2.3, in practical management process, the radial separation method is the most practical. Figures 1 and 2 are comparison curves of radial distance difference Dr and approximate value before and after control work in a practical example, and their relative error curves. It could be seen from the two figures that formula 11 can estimate the separation effect quickly and effectively.

Fig. 1. Compared curves of approximate and practical value.

When M2  M1 ¼ 180 , the estimated value of intensive from approximate formula 11 is the highest from Fig. 1. And the difference of radial distance jDr j before and after control work is max. When M2  M1 ¼ 0 , the estimated value of intensive from approximate formula 11 is min just as the Fig. 1. And the difference of radial distance jDr j before and after collision-avoidance control work is close to zero. That is, no matter how much control velocity DV is applied, the effect of radial separation cannot be achieved. The orbit evaluation after actual control shows that the avoidance principle could effectively reduce the risk of spacecraft collision.

Fig. 2. Relative error curves between approximate and practical value.

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4 Conclusion The rapid increase of space targets has seriously affected the safe operation of spacecraft in orbit. The effective implementation of collision-avoidance control is the basic means to ensure the safety of spacecraft. It is very important for the safety implementation of the whole collision-avoidance work to generate effective collisionavoidance control strategy quickly. This paper provides strong support for fast primary selection of spacecraft collision-avoidance control strategy to ensure the safety of the implementation of collision-avoidance work.

References 1. Petera RP (2001) General method for calculating satellite collision prabability. J Guid Control Dyn 24(4):716–722 2. Du H et al (2007) Space debris, 1st edn. China Aerospace Publishing House, Beijing 3. Lou GQ (2009) Analysis and enlightenment of US-Russia collision. Int Space (6): 23–27 4. McCamish SB, Romano M, Nolet S et al (2009) Flight testing of multiple-spacecraft control on SPHERES during close-proximity operations. Spacecr Rocket 46(6):1202–1213 5. Cheng T (2006) Collision probability analysis and application of cataloged space debris, 1st edn. Chinese Academy of Sciences, Beijing 6. Petera R (2007) Space vehicle conflict probability for ellipsoidal conflict volumes. J Guid Control Dyn 30(6):1818–1821 7. Leleux D, Spencer J (2002) Probability-based space shuttle collision avoidance. NASA Report 8. Guo R (2005) Study on space debris collision early warning and maneuver strategy to low earth orbit spacecraft. Master’s degree thesis, National university of defense technology, Changsha 9. Shang RW (1998) Satellite orbit attitude and dynamic. Master’s degree thesis, Beijing University of Aeronautics and Astronautics Press, Beijing

Close Relative Navigation to a Non-cooperative Maneuvering Target Using Variable Dimension Filters Qiyang Hu1 and Dayi Wang2(&) 2

1 Beijing Institute of Control Engineering, Beijing 100090, China Beijing Institute of Spacecraft System Engineering, Beijing 100094, China [email protected]

Abstract. Close relative navigation to non-cooperative spacecraft is the critical technique for the on-orbit servicing mission, the research on which has theoretical value and engineering significance. A variable dimension navigation filters is proposed in this paper to deal with the close relative navigation to a non-cooperative maneuvering target. First, the attitude and orbit motions of target as well as measurement of binocular cameras are modeled. Then, the variable dimension filters as well as the maneuver detection method are designed. The accuracy of the proposed relative navigation is proved by the numerical simulation results. Keywords: Non-cooperative target Maneuver detection


Close relative navigation


1 Introduction Autonomous On-orbit Servicing (OOS) refers to the on-orbit refueling, maintenance and resemble for a service target through a spatial intelligent servicer satellite. OOS can effectively reduce cost and prolong the lifespan of spacecrafts, showing great practical significance. The acquirement of the pose (position and attitude) of the target relative to the servicer satellite is the perquisite for OOS mission. However, the service target of OOS often belongs to “non-cooperative target”. Because these non-cooperative targets are not designed originally for rendezvous and docking mission, no reflectors are installed on their surface to facilitate identification and measurement. Besides, no valid link is available which can transmit measurement data from the target. What’s more, they are often freely tumbling under no effective control. Consequently, the properties of non-cooperative target mentioned above will bring new challenges dealing with relative navigation in OOS mission [1–3]. According to investigation, current relative navigation schemes are mainly based on optical measurements. Camera (including monocular and binocular) and Lidar are two types of optical sensors that are suitable for relative navigation in OOS. Many progresses have been made in the research of camera-based relative navigation method, which rely on the image processing technique to extract the feature from surface of target. [4] establish the coupled dynamics model of the feature points on the surface of © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 325–333, 2020. https://doi.org/10.1007/978-981-32-9698-5_37

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the target. The estimation of relative pose is then realized by tracking 10 random feature points using binocular. In [5] least square and convex optimization method are used to estimate the dynamics and kinetics parameters of target respectively. In [6], the tight/loose coupled relative navigation scheme concept are introduced, and different navigation filters are compared. On the other hand, the point cloud from Lidar directly reflects the relative range and attitude. In [7] a noise-adaptive EKF and the IPC algorithm are combined to estimate and track the state of motion of target. Then observability of lidar based relative navigation method is researched. [8] proposed the information fusion frame for the lidar-based relative navigation based on measurement from multiplatform. According to existing research, the relative orbit dynamics models (based on relative position/velocity or relative orbit elements) are used to describe the relative translational motion between chaser and target. However, the above orbit models are all based on the assumption of simple two-body motion, which means that no active maneuver is taken into consideration. Once the non-cooperative is maneuvering, the existing filter method may fail to acquire an accurate model, influencing the navigation performance. Consequently, the Close autonomous relative navigation method to a non-cooperative maneuvering target deserve deeper research. Variable dimension method is among the most efficient method to deal with maneuvering target tracking in ground-based measurement or space-based relative orbit determination. Different from the case mentioned above, the attitude information of target has to be estimated during close relative navigation. In this paper, a variable dimension filter is proposed dealing with the close relative navigation to a maneuvering target. To the author’s knowledge, it is the first time that the maneuvering is taken into consideration for close autonomous relative navigation to non-cooperative target. The structure of this paper is as follows: Sect. 2 establish the system model of navigation scheme, including dynamic model and measurement model. Section 3 illustrate the navigation filter scheme, including the filter structure and the maneuvering detection method. Section 4 conduct the numerical simulation to test the performance of the proposed algorithm.

2 Problem Formulation Consider a typical relative navigation scene for OOS mission, where a chaser (usually a servicing spacecraft) is equipped with optical sensor (a lidar in this paper) to fly around and observe the target in close range, both of which are running in respective orbit around the earth at the same time. To describe the relative motion of the two spacecraft in space, the coordinates systems to be used in this paper is defined as follows. The orbit system of chaser L is attached to the center of mass of the chaser, under which the CW equation is described. The body frame of the target and chaser are denoted as T and C, which are attached to the center of mass respectively. Both of the body frames are assumed to be parallel with respective principal axis of inertial. It is worth noting that the body frame of chaser C is assumed to be aligned with L in this paper for simplicity.

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327

Dynamics Model

Relative Attitude Dynamics Equation The attitude direction cosine matrix of target relative to chaser is defined as DðqÞ 2

q21  q22  q23 þ q20 4 DðqÞ ¼ 2ðq1 q2 þ q0 q3 Þ 2ðq1 q3  q2 q0 Þ

2ðq1 q2  q0 q3 Þ q21 þ q22  q23 þ q20 2ðq2 q3 þ q1 q0 Þ

3 2ðq1 q3 þ q2 q0 Þ 2ðq2 q3  q1 q0 Þ 5 q21  q22 þ q23 þ q20

ð1Þ

where q ¼ ½ q0 q1 q2 q3 T is the attitude quaternion between C and T. The relative angular of target relative to chaser expressed in C is ½xC ¼ DðqÞxT  xC

ð2Þ

where xC and xT are angular velocity of chaser and target expressed in C and T respectively. According to, the kinetic equation of quaternion is 1 1 q_ ¼ QðqÞ½xT ¼ QðqÞDðqÞT ½xC 2 2

ð3Þ

Where 2

q1 6 q0 QðqÞ ¼ 6 4 q3 q2

q2 q3 q0 q1

3 q3 q2 7 7 q1 5 q0

ð4Þ

The motion of relative angular velocity conforms to x_ ¼ DðqÞIT1 ½NT  DðqÞT ðx þ xC Þ  IT DðqÞT ðx þ xC Þ  xC x  IC1 ½NC  xC  IC xC 

ð5Þ

where IT and IC are the inertia tensor matrix, NT and NC are external moment. Relative Translational Dynamics Equation The translational motion of the target relative to chaser are described by the following CW equation under the assumption that the chaser is in a circular orbit.

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2

0 6 0   6 6 0 q_ 0 ¼6 6 3n2 €0 q 6 4 0 0

0 0 0 0 0 0 0 0 0 0 0 n2

1 0 0 0 2n 0

0 1 0 2n 0 0

3 2 3 0 0 6 0 7 07 7  6 7 6 7 17 7 q0 þ 6 0 7 6 mx 7 _ 07 q 7 0 6 7 5 4 my 5 0 0 mz

ð6Þ

Where q0 and q_ 0 are the position and velocity of the center-of-mass of the target relative to that of the chaser expressed in C respectively. n is the angular velocity of truly anomaly of the chaser’s orbit and assumed to keep constant during the proximity T to the target. M ¼ ½ mx my mz  is the unknown maneuvering of the target. 2.2

Measurement Model

Binocular camera installed on the chaser is the optical sensor used in the proposed relative navigation scheme, which can track the feature points on the surface of target. In this paper, two image planes of the camera are assumed to be parallel and the frame of the left camera coincides with the body frame of chaser C. When the coordinates of a feature point Pi in the left and right image planes are ðul ; vl Þ and ður ; vr Þ, respectively, its coordinate in the frame of the left camera (equals to C) can be calculated: 2

3 2 3 zi ul =f xi 5 ½qi C ¼ 4 yi 5 ¼ 4 zi vl =f fb=ðul  ur Þ zi

ð7Þ

where f is focal, b is baseline. The coordinate of the feature point in C then can be expressed as ½qi C ¼ q0 þ DðqÞPi

ð8Þ

where Pi is the coordinate of the feature points in T. When the target is assumed to be a rigid body, P is constant, conforming the following equation P_ i ¼ 0ði ¼ 1; 2. . .NÞ

ð9Þ

3 Variable Dimension Relative Navigation Filter A variable dimension relative navigation filter is designed to deal with unknown maneuver of the non-cooperative target. At the beginning of the tracking, the M is set zero, assuming there is no maneuver. The measurements from the binocular camera are fed to a vanilla navigation filter. After one filtering period, the maneuvering detection

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index should be calculated. Once the maneuver is detected, it is regarded as unknown state to be estimated in a filter with augmented dimension. 3.1

Filter Design

State of Filter Different from the mid- or far-range tracking problem, the quaternion, relative angular velocity as well as the relative position and velocity should be estimated. The inertial tensor is parameterized as two inertial ratios as follows 

k1 ¼ Ix =Iz k2 ¼ Iy =Iz

ð10Þ

Then then inertial matrix can be rewritten as IT ¼ diagð½ k1

k2

1 Þ

ð11Þ

where k1 and k2 are constants defined as inertial ratios conforming to k_ 1 ¼ k_ 2 ¼ 0

ð12Þ

What’s more, the coordinates of feature points in the body frame of target should also be regarded as unknown parameters to be estimated. According to the analysis above, the state vector is designed as x ¼ ½q0 q_ 0 q x k1 k2 P1 P2 : PN 

ð13Þ

Once the maneuver is detected, the state vector is augmented as xaug ¼ ½q0 q_ 0 q x k1 k2 P1 P2 : PN nx ny nz 

ð14Þ

The unknown maneuver conforms to the following kinetics equation n_ x ¼ n_ y ¼ n_ z ¼ 0

ð15Þ

Measurement of Filter According to the measurement principal of binocular camera, the coordinates of the feature point in C can be regarded as measurement for filter. Let the measurement vector of the feature point is zi ¼ ½qi C ¼½ xi Then the total measurement vector

yi

zi 

ð16Þ

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z ¼ ½ z1

z2

. . . zn  ¼ hðxÞ þ v

ð17Þ

where v is measurement noise. 3.2

Cubature Kalman Filter Algorithm

Because of the linearity of both dynamic and measurement function, the filter algorithm should be selected which can deal with nonlinear system. In this paper, Cubature Kalman Filter (CKF) is used as the navigation filter, which approximates the first and second order moment of random variable based on the 2n Cubature points. (n is the dimension of system). Compared with conventional EKF algorithm, it has higher accuracy and gets rid of the jacobian matrix, the computation of which is complex. Besides, CKF avoids the tunable parameters, ensuring that the covariance matrix is positive definite theoretically. Different from UKF, it gets rid of the central sampling points. The CKF algorithm can be seen in any textbook about optimal estimation. 3.3

Maneuvering Detection

In this paper, the normalized innovation squared (NIS) serve as the maneuver detection index. NIS ¼ ðyk  ^ykjk1 ÞT S1 ykjk1 Þ k ðyk  ^

ð18Þ

According to filter theory, the NIS conform to chi-squared distribution with n degree-offreedom (n is the dimension of the measurement vector.) Sk is the covariance of the innovation, which is predetermined and not subject to the change of model. Once the target is maneuvering, the change of dynamic modeling may result in the change in the estimated measurement, leading to the inconsistency between distribution of innovation and the estimated covariance. Then, the NIS may increase. Consequently, when the measurement is fed to the filter, the NIS should be calculated and compared to a designed threshold. The target is considered maneuvering once the following condition is satisfied NIS [ treshhold

ð19Þ

4 Numerical Simulation To verify the performance of the relative navigation scheme, the case of maneuver should be taken into consideration and corresponding numerical simulation should be implemented in this paper, the simulator software is Matlab, which is used to generate measurements, integrate the orbit and attitude dynamics and finally realize the relative navigation filter algorithm. The chaser is assumed to be in a circular orbit with the altitude 7170 km. The corresponding angular velocity of true anomaly is 7170 km. During numerical simulation, six feature points are assumed to be tracked without occultation, the coordinates of which in the body frame of target T are as follows. To illustrate the performance, a vanilla filter is

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included in the simulation experiment as a reference. The ode45 algorithm is used as integration algorithm. The simulation time span is 300 s. Measurement Sampling period is one second. At 90 s, a constant accelerate rate M ¼ ½ 0:1 0:1 0:1 T is added to the relative translation dynamics equation, simulating the case when the target is maneuvering. The results of the simulation are as follows (Figs. 1, 2, 3, 4, 5 and 6). As can be seen from the above figures, the maneuver has obvious influence on the state estimation, bringing challenge to the design of relative navigation scheme. The vanilla filter can’t deal with the maneuvering of the target. After the maneuvering is considered in the 90 s, the error of the estimated attitude and angular velocity grow much larger. The estimation of other state even fails to converge. On the other hand, the proposed variable dimension filters acquire better performance. All the estimation of state can converge quickly after a short time of disrupt. For instance, the estimation of the relative position and velocity can converge again in less than 5 s, as illustrated in Fig. 1. The results of the estimation also indicate that the maneuver can be detected quickly so that the augmented dimension filter can start to work. The performance of results of numerical simulation verifies the validity of the proposed maneuver detection and variable dimension filtering method.

Fig. 1. Estimation of position

Fig. 2. Estimation of velocity

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Fig. 3. Estimation of attitude

Fig. 4. Estimation of relative angular velocity

Fig. 5. Estimation of inertial ration

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Fig. 6. Estimation of position of feature position

5 Conclusion To address the relative navigation in close range to a non-cooperative maneuvering target, variable dimension filters method is proposed in this paper, which detect the maneuvering and estimate the relative motion of target. First, the dynamic model and measurement model are built. Then, the maneuvering detection scheme as well as a variable dimension filter structure are designed. Finally, the numerical simulation is conducted, the result of which verify the validity of the proposed filter scheme.

References 1. Li WJ, Cheng DY, Liu XG et al (2019) On-orbit service (OOS) of spacecraft: a review of engineering developments. Prog Aerosp Sci 208:32–120 (2019) 2. Pesce V, Lavagna M, Bevilacqua R (2017) Stereovision based pose and inertia estimation of unknown and uncooperative space objects. Adv Space Res 59(1):236–251 3. Wang DY, Hu QY, Hu HD et al (2018) Review of autonomous relative navigation for noncooperative spacecraft. Control Theory Appl 35(10):1392–1404 4. Segal S, Carmi A, Gurfil P (2014) Stereovision-based estimation of relative dynamics between noncooperative satellites: theory and experiments. Trans Control Syst Technol 22(2):568–584 5. Qian F, Zhu ZH, Pan Q et al (2018) Relative state inertial estimation of unknown tumbling target by setero vision. IEEE Access 6:54126–54138 6. Pesce V, Opromolla R, Sarno S et al (2019) Autonomous relative navigation around uncooperative spacecraft based on a single camera. Aerosp Sci Technol 84:1070–1080 7. Li YP, Wang YP, Xie YC (2019) Using consecutive point clouds for pose and motion estimation of tumbling non-cooperative target. Adv Space Res 63(5):1576–1587 8. Mahboubeh ZJ, Seyed MBM (2018) Motion estimation of uncooperative space objects: a case of multi-platform fusion. Adv Space Res 62(9):2665–2678

Vision-Based Vehicle Detection in Foggy Days by Convolutional Neural Network Guizhen Yu1, Sifen Wang1, Mingxing Li2(&), Yaxin Guo1, and Zhangyu Wang1 1

2

School of Transportation Science and Engineering, Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing 100191, China School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China [email protected]

Abstract. Vehicle detection plays an important role in advanced driving assisted system and autonomous driving system. However, the existing vehicle detection methods are not robust in harsh environments, especially in foggy environment. To solve this problem, a vision-based vehicle detection structure using convolutional neural network is presented to detect the vehicle in foggy days. In our vehicle detection structure, a pair of encoders and decoders is used to estimate atmospheric illumination and transmissivity, and to establish the defogging image firstly. And then, the vehicle detection is implemented by a proposed vehicle detection method which predict the left-top key point as well as the right- bottom key point of the vehicle, thus get the bounding box of the vehicle. To verify the effectiveness of the new method, a data set based on the video generated from PreScan simulation platform is set up. And the new vehicle detection method is tested in multiple scenarios such as left turn, right turn, uphill, downhill. Experimental results show that our vehicle detection structure can effectively detect vehicles in foggy days. Keywords: Vehicle detection PreScan


Defogging
Convolutional neural network


1 Introduction Vehicle detection, as the most important and fundamental part of assisted driving, has been paid more and more attentions by researchers. Scholars have been studying vehicle detection under normal weather conditions and have achieved many results. However, as China’s natural environment has been deteriorated late years, severe weather often occurs, the most noteworthy one of which is foggy conditions. At present, vehicle detection algorithms based on vision mainly focus on the favorable daytime environment. Li et al., for example, proposed a vehicle detection algorithm based on multi-feature fusion [1]. Fan et al. proposed a Faster R-CNN deep learning framework to achieve vehicle detection [2]. Zhou et al. proposed a method of real-time vehicle detection on the basis of YOLO algorithm [3], which is a solution to © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 334–343, 2020. https://doi.org/10.1007/978-981-32-9698-5_38

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vehicle identification by analyzing visible images. These algorithms have a significant performance on vehicle detection under normal weather conditions. However, due to the low contrast of images acquired in foggy weather, vehicle information cannot be segmented from foggy images, resulting in the inability of vehicle feature extraction. Therefore, these algorithms are basically not applicable in foggy weather. For images of road under foggy weather, firstly, it is necessary to defog them and restore them to fog-free images with high contrast and easy identification. At present, there are various image defogging algorithms based on the physical model, the most widely used one is the end-to-end network algorithm such as He et al. [4]. Cai [5] et al. This method as well as other similar methods to estimate transmissivity do not solve the estimation problem of atmospheric illumination in the situation. Zhang and Patel [6] proposed a solution to this problem by generating an antagonistic neural network to estimate atmospheric illumination and transmissivity. In this method, an independent neural network architecture is used to build the unknown variables in the model of atmospheric scattering. On the basis of summarizing the applicability of various algorithms, this paper proposes a vehicle detection algorithm which mainly contains two steps: image defogging and vehicle detection as shown in Fig. 1. In image defogging part, a deep learning algorithm is applied to defog the image, and get an elegant image. After defogging the image, vehicle detecting is implemented and the final vehicle detection results are established.

Fig. 1. Framework of vehicle detection.

2 Image Defogging The fog reduces the content of the image and also blurs the information, which has a negative impact on the vision-based decision. In this section, an image defogging method based on the convolutional neural network is established. The network utilizes a pair of encoders to decode using the atmospheric illumination and transmissivity, both of which are estimated. The structure is adapted from an efficient image segmentation network, and the image is refined with a fully connected pyramid pooling network to form the final defogged image.

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Atmospheric Model

In general, the fog present in an image can be formulized by the following classical model of the scatter of atmosphere [4]: I ð yÞ ¼ J ð yÞT ð yÞ þ Að1  TðyÞÞ

ð1Þ

In this formula above, I(y) is the blurred image obtained by the camera, J(y) is the fog-free image that serves as the desired output, A is the global atmospheric illumination, and T(y) is the transmissivity. Thus, a fog-free image can be retrieved via the estimation of the global atmospheric illumination and the transmissivity of the foggy image obtained. Many successful techniques apply this approach as a basis to estimate the transmissivity of image defogging with hand-engineered features. Recently, it has also been proposed to use neural network methods to estimate the properties of these scenes. For example, U-Net [7] learns the properties of atmospheric illumination and applies a dense network to learn transmissivity estimates. Furthermore, Li et al. [8] show that the model of atmospheric scattering depicted by Eq. (1) can be rewritten via a linear transform to a form with an uni-variable and bias. JðyÞ ¼ KðyÞIðyÞ  KðyÞ þ k KðyÞ ¼

1 T ð yÞ ð I ð yÞ

 AÞ þ ðA  kÞ

I ð yÞ  1

ð2Þ ð3Þ

This formula automatically conforms to the deep learning framework. It also implies the validity of the pure convolution method. Therefore, this paper applies the method of deep learning to estimate the global atmospheric illumination and the transmissivity of captured foggy images, and finally obtains the defogging of images. 2.2

Defogging Network Structure

As shown in Fig. 2, our application of the convolutional neural network Dual-FastNet [9] is established upon past achievements in image segmentation and image defogging based on deep learning. This network is inspired by a previous atmospheric model network. Instead of using a single encoder-decoder, the method utilizes two independent encoder-decoder models to respectively learn atmospheric illumination A and transmissivity T(y). The results of the estimations then serve as inputs for the calculation of the defogged image applying the formula depicted in Eq. (1). For each FastNet, we adopted the LinkNet architecture, but removed the final softmax and prediction layer, in attempt to deliver features straight to the pyramid pool network at complete spatial resolution of input to learn image features. LinkNet uses the pretrained ResNet18 model layer as its encoder module. When forming the final output image, the pyramid pooling network gradually embeds the input on multiple scales, and then adjusts the size of all scale embedding according to the output resolution to maintain multi-scale features.

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Fig. 2. Network architecture of defogging.

3 Vehicle Detection In the application of automatic driving, the high processing speed performance of the vehicle detection is necessary [10, 11], thus, in this paper we apply the CornerNet-Lite [12], a popular object detection framework for vehicle detection. 3.1

Vehicle Detection Framework

Instead of detecting the vehicles as a series of bounding boxes which is widely used in one-stage detectors [11], we detect the vehicle as a series of point pairs: the left-top key point meanwhile the right- bottom key point of the vehicle in the images, thus get the bounding-box of the vehicle. Our vehicle detection network architecture is elaborated in Fig. 3. Lightweight Hourglass networks are adopted as the backbone network for this paper which was first used in human posture estimation. Behind the backbone network, there are two independent branches for detecting the left-top points as well as the right-bottom points of the vehicle respectively. In each vehicle corner point detection branch, containing three subbranches: heatmaps prediction subbranch, embeddings subbranch, and the offset correction subbranch. The details of the submodules are explained in Sect. 3.2. Besides, unlike many other object detection frameworks which using different scales features map for object prediction, we only used the feature map from the output of the hourglass network for vehicle corner point prediction. Real-time is very important for vehicle detection algorithm, inspired by [12, 13], we further lightweight the model. In the vehicle detection network, hourglass network which is built from residual connection blocks and consists of two 3  3 convolution layers and a skip connection are the parts that consume the most computing resources. Thus, we adopted the approach from the SqueezeNet [14] and MobileNets [13] to speed up the algorithm. In our vehicle detection network, we replace the residual block with the fire module. In fire module, a 1  1 kernel is first used to cut down the input channels, and then the output feature map is expanded by a mixture of 1  1 and 3  3 kernels. Besides, we replace the 3  3 standard convolution with a 3  3 depthwise separable convolution, which is proposed in MobileNets [13] to further reduce the computation of the vehicle detection model and improves the vehicle detection time.

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Fig. 3. Network architecture of vehicle detection

3.2

Vehicle Points Detection

In our network, we take the vehicle detection as the left-top key points and the rightbottom key points prediction of the vehicle, thus, behind the backbone network, there are two independent vehicle corners detection modules to detect the left-top key points and right- bottom key points of the vehicle respectively. Detection Corners As shown in Fig. 3, the heatmaps of the left-top key point and right- bottom key point are generated through the convolutional neural network respectively. The output of each heatmap is Hf  Wf  Cf , where Hf represent the width of the output feature map meanwhile Wf represent the height of the output feature map, and the Cf represent the channel of the output feature maps which indicate the kind of vehicle to detect, and each channel is a binary data which presents the key point location of that class. As illustrated in Fig. 4, the yellow rectangles indicate the ground-truth, and the red box represents the prediction result, although the top left and bottom right corner do not exactly coincide with the ground-truth, the predicted two corners are also good indicators of the vehicle to be predicted. Thus, we reduced the penalty for a negative sample within r radius of a positive sample, and used a variation of focal loss to train the heatmap:

Fig. 4. Ne Heatmap for vehicle training.

Vision-Based Vehicle Detection in Foggy Days by CNN

1 XC XH XW Lh ¼  c¼1 i¼1 j¼1 N

( 

  ð1  pcij Þa log pcij b   1  ycij ðpcij Þa log 1  pcij

ycij ¼ 1 ycij 6¼ 1

339

ð4Þ

where the pcij represents the probability of predicting the point at location (i, j) as the vehicle corner point, N is the number of vehicles in a picture, ab are the super parameter used to control the distribution of each point. When the ði; jÞ in the near r radius of the ground-truth corner, the penalty value i.e. ycij is a non-normalized 2D gaussian distribution e

x2 þ y2 2d2

, and the d ¼ 13 r.

Classify Key Points Multiple vehicles are usually detected in a single image as shown in Fig. 5. However, the left-top and right-bottom key point detection module can detect multiple corner points in each branch, thus we need to classify the same vehicle key point in two different branches.

Fig. 5. Multiple vehicles detected.

In our embeddings subbranch, network prediction an embedding vector for each corner which is inspired from [15]. The embedding vectors from the same vehicle of the corner are very close, meanwhile, the embedding vectors from the different vehicle are very large, thus, we can judge whether two corners belong to the same car with the embedding vectors. And, our network apply the following loss function to train embedding: N  2  2 1X ½ etj  ej þ ebj  ej  N j¼1

ð5Þ

N N X X 1 maxð0; D  jek  ei jÞ NðN  1Þ k¼1 i¼1;i6¼k

ð6Þ

Ls ¼

Ld ¼

where etj is the left-top key point embedding, ebj is the right-bottom key point embedding, ej is the mean value of the two embeddings. Through the above method, the two corners of the same car can be well classified.

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4 Experiments We conducted our experiments on the Pytorch [16] which is a popular deep learning framework. We train the model parameters until the training loss converges without pretraining weights, and use the Adam to optimize the losses which is the summed up over all the attention maps and embeddings in a mini-batch. 4.1

Dataset

To make a quantitative analysis of the vehicle detection structure, the vehicle video data on foggy days are needed firstly, however, it is hard to collect. On the other hand, driving scenes in foggy weather can be simulated in Prescan, hence, we used the Prescan to generate the video in fog days. PreScan is a simulation platform for the verification of intelligent vehicle systems. As shown in Fig. 6, we generated a serial of video which contains straight, left turn, right turn, uphill, downhill fog scenes. Based on the generated video we select the images containing the vehicle and built a set of vehicle datasets. The dataset provides 3,800 images which is grouped into the training set and test set (i.e., 2,800, and 1000 images, respectively), and the resolution of the dataset is 960 * 720.

Fig. 6. Dataset example.

4.2

Detection Results

In this paper, we apply two indicators to evaluate the effectiveness of the vehicle detection structure: one is the false negatives rate (FPR) and the other is true positive rate (TPR). TPR refer to the ratio of the right detected vehicle in all vehicles of all the testing set, meanwhile FPR refer to the ratio of the miss detected vehicle in all vehicles. The formula of TPR and FPR is shown as follows: TPR ¼

the vehicles detected correctly the number of all vehicles in testing set

ð7Þ

the number of vehicle miss detected the number of all vehicles in testing set

ð8Þ

FPR ¼

In addition, the detected vehicle is considered to be correct only when the Intersection over Union (IoU) between the detected vehicle result and the ground-truth

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vehicle bounding box is greater than 0.5. The detection statistical result of our vehicle detection method are elaborated in Table 1. Table 1. Experiments result Metric Result TPR 95.2% FPR 4.15%

In order to further demonstrate the promotion of the vehicle detection structure proposed in this paper, especially the influence of defogging algorithm on vehicle detection, we removed the defogging algorithm to conduct vehicle detection directly. Besides, we employ the SSD [11] which is the representative one stage object detection method and yolo-v3 [17] to evaluate the detection ability in our simulation datasets and further compare to our vehicle detection methods. The experiment results are elaborated in Table 2. Table 2. Experiments result. Method

Evaluation metric TPR FPR Without defogging 89.2% 6.1% SSD 87.4% 6.7% Yolo-v3 90.3% 6.4% Our method 95.2% 4.15%

Fig. 7. Vehicle detection results after defogging.

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Fig. 8. Vehicle detection results before defogging.

The above table shows that without defogging algorithm, the accuracy of our vehicle detection will be greatly affected. The detection results are shown in Figs. 7 and 8.

5 Conclusion In this article, a vehicle detection method to detect the vehicle in foggy days is established. The proposed method contains two parts: image defogging part and vehicle detection part. In image defogging part, we utilize a CNN to generate the defogging image, and in vehicle detection part, we detect the left-top key point and right-bottom key point of the vehicle. We have detected the vehicle in multiple scenarios which generated from PreScan simulation platform and show a positive result. Further work is aimed to improving the real-time performance of the algorithm and apply the method for real-world application. Acknowledgments. This work is partially supported by the Beijing Municipal Science and Technology Project under Grant #Z181100008918003 and the National Key Research and Development Program of China (2016YFB0101001). The authors would also like to thank the insightful and constructive comments from anonymous reviewers.

References 1. Li W et al (2014) Multifeature fusion vehicle detection algorithm based on choquet integral. J Appl Math 1–11 2. Fan Q, Brown L, Smith J (2016) A closer look at Faster R-CNN for vehicle detection. In: 2016 IEEE intelligent vehicles symposium (IV). IEEE, pp 124–129 3. Zhou Y, Nejati H, Do TT et al (2016) Image-based vehicle analysis using deep neural network: a systematic study. In: 2016 IEEE international conference on digital signal processing (DSP). IEEE, pp 276–280 4. He K, Sun J, Tang X (2010) Single image haze removal using dark channel prior. IEEE Trans Pattern Anal Mach Intell 33(12):2341–2353 5. Cai B et al (2016) DehazeNet: an end-to-end system for single image haze removal. IEEE Trans Image Process 25(11):5187–5198 6. Zhang H, Patel VM (2018) Densely connected pyramid dehazing network. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 3194–3203

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7. Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. In: International conference on medical image computing and computer-assisted intervention. Springer, Cham, pp 234–241 8. Li B, Peng X, Wang Z et al (2017) Aod-net: all-in-one dehazing network. In: Proceedings of the IEEE international conference on computer vision, pp 4770–4778 9. Morales P, Klinghoffer T, Lee SJ (2019) Feature forwarding for efficient single image dehazing. arXiv preprint arXiv:1904.09059 10. Badrinarayanan V, Kendall A, Cipolla R (2017) SegNet: a deep convolutional encoderdecoder architecture for image segmentation. IEEE Trans Pattern Anal Mach Intell 39 (12):2481–2495 11. Liu W, Anguelov D, Erhan D et al (2016) SSD: single shot multibox detector. In: European conference on computer vision. Springer, Cham, pp 21–37 12. Law H, Teng Y, Russakovsky O et al (2019) CornerNet-Lite: efficient keypoint based object detection. arXiv preprint arXiv:1904.08900 13. Sandler M, Howard A, Zhu M et al (2018) Mobilenetv2: inverted residuals and linear bottlenecks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 4510–4520 14. Iandola FN, Han S, Moskewicz MW et al (2016) SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and > < xF! ðk þ 1Þ ¼ xF! ðkÞ v ðk þ 1Þ ¼ vF ðk Þ þ TuðkÞ þ wðkÞ > > : F vF! ðk þ 1Þ ¼ 0 where wðk þ 1Þ ¼ FwðkÞ is disturbances, F 2 Rnn . Thus, the control algorithm of followers is ui ¼ 

X
 X
 x i ð k Þ  xj ð k Þ  vi ð k Þ  vj ð k Þ j¼Ni

j¼Ni

This means that   uðk Þ ¼  LF xF þ LFc xFc  LF vF þ LFc vFc   : 1 ¼ LF xF þ L1 F LFc xFc  LF vF þ LF LFc vFc

ð9Þ

1 Let y1 ðkÞ ¼ xF ðkÞ þ L1 F LF! xF! ðk Þ, y2 ðk Þ ¼ vF ðk Þ þ LF LF! vF! ðk Þ, we get

y1 ðk þ 1Þ ¼ xF ðk þ 1Þ þ L1 F LFc xFc ðk þ 1Þ ¼ xF ðkÞ þ TvF ðkÞ þ L1 F LFc xFc ðk Þ ¼ y1 ðkÞ þ TvF ðkÞ ¼ y1 ðkÞ þ Ty2 ðkÞ

ð10Þ

y2 ðk þ 1Þ ¼ vF ðk þ 1Þ þ L1 F LFc vFc ðk þ 1Þ ¼ vF ðkÞ  TLF y1 ðkÞ  TLF y2 ðkÞ þ wðkÞ ¼ y2 ðk Þ  TLF y2 ðkÞ  TLF y1 ðkÞ þ wðkÞ ¼ ðI  TLF Þy2 ðkÞ  TLF y1 ðkÞ þ wðkÞ

ð11Þ

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This means that, y ð k þ 1Þ ¼

y 1 ð k þ 1Þ y 2 ð k þ 1Þ



¼

I TLF

T I  TLF



y 1 ðk Þ y 2 ðk Þ

þ



0 w ðk Þ I

The system equations change to 8 < yðk þ 1Þ ¼ AyðkÞ þ Gwðk Þ xF! ðk þ 1Þ ¼ xF! ðkÞ ; : wðk þ 1Þ ¼ Fwðk Þ

ð12Þ

ð13Þ





I T 0 where A ¼ ,G¼ . TLF I  TLF I From Lemma 1, assuming that 8k 2 f1; . . .; Ng, it follows that (

yT ð0ÞRyð0Þ  d2y wT ð0Þwð0Þ  d2w

ð14Þ

where R is the positive definite matrix, 0  dy \e, dw  0. Therefore, the discrete-time multi-agent system (4) satisfying the condition (5) and (8) under the control algorithm (5) to achieve the finite-time bounded on ðdy ; dw ; e; R; NÞ. Corollary 2. Considering a networked system composed of n followers and m leaders. If the assumption 2 is established, the discrete-time multi-agent networked system with leaders based on control algorithm (5) can realize containment control in finite time, if there are positive definite matrices P1 and P2 satisfied 

AT P1 A  P1 P1 A

 AT P1 \0; P1 þ AT F T P2 FA  P2

1 ~ Þd2 þ kmax ðP2 Þd2w   e2 : ½k ðP ~ 1 Þ max 1 y kmin ðP From Lemma 1, we can get that second-order discrete-time multi-agent systems related to ðdy ; dw ; e; R; NÞ achieve finite-time asymptotic stability. That is, containment control in finite time.

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4 Simulation Results

Fig. 1. Topology graph for second-order multi-agent systems

Considering a topology structure graph consist of followers 1–5 and leaders 6–8, as shown in Fig. 1. It is assumed that the weights of lines in the topology graph are 1, thus the Laplacian matrix of second-order multi-agent systems is 2

2 6 1 6 6 0 6 6 0 L¼6 6 0 6 6 0 6 4 0 0

1 2 1 0 0 0 0 0

0 1 2 1 0 0 0 0

0 0 1 3 1 0 0 0

0 0 0 1 2 0 0 0

1 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0

3 0 0 7 7 0 7 7 1 7 7 0 7 7 0 7 7 0 5 0

Let the initial state of followers is x1 ¼ ð0; 4Þ, x2 ¼ ð4; 0Þ, x3 ¼ ð0; 2Þ, x4 ¼ ð2; 0Þ and x5 ¼ ð3; 0Þ. The initial state of leaders is x5 ¼ ð6; 8Þ, x6 ¼ ð8; 8Þ and x7 ¼ ð8; 6Þ. Let the disturbance is wðk Þ ¼ sinðtÞ. The numerical simulation is shown in Fig. 2, as we can see, the position state of followers with disturbances under the control algorithm (6) eventually converges to the planar triangular region surrounded by three leaders, and the dynamic multi-agent system can achieve the containment control.

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Fig. 2. Motion trajectory of MAS with sinusoidal disturbances

5 Conclusion In this paper, the problem of containment control for the discrete time of multi-agent systems is studied. The discrete time system model with external disturbances is designed. In order to achieve the coordinated control between multi-agents in the dynamic system, the containment control algorithm of the second-order networked system with leaders is proposed. Based on the Lyapunov function and algebraic graph theory, the containment control of the discrete-time multi-agent systems with disturbances is investigated. By computer simulation, the numerical example of the control algorithm is carried out, and eventually, the followers can converge to the area surrounded by multi-agent in finite time. The validity of the theory of this paper is verified. Acknowledgements. The research is supported by the National Natural Science Foundation of China (61673200, 61771231), the Major Basic Research Project of Natural Science Foundation of Shandong Province of China (ZR2018ZC0438) and the Key Research and Development Program of Yantai City of China (2019XDHZ085).

References 1. Wang ZX, Da-Jun DU, Fei MR (2014) Average consensus in directed networks of multiagents with uncertain time-varying delays. Acta Automatica Sinica 40(11):2602–2608 2. Li L, Fang H (2012) Consensus tracking of leader-following multi-agent systems with sampling delay. J Huazhong Univ Sci Technol 40(8):88–92 3. Pan T, Mo L, Cao X (2016) Mean square consensus of multi-agent systems under Markovian switching with colored noises. Control Theory Appl 33(3):361–367 4. Ma Q, Miao G (2014) Letters: distributed containment control of linear multi-agent systems. Neurocomputing 133(10):399–403 5. Cao Y, Ren W, Egerstedt M (2012) Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks. Automatica 48(8):1586–1597

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6. Liu H, Cheng L, Tan M, Hou Z-G (2015) Containment control of continuous-time linear multi-agent systems with aperiodic sample. Automatica 57:78–84 7. Wang F, Yang H, Liu Z, Chen Z (2017) Containment control of leader-following multi-agent systems with jointly-connected topologies and time-varying delays. Neurocomputing 260:341–348 8. Ding S, Li S (2011) A survey for finite-time control problems. Control Decis 26(2):161–169 9. Zhu Y-K, Guan X-P, Luo X-Y (2013) Finite-time consensus of heterogeneous multi- agent systems. Chin Phys B 22(3):038901 (1–6) 10. Li S, Du H, Lin X (2013) Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47(8):1706–1712

Scattering Prediction from Data of Scale Model Based on Regression Method in SPSS Jingcheng Zhao, Zongkai Yang(&), and Tao Tang Beihang University, Beijing 100191, China [email protected]

Abstract. Radar cross-section (RCS) measurement of large targets has always been an important research direction in the field of electromagnetism. The measurement of full-scale targets is expensive, and it is difficult to meet the test conditions. This problem can be solved theoretically by the similarity principle of electromagnetism. The RCS measurement of large targets using a scale model is the main method studied in this thesis. The article first analyzes the thin cylindrical model of a perfect conductor and a polytetrafluoroethylene (PTFE) dielectric. The data is obtained by FEKO software, and is simply processed and imported into SPSS for regression analysis to fit the formula. The relationship of the RCS between the original model and the scaled model under different scaling factors is analyzed. The formula of regression fitting and the formula derived by theory are compared to verify the effectiveness of the method. Finally, the same method is applied to the perfect conductor with absorbing material on the surface. By comparing the relative error between the formula and the original data, the applicability of this method is further verified and expanded. Keywords: RCS


Scale model
SPSS
Regression

1 Introduction The physical quantity used to quantitatively express the ability of radar targets to scatter irradiated electromagnetic waves is called the radar cross-section (RCS) [1]. The RCS is a significant index in the research and development process of aircraft design, as it can be used to quantify the stealth performance of aircraft [2]. It can also be used for highresolution imaging of the target in one, two, or three dimensions. When measuring the RCS of large targets, not only is full-scale measurement difficult for meeting the test environment conditions, but the processing cost of a full-scale RCS model is very high [3]. Measuring a scale model can effectively solve these problems [4]. According to the principle of similitude in electromagnetism, a scale model reduces the size of the model and the radar wavelength. For the scale model of a perfect conductor, the RCS value of the corresponding original model can be obtained by using the principle of similitude. Full-space scaling theory that satisfies the ideal scaling conditions is derived from Maxwell equations, velocity invariant conditions, and impedance invariant conditions [5]. On the premise of satisfying these conditions, the geometric shape of the model is exactly similar to the actual target, but its size is © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 361–370, 2020. https://doi.org/10.1007/978-981-32-9698-5_41

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reduced in the same proportion to ensure that the electrical size of the target remains unchanged under testing. In the case of a perfect conductor, it is only necessary to reduce the model size to 1/ N and increase the measurement frequency by N times. However, in the actual RCS measurement process, most of the measured models are dielectric models. In this case, it is necessary to increase the conductivity of the dielectric by N times, which is difficult for testing [6]. At present, RCS scaling measurement is more common in the case of metal or noconsumption, low-loss dielectrics. In fact, metal surface coated with absorbing material is the most common means of reducing the target RCS, but under this circumstance, the conductivity of the material is immutable. This similarity principle is very difficult to implement during the study of the scale model. At present, the research of scale models primarily includes the following contents. In a study by Hu et al. [7], the RCS frequency curve of the model was first measured according to the shortest wavelength test equipment that could be provided, and then extrapolated from the curve to the frequency point required by the ideal scale ratio; however, there is no error analysis in this article. Hongwei and Zhe [8] found that the RCS of the target can be derived by measuring the scale model and using the corresponding data processing and inversion calculation methods, but the error of this method is large. Some researchers have derived a simple formula for estimating the RCS using a scale model, but only for simple scattering models [9, 10]. Other researchers have simulated and analyzed the relationship between the RCS of the scaled model and the original model, but did not make quantitative exhaustive analysis; instead, they simply compared the resulting graphs [11–15]. In this paper, the simulation data is obtained from FEKO, and the data regression equation is processed by using Statistical Product and Service Solutions (SPSS) software to solve the dielectric target scale model. In the Sect. 2 of the paper, the model of the thin conductor cylinder is selected. A perfect conductor thin cylinder with different scale factors is then simulated by FEKO software. After the simulation data is obtained, SPSS is used for regression analysis, and the results are compared with the scale model formula. In Sect. 3, the RCS scale relationship of the thin cylindrical material of the dielectric material is analyzed using the same method used in Sect. 2 to determine the applicability of this method. Section 4 simulates the dielectric cylinders with absorbing materials on the surface under different scale factors. The four groups of data are used to predict another group of data, and are compared with the actual simulation data to verify the correctness and feasibility of the method. Section 5 presents the conclusion.

2 Perfect Conductor Cylinder Simulation Regression 2.1

Hardware Circuit Design Method

There are many cases of the principle of similitude in electromagnetism. One of the common cases is as follows: if the dielectric constant e and the magnetic permeability l are constant, and the conductor conductivity r is a finite value, then when the size is

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reduced to 1/N, the operating frequency is required to change by N times, and the conductivity is also increased by N times [16]. When measuring electromagnetic scattering, the size of the RCS is related to the scale factor n. The RCS of the original model is n2 times that of the scale model [17]. When the scale model RCS is transformed to the original model RCS, we need to add a factor as in Eq. (1): 10 lg n2 ¼ 20 lg n:

ð1Þ

The main work of this chapter is to verify the validity of the SPSS regression method by fitting the equation to the perfect conductor thin cylinder model. 2.2

The Simulation of an Ideal Conductor Cylinder

First, the perfect conductor thin cylinder is simulated. In FEKO, the model parameters with scale factors of 0.96, 2, 4, and 8 are set separately, and the models of these scale factors are simulated. The specific model parameters are presented in Table 1. Table 1. Parameters of scale model Serial number Diameter (mm) Length (mm) Scale factor Calculation frequency (GHz) 1 159 2092.1 0.96 1.91 2 152 2000 1 2 3 76 1000 2 4 4 38 500 4 8 5 19 250 8 16

First, the models of different scale factors are set in FEKO. As shown in Fig. 1, the cylinder is placed along the z-axis, and the mesh operation is normalized. The incident plane wave range is 0° to 360°, and the angle step is 1°. The RCS of the perfect conductor cylinder is simulated in 360 directions, as shown in Fig. 2.

Fig. 1. The model of the thin cylinder in FEKO.

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Fig. 2. Set requests in FEKO.

The data derived from FEKO simulation is in ASCII format. FEKO simulation can automatically generate curves of RCS that vary with the angle. Figure 3 displays the image generated when the scale factor is 0.96.

Fig. 3. The image of the RCS when the scale factor is 0.96.

However, these graphs are not conducive to visual comparison, so we again export the five groups of data obtained from simulation and process them via the radar map. As is shown in Fig. 4, we can more clearly see the relationship of the RCS data under different scale factors. It can be seen from Fig. 4 that with the increase of the scale factor, the simulated RCS data intuitively shrinks regularly with fixed values, but the relationship between the data is not given quantitatively. Therefore, further processing of the data is required.

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Fig. 4. The image of RCS with different scale factors.

2.3

Fitting Regression by SPSS

SPSS includes a variety of sophisticated statistical methods and models, providing statistical analysis users with a full range of statistical algorithms; it provides a variety of data preparation and data processing techniques [18]. The objective of our regression is to analyze the relationship between the RCS of the original model, the RCS of the scale model, and the scaling factor n. First, we need to unify the unit magnitude of RCS and n, and the unit of RCS is dBsm. Therefore, we need to take n as logarithm, and then conduct regression research. The data is imported into SPSS, the independent variable is set to lg(n) and the RCS (x) of the original model, and the dependent variable is set to RCS (y) of the scale model. The correlation analysis of the coefficient can be obtained by regression analysis, as is shown in Tables 2 and 3. Table 2. Coefficient of regression Coefficient Constant 0.013 x 1.001 lg(n) −20

Standard error t 0.003 3.807 0.000 8386.780 0.004 −4686.100

Saliency 0.000 0.000 0.000

According to Table 3, we find R equals 1, which demonstrates that these three variables are completely linearly correlated. According to Table 2, we can obtain the fitting equation as follows:

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y ¼ 1:001x  20lgðnÞ þ 0:013:

ð2Þ

Table 3. Correlation analysis R Square of R Adjusted squared R Standard estimated error 1.000 1.000 1.000 0.03452220

Compared with Eq. (1), the regression is correct. This method can be perfectly applied to the model of the perfect conductor.

3 Simulation of Dielectric Cylinder In the perfect conductor, the resistance is zero and the conductivity is infinite, which does not exist in practice. Therefore, in this chapter, the same method is used to simulate and return the fine cylinders of the polytetrafluoroethylene dielectric and the pure absorbing material dielectric. The simulated fine cylinder dimensions are provided in Table 1. Teflon is extensively used in defense, aerospace, electronics, and other industries [19], and as it has a very important role in these industries, it has significant research value. First, polytetrafluoroethylene chloride was simulated, and the data obtained is presented in Fig. 5.

Fig. 5. Simulation results of fine Teflon cylinder with different scale factors.

Using the same method as the previous chapter, the regression data is calculated by SPSS, and Table 4 can be obtained. The relationship between the RCS (y) of the scale factor and the RCS (x) of the original model can be obtained from Table 4, as given by Eq. (3):

Scattering Prediction from Data of Scale Model

y ¼ x  20lgðnÞ þ 0:002:

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ð3Þ

Table 4. Coefficient of regression Coefficient Constant 0.002 x 1.000 lg(n) −20.000

Standard error t 0.001 3.807 0.001 −30973.12 0.000 33647.80

Saliency 0.000 0.000 0.000

Comparing Eqs. (2) and (3), it can be determined that the relationship between the RCS of the scale factor and the RCS of the original model is basically the same under the perfect conductor and the theoretically derived results. This is because the conductivity of the perfect conductor is infinite, and the conductivity of the ideal PEFR dielectric is 0. In both cases, there is no need to change the dielectric constant and permeability of the dielectric when the model shrinks. Therefore, the regression equation is same as the theoretically derived formula, which further validates the effectiveness of regression method in SPSS.

4 Analysis of Simulation Results In actual engineering, most of measured targets are composite materials, and the electrical conductivity of these composite materials and absorbing materials is finite, not zero. The thickness of absorbing materials is usually fixed. In addition, when the target surface is attached with absorbing materials and the model is reduced according to the scale factor, the size of the model material cannot be reduced by n times, or the conductivity of the material is increased by n times. In this case, calculating the RCS of large targets is still a problem that requires further study. The absorbing material can attenuate the electromagnetic wave scattering of targets [20], which is a key factor for improving the stealth performance of aircraft. Silicon carbide is a common absorbing material that has excellent properties such as high strength, high temperature oxidation resistance, and adjustable electrical resistivity, and therefore has important application prospects in structural absorbing materials. The material is defined in FEKO, and the dielectric constant is set, as shown in Eq. (4): eps1 i þ j  eps1 r ¼ 4:19 þ 2:07j:

ð4Þ

The permeability of the absorbing material is defined as 1.02, and the dielectric loss tangent is determined, as shown in Eq. (5): tand ¼ tan1d ¼

eps1 r  0:494: eps1 i

ð5Þ

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The dielectric module is given by Eq. (6): eeff ¼ e0 er ð1  jtandÞ:

ð6Þ

The thickness of the material is set to 1 mm, and the thickness of the absorbing material does not change when the scale model changes in size according to different scale factors. The simulation results are displayed in Fig. 6.

Fig. 6. Simulation results of target surface attached with absorbing materials.

The data of FEKO simulation was processed by SPSS. The coefficients of the RCS of the scale model (y) and the RCS of the original model (x) under different scale factors are presented in Tables 5 and 6.

Table 5. Coefficient of regression Coefficient Constant −0.594 x 0.878 lg(n) −26.394

Standard error t 0.293 −2.029 0.011 77.594 0.359 −73.465

Saliency 0.000 0.000 0.000

Table 6. Correlation analysis R Square of R Adjusted squared R Standard estimated error 0.964 0.929 0.929 2.649

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We can obtain Eq. 6 from Table 5: y ¼ 0:878x  26:394lgðnÞ  0:594:

ð6Þ

It can be seen in Table 6 that the correlation coefficient is 0.964. There is no doubt that these factors are strongly correlated and the regression method is also effective, although there exists a certain amount of error. Comparing the regression formula with the original data and calculating the average value of the relative error, the overall error is determined to be 0.8 dB, which is within the acceptable range.

5 Conclusion The RCS simulation of perfect conductors and Teflon dielectric uses the data obtained by FEKO simulation, and uses SPSS to study the relationship between the RCS of the original model and the RCS under different scale factors. The regression equations are also consistent with the theoretically derived equations, demonstrating the effectiveness of this method in studying the RCS of scale models. The same method was subsequently used to simulate the regression of the conductor dielectric with an absorbing material on the surface. The equation of the regression with the original data has an error of 0.8 dB. The data of the current training model includes 1800 sampling points. The parameters of the model will be further optimized, and the error will be further reduced. After research, it is verified that the method proposed in this paper is not only applicable to the case in which the conductivity is zero or infinity, but also has applicability in complex cases in which the conductivity is limited and the surface of the model is attached with absorbing materials.

References 1. Li J, Sun Q (2008) RCS numerical analysis of conducting and non-conducting dielectric airfoils. Aeronaut Comput Technol 1:23–25 2. Jie CX, Lei L, Wei SX et al 2005 Study on RCS scaling relationship of perfect conducting objects. In: 2005 Asia-Pacific microwave conference proceedings, vol 4. IEEE, p 4 3. Knott EF, Schaeffer JF, Tulley MT (2004) Radar cross section. SciTech Publishing, New York 4. Liu H, Shi Z, Wu Z et al (1997) Data processing and inversion computing technology for RCS scaling measurement of stealth targets. J Microwave Sci 1:15–19 5. Jie CX, Lei L, Wei SX et al (2006) Study on RCS scaling relation of perfect conductor target in half space. J Radio Sci 21(6):939–943 6. Quan S (2013) Higher engineering electromagnetic theory. Beijing University of Aeronautics and Astronautics Press, p 157–158 7. Yan H, Zhendong S et al (2004) Application of electromagnetic similarity in computing RCS of basic scatters. J Appl Sci 22(1) 8. Liu Hongwei, Zhe Wu (1997) Data processing and inversion computing techniques for RCS scaling measurement of stealth targets. J Microwave Sci 1:15–19

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9. Yamada Y, Michishita N, Nguyen QD (2015) Calculation and measurement methods for RCS of a scale model airplane. In: The advanced technologies for communications. IEEE 10. Hongwei L, Zhendong S, Pu T (1995) RCS scale-model-testing method by variance in the size for simply shaped scatterers. J Electron (China) 2:177–180 11. Shi Z, Ding C, Chen J (1993) Dimensional analysis and physical similarity of lossy electromagnetic systems. Chin Phys Lett 10(6):347–350 12. Susetio A, Oki T, Morishita H (2016) Monostatic radar cross section evaluations of scale model single layer dielectric radar absorbing material at S and X bands. In: Antennas & Propagation. IEEE 13. Okada H, Tajima Y, Yamada Y et al (2008) RCS measurement of a scale model rocket. In: International workshop on antenna technology: small antennas & novel metamaterials. IEEE 14. Rensburg DJJV, Malherbe JAG, Mcnamara DA (1992) Computation of electromagnetic plane-wave scattering from a curved dielectric shell using a physical optics approach. Microwave Opt Technol Lett 5(7):326–328 15. Shi Z, Ding C, Jia Y (1993) Effects of absorbent materials on the RCS of a partially coated scatterer. Microwave Opt Technol Lett 6(2):109–111 16. Vinoy KJ, Jha RM (1996) Radar absorbing materials: from theory to design and characterization, Kluwer Academic Publishers, Boston 17. Yamada Y, Michishita N, Nguyen QD (2014) Calculation and measurement methods for RCS of a scale model airplane. In: 2014 international conference on advanced technologies for communications (ATC 2014). IEEE, pp 69–72 18. West BT (2009) Analyzing longitudinal data with the linear mixed models procedure in SPSS[J]. Eval Health Prof 32(3):207–228 19. Koch EC (2002) Metal-Fluorocarbon-Pyrolants: III. development and application of Magnesium/Teflon/Viton (MTV). Propellants Explos Pyrotech 27(5):262–266 20. Vinoy KJ, Jha RM (1996) Radar absorbing materials: from theory to design and characterization. Kluwer Academic Publishers, Boston

Coal Mine Power Quality Assessment System Based on Improved Entropy Weight Method Jingyan Liu(&), Yumei Wang, and Wenliang Yang School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China [email protected]

Abstract. This paper proposes an improved entropy weight method based on power quality comprehensive evaluation method. Firstly, the improved entropy method is used to determine the target weight, and the subjective weight of combination weighting is determined based on the scale expansion of analytic hierarchy process. The traditional entropy method in all entropy tend to be 1 of entropy with the information entropy, the entropy weight distribution unreasonable problems are corrected. Then, the method of combining probability statistics and fuzzy mathematics is used to evaluate power quality comprehensively. The analysis and calculation show that the result of the comprehensive evaluation system is more objective, perfect and practical. Keywords: Comprehensive evaluation


Entropy method
Power quality

1 Introduction The use of various rectifiers, frequency converters and other non-linear devices in the power supply system of coal mine enterprises causes power quality problems such as harmonic, voltage distortion and low power factor in the power supply system. The pros and cons of power quality is composed of multiple index comprehensive evaluation, thus the determination of index weight is the primary problem. The common method to empowerment with Delphi method and analytic hierarchy process (AHP) such as subjective values. The method and the variation coefficient method, the dispersion method, the entropy weight method and so on the objective weight method [1–3], and the combination of subjective and objective combination method. At present, the commonly used weighting methods include Delphi method, analytic hierarchy process [4, 5] and other subjective weighting methods, and the variation coefficient method, the dispersion method [6], the entropy weight method and so on objective weight method and the combination of subjective and objective combination method [7, 8]. In the combination of AHP and entropy weight method, consistency test is needed for the judgment matrix established when AHP determines the weight, which requires a large amount of calculation and subjectivity in the establishment of membership function, and the scale extension method can improve it; When all entropy values are close to 1, a small difference will cause the entropy weight to change exponentially, making the entropy weight and the entropy value of the information transfer inconsistent, leading to unreasonable weight distribution. To solve this problem, this paper USES the improved © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 371–380, 2020. https://doi.org/10.1007/978-981-32-9698-5_42

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entropy method to calculate the objective weight, then with AHP scale extension method to determine the subjective weight of combination empowerment, determine the weight of indicators, and the method of using probability statistics and the integration of fuzzy mathematics to comprehensive evaluation of indexes and weights, the comprehensive evaluation system for the power quality.

2 Evaluation Index Weight Calculation 2.1

The Entropy Weight Method to Calculate the Weight

Entropy weight method is an objective weight calculation method, which USES the characteristics of entropy to express information, that is, the greater the difference between evaluation objects, the more information the index contains, and the lower the entropy. Therefore, entropy weight method highlights local differences. The greater the level difference of the evaluation object, the greater the index weight and its influence on the evaluation result. In the quantitative evaluation of power quality, the dimensionality of each index is different. It is necessary to convert the data of each evaluation index into the dimensionless value with the same type through the uniform processing. In this paper, the index preprocessing is carried out through the extreme value processing method. The idea of using entropy weight method to calculate index weight is: Firstly, all indexes are processed uniformly, and then the entropy value ei ði ¼ 1; 2;


nÞ of each index is calculated, The entropy weight is determined by the entropy value, that is, the entropy is small, so the index data sequence has a great impact on the power quality assessment when there is a large change in the entropy value. The specific process is as follows: First of all, according to the power
 quality assessment factors and assessment index, calculated judgment matrix F ¼ fij . Calculates the relative importance of a certain index entropy, the transfer of information as follows: Ej ¼ 

m 1 X fij ln fij ln m j¼1

ð1Þ

Finally, the entropy weight determined by the entropy weight method is: 1  Ej a0j ¼ P n ð1  Ej Þ

ð2Þ

j¼1

When calculating the weight of the index after the consistency treatment, the entropy value approaches to 1. According to the formula of calculating the weight of the index by the method of entropy weight, the entropy weight of several groups of

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entropy values approaching to 1 in the following table is calculated by using MATLAB. The calculation results are shown in Table 1: Table 1. Calculation weight of entropy weight method Serial number Entropy 1 (0.9996, 0.9997, 0.9998, 0.9999) 2 (0.996, 0.97, 0.998, 0.999) 3 (0.96, 0.97, 0.98, 0.99) 4 (0.6, 0.7, 0.8, 0.9 )

Entropy weight distribution (0.4000, 0.3000, 0.2000, 0.1000) (0.4000, 0.3000, 0.2000, 0.1000) (0.4000, 0.3000, 0.2000, 0.1000) (0.4000, 0.3000, 0.2000, 0.1000)

Analysis of the data shows that: (1) when the entropy value tend to 1, calculated by entropy weight method to weight, small changes can cause the same set of entropy a0j even doubling number changes obviously; (2) by comparing the four groups of data in the table, it can be seen that the entropy difference of each group is 0.1, 0.01, 0.001 and 0.0001 respectively, while the entropy weight calculated by the entropy weight method is the same for several groups of data. But because entropy is the measure of information, the entropy value “0.6, and 0.9” and “0.9996 and 0.9999” contains the amount of information is different, the calculated by entropy and entropy weight method is the same, the entropy weight distribution is not reasonable. Therefore, the entropy weight method needs to be improved. 2.2

Improved Entropy Method to Calculate Weight

For the entropy weight method, there is the problem of entropy weight distribution. The entropy weight method A calculates the entropy weight: n P

a1j ¼

Ej þ 1  2Ej

j¼1 n P n P

ð

k¼1 j¼1

ð3Þ Ej þ 1  2Ek Þ

This approach can solve the problem of traditional method of weights allocation is not reasonable, but when there is a Ej ¼ 1, will not be equal to zero, the weighting coefficient aj have contrary entropy also weight method. In view of the above problems, entropy weight method B modified the entropy weight formula as follows: ( a2j ¼

ð1  EÞa0j þ Ea3j 0

Ej \1 Ej ¼ 1

ð4Þ

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Where E is the average of the not for 1 entropy value. a3j ¼

ð1 þ E  Ej Þ n P ð1 þ E  Ek Þ

ð5Þ

k¼1;Ek 6¼1

When the two entropy values differ greatly, the entropy weight method A and the entropy weight method B cannot reflect the entropy value difference. Therefore, A new entropy weight method C is introduced to correct them, and the calculation formula is as follows: ( aj ¼

n

n

ð1  E Þa0j þ E a3j 0

Ej \1 Ej ¼ 1

ð6Þ

Where, aj is the weight of the jth index; Ej is the entropy of the jth index. Selection according to the above analysis, the distribution of the four groups of representative of entropy, using MATLAB to each group of data were calculated using four kinds of entropy weight method (accurate to four decimal places, n take 35.35), entropy selection and entropy results as shown in Table 2 (A, B, C and d are the calculation results of entropy weight method, entropy weight method A, entropy weight method B and entropy weight method C respectively):

Table 2. Calculation weights of four entropy weight methods Distribution situation Entropy Entropy weight Entropy tends to 1 (0.996, 0.997, 0.998, 0.999) (a) (0.400, 0.300, 0.200, 0.100) (b) (0.2503, 0.2501, 0.2499, 0.2497) (c) (0.2507, 0.2502, 0.2498, 0.2493) (d) (0.2630, 0.2543, 0.2457, 0.2307) Entropy discrete (0.96, 0.67, 0.31, 0.10) (a) (0.0204, 0.1684, 0.3520, 0.4592) distribution (b) (0.1386, 0.2104, 0.299, 0.3515) (c) (0.0801, 0.1896, 0.3255, 0.4048) (d) (0.0204, 0.1684, 0.3520, 0.4592) Entropy values (0.999, 0.998, 0.899, 0.100) (a) (0.0010, 0.0020, 0.1006, 0.8964) differ greatly (b) (0.2000, 0.2002, 0.2200, 0.3799) (c) (0.1407, 0.1411, 0.1844, 0.5338) (d) (0.0010, 0.0020, 0.1006, 0.8964) Entropy smaller (0.42, 0.30, 0.20, 0.10) (a) (0.1946, 0.2349, 0.2658, 0.3020) (b) (0.1954, 0.2351, 0.2682, 0.3013) (c) (0.1982, 0.2359, 0.2673, 0.2986) (d) (0.1946, 0.2349, 0.2658, 0.3020)

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On the above-mentioned analysis shows: when the entropy approach in 1, a calculation results of entropy distribution is multiplied, weight distribution is not reasonable, b, c, d of the calculation results of a revised, relatively objective; When the entropy value is distributed discretely, the entropy value differs greatly and the entropy value is small, the calculation results of b and c weaken the gap between entropy weights, so that there is a gap between weight distribution and objective facts. Moreover, b weakens the entropy gap more obviously than c, while a and d have more objective entropy weight distribution; According to the entropy weight calculation results of a and d, the entropy weight calculation results of the two methods are exactly the same when the entropy value is close to 1. Therefore, the entropy weight method C can be used to replace the entropy weight method to calculate the objective weight. 2.3

Weight Determination

In this paper, AHP scale extension method is used to calculate the subjective weight, and scale construction method is used to optimize the analytic hierarchy process, It can ensure that the judgment matrix can meet the consistency requirement in any scale, and there is no need to establish membership
 function, which greatly reduces the computation. The judgment matrix is R ¼ rij , Table 3 is the meaning of comparative scaling in this paper.

Table 3. Meaning of comparative scaling Scale 1 1.2 1.4 1.6 1.8

Meaning (importance of two factors) Equal importance One factor is slightly more important One factor is important One factor is more important One factor is absolutely important

When calculating subjective weights by AHP scaling expansion method, the n indexes of the system are first arranged in descending order of importance. Then compare the two indicators xi and xi þ 1 , the scale value is recorded as bi , according to the transferability of the importance of each indicator can get the other element scale. The judgment matrix is: 2

1

6 1=b 6 1 6 6 1=b1 b2 6 6 1=b1 b2 b3 R¼6 6 6 .. 6. 6 6 4 1=b1 b2


bn2 1=b1 b2


bn1

b1

b1 b2

b1 b2 b3






1

b2

b2 b3






1=b2

1

b3






1=b2 b3 .. .

1=b3 .. .

1 .. .




.. .

1=b2 b3


bn2 1=b2 b3


bn1

1=b3 b4


bn2 1=b3 b4


bn1

1=b4 b5


bn2 1=b4 b5


bn1









b1 b2


bn1

3

b2 b3


bn1 7 7 7 b3 b4


bn1 7 7 7 b4 b5


bn1 7 7 7 .. 7 . 7 7 5 bn2 1

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The judgment matrix has consistency and can be directly used to calculate the weight of the indicator. The calculation formula is: vffiffiffiffiffiffiffiffiffiffiffi, vffiffiffiffiffiffiffiffiffiffiffi uY n n u n X Y u u n n t ð7Þ ci ¼ t rij rij j¼1

i¼1

j¼1

In order to take care of the subjective preference of the decision-makers and the objectivity of the indicator data, to achieve subjective and objective consistency, it is necessary to linearly calculate the subjective weight and the objective weight, so that the combined weight value and the original weight vector of the subjective and objective weight vector The difference between the corresponding evaluation value vectors is as small as possible, and the comprehensive weight calculation formula is: ai c i wi ¼ P ; i ¼ 1;


; n ð8Þ n ai c i j¼1

3 Power Quality Assessment A comprehensive evaluation is carried out by combining probability theory with fuzzy mathematics. First, according to the national standard, the grades of various power quality are divided into m grades within the scope of the national standard. Each index is evaluated by using probability statistics, and comprehensive evaluation is made by fuzzy mathematics to obtain an assessment. As a result, the specific steps are: (1) Determine the factor set Di ¼ fd1 ; d2 ;


; dm g and the evaluation set Qj ¼ fq1 ; q2 ;


; qn g of the assessment; (2) Divide each indicator into m grades according to its national standard, set the evaluation time T; and calculate the probability of each indicator at each level; (3) The matrix F of each index is constructed in descending order to form a matrix F ¼ ½fij  (i ¼ 1;


; n; j ¼ 1;


; m; fij represents the probability of the i-th phase index in level j); (4) Using the combined weighting method to calculate the evaluation weight W ¼ ½w1 ; w2 ;


; wn , using fuzzy mathematics to comprehensively judge it, and the evaluation result is: Z ¼W F

ð9Þ

(5) The final assessment Z 0 solved: 0

Z ¼

m X k¼1

kZk

, m X

Zk

ð10Þ

k¼1

Where Zk is the kth column in Zk , which is the result of each level. The weighted average method can consider each factor comprehensively to make the results more comprehensive and accurate.

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4 Case Analysis The power quality indicator of a 6 kV coal mine power supply system was monitored for 120 min. Power quality comprehensive evaluation factor set Di = {voltage sag, voltage deviation, voltage fluctuation, voltage flicker, frequency deviation, three-phase unbalance, harmonic}, evaluation set Qj = {very poor, poor, qualified, good, Quality}, according to national standards, the indicators are divided into 5 levels, and the evaluation factors correspond to 5 corresponding power quality levels. For example, the division of the voltage sag evaluation level, according to the IEC, the allowable range of voltage sag is 10%–90%, the average is divided into 5 levels, followed by 10%–26%, 26%–42%, 42%–58%, 58%–74%, 74%–90%, and other indicators are similar. The time statistics of each indicator are shown in Table 4: Table 4. Time statistics of various indicators of power quality Index

Time at all levels/s Level 1 Level 2 Voltage sag 1.868 0.6592 Voltage deviation 0 70 Voltage fluctuation 3836.2 5969.2 Voltage flicker 0 4299 Frequency deviation 3998 3012 Three-phase unbalance 0 0 Harmonic 0 1562

Level 3 Level 4 Level 5 1.21 0 2.404 7440 850. 0 1973.2 397.9 0 3697.5 1800.2 1833.6 238 0 0 0 2348 4760 5684 0 0

(1) Calculation of objective weights (1) Calculate the probability of each level, and know each fij , so that the evaluation moment can be obtained: 2

0:5515 0:4156 0:0328 0:0000 0:0000

3

7 6 6 0:0000 0:2156 0:7844 0:0000 0:0000 7 7 6 7 6 6 0:3151 0:4902 0:1620 0:0327 0:0000 7 7 6 7 6 6 F ¼ 6 0:0000 0:3696 0:3179 0:1548 0:1577 7 7 7 6 6 0:0000 0:0084 0:8899 0:1017 0:0000 7 6 7 6 7 6 0:3042 0:1073 0:1970 0:0000 0:3915 7 4 5 0:0000 0:0000 0:0000 0:3303 0:6697

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(2) information amount calculated for each evaluation factor E for each pass, E can be obtained according to the simulation were: E ¼ ½0:5003; 0:3239; 0:6960; 0:8154; 0:2339; 0:8007; 0:3942 (3) calculate the weights for each objective, the indexes will be consistent process, using an improved method and entropy method was simulated, respectively, the objective weights obtained are shown in Table 5: (2) Calculation of subjective weights (1) First, according to expert opinions and experience, the order relationship of evaluation indicators is arranged as follows: 1 frequency deviation, 2 harmonic distortion, 3 voltage fluctuation, 4 voltage flicker, 5 voltage deviation, 6 voltage sag, 7 three-phase unbalance. Determined by the relative importance, the scale values are: r12 ¼ 1:8 r23 ¼ 1:6 r34 ¼ 1 r45 ¼ 1:6 r56 ¼ 1:2 r67 ¼ 1:2 Table 5. Calculated objective weight

Entropy Entropy Law Improved entropy method

Frequency deviation

Harmonic distortion

Voltage Voltage fluctuation flicker

Voltage Voltage deviation sag

0.982 0.1748

0.985 0.1456

0.968 0.3107

0.982 0.1748

0.991 0.0874

0.992 0.0777

Threephase unbalance 0.997 0.0291

0.1561

0.1440

0.2128

0.1561

0.1197

0.1157

0.0955

(2) Computational judgment matrix: From Eq. (1), MATLAB simulation can obtain its judgment matrix as 3 1:0000 1:8000 2:8800 2:8800 4:6080 5:5296 6:6355 7 6 6 0:5556 1:0000 1:6000 1:6000 2:5600 3:0720 3:6864 7 7 6 6 0:3472 0:6250 1:0000 1:0000 1:6000 1:9200 2:3040 7 7 6 7 6 R ¼ 6 0:3472 0:6250 1:0000 1:0000 1:6000 1:9200 2:3040 7 7 6 6 0:2170 0:3906 0:6250 0:6250 1:0000 1:2000 1:4400 7 7 6 7 6 4 0:1808 0:3255 0:5208 0:5208 0:8333 1:0000 1:2000 5 0:1507 0:2713 0:4340 0:4340 0:6944 0:8333 1:0000 2

(3) Calculating subjective weights: From the simulation of formula (2), we can get that the subjective weights ci are respectively: c ¼ ½0:3575; 0:1985 ; 0:1241 ; 0:1241 ; 0:0775 ; 0:0646 ; 0:0539

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(3) Synthetic Weight is calculated by the formula (8), respectively, by entropy method and the weight W calculated integrated improved entropy method were: W1 ¼ ½0:3786; 0:1752 ; 0:2337 ; 0:1315 ; 0:0411 ; 0:0304 ; 0:0095 W2 ¼ ½0:3668; 0:1880 ; 0:1737 ; 0:1274 ; 0:0610 ; 0:0492 ; 0:0339 (4) To obtain the evaluation result, use the entropy weight method and the improved entropy weight method to obtain the comprehensive weight. The judgment result obtained by formula (9) is: Z1 ¼ ½0:2916; 0:3618; 0:2720; 0:0353; 0:0388 Z2 ¼ ½0:2720; 0:3310; 0:2921; 0:0428; 0:0621 (5) The weighted average is used to obtain the final result, and the weighted average of the evaluation results obtained by using the comprehensive weight is obtained by the formula (10): Z10 ¼ 0:3363, Z20 ¼ 0:2614. The calculation results show that the value of Z10 is between 3 and 4 the power quality assessment result is between pass and poor; the value of Z20 is between 2 and 3, and the power quality assessment result is between good and qualified. The above calculation results show that the voltage fluctuation is different from the three-phase unbalanced entropy value by 0.029, and the entropy weight obtained by the entropy weight method is 10 times different, and the entropy weight distribution is unreasonable; The improved entropy weight method reduces the entropy weight difference by a factor of two, and the entropy weight distribution is more reasonable, which makes the power quality assessment result better and worse, and the evaluation result is more scientific and accurate.

5 Analysis of Experimental Results Considering the importance of weight in the comprehensive assessment process of power quality in coal mining enterprises, based on the comprehensive evaluation method and weighting method of power quality, it is proposed to combine the objective weights determined by the improved entropy weight method with the subjective weights determined by the AHP scale expansion method to determine the comprehensive weight of each indicator. This paper amends the inconsistency between the entropy weight and the information transmitted by the traditional entropy weight method when all the entropy values are approaching 1, so as to make the determination of the weight more scientific and reasonable. The combination of the two methods makes the subjective and objective unified and more realistic.

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References 1. Jiang Y, Li W, Zhao Y, Yu F (2015) Comprehensive evaluation of quality performance of power grid operation based on rough set and evidence theory. Power Syst Prot Control 43 (13):1–7 2. Xueqian F, Chen Y, Jin X (2015) A comprehensive evaluation method for power quality of distributed power sources. Chin J Electr Eng 35(01):128–132 3. Ma C, Liu H, Gong W (2016) DPV power quality assessment based on improved entropy weight method. High Voltage Apparatus 52(05):192–198+204 4. Liao J, Zhou N, Wang Q, Li C, Wei Y (2018) Definition and correlation analysis of power quality index of DC distribution network. Chin J Electr Eng 38(23):6847–6860+7119 5. Li L, Liu J, Ling Y (2015) Comprehensive evaluation of power quality based on the combination of matter element theory and evidence theory. Trans China Electrotechnical Soc 30(12):383–391 6. Leilei S, Qingquan J, Haidong S (2019) Data-driven power quality partitioning governance strategy. Proc Chin Soc Electr Eng 39(04):992–1001 7. Xueqian F, Chen Y (2014) Comprehensive evaluation of power quality based on ideal solution. Electric Power Automation Equipment 34(04):26–30 8. Yin Y, Renjie W, Chang B (2018) Model and method of cloud evaluation service for complex power grid power quality knowledge. Power Autom Equipment 38(05):241–247

A Virtual Instrument of Temperature Measurement for LPG Cylinder Incinerato Longjun Zhu1, Yingchi Zhang2(&), and Xuedong Jing2 1

2

School of Engineering, Shanghai Normal University Tianhua College, Shanghai 201800, China School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai, China [email protected], [email protected]

Abstract. This paper develops an virtual instrument (VI) for measuring the variation of temperature during LPG (Liquefied Petroleum Gas) cylinder incinerator based on LabVIEW platform. This VI consists of hardware and software. The former includes thermocouples, an ADC based on PCI bus, and an industrial PC; while the latter consists of an algorithm for temperature measurement and the corresponding program. Based on the LabVIEW platform, an measurement system including filter compensation, data monitoring, and data storage has been established. The accuracy and feasibility of the VI has been verified by the field experiments. Compared with the traditional temperature measuring instrument, the VI are more appropriate for temperature measurement of the LPG cylinder incinerator, especially its flexibility and countermeasures to improve the measurement accuracy. Keywords: Kiln temperature measurement PCI data acquisition card
Filter


Virtual instrument


1 Introduction 1.1

A Subsection Sample Introduction

As a main part of the reuse of liquefied gas cylinders, the LPG cylinder is incinerated to clean the residual fuel in the used cylinder [1]. It is necessary to determine the most suitable kiln temperature field for LPG cylinders so as to ensure the recycling rate and safety of the cylinder after incineration [2], however there is no suitable means to achieve this purpose hitherto. The virtual instrument has been developed [3], and the temperature changes during the operation of the incinerator could be monitored in real time [4]; meanwhile a database has been set up and alarm device to record temperature data has also presented. These means could provide data support for the improvement and specification of the same type of furnace temperature measurement and liquefied gas cylinder process [5]. For the heating mode of the incinerator, different specifications of the LPG cylinder have different requirements for processing specifications and processes. The main purpose of this study is to examine the safety of liquefied petroleum cylinders which have been incinerated after the first inspection cycle and the second inspection cycle. within © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 381–387, 2020. https://doi.org/10.1007/978-981-32-9698-5_43

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the range of 550 °C to 800 °C, the experiment carries on every 50 °C. The LPG cylinders after incineration at different temperature above has been tested to ensure the safety of cylinder recycling. The experiments result indicates the approach above is practical.

2 The Composition of the Temperature Measurement System 2.1

Instrument Design Requirements

(1) Meeting the incineration temperature requirements of liquefied petroleum cylinders, the temperature range is from 0 °C to 1000 °C, and the measurement error is within 20 °C. (2) The system needs to monitor the temperature data of the entire workflow in real time, it can send an alarm for the abnormal temperature, and an emergency stop device is required. (3) The temperature measurement system can adapt to the severe working environment and compensate for environmental errors. 2.2

Temperature Measurement System

The schematic diagram of the kiln temperature measurement system is shown in Fig. 1. The system consists of a temperature acquisition module and a data processing module. The temperature acquisition module includes a K-type armored temperature sensor and a PCI-1716 data acquisition card (DAQ). The data processing module is based on the LabVIEW virtual instrument platform to complete the acquisition, compensation, analysis and monitoring for temperature data.

Fig. 1. System block diagram of LPG cylinder incinerator kiln temperature measuring device

3 Temperature Acquisition Module Design 3.1

The Composition of the Temperature Acquisition Module

The temperature data acquisition module is composed of K-type armored thermocouple WRNK-191 probe thermocouple, the temperature transmitter and the related equipment. It can be applied to liquid vapor and gaseous medium in the range of 0 °C to 1300 °C and the surface temperature of solids. The armored protection line can effectively prevent the interference caused by the bad environment in the experimental place. The compensation wires and temperature transmitters can effectively eliminate errors during transmission. By application of the shielding wire, strong anti-interference ability can be

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obtained. The IEC752 standard defines a function between the thermocouple resistance and temperature that satisfies the Callendar Van Dusen equation [8]: Rt ¼ R0 ð1 þ At þ Bt2  100Ct3 þ Ct4 Þ

ð1Þ

Where Rt and R0 are resistance values at temperatures of t °C and 0 °C respectively, where A, B, and C are constants. The function between the thermocouple resistance and temperature is a monotonically convex curve, and there is a nonlinear relationship between them:

tR ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R0 A þ ðR0 AÞ2 4R0 BðR0  RT Þ 2R0 B

ð2Þ

By application of the node VI from the formula of the virtual instrument, the accurately calculate the high-order value could be calculated while eliminating the error. The relation between the output of thermocouple and the real temperature is shown in Fig. 2. The output resistance signal of 0–10 V DC in the range can be linear with the output resistance signal of the thermal resistance thermometer [9].

Fig. 2. Linear relationship between DC signal and output temperature

3.2

Sampling Frequency

The temperature data potential obtained by the thermocouple is processed by the temperature transmitter to the analog signal, and ADC of PCI-1716 is used to input data acquisition card in IPC. According to the sampling theorem, When the sampling frequency fs.max is greater than 2 times of the highest frequency fmax in the signal (fs:max  2fmax ), the sampled digital signal completely retains the real information of the original signal. In practical application, the sampling frequency is guaranteed to be 2.56–4 times of the highest signal frequency, and the temperature sampling rate is determined to be 80 Hz and divided into the thermocouple data acquisition channel on average. The maximum symbol transmission rate B = 2W Baud (where W is the bandwidth) of an ideal low communication channel. C ¼ B  log2 N

ð3Þ

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4 Data Processing Module 4.1

Virtual Instrument Programming

After determining the temperature acquisition module, the main functions of the system are implemented by the software system based on virtual instrument. The analog signal output by the temperature acquisition module is converted to digital ones after is filtered and proceeds error compensation via the virtual instrument platform. The temperature of the furnace temperature field can be directly displayed, and the collected data can be saved to the database through the program. Compared with the detection temperature setting requirement, an alarm is issued when the temperature is abnormal, and the system operation is suspended at the same time [10] (Fig. 3).

Fig. 3. Partial program diagram of temperature measuring device

4.2

Environmental Error Compensation

The VI designed in this paper is adopted to correctly measure the temperature during the process of liquefied gas cylinder incinerator, though the electromagnetic environment of the kiln is very complex, including many kinds of electric and electric equipment with strong electricity and electric and electronic equipment with high power and current. In order to decrease the influence of the electromagnetic disturb, the measure and is compensated by using a low pass filter circuit [11]. The low pass cutoff for differential mode noise is: fd ¼

1 2pRa ð2Cd þ Cc Þ

ð4Þ

The low pass cutoff for common mode noise is: fc ¼

1 2pRa Cc

ð5Þ

At the same time, the electromagnetic induction, electrostatic coupling and the cable noise generated by the temperature transmitter could produce big errors in practical applications. Through the integrated design of the transmitter and the

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connector in the shielding box, the shielded wire and the armored protective wire is combined to ensure the effectiveness of data collection. The validity of data acquisition is guaranteed by the integrated design of transmitter amphenol connector in shielding box and the use of shielding wire and armored protection wire. If the sensor data error occurs, the system will issue a warning and record the error data in the database. During the operation of the system, data will be transferred to the data cache for processing to resolve time delay issues.

5 Analysis of Experimental Results In order to verify the accuracy and feasibility of the temperature measurement system, the temperature measurement system has been installed in the liquefied gas cylinder incinerator, and the temperature of the whole working process was tested. Program flow chart is shown in the Fig. 4.

Fig. 4. Temperature measurement system work flow chart

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Through field testing, the system above can measure the surface temperature of LPG cylinder, while the steady state error is no more than 10 °C. It can completely satisfy the test of various temperatures in the process of industrial liquefied gas cylinder quality test. In the VI, data acquisition was carried out for 6 temperature measuring points within the measuring range. The sampling period of temperature data is 0.3 s, and the temperature collection parameters are saved and recorded. 100 sets of data in each temperature range were uniformly intercepted, and the average value of each 10 groups was taken. The final results are shown in Table 1. Table 1. Experimental data Temperature 1 set of data 2 set of data 3 set of data 4 set of data 5 set of data 6 set of data 7 set of data 8 set of data 9 set of data

measuring points 550 °C 600 °C 650 °C 700 °C 750 °C 800 °C (°C) 534.67 587.20 648.53 699.01 755.13 807.40 (°C) 542.83 594.31 656.37 698.46 749.66 805.94 (°C) 548.85 598.39 657.15 696.99 750.17 797.97 (°C) 551.14 602.05 658.75 696.14 745.73 802.96 (°C) 551.83 601.43 658.33 700.30 750.89 801.21 (°C) 558.09 605.32 658.45 703.49 751.86 799.39 (°C) 561.47 607.03 659.29 698.46 753.68 796.39 (°C) 553.92 601.78 650.53 700.30 757.51 802.40 (°C) 549.29 607.57 647.72 696.53 748.76 811.65

In order to ensure the accuracy of the experimental data, 10 sets of temperature measuring rings has been put in the 600 °C measurement interval. The ceramic ring retracts when heated in a kiln, and the shrinkage of the ring is linear to the temperature. The temperature measurement ring can get the highest temperature during the incineration process to verify the accuracy of the temperature measurement system. The average diameter of the temperature measuring ring is 18.49 mm. According to the comparison table, the maximum temperature is 608 °C, which is basically consistent with the temperature measurement system. It can meet the requirements of liquefied gas cylinder incineration testing standards.

6 Conclusion This paper designs a temperature measurement system for LPG cylinder incineration kiln. The instruments can collects temperature signals via a K-type armored thermocouple; meanwhile it can monitor the temperature in the kiln during the incineration in realtime. Both the measurement accuracy and the range can meet the requirements of liquefied gas cylinder incineration.

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References 1. Dormohammadi A, Gholami EZA (2014) Risk analysis by means of a QRA approach on a LPG cylinder filling installation. Process Saf Prog 33(1):77–84 2. Tauseef SM, Abbasi T, Abbasi SA (2010) Risks of fire and explosion associated with the increasing use of liquefied petroleum gas. J Fail Anal Prev 10(4):322–333 3. National Instrument Corporation (2006) LabView user manual, 2006-04 4. Shi Z-h, Lin J, Zhou F-d (2016) Precision synchronous acquisition system based on virtual instrument. China Meas Test 42(2):67–70 5. Shtern YuI, Kozhevnikov YaS et al (2013) A procedure and a hardware-software system for the automated calibration of temperature measuring instruments. Meas Tech 56(5):497–502 6. Abadlia L, Gasser F, Khalouk K et al (2014) New experimental methodology, setup and LabView program for accurate absolute thermoelectric power and electrical resistivity measurements between 25 and 1600 K: application to pure copper, platinum, tungsten, and nickel at very high temperatures. Rev Sci Instrum 85(9):095121 7. Shevtsov SA, Kargashilov DV, Shutkin AN (2018) Fire and explosion safe technology of storage and regasification of liquefied petroleum gas. Chem Petrol Eng 54(1–2):38–40 8. Fernicola VC, Iacomini L (2008) Approximating the ITS-90 temperature scale with industrial platinum resistance thermometers. Int J Thermophys 29(5):1817–1827 9. Milic SD, Sreckovic MZ (2008) A stationary system of noncontact temperature measurement and hotbox detecting. IEEE Trans Veh Technol 57(5):2684–2694 10. Zhou Q, Jian G, Chao L et al (2012) Design and implementation of noise measurement system of solar cells based on LabVIEW. Lect. Notes Electr Eng 128:629–635 11. Lukac R (2003) Adaptive vector median filtering. Pattern Recogn Lett 24(12):1889–1899

Fast Image Multi-style Transfer and Its Quality Assessment Xianfeng Zhao(&) and Hai Gao University of Science and Technology Beijing, Beijing 100083, China [email protected]

Abstract. Image style transfer based on deep learning is an image processing method, which uses deep convolutional neural networks (CNN) to yield artistic images with some specific styles by segregating and restructuring the styles and contents of images [1]. Considering that several drawbacks still exists in the neural style transfer, such as the intrinsic limitation of single style transfer and the time-consuming process of optimizing model. At this time, we could remedy aforesaid weaknesses by the means of making use of fast multi-style transfer and its image quality assessment (IQA). On one hand, it aims to solve the monotony of color and the loss of stereoscopy results from single style image. On the other hand, it evaluates the synthesized image quality in real time, and makes the feedback of IQA to model itself for modifying relevant parameters of the algorithm, providing reference for selecting appropriate time to stop iterating to save immediate model. In this paper, we present the improved approaches for image style transfer to obtain preferable visual effect and save significant time. Keywords: CNN


Fast image multi-style transfer
IQA
Deep learning

1 Introduction Recently, more and more public has begun to pursue private artistic enjoyment, however, it will take a long time for the amateur to foster a solid painterly strength and profound artistic accomplishment. That’s why we study whether it can provide an efficient calculation strategy, to move certain art styles to other pieces. Since deep learning network has appeared, image style transfer has accomplished a series of breakthrough research results. As the pioneers of this filed, Gatys et al. exploit CNN as a feature extractor to define the loss function, to calculate the total loss, by adopting the idea of gradient descent adjusting parameters [2]. Not just like the prior work that have merely revolved around iterative techniques, in terms of the image conversion tasks, Johnson et al. put forward Fast Style Transfer that apply the perceptual loss function to train the feed-forward network [3]. Using a trained image transform net with a given style feature, the generated image can be synthesized through only a forward propagation calculation, and the content image can be replaced by random picture. Therefore, we are able to enhance the local speed by more than three orders of magnitude. Although fast style transfer is faster than normal style transfer, the method still needs to spend a long time on training the feed-forward network. Besides, the © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 388–397, 2020. https://doi.org/10.1007/978-981-32-9698-5_44

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optimizing process blindly reduces the total loss of the network, which cannot reflect its real internal situation directly and is uncontrollable. The generated image can inherit the characteristics of the style picture, but the original color expression and layer texture will be lost. Thus, there is further room for the improvement in fast style transfer. In order to retain the merits of original picture and cut down the global time of fast style transfer, we introduce multi-style and IQA into the existing model. By combining different style features that boosts the versatility of the model for different content images, the IQA could be used to optimize the learning rate to speed up the model convergence and predict the supreme point as a threshold switching for interrupting model iterating in advance [4]. This paper proposes the reformative structure for the performance of extremely higher global speed style transfer in the feed-forward mode, with a tiny visual qualitative fall. We organize the rest of this paper as follows: Sect. 2 describes our proposed methods in details. Section 3 conducts extensive experiments on fast multi-style transfer and its image quality assessment to illustrate the encouraging performances of the proposed algorithm. Finally, Sect. 4 presents a brief summary.

2 Methods Description 2.1

Fast Multi-style Transfer Design Method

Fast Style Transfer, as the basic framework of fast multi-style transfer, its structure is shown in Fig. 1. This model is mainly composed of two networks: the loss network and the image transform net. Among them, the ys , yc and ^y are style pictures, content pictures and generated pictures respectively, the input image x is from training dataset, fw signs several parameters of the image transform net. What the key function of loss network is that style and content of images can be expressed separately [5]. The loss network utilizes a pre-trained VGG-16 as feature extractors to quantify image, to define the content loss and style loss. They are usually chosen from the outputs of the internal layers. Specifically, the content loss
uses the  characteristics of the relu3_3 layer output of VGG-16, corresponding to

;;relu3 lfeat

3

in Fig. 1; the style loss uses the output

2 ;;relu2 2 ;;relu3 3 ;;relu4 3 , lstyle , lstyle , lstyle ). (l;;relu1 style

features of the four intermediate layers The method calculates the loss of content image with a per-pixel classification loss. l and Pli;j are their Let ~ p and ~ x be the content image and the generated image, and Fi;j respective feature representations in layer l. Then, the square error loss between two feature representations is defined:  !  1X i; jðFli;j  pli;j Þ2 Lcontent ! p ; x ;l ¼ 2

ð1Þ

The Gram matrix is used to calculate the loss of the style image. The idea of using the Gram matrix is to express the texture characteristics of image, and it’s irrelevant to the fact that it has to have a relationship with the location, so it can be used to measure

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the texture characteristics [2]. As shown in (2): Gli;j is the inner product between vector feature mapping i and j in layer l [1]. X Gli;j ¼ Fl Fl ð2Þ k ik jk

Fig. 1. The framework of fast neural style transfer.

For (3), Let ~ a be the style image, Lstyle ð~ a;~ x; lÞ is the mean square distance between the style image’s Gram matrix Gli;j and the Gram matrix of the image to be generated Ali;j in layer l:  !  Lstyle ! a ; x ;l ¼

X 1 i; jðGli;j  Ali;j Þ2 2 2 4 Nl Ml

ð3Þ

The texture features can be regarded as the style of images, so the loss of style image can be defined as (4): Lstyle ð~ a;~ x;Þ is the weighted average sum of the style losses in the specified layers, wl represents their respective weights.  ! X Lstyle ! a; x ¼ wl Lstyle ð! a ;! x ; lÞ

ð4Þ

l

The fast style transfer is prone to cause the loss of color and texture that is just the most emotional element of painting. For making the generated pictures obtain the better visual performance, we need to incorporate different style features into the original algorithm according to the intended purpose. In (4), where L is the number of style images, El and wl presents style feature and weight from a single picture. Ltotal

style ð

! a ;! xÞ¼

XL l¼0

wl El

ð5Þ

In this way, the total loss function is the aforementioned perceptual loss function.

Fast Image Multi-style Transfer and Its Quality Assessment

Ltotal ð! p ;! a ;! x Þ ¼ a Lcontent ð! p ;! x Þ þ b Ltotal

! a ;! xÞ

style ð

391

ð6Þ

The image transform net is a feed-forward network. Its main principle is to convolute the image, and then perform the “deconvolution” calculation. In this mode, the first step in training is to evaluate the style image and content image utilizing only the loss network. The resulting output image is fed through the loss network and the activation maps are saved [4–6]. Secondly, the feed-forward network would be trained through minimizing gradients from the total loss. Finally, Once the feed-forward network has been successfully trained, the loss network is discarded. When changing the content image, it is unnecessary to input the style image again, but only to restore the pre-stored network parameters. It only takes a few seconds to generate images by this method, and the trained style conversion network knows the semantic content of style images [1]. 2.2

Image Quality Assessment Method and Its Application

The quality of fast multi-style transfer is closely related to the size of the dataset and the number of iterations. Because the ultimate goal of the algorithm is to minimize the total loss of the style image and the content image to be transformed, once the model starts to iterate, it is neither interrupted nor controlled until the scheduled times have been completed. With pre-stored models belong to the same style features but the different iterations, these generated images are shown in Fig. 2. Obviously, the generated images had been distorted in the time of lower iterations, the image is not much different from before when it is too large [7]. Thus, predicting perceived visual quality computationally is crucial for the optimization and evaluation of such a system and its modules. The image quality assessment (IQA) methods are roughly divided into subjective quality evaluation (SQE) and objective quality evaluation (OQE). The digital images are intended to be viewed by humans so that the SQE is essential for the most problems in image communication and processing. However, it is more susceptible for other factors than the OQE and not a fixed standard measurement method [8].

(200)

(800)

(4000)

(8000)

(12000)

(24000)

Fig. 2. The generated images with different iterations.

Synthesizing the above two methods, we can quantify the real state of the net-work reliably and directly by real-time monitoring the IQA in training model. In this paper,

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the SQE is achieved by looking for volunteers using the comparison method to score pictures similar to Fig. 2, the mean of results is counted by (7). For OQE, converting the three-channel RGB pictures into one-dimensional point sets, according to (8–13) and using the spatial domain method to calculate its mean, variance, signal noise ratio (SNR). The relevant formulas are as follows. (1) Subjective quality evaluation: MeanðxÞ ¼

n 1X wi xi n i¼0

ð7Þ

(2) Objective quality evaluation: n 1X xi n i¼0

ð8Þ

n 1X ðxi xÞ2 n i¼0

ð9Þ

EðxÞ ¼

D ð xÞ ¼

Snr ¼ EðxÞ

.pffiffiffiffiffiffiffiffiffiffi DðxÞ

ð10Þ

(3) Multi-Style objective quality evaluation: Eðax þ byÞ ¼ aEðxÞ þ bEðyÞ

ð11Þ

Cov(x,y) ¼ E(xy)  E(x)E(y)

ð12Þ

Dðax þ byÞ ¼ a2 DðxÞ þ b2 DðyÞ þ 2abCovðx,yÞ

ð13Þ

By IQA, we can predict the best value in advance, indirectly understand the level of this training feedforward network [8]. Once the quality evaluation of the generated image in real time reaches the optimal value, the training will be stopped [9]. In this way, it will shorten the local time. In addition, it can also be used to modify parameter, such as Learning Rate, as an important hyper parameter, it controls the speed of adjusting the weight of neural network based on diminishing gradient. By (14), appropriate modification of learning rate can accelerate the convergence of the model [10]. The final IQA and its application of flow chart is shown in Fig. 3. Learning rate ¼ Learning rateo  ð1 þ c  AbsðDÞÞ

ð14Þ

Fast Image Multi-style Transfer and Its Quality Assessment

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Ineration >num Y Subjective quality evaluation

Generated image

Y

Zero

Interation

And Y

Stop Train

Image dataset

Analysis

Objective quality evaluation

EvaluaƟon formula

operation

+

Abs

Train operation Learning Rate

Style image

WeighƟng LR

Orginal Learning Rate

Fig. 3. Basic flow of IQA and its application.

3 Analysis of Experimental Results 3.1

Fast Multi-style Transfer Implementation

In order to prove the superiority of fast image multi-style transfer, training these models with only a single style image or multiple style images according to the specified images is shown in Fig. 4, and their synthetic image is shown in Fig. 5. For style-1 transfer, although the texture features of the content image are retained, its color is single and overall brightness is darker. The style-2 transfer’s color is too messy to distinguish its own outline clearly. For multi-style transfer c, d, it can be seen that using similar lightness and slightly different colors to construct these generated images with the basic texture content and three-dimensional structure of the original images. Meanwhile, adjusting the relative weights to enhance or weaken a certain style feature, which makes the images more natural and stereoscopic and improving the quality of image stylization.

(a)

(b) Fig. 4. Input pictures. (a) content. (b) style-1. (c) style-2.

(c)

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(a)

(b)

(c)

(d)

Fig. 5. Contrast of different synthetic images. (a) style-1 transfer. (b) style-2 transfer. (c, d) multi-style transfer with different weights.

3.2

Fast Multi-style Transfer Design Method

Taking d (Fig. 5) as an example, its several intermediate models were taken to transform images, 200 volunteers were selected to score the quality of these images in five levels. The statistical classification of the results obtained by (7) is shown in Fig. 6. It is clear that the increasing rate of score decreases after 12K times, and tends to be stable after 22K times, finally the quality evaluation has a slowly downward trend if the number of iterations continues to increase.

1 200

1.5

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2

2.4

800

2000

3.1

4000

3.8

4.4

4.7

5

4.9

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8000 12000 16000 22000 30000 40000

Fig. 6. Subjective image quality evaluation score statistics.

Tensor-board (a visualization tool) is activated to monitor the training process of same pictures as above, and the mean, variance and SNR of the generated image are calculated by (8–13). Their results are shown in Fig. 7. It is observed that the OQE tends to be stable when the number of iterations is about 20K, and confirming that the predicted OQE is in good agreement with SQE. Although the input images from the COCO, a public dataset provided by MS in 2014, change constantly during the training process, the quality evaluation of the generated image does not change dramatically but gradually. Since the weights of style loss and content loss (250:1), it is concluded that the IQA of generated image depends on style characteristics rather than the content.

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Fig. 7. Objective image quality evaluation parameters.

In order to objectively verify the intrinsic relationship between style pictures and the generated pictures, several groups of multi-style transfer are selected, and the relative results are shown in Table 1. Among these evaluations, The SNR of style features is the closest to the best quality evaluation of the generated image [11]. Table 1. Different groups of multi-style quality evaluation parameters. Order Styles Weight Mean G 1 A, B 1:1 148.7 2 A, B 2:1 126.7 3 C, B 1:1 158.5 4 C, B 2:1 140.2

3.3

S 140.5 119.3 153.4 138.7

Var G 3856 4697 5989 5685

S 3587 4220 5544 5479

Snr G 2.36 1.85 2.05 1.86

S 2.35 1.84 2.06 1.87

The Result of the Improved Methods

We can optimize the model by the SNR of style features, generated image. When the learning rate is set too small or too large, it will greatly reduce the convergence speed or cause the parameters to oscillate on both sides of the optimal solution [12]. Given these, let c = 3 in (14). In view of the versatility of the model and preventing misjudgment that caused by the violent fluctuation of the SNR during the previous iterations, the number of iterations is limited more than 10K. Taking d in Fig. 5 as an example, the results of these improved methods shown in Fig. 8. Under model 1 (original model), the iterative times exceeds 40K (4 h 28 min). Under model 2 (setting interruption), the times decreases to about 18K (1 h 55 min). And model 3 (weighting learning rate and setting interruption) can compress the iterations to 12K (1 h 3 min). Therefore, we propose a joint improved method, which can reduce more than the 50% of relative time.

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2.5

method1 method2 method3

SNR

2.3 2.1 1.9 1.7 1.5 2K

4K

6K

8K 10K 12K 14K 16K 18K 20K 22K 24K 26K 28K 30K

Iteration Fig. 8. Relative iterations consumed by different methods.

4 Conclusion In the paper, we propose an improved method that can save a mass of time with hardly changing the quality of generated images. Despite all this, this method requires the operator to have the most basic art knowledge and aesthetic ability to select different style features and their weights. Otherwise, the desired effect may not be achieved. The next work focuses on employing CNN to simulate human non-reference quality assessment to realize the independent selection of multi-style features and weights, minimize human intervention as much as possible and enhance its flexibility and efficiency in practical applications.

References 1. Li Y, Zhang T, Han X, Qi Y (2018) Image style transfer in deep learning networks. In: 2018 5th international conference on systems and informatics (ICSAI) 2. Gatys LA, Ecker AS, Bethge M (2015) A neural algorithm of artistic style. arXiv preprint arXiv:1508.06576 3. Johnson J, Alahi A, Fei-Fei L (2016) Perceptual losses for real-time style transfer and superresolution 4. Zhang W, Borji A, Wang Z et al (2016) The application of visual saliency models in objective image quality assessment: a statistical evaluation. IEEE Trans Neural Netw Learn Syst 27(6):1266–1278 5. Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 6. Bryan B, Raymond P, Andreas S (2018) Faster Art-CNN: an extremely fast style transfer network. In: IEEE western New York image and signal processing workshop 7. Wang Z, Bovik AC, Lu L (2011) Why is image quality assessment so difficult? In: IEEE international conference on Acoustics IEEE 8. Bovik AC (2013) Automatic prediction of perceptual image and video quality. Proc IEEE 99:1–17

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9. Srivastava N, Hinton G, Krizhevsky A et al (2014) Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 15(1):1929–1958 10. Montavon G, Samek W, Müller K-R (2017) Methods for interpreting and understanding deep neural networks. Digit Sig Process 73:1–15 11. Bosse S, Siekmann M, Wiegand T, Samek W (2017) A perceptually relevant shearlet-based adaptation of the PSNR. In: IEEE international conference image processing (ICIP), pp 315– 319 12. Soundararajan R, Bovik AC (2012) RRED indices: reduced reference entropic differencing for image quality assessment. IEEE Trans Image Process 21(2):517–526

Application Research on Information System Security Situational Awareness Houqun Yang(&) and Juan Hu School of Computer Science and Cyberspace Security, Hainan University, Haikou 570228, Hainan, China [email protected]

Abstract. Aiming at the problem of high complexity of situational awareness model in which the different test levels, control points and requirements are correlated with each other in the network security level protection test, an improved convolutional neural network security situational awareness method based on one-hot is proposed. Combining the advantages of feature selection of prior selection and posterior selection, the correlation prediction based on multiple different levels and different observation index points is realized. The experimental results show that the proposed method significantly improves the correlation discovery of different parameters between multiple levels, and reduces the classification prediction time. The accuracy of situational awareness is higher than that of deep learning based on feature data. Keywords: Situational awareness


One-hot
Convolutional neural network

1 Introduction Information system security situation dynamic perception is a comprehensive research technology that acquires security assessment monitoring point data in real time, extracts related dynamic related situational factors, and scientifically judges the security situation of information system. It belongs to the core research category of security situational awareness technology. The data of safety assessment is mainly discrete data, which is not conducive to the transmission of gradients for deep learning models such as convolutional neural networks. Therefore, in order to solve the problem of information system security, it is necessary to learn from the deep learning neural network for image recognition and other processing methods, and redesign and innovate the discrete data processing method. With the development of information system security game, the complexity and nonlinearity of information system intrusion randomness, suddenness and security situation change are increasing. The security system of information system puts higher and higher accuracy and efficiency requirements on situational awareness. In recent years, research methods of security situational awareness have emerged, especially the methods of deep neural network technology have become hot spots. Different from traditional methods such as Bayesian network and Nearest Neighbor classification. The neural network-based method directly constructs a mapping model © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 398–407, 2020. https://doi.org/10.1007/978-981-32-9698-5_45

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of data of situation and predicts it by training a shallow network with hidden layer nodes. It has the advantages of clear structure and strong self-learning performance. Deep neural networks are typical deep learning models, and other deep learning models are extended on the basis of DNN. DNN is essentially a chain of functions, each function is a layer, each layer consists of neurons. Neurons are connected by weights and deviations. In the training process of the DNN, the weights and deviations are determined by minimizing the value of the loss function on the training data set [1], which is the optimization technique. The regularization technique [2] is used to avoid DNN overfitting [3], the goal of which is to match the trained model to the real data generation process. Compared with traditional machine learning algorithms, deep learning improves detection efficiency, reduces false positive rate, and can automatically identify and identify attack features, which helps to identify potential security threats. The field of cyberspace security using deep learning mainly includes malware detection and intrusion detection. Among them, representative work is document [4] and literature [5]. Although studies have shown that deep learning has a good experimental effect on the intrusion detection public dataset, most of the public datasets are desensitized feature data, such as the KDDCUP99 and NSL-KDD datasets. These data cannot restore the true data distribution. When the data mining process cannot be learned or restored, it is difficult to apply the research algorithm to real network traffic monitoring.

2 Related Theory 2.1

Convolutional Neural Network

CNN is a multi-stage globally trainable artificial neural network model. It can design a specific network structure for specific problems, and learn abstract, essential and highorder features from raw data through preprocessing. A typical CNN is composed of a convolutional layer, a downsampling layer, a fully connected layer, and a classifier. The original image is entered at the input level, the size of which determines the size of the input vector. The neurons automatically extract the local features of the image. Each neuron is connected to the local receptive domain of the previous layer. The neurons in each plane in each layer extract local features of specific regions in the image, such as edge features and directional features. The operation of the convolutional layer is a mapping from one plane to the next, and the sampling layer can be regarded as a fuzzy filter, which plays the role of quadratic feature extraction. The spatial resolution between hidden layers is decremented, and the number of planes contained in each layer is incremented, which can be used to detect more feature information. Finally, the fully connected layer connects all the features and sends the output values to the classifier, such as the Softmax classifier. Classical CNN models include LeNet [6], AlexNet [7], GoogleNet [8], VGG [4], ResNet [9] and so on. Assuming that the layer ‘, is a convolution layer and the layer ‘ +1 is a subsampling layer, the calculation formula of the jth feature map Xj‘ of the layer ‘ is as follows:

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Xj‘ ¼ f ð

X i2Mj

Xi‘1  kij‘ þ b‘j Þ

ð1Þ

The residual calculation of the BP algorithm is equal to the weighted sum of the weights and residuals of all the nodes connected to the layer ‘ + 1 and multiplied by the derivative of the point to z. The next layer of the convolutional layer is the subsampling layer, which uses one-to-one non-overlapping sampling, so the residual calculation is simpler. The residual formula of the jth feature map of the layer ‘ is calculated as follows: 0

d‘j ¼ b‘j þ 1 ðf ðu‘j Þ  upðd‘j þ 1 ÞÞ

ð2Þ

Equations (3) and (4) represent the gradient of the bias and the gradient of the convolution kernel, respectively. @E X ‘ ¼ ðdj Þuv @bj u;v

ð3Þ

@E X ‘ ¼ ðdj Þuv ðp‘1 i Þuv @kij‘ u;v

ð4Þ

Let the layer ‘ be the subsampling layer and the layer ‘  1 be the convolution layer. Since it is one-to-one sampling, assuming the sampling size is 2  2, the calculation formula is: ‘ x‘j ¼ f ðb‘j downðx‘1 j Þ þ bj Þ

ð5Þ

d‘j ¼ f ðu‘j Þ  conv2ðd‘j þ 1 ; rot180ðk‘j þ 1 Þ; 'full'Þ

ð6Þ

The residual is calculated as: 0

Similarly, in the downsampling layer, a calculation error is needed to update the weight additive bias b and the multiplicative bias b, and the gradient of the additive bias b is obtained by Eq. (3). The gradient calculation of the multiplicative bias b is obtained by: @E X ‘ ¼ ðdj  dj‘ Þuv @bj

2.2

ð7Þ

GoogLeNet

The typical GoogLeNet [8] network structure has 22 layers of parameter calculations. Compared to AlexNet and VGG, which directly increases the network depth and the number of convolutional layers, GoogLeNet not only deepens the depth of the overall

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network structure, but also introduces the Inception structure to extend the width of the network. It avoids the problems of gradient disappearance, gradient explosion and over-fitting caused by pure network depth deepening. In addition, the network finally replaces the fully connected layer with a global average pooling layer (i.e., the picture size becomes 1  1), making convergence faster and reducing overfitting. The Inception V1 structure uses the NIN idea [10], which convolves simultaneously on multiple scales, so that features of different scales of the image can be extracted. The richer features also mean that the final classification is more accurate. On the basis of V1, V3 proposes the design and optimization of neural network structure. The method of improving Inception is divided into: small convolution kernel which is decomposed into symmetry and decomposed into asymmetric convolution kernel. Figure 1 replaces the 5  5 convolution kernel with two 3  3 convolution kernels. The second method in Fig. 1 is to replace the n  n convolution kernel with the 1  n and n  1 convolution kernel stacks, and the amount of computation will decrease. However, the second decomposition method does not perform well on the largedimensional feature map, and performs well in the feature map 12–20 dimension. The asymmetric decomposition method has several advantages: it saves a lot of parameters; increases a layer of nonlinearity and improves the expression ability of the model; can handle more abundant spatial features and increase the diversity of features.

3 Classification Prediction Algorithm Based on One-Hot and Improved Convolutional Neural Network This paper conducts information system security assessment based on different levels of security detection data. The purpose is to automatically learn and extract the characteristics of detection data, and perform feature association analysis based on prior screening and posterior screening methods, and then classifier classification to avoid extraction. The original detection data features, and then use the algorithm to carry out the complex process of training classification.

4 Feature-Dimensional Reconstruction Based on One-Hot The one-hot encoding is also known as a valid encoding by using an N-bit status register to encode the N states, each state having a separate register bit, and only one bit is active at any time. The advantage is that it can process non-continuous numerical features and is easy to design and implement, and does not require operations such as decoders, and at the same time, features are expanded to some extent. By analyzing the monitoring data, it can be known that, at the level of data integrity, the first dimension of the evaluation item: the detection system management data is destroyed in the integrity of the transmission process, and the character type has five symbols: network device, operating system, database management system, application system, no such content. These dimension features represents a data integrity detection function, and the unique thermal coding technique maps the features of five symbols into

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Fig. 1. Inception V3 module after factorization of the n  n convolution.

5-dimensional vectors, which are mapped respectively to [1,0,0,0,0], [0,1,0,0,0], [0,0,1,0,0], [0,0,0,1,0], [0,0,0,0,1]. Table 1 shows the mapping for application security.. Table 1. Mapping rule of application security. ID-LCM ID-Iuc AC-URM SA-DMO CC-init SFT-AP RC-MC

4.1

1 4 7 10 13 16 19

ID-cc 2 ID-Failue 3 AC-Fun 5 AC-Coverage 6 AC-role 8 SA-Fun 9 SA-event 11 comm int 12 CC-encryption 14 SFT-validity 15 RC-AE 17 RC-CL 18

Feature Selection

The fundamental purpose of feature selection is to select a subset of features that have a positive driving force for classification performance. The main task is to remove

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irrelevant features and redundant features in the original feature set. The irrelevant features mainly refer to features that do not have too much guidance for classification and have low discrimination to categories. These features usually increase the computational cost of the classification process and have no effect on classification performance. However, the existence of redundant features may affect the degree of discrimination of the remaining features to the categories, resulting in a reduction in classification effects. Therefore, how to correctly define and measure irrelevant and redundant features becomes a key element of feature selection. In this paper, the method of prior selecting and posterior selecting is adopted. At the same time, the Pearson coefficient is used to remove the features with particularly obvious collinearity, and the features with extremely uneven distribution are deleted. Filter using the wrapper method. In the search process of the feature selection algorithm, the only criterion for determining the pros and cons of the non-empty feature subset is the feature evaluation function, which directly affects the process of feature selection and whether the final result is in line with expectations. For the wrapper method, for each iteration of the loop, consider the classification accuracy of the standard time classification algorithm of the selected features. The final selected feature subsets are selected by the method, and the classification performance is the final goal. The performance of the process is relatively good. However, since the classification accuracy rate is determined for each selected feature subset each time, the computational complexity is high. 4.2

OGI-Based Security Detection Classification Algorithm

The size of the two-dimensional detection data after one-hot encoding does not exceed 1000  10. Since each state has only one valid bit, it is a sparse matrix after encoding. The convolutional layer in the traditional CNN algorithm convolves the image using only one scale convolution kernel, and outputs the data of fixed dimension. All the output features are basically evenly distributed over this single scale range, so a sparse distribution is still obtained. The feature set of GoogLeNet uses different convolution kernel scales to obtain different sparsely distributed feature sets. Since the features are extracted at multiple scales, the output features are no longer uniformly distributed, but the highly correlated features are gathered together, while the unrelated non-critical features are weakened. Thus, even if the same number of features are output, the Inception method outputs less feature redundancy information and has a faster convergence rate. This paper proposes a new composite convolution structure. In the separation and convolution phase of the deep separable convolution technique, the convolutional layer is further split into two convolutional layers of 1  n and n  1 using the idea of volume integral solution; then a volume of 1  1  f is used. The product core performs point convolution, and the input of each feature surface is fused and output to the feature map with the feature surface number f. This approach further reduces the amount of computation and increases the depth, which is better for improving accuracy and extracting more abstract features [11]. This paper uses the GoogLeNet deep learning model. The main technical route of the system security detection algorithm (OHE-GoogLeNet + Improved, OGI for short) based on the unique heat coding, GoogLeNet and improved convolution structure is shown in

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Fig. 3. The algorithm uses the unique heat coding to reconstruct the original data packet after data reduction, and then uses GoogLeNet to perform convolutional sparse feature learning. Finally, it is classified by Softmax classifier and the results are statistically analyzed.

Test Point Data Input

Normalization Processing

Reconstruction of feature dimension based on one-hot

Learning algorithm

Whether to meet the stopping criteria

no

wrapper method

yes Sparse feature learning based on GoogleNet

Softmax classification

Fig. 2. Security situational awareness technology route based on improved convolutional neural network (predictive model).

According to Fig. 2, the specific evaluation steps are designed as follows: Step 1: Collect the test point raw data, extract the observation indicators for fusion, generate the input sample space of the model, and evaluate the situation of the sample data, and use the result as a label. Step 2: Data normalization processing and one-hot encoding; Step 3: Introduce a feature evaluation function to assess whether the process of feature selection and the final result are in line with expectations Step 4: Initialize the parameters W and offset B of each layer of the convolutional neural network, and set hyperparameters such as iteration number and learning rate. Step 5: Based on the sample space, the training set is constructed. The input vector enters the model from the first composite convolution structure, and the forward mapping is performed between the layers until the test result is output. Step 6: For the volume integration solution stage, the size of the two convolution kernels of 1  n and n  1 is adjusted by adding 1 to the lowest of 3 to perform horizontal comparison.

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Step 7: Input the test index data into the well-trained convolutional neural network model, and obtain the security level evaluation value of the information system through the forward mapping process. The purpose of the optimizer is to optimize the gradient update process. In the deep learning model, the commonly used optimizers are mainly SGD, RMSprop, Adagrad, Adamelta, Adam and Nadam. Under the condition that the learning rate is small, the Adalelta, SGD and Adagrad optimizers perform poorly, and the optimization effect is not ideal. The RMSprop, Adam and Nadam optimization effects are better. In this paper, Adam is used as the model optimizer. The purpose of regularization is to reduce the degree of over-fitting of the model and improve the generalization ability of the model. The CNN model regularization mainly uses the L2 and Dropout methods.

5 Experimental Simulation 5.1

Experimental Dataset

The data set used in this experiment is the safety evaluation data of 1000 information systems. Data is presented in five levels, including physical security, network level, host security, application security and data security, and backup recovery. Each information system has an average of about 500 assessment points. After finishing, there are about 450,000 records in the data set. Due to the limitations of the experimental environment, in order to speed up the experiment, the experiment randomly extracted 105,200 data from the 450,000 data as a training set and 56,320 data as a test set (Table 2). Table 2. Distribution of test point security level. All type Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Training set 105200 45 466 8501 24682 71506 Test set 56320 15 243 6043 13652 36367

5.2

Experimental Environment

The experimental tool is based on the Python TensorFlow package and uses the GPU to speed up the experimental process. This experiment mainly discusses the influence of different model parameters in the convolutional neural network on the final classification effect. The appropriate model parameters are selected by setting different groups of contrast experiments. We set up 6 experiments to explore the effects of six different hyperparameters on the model: The number of hidden layers, the size of the convolution kernel, the sliding step size of the convolution kernel, the length of the pooled kernel, the sliding step size of the pooled kernel, and the number of epoch. In this experiment, the activation function of the convolutional neural network is chosen to be the Relu function, which is superior to the traditional sigmoid function and tanh function. This experiment uses the TensorFlow

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platform to complete the development of convolutional neural network algorithms. Model training was performed using randomly selected 105,200 training set data, and the model was tested using randomly selected 56320 test set data. Evaluation Criteria. The evaluation criteria in this experiment is the classification accuracy. Parameter Setting. In this experiment, the activation function of the convolutional neural network model is the Relu function. The number of convolution kernels of the first layer is 9, and the number of convolution kernels of each subsequent convolution layer is twice that of the previous layer. That is, the number of convolution kernels of the second convolutional layer is 18, and the number of convolution kernels of the third convolutional layer is 36. The weights are initialized using a truncated Gaussian distribution with a standard value of 0.1, which breaks the symmetry and zero-gradient problems. The filling method of the convolution layer is SAME mode, and the filling mode of the pooling layer is VALID mode. The pooling layer uses the maximum pooling method. The optimization algorithm uses the Adam algorithm. Experiment Procedure. The experimental results are shown in Fig. 3.

a: the Number of Hidden Layers and accuracy

b: kernel size and accuracy

c: Sliding step and accuracy

d: the size of pooling unit and accuracy

Fig. 3. Experimental result.

Increasing the number of hidden layers will increase the classification accuracy, but after the number of hidden layers exceeds 3, the accuracy of classification will continue to decrease. When the number of hidden layers is 3, the classification accuracy reaches 87%, which is close to the maximum value. When the convolution kernel is set to 3, the model has the best classification effect. If the sliding step size of the convolution kernel is set to 1, the model classification accuracy rate is 89.2%. If you continue to increase the step size, the accuracy will drop. When the convolution step is too large, the features will not be fully exploited. When the convolution step is too small, some redundant features will appear. Therefore, setting the step size of a reasonable convolution window is also a key point of network design. When the size of the pooled core is 1, the classification accuracy

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rate exceeds 89.5%. The pooling layer selects the maximum value from the local features as the output value. The size of the pooling window is too large, and the error when extracting features is relatively large. If the size is too small, the effect of feature dimension reduction is not obvious. When the number of epoch is 495, the accuracy of the classification reaches 99.1%. As the number of epoch continues to increase, the accuracy of classification is almost stable. As the epoch increases, the training time of the model will also increase. Therefore, when actually training the model, we need to balance the accuracy and training time and choose the appropriate epoch.

6 Conclusion In this paper, for hierarchical detection data, dimension reconstruction using one-hot coding is proposed, and feature extraction and training of Softmax classifier are carried out by using Google LeNet in CNN. The experimental results show that this method improves the situation prediction effect of information system, fits the network security situation change curve well, and is superior to other in-depth learning methods based on feature data in detection accuracy, miss detection rate and false detection rate. The next research will focus on the classification and detection of small sample data in multi-level scenarios, and the use of Residual Networks (ResNet) to solve the degradation of depth model. Acknowledgment. This research is supported by the National Natural Science Foundation of China (61562020, 61862021), Hainan Provincial Natural Science Foundation of China (618QN217).

References 1. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by backpropagating errors. Nature 323(6088):533–536 2. Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge 3. Srivastava N, Hinton G, Krizhevsky A et al (2014) Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 15:1929–1958 4. Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. https://arxiv.org/pdf/1409.1556.pdf. Accessed 02 Aug 2017 5. Staudemeyer R (2015) Applying long short-term memory recurrent neural networks to intrusion detection. South Afr Comput J 56:136–154 6. Lecun Y, Bottou L, Bengio Y et al (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324 7. Deng L, Yu D (2014) Deep learning: methods and applications. Found Trends Signal Process 7(3–4):197–387 8. Szegedy C, Wei L, Jia Y et al (2015) Going deeper with convolutions, pp 1–9 9. He K, Zhang X, Ren S et al (2016) Deep residual learning for image recognition, pp 770–778 10. Lin M, Chen Q, Yan SC (2013) Network in network. arXiv:1312.4400 11. Huang W, Stokes JW (2016) MtNet: a multi-task neural network for dynamic malware classification. Springer, pp 399–418

Research on Vehicle Motion Control Strategy Based on Machine Vision Jianping Mo1(&) and Haijiang Lan2 1

2

School of Vocational and Technical Education, Guangxi Science and Technology Normal University, Laibin 546199, China [email protected] School of Mechanical and Electrical Engineering, Guangxi Science and Technology Normal University, Laibin 546199, China

Abstract. This paper proposes a machine vision-based detection scheme to complete the automatic advancement and overtaking control of the vehicle. Firstly, the optimal segmentation threshold of the acquired image is obtained by the optimized maximum inter-class variance method, and the threshold is used to binarize the image to obtain the track information, realize the direction control, complete the automatic travel of the vehicle, and then adopt the region growth. The method detects the image of the preceding car in the track, and then obtains the distance between the two cars to complete the detection and control of the distance. Finally, the optimized inter-frame difference method is used to dynamically detect the overtaking behavior and complete the overtaking process. Compared with the traditional way, this method has certain advantages. Keywords: Machine vision Control strategy


Motion control
Image processing


1 Introduction The machine vision system uses machine vision products to convert the target object into image information, and then uses the image information processing system to extract the target area, number, length and other characteristics according to the pixel distribution, brightness and color information. Identify and control the actions of the field device from the results of the identification [1]. In the intelligent vehicle operation control, vehicle path planning is a hot issue of research. Two-car chase requires that two cars can not collide and contact, and the car should be as close as possible to improve the efficiency of vehicle operation. In daily life, driving a vehicle when the road is crowded is a similar problem. Therefore, studying the chasing problem of two cars is of great significance for the safe driving of intelligent vehicles [2, 3]. In this paper, based on the image information acquired by the CMOS camera, the operation control, path recognition and overtaking in the process of double-car chase are realized through arithmetic processing.

© Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 408–416, 2020. https://doi.org/10.1007/978-981-32-9698-5_46

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2 Image Acquisition and Processing 2.1

Image Acquisition Device

This paper uses OV7620 with a resolution of 640  480 as the image acquisition device. In order to balance the image processing speed and ensure the integrity of the picture information, this paper adopts the “singular field acquisition even field processing” method, that is, the image acquisition is performed when the odd-numbered field interrupt signal is generated, and the last odd field is generated when the evennumbered field interrupt signal is generated. The acquired image information is processed without image acquisition. In order to avoid the blanking area, 400  280 image data is finally obtained. 2.2

Image Processing

Image Compression. In this paper, the non-uniform compression method is adopted, that is, the image data to be collected is saved in one row every five rows, and four columns are stored in one column, and finally a compressed image of 80  70 is formed. Superimposed Linear Window Median Filter Denoising. Median filtering is an algorithm that sorts the gray values of pixel points in the sliding window and then extracts the median value as the filtering result [4]. The design of the sliding window plays a decisive role in the time complexity and filtering effect of the algorithm. Generally, it uses one or more shapes of window processing, but this method wastes a lot of time. The algorithm is no longer limited to a single shape. Horizontal and vertical two-dimensional two-dimensional superposition method for processing. First, the image array is horizontally slid by a three-pixel dot window for median filtering, and then the image array is vertically slid by a three-pixel dot window for median filtering. The horizontal and vertical bidirectional linear superposition method can smooth the image from two latitudes with greatly reduced time. Dynamic Threshold Segmentation Image. The key point of image segmentation is the determination of the threshold, and the camera relies on the external illumination environment. Once the static threshold is used, the appropriate image data can be obtained only under certain illumination conditions [5]. For the smart car race, the components of the path are blue background and white track, and the difference between the two parts is obvious. Therefore, the dynamic threshold acquisition method often uses the maximum inter-class variance method. However, the calculation of the maximum inter-class variance method is too large. In order to reduce the computational time complexity, the algorithm is optimized. The gray value of the image data ranges from 0 to 255, a total of 256 orders of magnitude, where 0 is black and 255 is white. The background of the track is blue, between the two, so the optimal threshold will not appear at both ends, and the boundary range is actually tested to find that the target range of the threshold is [50, 200], so only in this range It can be tested inside. The gray value i is selected from the target range in turn. Every time the current gray value i is

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assumed to be the best threshold, all gray value ranges smaller than i are regarded as foreground, and all gray value ranges larger than i are regarded as background. The number of gray values w0 and w1 in foreground and background intervals are counted respectively. Then the average gray values u0 and u1 in foreground and background intervals are calculated respectively. Then the g of inter-class variance satisfies:


g ¼ w0
w1
ðu0  u1 Þ2 g / ðu0  u1 Þ2 / ju0  u1 j

ð1Þ

In order to simplify the scale of the operation, we only require the value corresponding to the maximum. According to the optimal threshold obtained by the above method, the image is divided to obtain a significantly different binarized image. Edge Extraction. Common edge extraction methods include two-sided detection and edge tracking detection [6, 7]. The center-to-edge detection method cannot handle the occurrence of multiple trip points in a row, which is easy to cause edge extraction errors and consumes a lot of processing time. While the edge tracking method can handle multiple trip point problems better, it relies too much on the edge extraction result of the previous line. This paper improves the edge detection algorithm. For the bottom row, the bottom edge clamp is forced out by center-to-edge detection and direct edge detection to ensure the most stable edge. For the remaining lines, the edge tracking method is used, and the edge point obtained last time is taken as the starting position of the current detection. For the left border, if the current position is white, it is currently in the track, you should continue to detect the left edge to the left. If it is black, it means the background, it should be detected to the right; for the right border, if the current position is white, it means that it is currently located. In the track, it should be detected on the right side. If it is black, it means the background. It should be detected on the left side. Cycle through this until the entire image is retrieved. Track Type Judgment and Processing Curve Feature Enhancement. For the large S curve, the camera can not obtain the left and right edges at the same time, there is bound to be a boundary blanking area, and it is easy to obtain the edge of the adjacent track, thereby disturbing the normal driving of the car model. Therefore, the feature reinforcement of the large S curve must be performed. Firstly, the large S curve is identified. The main feature is that the unilaterally lost line and the midline slope sign are the same, and the left or right bend can be further determined according to the positive and negative signs of the midline slope sign. Taking the right curve as an example, starting from the boundary disappearing area, all the columns of the left and right boundaries of the upper image are assigned to the right boundary of the image, thereby obtaining a larger deviation, so that the steering gear can give a larger angle, complete Enhancement of the characteristics of the large S curve. Fracture Fitting of the Cross and the Ring. Both the cross curve and the ring have both sides lost at the same time, so the distinction between the two types of tracks is also very difficult. According to the characteristics of the track image, the biggest feature

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distinguishing point is the number of inflection points and the angle at the inflection point. The image size is 80  70, and the middle line is selected as a reference. The upper image is used as the upper part of the image, and the lower image is used as the lower part of the image (Table 1). Table 1. Feature comparison Type\ Feature Ring entrance Ring exit

Number of inflection points 2

Inflection point position

Corner angle

2 lower

 90°

2

 90°

Cross corner

4

One on each of the upper and lower 2 upper and lower

Upper > 90°, lower < 90°

For the deviation control, only the deviation needs to be reflected, so in order to save the operation time and complexity, the missing line fitting is fitted by a linear regression equation. The linear regression equation is shown in Eq. (2). 8 n P > xi yi nxy > > > i¼1 ^ > b ¼ < n P x2i nx2 ð2Þ i¼1 > > > ^ > ^a ¼ y  bx > : y ¼ ^a þ ^bx Where xi is the row coordinate of the effective edge point in the image, and yi is the column coordinate of the effective edge point. x is the average of the row coordinates of the effective edge pixel, y is the average of the column coordinates of the effective pixel point, n is the effective number of rows, ^a is the line intercept, and ^ b is the slope of the regression line.

3 Overtaking Treatment 3.1

Distance Detection and Control

In the process of chasing, the two cars are prone to collision if the distance is not properly controlled, so it is necessary to detect and control the distance between the two vehicles. The focal length of the camera is fixed, so that the object imaging position of a fixed distance is relatively fixed once its height and angle are fixed. Thereby, the actual distance difference can be obtained by detecting the imaging position of the preceding vehicle. After the binarization, the foreground and background of the image are significantly different. The whole vehicle is imaged as a black connected domain.

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Therefore, the front vehicle can be detected by detecting the black connected domain. This paper uses the region growing method to detect the black connected domain of the front vehicle imaging. 3.2

Front Car Stop

The front car needs to first select the parking position. In the long straight road, the parking position is selected in the place where the curve is about to enter; in the branch circular path, the parking position is selected on either side of the ring road; in the nonequal branch ring, the parking point is selected in the ring with the longer side of the path. Change the front car mark after parking and set it as the rear car mark. Long Straight Parking. The long straight road is easy to accelerate. If the parking is in the middle, the whole overtaking process will prolong many straight traffic times. In the long straight road, the vehicle will decelerate and the vehicle will start at a lower speed. Therefore, the overtaking location is selected as a straight road. It is more suitable to enter the bend. As shown in Fig. 1, the front car parking adopts the parallel shifting axis strategy. Taking the right curve as an example, the center line of the path is moved to 1/4 of the left side of the image. After the front car stops, the starting speed is lower, and the rear car speed is relatively large, so the front car chooses to stop in the outer lane, and the rear car drives on the inner road, and both cars are more likely to bend.

Fig. 1. Schematic diagram of parallel shifting axis

Roundabout Parking. The circular road has double-sided traffic and is the best road for overtaking. But to ensure that the two cars go to different side lanes. For the equal branch ring, it is stipulated that the front car stops at the left side; for the non-equal branch ring, the side where the front car stops the longer path is convenient for the rear car to catch up. First, the annular inlet is identified according to the feature, and then deceleration is started. When the annular exit mark appears in the field of view, the vehicle speed is set to zero. If the initial ring-entry speed is too large, a certain brake pulse can be selected according to the actual track condition to speed up the deceleration process.

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413

After Car Overtaking

The following is a long straight and a round-back mid-vehicle overtaking scheme. After the overtaking, the rear vehicle flag changes and is set as the front vehicle mark. Overtaking in Straight. As shown in Fig. 2, in the straight road, because the parking position of the front vehicle is on the roadside, after binarization, it is imaged as a black pixel point, which is connected with the track. Because the optimized edge tracking method is used for the edge. Detection, so for the rear car, the image of the front car is connected with the edge of the track, and is regarded as part of the track in the rear view of the car. Therefore, no special treatment is needed for the car, and the rear car can be automatically changed according to the center line. Complete overtaking.

(a)Change in the mid-line of the preceding vehicle (b) Mid-line change during the overtaking process Fig. 2. The effect of the front car stop on the midline of the rear car

Overtaking in the Ring Road. In the circular road, the front car stops at the side of the ring, and the rear car enters the other side. No special treatment is required for the image, and it can be normally exited. 3.4

Optimize the Interframe Difference Method to Detect Overtaking

After the front car stops, it is equivalent to a still camera, and continuous continuous shooting is equivalent to capturing video. The process of passing the car will be displayed in the frame of one frame, and the capture of the rear car is similar. For moving target detection in the video. The moving target detection methods commonly used in video sequences mainly include background difference method, optical flow method and interframe difference method [8–10]. The moving target detection method combined with continuous interframe difference and background difference can better detect slow moving targets. In this paper, based on the above methods, a more suitable detection method is proposed for the detection of rear vehicle motion during overtaking. The idea of the algorithm is to first record the background frame after parking in front of the car, and count and record the number of black pixels of the background frame. Then take consecutive frames and separately count the difference in the number

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of black pixels between the current frame and the background frame. During the process of the rear car from the appearance to the disappearance, the number of black pixel points will increase from gradually increasing to decreasing gradually, and the difference between the image frame and the background frame obtained after the front car is out will be very small. Figure 3 shows the overtaking image in the straight track, and Fig. 4 shows the overtaking image in the circular path.

Background frame (b) After the car appears (c) Overtaking is completed (d) After the car leaves (e) After the car leaves Fig. 3. Overtaking image in the straight

Comparing the continuously acquired frame with the background frame, when it is found that there is not much difference, for the two-car system used in this paper, the experimental error is about 3%, and the variation range is controlled at about 12 pixels. Overtaking is completed, the speed loop is activated, and a new chase is performed.

(a) Background frame (b) After the car appears (c) After the car appears completely (d) After the car is driven out (e) After the car is completely driven out Fig. 4. Overtaking image in the circular path

4 Testing and Analysis In order to verify the effectiveness of the machine vision-based overtaking strategy, the same intelligent dual-vehicle system adopts the same image processing, line-hunting method and control strategy under the same illumination conditions in the laboratory, respectively, and the overtaking control method of adding ultrasonic and wireless modules respectively The motion detection overtaking method proposed in this paper is compared and tested. The speed of the vehicle is kept at 3 m/s and the initial spacing of the two vehicles is 50 cm. The test results are given in Table 2 below.

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Table 2. Test results Mode\Type Long straight Uniform small loop Non-uniform large loop Traditional way 95% 94% 80% Current mode 95% 99% 92%

From the data in Table 2, the motion detection method based on machine vision and the traditional combination of ultrasonic and wireless modules are ideal for overtaking on long straight roads. However, in the circular path, since the ultrasonic angle forms a blind zone in the circular path, the conventional method has a big problem, especially in the non-uniform large circular track, the motion detection method based on machine vision does not have the blind zone problem of the ultrasonic module, and the success rate Increased by nearly 12%.

5 Conclusion In this paper, through the deeper mining of the images collected by the camera, an overtaking strategy based on motion detection is presented. This strategy reduces the number of sensor modules used under the premise of overtaking. For the distance detection, the imaging position of the preceding vehicle is detected by the principle of regional growth, which replaces the function of the ultrasonic module in the traditional detection mode, and avoids the blind zone problem of the module itself. The test results verify the effectiveness of the method. At the same time, in the overtaking mode, machine vision is used for indirect communication, which is closer to the artificial overtaking mode in real life. This has certain reference significance for the development and research of dual car chase system and artificial intelligence.

References 1. Kruglov VN, Kruglov AV, Karev AL, Gruh AG, Khurelchuluun I (2019) LED projector of pulse backlight for machine vision system. IOP Conf Ser Mater Sci Eng 507(1):012021 2. Zhang T, Liu Y, Zhao P, Tian Q (2016) Research on Intelligent vehicle chase control system based on PID neural network. Technol Innov (15):13–14 3. Longdong W, Qiguo Y (2015) Design of chasing movement of double electromagnetic vehicles based on K60 chip. China Water Transp 11:72–73 4. Jingjing H (2017) The median filtering of mine video surveillance image based on noise detection. Metal Mine 02:117–120 5. Lai C, Song L, Han Y et al (2019) Material image segmentation with the machine learning method and complex network method. MRS Adv 4(19):1119–1124 6. Wang S, Jin C (2018) Denoising of non-local mean image based on edge extraction. Electron Meas Technol 41(11):99–102 7. Han Y, Hou H, Bai Y et al (2018) A closed point cloud edge extraction algorithm based on edge coefficient. Laser Optoelectron Progress 55(11):161–166

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8. Wang R, Chen W, Li X (2019) Research on inertial/optical flow integrated navigation method for weak optical flow environment. Electron Opt Control 26(01):97–103 9. Zhang W, Zhang W, Song F, Zhao Y (2018) Fixed-point hover control of small quadrotor UAV based on optical flow and ultrasonic module. Chem Autom Instrum 45(04):289–293 10. Zhao B, Zheng M, Zhang F (2018) Improved target recognition algorithm based on frame difference and background difference. Commun Technol 51(11):2733–2739

Modelling and Simulation of an Electric Trimmable Horizontal Stabilizer Actuator Based on Bond Graph Xudong Han1, Junsheng Ma2, Jian Fu1(&), Liming Yu3, Wensen Zhang1, and Yongling Fu1 1

School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China [email protected] 2 Nanjing Engineer Institute of Aircraft System Jincheng, AVIC, Nanjing 211100, China 3 Shenyuan Honors College, Beihang University, Beijing 100191, China

Abstract. The trimmable horizontal stabilizer actuator (THSA) is a key part of the aircraft flight control system. This paper focuses on the new electrical type of THSA. System structure and control scheme are firstly introduced and then the mathematical models of its key components are established. The bond graph method is used for system-level modeling and component-level modeling for easily analysis of the power and signal transformation. Finally, the simulation analysis is carried out in 20-sim virtual simulation environment. The result verifies the basic performance for control design and shows the extendibility of the proposed models. Keywords: THSA


Bond graph
EMA
20-sim

1 Introduction With the development of more electric aircraft, power-by-wire (PbW) actuation systems are increasingly applied for today’s latest generation aircraft. The two well-known types of PbW actuators are electro-hydrostatic actuators (EHA) and electro-mechanical actuators (EMA) [1–3]. PbW actuators have some specific advantages when compare to the conventional ones [4]. THSA is an important part of the flight control system in the aircraft for ensuring the dynamic performance and safety. In THSA, one of its main components is the ball screw. When the screw is driven to rotate by the power provided by the electrical motor or the hydraulic motor, the nut moves along the axis of the screw, thereby rotating the horizontal stabilizer to achieve the position control of the horizontal tail angle of attack. During the flight, the horizontal stabilizer actuator mainly realizes two functions. One is to drive the horizontal stabilizer surface to rotate around its rotation axis, in order to achieve the longitudinal balance of the aircraft; The other one is to provide support for the horizontal stabilizer, which is used to counteract the hinge moment of the aerodynamic load acting on the hinge of the stabilizer. At present, aircrafts such as © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 417–425, 2020. https://doi.org/10.1007/978-981-32-9698-5_47

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the A400M and A380 use the source of the hydraulic motors to drive the THSA, and the electrical motor is used as a backup, while the B787 and A350 are fully applies the electrical motor as the power source in THSA. Bond graph theory is a modeling method for studying the dynamic performance of physical systems. It was proposed by H.M. Paynter of MIT in the early 1960s, and then further developed and improved by many scholars such as Rosenberg and Karnopp [5]. It is able to create a dynamic model of an engineering system in which multiple energy forms coexist with a uniformly defined specific graphical symbol [6]. At present, the bond graph theory has become a new type of discipline, and it is widely used in many engineering fields, such as machinery, hydraulics, thermodynamics and so on. Compared with other mathematical models, it has the advantages of simple structure, clear physical meaning and great topological property. Reference [7] shows different types of arrangements for innovative THSA concepts and presents the integration analyses of innovative systems into the fuselage. Reference [8] presents an application of four optimal H∞ controller synthesis methods to the THSA control problem. Reference [9] designs a H∞ controller to control the rotational speed of the hydraulic motors for a THSA with two primary load paths. However, there is little information available in literature about the modeling and simulation on bond graph of THSA, which is significant to analyzing system performance. This paper describes the structure of an electric THSA and introduces the composition of each part in Sect. 2. The main components are analyzed and mathematical models are established in Sect. 3. The bond graph model is established and the simulation is carried out according to the working conditions in Sect. 4. The simulation result shows the correctness of the model and key dynamic performances.

2 System Description The horizontal tail is located at the rear of the aircraft and serves to maintain the stability of the aircraft during flight and to control the pitch of the fuselage. Typically, the horizontal tail consists of a horizontal stabilizer and an elevator. The object of this study is the horizontal stabilizer actuator. The horizontal stabilizer actuation system controls the movement of the actuator by accepting the deflection signal of the flight control system to achieve the deflection of the steering surface, so that the aircraft has proper static stability. 2.1

System Structure

The ETHSA mainly comprises a control electronics, a power unit, a motor, a torque limiting clutch, a gear reducer, a ball screw and a no-back mechanism. Its structure is shown in Fig. 1. The torque output from the motor is transmitted through the gear reducer and the ball screw to the horizontal stabilizer to overcome the air load, which is to achieve the purpose of trimming. Among them, the torque limiting clutch is used to protect the motor from being damaged when the load torque is too large. The no-back mechanism is used to prevent the screw from rotating by the air load when the moving

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direction of the horizontal stabilizer is consistent with the direction of the air load, thereby preventing the horizontal stabilizer from moving.

Fig. 1. Principle structure of ETHSA

2.2

Control Scheme

Figure 2 describes the control scheme of the ETHSA. Controller sends position commends to the motor driver after it received the speed commends of THSA from the flight control computer. The servo motor is controlled by three loops strategy including the current loop, speed loop and position loop. The outer loop of the system is the speed loop of the actuator. The move speed signal of the nut is fed back to the controller, which accepts the traditional PID control algorithm.

Fig. 2. Control scheme of ETHSA

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3 Mathematical Model of Major Components ETHSA is a multi-energy domain system involving power electronics, machinery, hydraulics, and thermal. The relationship of energy flow inside it is extremely complicated. In this section, mathematical models of the main components are established by analyzing their working principle. Subsequently, the bond graph model is built, which can analyze and describe multiple forms of the energy flow in a unified graphical form. 3.1

Electric Motor

In this paper, a permanent magnet synchronous motor (PMSM) is used as the servo motor. Ideally, the electrical energy is converted into mechanical energy by it. This effect can be described by a gyrator GY(k_t). 

Tm ¼ kt Im xm ¼ Um =kt

ð1Þ

where Tm is the torque, xm is the motor speed, kt is the torque constant, Im is the motor current, and Um is the armature voltage. Besides, the inductance and resistance of stator windings can be described by an inductance component I(L_m) and a resistance component R(R_m) respectively. Um ¼ Lm

dIm þ Rm Im þ Us dt

ð2Þ

where Lm is the winding inductance, and Rm is the winding resistance. Considering the mechanical part, the mechanical energy is mainly consumed by the mechanical friction and the inertia of the motor rotor. A resistance component R (B_m) represents the mechanical friction and an inductance I(J_m) can be used to described the inertia. Tm ¼ Jm

dxm þ B m x m þ Tr dt

ð3Þ

where Bm is the viscous damping coefficient of motor, and Jm is the rotor inertia. The bond graph model of the motor is shown in Fig. 3, which is based on the above analysis.

Fig. 3. BG model of the motor

Fig. 4. BG model of the torque limiting clutch

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Torque Limiting Clutch

The torque limiting clutch is used to protect the motor output from exceeding the defined load. When the torque at the load end is greater than the limit torque, the tilting roller friction disc used in the torque limiting clutch will rotate relatively. At this time, the original static friction between the friction discs will be converted into dynamic friction. The friction loss can be represented by a modulation resistive element MR, whose parameter r can be expressed as:  r¼

0 ; T  Tlim ðT  Tlim Þ=xm ; T [ Tlim

ð4Þ

where T is the torque required for the motor output, and Tlim is the torque limited by the torque limiting clutch, xm is the motor angular velocity. According to the above analysis, the bond graph model of torque limiting clutch is shown in Fig. 4. 3.3

Gear Reducer and Ball Screw

The gear reducer is used to reduce the speed of the motor output and increase the torque. It is composed of a gear train enclosed in a casing. It achieves various transmission ratios through different stages and gear ratios. In this paper, the multi-stage gear transmission is simplified into a pair of gear transmissions, and the equivalent transmission ratio is i. 

T1 ¼ T2 i x1 i ¼ x2

ð5Þ

where T1 and T2 are respectively the torque of the driving wheel and the driven wheel, and x1 and x2 are respectively the rotational speeds of the driving wheel and the driven wheel. Therefore, gear reducer can be represented by a transformer component TF in an ideal situation. The ball screw is also a mechanism for transmitting motion and force between the two axes of the space, which converts the rotational motion into a linear motion by the screw and the helical pair. The relationship of motion and force between the two axes is: 

p TS ¼ FN 2p p xS 2p ¼ vN

ð6Þ

wherein, TS and xS respectively represent the torque and the rotational speed of the screw, FN and VN respectively represent the output force and speed of the nut, and P represents the lead of the screw. The ball screw satisfies the characteristic equation of transformer TF, which parameter is p/2p.

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When the screw nut is moving, the rigidity of the lead screw and the damping of the screw pair need to be taken into account, which are represented by a capacitance C and a resistance R. They lead to speed loss so they are linked to a 0-junction. Based on the above analysis, the bond graph model of the gear reducer and ball screw are shown as Figs. 5 and 6.

Fig. 5. BG model of the gear reducer

3.4

Fig. 6. BG model of the ball screw

No-Back Mechanism

No-back mechanism is a class of rotary braking devices which develop friction between a pair of relatively-rotating axially-loaded disks by means of rollers carried in a slotted plate between the disks. The slots containing the rollers are arranged at a skew angle relative to radii from the center of rotation so that, as the rollers roll between disks, they tend to track inwardly or outwardly on the disk surfaces. The ball screw has a transverse flange with flat radial surfaces at the top and bottom. The ball screw receives and transfers a bi-directional axial and torque load from the load resulting from the horizontal stabilizer hinge moment in an THSA. The brakes include ratchet wheels which control the direction of braking force application depending on whether the ball screw is under tension or under compression. When the horizontal stabilizer moves in the same direction as the air load direction, it prevents the screw nut from rotating under the air load to achieve the purpose of preventing reversal. Considering the complexity of the principle of the no-back mechanism, this paper only considers the modulation resistance element MR to represent the friction torque loss caused by the no-back mechanism under ideal conditions. Figure 7 shows the bond graph model of the no-back mechanism.

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Fig. 7. BG model of the no-back mechanism

4 System Model Integration and Simulation After the separate bond graph models of major components are established, they will be integrated to form the complete system model and then the simulation will be carried out. In addition to the mathematical models of the main components described above, there are other effects that need to be considered to make the model more complete. For the connection stiffness and damping effect of the nut and the rudder surface, this paper uses capacitance C and resistance R to represent respectively. The same is true for the connection stiffness and damping of the upper universal joint and the fuselage. The equivalent mass of the upper and lower gimbal housings and the equivalent moment of inertia of the lead screw are indicated by the inertial element I. The load is in the form of the equivalent translational motion, which equivalent mass is also represented by inertial element I. These components are spliced together, and the controller is designed according to the control scheme. The complete bond graph model is shown in Fig. 8.

Fig. 8. BG model of THSA

Figure 9 shows the comparison between the desired speed and actual speed under the step response. When the speed command is 0.03 m/s at 0.3 s, the step response curve indicates that the output of the ETHSA system follows the speed command well and has great dynamic performance. When an air load of 40,000 N is added at 1.3 s,

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the moving speed oscillates for a short period of time, and return to a steady state after about 0.2 s. The stability value is 0.02954 m/s and the steady state error is 1.53%.

Fig. 9. Step response curve of the horizontal stabilizer movement speed

5 Conclusion In this paper, the structure of the electric trimmable horizontal stabilizer actuator is introduced, Bond graph method has been applied for system-level and component-level modeling. The simulation work is done according to the Bond graph models and realized in 20-sim software. The level of complexity for the system model is chosen according to the engineering needs. And various physical effects are opportunely taken into account in the proposed model. The simulation results are shown for the basic control design, when the model needs to be used for energy consumption and efficiency analysis, then more parasitic effects need to be considered for more complex models.

References 1. Maré J-C, Fu J (2017) Review on signal-by-wire and power-by-wire actuation for more electric aircraft. Chin J Aeronaut 30(03):857–870 2. Jinker P, Claeyssen F (2006) New actuators for aircraft and space applications. In: 10th international conference on new actuators, Bremen, Germany, pp 14–16 3. Botten SL, Whitley CR, King AD (2000) Flight control actuation technology for nextgeneration all-electric aircraft. Technol Rev J 8:55–68 Millennium Issue, Fall/Winter 4. Fu J, Maré JC, Yongling F, Xu H (2015) Incremental modelling and simulation of power drive electronics and motor for flight control electro-mechanical actuators application. In: IEEE international conference on mechatronics and automation, Beijing, China

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5. Karnopp DC, Margolis DL, Rosenberg RC (2005) System dynamics: modeling and simulation of mechatronic systems. Wiley, New York, pp 20–53 6. Yu L, Zhang Y, Liu H (2016) Performance analysis and optimization design of dissimilar redundant hybrid electro-hydraulic actuation system. In: IEEE/CSAA international conference on aircraft utility systems, Beijing, China 7. Johnsen S, Thielecke F (2011) Integration analysis of trimmable horizontal stabilizer actuators and technology evaluation. CEAS Aeronaut J 2(1–4):11–19 8. Huang Y, Pe T, Popov AP, Werner H, Thielecke F (2010) Control of a two-load-path trimmable horizontal stabilizer actuator of an aircraft—comparison of ℋ∞ design approaches. In: 2010 49th IEEE conference on decision and control (CDC) 9. Wachendorf N, Thielecke F, Carl U, Pe T (2008) Multivariable controller design for a trimmable horizontal stabilizer actuator with two primary load paths. In: ICAS secretariat 26th congress of international council of the aeronautical sciences 2008, ICAS 2008, vol 4, pp 1796–1807

3D Super-Resolution Reconstruction Based on Multi-view Representation Yujia Du1,2,3, Yanping Zheng1,2,3, Haisheng Li1,2,3(&), and Li Tan1,2,3 1

3

School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China [email protected] 2 Beijing Key Laboratory of Big Data Technology for Food Safety, Beijing, China National Engineering Laboratory for Agri-Product Quality Traceability, Beijing, China

Abstract. Despite the progressed achievement on three-dimensional generation, the results of the research on high-resolution models are not satisfactory. In order to generate 3D objects in high resolution, we implement a 3D model super-resolution reconstruction system. First, a set of orthogonal depth maps are acquired based on each input 3D model, which has a low resolution. Then we upscale these images by training a super-resolution network. The highresolution orthogonal depth maps we obtained include rich information and are used to carve models in high resolution. Absolutely, our system is a reconstruction process from images to high quality 3D objects in voxel space. Considering the effect of the resolution of the image on the reconstruction results, we design a suitable super-resolution network to obtain a high-resolution depth map. We have conducted experiment on a subset of ShapeNet dataset and the experimental results show the effectiveness of our method. Keywords: 3D reconstruction Multi-view representation




Super-resolution network




Deep learning




1 Introduction With the continuous development of computer technology and the internet, a 3D vision system is hoped to be established to explore the 3D world. The important task of the computer 3D vision system is to provide a guarantee for high-quality environmental interaction, which relies on effective and efficient modeling techniques. In other words, how to build high-quality model data is of great significance for the progress of computer 3D vision. In recent years, using deep learning methods to solve the problem of 3D shape generation has become a hot spot and highlight. The deep learning model for processing 3D models can be divided into methods based on voxel, point clouds, meshes and multi-views according to the representation of the 3D shape. Although many efforts have been made in 3D generation, the resolution of 3D volume is still limited at a low level. To tackle this issue, we proposed a 3D super-resolution method based on multi-view residual network. © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 426–434, 2020. https://doi.org/10.1007/978-981-32-9698-5_48

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The rest of the paper is structured as follows. Section 2 provides an introduction of 3D object representation and 2D super-resolution. Section 3 introduces our 3D object super-resolution reconstruction process and illustrates the network architecture. Section 4 describes the training details of the super-resolution network and presents experimental results. Finally, the conclusion is detailed in Sect. 5.

2 Related Work 2.1

Geometric Representation of 3D Models

In the task of generating 3D shape, since the output is 3D data, choosing different representations is directly related to the construction of the network, the design of loss function and the quality of the output. These representations can be divided into methods based on voxel, point clouds, meshes and multi-views. Voxel-based representation is a direct extension from 2D to 3D, which has the advantages of simplicity [1]. However, this method is often limited to low resolution such as 323 and 643 due to the computational and high memory cost [2, 3]. To reduce these costs of full-voxel based methods, sparse voxel-based representation was proposed, which makes high-resolution voxel output possible [4–6]. As the existing bestperforming method, OctGen [4] could only show results up to 2563 resolution. Smith et al. [7] generated 3D shapes at 5123 resolution firstly. MVD was employed in this method as the network of image super-resolution, which is instability and often accompanies with artifacts. We solve this problem by optimizing network architecture and obtain more realistic 3D objects. For 3D generation, the model representation methods based on meshes and point clouds have achieved good results [8–10]. However, it is difficult to process the model information due to their irregular data structure. The multiview-based method can easily achieve good results by processing the color information and depth values contained in the 2D image and incorporating them into the 3D space [11, 12]. Nevertheless, there are few studies on applying it to reconstruct model in high resolution. Our work combines the voxel-based representation with multi-view representation to produce objects in high resolution. 2.2

2D Super-Resolution

High-resolution images provide more details that will play a key role in further image applications. Therefore, single image super resolution (SISR) technology has important practical significance. The early SISR method used a filter to make a simple prediction of the image [13], and the image reconstructed by this scheme is relatively blurred. Since the work of SRCNN was proposed [14], SISR has been combined with deep learning, and its visual quality is far superior to traditional methods [15]. As the milestone in the development of SISR, SRGAN [16] is the first super-resolution framework to magnify 4 times the natural image. MVD [7] is derived from the generator of SRGAN which brings problems that the network is instability and often accompanies with artifacts. In view of these problems, we apply the generator network structure of ESRGAN [17] to our experiment and get high-resolution depth maps with rich information.

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Top

Back

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Right

Bottom

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Fig. 1. Low-resolution ODMs

3 Approach In this section, we describe the 3D high-resolution reconstruction process. Firstly, we put low-resolution models in the system, and acquire a set of orthogonal depth maps (ODMs), as shown in Fig. 1. Then we upscale these images by training them in the super-resolution network. The high-resolution ODMs we get with rich information are the key part of our experiment. In order to modify the visual quality, we design the super-resolution network based on enhanced super-resolution generative adversarial networks (ESRGAN) generator [17]. Finally, mapping the high-resolution ODMs to the voxel model to generate 3d objects in high resolution. In our system, the input objects at resolutions as 323 can successfully generate 3D objects at resolutions up to 2563 and 5123. Figure 2 illustrates the whole pipeline of our approach.

Low-Resolution ODMs

Image super-resolution network

High-Resolution ODMs Model Carving Final Model

Low-Resolution Model

Nearest Neighbor Up-Samping

High-Resolution Model

Fig. 2. The process of 3D object high-resolution reconstruction

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Super-Resolution Network

As shown in Fig. 3, our network consists of 3 single-layer convolution structures, k residual-in-residual dense block (RRDB) structures, up-sampling structures and skipconnections. By replacing the residual block structure of MVD [7] with the more complex RRDB, the feature information obtains different layers can be fully integrated. Removing the BN layer can effectively address the problem of artifacts and improves the generalization ability of the network. Therefore, only the Conv layer and the Relu layer are contained in each residual dense block. The residual scaling parameter c is set to ensure that the network training is carried out quickly and steadily.

Conv Relu

Conv

Conv

Conv Relu

RRDB K

Upsampling

RRDB

Conv Relu

Conv Relu

Conv

RRDB

Conv

Dense block

×Ƴ

Dense block

×Ƴ

×Ƴ

Dense block

Fig. 3. The super-resolution network and k is the numbers of RRDB structure, k = 4

3.2

High-Resolution 3D Object Reconstruction

Our work begins by obtaining a set of ODMs, which come from six directions of lowresolution objects including front, back, left, right, top and bottom. It will increase the training difficulty and reduce the learning effect if all the information obtained from the super-resolution network is directly used in model carving. To address this concern, we use the method in the work of Smith et al. [7] to decompose the super-resolution work into a pair of deep networks with the same structure. The network GS predicts model silhouette and network GD predicts the variations in depth. GS is trained by minimizing the mean squared error (MSE) between the predicted and true silhouette of the high-resolution ODM (ODMH). Therefore, the loss for GS is, LossðaÞ ¼

N  X  GS ðODM i ; aÞ  ODM i  L H 2

ð1Þ

i¼1

where a is the parameter of GS, and ODML is the low-resolution ODM and ODMH is the high-resolution ODM.

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GD output the prediction of high-resolution depth map DH within a fixed range r by passing through a sigmoid, DH ¼ rSigmoidðGD ðODML ; bÞÞ þ f ðODML Þ

ð2Þ

where b is the parameter of GD while f (.) represents the nearest neighbor up-sampling. GD is trained by minimizing the mean squared error (MSE) between the predicted and true silhouette of DH, and a smoothing regularizer is added to constrain the loss result [18]. Therefore, the loss for GD is, LossðbÞ ¼

N  X  ðDi  ODM i Þ  ODM i  þ kVðDi Þ H H H 2 H

ð3Þ

i¼1

where  is Hadamard multiplication. kVð:Þ represents the smoothing regularizer, Combining silhouette prediction with DH, the result of high-resolution orthogonal depth map (ODMPH) is obtained, ODMPH ¼ GS ðODMLi ; aÞ  DH

ð4Þ

We use ODMPH to carve the structure and detail on the high-resolution 3D objects obtained by the up-sampling. For the structure carving, as there is numerous overlap in the surface of the ODMs, the requirement of removing voxel is that at least two ODMs mark that block is not occupied. In order to improve the quality and speed of carving, we add symmetry restraint to this work.

4 Experiment 4.1

Dataset

Our dataset comes from three object classes in the ShapeNet dataset [19] which includes 8000 car models, 7000 chair models and 4000 plane models. First, we convert the CAD models into voxel formats at 323 resolution and 2563 resolution. Then acquire a set of ODML and ODMH from each object. The ratio of training, test, and validation sets is 70:20:10. 4.2

Super-Resolution Network Training Details

Our network structure is shown in Fig. 3. The kernel size for all layers is 3  3 and the stride length is 1. Except for the last convolution layer, the depth of all layers is 128. The last convolution layer reduces the color channel of the image, with a depth of 1. We train the network using ADAM with the parameter of 0.9 and a batch size of 32. The learning rate is initialized as 1  10−4. The network is trained by using the loss

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function in Eq. (2) with r = 70 for 2563 objects and r = 90 for 5123 objects. The parameter of smoothing regularizer in Eq. (3) is k = 10 for 2563 objects and k = 20 for 5123 objects. 4.3

Results

In this section, we conduct comparisons with several results of our super-resolution reconstruction approach. To demonstrate the efficiency of our method for image superresolution, we choose MVD [7] as the baseline. We present some representative results in Fig. 4. According to the visualization results, we can see that our results has fewer missing and redundant pixel due to erroneous predictions of the super-resolution process.

Low-Resolution

MVD(2563)

Ours (2563)

Chair

Plane

Car

Fig. 4. Super-resolution results of ODMs

In order to evaluate the experiment results of 3D object super-resolution reconstruction more intuitively, we present some visual comparisons between our method and baseline at 2563 resolution in Fig. 5 and 5123 resolution in Fig. 6. It can be observed from the visualization results that our results are closer to the ground truth.

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Fig. 5. 3D objects super-resolution reconstruction results at 2563

Input (323)

MVD(5123

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Fig. 6. 3D objects super-resolution reconstruction results at 5123

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5 Conclusion Reconstructing the 3D shape of high resolution is a challenging task in computer vision field. The proposed framework splits this challenging task by combining multi-view representation with voxel-based representation. We achieve a set of orthogonal depth maps from the input low-resolution objects and predict the structure of objects at high resolution by putting these images in the super-resolution network. Compared to the baseline method, we generate more realistic 3D objects by adjusting the superresolution network architecture. All of the evaluation results demonstrate that our method outperforms previous methods. Acknowledgments. This work is partially supported by National Natural Science Foundation of China (61877002, 61702020), Beijing Natural Science Foundation grant number (4172013), Beijing Natural Science Foundation-Haidian Primitive Innovation Joint Fund grant number (L182007) and Beijing Municipal Commission of Education PXM2019-014213-000007.

References 1. Wang PS, Liu Y, Guo YX et al (2017) O-CNN: octree-based convolutional neural networks for 3D shape analysis. ACM Trans Graph (TOG) 36(4):72 2. Choy CB, Xu D, Gwak JY et al (2016) 3D-R2N2: a unified approach for single and multiview 3D object reconstruction. In: Leibe B, Matas J, Sebe N, Welling M (eds) European conference on computer vision 2016, vol 9912. LNCS. Springer, Cham, Switzerland, pp 628–644 3. Wu J, Zhang C, Xue T et al (2016) Learning a probabilistic latent space of object shapes via 3D generative-adversarial modelling. In: 30th international proceedings on neural information processing systems. Neural Information Processing Systems, La Jolla, pp 82–90 4. Tatarchenko M, Dosovitskiy A, Brox T (2017) Octree generating networks: efficient convolutional architectures for high-resolution 3D outputs. In: 20th international proceedings on the IEEE international conference on computer vision. IEEE, New York, pp 2088– 2096 5. Riegler G, Ulusoy AO, Bischof H et al (2017) OctNetFusion: learning depth fusion from data. In: 5th international proceedings on international conference on 3D vision. IEEE, New York, pp. 57–66 6. Häne C, Tulsiani S, Malik J (2017) Hierarchical surface prediction for 3D object reconstruction. In: 5th international proceedings on international conference on 3D vision. IEEE, New York, pp 412–420 7. Smith E, Fujimoto S, Meger D (2018) Multi-view silhouette and depth decomposition for high resolution 3D object representation. In: 32th international proceedings on neural information processing systems. Neural Information Processing Systems, La Jolla, pp 6478– 6488 8. Fan H, Su H, Guibas LJ (2017) A point set generation network for 3D object reconstruction from a single image. In: 30th international proceedings on the IEEE conference on computer vision and pattern recognition. IEEE, New York, pp 605–613 9. Wang N, Zhang Y, Li Z et al (2018) Pixel2Mesh: generating 3D mesh models from single RGB images. In: 15th international proceedings on the european conference on computer vision. Springer, Cham, pp 52–67

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10. Yang Y, Feng C, Shen Y et al (2018) FoldingNet: point cloud auto-encoder via deep grid deformation. In: 31th international proceedings on the IEEE conference on computer vision and pattern recognition. IEEE, New York, pp 206–215 11. Lun Z, Gadelha M, Kalogerakis E et al (2017) 3D shape reconstruction from sketches via multi-view convolutional networks. In: 5th international proceedings on international conference on 3D vision. New York, pp 67–77 12. Lin CH, Kong C, Lucey S (2018) Learning efficient point cloud generation for dense 3D object reconstruction. In: 32th international proceedings on AAAI conference on artificial intelligence. AAAI, Menlo Park 13. Duchon CE (1979) Lanczos filtering in one and two dimensions. J Appl Meteorol 18 (8):1016–1022 14. Dong C, Loy CC, He K et al (2016) Image super-resolution using deep convolutional networks. IEEE Trans Pattern Anal Mach Intell 38(2):295–307 15. Karras T, Aila T, Laine S et al (2017) Progressive growing of GANs for improved quality, stability, and variation 16. Ledig C, Theis L, Huszár F et al (2017) Photo-realistic single image super-resolution using a generative adversarial network. In: 30th international proceedings on the IEEE conference on computer vision and pattern recognition. IEEE, New York, pp 4681–4690 17. Wang X, Yu K, Wu S et al (2018) ESRGAN: enhanced super-resolution generative adversarial networks. In: 15th International proceedings on the European conference on computer vision. Springer, Cham 18. Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phys D Nonlinear Phenom 60(1–4):259–268 19. Chang AX, Funkhouser T, Guibas L et al (2015) ShapeNet: an information-rich 3D model repository. Comput Sci. arXiv preprint arXiv:1512.03012

3D Shape Classification Based on Point Convolutional Neural Network Combining Multi-geometric Features Guang Zeng1,2,3, Yujuan Wu1,2,3, Haisheng Li1,2,3(&), and Li Tan1,2,3 1

3

School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China [email protected] 2 Beijing Key Laboratory of Big Data Technology for Food Safety, Beijing, China National Engineering Laboratory for Agri-Product Quality Traceability, Beijing, China

Abstract. Point cloud has become increasingly prevalent in 3D computer vision tasks owing to its simplicity, flexibility and powerful representation capability. However, for 3D shapes classification, how to obtain discriminative and effective feature descriptors from point clouds is still a challenging task. In this paper, we implement a point convolutional neural network combining multigeometric feature to classify 3D shapes. We firstly obtain hidden geometric information from raw input point. And then a set of point information that consists of three-dimensional coordinates, normal vectors and curvatures is input to network. The extracted feature combining local geometric information can represent 3D shapes more effectively. Experiments on the Modelnet40 dataset show the effectiveness of the proposed method. Keywords: Shapes classification
Point cloud Point convolutional neural network


Normal
Curvature


1 Introduction The three-dimensional shapes have been extensively used in area of game, film, and other fields with abundant information such as color, texture, and geometric relationships [1]. In recent years, with the emergence of laser scanners and 3D printers, the number of 3D models has increased explosively. Therefore, how to effectively classify and manage these three-dimensional models has become an intensive research problem. In order to solve the problem of model classification, the key step is to find a suitable feature. Previous work resorted to the hand-crafted shape descriptor [2], which is designed according to the geometric properties of the surface, and then some machine learning algorithms are employed to achieve model classification [3, 4]. However, these descriptors cannot generalize well across different domains. With the development of deep learning techniques, some researchers use the geometric features extracted as low-level features input for neural network model to generate high-level features, which improve the feature representation of 3D shape [5, 6]. © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 435–442, 2020. https://doi.org/10.1007/978-981-32-9698-5_49

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Others methods is to project 3D data into multi-view 2D images. In Su et al.’s MVCNN [7], a 3D shape model is rendered with different virtual cameras from fixed views, and these images combined with a max pooling operation and classified with a CNN based architecture. However, in these methods, 3D spatial geometry information is inevitably lost when converting 3D shape into 2D format. Point cloud is a common type of geometric data structure. We directly use unordered point cloud as input. Firstly, we introduce the algorithms that using point clouds to calculate normal and curvatures. Then a permutation matrix is learned to realize the invariance of points by X-conv [8]. The produced result from permutation matrix and geometry features is input to the convolutional neural network. Finally, we can classify shapes through basic classification network architecture. The rest of the paper is organized as follows. Section 2 gives a brief introduction of deep learning on point cloud data. Section 3 gives algorithms of obtaining normal and curvatures. Section 4 illustrates the used network architecture and implementation details. Section 5 presents experimental results on the Modelnet40 dataset. Finally, conclusion is described in Sect. 6.

2 Related Work 3D point cloud descriptors have recently been extensively addressed in many fields. The main approaches extracting features from 3D point cloud can be categorized into two groups: local descriptor [9, 10] and global descriptor [11, 12]. Maturana et al. [13] proposed a three-dimensional convolutional neural network VoxNet, which firstly performs voxel representation of point cloud data, then performs convolution, pooling and full connection operations, and finally obtains effective features. Considering the sparsity of 3D data, Wang et al. [14] proposed Octree which can save computation by skipping convolution in unoccupied space. However, among the proposed methods, the low resolution nature of voxel grids is still a main reason that restrict the scale of the point clouds. Contrary to these works, some recent methods directly process point sets and achieve state of the art results in classification task. Qi et al. [15] proposed PointNet which can well handle the problem of irregular point cloud data by a symmetric function. Kd-Net [16] transform the point cloud to kd-tree which explicitly utilizes the spatial distribution of point clouds and extracts hierarchical feature. PointNet++ [17] is designed to handle local feature extraction adequately using PointNet recursively on input point set partition. Our approach is operating point convolutional neural network to combine geometric information with point cloud itself.

3 Geometric Features Extraction The input of our network include normal vectors and curvatures. Therefore, it is the first step to obtain these geometric features from input point cloud. The fused input of the point convolutional neural network is shown in Fig. 1.

3D Shape Classification coordinate

Point cloud representation

normal

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⎡ x11 , y11 , z11 , n11 , n12 , n13 , k11 , k12 , k13 , k14 ⎤ ⎢ ⎥ ⎢ x21 , y21 , z21 , n21 , n22 , n23 , k21 , k22 , k23 , k24 ⎥ ⎢ ⎥ ⎢ ⎥ ⎣⎢ xn1 , yn1 , zn1 , nn1 , nn 2 , nn 3 , kn1 , kn 2 , kn 3 , kn 4 ⎦⎥

...

Fig. 1. Point clouds of geometric information fused

3.1

Point Cloud Normal Information

We use Mitra et al. [18] proposed method to obtain normal from input points. Firstly, for a given point O, we compute the total least square plane fitting those points inside a sphere of radius r centered at O. The normal vector to the fitting plane is our estimate of the undirected normal at O. Therefore, we would like to find an appropriate radius r. It is as follows to minimize the angle between the estimated normal and the true normal.   1=3 1 rn c1 pffiffiffiffiffi þ c2 r2n r¼ ð1Þ j eq Where q is the sampling density of the point cloud data and j is local curvature at O, e [ 0 be some small positive number, rn represents standard deviation of the noise. Constants c1 and c2 are small and depend on the distribution of the point cloud data. The normal estimation algorithm is shown in Algorithm 1.

Algorithm 1: Normal Estimation Input: point cloud P; Output: normal; for each point p in P do compute the best fit least square plane for k neighbor points; compute the distance s , d , u ;

(

)

compute ρ , κ , ρ=k / π s 2 , κ =2d / u 2 and obtain r in Equation 1; compute the total least square plane fitting and obtain normal; end Where s is the distance from p to its k-th nearest neighbor,d is the distance from p to fitted plane and u is the average distance from p to all the points pj. pj, 1  j  k be the k nearest sample points around p. 3.2

Point Cloud Curvatures Information

We use Yang et al. [19] proposed algorithm to obtain input curvatures including Gaussian curvatures, mean curvatures, max and min curvatures. Amenta et al. [20] explicit defined Moving Least-Squares (MLS) and achieved to project a point onto MLS surface based on given definition. Therefore, we can obtain MLS surface

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curvatures from normal and coordinate due to the fact that MLS surface is an implicit surface [21]. The original form of MLS is converted to implicit form. gðxÞ ¼ nðxÞT



@e ðy; nðxÞÞ  y¼x @y

 ð2Þ

where n represents vector field and e is energy function. The curvatures estimation algorithm is shown in Algorithm 2.

Algorithm 2: Curvatures Estimation Input: normal and coordinate; Output: curvatures; Procedure: 1. Project a point onto MLS surface S; 2. Convert original form of MLS to implicit form g ( x) ; 3. Compute mean curvature and Gaussian curvature of g ( x) according to normal

and coordinate; 4. Obtain principal curvatures from mean curvature and Gaussian curvature;

4 Method Irregularly distributed point patterns should be solved firstly when using deep learning technology to process 3d point cloud data. In this Architecture, the network mainly consists of three components: four X-Conv subnetworks, three fully-connected layers and a softmax layer. We use X-Conv subnetwork to achieve the permutation invariance of input points and aggregate the features of input point. Then extracted features can be fed into convolutional neural network. Finally, 3D point shapes can be classified by the softmax layer. Detailed network frame is shown in Fig. 2.

Fig. 2. Framework of Point cloud classification algorithm

3D Shape Classification

4.1

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X-Transformation Operator

It is a key step to apply X-transformation operator in our network. We use a subnetwork to take the information of points as input, and learn different permutation matrices for different sets of points, so that the result obtained by multiplying the permutation matrix and the corresponding fused geometric information is equivalent to the original input in some potential space. The process of resolving unordered point cloud input is shown in Fig. 3. We assume the input set of network is P ¼ ðp1 ; p2 ; p3 ; p4 Þ, associated with feature ðfa ; fb ; fc ; fd Þ. The raw input point cloud data learns 4  4 transformation for the coordinates of P with a MLP and then use it to adjust weights of the input point features. Because output features remain constant practically when order of P changes, the network can continue to forward accurately.

Fig. 3. Process of resolving unordered point cloud

4.2

Point Convolutional Neural Network

Compared to image convolutional neural network, there are two main differences in point convolutional neural network. One is the ways of extracting feature by searching k neighboring points around the representative point. The other is learning local information by X-Conv network. The input points with original features are aggregated into fewer representative points which combine more features by a convolutional operator. The network of learning permutation matrix is shown in Fig. 4. The first convolutional layer with kernel of shape 1  K aggregate k neighboring points information into a point. Then a K  K convolution kernel is used to lift the feature dimension to K  K. Next two dense layers keep this shape and obtain a permutation matrix.

5 Experiments The experiments were implemented on the workstation equipped with an Intel(R) Xeon(R) CPU E5-2630 v3 (2.40 GHz) and a Tesla K40 m GPU (11.17 GiBmemory).

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Fig. 4. Learning process of permutation matrix

5.1

Experimental Dataset

We evaluate our algorithm on the ModelNet40 [22] benchmark for shape classification. The ModelNet40 contains 12,311 objects from 40 categories, among which 9,843 objects belong to training set and the rest 2,468 models for testing. Some of the models are shown in Fig. 5.

Fig. 5. Part of the 3d model of ModelNet40

5.2

Experimental Result

We illustrate the classification accuracy for state-of-the-art methods using various 3D representations, such as multi-views, point cloud, voxel and octree. The results are shown in Table 1. It can be found that the method proposed in this paper has an improved classification accuracy. As an example, compared with PointCNN, it performs 0.2% and 0.3% respectively by adding only normal information and both normal and curvature. In addition, we found that the training time is shorter than the training time of the single coordinate as input. The possible reason is that we provide more geometric information to network, which makes the network hold more prior knowledge.

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Table 1. Accuracy comparison Method MVCNN VoCNN O-CNN PointNet PointNet ++ PointCNN OUR1 OUR2

Representation Images Voxel Octree Point Point Point Point+normal Point+normal+curvature

Core operator 2D convolution 3D convolution 3D convolution Pointwise MLP Multi-scale Pointwise MLP X-Conv X-Conv+normal X-Conv+normal+curvature

Accuracy 90.1 89.9 90.6 89.2 90.7 91.7 91.9 92.0

6 Conclusion This paper introduces a new approach for 3D object classification by combining geometric information and point convolutional neural networks. This technique utilizes efficiently normal and curvature information based on input. Firstly, the way of obtaining geometric information is introduced. In addition, we explain it is inappropriate to use the convolution directly to the point cloud for its unordered distribution. To solve this problem, we use a permutation matrix which is trained by X-Conv. Finally, extracted geometric information is fed to convolutional neural networks to achieve classification. Experiment results showed better performance of the proposed algorithm on ModelNet40 compared to prior works. Future work will add more other information such as RGB colors to enrich 3D shape representation. And further improvement in the classification accuracy rate is expected. Acknowledgments. This work is partially supported by National Natural Science Foundation of China (61877002, 61702020), Beijing Natural Science Foundation grant number (4172013), Beijing Natural Science Foundation-Haidian Primitive Innovation Joint Fund grant number (L182007) and Beijing Municipal Commission of Education PXM2019-014213-000007.

References 1. Tangelder JWH, Veltkamp RC (2004) A survey of content based 3D shape retrieval methods. In: 6th international conference on shape modeling and applications. IEEE, LA, pp 145–156 2. Xie J, Fang Y, Zhu F et al (2015) Deepshape: deep learned shape descriptor for 3D shape matching and retrieval. In: 28th IEEE conference on computer vision and pattern recognition. IEEE, NY, pp 1275–1283 (2015) 3. Cıbuk M, Budak U, Guo Y et al (2019) Efficient deep features selections and classification for flower species recognition. Measurement 137:7–13 4. Vishwanathan SVM, Murty MN (2002) SSVM: a simple SVM algorithm. In: International joint conference on neural networks. IEEE, NY, pp 2393–2398 (2002) 5. Fang Y, Xie J, Dai G et al (2015) 3D deep shape descriptor. In: 28th IEEE conference on computer vision and pattern recognition. IEEE, NY, pp 2319–2328

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6. Dai G, Xie J, Zhu F et al (2016) Learning a discriminative deformation-invariant 3D shape descriptor via many-to-one encoder. Pattern Recogn Lett 83:330–338 7. Su H, Maji S, Kalogerakis E et al (2015) Multi-view convolutional neural networks for 3D shape recognition. In: IEEE international conference on computer vision. IEEE, NY, pp 945–953 8. Li Y, Bu R, Sun M, et al (2018) PointCNN: Convolution on X-transformed points. In: 32nd conference on neural information processing systems. NIPS, LA, pp 820–830 9. Guo Y, Sohel F, Bennamoun M et al (2013) Rotational projection statistics for 3D local surface description and object recognition. Int J Comput Vision 105(1):63–86 10. Tombari F, Salti S, Di Stefano L (2010) Unique signatures of histograms for local surface description. In: Daniilidis K, Maragos P, Paragios N (eds) 11th european conference on computer vision. LNCS, vol 6313. Springer, Heidelberg, pp 356–369 11. Wohlkinger W, Vincze M (2011) Ensemble of shape functions for 3D object classification, In: The IEEE international conference on robotics and biomimetics. IEEE, NY, pp 2987– 2992 12. Aldoma A, Tombari F, Rusu RB et al (2012) OUR-CVFH–oriented, unique and repeatable clustered viewpoint feature histogram for object recognition and 6DOF pose estimation. In: joint DAGM (German association for pattern recognition) and OAGM symposium. Springer, Heidelberg, pp 113–122 13. Maturana D, Scherer S (2015) VoxNet: a 3D convolutional neural network for real-time object recognition. In: IEEE/RSJ international conference on intelligent robots & systems. IEEE, NY, pp 922–928 14. Wang PS, Liu Y, Guo YX et al (2017) O-CNN: octree-based convolutional neural networks for 3D shape analysis. ACM Trans Graph (TOG) 36(4):72 15. Qi CR, Su, H (2017) Pointnet: deep learning on point sets for 3D classification and segmentation. In: 30th IEEE conference on computer vision and pattern recognition. IEEE, NY, pp 652–660 16. Klokov R, Lempitsky V (2017) Escape from cells: deep kd-networks for the recognition of 3D point cloud models. In: 16th IEEE international conference on computer vision. IEEE, NY, pp 863–872 17. Qi CR, Yi L, Su H, et al (2017) Pointnet++: deep hierarchical feature learning on point sets in a metric space. In: 31st conference on neural information processing systems. NIPS, LA, pp 5099–5108 18. Mitra NJ, Nguyen A.: Estimating surface normals in noisy point cloud data. In: 19th ACM symposium proceedings on computational geometry proceedings. World Scientific Publ Co. Pte. Ltd., Singapore, pp 322–328 19. Yang P, Qian X (2007) Direct computing of surface curvatures for point-set surfaces. Symp Point Based Graph 7:29–36 20. Amenta N, Kil YJ (2004) Defining point-set surfaces. ACM Trans Graph (TOG) 23(3):264– 270 21. Dey TK, Sun J.: An adaptive MLS surface for reconstruction with guarantees. In: Third eurographics symposium on geometry processing. Eurographics Association, Aire-la-Ville, pp 43–52 (2005) 22. Wu Z, Song S, Khosla A, et al. (2015) 3D shapenets: a deep representation for volumetric shapes. In: 28th IEEE conference on computer vision and pattern recognition. IEEE, NY, pp 1912–1920

Evolutionary Generation of Test Data Based on Reduction of Initial Population Data Wei Gao1, Yan Song1, and Baoying Ma2(&) 1

School of Computer and Information Technology, Mudanjiang Normal University, Mudanjiang 157011, Heilongjiang, China 2 College of Health Management, Mudanjiang Medical University, Mudanjiang 157011, Heilongjiang, China [email protected]

Abstract. When Genetic Algorithm is used to evolve test data for path coverage, if the similarity of some test data of initial population is high, it will cause the lack of diversity of individuals, which directly affects the rate of optimal solution at subsequent evolution generation. A method for evolutionary generation of test data based on reduction of initial population data is proposed. A program will be expressed as a binary tree according to the branch number of the tested program. And all the executable paths of a program will be represented as binary encoding, different path of that program are obtained, test data reduction is conducted according to the similarity. The reduced data are evolved as the initial population of the Genetic Algorithm to generate test data to meet the requirements. The proposed method is used to generate test data of three benchmark programs, and compared with existing method, the experimental results show that the proposed method can effectively generate test data after reduction of initial population data, and have better performance in the number of generations and running time. Keywords: Path coverage
Genetic Algorithm
Initial population data Executable path
Equivalence class
Data reduction




1 Introduction Software testing is a time-consuming and labor-consuming work. Its goal is to find as many defects as possible with the least test data on the premise of meeting the testing criteria, thus reducing the cost of software development. Among several criteria for measuring software test coverage, path coverage is the test criterion with the highest coverage in white box test, which means that enough test data are selected in the test so that every possible path of the program is executed at least once [1, 2]. During the generation of test data based on genetic algorithm, the selected initial population is usually a randomly generated test data set (i.e. test component). Since the continuously increasing test data may affect the maintenance cost, it is necessary to reduce the size of the test component. The reduction of the test component can be realized by deleting redundant test cases [3], but the reduction of the test component requires that neither the test coverage nor the fault detection capability can be reduced [4–6]. Therefore, it is necessary to find a suitable subset of test data when reducing test © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 443–451, 2020. https://doi.org/10.1007/978-981-32-9698-5_50

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components, which is sufficient to meet the given test requirements and reduce the cost of test data generation. In order to solve the problem of test component size, Jones et al. [7] studied the use of test case reduction algorithm. In the proposed method, the statement/branch coverage sufficiency criterion was considered, and according to the priority algorithm of the original test component and test component, the order of test cases in the reduced test component was determined, so that the reduced test component provided the same software coverage as the original component. Muthyala et al. [8] introduced data mining technology to cluster similarity data to reduce the number of test data, and the coverage of the clustered data to the program was taken as the measurement standard. Alavi et al. [9] proposed a test component reduction method for clustering similar data. Firstly, the number of clusters is determined according to the condition combination state in the program, and then the K-means algorithm is applied for clustering. However, due to the uncertainty in the selection of the initial clustering center and the need to continuously adjust the sample classification and calculate the adjusted new clustering center, the clustering time of the proposed method is long when the amount of data is very large. Kumar et al. [10] estimated the initial number of clusters with the Cyclomatic complexity of the program, and used the fuzzy C-means output clustering center as the input of the genetic algorithm. After that, the number of clusters was adjusted according to the situation that the data passed through the program, and the fuzzy C-means algorithm was repeatedly executed until the clustering center had a minimum offset. In the method, Cyclomatic complexity was used to estimate the initial number of clusters. Every time a new cluster was added, the fuzzy C-means algorithm was re-executed to check the coverage of test data. The running time was long and the calculation was large. In addition, literature [11–13] proposed to reduce the number of test cases by using equivalence class testing, boundary value testing, paired testing and other technologies. In this article, similar data are classified based on the feasible path of the program, an effective reduction method for test data is put forward, and test data meeting the target are evolved and generated, thereupon offer the reduction method for test data to effectively decrease test data quantity in the initial population under the genetic algorithm.

2 Generation of Feasible Path 2.1

Binary Tree Representation of the Program

In this article, the antecedent of the branch statement is represented as one node and the antecedent of the select statement nested in two branches of this node is represented as its two child nodes; the multi-branching structure is decomposed into multiple double branch structures and Z-path is introduced to cover it [14]; the loop structure alters into double branch select structure, and thus one program under test can be represented as one binary tree; hereby description will be provided with an example program (see Fig. 1).

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Fig. 1. The sample program and its binary tree representation.

2.2

Generation of Feasible Path

According to the method mentioned above, the binary tree structure generated by the source program in Fig. 1(a) can be represented as Fig. 1(b). In Fig. 1(b), r1–r8 represents leaf nodes, one path in the program under test refers to that from the root node of the tree n1 to the current leaf node; it’s not hard to tell there are 8 paths in this example. N and Y in the Figures X represent execution of the false branch statement and that of true branch statement respectively; if the true branch statement is executed, it will be represented by 1, otherwise, the false branch will be represented by 0; in this way, 8 paths represented by 1 or 0 can be obtained. For example the path from node n1 to r1 can be represented as: 000, i.e. the test data traverse the false branch of node n1, the false branch of node n2, and the false branch of node n3; in a similar way, the code of the path from node n1 to r7 is: 110, i.e. the test data traverse the true branch of node n1, the true branch of node n2, and the false branch of node n3. It’s not hard to conclude that the 8 paths generated by the program in Fig. 1 are: 000, 001, 010, 011, 100, 101, 110, 111, corresponding to all feasible paths of the program. It is easy to tell from the path binary tree constructed in the article that the total number of paths in the program is the number of leaf nodes in the tree, each path starts from the tree root, goes by several branch nodes in the tree and finally ends at the leaf node of the tree, i.e. after the running of the program, the path traversed by any test data must be one of the paths.

3 Definition of Test Data Similarity Definition 1: For path pk 2 L, and test data xi , xj 2 S, aik ðtÞ 2 T ðtÞ, ajk ðtÞ 2 T ðtÞ, if aik ðtÞ ¼ ajk ðtÞ ¼ 1, then it is defined that the test data xi is similar to test data xj with respect to path pk.

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According to Definition 1, the similarity of multiple test data xi ; xj ;


xs with respect to path pk can be defined. Definition 2: For 8 path pk 2 L, and test data xi ; xj ;


; xs 2 S, aik ðtÞ; ajk ðtÞ. . .ask ðtÞ 2 T ðtÞ, if aik ðtÞ ¼ ajk ðtÞ. . .ask ðtÞ ¼ 1, the test data xi ; xj ;


xs is defined to be similar with respect to path pk. According to Definitions 1 and 2, it can be concluded that for correlation matrix T(5) constructed in formula (2), among one column (that is corresponding to a certain path pk), if the test data have a value being 1, they are similar with respect to path pk; then from matrix T(5), the test data x1, x2 and x3 are similar with respect to path p2. Definition 3: Equivalence class elements of test data. For 8xi 2 S, and path pj 2 L, aij ðtÞ 2 T ðtÞ, if aij ðtÞ ¼ 1, all test data xi meeting conditions constitute the equivalence class set of test data Ej, and test data xi is defined an element in the equivalence class set of test data traversing path pj. According to the definition of test data similarity, if multiple test data traverse the same path, they have similarity and constitute the equivalence set of test data traversing the same path. For example, according to correlation matrix T(5), test data x1, x2, and x3 are similar with respect to path p2, thus x1, x2, and x3 are elements of equivalence set E2 of test data traversing path p2.

4 Reduction Algorithm for Test Data The method provided in this article considers equal reduction of all equivalence classes; suppose that the population after reduction is Snew ¼ £, the number of test data before reduction is N, C is the expected total number of data for reduction (C > 0), and the initial value Count = 0, the reduction algorithm for test data is as follows: (1) Run the program with all test data as input, and record traversed paths and save them in L; (2) Divide test data into K equivalence classes E1*EK according to the traversed paths; (3) Select randomly one path pi ð1  i  K Þ from L; find all elements in the equivalence class Ei of test data traversing path pi; suppose there are Ci (Ci) and Counti is the data number actually reduced in the equivalence class; excute: K  P Counti \C &&ðCi  Counti Þ [ N=KÞ While i¼1

{Select test data xj in Ei in turn; Count ¼ þ 1; Count Add test data xj into the new population Snew and delete the test data from Ei}; (4) Delete path pi from L, if L 6¼ £, turn to step (3).

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5 Evolution and Generation of Test Data Based on Initial Population Reduction 5.1

Generation Process of Test Data Under the Method in This Article

Firstly, generate randomly a certain amount of test data; then obtain the path traversing situation of all test data after the running of instrumented program; if there are test data traversing the target path, the algorithm terminates, otherwise the test data - path correlation matrix is established; reduce the test data according to the method provided in this article, generate thereupon the initial population Snew of genetic algorithm and then further generate test data meeting the target; specific steps are as follows: (1) Assign value to the control parameter needed by the algorithm, encode the path of the program under test, and instrument the program under test; (2) Initialize test data; (3) Encode the evolutionary test data and execute the program under test; (4) Judge whether any test data traverse the target path or not; if any, save the test data corresponding to the evolutionary test data; if test data traverse all target paths, turn to step 9, otherwise turn to step 5; (5) Reduce the test data according to method provided in this article, and output the initial population data of genetic algorithm; (6) Judge whether the termination criteria are met, if so, turn to step 9; (7) Calculate the fitness of evolutionary test data; (8) Implement selection, cross and mutation operations to generate child evolutionary population; turn to step 3; (9) Stop evolution, decode the evolutionary individual, and output test data. 5.2

Selection of Fitness Function in the Genetic Algorithm

There exist many design methods for the evolution and generation of fitness function in view of the path covered test data, such as the method considering the branch distance, layer proximity or both combined and that considering matching degree of traversing path of test data with each target path. With regards to the selection of fitness function in this article, the fitness of test data is calculated through comparing the matching degree of the test data traversing path code with each target path code.

6 Experiment To verify the effectiveness of the method provided, a comparison of the method provided in this article with that in literature is conducted through an experiment. Triangle classification program, maximum value and minimum value program, and bubble sort are selected for this experiment; please refer to Table 1 for the description of related programs. In the experiment, experiment parameters related to the genetic algorithm are designed as: binary coding for the individual, roulette as the selection mode, singlepoint crossover and crossover probability being 0.9, single-point mutation and

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mutation probability being 0.3, and the generation of test data for all target paths as the termination condition for the algorithm. Table 1. Program description. Program name

Triangle classification Seek the maximum and minimum value Bubble sort

6.1

Number of branch statements 3 choices

Branch statement composition

1 2 2 1

Nesting 2 Parallel Choices in Loop

cycle, choices cycle, choices

Three levels of selection nesting are formed

Two layers of circular nesting are formed, and one option is available in the inner layer nesting

Experiment with Triangle Classification Program

In order to compare the method provided in this article with the method proposed by Alavi etc. (Alavi method for short below), in view of all target paths (4 feasible paths) of the triangle classification program, same data searching space [0, 50]3 are set, and the number of individuals delivered to the initial population of genetic algorithm after reduction is the same for the two methods. To reduce error, 100 experiments have been conducted for each case of the program, the evolutionary algebra that finds each target path is recorded during the experiments, and the average of the evolutionary algebra in the 100 experiments is calculated. Since the evolutionary time for the running of each experiment has only several milliseconds, only the total evolutionary time for the 100 experiments has been recorded, and the results are shown as Table 2. Table 2. Experimental results of triangle classifier program. Number of data

30 50 100 200 500

Average number of evolutionary generation This Alavi Algebraic method method ratio (%) 66.92 516.11 12.97 74.99 515.65 14.54 70.19 528.92 13.27 69.76 461.98 15.10 70.14 384.24 18.25

Total evolution time This method 0.080 0.089 0.090 0.093 0.094

Alavi method 0.718 0.733 0.832 0.883 1.354

Time ratio (%) 11.14 12.14 10.82 10.53 6.94

It can be told from Table 2 that: (1) In the case of same searching space, with the gradual increasing of the number of test data, both methods change in the finding of evolutionary algebra for target path, and in total evolutionary time; and in the aspects of the evolutionary algebra and evolutionary time, the method provided in the article is

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steadier, operates less algebras and uses less time, compared with Alavi method; the reason is that in the Alavi method, conditions and composite state are considered for data reduction, K-means algorithm is employed for data reduction, and clustering takes a lot of time in itself; however, in the test data reduction under the method provided in this article, what is considered is the feasible path, and test data is reduced based on the path, which will produce active influences on the generation of test data oriented towards path coverage. (2) In the case of different number of initial data, the two methods differ in algebra ratio and time ratio, with the maximum algebra ratio and maximum time ratio being 18.25% and 12.14% respectively, which indicates that to find the data to cover the target path, the method provided in the article only uses 1/5 evolutionary algebras and 1/6 evolutionary time compared with Alavi method; this is because that Alavi method employs K-means algorithm to cluster the test data based on the condition state of the program, while the shortcoming of the algorithm is its long running time. (3) With the increasing of the number of data being input, the time ratio tends to be stable, which indicates that the method provided in this article shows higher superiority under the larger input of data. Now, examination needs to be performed for the finding of the evolutionary algebra of test data covering each target path. For this purpose, take the input data scope being [0, 100] as an example (since after the reduction of test data, the number of initial population data in the genetic algorithm is relatively few, the input data scope selected is not large); the initial populations are 1,000; and record 100 experiments and find the evolutionary algebra of test data covering each target path; calculate the average value as shown in Table 3. Table 3. Average evolution generations for test data covering each target path Method

Average number of evolutionary generation Non-triangular Ordinary triangle Isosceles triangle Equilateral triangle This method 1.00 1.00 1.00 53.42 Alavi method 1.02 1.32 3.33 567.94

It can be told from Table 3 that: (1) It is easy to find test data covering non-triangle and ordinary triangle paths, and the two methods can find such data within the 2nd generation; (2) The test data covering isosceles triangle can also be found in relatively few evolutionary algebras, and the two methods differ not too much; (3) It is hard to find the test data covering equilateral triangle, and in average, this method provided in the article takes 53.42 generations to find such data; while the Alavi method takes 567.94 generations to find such data. It can be told that for the finding of test data that have difficulty in covering the path, the method provided in the article is evidently superior to Alavi method.

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Experiments in Two Other Benchmark Test Programs

To further verify the performance of the method provided in this article, experiments have been conducted on 2 other benchmark test programs with different structures, with the input data scope being selected at [0, 100]; both initial population sizes are 1,000, and the number of target paths for the bubble sort, and that for the maximum value and minimum value program are 6 and 8 respectively. The algorithm termination condition is the finding of test data covering all target paths, and the total evolutionary time and average evolutionary algebra are recorded; the results are shown as Table 4. Table 4. Experimental results of the other two benchmark programs. Program

Bubble sort Seek the maximum and minimum value

Number of evolutionary generation This Alavi Algebraic method method ratio (%)

This method

Alavi method

3.00 1.87

0.031 0.180

1.263 1.981

3.35 55.43

89.55 3.37

Total evolution time Time ratio (%) 2.45 9.09

It can be told from Table 4 that for two test programs in it, the application of the method provided in the article results in less average evolutionary algebras and evolutionary time compared with Alavi method; in the bubble sort, the two methods differ not too much, the reason of which is that only three numbers are set for sorting in the experiments and such experiment difficulty is low. However, this is adequate to tell that the results for the two programs are consistent with that for the triangle classification program, and the method provided in the article uses less evolutionary time and average algebras in the finding of test data covering the target path, which fully demonstrates that for the 3 benchmark test programs, the method provided in the article is superior to Alavi method.

7 Conclusion In view of the path coverage criteria in software test, this article puts forwards a kind of test data evolution and generation method based on the initial population reduction, in which all feasible paths are found through construction of Huffman tree for a program, the data similarity with respect to path is put forward to further classify and reduce test data, and reduced data is regarded as the initial population in the genetic algorithm for the evolution and generation of test data meeting the requirements. Finally, the method provided in the article is compared with existing methods through three benchmark test programs, and experiment results show that in the aspect of finding test data covering target paths, the method provided in the article uses less average evolutionary algebras and evolutionary time for the generation of test data, and thus higher efficiency.

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However, how to combine clustering algorithm with the test data reduction method based on feasible path of the program to further improve the quality of initial population in genetic algorithm is the study content for next step. Acknowledgments. This work was supported by the Research Projects of Basic Scientific Research Business Expenses in Institutions of Higher Learning of Heilongjiang Province (1353MSYYB007, 2018-KYYWFMY-0104). Science and Technology Project of Mudanjiang Normal University (GP2019003). Science and Technology Project of Mudanjiang (Z2018g023).

References 1. Roper M, Macleani Brooks A et al (1995) Genetic algorithms and the automatic generation of test data. Technical report, University of Strathelyde 2. Whittaker JA (2000) What is software testing? And why is it so hard? IEEE Softw 17:70–79 3. Singh NP, Mishra R, Yadav R (2011) Analytical review of test redundancy detection techniques. Int J Comput Appl 27:30–33 (0975–8887) 4. Khan R, Malik R (2009) The impact of test case reduction and prioritization on software testing effectiveness. Paper presented at the international conference on emerging technologies, pp 416–421 5. Pringsulaka P, Daengdej J (2006) Coverall algorithm for test case reduction. Paper presented at the IEEE aerospace conference 6. Pan N, Zeng F, Huang YH (2010) Test case reduction based on program invariant and genetic algorithm. Paper presented at the 6th international conference on wireless communications networking and mobile computing (WiCOM), pp 1–5 7. Jones JA, Harrold MJ (2003) Test-suite reduction and prioritization for modified condition/decision coverage. IEEE Trans Softw Eng 29:195–209 8. Muthyala K, Naidu R (2011) A novel approach to test suite reduction using data mining. Indian J Comput Sci Eng 2:500–505 9. Roya A, Shahriar L (2011) The new approach for software testing using a genetic algorithm based on clustering initial test instances. In: 2011 international conference on computer and software modeling, pp. 225–231 10. Gaurav K, Pradeep KB (2013) Software testing optimization through test suite reduction using fuzzy clustering. CSIT 1:253–260 11. Saraph P, Last M, Kandel A (2003) Test case generation and reduction by automated inputoutput analysis. In: IEEE international conference on systems, man, and cybernetics, pp 768–773 12. Dong W (2008) Test case reduction technique for BPEL-based testing. Paper presented at the international symposium on electronic commerce and security, pp 814–817 13. Raamesh L, Uma GV (2010) An efficient reduction method for test cases. Int J Eng Sci Technol 2:6611–6616 14. Xia H, Song X, Wang L (2006) Research of test case auto generating based on Z path coverage. Mod Electron Technol 6:92–94

The Design of Fuzzy Temperature Controller Based on the Spray Cooling Experiment Longjun Zhu1(&) and Jialong Ren2 1

2

Shanghai Normal University Tianhua College, Shanghai 201815, China [email protected] Jiangsu University of Science and Technology, Zhenjiang 212003, China

Abstract. In order to control the temperature of cutting field better in the spray cooling experiment, by analyzing the design process of fuzzy controller, a method for implementing fuzzy temperature controller is proposed based on online inference way on PLC and the statement list of some crucial steps are given. According to the simulation result, it proves that the controller still has more stable control effect with 20% variation of the parameter, that means it has better robustness. Keywords: PLC


Fuzzy control
On-line inference

1 Introduction Amount of heat which produced by material removal processing would reduce the service life and impair the product quality. To reduce the produced heat and to dissipate the heat are the key issues of metal processing systems [1]. In this field, the most effective method is cool down and lubricate the processing zone. Spray cooling technology has broad application prospects as an economical and green cooling and lubrication method, but the control logic of spray dose and use time and processing zone temperature is a difficult point for the effective application of this technology. The temperature control of metal processing zone has the characteristics of large time lag and nonlinearity. At present, it is impossible to establish a precise mathematical model. The classic PID control seems could not competent the acquirement. In recent years, the re-emergence of artificial intelligence technology has provided a new direction for solving such problems. The intelligent fuzzy control method constructed by simulating human thinking is one of the effective solutions [2]. There are two major hardware application methods of fuzzy control, which are PLC and single-chip microcomputer. However, the weak anti-interference ability of the single-chip micro-computer cannot meet the needs of actual complicated working conditions. While the application of PLC usually uses the method of Offline calculation and online checklist to establish fuzzy control. For different control systems and control requirements, it is necessary to recalculate the control look-up table, that is lack of versatility.

© Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 452–460, 2020. https://doi.org/10.1007/978-981-32-9698-5_51

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2 Fuzzy Temperature Controller Design 2.1

Structure of the Fuzzy Control System

The overall structure of the spray cooling experimental device is shown in Fig. 1. The functions of the control system mainly include data acquisition, temperature control and display of the cutting zone, and fault alarm.

Fig. 1. Overall structure of the spray experiment device.

In Fig. 1, an electric furnace is used to heat the workpiece for simulating the temperature rise process of the workpiece. The gas exits the compressor and passes through the water separator to filter out the impurities, and then passes through the normally closed two-way solenoid valve. After that, a small part reaches the water tank through the hose, presses the water into the liquid flow controller and then reaches the nozzle. Most of the gas reaches the nozzle through the air flow controller, and the gas and liquid are mixed in the nozzle to form a spray, and sprayed to the cutting zone in the form of a high-pressure jet. The controller controls the flow rate of the atomizing fluid sent to the nozzle by adjusting the opening degree of the electromagnetic proportional valve to achieve real-time control of the size of the spray, so that the temperature of the cutting zone is always stable within the allowable error range of the expected temperature, that means dynamic stability. The control device of this spray cooling experiment cannot obtain a sufficiently accurate mathematical model for the relationship between liquid flow, gas flow and temperature. Therefore, this paper uses a two-dimensional fuzzy controller to obtain the exact value of the cutting zone temperature by sampling with a temperature sensor, and then compares this amount with the temperature given value to obtain the deviation signal e and the deviation variation ec. The deviation e and the change ec are quantized and processed as the input linguistic variables of the fuzzy controller to apply fuzzy reasoning, fuzzy decision and explicitation. Then the input multiplied by the scale factor Ku to convert to the basic

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domain, and finally the D/A conversed output is applied to the Control object. Its structure is shown in Fig. 2. e(t ) [ − xe , xe ]

r (t )

Input

−

Ke

Fuzzy controller

u1 (kT )

u (kT )

Ku

ec(t )

d/dt

Object

c(t )

Output

Ke Signal acquisition Fig. 2. 2D fuzzy controller structure.

2.2

Fuzzy Control Algorithm

2.2.1 Fuzzification of Input Variables The input of the fuzzy controller is the value of the linguistic variable, which is a fuzzy set, so the input quantity needs to be converted into the discrete domain of the fuzzy set. In this design, the error e and the error rate of change ec are all transformed into the discrete domain {–6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6}. The fuzzy subsets are {NL, NM, NS, ZO, PS, PM, PL}, and each element in the subset represents negative large, negative moderate, negative small, zero, positive small, positive Moderate, and positive large. According to the membership function curve, the assignment table of each fuzzy linguistic variable can be conveniently inferred. This paper uses the widely used triangle membership function. 2.2.2 Establishment of Fuzzy Control Rule Base One of the keys to implementing successful controls is to develop sophisticated fuzzy control rules. According to the operating experience of spray-cooled cutting operators, the standard form of fuzzy rules adopted in this paper is: If e is A1j and ec is Ak2 ,Then u is Bpq . 2.2.3 Fuzzy Inference Engine Fuzzy reasoning mainly includes two aspects, one is matching, which determines which rules are activated by the current input; the other is reasoning, that is, the conclusion is derived through the current input and the rules activated in the rule base [3]. 2.2.4 Explicitation The result of fuzzy reasoning is generally a fuzzy value, which cannot be directly used as the control quantity of the controlled object, that calls to be converted into an accurate quantity that can be executed by the actuator [4]. This process is called a deblurring process, or a fuzzy decision, which is a mapping from fuzzy space to clear space. The quantized value U of the control quantity is obtained by a deblurring method of the maximum membership degree method, the center of gravity method, and

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the weighted average method, etc., multiplied by the scale factor ku to obtain an accurate value of the control amount. The D/A conversed output is applied to the air flow controller and the liquid flow controller of controlled object.

3 Programming Implementation of Fuzzy Control Algorithm on PLC 3.1

PLC Selection

It can be seen from Fig. 1 that only one analog input (temperature acquisition) and one analog output (control signal) are required, so the EM235 analog expansion module with four analog inputs and one analog output function is applicable. The fuzzy control adopts Siemens S7-200 PLC to realize programming. The A/D and D/A conversion of the EM235 analog expansion module does not require special programming. In the program, it can be read directly by the instruction AIW, and output by the instruction AQW. The preliminary allocation of specific I/O point addresses is shown in Table 1: Table 1. The allocation of specific I/O point. Type Input

Sign START STOP Output V LED1 LED2

3.2

Address I0.0 I0.1 Q0.0 Q0.0 Q0.1

Function Start Stop Output coil Normal Breaking

Programming Process

The working mode of the PLC is cyclic scanning. In order to reduce the scanning period, it applied the method of first writing each program in stages and then integrating them by calling sub-programs to realize the fuzzy control of online reasoning. The block diagram of its programming flow is shown in Fig. 3. 3.3

The Specific Implementation of Fuzzy Program

3.3.1 Quantization Processing Program Design of Input The quantization process of the input is mainly to transform the basic domain of the deviation and the rate of change of the deviation into the fuzzy domain, and determine the corresponding membership degree and linguistic value. In order to facilitate the programming implementation, the linguistic value of the fuzzy variable is represented by a number, that is, the fuzzy set “NL” is represented by the number “1”, the fuzzy set “NM” is represented by the number “2”, and the fuzzy set “NS” is represented by the number “3”, etc. By analogy, the fuzzy set {NL, NM, NS, ZO, PS, PM, PL} can be represented by numbers as {1, 2, 3, 4, 5, 6, 7}.

456

L. Zhu and J. Ren Start

Get sample input, A/D conversion, calculate e,ec Quantitative processing and conversion to fuzzy universe E and EC For input, the linguistic value and corresponging membership are calculated According to the linguistic value,which rules are activated and the inferred linguistic value and the membership degree of the preceding rules are calculated De-fuzzification, using COG method The output control quantity is multiplied by the proportion factor to get the exact value. The final control quantity is obtained by D/A conversion.

End

Fig. 3. Fuzzy controller program flow chart.

The fuzzy set theory field of the input and output variables {–6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6} is offset by 7 into {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} at same time, the membership of the input variables e and ec can be expressed in Table 2. Table 2. Representation of membership degree vector of input variables e and ec with fuzzy numbers. Membership function value Membership function e or ec

1 2 3 4 5 6 7

Input deviation e or input deviation change rate ec 1 2 3 4 5 6 7 8 9 10 11 1.0 0.5 – – – – – – – – – – 0.5 1.0 0.5 – – – – – – – – – – 0.5 1.0 0.5 – – – – – – – – – – 0.5 1.0 0.5 – – – – – – – – – – 0.5 1.0 0.5 – – – – – – – – – – 0.5 1.0 – – – – – – – – – – –

12 – – – – – 0.5 0.5

13 – – – – – – 1.0

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The data of this table is sequentially stored in VD100 to VD460 in rows, and the storage of this table can be directly realized by the data block in the Siemens S7200PLC. The membership degree and linguistic value of the element E or EC in the fuzzy domain of the input quantities e and ec are determined, and the base address plus the offset address is used for query, and the membership degree and the linguistic value are stored by the pointer instruction and the loop program. Part of the implementation process is as follows:

If the membership functions of E and EC are different, simply store them separately in the data block. The query procedure is similar and will not be described here. 3.3.2 Programming of Fuzzy Reasoning Because the two-dimensional fuzzy controller is used, the input is the fuzzy value of the deviation and deviation variation, which can be calculated by the following formula: eðtÞ ¼ YðktÞ  T

ð1Þ

ecðtÞ ¼ YðktÞ  Yðkt  tÞ

ð2Þ

Which T——desired temperature value; YðktÞ——Current sampling temperature value; Yðkt  tÞ——Last sampled temperature value.

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When determining the fuzzy control rule table, using the test data analysis and the trend of deviation and deviation to summarize the method, that when the deviation is large, the control quantity should be selected according to the principle of eliminating the deviation as soon as possible; when the deviation is small, the control quantity should be selected according to the principle of ensuring the stability of the system to prevent the system from overshooting. Summarize all fuzzy control rules as shown in Table 3, where the linguistic variables are represented by numerical values. The linguistic value represented by the number is also stored in the continuous V area by the data block. The number representing the linguistic value obtained by the quantization process is used as the number of rows and columns of the fuzzy inference. And the continuous V region is queried, and the rule conclusion is inferred. And store it. Query such consecutive V regions, infer the rule conclusions and store them.

Table 3. Fuzzy control rules table for two inputs and one output expressed by fuzzy numbers. Control amount u

Input variable deviation e 1 2 3 4 5 6 7

Input variable deviation rate ec 1 2 3 4 5 6 1 1 2 2 2 3 1 1 2 2 3 4 1 2 2 3 4 5 1 2 3 4 5 6 2 3 4 5 6 6 3 4 5 6 6 7 4 5 6 6 6 7

7 4 5 6 7 7 7 7

3.3.3 Defuzzification Programming Since the membership functions of e and ec are selected to ensure that each value belongs to at most two fuzzy subsets, up to four rules are activated in fuzzy inference, and the inferred results belong to up to four output fuzzy subsets, plus corresponding memberships, 8 addresses are required for storage at all. The output membership function (triangle function) takes the “take small” operation and uses high h (subordinate degree) to cut the top, so that the area “S” under the membership function of the implication fuzzy set can be easily calculated. Let “S1” be the result of the area under the rule implication fuzzy set membership function multiplied by the center value of the corresponding triangle in the output membership function, thenPuse COG’s P antifuzzification method. It could conclude that u0 ¼ n=d, which n ¼ s1 , d ¼ s.

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4 Fuzzy Control System Simulation Simulation is carried out by Simulink module in MATLAB, and the response curve of fuzzy control is compared with traditional PID control under the action of unit step signal. The result is shown in Fig. 4:

Fig. 4. Simulation of unit step input simulation.

The robustness of the PID control and fuzzy control are analyzed by changing the parameters of the transfer function. The response curve when the parameter changes by 20% is shown in Fig. 5.

Fig. 5. Simulation comparison of 20% parameter changes.

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It can be seen from Figs. 4 and 5 that the fuzzy control has achieved good results, with a small overshoot and a short adjustment time. Even if the parameters change greatly, the fuzzy control effect is better than the traditional PID control.

5 Conclusion In this paper, the online reasoning of fuzzy control using PLC is completed, and it is verified by simulation. It could ensure the constant temperature of the cutting zone, and has good robustness and good control effect. The controller fully embodies the characteristics of flexible, reliable and anti-interference of the PLC control system, and also improves the intelligence degree of the system. At the same time, the realization of online reasoning makes the control system have certain versatility.

References 1. Peng Y, Hu J (2006) Application of spray-cooling in cutting. New Technol New Process 06:21–22 2. Wang L, Ye J, Wang Z, Li M (2017) The design and simulation of fuzzy temperature control system for technical reform in the nitriding electric-furnace. Fuzzy Syst Math 2:138–145 3. Liu W, He L, Tang J, Liu P, Wang X, Jiang Z (2014) Research on cutting temperature of TC4 titanium alloy based on composite spray cooling. Tool Eng 4:25–27 4. Wang J, Gong M, Li Y, Wang J (2015) Simulation analysis of thermal control system using capillary separate spray cooling loop based on mechanical pump. Spacecraft Environ Eng 06:599–606

Tracking Control of Multi-motor Servo System with Input Saturation Shuangyi Hu, Xuemei Ren(&), and Yongfeng Lv School of Automation, Beijing Institute of Technology, Beijing, China [email protected]

Abstract. A dynamic surface tracking control strategy is proposed for multimotor servo systems with input saturation. By using hyperbolic tangent function and the auxiliary control signal, the solution of the problem is provided, which is caused by the non-smoothness of saturation function. Based on the introduced nonlinear auxiliary equation, a dynamic surface control method is proposed to overcome the input constraints. Dynamic surface technology is used to solve the problem of “differential explosion” in the design of backstepping control. By using the Lyapunov stability theory, it is proved that all signals of the closedloop system are semi-globally uniformly ultimately bounded. The simulation results demonstrate the validity of the algorithm. Keywords: Multi-motor servo systems Input saturation
Auxiliary equation


Dynamic

surface tracking control




1 Introduction With the wide application of many large inertia and high power systems in industry, multi-motor drive servo system has become one of the research and development directions in the field of servo control system, and has been applied in the fields of industry and military affairs [1–3]. In addition, there is input saturation in multi-motor servo system, which may lead to system performance degradation or instability [4]. At present, there are few papers on multi-motor servo systems with input saturation, but there have been many research results on saturation control methods for non-linear systems [5–7]. Hyun et al. [8] applied anti-windup technology to deal with the saturation problem of single-input adaptive control system with strict feedback form, and proposed a control algorithm of modified adaptive law. Gao et al. [9] proposed a saturation compensation strategy based on neural network. The neural network was used to compensate the limited part beyond saturation, but the limited part contained the control signal to be designed. For a class of uncertain non-linear systems with input saturation and external disturbance, the saturation characteristic was compensated by backstepping method in the process of controller design. However, the method required repeated differential of virtual control variables in the design of controller, especially for high-order systems, which increased the complexity of the algorithm [10]. In this paper, an approach of adaptive dynamic surface control for multi-motor servo system with non-linear and saturation characteristics is proposed. This method takes full account of the saturation structure characteristics, without any constraints, © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 461–469, 2020. https://doi.org/10.1007/978-981-32-9698-5_52

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and broadens the application scope of the system design. The stability analysis illustrates that the designed controller can ensure that all signals of the servo system are semi-globally uniformly and eventually bounded. The rest paper is organized as follows. Section 2 describes a n-motor servo system with input saturation. A dynamic surface tracking controller is provided in Sect. 3. Section 4 proves the stability and some simulation results are presented in Sect. 5. Finally, Sect. 6 summarizes several conclusions.

2 System Description Consider the following multi-motor servo system with input saturation 8
 P n > < Jl €hl ðtÞ þ bl h_ l ðtÞ ¼ Ti ðtÞ
1 > : Jm €hmi ðtÞ þ bmi h_ mi ðtÞ ¼ ui ðtÞ  Ti ðtÞ; i ¼ 1; 2; . . .; n

ð1Þ

where hl and h_ l are the position and velocity of load, hmi and h_ mi denote the position and velocity of motor i, bl and bmi are friction torque, ui is the control signal, Jl and Jmi represent the moments of inertia and Ti is the transmission torque, which is defined as  Ti ¼ cðhmi  hl Þ  ca

2

1 þ ebðhmi

 1 h Þ l

ð2Þ

where c and a denote the torsional coefficient and backlash width, b is a positive constant. Considering the input saturation problem in the actual system, yields  ui ¼ satðvi Þ ¼

vi ; jvi j\uMi uMi ; jvi j  uMi

ð3Þ

where uMi is the saturation level of ui . From (3), we know that the saturated input function is not differentiable at jvi j ¼ uMi . To solve the problem, design the following hyperbolic tangent function to approximate the saturated input function (3) 

vi f ðvi Þ ¼ uMi tanh uMi

 ¼ uMi

evi =uMi  evi =uMi evi =uMi þ evi =uMi

ð4Þ

Then the function (3) can be rewritten as ui ¼ f ðvi Þ þ di where di is the approximation error, which satisfies

ð5Þ

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jdi j ¼ jsatðvi Þ  f ðvi Þj  juMi  uMi tanhð1Þj ¼ dMi ð6Þ h i Define state variables ½x1 ; x2 ; x3i ; x4i  ¼ hl ; h_ l ; hmi ; h_ mi . Then the system (1) can be rewritten as 8 x_ 1 ¼ x2 >
> n > P > < x_ 2 ¼ 1 cx3  cnx1  ca Jl i¼1

2 1 þ ebðhmi hl Þ

> x_ 3i ¼ x4ih >
> > : x_ ¼ 1 u  cx þ cx þ ca 4i i 3i 1 Jm

1

2 1 þ ebðhmi hl Þ

 

 J1l bl ðx2 Þ

 1  bmi ðx4i Þ

i

ð7Þ

Considering the unknown nonlinearity in the system (7), a radial basis functions neural network is proposed as follows 

g1 ¼ W1T U1 þ r1 g2i ¼ W2T U2i þ r2i

ð8Þ


 n P 2 where g1 ¼ J1l bl  cnx1  ca  1 , 1 þ ebðhmi hl Þ i¼1
 h i 2 g2i ¼ J1m cx1 þ ca  1  cx3i  bmi , W1 ; W2 and r1 ; r2i are the ideal bðhmi hl Þ 1þe

weights of the neural network and approximation errors, which are all bounded. U1 and U2i represent the base vectors. According to the equality (5) and the neural network (8), the system (7) can be rewritten as 8 x_ 1 ¼ x2 > > < x_ ¼ c x þ W T U þ r 2 1 1 1 Jl 3 _ ¼ x x > 3i 4i > : x_ ¼ f ðvi Þ þ di þ W T U þ r 4i 2i 2 2i Jm

ð9Þ

3 Dynamic Surface Controller Design In the previous section, the saturated input is approximated by the smooth function (4). It is not difficult to see that f ðvi Þ can be regarded as the actual input and di can be regarded as the disturbance after the multi-motor system is constrained. For multimotor servo system (9), a dynamic surface method is proposed to design the tracking controller in this section. Firstly, define tracking errors as (

e1 ¼ x1  yd ei ¼ xi  gid ; i ¼ 2; 3; 4; 5

ð10Þ

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where yd is the reference signal, x3 ¼

n P

x3i ; x4 ¼

i¼1

n P

x4i , gid is the signal filtered by the

i¼1

virtual control variable gi which will be presented later. Taking the derivative of e1 , yields e_ 1 ¼ x_ 1  y_ d ¼ x2  y_ d

ð11Þ

Select Lyapunov function candidate 1 V1 ¼ e21 2

ð12Þ

V_ 1 ¼ e_ 1 e1 ¼ ðx2  y_ d Þe1

ð13Þ

Its time derivative is

Then the virtual control law g2 is chosen as g2 ¼ k1 e1 þ y_ d

ð14Þ

where k1 is a positive constant. Let g2 pass through a first-order filter given by s2 g_ 2d þ g2d ¼ g2 ; g2d ð0Þ ¼ g2 ð0Þ

ð15Þ

where s2 is a positive constant. Next the derivative of e2 is proposed as follows e_ 2 ¼ W1T U1 þ

c x3  g_ 2d þ r1 Jl

ð16Þ

Choose Lyapunov function candidate V2 ¼ V1 þ

1 2 1 2 ~T ~ e þ z þ W1 C1 W1 2 2 2 2

ð17Þ

~ 1 ¼ W1  W ^ 1, W ^ 1 is the estimate of W1 , C1 is a positive where z2 ¼ g2d  g2 and W matrix. Take the derivative of V2 ~_ 1 ~ 1T C1 W V_ 2 ¼V_ 1 þ e_ 2 e2 þ z_ 2 z2 þ W     c g  g2d ^_ 1 ~ 1T C1 W ¼V_ 1 þ W1T U1 þ x3  g_ 2d þ r1 e2 þ 2  g_ 2 z2  W Jl s2  
 2 ^_ 1 ^ 1T U1 þ c x3  g_ 2d e2 þ r1 e2  z2  g_ 2 z2 þ W ~ 1T U1 e2  C1 W ¼  k1 e21 þ W Jl s2

ð18Þ

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^ 1 are obtained by From (18), the virtual control law g3 and the update law for W  Jl  ^ 1T U1 þ g_ 2d k2 e2  W c   ^ ^_ 1 ¼ C1 W 1 U1 e2  a1 W1

g3 ¼

ð19Þ ð20Þ

where k2 and a1 are positive constants. Let g3 pass through the following first-order filter s3 g_ 3d þ g3d ¼ g3 ; g3d ð0Þ ¼ g3 ð0Þ

ð21Þ

where s3 is a positive constant. Take the derivative of e3 e_ 3 ¼ x_ 3  g_ 3d ¼ x4  g_ 3d

ð22Þ

Choose Lyapunov function candidate V3 ¼ V2 þ

1 2 1 2 e þ z 2 3 2 3

ð23Þ

where z3 ¼ g3d  g3 . Its time derivative is presented as V_ 3 ¼V_ 2 þ e_ 3 e3 þ z_ 3 z3 ¼  k1 e21  k2 e22 

z22 z2 þ r1 e2  g_ 2 z2 þ ðx4  g_ 3d Þe3  3  g_ 3 z3 s2 s3

ð24Þ

Then the virtual control law g4 is chosen as g4 ¼ k3 e3 þ g_ 3d

ð25Þ

where k3 is a positive constant. Let g4 pass through the following first-order filter s4 g_ 4d þ g4d ¼ g4 ; g4d ð0Þ ¼ g4 ð0Þ

ð26Þ

where s4 is a positive constant. The derivative of e4 is given as e_ 4 ¼

n X f ð v i Þ þ di i¼1

where U2 ¼

n P i¼1

U2i ; r2 ¼

n P

Jm

r2i .

i¼1

Select Lyapunov function candidate

þ W2T U2 þ r2  g_ 4d

ð27Þ

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V4 ¼ V3 þ

1 2 1 2 ~T ~ e þ z þ W2 C2 W2 2 4 2 4

ð28Þ

~ 2 ¼ W2  W ^ 2, W ^ 2 is the estimate of W2 , C2 is a positive where z4 ¼ g4d  g4 and W matrix. Take the derivative of V4 ~_ 2 ~ 2T C2 W V_ 4 ¼V_ 3 þ e_ 4 e4 þ z_ 4 z4 þ W z22 z23   g_ 2 z2  g_ 3 z3 þ r1 e2 s2 s3 ! n
 X f ðvi Þ þ di ^ T z2 ^_ 2 ~ 2T U2 e4  C2 W þ W2 U2 þ r2  g_ 4d e4  4  g_ 4 z4 þ W Jm s4 i¼1

¼  k1 e21  k2 e22  k3 e23  þ

ð29Þ

^ 2 as Based on (29), design the virtual control law g5i and the update law for W   ^ 2T U2i þ g_ 4d =n  dMi signðe4 Þ g5i ¼ Jm k4 e4 =n  W

ð30Þ

  ^_ 2 ¼ C1 ^ W 2 U2 e4  a2 W2

ð31Þ

where k4 and a2 are positive constants. Let g5i pass through the following first-order filter s5 g_ 5id þ g5id ¼ g5i ; g5id ð0Þ ¼ g5i ð0Þ

ð32Þ

where s5 is a positive constant. Define x5i ¼ f ðvi Þ; e5i ¼ x5i  g5id ; z5i ¼ g5id  g5i , and the auxiliary control signal qi and the following auxiliary equations are introduced v_ i ¼ ci ðf ðvi Þ  g5id Þ þ qi

ð33Þ

where qi [ 0. Select Lyapunov function candidate V5 ¼

n n 1X 1X e25i þ z2 2 i¼1 2 i¼1 5i

ð34Þ

It is obvious that V_ 5 ¼

n X i¼1

ðe_ 5i e5i þ z_ 5i z5i Þ ¼

n  X @f ðvi Þ i¼1

vi

 ðci e5i þ qi Þ  g_ 5id

  z5i þ g_ 5i z5i e5i þ s5 ð35Þ

Then the auxiliary control signal qi is designed as

Tracking Control of Multi-motor Servo System with Input Saturation

qi ¼ ðk5i e5i þ g_ 5id Þ=hi
 where hi ¼ @f vðivi Þ ¼ 1  tanh2 uvMii [ 0, k5i is a positive constant.

467

ð36Þ

4 Stability Analysis Theorem 1: Consider the multi-motor servo system (9). If design tracking controllers as (14), (19), (25), (30) and (36) and choose the update laws of NN weights (20) and (31), then, all signals of the system is semi-globally ultimately uniformly bounded. Proof: Consider the Lyapunov function candidate V ¼ V4 þ V5

ð37Þ

From (29) and (35), one has V_ ¼V_ 4 þ V_ 5 ¼ 

4 X

4 X z2

4 X

2 X

~ iT W ^i ai W s i i¼1 i¼2 i¼2 i¼1  n n n  X X X z5i ðdi e4  dMi je4 jÞ  þ ðhi ci þ k5i Þe25i þ þ g_ 5i z5i s5 i¼1 i¼1 i¼1 ki e2i 

i



g_ i zi þ r1 e2 þ r2 e4 þ

ð38Þ

According to (14), g_ 2 ¼ k1 e_ 1 þ €yd ¼ k1 ðx2  y_ d Þ þ €yd ¼ S2 ðx2 ; y_ d ; €yd Þ

ð39Þ

where S2 ðx2 ; y_ d ; €yd Þ is a continuous bounded function. Similarly,   ^ 1 ; g_ 4 ¼ S4 ðx4 ; y_ d ; y_ d ; €yd Þ g_ 3 ¼ S3 x3 ; y_ d ; y_ d ; €yd ; W   ^1 g_ 5i ¼ S5i x5i ; y_ d ; y_ d ; €yd ; W

ð40Þ

where S3 ; S4 ; S5i are all continuous bounded functions. Using Young’s inequality, yields 1 2 1 2 1 2 1 2 r þ r þ e þ e 2 1 2 2 2 2 2 4 2 1 1 ~ iT W ~ i ^ i  1 kWi k2  1 W g_ i zi  z2i þ S2i ; W 2 2 2 2 r 1 e 2 þ r2 e 4 

Then the equality (38) can be rewritten as

ð41Þ

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    n X _V   k1 e21  k2  1 e22  k3 e23  k4  1 e24  ðhi ci þ k5i Þe25i 2 2 i¼1   4  n  2 X X X 2 1 1 2 1 1 2 1 ~ i þ K   zi   z5i  ai W s5 2 s5 2 2 i¼1 i¼2 i¼1 where K ¼ 12 r21 þ 12 r22 þ

1 2

4 P i¼2

S2i þ

1 2

n P i¼1

ð42Þ

S25i þ 12 kW1 k2 þ 12 kW2 k2 .

Let k2 

1 1 1 1 [ 0; k4  [ 0;  [ 0; i ¼ 2; 3; 4; 5 2 2 si 2

ð43Þ

n o Define l ¼ min k2  12 ; k4  12 ; s1i  12 ; hj cj þ k5j ; am Cm , one has m¼1;2 i¼2;3;4;5 j¼1;2;...;n

V_   lV þ K

ð44Þ

From (43), yields V ðt Þ 

K þ V ð0Þelt l

ð45Þ

Based on (45), it follows that all signals of the system is semi-globally ultimately uniformly bounded.

5 Simulation Results To validate the proposed method, simulations on four-motor drive servo system are provided. The parameters are chosen as Jl ¼ 0:028 kg
m2 , Jm ¼ 0:185 kg
m2 , k1 ¼ 35; k2 ¼ 80; k3 ¼ 12; k4 ¼ 9; k5i ¼ 1, s2 ¼ s3 ¼ s4 ¼ s5 ¼ 0:002, ci ¼ 1, uMi ¼ 3, C1 ¼ C2 ¼ 0:05, a1 ¼ a2 ¼ 0:1. The system initial values are given as hm1 ¼ hm2 ¼ hm3 ¼ hm4 ¼ 0:1; h_ m1 ¼ h_ m2 ¼ h_ m3 ¼ h_ m4 ¼ 0:2.

Fig. 1. Position synchronization

Fig. 2. Position synchronization error

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As shown in Figs. 1 and 2, in the case of saturation of control variables, the proposed control method can effectively overcome the influence of saturation nonlinearity and greatly improve the system performance.

6 Conclusion Considering the non-linearity and input saturation of the multi-motor servo system, an adaptive dynamic surface control method is proposed in this paper. This approach fully considers the structural characteristics of saturation and does not need constraints. It can effectively weaken the adverse effect of input saturation on system performance. Combining with the dynamic surface method, the design of controller is simplified, which has better practicability. Finally, by imitating. Finally, simulation results have shown that the provided control method achieves position tracking accurately. Acknowledgments. This work was supported by National Natural Science Foundation of China (Nos.61433003, 61973036).

References 1. Su Y, Gang X (2010) Research of multi-motor synchronous driving system based on fuzzy smith control. In: International conference on electrical and control engineering, pp 5466– 5469 2. Chen W, Wu Y, Du R, et al (2012) A fault-tolerant control method for the servo systems driven by multimotor. In: international conference on mechatronics and automation, pp 391– 396 3. Sun G, Ren X, Li D (2015) Neural active disturbance rejection output control of multimotor servomechanism. IEEE Trans Control Syst Technol 23(2):746–753 4. Su H, Chen MZQ, Chen G (2015) Robust semi-global coordinated tracking of linear multiagent systems with input saturation. Int J Robust Nonlinear Control 25(14):2375–2390 5. He W, Dong Y, Sun C (2015) Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Trans Syst Man Cybern: Syst 46(3):334–344 6. Zhou Q, Li H, Wu C et al (2016) Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach. IEEE Trans Syst Man Cybern: Syst 47(8):1979–1989 7. Chen M, Tao G, Jiang B (2015) Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation. IEEE Trans Neural Netw Learn Syst 26 (9):2086–2097 8. Do HM, Basar T, et al (2004) An anti-windup design for single input adaptive control systems in strict feedback form. In: American control conference 9. Gao W, Selmic RR (2006) Neural network control of a class of nonlinear systems with actuator saturation. IEEE Trans Neural Netw 17(1):147–156 10. Wen C, Jing Z, Liu Z et al (2011) Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Trans Autom Control 56 (7):1672–1678

Adaptive Parameter Estimation for Hammerstein Systems with Asymmetric Dead-Zone Dynamics Haoran He1, Jing Na1(&), Guanbin Gao1, Shubo Wang2, and Qiang Chen3 1 Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China [email protected] 2 School of Automation, Qingdao University, Qingdao 266071, China 3 College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China

Abstract. In this paper, an integrated adaptive parameter estimation scheme is proposed for Hammerstein system with asymmetric dead-zone dynamics. For this purpose, a canonical representation for piecewise linear functions is applied to approximate the dead-zone module characteristics. According to the derived integrated identification mode, the dead-zone parameters and the coefficients of the linear system can be estimated simultaneously without calculating the intermediate variables and using the two-step identification. Then a recently proposed adaptive law is used to achieve online parameter estimation. A numerical simulation is given to testify the validation of the proposed method. Keywords: Adaptive parameter estimation
Hammerstein system Asymmetric dead-zone nonlinearities
System identification




1 Introduction The Hammerstein system is a kind of cascade systems containing a static nonlinear element and a dynamic linear element [1]. In mechanical and electrical engineering applications, the Hammerstein model with asymmetric dead-zone dynamics has been widely used to describe the behavior of actuator and driving element e.g., electrohydraulic valve, servo electromotor and transistor. It is well known that the asymmetric dead-zone is a non-differentiable function which is not sensitive to small input, and such nonlinearities deteriorate the control system performance. As shown in Fig. 1, an asymmetric dead-zone can be described by using six parameters ðK1 ; K2 ; D1 ; D2 ; umax ; umin Þ, where K1 ; K2 are the segment slopes, D1 ; D2 denote the thresholds and umax ; umin are the maximum and minimum of output. It should be noted that, for mechanical or electronic actuator, the value of umax ; umin can be easily obtained as they are the physical characteristics of the actuator. However, the other parameters are generally difficult to measure, and thus we will focus on the online

© Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 470–479, 2020. https://doi.org/10.1007/978-981-32-9698-5_53

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estimation of these unknown parameters in the dead-zone model. This leads to the identification of Hammerstein systems, which include a dead-zone and a linear plant. u (t ) umax

K2

D1 D2

K1

v(t )

umin

Fig. 1. Asymmetric dead-zone dynamics

In this topic, a method for estimating the unknown parameters and some auxiliary variables [2] was proposed in [3], in which the nonlinear model was only defined for the system with large input. However, this parameter estimation process has to be performed by using two pseudorandom binary signals with different amplitudes [4]. In [5], the author proposed a separable nonlinear least square method to estimate the symmetrical dead-zone function, while it may be difficult to apply for asymmetric dead-zone. To obtain a linear regression model, a recursive recognition algorithm was proposed in [6], while the values of the thresholds and slopes can not be obtained. Specifically, a difficulty for the identification of such systems is the use of the intermediate variable between the two subsystems, which cannot be measured directly. In order to overcome these limitations, an adaptive parameter estimation method is proposed in this paper for integrated identification of Hammerstein systems with asymmetric dead-zone dynamics. We first tailor a piecewise linear function to describe the dead-zone dynamics to derive an integrated model. Then by applying the adaptive parameter estimation algorithm mentioned in [7–9], the dead-zone nonlinear parameters and the unknown parameters of the linear subsystem can be identified simultaneously. The paper is organized as follows: the problem reformulation is given in Sect. 2. The estimation of the dead-zone parameters and the unknown plant parameters are addressed in Sect. 3. Section 4 presents a numerical simulation to show the efficiency of proposed method. Finally conclusions are outlined in Sect. 5.

2 Problem Description As shown in Fig. 2, the Hammerstein system consists of a nonlinear dead-zone element and a linear subsystem. vðtÞ and yðtÞ represent the measurable input and output of the Hammerstein system, while uðtÞ is the internal system signal which cannot be obtained directly.

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v(t )

u (t )

Linear subsystem

y(t )

Fig. 2. Hammerstein model with dead-zone nonlinear dynamics

The nonlinear dead-zone dynamics can be represent by 8 < K1 ðvðtÞ  D1 Þ; uðtÞ ¼ GðvðtÞÞ ¼ 0; : K1 ðvðtÞ  D1 Þ;

v  vðtÞ\D1 D1  vðtÞ  D2 D2 \vðtÞ  v

ð1Þ

where V ¼ ½v; v define the lower and upper boundary of the input signal, K1 ; K2 are the slopes and D1 ; D2 are the inflection points. Then we consider the following linear subsystem. x_ ¼ Ax þ Bu

ð2Þ

where A 2 Rnn is the system matrix, B 2 Rn is the input matrix, x 2 Rn is the system state, and u 2 R is the input. Substituting (1) into (2), we have x_ ¼ Ax þ BGðvÞ

ð3Þ

In this case, it should be noted that all parameters in the system matrix A, input matrix B and dead-zone function are all unknown. Hence, the purpose of this paper is to design a parameter estimation method to estimate all unknown parameters without using the intermediate variable u.

3 Parameter Estimation 3.1

Canonical Piecewise-Linear Representation for Asymmetric DeadZone

The authors of [10] proposed a method to approximate any continuous piecewise-linear function, in which there is no requirement on the system function and the approximation accuracy can be minimized by tuning model parameters. Hence, for any given ndimensional piecewise function hðzÞ; z 2 Ri with domain D  Ri , we can employ the method proposed in [10] to describe it. First of all, the domain D can be S divided into N non-overlapping subdomains Dj ðj ¼ 1;


; NÞ, under the condition of 1  j  N Dj ¼ D. Then, the function hðzÞ can be approximated by

Adaptive Parameter Estimation for Hammerstein Systems

hðzÞ ¼ p0 þ

N1 X

473

p1j xð0; z1  a1j ; b1j  a1j Þ

j¼1

þ

N2 X

p2j xð0; z2  a2j ðz1 Þ; b2j ðz1 Þ  a2j ðz1 ÞÞ þ




ð4Þ

j¼1

þ

Ni X j¼1

*

*

*

*

pij xð0; zi  aij ðz i1 Þ; bij ðz i1 Þ  aij ðz i1 ÞÞ *

where each pair of aðz i1 Þ; bðz i1 Þ defines the lower and upper boundaries of the * subdomain of z i1 ; Nj ðj ¼ 1;


; iÞ denote the number of subdomains, and x is a basis function. Consider the one-dimensional form of the piecewise linear function hðzÞ with the definition domain Z ¼ ½z; z. The domain Z is divided into N non-overlapping subdomains Zi ; ði ¼ 1;


; NÞ. Therefore, the function hðzÞ can be described as hðzÞ ¼ p0 þ

N X j¼1

pj xj ð0; z  aj ; bj  aj Þ

ð5Þ

where aj ; bj denote the lower and upper boundaries of the jth subinterval Zj , respectively, and pj ðj ¼ 1;


; NÞ represent N unknown parameters to be estimated. xj ð0; z  aj ; bj  aj Þ is the basis function given as follow. xða; b; cÞ ¼ maxða; minðb; cÞÞ

ð6Þ

Remark 1: In fact, the above basis function is a special piecewise linear function, and the unknown parameter pi is the unknown slope of the local linear function xj ¼ z  aj when aj  z  bj . Considering the dead-zone function (1), the domain of definition V ¼ ½v; v can be divided into kð  2Þ segment. v ¼ m1 \m2 \


\mj \


\mk \mk þ 1 ¼ v

ð7Þ

in which k is a designed parameter. Note that the higher approximation accuracy can be achieved by using a larger k, while a larger k may also increase the computational burden. Thus, we should make a trade-off between the approximation accuracy and computational cost when we select the value of k. Then, the dead-zone can be parameterized as a piecewise function ^ ^uðtÞ ¼ GðvðtÞÞ ¼ p0 þ

k X j¼1

pj xj ð0; vðtÞ  mj ; mj þ 1  mj Þ

ð8Þ

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The four estimated parameters of dead-zone dynamics are presented as follows. Assuming the first term with a zero coefficient is aj1 , we define pj ¼ 0 and j1 ¼ minpj ¼0 j, such that the estimated value of D1 can be given as ^ 1 ¼ aj1 D

ð9Þ

Similarly, the last term with a zero coefficient bj2 , then we have ^ 2 ¼ bj D 2

ð10Þ

Since pi defines the slope of local linear function xj ¼ z  aj , the parameters K1 ; K2 can be calculated as P ^1 ¼ K

j\j1

P

pj

j1  1

^2 ¼ ;K

j [ j2

pj ð11Þ

k  j2

Remark 2: It is noted that p0 is the minimum value of input, and it is usually known for actuators used in the mechanical and electronic field, such as the terminal speed of motor and limit position of hydraulic valve. 3.2

System Reformulation and Adaptive Parameter Estimation

In order to facilitate the subsequent expression, we reformulate Eq. (8) as ^uðtÞ ¼ p0 x0 þ

k X

pj xj ð0; vðtÞ  mj ; mj þ 1  mj Þ ¼

j¼0

k X

pj xj ¼ P
X

ð12Þ

j¼0

where x0 ¼1 and P ¼ ½p0 ;


pk ; X ¼ ½x0 ;


; xk T . Then the Hammerstein system (3) can be rewrite as x_ ¼ Ax þ BPX

ð13Þ

According to the adaptive parameter estimation algorithm proposed in [7], the system (13) can be described as " x_ ¼ ½ A

BP 

x X

# ¼ h
Uðx; XÞ

ð14Þ

where h 2 Rnðn þ k þ 1Þ is the unknown parameter matrix to be estimated, and Uðx; XÞ 2 Rn þ k þ 1 is the known regressor vector. It is clear that Uðx; XÞ is bounded for bounded x; X. To facilitate the parameter estimation, the following assumption is provided.

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Assumption 1: The system states x and the input X are all accessible for measurement and bounded. To estimate the unknown parameters, we define the filtered variables xf ; Uf of x; U as (

k x_ f þ xf ¼ x; xf ð0Þ ¼ 0 k U_ f þ Uf ¼ U; Uð0Þ ¼ 0

ð15Þ

where k [ 0 is a filter parameter. According to (14) and (15), we have x_ f ¼

x  xf ¼ h
Uf k

ð16Þ

Construct an auxiliary matrices M and N as 8 _ ¼  kM þ Uf UTf ; Mð0Þ ¼ 0

> ekðtrÞ Uf ðrÞUTf ðrÞdr MðtÞ ¼ > < 0

> > > : NðtÞ ¼

Z

0

t

ekðtrÞ Uf ðrÞ

  xðrÞ  xf ðrÞ T dr k

ð18Þ

Another auxiliary matrix H can be defined as HðtÞ ¼ MðtÞ^hT  NðtÞ

ð19Þ

where ^h is the estimation of the unknown parameter h. To guarantee the parameter estimation convergence, we need to analyze the positive definiteness property of MðtÞ. Define dmax ð
Þ; dmin ð
Þ as the maximum and minimum eigenvalues of the corresponding matrices, then we have: Lemma 1: The matrix MðtÞ in (19) is positive definite (e.g.,dmin ðMðtÞÞ [ g [ 0) provided that the regressor matrix UðtÞ in (14) is persistent excitation (PE). Proof: Please refer to [7] for the detailed proof. A simple parameter estimation approach is given as: Lemma 2: Assuming U is PE for system (14) with MðtÞ; NðtÞ defined in (17), then h ¼ N T ðtÞðM 1 ðtÞÞT . Proof: It follows from (16)–(18) that NðtÞ ¼ MðtÞhT is true, which implies that h ¼ N T ðtÞðM 1 ðtÞÞT as long as U is PE and thus M 1 ðtÞ exists based on Lemma 1.

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Lemma 2 provides a possible method to estimate unknown parameters as used in [11, 12]. However, in order to avoid calculating the inverse matrix M 1 ðtÞ online, we use the adaptive estimation scheme as shown in [7] as ^h_ ¼ CH T

ð20Þ

with C [ 0 being a constant diagonal gain matrix. Theorem 1: Consider system (14) with the adaptive law (20), if the regressor matrix U is PE, then the parameter error ~h ¼ h  ^h exponentially converges to zero with the rate  l¼2g dmax ðC1 Þ. hT Þ 。the derivative V_ Proof: Choose the Lyapunov function as V ¼ trð1=2~ h C1 ~ along (20) is obtained as _T V_ ¼ trð~h C1 ~h Þ ¼ trð~hM ~hT Þ   lV

ð21Þ

 in which l ¼ 2g dmax ðC1 Þ is a positive constant for all t [ 0. Equation (21) implies the exponential convergence of the error ~h to zero with the rate l. ^ P ^ are lumped together when we Remark 3: Although the estimated parameters B; ^ is implement the parameter estimation algorithm, the parameter p0 (the first value of P) ^ ^ ^ known. Therefore, the parameters B; P can be derived from h separately.

4 Simulation To illustrate the effectiveness of the proposed integrated parameter estimation method, a simulation example is provided. A second order linear system with an asymmetric dead-zone input is used, which is described as  x_ ¼

0

1





0



xþ GðvÞ 1:5 0:8 1:2 8 > < 1:4286  ðv  ð0:3ÞÞ; 1  v\  0:3 GðvÞ ¼ 0; 0:3  v  0:2 > : 1:25  ð0:2  vÞ; 0:2\v  1

ð22Þ

The asymmetric dead-zone characteristic parameters are k1 ¼ 1:4286; k2 ¼ 1:25; D1 ¼ 0:3; D2 ¼ 0:2 and the nominal value of the estimated parameter for this linear system are A11 ¼ 0; A12 ¼ 1; A21 ¼ 1:5; A22 ¼ 0:8; B11 ¼ 0; B12 ¼ 1:2. In the simulations, we set the input signal u ¼ sinð2tÞ to retain the boundedness of the input and output. The domain of the asymmetric dead-zone is ½1; 1, and is evenly divided into 20 segments. The results of the proposed algorithm are shown in Figs. 3, 4 and 5, respectively. Figure 3 shows the result of approximation for nonlinear dead-zone

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dynamics using the proposed method. The results of four estimated parameters for dead-zone dynamics are K1 ¼ 1:4281; K2 ¼ 1:2497; D1 ¼ 0:3; D2 ¼ 0:2. The profiles of parameter estimation for the dead-zone dynamics and the linear system is given in Figs. 4 and 5. It is found that the proposed parameter estimation scheme can ensure that the estimated parameters converge to the nominal values in 5 s. From these results, we can conclude that the proposed method can be used to estimate all parameters involved in the system with dead-zone nonlinearity.

Fig. 3. Approximation of the dead-zone

Fig. 4. Parameters estimation for dead-zone dynamics.

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Fig. 5. Parameters estimation for linear system.

5 Conclusion This paper developed an adaptive parameter identification algorithm for Hammerstein systems with asymmetric dead-zone dynamics. The dead-zone characteristics is first approximated by a canonical piecewise parameterized model. Then an integrated identification model including the dead-zone and a linear plant is constructed. With the help of the proposed identification method, the characteristic parameter of both the nonlinear and linear subsystems can be estimated simultaneously by means of a recently proposed algorithm. The effectiveness of the identification algorithm can be confirmed by the given simulation results. Future work will be carried out to address Hammerstein systems with other non-smooth dynamics such as saturation, and friction. Acknowledgments. This work was supported by the National Natural Science Foundation of China (number 61873115) and Yunnan Provincial Education Department (number 2018Y020).

References 1. Billings SA, Fakhouri S (1982) Identification of systems containing linear dynamic and static nonlinear elements. Automatica 18(1):15–26 2. Giri F, Rochdi Y, Chaoui F-Z (2009) Hammerstein systems identification in presence of hard nonlinearities of preload and dead-zone type. IEEE Trans Autom Control 54(9):2174–2178 3. Gu X, Bao Y, Lang ZA (1988) Parameter identification method for a class of discrete time nonlinear systems. In: Proceedings of 12th IMACS world congress, Paris, pp 627–629 4. Vörös J (1997) Parameter identification of discontinuous Hammerstein systems. Automatica 33(6):1141–1146 5. Bai E-W (2002) Identification of linear systems with hard input nonlinearities of known structure. Automatica 38(5):853–860

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6. Voros J (2003) Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones. IEEE Trans Autom Control 48(12):2203–2206 7. Na J, Mahyuddin MN, Herrmann G, et al (2013) Robust adaptive finite-time parameter estimation for linearly parameterized nonlinear systems. In: Proceedings of the 32nd Chinese control conference, Xi’an, pp 1735–1741 8. Na J, Mahyuddin MN, Herrmann G et al (2015) Robust adaptive finite-time parameter estimation and control for robotic systems. Int J Robust Nonlinear Control 25(16):3045– 3071 9. Yang J, Na J, Gao G (2018, 2019, to be published) Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence. Int J Adapt Control Signal Process. https://doi.org/10.1002/acs.2982 10. Wang S, Huang X, Junaid KM (2008) Configuration of continuous piecewise-linear neural networks. IEEE Trans Neural Netw 19(8):1431–1445 11. Adetola V, Guay M (2008) Finite-time parameter estimation in adaptive control of nonlinear systems. IEEE Trans Autom Control 53(3):807–811 12. Adetola V, Guay M (2010) Performance improvement in adaptive control of linearly parameterized nonlinear systems. IEEE Trans Autom Control 55(9):2182–2186

A Quantitative Analysis on Gmapping Algorithm Parameters Based on Lidar in Small Area Environment Hongyu Wang1,3, Mengxing Huang2(&), and Di Wu1,3 1

College of Computer and Cyber Security, Hainan University, Haikou 570228, China 2 College of Information and Communication Engineering, Hainan University, Haikou 570228, China [email protected] 3 State Key Laboratory of Marine Resource Utilization in South China Sea, Hainan University, Haikou 570228, China

Abstract. This paper focuses on the influence of two important parameters of Gmapping algorithm on the mapping accuracy. We also compute the PC consumption during mapping an indoor environment. It provides reliable reference criteria for autonomous mobile robots to map the indoor circumstances. An accurate and cost-effective mapping method is a Simultaneous Localization and Mapping (SLAM) technology problem that needs to be solved. It provides a basis for autonomous mobile robots to navigate, avoid obstacles and reach the target region smoothly. We analyze the advantages and deficiencies of several main SLAM algorithms in the current ROS framework, and propose to use Gmapping algorithm to build a map in unknown environment. We compare the cost of mapping under a specific scenario, which provides the Gmapping algorithm with an optimal low-cost solution to build a 2D grid map in a small range of indoor situation. Keywords: Gmapping Cost-effective
SLAM




Autonomous mobile robots




Indoor environment




1 Introduction In many robotic application, accurate mapping is essential for autonomous mobile robots [1], because of its momentous role in navigation, path planning, etc. Researchers also need a precise map to explore unknown areas by using robots so that they can avoid dangers and obstacles accurately in the execution of tasks. One of the goals of this paper is to build a two-dimensional map model based on the laboratory environment. There are many choices of cartographic model, such as 2D grid map, 3D pointcloud map and topological map [2]. In this study, we choose grid map due to its simplicity of mapping and integrity of environmental information. Meanwhile, it is handy for path planning and autonomous location. A lot of sensors are used to solve the localization problem, such as camera (monocular or stereo), sonar and odometry. In this work, we use LiDAR, compared with the camera, LiDAR has the merits of long © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 480–492, 2020. https://doi.org/10.1007/978-981-32-9698-5_54

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detection distance and accurate acquisition of three-dimensional information. In addition, it has high stability and good robustness [3], because the noise and illumination conditions related to distance measurement are independent. ROS is the standardized robot software framework developed by the Stanford University Artificial Intelligence Laboratory (SAIL) during the Stanford AI Robot project [4]. We develop an autonomous mobile robot based on LIDAR and Inertial Measurement Unit (IMU), and select ROS as the robot control platform. After that we study the parameter optimization of Gmapping algorithm in the real world. At present, the relevant literature tends to improve the RBPF algorithm in simulation environment, but ignores the adaptability and robustness of the algorithm itself in specific scenario applications. In addition, most SLAM evaluation methods rely on available standard datasets [5]. However, the implementation effect of these SLAM algorithms in ROS framework needs further study. It is necessary to combine with the specific experimental conditions to evaluate the performance of the algorithm, due to the value of algorithm parameters affects the final map. This paper studies the Gmapping algorithm based on LIDAR and ROS in a specific scenario. All the tested techniques use occupancy grids as the final output, which are analyzed using a metric for map similarities [5]. Most of the sweeping robots currently on sale are equipped with LIDAR to build indoor maps instead of visual odometry (VO), due to LIDAR has the low cost and high efficiency. Our work can provide a specific reference standard for software and parameter configuration of sweeping robots in family services, and reach the optimal implementation of mapping algorithm at low computational cost. The rest of the paper is organized as follows. In Sect. 2, we study the strengths and weaknesses of several common SLAM algorithms in ROS development platform, and focus on GmappingSLAM algorithm. The system overview is presented in Sects. 3 and 4 shows the scheme of the experiment. In Sect. 5, we do some quantitative research and comparative experiments with a specific application scenario, in order to find the optimal parameters of Gmapping algorithm at low-cost mapping in small indoor environment. Finally, the relevant conclusions are demonstrated in Sect. 6.

2 2D SLAM Algorithms The current mainstream SLAM framework consists of two parts, the front-end and the back-end (Fig. 1). The front-end part consists of generating the pose estimate of the robot, and the scanning data is used to graph-construction. Furthermore, the back-end part is mainly about the closed-loop detection and graph optimization. The robot uses closed-loop detection to determine whether the map overlapping occurs or not. If the closed-loop exists, then a graph optimization is performed. The SLAM algorithm can be described as a solution process for the interdependence between robot poses and map estimation. We conduct a brief description of two most widely used SLAM algorithms in the ROS framework. Then, the advantages and weaknesses of the Hector SLAM and Gmapping SLAM algorithms are summarized respectively.

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Fig. 1. Overview of the SLAM system.

2.1

HectorSLAM

The main contribution of Hector algorithm is the introduction of 3D navigation system, which is different from the traditional 2D grid-based SLAM algorithms. The algorithm can realize 6-DOF motion planning including translation and rotation [6], which can provide a solution for Unmanned Aerial Vehicles (UAV) SLAM. One of the main drawbacks of Hector is that it does not use any position feedback like odometry [7], so the robot pose relies too much on the scan information of the external sensors. Besides, Hector does not provide robot pose graph optimization [6], and therefore the pose error will accumulate with the increase of speed and time. The algorithm focuses on using a high update rate and low distance measurement noise to estimation the robot movement in real-time [8]. For these reasons, the effect and accuracy of the algorithm are affected by the scanning frequency of LIDAR. The researchers show the application of Hector algorithm, such as Urban Search and Rescue (USAR) [6], coastal surveying and mapping on Unmanned Surface Vehicles (USV), automatic driving of Unmanned Ground Vehicles (UGV) and outdoor exploration of Unmanned Aerial Vehicles (UAV). But they neglect the application of this SLAM method of LIDAR based on mechanical rotary scanning is heavily biased to the weather in outdoor scenes. Under downpour, heavy snow, dense fog, etc. conditions, the detection ability of infrared wave will be greatly reduced, and the sensing distance will also be affected. 2.2

Gmapping Based on RBPF

Murphy, Doucet, and colleagues introduced Rao-Blackwellized particle filters (RBPF) as an effective means to solve the SLAM problem. Each particle in an RBPF represents a possible robot trajectory and a map [9], so a key problem is how to reduce the number of particles [9] while ensuring the accuracy of map. In the process of building a large area map, the complexity of GmappingSLAM algorithm and hardware consumption will increase with the size of map. A smaller number of particles cannot guarantee the

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accuracy of map, while a larger number of particles will increase the computational cost of PC and Raspberry Pi, resulting in extra repetitive work. Additionally, the resampling step can potentially eliminate the correct particle [9] and retain the meaningless particles that carry duplicate maps. This effect is also known as the particledepletion problem, or particle impoverishment [9]. These are two major drawbacks of the RBPF SLAM approach. Gmapping is a particle filter algorithm based on RBPF, unlike traditional RBPF, it uses improved proposal distribution and adaptive resampling. Using Gmapping to fuse the information of LIDAR and odometry to construct 2D grid map can be divided into the following five steps. 1. Initialization: When t is equal to 0, an appropriate number of N particles are selected randomly to specify the robot pose at this time, and the region where the robot pose locate is regarded as a local map. Particles are evenly distributed in this region, and the weight of each particle is initialized as follows: wð0iÞ ¼ 1=N

ð1Þ

2. Sampling: The improved proposal distribution combines scan-matching data of LIDAR and odometry information. The latest observation data of LIDAR determines the sampling area of particles by scanning matcher. If the scan-matcher reports a success, a new proposal is sampled around the pose returned by the scanmatcher [10]. Then, a Gauss approximation N is used to evaluate the scores of PðiÞ ðiÞ sampled points. For each particle, the parameters lt and are determined t individually [9]. When the scan-matching process fails, the original odometry ðiÞ motion model is used as a proposal to estimate the new pose xt of particle i. 3. Update of the Importance Weighting: In most cases, the maximum value of the target distribution is only one. Selecting the most similar particle to the target distribution from the improved proposal distribution, ignoring the particles of the meaningless regions, and calculating the particle weights.   iÞ ðiÞ ðiÞ wðt iÞ ¼ wðt1
p zt j mt1 ; xt1 ; ut1 Z     ðiÞ ðiÞ ðiÞ ¼ wt1
p zt j mt1 ; x0
p x0 j xt1 ; ut1 dx K      X ðiÞ ðiÞ ðiÞ p zt j mt1 ; xj
p xj  xt1 ; ut1 ’ wt1


ð2Þ

j¼1

4. Adaptive Resampling: As the number of iterations increasing, the variance of the particle weights increases continuously, and the particle degradation occurs. The main idea of resampling is to duplicate more particles with larger weights by discarding the particles with smaller weights that do not work in order to keep the total number of particles. In terms of the formulation of Doucet et al. [11], a criterion determines when to perform the resampling step and evaluate the importance weights (Eq. 3).

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Neff ¼ 1=

N  X

~ ðiÞ w

2

ð3Þ

i¼1

5. Map estimation: According to robot latest pose and observation information of external sensors to update map. According to the conclusion of [5], KartoSLAM, HectorSLAM and Gmapping have higher mapping accuracy in small area indoor environment. We choose Gmapping to build indoor maps because it requires lower CPU computational cost and higher mapping precision. Gmapping makes effective use of wheel odometry information, which can provide robot prior pose. This data fusion method reduces the requirement for LIDAR and the cost of hardware configuration efficiently. On the other hand, Hector is unable to use odometry and therefore requires higher LIDAR configuration and poor robustness. Furthermore, Karto is a graph optimization method based on Sparse Pose Adjustment (SPA) [12], which is more suitable for constructing large outdoor maps.

3 System Implementation In this section, the description is mainly about the hardware platform and software overview of the robot that we built. 3.1

Hardware Platform

RPLIDAR A1 adopts rotary scanning and laser triangulation ranging technology. During each ranging process, the laser point sensor module will emit modulated infrared laser signals, which will be received by the visual acquisition system after the reflection of the laser signals reaching the target object. This radar has the merits of low cost, small size and high resolution. For these reasons, it is applicable to the indoor autonomous mobile robots (Fig. 2).

Fig. 2. The geometric method of triangulation technology.

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From similar triangles, the perpendicular distance to the object is q ¼ fs=x

ð4Þ

The distance along the laser ray depends also on the angle of the laser with respect to the image axis [13] (Fig. 3). d ¼ q= sinðaÞ

ð5Þ

Fig. 3. A self-developed crawler robot equipped with RPLIDAR A1, which we have built and use for research work.

Fig. 4. The hardware framework of the crawler robot in brief.

The hardware overview of the robot is shown in Fig. (4). The PC and Raspberry Pi are configured under the same wireless LAN. The Remote PC connects to the Raspberry Pi of the robot via WIFI and Secure Shell (SSH) key, moreover, RPLIDAR A1 transmits the scanning information of the external environment to Raspberry Pi through USB interface. STM 32 is selected as the main control board of the robot to command the

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motor driver. The odometry records the data of the left and right motors, in detail, one motor (Motor1) controls the left track and the other (Motor2) controls the right track. PID feedback regulates the duty cycle of the PWM signal to control the speed and direction of motors. Finally, odometry feeds the recorded data back to Raspberry Pi. 3.2

Software Overview

Robot software platform uses ROS (kinetic) based on C++ and python language, which is installed on Ubuntu 16.04 operating system. Rviz is used as a visual user interface of ROS to visualize robot localization, mapping and navigation. The robot applies Gmapping package to generate 2D occupancy grid map of the indoor environment.

4 Experimental Setup Rviz is used as the tool to visualize the map on a laptop with an 8GB RAM and 2.0 Ghz i7 processor. The PC uses Windows 10 operating system and simulates Ubuntu 16.04 operating system by installing VMware Workstation Pro. One benefit of this approach is that developers do not have to reinstall the operating system repeatedly to set up the development environment when they need. There are two important parameters in Gmapping algorithm, and their values affect the PC resource utilization rate and the final mapping effect directly in the process of mapping. The main task of our experiment is to change the values of these two parameters and run the Python script that we code to monitor the changes of memory occupancy rate and CPU usage during the whole experiment. Besides, the script records data per second and feed it back to the console panel of Pycharm. During the mapping process, the script also runs synchronously in the Pycharm IDE. • Particles (int, default: 8). Number of particles in the Gmapping algorithm. Because particles are constantly updated and degraded iteratively in the process of mapping, selecting an appropriate number of particles can make the algorithm have a higher speed and a lower hardware resource usage rate while ensuring the accuracy of map. • minimumScore (float, default: 30). Minimum matching score, which represents the lowest score for evaluating good results of LIDAR scanning matching. It determines the confidence level of the Gmapping algorithm in the mechanical scanning data of LIDAR. The higher requirement for the matching algorithm, the easier the LIDAR matching will fail and turn to rely on the odometry data. In addition, the low setting of the parameter value will cause a lot of noise in the map, so it needs to be weighed and adjusted. We make a quantitative analysis of the Gmapping algorithm performance at Room 607, State Key Laboratory of Marine Resource Utilization in South China Sea, Hainan University. The experimental scenes include 7.60  7.15 m2 indoor environment and 9.82  2.10 m2 outdoor corridor.

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5 Results Analysis We do quantitative analysis by adjusting the values of particles and minimumScore. The accuracy of the generated maps in each case is an important indicator for evaluating the parameter values. In addition, the CPU computational effort and memory usage are also important evaluation criteria. The purpose of our experiment is to find the optimal parameter values based on these three evaluation conditions. A. Optimization of Particle Number A practical application of autonomous mobile robot is biased toward smart home and home service, and SLAM has a widely applicable prospect in solving various problems faced by robots in indoor environment. Considering that situations, we choose to test the algorithm within an area of 100 m2, which is in line with the size of the common indoor area. The total area of our map is 74.96 m2, and our experiment is to find the best particle number of Gmapping algorithm in this area.

Fig. 5. Maps built for our Lab and corridor by using (a) 10 particles, (b) 20 particles, (c) 30 particles and (d) 40 particles.

The size of all map grids is set up to 0.05 m. We can see clearly from Fig. 5, in case of (d), the map becomes blurred obviously. This kind of noise is mainly caused by the large number of particles, which degrades the edge of the map, and it is also called particle depletion [9]. In the first three cases, the mapping accuracy has not been changed significantly, so in the next step, we do some research on the memory usage rate and CPU computational cost required by different number of particles during mapping the small area, in order to get the best answer through screening.

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Fig. 6. Resources utilization rate of the laptop we have tested with different particle numbers. (a) 10 particles, (b) 20 particles, (c) 30 particles, and (d) 40 particles.

The duration of each experiment is about 17 min, we count the resource utilization rate of the laptop per second within about 1000 s (Fig. 6). We can see that the usage ratio of memory and CPU has increased dramatically since the 300th sec, and the reason is that we open VMware Workstation Pro to configure the ROS environment at 300th sec. Comparing to running ROS, the initial 300 s are the state of the laptop without launching the virtual machine. After comparison, we can find that it takes a lot of memory to set up ROS via VMware in Windows system. Moreover, we can discover that there is a positive correlation between the number of particles and the consumption of laptop resources, and the utilization rate of CPU and memory will increase with the growing of map (especially in (d)). Table 1. The average usage rate of the laptop within 1000 s increasing the particles number. Particles 10 20 30 40 CPU (%) 17.36 17.03 22.16 28.44 Memory (%) 54.34 59.67 63.72 61.12

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For screening the optimal number of particles more intuitively, we have calculated the average usage ratio of CPU and memory in case of different number of particles in the total experiment time. From the results of Table 1, we can see that the CPU load and memory consumption converge to the minimum when the number of particles is 10. Meanwhile, there is a positive correlation between the PC resources consumption and the number of particles. B. Optimization of minimumScore minimumScore determines whether to use sensor information or the motion estimate of the robot based on the odometry data. There are two kinds of errors in LIDAR, one is the measurement error based on Gaussian distribution, the other error is caused by moving objects in the environment. However, using odometry data merely means discarding the useful information scanned by LIDAR, and mapping is often imprecise, therefore, it is necessary to select an appropriate score value.

Fig. 7. Influence of different score values on the accuracy of gmapping in mapping the Lab and corridor. With 50 Score value the map seems to generate errors at the doorway (a). Under the conditions of 100 Score (b), 150 Score (c) and 200 Score (d), the most accurate map is (d).

As can be seen from Fig. 7, when the score value is 50, there is a large error in the mapping of the entrance to the outdoor corridor, and the upper-right corner of the indoor map is not complete enough. Furthermore, the contour of the map edge is clearer than other maps in the case of the score value is 200.

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Fig. 8. Resources utilization rate of the laptop we have tested with different values of minimumScore. (a) 50 Score value, (b) 100 Score value, (c) 150 Score value, (d) 200 Score value.

We use the same method to calculate the influence of changing score value within 1000 s on CPU load and memory consumption. As visualized in Fig. 8, the memory consumption rises steadily with the growing of mapping scope, besides, the score value tends to influence the CPU computational effort. Table 2. The average usage rate of the laptop within 1000 s increasing the minimumScore value. minimumScore 50 100 150 200 CPU (%) 19.02 24.18 20.48 27.03 Memory (%) 58.54 58.17 55.32 58.73

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In order to filtrate the optimal solution more visibly, we have computed the average utilization rate of CPU and memory within 1000 s in the case of different score values. Table 2 depicts that when the score value is equal to 150, the CPU load and memory usage of the laptop are the smallest. However, the results in Fig. 7 prove changing the score value to 200, we obtain the most accurate map. Considering that the accuracy of map is the most important factor, and in this case, the resources consumption of the PC is acceptable, we regard 200 as the optimal score value.

6 Conclusion In this paper, we present a low-cost optimal solution of Gmapping algorithm to achieve the best mapping effect in indoor scenes with a total area of 74.96 m2. The significance of this work is to provide a reference standard for parameter setting of sweeping robots and other domestic service robots, which are popular in the market at present. Although the Gmapping algorithm can map thousands of square meters in theory, we often need to analyze the application of the algorithm combined with the specific situation. In case of a confined environment under a specified scenario, such as indoor environment, it is unnecessary to set large parameters for GmappingSLAM to build maps, which will increase the cost of computer and robot hardware, and often acquire an unsatisfactory experimental result. Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant No. 61462022).

References 1. Sidaoui A, Elhajj, IH, Asmar, D (2018) Human-in-the-loop augmented mapping. In: 2018 IEEE/RSJ international conference on intelligent robots and systems (IROS), pp 3190–3195. IEEE, Madrid 2. Zhao C, Hu H, Gu D (2015) Building a grid-point cloud-semantic map based on graph for the navigation of intelligent wheelchair. In: 21st international conference on automation and computing (ICAC), pp. 1–7. IEEE, Glasgow 3. Yin, P, et al (2018) Stabilize an unsupervised feature learning for LiDAR-based place recognition. In: 2018 IEEE/RSJ international conference on intelligent robots and systems (IROS), pp 1162–1167. IEEE, Madrid 4. Fernández E, Crespo LS, Mahtani A, Martinez A (2015) Learning ROS for Robotics Programming, 2nd edn. Packt Publishing, Birmingham 5. Santos JM, Portugal D, Rocha RP (2013) An evaluation of 2D SLAM techniques available in robot operating system. In: 2013 IEEE International symposium on safety, security, and rescue robotics (SSRR), pp 1–6. IEEE, Linkoping 6. Kohlbrecher S, von Stryk O, Meyer J, Klingauf U (2011) A flexible and scalable SLAM system with full 3D motion estimation. In: 2011 IEEE international symposium on safety, security, and rescue robotics, pp 155–160. IEEE, Kyoto 7. Madhira K, Patel J. Kothari D. Panchal D, Patel D (2017) A quantitative study of mapping and localization algorithms on ROS based differential robot. In: 2017 Nirma university international conference on engineering (NUiCONE), pp 1–5. IEEE, Ahmedabad

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8. Lang Q, et al (2016) An evaluation of 2D SLAM techniques based on kinect and laser scanner. In: Sun F, Liu H, Hu D (eds) Cognitive systems and signal processing. ICCSIP 2016. Communications in Computer and Information Science, vol 710, pp 276–289. Springer, Singapore 9. Grisetti G, Stachniss C, Burgard W (2007) Improved techniques for grid mapping with Raoblackwellized particle filters. IEEE Trans Robot 23(1):34–46 10. Abdelrasoul Y, Saman, ABSH, Sebastian P (2016) A quantitative study of tuning ROS Gmapping parameters and their effect on performing indoor 2D SLAM. In: 2016 2nd IEEE international symposium on robotics and manufacturing automation (ROMA), pp 1–6. IEEE, Ipoh 11. Doucet A, de Freitas N, Gordan N (eds) (2001) Sequential Monte-Carlo methods in practice. Springer-Verlag, New York 12. Konolige K, Grisetti G, Kümmerle R, Burgard W, Limketkai B, Vincent R (2010) Efficient sparse pose adjustment for 2D mapping. In: 2010 IEEE/RSJ international conference on intelligent robots and systems, pp 22–29. IEEE, Taipei 13. Konolige K, Augenbraun J, Donaldson N, Fiebig C, Shah P (2008) A low-cost laser distance sensor. In: 2008 IEEE international conference on robotics and automation, pp 3002–3008. IEEE, Pasadena

A Vision-Based Method for Vehicle Forward Collision Warning Yanfei Zhang, Zhangyu Wang, Bin Zhou(&), Guizhen Yu, Chaowei Hu, and Li Zhang School of Transportation Science and Engineering, Beijing Advanced Innovation Center for Big Data and Brain Computing, Beijing Key Laboratory for Cooperative Vehicle Infrastructure Systems and Safety Control, Beihang University, Beijing 100191, China [email protected]

Abstract. Forward Collision Warning (FCW) system can automatically measure the distance between obstacles and provide early warning, which can effectively provide safety guarantee for vehicle travel and reduce the probability of traffic accidents. The vision-based approaches are always popular because vision sensors have the characteristics of low cost and rich image information. In this paper, a vision-based forward collision warning method is proposed. The method contains three main stages: (1) detect obstacle based on multi-feature fusion using convolution neural networks (CNN), (2) estimate the relative distance, relative velocity from vehicles and collision time, (3) design obstacles hazard level discrimination strategy for different road scenarios. The algorithm is tested on our own dataset and the experiment results showed that the method has good feasibility and robustness. Keywords: Obstacle detection
Convolution neural network Hazard level discrimination
Forward collision warning




1 Introduction Forward collision warning (FCW) system can provide accurate on-road obstacles warning information in order to improve the active safety of vehicle. As the key technique of FCW, vision-based detection approach is always popular for many research institutions and researchers. Because rich visual information plays an important role in some applications including obstacles detection, lane detection and so on. Meanwhile, the computer vision especially object detection algorithms are growing by leaps and bounds. Besides, it’s flexible and convenient to build a perception system with a low-cost camera. Before the driving assistance system gives the warning information, it is necessary to divide the danger degree of the detected obstacles in advance. According to some existing research [1], the commonly used methods can be summarized into two kinds. One is to compare the own vehicles with the relative distance between the obstacles in front and the set dangerous distance, the closer the relative distance is, the more dangerous; the other is to estimate the collision time with the obstacle, and then © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 493–502, 2020. https://doi.org/10.1007/978-981-32-9698-5_55

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compare the result with the set safety time, the shorter the collision time, the more dangerous it is. Lots of techniques for FCW system depend on a great deal of sensors such as lidar, GPS, radar, stereo cameras which are a little big and expensive. Chang et al. [2] proposed a monocular vision-based vehicle detection and tracking method based on the adaptive boosting cascade classifier, had high real-time performance. Qun et al. [3] adopted You Only Look Once (named YOLO) vehicle detection algorithm and proposed a nested Kalman filter method that can predict and stabilize the detected distance, and then predict and stabilize the detected vehicle speed and collision time to build the FCW system. As the overall framework is shown in the Fig. 1, the obstacle detection method based on convolution neural networks (CNN) is adopted. Then, some algorithms are designed to estimate the relative distance, relative velocity from vehicles and collision time. Next, a front vehicle hazard level discrimination method for different road scenarios is proposed, finally the early warning information is provided. Then, the presented method is verified by experiments, and is proved to have high precision and robustness for some complex environment.

Fig. 1. Framework of the proposed method.

The rest of this paper is organized as follows: Sect. 2 introduces the methodological details of the efficient obstacle detection method, followed by the hazard level discrimination strategy based the relative distance, relative velocity from vehicles and collision time in Sect. 3, and the Sect. 4 shows the experiment results. Finally, a conclusion is presented in Sect. 5.

2 The Obstacle Detection Method 2.1

A Subsection Sample

Yolov3 [4] is a general object detection algorithm balancing the speed and accuracy, and is adopted to detect the vehicle, non-motorized vehicle and pedestrian int the paper, the structure is shown in Fig. 2.

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Fig. 2. The block diagram of the object detection method.

In the obstacle detection method, the network named Darket-53 is used to extracts the features of the input image, then features from the prior feature map and upsampled features are connected, also, a few more convolutional layers to process this combined feature map are added, which predicts a 3-d tensor encoding bounding box, objectness, and class predictions. Next, the three different scales of boxes are predicted. The logistic regression is used for each bounding box to predict an objectness score. The network predicts 4 coordinates for each bounding box, tx ; ty ; tw ; th . If the cell is offset from the top left corner of the image by ðcx ; cy Þ and the bounding box prior has width and height pw ; ph , then the predictions correspond to: bx ¼ rðtx Þ þ cx bw ¼ pw etw


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3 The Vehicle Forward Collision Warning Method Upon completion of the obstacle detection task, only are the position and category of the vehicle’s forward obstacle in each frame of image obtained, but for Forward Collision Warning system, it is vital to know every obstacle and its relative distance, relative velocity of the vehicle motion information, then classify dangerous degree of obstacles for the final forward collision warning information. 3.1

Vehicle Motion Information Estimation

For the driving assistant system, it is necessary to measure the lateral and longitudinal distance of the vehicle forward obstacle, which can be directly used to analyze the movement state of the obstacle [1], and then to judge its dangerous degree. The longitudinal distance method based on the geometric relationship, which is used by this

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paper, can be directly calculated between the image pixel coordinate system and the world coordinate system [5]. In the paper [1], we select the center point of the edge of the detected obstacle target frame as the object, and substitute it into the fitting cubic curve equation to calculate the lateral distance of the obstacle [6]. When calculating the relative speed of obstacles in each frame image, we take the detection results of the previous five consecutive frames as reference, assuming that the processing time of each picture in the five frames is set T, T ¼ fti ; ti þ 1 ; ti þ 2 ; ti þ 3 ; ti þ 4 g, the vertical distance of the same obstacle in five frames is set D, D ¼ fDi ; Di þ 1 ; Di þ 2 ; Di þ 3 ; Di þ 4 g, lateral distance set H, H ¼ fHi ; Hi þ 1 ; Hi þ 2 ; Hi þ 3 ; Hi þ 4 g, the longituP dinal relative velocity of the current obstacle is: VDi ¼ ðDi þ 4  Di Þ= ii þ 4 ti , the Pi þ 4 lateral relative velocity of the current obstacle is: VHi ¼ ðHi þ 4  Hi Þ= i ti Estimating the collision time is usually for the obstacles in the direction of vehicle motion. It is usually obtained by dividing the longitudinal relative distance by the relative velocity. In this paper, obstacles with relative transverse distance within 5 m are selected for calculation. The estimated collision time is as the following formula: Ti ¼ ðDi þ 4  1:7Þ=VDi

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Vehicle Motion Information Estimation

In the detected vehicle forward obstacles, not all obstacles will pose a threat to the vehicle, and different obstacles have different degrees of danger. Therefore, it is necessary to calculate the obstacle movement information and rate the hazard level for all targets, then the obstacle information is displayed one by one according to the hazard level. On the other hand, for different types of motor vehicles in different road scenarios, the possible motion states are different, so different criteria need to be set for judgment. Road environment can usually be divided into structured road and unstructured road. For structured road, lane line is helpful to distinguish whether the obstacles ahead are in their own lane or whether the vehicle target of the adjacent lane has the intention of changing lanes. Generally speaking, for forward vehicles, the most serious threat to their own vehicles is the vehicle closest to the current lane, followed by the vehicle closest to the adjacent lane. If their vehicles are in the middle lane, the vehicle on the left side is usually more dangerous than the vehicle on the right side. The reason is that the vehicles are generally used to driving on the right, so the vehicle on the left side is more likely to change lanes. Besides, the vehicles on the dashed line side are more dangerous than those on the solid line side. For pedestrians and non-motorized vehicles in the structured road and all kinds of obstacles in the unstructured road, the criteria for judging the hazard level of the obstacle ahead are first the longitudinal relative distance, if the longitudinal distance is within the dangerous distance, the hazard level of the obstacle is the highest; if the longitudinal distance is beyond the dangerous distance, the relative speed of the horizontal and vertical direction should be considered, and the hazard level of the target close to is medium, followed by the target far away.

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Obstacles of the same risk level can be sorted according to the relative distance, and the nearer the obstacle, the higher the dangerous degree.

Table 1. Criteria for classification of obstacles Road

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The Table 1 is the classification of hazard levels for different types of obstacles in different road environments under different states. Red represents the highest level, yellow shows the intermediate level, and green is representative of the lowest level. Generally speaking, the criteria for judging the degree of danger mainly includes: road environment, solid and dashed lanes on both sides, lanes where obstacles are located, relative distance in horizontal and longitudinal directions and relative speed. For Lane detection, this paper uses an existing fast lane detection algorithm based on inverse perspective transformation and Hough linear transformation [7]. After obtained

Fig. 3. The schematic of test results

the lane line equation in each frame, the relative position relationship between lane line and obstacle can be judged by combining the results of obstacle detection. Figure 3 is a sketch of obstacle detection results in several typical road scenarios. (1) Structured road, as shown in Fig. 3(A), the lane where the vehicle is located is non-changeable lane, the green solid line is solid lane, the orange solid line is vertical dangerous distance, and the vehicle in front of the current lane is within the dangerous distance, so the hazard level is the highest, indicated by the red box. The possibility of vehicles in the adjacent lane changing lanes in violation of traffic rules is small, so the hazard level is low and is indicated by a green box. (2) 2 Structured road, as shown in Fig. 3(B), there is the dashed lines on one side and the solid lines on the other. Vehicles on the dashed lines are relatively close in the longitudinal direction, so they are the most dangerous obstacles, which are represented by red boxes; vehicles on the front of the current lane are less dangerous because of the relatively long longitudinal distance, represented by yellow boxes; vehicles on the left lane are outside the solid line of the lane, so the risk level is the smallest, expressed in green boxes.

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(3) unstructured road, as shown in Fig. 3(C), part of the obstacles are within the danger longitudinal distance, and the transverse distance is decreasing, represented by red box; Some obstacles beyond the danger distance are shown in the green box. (4) unstructured road, as shown in Fig. 3(D), all the obstacles are within the danger longitudinal distance, and the relative distance of pedestrians is approaching, represented by red box; The vehicles are moving away, shown in yellow. This paper only tracks and measures the most dangerous obstacles. Firstly, set up a number of dangerous obstacles threshold N (3 * 5), secondly sort the hazard level after detecting obstacles each time based on only the relative distance and the lane line information, then choose the most dangerous N the target input to tracking algorithm in the process [8].

4 Experiments It is necessary to test the accuracy of the algorithm to classify the risk of the detected obstacles. Video data of three road scenarios, i.e. ordinary structured road, highway and unstructured road, are selected as test samples. Taking the general structured road scenario as an example, the test results show that as shown in Fig. 4, a car in front of its vehicle lane is far away, which is regarded as the most dangerous target and expressed in red box; the target on the solid side of the lane is the least dangerous, and the result is expressed in green box, which does not calculate the movement information.

Fig. 4. Obstacle detection results in general structured road scenes

Table 2 records some of the data. It can be seen that the relative distance between the vehicle and the obstacle increases gradually in the previous period of time, and then decreases. The relative velocity is almost greater than 0 in the previous period of time, and then begins to approach the negative value, which is consistent with the actual situation.

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Figure 5 is part of the test results under the environment of high-speed loop. The hazard degree of obstacles on the side of dashed line is medium, and the test result is yellow box. The hazard degree of obstacles beyond the dangerous distance of adjacent lane is low, and the test result is green box. The hazard degree of obstacles within the dangerous distance of pressing line or current lane is high, and the test result is red box. Figure 6 shows the partial test results of unstructured road. The vehicle on the far left is out of the danger distance and does not approach without a tendency. The pedestrians in the middle is the most dangerous, and the detection result is red box. The pedestrians far away from the danger distance has the lowest danger degree, and the detection result is expressed in yellow box.

Fig. 5. Detection results of obstacles in highway loop road scene

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Fig. 6. Obstacle detection results of unstructured road scene

5 Conclusions In the paper, a vision-based vehicle forward collision warning method is designed. The algorithm is divided into three stages: (1) detect obstacles based on convolution neural networks (CNN), (2) estimate the relative distance, relative velocity from vehicles and collision time after measuring the lateral and longitudinal distance of the vehicle forward obstacle, (3) design obstacles hazard level discrimination strategy according the for different road scenarios and different types of obstacles. The algorithm is tested on our own dataset and the experiment results show that the method performed well and showed high reliability in various kinds of road conditions. Acknowledgments. This work was supported by the National Key Research and Development Program of China (2016YFB0101001), the Beijing Municipal Science and Technology Project under Grant # Z181100008918003 and the Beijing Municipal Science and Technology Project under Grant #D171100005117001. The authors would also like to thank the insightful and constructive comments from anonymous reviewers.

References 1. Wang SC (2012) Development and experimental verification of the decision algorithm of the front anti-collision early warning system. Doctor, Jilin university 2. Chang JW, Kang SJ (2018) Real-time vehicle detection and tracking algorithm for forward vehicle collision warning. J Semicond Technol Sci 18(5):547–559 3. Lim Q, He Y, Tan U (2018) Real-time forward collision warning system using nested kalman filter for monocular camera. In: Proceedings of the 2018 IEEE international conference on robotics and biomimetics, 12–15 December, Kuala Lumpur, Malaysia 4. Redmon J, Farhadi A (2018) YOLOv3: an incremental improvement. https://pjreddie.com/ darknet/yolo/ 5. Liu HZ, Yuan JZ, Zheng YR (2015) Computer vision algorithms and intelligent vehicle applications. Publishing House of Electronics Industry, Beijing

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6. Yu GZ (2018) A forward object lateral distance calibration method based on monocular camera, China: CN109087361A 7. Yu GZ, Wang ZY et al (2018) Efficient lane detection using deep lane feature extraction method. SAE Int J Passeng Cars Electron Electr Syst 1(11):57–66 8. Hu CW, Wang YP, Yu GZ, Wang ZY et al (2018) Embedding CNN-based fast obstacles detection for autonomous vehicles. SAE Technical Paper

Design and Simulation of a Self-balanced and Wheel-Legged Robot Lufeng Zhang, Qing Guo, and Xuemei Ren(&) Beijing Institute of Technology, Beijing 100081, China [email protected]

Abstract. This paper presents a wheel-legged robot that can move by wheel and jump by leg. Since the center of gravity is designed below the wheel axis, this robot can keep balance rely on its own mechanical structure. The key part for hopping of this robot is the gear system and torsional spring. The detailed process and principle of the hopping motion is introduced in this paper. The implementation of the hopping and how the parameter of the chosen torsional spring influenced the height that the robot can reach is simulated in Adams software. Keywords: Wheel-legged robot


Hopping
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1 Introduction As deep space exploration has become more and more important to countries all over the world, taking the exploration of Mars as an example, the surface of Mars is heavily pitted, with mountains, canyons, craters, small pits, shield-shaped volcanoes, riverbeds, flats, etc.; The surface of Mars is severely weathered and forms various sand dunes. In response to monitoring, detection and search and rescue missions in extreme environments such as deep space exploration (with gullies and obstacles), people have put forward certain design requirements for inspection robots with obstacle-tolerance capabilities: small size for carrying, quality Lighter to save energy and power consumption (such as the fuel required to launch a spacecraft is extremely expensive). The main way to use the special-shaped wheel on the pavement with obstacles to overcome obstacles is to design a structure so that the wheel diameter can be changed to adapt to different obstacles when the obstacle is overcome. The process of change includes actively and passively change. The deformable two-wheeled vehicle developed by the School of Mechanical and Aerospace Engineering of Seoul National University, Korea, combines the characteristics of a round wheel and a leg wheel [1] shown in Fig. 1(a). When moving forward on a flat surface, the wheel maintains a normal circular shape. When encountering an obstacle, the variable-wheeling robot relies on friction and self-gravity to unfold the legs on the wheel, thereby achieving the purpose of climbing the obstacle, and experimentally verifying that the two-wheeled vehicle can span the height The obstacle of 2.6 times of its own wheel has a high obstacle efficiency. However, the wheel diameter of the two-wheeled vehicle is a sliding force generated by the pressure of the wheel contacting the obstacle to move a “leg”, thereby driving the other two. When the “legs” are unfolded, the controllability © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 503–510, 2020. https://doi.org/10.1007/978-981-32-9698-5_56

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of the wheel’s variable diameter is poor, and the car that moves after the variable diameter causes the position of the center of gravity to change greatly due to the irregularity of the outer side of the wheel, thereby causing the movement to be unstable. In addition, the design of the tail of the cart that is in direct contact with the ground increases the resistance to motion. Another variable-diameter wheel robot developed by the School of Mechanical and Aerospace Engineering of Seoul National University in South Korea uses the origami mechanism [2] seen in Fig. 1(b). The deformation process of the wheel is mainly driven by a DC motor rotating the shaft. Moving, and finally tightening or loosening the wheel by the cable to achieve the reduction and expansion of the wheel diameter, the principle is simple and easy to implement. The variable-diameter wheel robot based on the origami mechanism weighs only 470 g, and the wheel diameter varies from 55 mm to 120 mm, which highlights its small size for easy exploration and obstacles. Developed by Boston Dynamics, Sand Flea is a scouting robot weighing only 5 kg [3] (see in Fig. 1(c)). It can fly like a remote-controlled model car on a flat surface. The robot can jump around 9.1 m. The height and Sand Flea’s built-in gyroscope keeps it level during the flight phase of the jump process, providing a clear view of the onboard camera and ensuring a smooth landing. Since the jumping power is derived from the vehicle fuel, it can only rely on the piston to jump 25 times. Another wheel-legged bouncing robot “Handle” [3] (Fig. 1(d)) developed by Boston Dynamics, the biggest feature of “Handle” is the combination of wheels and legs, which will bring wheeled robots and legs. The advantages of robots are obtained. The functions of “Handle” include rapid acceleration and braking, turning and high-speed cornering during the movement; single-wheel over-slope and stable during operation; can be glided in outdoor snow, bouncing and transportable 45 kg weight. “Handle” can operate smoothly in a variety of harsh environments, such as mountains, snow and rugged terrain. The robot is about 1.98 m high, with a travel speed of about 14 km per hour and a vertical jump height of about 1.2 m.

Fig. 1. Different robots for crossing obstacles

2 Mechanical Design 2.1

Design of the Quick-Return Structure

The quick return characteristic means that the return time and the travel time of the mechanism (such as the linkage mechanism) are different, the return speed is faster than the stroke speed, and the application of the quick return characteristic of the mechanism in the engineering has three situations: the first case is the working stroke requirement.

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Slowly advance, in order to facilitate the work of cutting, stamping, etc. [4], and to save the return time, it is required to return quickly, such as the planer and the inserting machine; the second case is the crushing of some jaws. The machine is required to move quickly and retreat, so that the broken ore can be withdrawn from the slab in time to avoid over-grinding of the ore (due to the certain size requirement of the crushed ore); the third case is that some equipment is in the positive In the reverse stroke, all work, so there is no urgent return requirement. In order to indicate the degree of rapid return of the rapid return movement, the commonly used stroke speed variation coefficient K is used to measure [4], i.e. K ¼ v2 =v1 ¼ t1 =t2

ð1Þ

where v1 , v2 are the speeds of the stroke and the return, respectively, and t is the time used. The larger the value of K, the more significant the mechanism of the quick return movement of the mechanism. The energy storage-release mechanism in the bounce mechanism requires the quick return characteristic to store the energy. Released in a very short time, allowing the bouncing body to get the initial speed required for bouncing. The common mechanism with the characteristic of quick-return is summarized in the table below: Table 1. Mechanism with the characteristic of quick-return. Robot [5–7] [8] [9] [10] [11] [12]

Mechanism for energy store and release Cam Gear train with uncomplete gear Planetary gear structure Explosive fuel Eccentric crank slider mechanism Escapement mechanism

Compare the mechanism with quick return characteristics in Table 1, in which the fuel explosion provides a source of jumping energy. Although it is explosive and provides a large kinetic energy, the jump is often not continuous and the number of jumps is limited. The cam mainly relies on the cam. The difference between the maximum return and the minimum return of the mechanism, the difference is the compression of the elastic element, and the cam mechanism as the energy storage and release device, the main advantage is that the energy release instant does not extend the energy release time due to its structure, thereby reducing the supply to The acceleration of the take-off, on the contrary, the gear train structure will delay the release time of the energy due to the self-friction when the gear is reversed, and the disadvantage of the cam mechanism is that the overall size is large due to the maximum return stroke, which is contrary with the requirement that the small size needed by the jumping robot. 2.2

Robot Structure Deign

The bounce performance of the bounce robot is directly determined by the structure of the bounce robot. As mentioned above, a key structure in the bounce robot is an energy

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storage-release mechanism with a snapback characteristic. In addition, the bounce robot also needs to have a jump motion. Direct actuators (such as single-leg, two-link, fourbar mechanism, etc.), here mainly design the structural scheme of the self-balancing wheel bounce robot, because the bouncing robot designed in this paper combines the jumping motion with the wheel motion, and In the process of movement, it is necessary to maintain balance. Therefore, for the balance problem, it is proposed to rely on its own structure to achieve balance or rely on control algorithm to achieve balance, so as to propose different structural design schemes. The main content of this chapter is to propose different self-balancing bouncing wheeled robots. The design scheme introduces its main structure, expounds its motion principle, and based on the simulation results of the virtual prototype, makes the final structural design choice, and provides a reasonable scheme design for the production of the experimental prototype. This program focuses on the balance realization of self-balancing bouncing robots, that is, relying on its own structure to achieve balance. In this case, tumbler is taken as an example. Since the quality of the tumbler is mostly concentrated in the lower part, it always depends on its structure when it is dumped. Return to the equilibrium position, and the lower the center of gravity, the more stable the tumbler is in the equilibrium position. According to the principle of the tumbler, in order to realize the self-balancing bouncing robot only relying on its own structure, the structural scheme design in this section mainly designs the overall center of gravity of the robot below the wheel axis, so that the robot does not need any control algorithm to achieve balance. Its specific structural design is shown in Fig. 2. 1

2

3

4

5

6 11

10

9

8

7

Fig. 2. CAD model of the self-balance and wheel-legged robot: 1-Outer wheel 2-Inner wheel 3Gear cover 4-Motor frame 5-Internal gear baffle 6-Internal gear 7-Wheel motor 8-Jumping motor 9-Gear system 10-Calf 11-Thigh

As shown in Fig. 3-1, the self-balancing bounce two-wheeled vehicle has three drive motors, all of which are DC motors. The left and right motors drive the left and right wheels respectively. When the motor rotates at the same speed, the robot moves forward or backward. After the motor speed or steering is different, the robot performs the turning motion, that is, the turning motion is performed in the differential manner.

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The wheel is characterized by the internal gear driving the external gear, and the external gear is fixedly connected with the wheel, thereby driving the wheel and the internal gear baffle The role is to fix the internal gear and prevent the internal gear from moving left and right. The bounce actuator of the bounce robot is a two-bar mechanism with a torsion spring mounted at the joint for use as an elastic element for storing energy. The energy storage-release mechanism with the snapback characteristic is a gear train driven by a third motor located in the middle portion, and the specific process of storing and releasing energy is as follows:

(1)

(2) Fig. 3. The process of energy storage and release

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As shown in Fig. 3, the bouncing energy storage-release mechanism of the selfbalancing two-wheeled vehicle adopts a planetary gear mechanism. The planetary gear shown in (1) is in a disengaged state, and the gear rotates counterclockwise to engage the figure (2) The state shown, if the drive gear is continued to rotate, the pulley gear will rotate under the rotation of the planetary gear, and the winding on the pulley will be tightened, thereby compressing the torsion spring, and the torsion spring is compressed to a certain extent, and the motor is reversed. When the planetary gear is disengaged, the winding will be suddenly released under the action of the torsion spring restoring force, so that the two-bar mechanism will act on the ground under the action of the torsional spring.

3 Simulation Results In order to compare this design scheme with the other two schemes below, it is necessary to simulate the virtual prototype of the designed structure to observe its jumping effect and bounce height, and observe the posture of the robot during the simulation or the actual experiment. The problems that arise are combined with all the simulation results above to compare the advantages and disadvantages of the designed solution. As shown in Fig. 4, the simulation curve of the wheeled bouncing robot under five different stiffness coefficients can be found that as the torsion spring stiffness coefficient becomes larger, the bounce height also increases, when the stiffness coefficient K = 0.7 N. At mm/deg, the maximum jump height is 85 mm. Figure 5 shows the stiffness coefficient as K = 0.5 Nmm/deg, the attitude exhibited by the wheeled bouncing robot at different stages, that is, the initial acceleration required to release the jump from the reel to the two-bar mechanism and the ground, and finally reaches the highest point, the round can be found. During the process of leaving the ground to reach the highest point, the bouncing robot will have a certain flip. After the landing, the force of the calf mechanism and the ground will hinder the recovery of the torsion spring. At this time, the motor that drives the wheel to rotate forward or reverse to drive the jump is needed. When rotated, the lower leg can be retracted to the posture of the first figure in Figs. 4 so that the robot can continue to advance in a wheeled mode.

Fig. 4. Different jumping height under different spring stiffness coefficient

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Fig. 5. Simulation in Adams software

4 Conclusion and Future Work This paper designs a self-balancing bouncing wheeled robot, which provides a novel design concept for monitoring, searching and rescue tasks. However, in the process of researching the design of bounce mechanism, there are still some shortcomings. The following points will be explored and improved to make prototypes and test: Controllability of bounce height; A more efficient energy storage-release mechanism design with snapback characteristics; High component integration of bouncing robots and miniaturized design of robots. Acknowledgments. This work is supported by National Natural Science Foundation (NNSF) of China under Grant No. 61433003, and No. 61973036.

References 1. Kim YS et al (2013) Wheel transformer: a miniaturized terrain adaptive robot with passively transformed wheels. In: IEEE international conference on robotics and automation. IEEE, pp 5625–5630 2. Lee DY et al (2014) Fabrication of origami wheel using pattern embedded fabric and its application to a deformable mobile robot. In: IEEE international conference on robotics and automation. IEEE, p 2565 3. Boston Dynamics, Jumping Robot [OL] (2017). www.bostondynamics.com. Accessed 21 July 2017 4. Heng S (2010) Mechanism theory, Beijing 5. Kovac M et al (2008) A miniature 7g jumping robot. In: IEEE international conference on robotics and automation. IEEE, pp 373–378 6. Jun BR, Kim YJ, Jung S (2016) Design and control of jumping mechanism for a Kangarooinspired robot. In: IEEE International conference on biomedical robotics and biomechatronics. IEEE, pp 436–440 7. Buksh SR, Chen X, Wang W (2009) Design and modeling of a flea-like jumping robot. In: IEEE international conference on control and automation. IEEE, pp 1862–1867

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8. Song G et al (2009) A surveillance robot with hopping capabilities for home security. IEEE Trans Consum Electron 55(4):2034–2039 9. Jung GP et al (2016) An integrated jumping-crawling robot using height-adjustable jumping module. In: IEEE international conference on robotics and automation. IEEE, pp 4680–4685 10. Scarfogliero U, Stefanini C, Dario P (2009) The use of compliant joints and elastic energy storage in bio-inspired legged robots. Mech Mach Theory 44(3):580–590 11. Chang D et al (2013) Design of a slider-crank leg mechanism for mobile hopping robotic platforms. J Mech Sci Technol 27(1):207–214 12. Zaitsev V et al (2015) Locust-inspired miniature jumping robot. In: IEEE/RSJ international conference on intelligent robots and systems. IEEE, pp 553–558

Online RPCA Background Modeling Based on Color and Depth Data Huini Fu(&) and Hengzhu Liu National University of Defense Technology, Changsha 410000, China [email protected]

Abstract. This paper applies online RPCA framework on color and depth data for background modeling and foreground segmentation. First, it could model a better background scene for video sequence in real-time. Second, it is a refinement for foreground segmentation. In this paper, depth data and color data are processed separately under online RPCA method, the structured sparse matrix are combined together using data fusion method for better foreground segmentation. Experiments show that our combined foreground results have a better and robust performance than results with one way alone. Keywords: Online RPCA


Matrix completion
Information fusion

1 Introduction Online detection tasks are promising field in real-time video surveillance and other computer vision applications. Background subtraction is a frequently used method in detection tasks. A fast and well established background model is important in activity detection and video analysis. In most tasks, online technique is in great demand and is much more efficient than offline technique. Under Robust Principal Component Analysis (RPCA) framework, online processing needs less storage space than batch processing in traditional RPCA framework. Robustness is important for the usability of surveillance system. Information fusion of different sensors is widely utilized to decrease false alarms. Depth data is a supplementary information to color data, it takes advantages in detection situations like shadows, color camouflage, and illumination changes. The advent of low-cost RGBD sensor (Microsoft Kinect, which is used in games at the beginning) triggers wide applications in computer vision. From the reading literatures, we can see that there are four main ways to do information fusion. First, fusion with channels. As mentioned in [1], the input RGB channels are added with a fourth channel - depth data, then codebook algorithm is applied with the fourchannel input data. Second, fusion with weight [2, 3]. Algorithms are applied to color data and depth data independently. Then two results are combined together using weights or tradeoffs. The third strategy is that when depth data is reliable, use the result obtained with depth data, otherwise use RGB result [4]. The fourth way to combine color and depth data is to apply a supervised learning refinement framework to reextract features of the color and depth results [5].

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In this paper, we proposed to utilize the online background modeling with color and depth data. With a fast optimization process we could get an estimated back-ground scene in a very short time, with a structured sparse premise, we could get a structured foreground, with information fusion, we could get a robust segmentation. In conclusion, this paper proposed an extended and refined method for background modeling and foreground segmentation.

2 Depth Map Data from Microsoft Kinect sensor are raw data, RGBD datasets used in this work are captured by Microsoft Kinect sensor, the raw depth data is denoted as z, the depth map can be normalized in this way, d¼

1 z 1

1  zfar

znear



1 zfar

 255

ð1Þ

Where znear and zfar denote the nearest and farthest raw depth.

3 Online RPCA Framework 3.1

Background Initialization

In this paper, we use fast RPCA proposed in [7] for long video matrix decomposition to make a fast background estimation for video. Compared with bilateral random projections (BRP) [8] which was frequently used in algorithms to rapidly generate low ranks, our initialization is more accurate. minfkZ k þ kkEk2;1 g; X ¼ XZ þ E

ð2Þ

Define Z  ¼ Vr W  , E ¼ X  XVr W  , (2) can be reformulated as,

minkV r W  k þ k
U r Sr ðV 0  W  Þ
2;1

ð3Þ

Corresponding augmented Lagrangian is,


l
0 V  W  ðV 0  W  Þ þ LðW; Q; LÞ¼kW  k þ k
Sr ðV 0  W  Þ
2;1 þ
2
r


2 L

l
F

ð4Þ

Define Q ¼ ðV 0  W  Þ; and applying ADM to augmented Lagrangian, we could get the optimized low rank matrix and sparse matrix.

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And below we give pseudo-code for the estimation process in algorithm 1.

3.2

Online RPCA Optimization

Online RPCA framework assumes the video background has little variations that can model background scene with low rank, while the sparse component can model foreground. X ¼ ½x1 ; x2 ; . . .; xn  2 Rdn is an image sequential matrix with each column representing a vectorized image, Online RPCA optimization is proposed to decompose the input sequential matrix X in the following way, minf

 1 kLk2F þ kRk2F þ kkE k2;1 g; X ¼ LRT þ E 2

ð5Þ

where k is a tradeoff parameter. Denote r as the rank. While in equivalent (6), L 2 Rdr denotes the subspace basis and R 2 Rnr denotes the corresponding samples coefficients. Thus the optimization problem in (6) can be rewritten in the following way. min

   
2 1 l
kLk2F þ kRk2F þ kkE k2;1 þ
X  LRT  E
F 2 2

ð6Þ

wherein the quadratic part is the constraints equation of (6) being put into the objective function, l is penalty parameter. Considering that the sample set X ¼ ½x1 ; x2 ; . . .; xn  2 Rdn , solving (7) indeed minimizes the following empirical cost function, f n ðLÞ ¼

1 Xn 1 Lðxi ; LÞ þ kLk2F i¼1 2n 2n

for each sample, the loss function is,

ð7Þ

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l 1 Lðxi ; LÞ ¼ minr;e kxi Lr  ek2F þ kr k22 þ kkek 2 2

ð8Þ

when the loss of each sample is minimized, the empirical cost function is optimized. The optimization process is alternating direction method of multiplier (ADM). This solver is a refinement version to quadratic penalty method. It ensures the algorithm converging fast without decreasing any adaptability. The augmented Lagrangian representation is 1 l Lðr; e; L; Y Þ¼ kr k22 þ kkek þ \Y; x  Lr  e [ þ kx  Lr  ek2F 2 2

ð9Þ

where Y is the lagrangian multiplier. Below we give pseudo-code for the online estimation process in algorithm 2.

3.3

Foreground Combination

After applying online RPCA background/foreground segmentation on grayscale (or color) data and depth data, we could get two structured sparse matrices. Then, we

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applying OTSU thresh to these matrix, Finally, with consideration of the illumination variations, we combine these two sparse matrices by the following strategy, Illumination changes are calculated as, DI ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DH 2 þ DS2

ð10Þ

H is the hue channel in HSV color space. Considering that when illumination variations are under a certain thresholding, and the depth values are in a valid range, the color and depth are both reliable. When light is dark, and the color variation is hard to distinguish, depth data are of high credibility. If there are great changes in illumination variations, the depth data are as the main reference until the light gets stable.  EC \ ED ; foreground mask ¼ ED ;

DI\e ½DI\e \ DC [ a \ DD\b [ DI [ e

ð11Þ

For example, the foreground in random image from ShSeq is processed in the following way (Fig. 1),

Fig. 1. Foreground segmentation procedure. (a) DH (b) DS (c) E of color data (d) E of depth data (e) Combined foreground mask.

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4 Analysis of Experimental Results Test the color sequence and depth sequence from RGBD datasets [9] separately under online RPCA framework, then combine the results. Experiments are conducted with matlabR2015b. Set parameters experimentally. The result is encouraging (Figs. 2, 3, 4, 5, 6).

Fig. 2. Original images from dataset from ColCamSeq, ShSeq, GenSeq in [9].

Fig. 3. Corresponding depth images after depth map computation.

Fig. 4. Background initialization with gray data.

Fig. 5. Background initialization with depth data.

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Fig. 6. Corresponding foreground segmentation results with online RPCA framework.

In conclusion, experiments show that our online RPCA framework with color and depth clues shares better performance in computation efficiency and detection efficiency. The results are encouraging. In the future, better information fusion methods will be further studied.

References 1. Fernandez-Sanchez EJ, Rubio L (2014) Background subtraction model based on color and depth cues. Mach Vis Appl 25(5):1211–1225 2. Camplani M, del Blanco CR (2002) Advanced background modeling with RGB-D sensors through classifiers combination and inter-frame foreground prediction. Household Appliances Mag (3):20–21 3. Tian D, Mansour H, Vetro A (2006) Depth-weighted group-wise principal component analysis for video foreground/background separation. Mech Eng (5):64–66 4. Nguyen, V-T, Vu, H (2006) An Efficient Combination of RGB and Depth for Background Subtraction. Mech Eng (5):64–66 5. Liang Z, Liu X, Liu H (2006) A refinement framework for background subtraction based on colour and depth data. Mech Eng (5):64–66 6. Fu H, Wang B, Liu H (2018) Online RPCA on Background Modeling. In: Jia Y, Du J, Zhang W (eds) proceedings of 2018 Chinese intelligent systems conference. Lecture notes in electrical engineering, vol 529. Springer, Singapore 7. Fu H, Wang B, Liu H (2017) Fast robust PCA on background modeling. In: Jia Y, Du J, Zhang W (eds) proceedings of 2017 Chinese intelligent systems conference. Lecture notes in electrical engineering, vol 460. Springer, Singapore 8. Zhou T, Tao D (2011) GoDec: randomized lowrank & sparse matrix decomposition in noisy case. In proceedings of the 28th international conference on machine learning, pp 33–40 9. Camplani M, Salgado L (2014) Background foreground segmentation with RGBD kinect data: an efficient combination of classifiers. J Vis Commun Image Represent 25:122–136

Research on Vehicle Forward Target Recognition Algorithm Based on Vision and MMW Radar Fusion Guizhen Yu, Sijia Zhang, Huan Niu, Bin Zhou(&), Guoqiang Liu, and Da Li Beihang University, Beijing 100191, China [email protected]

Abstract. Vehicle forward target recognition is the most concerned part in the field of environmental perception. In order to overcome the limitation of single sensor in target recognition, this paper proposes a forward target perception algorithm based on fusion of camera and millimeter wave (MMW) radar. Considering the characteristics of object and sensor, this paper divides vehicle forward targets into two categories: close-range target and distant target. For the close-range target, the target information obtained by the two sensors is matched and fused at the data level by using object recognition, monocular vision ranging, Kalman filter and other algorithms. For the distant target, the initial position is determined by the radar detection point, and the target is accurately classified by the visual algorithm. Experimental results show that the proposed algorithm can effectively reduce the rate of missed detection and improve the target stable recognition distance to 90 m. Besides, more accurate and abundant target information can be obtained by this method. Keywords: Region of interest Sensor fusion


Close-range target
Distant target


1 Introduction In recent years, information fusion and comprehensive judgment of multiple sensors have become a new trend to improve the safety of autonomous driving and enable vehicle environmental perception. And the information acquisitioning ability of camera and the weather adaptability of the MMW radar make them the two most commonly used sensors in the field of information fusion. In early studies, multi-sensor information fusion algorithm simply overlaps information at the data level. However, with the continuous progress of radar information processing algorithms and visual algorithms, feature-based and decisionmaking fusion methods have attracted more and more attention from researchers. Chavez-Garcia et al. [1] proposed to use radar and camera raw data as input to detect moving objects, and then use D-S evidence fusion theory to fuse the information of these moving objects. Although the detection accuracy is improved compared with using single sensor, the image traversal processing is required, which is difficult to © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 518–528, 2020. https://doi.org/10.1007/978-981-32-9698-5_58

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satisfy people’s requirements on real-time performance. Alencar et al. [2] suggested to use K-means clustering analysis, SVM and Nuclear principal component analysis to comprehensively analyze camera data and MMW radar data, however, this method is only applicable to the recognition of close-range targets in fine weather. Many researchers [3–5] have proposed to preliminarily determine the region of interest (ROI) from the detection target in-formation of MMW radar, and then use AdaBoost, active contour detection, frame difference method or other processing methods to confirm the targets. These methods mainly rely on the detection results of MMW radar. If the target is in the radar detection blind area, it cannot be detected, and a lot of original data information will be lost. Based on this, this paper divides the target into distances according to the characteristics of the sensor and the target, and presents corresponding recognition algorithms, so as to achieve accurate perception of surrounding targets.

2 System Architecture and Principles The recognition algorithm proposed in this paper only considers targets within 90 m. Objects at close range are relatively occupy more pixels in an image and can be observed by two sensors at the same time in most cases, requiring high accuracy of horizontal and longitudinal distance. And objects at a distance can usually only be detected by radar. Take these factors into account, we adopt different strategies to identify objects with different distances. The overall frame diagram is shown in Fig. 1.

Distant object

MMW Radar

Camera

Filtering algorithm Life cycle algorithm

Extract the region of interest Projection transformation

Object classification algorithm

Sensor joint calibration

Output fusion result

Camera

Object recognition algorithm

monocular vision distance measurement

Target associated Target status update Sensor weight distribution

Close-range object

Fig. 1. The overall frame diagram of algorithm

In this paper, objects within 50 m are considered as close-range targets, while other objects are considered as distant targets. 2.1

Sensor Calibration

Sensor calibration is the basis of information fusion, and its main purpose is to achieve spatial unity between sensors. Accurate calibration results will simplify the calculation and bring convenience to the algorithm design. Based on the principle of perspective imaging and coordinate axis transformation, the following equation is established:

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2 3 2 u 1=dx Zc 4 v 5 ¼ 4 0 1 0

0 1=dy 0

32

u0 f v0 5 4 0 1 0

0 0 f 0 0 0

3

0  R 05 T 0 1

2 3  XW 7 T 6 6 YW 7 1 4 ZW 5 1

ð1Þ

Where, (XW, YW, ZW), (u, v), ZC respectively represents the coordinates of the world coordinate system, pixel coordinate system and camera coordinate system. R is the rotation matrix, which is determined by yaw angle, pitch angle and roll angle. T is the translation matrix, f is the focal length, u0 and v0 are the number of horizontal and vertical pixels that differ between the pixel coordinates of the image center and the pixel coordinates of the image origin. 1/dx and 1/dy represent the number of pixels per unit length in the x and y directions, respectively. In this paper, the LevenbergMarquardt algorithm is used to solve the problem [6, 7]. 2.2

Information Preprocessing

For radar, CAN messages are obtained. After parsing them, the distance, speed and other information of the object can be obtained. For radar points whose indexes such as horizontal distance, longitudinal distance, velocity and probability of target existence are all within a certain threshold, this paper considers that they are generated by the same target and directly cluster them. For the abnormal points that do not satisfy the continuity of space and time, remove them from the target list, for example: ti/te < threshold or |y(n + 1) – y(n)|  threshold, where, ti stands for invalid cycle, te represents for effective period, n is the sampling point number and y is distance. At the same time, the radar detection target is tracked to prevent frame loss. For camera, picture sequences are obtained. In this paper, convolutional neural network [8] is used to process image sequence, includes offline training and online testing. The specific flow chart is shown in Fig. 2. Training set with labels Forward propagation algorithm + Gradient descent algorithm + Back-propagation algorithm Image sequence

Feature extraction network + Candidate area network + Fast region convolutional neural network Off-line training model

Bounding box Object catagory

Fig. 2. The flow chart of Image sequence preprocessing

After the position of the target in the image is determined by the visual algorithm, the real distance between the target and vehicle is calculated by using the monocular vision ranging method [9].

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Sensor Fusion

2.3.1 Spatiotemporal Unification Spatiotemporal unification is the process of transforming data from different sources to the same spatiotemporal reference, including time synchronization and space alignment. Time synchronization is to unify the time of each sensor to the reference standard time. The space pair criterion is to establish the transformation relation from the different coordinate system of each sensor to a unified reference coordinate system. In the information acquisition, the method of multi-thread processing is adopted, one thread is responsible for acquiring and processing image data, and another is responsible for acquiring and processing radar data. When a frame of data is acquired, it is stored separately. When the fusion is triggered, the nearest radar data and video data are extracted to ensure the time synchronization to the greatest extent. For the space alignment, the radar target point is projected into the image according to the parameters obtained by the joint calibration of the sensor. 2.3.2 Target Association Due to the sensor measurement error, for each of the target in the image, there may exist zero, one or more observations. However, theoretically, each target has two observations at most. Therefore, an effective method is needed to establish the data correlation between the predicted state value and the observed value of the target. In this paper, we choose Mahalanobis distance to match the observed values. Compared with other similarity measurement methods, it can exclude the interference of the correlation between variables and fully consider the difference between each component of the vector. The Mahalanobis distance between the predicted state value and the observed value of the target is shown as follows: D¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½X ðkjk  1Þ  Z ðkÞT S1 ½X ðkjk  1Þ  Z ðkÞ

ð2Þ

Where X(k|k–1) represents the state value at time k predicted based on the state value at time k–1, Z(k) represents the measured value at time k. For the region where the observations are most likely to occur, Bar-shalom and Fortmann [10] has proposed the following definition:  Vk ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z : ½X ðkjk  1Þ  Z ðkÞT S1 ½X ðkjk  1Þ  Z ðkÞ  c

ð3Þ

Normally, when c = 3, statistically more than 99.8% of the valid observations will be included. In addition, the radar detection target points are projected onto the image in this paper, and the nearest radar points in the frame are taken as the matching points corresponding to the image. 2.3.3 Target Status Update Target state update refers to prediction of the current state through the previous state and correction of the current observation state to ensure a stable change of the output

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state. In this paper, Kalman filter is used to complete this task. According to the research object, the state equation of the system is given as: xi;k ¼ Fk xi;k1 þ vk ; i ¼ 1; 2; . . .; N

ð4Þ

Where xi,k is the state vector of the i-th target at time k. vk is a gaussian white noise with an average value of 0, its covariance matrix satisfies:   E vk ; vTk ¼ Qk

ð5Þ

The relationship between the observed value and the state value satisfies: zi;j;k ¼ Hj xi;k þ wj;k ; j ¼ 1; 2; . . .; M

ð6Þ

Where, zi,j,k represents the value of the i-th target observed by the j-th sensor at time k. Hj is the transformation matrix. wj,k is a gaussian white noise with an average value of 0, which is related to different sensor models, its covariance matrix satisfies:

E wj;k ; wTj;k ¼ Rj

ð7Þ

After the status update of time k–1 is completed, the state value and observed value of time k can be predicted as follows: 

^xi:kjk1 ¼ Fk ^xi;k1jk1 ^zi:j;kjk1 ¼ Hj;k ^xi;k1jk1

ð8Þ

Then the status of time k is updated to: ^xi:j;k ¼ ^xi;kjk1 þ Kij cij

ð9Þ

This is the result of the status update of the i-th target based on the measured value of the j-th sensor. Kij represents the Kalman gain matrix, and cij is the residual vector between the observed value and the predicted value. And the covariance matrix between predicted and observed values is defined as follows: Pi;kjk1 ¼ Fk Pi;k1jk1 FkT þ Qk

ð10Þ

Besides, Eq. (11) represents shows how to update the Kalman gain matrix.

1 Kij ¼ Pi;kjk1 HjT Hj Pi;kjk1 HjT þ Rj

ð11Þ

When all parameters have been calculated, it is necessary to complete the update of the state value of this frame, which is the weighted average of predicted states from each observation value:

Research on Vehicle Forward Target Recognition Algorithm

^xi;kjk ¼

XMi;k j¼0

bij^xij

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ð12Þ

Considering that the measurement errors between the camera and the MMW radar are different in various scenes, it is proposed to calculate the horizontal and longitudinal measurement errors of the camera and the MMW radar at different distances by dividing scenes, and take this to determine the weight, bij, in data fusion. In order to make the whole state update process self-cyclic, we also need to update the covariance of the state vector: Pi;kjk ¼

h i T b P  K S K ij ij i;kjk1 ij ij þ gij j¼0

XMi;k

ð13Þ

Where, ηij is the hypothesis deviation:   T gij ¼ ^xij  ^xi;kjk ^xij  ^xi;kjk

2.4

ð14Þ

Distant Target Recognition

When the vehicle is running at a high speed, the distant target will pose a threat to the normal running of the vehicle, and if not effectively identified, it will cause a major accident. Table 1. The longitudinal range detected by different data sources (m) No. ME Error Radar Error Real

1 8.06 3.1% 8 2.3% 7.82

2 17.50 5.4% 16.6 0% 16.6

3 30.81 4.2% 29.4 0.5% 29.56

4 31.88 3.4% 43.6 0.6% 43.36

5 50.50 9.6% 55.8 0.1% 55.85

6 55.75 10.5% 62.2 0.2% 62.3

7 63.75 12.2% 72.6 0% 72.6

8 71.13 11.5% 80.2 0.3% 80.4

9 79.81 13.9% 92.6 0.1% 92.66

The above fusion method is based on the fact that both camera and radar can acquire the effective data of the target, so as to carry out data level fusion. However, as can be seen from Table 1, for targets within 50 m, the longitudinal distance obtained by Mobileye is relatively accurate, while for targets beyond 50 m, the relative error is more than 10%, which makes it difficult to correctly match with radar data. And the ordinary target recognition algorithm cannot identify targets beyond 50 m at all. As for radar, by contrast, can obtain a more accurate longitudinal distance value, but it may return a lot of useless information. Based on this, for distant objects, this paper adopts another fusion method: the obtained radar points were projected into the picture according to the spatial conversion relation, and the size of bounding-box was roughly determined according to the distance. Then, using a caffenet-based algorithm to classify the object in the target box.

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The principle is similar to the target recognition algorithm. If it was the desired target, the corresponding information was returned. The specific frame diagram is shown in Fig. 3.

Data Preprocessing

Camera

Region of interest

Object Classification

Car or Preson

Yes

Unity of time and space

MMW Radar

Data Preprocessing

Data fusion

Effective target information

Fig. 3. The frame diagram of distant object detection algorithm

The size of the bounding-box (ROI) is related to the distance and image size. And it can be estimated by statistical results. For a picture of 640*480, the corresponding values of pixel size and longitudinal distance of objects in the image obtained by the experiment are shown in Table 2.

Table 2. Table of pixel values of different objects at different distances Longitudinal distance (m) 50 55 60 65 70 75 80 85 90

Horizontal pixel Ped Car 12 41 11 37 11 34 11 31 11 30 10 28 10 27 10 24 9 22

Vertical pixel Ped Car 33 32 28 30 27 30 27 28 25 25 25 24 25 23 24 21 24 21

The corresponding formula is obtained by fitting the width value of the horizontal and vertical pixels of the target. For pedestrians, the fitting formula for their distance and pixel width is: 

horizontal : y ¼ 15:64e0:005651x vertical : y ¼ 7:825e þ 09e0:4235x þ 34:49e0:004159x

For vehicles, the fitting formula is:

ð15Þ

Research on Vehicle Forward Target Recognition Algorithm



horizontal : y ¼ 0:33x þ 61:24 vertical : y ¼ 0:2967x þ 46:44

525

ð16Þ

After determining the ROI, the target classification algorithm is used for classification. It mainly includes two sub-steps: feature extraction and feature classification. Feature extraction mainly includes convolutional feature extraction, feature activation and mean sampling, which is similar to the aforementioned target recognition algorithm. And SoftMax function is adopted for feature classification in this paper. By using the above method, the probability that the target belongs to a certain category can be finally obtained. We select the category with the largest probability as the classification category of the current target. Other relevant information about the target is determined by the radar.

3 Experiment and Test Results We built an experiment vehicle platform with two sensors, including a webcam with lenses 8 mm and resolution of 640*480 pixels at 25 frames per second and a MMW radar with a distance range of 3–180 m at 20 frames per second. And all sensors are calibrated. A visual interface is designed to display the joint calibration results of the two sensors, as shown in Fig. 4.

Fig. 4. The visual interface of sensor joint calibration results

It can be seen that under the current parameters, the radar points can be well projected onto the image, that is, all projection points are located at the position of the angular reflector. For close-range targets, Fig. 5 shows the vehicle forward target recognition result, where, the red dots represent the target identified by the camera, the blue dots stand the target detected by the radar, and the green dots are the target that the fusion system outputs. It can be seen that the taxi in the left lane (No. 1) is located outside the radar detection area, so it is only recognized by the camera. Because of the limited range of object recognition algorithms, the white (No. 6) car and the red (No. 4) car in the distance are only detected by radar. In general, we believe that only the target of the

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current lane and the adjacent lane will cause danger, so the two leftmost target points (No. 1, 2) are removed in the output of fusion algorithm.

1

3 4

2

5

7

6

Fig. 5. Vehicle forward target recognition result

Part of the data for car 5 from different information sources is shown in Table 3. Table 3. Horizontal and vertical distance comparison of data sources Frame Fusion data x(m) y(m) 1 –0.36847 29.9723 2 –0.364218 30.330164 3 –0.355234 30.204264 4 –0.35625 30.237741 …… 39 –0.0351 31.73458 40 –0.0641 32.047886

Radar x(m) –0.52 –0.52 –0.52 –0.48

data y(m) 30.69 30.72 30.87 30.96

Camera data x(m) y(m) –0.276939 29.2546 –0.276939 29.2546 –0.25228 28.7169 –0.263634 29.2546

0.12 32.04 –0.0984 0.08 32.19 –0.1415

29.8128 32.4084

Where, x represents horizontal distance, y stands vertical distance. By comparing the fusion data with the camera and radar data, it can be seen that the horizontal distance is more biased toward the camera data, and the longitudinal distance is closer to the radar data in the fusion data, which is in line with the actual situation. By observing each frame data of the selected video, the number of targets identified by different data sources is counted, as shown in Table 4. This result does not filter the fused data, that is, vehicles in non-adjacent lanes were also counted.

Table 4. The number of targets identified by different data sources Frame Fusion Radar Camera

1 8 5 5

2 7 5 5

3 7 5 5

4 7 6 5

5 7 6 5

6 7 6 5

…… …… …… ……

40 7 6 5

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In addition to the number of targets, horizontal distance, vertical distance, speed and type information of the target will be output after fusion. It means that more abundant information can be obtained by fusing. For distant targets, Fig. 6 shows the final recognition results, where the blue dots represent targets detected by the MMW radar. The red and white rectangles indicate targets classified as vehicles and unknown obstacles, respectively.

Fig. 6. Distant target fusion algorithm result diagram

The MMW measurements corresponding to the above targets are shown in Table 5. Table 5. The longitudinal range detected by MMW radar (m) Object 3(a) 3(b) 3(c)

1 49.61 87.8 114.62

2 75.40 76.35 76.52

3 163.95 164.35 164.15

4 121.55 121.5 121.67

5 87.67 87.21 87.62

6 66.64 66.72 66.77

7 50.84 50.87 50.73

For the white vehicle in the Fig. 6, it can be stably classified as a vehicle. For the black vehicle, it can be seen that as its longitudinal distance increases, although the MMW radar can obtain its distance and determine the location of the ROI, the target pixel value is too small to conduct accurate classification. According to the statistics and analysis of the experimental results, the fusion method proposed in this paper can improve the detection distance of the target to 90 m. And according to the statistics, in good road conditions and weather conditions, the recognition accuracy of distant targets is above 93.4%.

4 Conclusion For the close-range target, the correlation between the measured value and the observed value is established through the Mahalanobis distance. And the target state information is updated by Kalman filter algorithm. For the distant target, the radar detection value is projected into the image to obtain the ROI, and the target classification algorithm is used to complete the discrimination. Several experiments were conducted using datasets from real driving scenario to verify the algorithm proposed in this paper. The results show that

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it can effectively reduce the rate of missed detection and improve the target stable recognition distance to 90 m. In addition, compared with the single sensor recognition method, this method can provide more accurate and richer target information. Acknowledgments. This work was supported by the National Key Research and Development Program of China (2016YFB0101001) and the Beijing Municipal Science and Technology Project under Grant # Z181100008918003. The authors would also like to thank the insightful and constructive comments from anonymous reviewers.

References 1. Chavez-Garcia RO, Vu T-D, Aycard O (2014) Fusion at detection level for frontal object perception. In: Intelligent vehicles symposium proceedings 2014. IEEE 2. Alencar FARR, Rosero LA, Filho CM, Osorio FS, Wolf DF (2015) Fast metric tracking by detection system: radar blob and camera fusion. In: 2015 12th Latin American robotics symposium and 2015 3rd Brazilian symposium on robotics (LARS-SBR). IEEE 3. Xiao W, Xu L, Sun H, Xin J, Zheng N (2016) On-road vehicle detection and tracking using MMW radar and monovision fusion. IEEE Trans Intell Transp Syst 17:2075–2084 4. Siyang H, Xiao W, Linhai X, Hongbin S, Nanning Z (2016) Frontal object perception for intelligent vehicles based on radar and camera fusion. In: Control Conference. IEEE 5. Guangyao Z et al (2017) Tramway obstacles detection based on information fusion of MMV radar and machine vision. Chin J Internet Things 1(02):76–83 6. Zhengyou Z (2000) A flexible new technique for camera calibration. IEEE Trans Pattern Anal Mach Intell 22(11):1330–1334 7. Heikkila J, Silven O (1997) A four-step camera calibration procedure with implicit image correction. In: Computer vision pattern recognition, CVPR. IEEE Computer Society, pp 1106–1112 8. Liu W, Anguelov D, Erhan D, Szegedy C, Reed S, Fu C-Y, Berg AC (2016) SSD: single shot multibox detector. In: European conference on computer vision, pp 21–37 9. Lei G et al (2006) Study on realtime distance detection based on monocular vision technique. J Image Graph 11(1):74–81 10. Bar-Shalom Y (1987) Tracking and data association. Academic Press Professional, Inc

Research on Vehicle Forward Pedestrian Recognition Based on Multi-line LIDAR Chenyang Guo, Guizhen Yu(&), Li Zhang, Huan Niu, Bin Zhou, Zhangyu Wang, and Da Li School of Transportation Science and Engineering, Beijing Advanced Innovation Center for Big Data and Brain Computing, Beijing Key Laboratory for Cooperative Vehicle Infrastructure Systems and Safety Control, Beihang University, Beijing 100191, China [email protected]

Abstract. Pedestrians are one of the most important elements in traffic scenes. In autopilot system, pedestrians need to be accurately detected. We found the latest research that 3D light detection and ranging (LIDAR) sensors can provide more accurate pedestrian location information. In this paper, the AdaBoost algorithm is used to improve the accuracy of the support vector machine (SVM) and high-accuracy pedestrian detection based on real-time 3D point cloud data. The first step is to process 3D points to 2D grid, followed by using kmeans clustering algorithm to extract candidate points of the pedestrian. Next, nine features are chosen to train the SVM, the AdaBoost iterative process is used to reduce the further error rate to meet the classification requirements. This method has achieved significant progress in our experiment, the average classification accuracy has been improved to 92.4% per scan. Keywords: LIDAR


Pedestrian detection
AdaBoost

1 Introduction Autonomous vehicles are commonly equipped with sensors such as laser, radar, camera, GPS and inertial measurement unit which helps vehicles to obtain surrounding information. Method for identification of pedestrian and vehicle is an important technology in the field of autopilot environmental awareness. Methods includes thresholdbased detection, point cloud clustering, SVM, features detection, CNN are commonly used for identification of target. But only a few of them can be robust in low light conditions. Combining target identification and target classification can improve the accuracy and robustness of the identification algorithm, however, its real-time performance is difficult to meet autopilot needs. A novel method is proposed to improve the real-time performance of the identification algorithm. LIDAR sensor is chosen to detect information around vehicles. The machine learning network is used to classify the point cloud to avoid real-time degradation caused by longer algorithm execution time. The AdaBoost algorithm and the SVM are chosen as a stronger classifier and basic classifier to avoid a sharp decline in detection performance. Assigning different weight parameters according to the error © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 529–538, 2020. https://doi.org/10.1007/978-981-32-9698-5_59

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rate of the SVM, and the weights obtained from the last accumulation are output as classification results.

2 Related Work Image target detection based on deep learning network performs well in good light conditions, but its detection ability reduce significantly in the dark or low light conditions. Multi-line laser radar has been used for target detection in low light conditions and many detection algorithms have been proposed to process point cloud data using a machine-learning method. Yamamoto et al. [1] proposed a pedestrian recognize method using active scan LIDAR, which including depth map and shape map. This paper gave a complete method to detect pedestrian using a single LIDAR sensor but simply relied on setting parameter threshold resulting in miss detection. Jun et al. [2] used a high-resolution LIDAR to detect object features. They trained the SVM classifier to complete the segmentation, which was regarded as a weak classifier compared with the vision classifier. Lin et al. [3] presented a method to distinguish bicyclists from pedestrians through training an 8-dimensional SVM, the target velocity was introduced as one of the features. By constructing decision surface plane functional and RBF kernel, the accuracy of target recognition was improved. Lin et al. [4] used CNN features and hand-craft features to train the model to detect pedestrians. The experiment showed a better result, but the recognition rate was lower compared with the near targets. New features were proposed by Kidono et al. [5], including slice features and reflection intensities of points, these novel features were used to improve the accuracy of classification results. Based on the different height of human body points, Spinello et al. [6] trained a group of classifiers to detect the pedestrian candidate points. Teichman et al. [7] proposed a mathematic method which uses the log odds estimators, this method spilled the point cloud into pedestrian, vehicle, bicycle, and background. The Bayesian approach was used by Dewan et al. [8] They utilize motion models based on a public dataset to detect pedestrian without prior information about objects. The 2.5D point data map was built by Asvadi et al. [9] with per scan, the updated map will be compared with the last map to compute a motion grid. Kaestner et al. [10] present an object detection algorithm to extract the object with different size and shape. Huang et al. [11] introduced a scheme to label the 3D point cloud. Objects will be redefined with different colors based on their attributes, so they could use the 3D CNN to build the model. Tang et al. [12] introduced a method to improve the sparse problem of longdistance target, they used distance-aware expansion approach which maps the 3D plane to 2D.

3 Proposed Method Figure 1 shows the details of the algorithm. It is an overview of our method for processing raw data from 3D space to the 2D plane, Fig. 2 shows the vehicle body coordinate system, the front of the vehicle and the LIDAR x-axis positively coincide.

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Fig. 1. Overview of our pedestrian detection framework.

Fig. 2. LIDAR coordinate system.

3.1

Pre-process

The first step is tantamount to map the point cloud vertically to the x-y plane while preserving the height of the point cloud and the reflectivity information. The 2D plane cloud obtained is meshed. Choosing this method to point cloud partitioning, adding an index of each point, so as to calculate the variable parameters of the cluster in each grid. After this, filtering and extraction operations are made on the two-dimensional point cloud data according to the set threshold. In order to accurately describe the scanning range, a fan-shaped grid area is set up which is the radius of the sector area. The grid cell size in the radial direction is fixed as 10 cm. The position of rotating clockwise 15° along the y-axis, with a maximum opening angle of 165°. The minimum horizontal angle is 10°. Before extracting the pedestrian candidate point cloud, we first remove the ground and other non-target points. The Random Sample Consensus algorithm is utilized to detect and extract the ground [13]. Experiment show that plane extraction effect is better when the error is 0.07 m. The extraction results are presented in Fig. 4. Four parameters are set as showed in Table 1 to retain the candidate point cloud. Weight coefficient is established by calculating the parameter matrix of the point cloud in each cell. The pedestrian candidate points are shown as Fig. 5, selected points rendered in white as compared with other points rendered in red (Fig. 3).

Fig. 3. Raw data of point cloud with pedestrian.

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Fig. 4. Ground extracts and removes.

Fig. 5. Pedestrian candidate points.

Table 1. Parameter threshold of pedestrian candidate points. Parameter Min_Points Points_Range_Z

Range/threshold 7 1.6  f2 < 1.8 1.8  f2 < 2.1 Points_Range_Y The points range in y-dimension 0.3  f3 < 1.0 1.0  f3 < 1.5 Points_Y_Variance The variance of y-dimension in a grid’s 0.1  f4  0.4 smallest unit

3.2

Description The minimum number of point cloud The points range in z-dimension

Weights 1 1 0.5 1 0.5 1

Feature-Extraction

We use a semantic segmentation editor tool to hand selected candidate points in the web, based on point cloud data format file (PCD). A total of 140 frames of point cloud data were marked, and pedestrians within 40 m in front of the vehicle are selected and marked with a point cloud index. Selected clouds in different distance and posture are shown as Fig. 6. Then nine parameters are chosen as the hand-craft-features, shown in Table 2. The number of points and minimum distance of the cluster are chosen, Premebida et al. [14], these parameters describe the characteristics of the low dimension of the point cloud cluster. We also choose the parameter f3 which is the volume of the cluster as a low dimension characteristic. Compared with cars, the cluster of the pedestrian has a special range of height to length ratio. Feature f6 is adopted from Navarro-Serment et al. [15], shown in Eq. 1, parameter n represents the number of point cloud cluster, and m ¼ ðxd ; yd ; zd Þ, represents the point’s 3D coordinate.

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Fig. 6. Raw data of point cloud with pedestrian. Table 2. Hand-craft features. No f1 f2 f3 f4 f5 f6 f7 f8 f9

Description Dimension Number of points 1 The minimum distance of target 1 Volume of the cube 1 Cube height to length ratio 1 Cube height to width ratio 1 The covariance matrix 6 The inertia tensor matrix of the point cloud cluster 6 Histogram of oriented gradients 40 The covariance matrix in 2D 9

f6 ¼

1 Xd
Þðmi  m
ÞT ðm i  m 1 d1

ð1Þ

f7 is the inertia tensor matrix of the 3D point cloud, shown in Eq. 2. 2P 6 f7 ¼ 4

d 2 2 i¼1 ðyd þ zd Þ P d xd yd Pi¼1 d i¼1 xd zd

3 Pd Pd x y x z d d d d Pi¼1 Pd i¼1 2 7 d ðxd þ z2d Þ y z 5 i¼1 Pd Pd i¼1 2 d d2 i¼1 yd zd i¼1 ðxd þ yd Þ

ð2Þ

Hog is an image descriptor that uses gradient direction histogram features to characterize the human body, extract body shape and motion information. Before calculating relevant parameters, the 3D point cloud is initially mapped to the y-z plane and deleting the noise point where the gradient is too large. Trimming the edge of the 2D image smoothed. Then the first-order differential template is utilized to find the approximation of the gradient, the gradient values in two directions are shown as Eq. 3. Gh ðx; yÞ ¼ f ðx þ 1; yÞ  f ðx  1; yÞ 8x; y Gv ðx; yÞ ¼ f ðx; y þ 1Þ  f ðx; y  1Þ 8x; y

ð3Þ

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The calculation process of the gradient direction based on the calculated gradient value component is shown as Eq. 4. And covariance matrix of the 2D point cloud cluster is shown as Eq. 5. 0

hðx;yÞ ¼ arctanðGh ðx; yÞ=Gv ðx; yÞÞ hðx; yÞ ¼ 2 f9 ¼

3.3

Pd

n

hðx;yÞ þ phðx;yÞ\0 hðx;yÞ

ðxd 
xÞ2 d1 4 Pd ðx 
xÞðyd 
yÞ i¼1 d d1 i¼1

Pd

ð4Þ 3

ðxd 
xÞðyd 
yÞ Pd d1 2 5 ðy 
yÞ i¼1 d d1 i¼1

ð5Þ

Pedestrian-Classification

SVM Training The SVM is a method to deal with the classification problem, the function formula of SVM is shown as Eq. 6. f ðxÞ ¼ ðx; ;ðxÞÞ þ b

ð6Þ

In order to avoid a single category that will reduce the classification effect, we randomly selected 50% of the non-pedestrian point cloud as a negative sample. Before training the SVM model, in order to prevent the feature from being too larger or too small to affect the calculate speed. A scaling operation with a range of 0-1 is performed on nine parameters of the two classifications, and a scaling factor d is obtained. The type of SVM is selected as c-svc and the parameter c is selected as the penalty factor. The Gaussian kernel function is chosen as the radius basis part to make the data linearly separable and map the original features to multidimensional. The function form is shown as Eq. 7. (  ) x  xf 2    k x  xf  ¼ exp 2c2

ð7Þ

xf representative kernel center, c is the width parameter of the function and radial range of the control function. When the distance between a point and the function center is large, the value of the kernel function is 0, and the distance is very similar, the value of the kernel function is 1 [16]. Even if the classifier has a high prediction accuracy for the known labels, it cannot guarantee the same accuracy for the test set. A k-fold crossvalidation method is used to improve the accuracy of the prediction. AdaBoost and SVM The AdaBoost algorithm is a kind of boosting lifting algorithm. By repeating learning, several weak classifiers are recombined into a strong classifier according to a certain

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ratio. It refers to the boosting algorithm with loss function as an exponential loss. The algorithm classifiers include two steps, the addition model and the forward step. Equation 8 represents the process of adding the weak classifiers into a strong classifier, where hðx; am Þ represents each weak classifier, and am is the best classification parameters of the weak classifier, bm is the proportion of weak classifiers, and q represents the classifier weight and classification parameters set. The forward stepping model is shown in Eq. 9. Fm ðx; qÞ ¼

Xn m¼1

bm hðx; am Þ

Fm ð xÞ ¼ Fm1 ð xÞ þ bm hm ðx; am Þ

ð8Þ ð9Þ

we choose the optimal value of the c parameter that is large enough to construct the Gaussian kernel in the weak classifier. The AdaBoost-SVM process [17] is described as shown in Table 3.

Table 3. AdaBoost-SVM algorithm.

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4 Results and Experiments The verification dataset consists of 440 randomly selected pedestrian point clouds and 600 non-pedestrian samples. Recognition accuracy, F-measures and mean-averageprecision statistical methods are used to verify algorithm validity. F-measures refers to the weighted of the accuracy and recall rate which avoids the mismatch of the model error description due to the conflict between the accuracy and recall rate. We also calculate the number of targets identified through our models. The numbers of targets identified at different distances as shown in Table 4. Table 5 shows the performance of our methods.

Table 5. Performance of algorithm. Methods Add slice and reflection intensities features [5] 3D CNN with point cloud labeling scheme [11] Distance-aware expansion approach [12] Just SVM Using SVM and AdaBoost

Accuracy 56.04% 77.30% 84.10% 88.1% 92.4%

F-measures 54.04% 57.67% 69.10% 80.4% 84.2%

MAP 69.87% 72.90% 78.83% 84.7% 87.4%

As can be seen from Table 5, compared with the simple use of the SVM model, the use of the SVM-AdaBoost model for pedestrian recognition shows a 3.8% improvement in F-measures parameter and a 2.7% improvement in MAP, indicating the high accuracy of the SVM-AdaBoost algorithm. Then the identification test for the targets of different distances is carried out. When the distance is larger than 25 m, the sparseness of the point cloud drops significantly. It can be concluded from Table 4 that the recognition rate is relatively higher in the range of 25 m, which has a certain influence on feature extraction and recognition.

5 Conclusion We propose a pedestrian recognition method based on the SVM classifier and AdaBoost algorithm which significantly improve the classification accuracy of the classifier to 92.4%. Also, taking into account the principle of the SVM classifier, the Adaboost algorithm is used to construct a stronger classifier, and the recognition effect is therefore significantly improved.

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Acknowledgments. This work was supported by the Beijing Municipal Science and Technology Project under Grant # Z181100008918003 and the National Key Research and Development Program of China (2016YFB0101001). The authors would also like to thank the insightful and constructive comments from anonymous reviewers.

References 1. Yamamoto T, Kawanishi Y, Ide I et al (2018) Efficient pedestrian scanning by active scan LIDAR. In: 2018 international workshop on advanced image technology (IWAIT). IEEE, pp 1–4 2. Jun W, Wu T, Zheng Z (2016) LIDAR and vision based pedestrian detection and tracking system. In: IEEE international conference on progress in informatics and computing. IEEE 3. Lin Z, Hashimoto M, Takigawa K et al (2018) Vehicle and pedestrian recognition using multilayer lidar based on support vector machine. In: 2018 25th international conference on mechatronics and machine vision in practice (M2VIP). IEEE, pp 1–6 4. Lin TC, Tan DS, Tang HL et al (2018) Pedestrian detection from lidar data via cooperative deep and hand-crafted features. In: 2018 25th IEEE international conference on image processing (ICIP). IEEE, pp 1922–1926 5. Kidono K, Miyasaka T, Watanabe A et al (2011) Pedestrian recognition using highdefinition LIDAR. In: 2011 IEEE intelligent vehicles symposium (IV). IEEE, pp 405–410 6. Spinello L, Arras KO, Triebel R et al (2010) A layered approach to people detection in 3d range data. In: Twenty-fourth AAAI conference on artificial intelligence 7. Teichman A, Levinson J, Thrun S (2011) Towards 3D object recognition via classification of arbitrary object tracks. In: 2011 IEEE international conference on robotics and automation. IEEE, pp 4034–4041 8. Dewan A, Caselitz T, Tipaldi GD et al (2016) Motion-based detection and tracking in 3d lidar scans. In: 2016 IEEE international conference on robotics and automation (ICRA). IEEE, pp 4508–4513 9. Asvadi A, Peixoto P, Nunes U (2015) Detection and tracking of moving objects using 2.5 d motion grids. In: 2015 IEEE 18th international conference on intelligent transportation systems. IEEE, pp 788–793 10. Kaestner R, Maye J, Pilat Y et al (2012) Generative object detection and tracking in 3d range data. In: 2012 IEEE international conference on robotics and automation. IEEE, pp 3075– 3081 11. Huang J, You S (2016) Point cloud labeling using 3D convolutional neural network. In: 2016 23rd international conference on pattern recognition (ICPR). IEEE, pp 2670–2675 12. Tang HL, Chien SC, Cheng WH et al (2017) Multi-cue pedestrian detection from 3D point cloud data. In: 2017 IEEE international conference on multimedia and expo (ICME). IEEE, pp 1279–1284 13. Douillard B, Underwood J, Kuntz N et al (2011) On the segmentation of 3D LIDAR point clouds. In: 2011 IEEE international conference on robotics and automation. IEEE, pp 2798– 2805 14. Premebida C, Ludwig O, Nunes U (2009) Exploiting lidar-based features on pedestrian detection in urban scenarios. In: 2009 12th international ieee conference on intelligent transportation systems. IEEE, pp 1–6

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15. Navarro-Serment LE, Mertz C, Hebert M (2010) Pedestrian detection and tracking using three-dimensional ladar data. Int J Robot Res 29(12):1516–1528 16. Keerthi SS (2002) Efficient tuning of SVM hyperparameters using radius/margin bound and iterative algorithms. IEEE Trans Neural Netw 13(5):1225–1229 17. Schapire RE, Singer Y (1999) Improved boosting algorithms using confidence-rated predictions. Mach Learn 37(3):297–336

An Approach of Non-stationary Harmonics Decomposition Based on Operator Approximated by Radial Base Function Ye Zeng1(&) and Qunjing Wang2 1

2

School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China [email protected] Engineering Research Center of Power Quality Ministry of Education, Anhui University, Hefei 230601, China

Abstract. With reference to the signal decomposition method based on operator, a method of approximating operator by radial basis function (RBF) is proposed. The power system frequency change is relatively small, by setting the frequency as a constant, this paper gives an algorithm that does not require iteration and calculate the instantaneous frequency, which can be directly used for the decomposition of non-stationary harmonics. Experimental results show the effectiveness of the proposed algorithm. There is a better decomposition of non-stationary fundamental wave compared with the differential operator represented by difference quotient. Compared with the signal decomposition based on ensemble empirical mode decomposition (EEMD) method, it shows that the proposed algorithm decomposes non-stationary fundamental wave without aliasing other order harmonics, and at the same time, the extracted fundamental power is larger. The algorithm also extracts other non-stationary harmonics. The result shows that constant frequency parameter is effective for decomposition. Keywords: Operator
Decomposition Harmonic
Non-stationary
EEMD




Radial basis function




RBF




1 Introduction Power system frequency can be considered constant. Non-stationary harmonics or inter-harmonics are signals whose frequency is constant and whose amplitude and phase are time-varying. Time-frequency method based on instantaneous frequency will encounter some difficulties for these signals, mainly because it has no physical meaning and cannot make further analysis based on power system such as impedance, power factor and power calculation, etc. One of the commonly used methods for nonstationary signal decomposition is based on the decomposition of spatial basis functions, such as decomposition based on wavelet bases, and the other is based on datadriven decomposition methods, such as EMD decomposition that decomposes the signal into a series of intrinsic mode functions (IMF) [1, 2]. In recent years, some scholars have proposed an operator-based adaptive decomposition and an improved null space pursuit (NSP) algorithm [3–5]. The paper is based on the decomposition of © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 539–548, 2020. https://doi.org/10.1007/978-981-32-9698-5_60

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differential operators. In general, function derivatives can be approximated by finite difference. The RBF function can approximate high order derivatives [6], and can have better accuracy than finite difference. This paper uses Gaussian RBF to approximate the differential operator, and sets the frequency as a fixed value for the non-stationary harmonic decomposition of the electric arc furnace current signal. The paper is organized as follows. The second section introduces the decomposition algorithm. The third section introduces the decomposition of the experimental signal and compares with EEMD. Conclusions are presented in the final section.

2 Analysis of Technique 2.1

Operator

The operator used in the paper is as follows
C ¼ ðd 2 dt2 þ x2 Þ2

ð1Þ

The non-stationary harmonics or inter-harmonics in the power system can be expressed as AðtÞ cosðxt þ uðtÞÞ

ð2Þ

where AðtÞ is varying amplitude and uðtÞ is varying phase. We have Cfða þ btÞ cos xt  ðc þ dtÞ sin xtg ¼ 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi )C ða þ btÞ2 þ ðc þ dtÞ2 cosðxt þ a tan 2ða þ bt; c þ dtÞÞ ¼ 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi If AðtÞ can expressed by ða þ btÞ2 þ ðc þ dtÞ2 and uðtÞ can expressed by a tan 2ða þ bt; c þ dtÞ, the signal expressed by AðtÞ cosðxt þ uðtÞÞ is in the null space of operator C. We can decompose this kind of signal when the signal frequency is constant. The method is as follows. 2.2

Signal Decomposition with Operator C

The model of signal decomposition is s ¼ uþr

ð3Þ

Where s is the source signal and u is the non-stationary harmonic to be decomposed. r is the residual signal. In order to obtain u, we can solve the following least squares problem [3]

An Approach of Non-stationary Harmonics Decomposition

n o min kCðs  rÞk22 þ kkr k22 r

541

ð4Þ

Where k is lagrangian multiplier with its unique solution at ^r ¼ ðCT C þ kIÞ1 CT Cs

ð5Þ

So, we extract the desired signal ^u ¼ s  ^r

ð6Þ

^ according to (4) and (5). If we know the constant frequency x, we can calculate u Here, s is the discrete sampled signal and C is the differential operator. The differential operator approximately calculated with the form of (17) and (18). In order to reduce the error, the radial base function (RBF) will be used to approximate the signal. 2.3

The Operator Approximated with RBF

Definition 1 [7]: If u : R þ ! R is a function of distance r ¼ ktk, and /ðtÞ ¼ uðrÞ, then function / is a radial (basis) function, where k
k denotes the Euclidean norm k
k2 (hereinafter abbreviated as k
k). Definition 1 means that if kt1 k ¼ kt2 k is satisfied, then we get /ðt1 Þ ¼ /ðt2 Þ. Here we choose the Gaussian RBF as follow uðrÞ ¼ eðerÞ

2

ð7Þ

with e is normalized shape parameter.  N Given the data tj ; sðtj Þ j¼1 , the interpolation formula with the RBF can be expressed as ^sðtÞ ¼

N X

  cj uðt  tj Þ

ð8Þ

j¼1

It satisfies the following interpolation condition N X

  cj uðtk  tj Þ ¼ sðtk Þ; k ¼ 1;


; N

ð9Þ

j¼1

For the tj different from each other, if we choose the positive definite RBF, the symmetric matrix U in (10) is positive and non singular [8], so the parameter cj in (10) has a unique solution.

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0

uðkt1  t1 kÞ B uðkt2  t1 kÞ B B .. @ .

uðkt1  t2 kÞ uðkt2  t2 kÞ .. .

10 1 0 1 sðt1 Þ uðkt1  tN kÞ c1 B C B C uðkt2  tN kÞ C C B c2 C B sðt2 Þ C C B .. C ¼ B .. C .. A@ . A @ . A .







.. .

cN

uðktN  t1 kÞ uðktN  t2 kÞ


uðktN  tN kÞ

c

U

ð10Þ

sðtN Þ s

So that Uc ¼ s ) c ¼ U1 s

ð11Þ

 N From (8) and (9), we know the sampled signal s ¼ ^sðtj Þ j¼1 . we have ( Cð^sðtÞÞ ¼ C

N X

  cj uðt  tj Þ

j¼1

) ¼

N X

   cj C uðt  tj Þ

ð12Þ

j¼1

n N o CðsÞ ¼ C ^sðtj Þ j¼1 ¼

(

N X

   cj C uðt  tj Þ

)tN

j¼1

¼ ½CUU1 s

ð13Þ

t¼t1

where 0

Cfuðkt  t1 kÞgt¼t1 B Cfuðkt  t1 kÞgt¼t2 B ½CU ¼ B .. @ . Cfuðkt  t1 kÞgt¼tN

Cfuðkt  t2 kÞgt¼t1 Cfuðkt  t2 kÞgt¼t2 .. . Cfuðkt  t2 kÞgt¼tN







.. .




1 Cfuðkt  tN kÞgt¼t1 Cfuðkt  tN kÞgt¼t2 C C C .. A . Cfuðkt  tN kÞgt¼tN ð14Þ

In (13), we define ½CUU1 ¼ CRBF

ð15Þ

In (5), CRBF takes place of C. That is ^r ¼ ðCTRBF CRBF þ kIÞ1 CTRBF CRBF s And then, we can extract the desired signal according (6).

ð16Þ

An Approach of Non-stationary Harmonics Decomposition

2.4

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Algorithm

The algorithm for non-stationary harmonics decomposition is as follows.

3 Experiments and Results In this section, we study the electric current signal of an electric arc furnace (EAF) at the melting stage measured in 33 kV bus. EAF supply and distribution system shown in Fig. 1.

220kV

Transformer SFZ8-40000 115kV/33kV Uk=10.17% YN,d11

33kV Voltage measurement Current measurement

SVC EAF

Fig. 1. The voltage and current measurement of the EAF.

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The grid frequency is 50 Hz. The signal is sampled 64 points per cycle. The equivalent sampling frequency is 3.2 kHz. The series length of decomposition is N ¼ 768. The parameter setting is as following table. In Table 1, x is dimensionless frequency. k is lagrangian multiplier. e is shape parameter of RBF. Table 1. Parameters setting.

x

Harmonic order 1 2 3

4

5

6

2p 64

2p 8

2p 4

2p 2

2p 32

2p 16

7 2p

k 6e-8 3.6e-6 4.5e-5 2.4e-4 9.3e-4 1.7e-3 1.8e-3 e 0.5 0.5 0.5 0.5 0.5 0.5 0.5

We compare the decomposition results with the results of differential operator represented by difference quotient and EEMD algorithm. The second difference quotient matrix is defined as 0

1

B B0 B. . D2 ¼ B B. B .. @. 0

2 .. . .. . .. .




1 .. . 1 ..

.







.. .






1

C 0 C C 2 1 C C C 1 2 A


1

ð17Þ

The fourth difference quotient matrix is defined as 0

1

B0 B B. B .. B B. D4 ¼ B .. B. B. B. B. @ .. 0

4 .. . .. . .. . .. . .. .




6 .. .

4 .. .

1 .. .




.. .

1 ..

4

6

4

1 ..

4

6

1 ..

4

..

..

. .

.




..

.

.




.




1 0






1

0 C C C 1 C C C 4 C C C 6 C C 4 A

ð18Þ

1

Figure 2 shows the electric current signal and the corresponding FFT amplitude spectrum. From Fig. 2, we can see that the spectrum of electric current of arc furnace is mainly distributed in the low frequency band, especially near the fundamental wave. We focus mainly on the decomposition of the fundamental wave. Figure 3(a) shows the non-stationary fundamental wave decomposition based on the operator approximated by RBF and difference quotient. Figure 3(b) and (c) show the FFT amplitude spectrum with RBF and difference quotient respectively. Compared

An Approach of Non-stationary Harmonics Decomposition

545

Fig. 2. The source signal and its spectrum. (a): the source signal (b): the spectrum.

to Figs. 3(b) and (c) contains more 2nd and 3rd harmonic components. We can get that the decomposition by RBF is better than the result by difference quotient. Figure 4 shows the fundamental wave decomposed by the RBF-operator method and EEMD. Figure 4(b) shows that the decomposed non-stationary fundamental wave is almost no aliasing with 2nd and other higher order harmonic. In Fig. 4(c), we find the decomposed signal by EEMD includes 2nd and 3rd harmonic. Furthermore, from fundamental wave spectrum line, we find the fundamental wave power lose more than in Fig. 4(b). The arc current is irregular and varies drastically at the melting stage. The current can be decomposed into 2nd and high order harmonics, mainly from 2nd to 7th [9]. Figure 5 show the decomposition results for each harmonic. Figure 5 shows the non-stationary harmonics from order 1 to 7 and its corresponding amplitude spectrum. We can see that the proposed algorithm extracts the signal of a certain frequency band, which does not require high accuracy value of the frequency. In addition, apart from the fundamental wave, the decomposition of other non-stationary harmonics has aliasing of adjacent harmonics. This part may be caused by lagrangian multiplier, or lagrangian multiplier and operators do not match. This still needs further study.

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Fig. 3. The non-stationary fundamental wave decomposition based on the operator approximated by RBF and difference quotient. (a): the non-stationary fundamental wave comparison. (b): the FFT amplitude spectrum with RBF. (c): the FFT amplitude spectrum with difference quotient.

Fig. 4. The decomposed signal by RBF-operator method and EEMD. (a): the non-stationary fundamental wave comparison (b): the FFT amplitude spectrum with RBF. (c): the FFT amplitude spectrum with EEMD.

An Approach of Non-stationary Harmonics Decomposition

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Fig. 5. The non-stationary harmonics from order 1 to 7 decomposed by the RBF-operator algorithm

4 Conclusion In this paper, using the algorithm based on operator approximated by RBF, there is a better decomposition of non-stationary fundamental wave compared with the differential operator represented by difference quotient Compared with the signal decomposition based on ensemble empirical mode decomposition (EEMD) method, on the one hand, it is efficient to extract most fundamental wave power than EEMD. On the other hand, the fundamental wave does not have aliasing with other higher order harmonics. We can see that the differential operator suggested in this paper is suit for the fundamental wave in this experiment. In addition, apart from the fundamental wave, the decomposition of other non-stationary harmonics has aliasing with adjacent harmonics. This part may be caused by lagrangian multiplier and operator selection. We can see that the proposed algorithm extracts the signal of a certain frequency band, which does not require high accuracy value of the frequency. Overall, the proposed algorithm is effective. Acknowledgments. This work was supported by the Key Project of Anhui Educational Committee, under Grant No. KJ2016A014.

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References 1. Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q et al (1998) The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis. Proc Math Phys Eng Sci 454(1971):903–995 2. Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adapt Data Anal 01(01):1–41 3. Peng S, Hwang WL (2008) Adaptive signal decomposition based on local narrow band signals. IEEE Trans Signal Process 56(7):2669–2676 4. Peng S, Hwang WL (2010) Null space pursuit: an operator-based approach to adaptive signal separation. IEEE Trans Signal Process 58(5):2475–2483 5. Hu X, Peng S, Hwang WL (2015) Adaptive integral operators for signal separation. IEEE Signal Process Lett 22(9):1383–1387 6. Ma L, Wu Z (2009) Approximation to the k-th derivatives by multiquadric quasi-interpolation method. J Comput Appl Math 231(2):925–932 7. Fasshauer GE (2007) Meshfree Approximation Methods with Matlab: (With CD-ROM), vol 6. World Scientific Publishing Co Inc., 17 8. Powel, MJD (1987) Radial basis functions for multivariable interpolation: a review. In: IMA conference on algorithms for the approximation of functions and data. pp 143–167. University Press 9. Dinghua Z, Weihua G, Weian W (2008) Comprehensive compensation system combining reactive power compensation and harmonic suppression for large-scale electric arc-furnace. Power Syst Technol Beijing 32(12):23

Boost and Ascent Trajectory Design and Guidance Approach for Rocket Launched Supersonic Aircraft Jianhui Liu(&), Lansong Wang, Mingang Zhang, Xiaoli Qin, and Yajie Ge Science and Technology on Space Physics Laboratory, Beijing 100076, China [email protected]

Abstract. This paper addresses the boost and ascent trajectory design and guidance problem for rocket launched supersonic aircraft. Based on the typical upper and lower bounds of dynamic pressure for scramjet engine powered aircraft, the corresponding altitude-velocity bound profiles are obtained. For the boost phase trajectory, the angle of attack (AOA) is chosen as control variable and expressed in parametric form, the nominal profiles for the lowest and highest initial ground altitudes are designed by solving nonlinear equations generated by numerical integration, and the nominal boost trajectory profiles for varied initial ground altitude are obtained by combination of these two profiles. For the scramjet powered ascent phase, AOA and equivalent ratio are chosen as control variables, by using the lower and upper velocity-altitude profiles, and based on a linear acceleration assumption, a feasible nominal ascent trajectory design method is presented. Based on the designed nominal profiles and control variables, a feedback control guidance approach is proposed for tracking and control of the entire perturbed ascent trajectory. Numerical simulation results for a test aircraft are provided, demonstrating the effectiveness of the proposed methods. Keywords: Rocket Guidance


Aircraft
Boost
Ascent
Trajectory
Design


1 Introduction In recent decades, much attention have been attracted to scramjet powered vehicles and aircrafts. Some research and engineering works have been done on trajectory design, guidance, simulation, and optimization for scramjet powered vehicle’s boost and ascent trajectory [1–4]. In Reference [1], based on constant dynamic pressure assumption, the minimum-fuel ascent trajectory optimization research work was done by surrogating different constant ascent accelerations. In Reference [3], a boost phase trajectory guidance approach for scramjet powered vehicle subject to transition condition constraint was discussed. But to the best of our knowledge, in literature, little was discussed about the trajectory design and guidance problem for both boost phase trajectory and ascent phase trajectory of the rocket launched scramjet powered supersonic aircraft. © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 549–557, 2020. https://doi.org/10.1007/978-981-32-9698-5_61

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In this paper, the design and guidance approaches for boost phase and scramjet powered ascent phase trajectory of a ground-based rocket launched test aircraft are discussed. In the studied model, both the maximum and minimum dynamic pressure constraints for the aircraft are considered about, and the effects of initial ground altitude on boost phase trajectory design are also studied. The test aircraft is vertically boosted by a solid rocket from ground, when the rocket is depleted, the booster and the aircraft are separated. The whole ascent trajectory is divided into two phases, i.e., the rocket boost phase and the scramjet powered aircraft ascent phase, and the terminal state of boost phase is the initial state of ascent phase.

2 Mathematical Model In this section, the dynamics model, the aerodynamic models, the thrust engine models, and constraint models are formulated. The aircraft is assumed to be a point mass, ignoring the dynamic response process of all control surfaces, that is, attitude control actions can be realized ideally, the non-rotating flat Earth model is used for mathematical modeling, and only the motion in the vertical plane is discussed. 2.1

Dynamic Model

The dynamic model can be described by following equations. h_ ¼ V sin h

ð1Þ

a¼

dV P cos a  D ¼  g sin h dt m

ð2Þ

mV

dh ¼ P sin a þ L  g cos h dt

ð3Þ

m ¼ m0  mf Z

t

mf ¼

md dt

ð4Þ ð5Þ

0

In Eqs. (1)–(5), P is the thrust of the rocket or scramjet, a is angle of attack, D is aerodynamic drag force, L is aerodynamic lift force, V is the velocity, a is the acceleration, h is the altitude, m is mass of vehicle, g is the gravitational acceleration (which is approximated by g0), h is the flight path angle, mf is the fuel consumption, md is the rate of fuel consumption.

Boost and Ascent Trajectory Design and Guidance Approach

551

Atmospheric Model The atmospheric density is assumed to be an exponential function of altitude: qðhÞ ¼ q0 eb0 h

ð6Þ

where b0 ¼ 0:00015; q0 ¼ 1:225ðkg=m3 Þ, is the atmospheric density at sea level, h is altitude (in meters). The atmospheric temperature Ta, air pressure ph, and speed of sound Vs are functions of altitude h, and they are approximated by interpolation from US 1976 Standard Atmosphere [5]. For the ascent phase, Ta and Vs are taken as constants, Ta = Ta0 = 215 K, Vs = Vs0 = 295.07 m/s. Mach number is computed by M ¼ MðhÞ ¼ V=Vs

ð7Þ

Rocket Engine Model The rocket engine’s thrust and rate of fuel consumption are modeled as follows. md ¼ mf =T

ð8Þ

P ¼ Isp md þ Sa ðp0  ph Þ

ð9Þ

In above Equations, Isp is the specific impulse of engine at sea level, mf is the mass of engine’s propellant, T is operating time of the boost rocket, Sa is area of engine’s exit nozzle, all of them are taken as constants. Scramjet Engine Model The scramjet engine’s specific impulse Isp , thrust, and rate of fuel consumption are functions of angle of attack and equivalence ratio g, they are modeled as follows. P ¼ Isp ðMÞmd ða; gÞ

ð10Þ

In above Equations, Isp is the specific impulse of scramjet engine. In ascent phase, the velocity variation range is small, so the effect of Mach number on specific impulse is ignored. They are piecewise curve fitted coefficients from tabulated data. Aerodynamic Model The vehicle’s aerodynamic lift and drag forces and coefficients are modeled as follows D ¼ qSCD ðaÞ

ð11Þ

L ¼ qSCL ðaÞ

ð12Þ

q ¼ 0:5qV 2

ð13Þ

In above formulas, q is dynamic pressure, CD is aerodynamic drag coefficient, CL is aerodynamic lift coefficient, S is the reference area.

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Boost Phase Trajectory Design and Guidance

Initial and Terminal Conditions for Boost Phase Initial altitude of ground-based launch site is H0, which can be varied from H0min to H0max. The terminal constraints for the boost phase trajectory are altitude Hbf and a small positive flight path angle Hbf . hð0Þ ¼ H0 ; Vð0Þ ¼ 0; hð0Þ ¼

p 2

hðTÞ ¼ Hbf ; hðTÞ ¼ Hbf

ð14Þ ð15Þ

Boost Phase Trajectory Design For three degrees of freedom (3DOF) boost phase trajectory design, the angle of attack (AOA) is chosen as design and control variable. The AOA is expressed as a parametric function of time t, expressed as follows. f ðtÞ ¼ pðt  t0 Þ=ð2ðt1  tÞ=ðt1  t0  2Þ þ ðt  t0 ÞÞ 8 0; t\t0 > > > > > > > a1max sin2 f ðtÞ; t0  t\t1 > > > > > > > a ¼ a1max sin2 f ðt1 Þ; t1  t\tm > < 1 aðtÞ ¼ a1 þ ðam  a1 Þðt  tm Þ; tm  t\tm þ 1 > > > > > am ; tm þ 1  t\t3 > > > > > > am ðt  t3 Þ; t3  t\t3 þ 1 > > > > : 0; t  t3 þ 1

ð16Þ

ð17Þ

In Eq. (17), tm and am are design parameters, t1 is a predesigned regulated parameter, t0 is the starting time of turnaround. The fourth order Runge-Kutta numerical integration formula is used to get process and terminal states. For every pair of tm and am parameters, integrate Eqs. (1)–(4), the terminal altitude hk, and flight path angle hk of boost phase are obtained. Choosing appropriate initial values, we can use Broyden’s algorithm [6] to solve following nonlinear Eqs. (18) and (19) with two unknown variables, tm and am. hk ðtm ; am Þ  Hbf ¼ 0

ð18Þ

hk ðtm ; am Þ  Hbf ¼ 0

ð19Þ

The solution of above equations tm and am are used to integrate Eqs. (1)–(4), the altitude hk, pitch angle and flight path angle hk as functions of time t are obtained at every time step as nominal trajectory profiles of boost phase, they will be used by curve fitting for feedback trajectory tracking guidance.

Boost and Ascent Trajectory Design and Guidance Approach

553

Nominal Trajectory Profiles Generation For initial altitude H0 = 0 km, terminal conditions of boost phase are Hf0, Hf 0 , using the design method described above, we can design boost phase trajectory profiles, including, pitch angle profile upr0 ðtÞ, flight path angle profile hpr0 ðtÞ, and, altitude profile hpr0 ðtÞ. Similarly, for initial altitude H0 = H0max, terminal conditions of boost phase are Hf1, Hf 1 , using the method described above again, we can obtain another group of boost phase trajectory profiles, including, pitch angle profile upr1 ðtÞ, flight path angle profile hpr1 ðtÞ, altitude profile hpr1 ðtÞ. For any initial ground altitude H0, 0 < ex ¼ ðey þ rÞhi  vi þ vr cos hei ¼ ðey þ rÞxi  vi þ vr cos hei 0 0 ey ¼ ðex þ lÞhi þ vr sin hei ¼ ðex þ lÞxi þ vr sin hei > 0 : eh ¼ xr  xi

ð12Þ

As we can see from Eq. 12, the convergence of ex ; ey depends on hei ðeh Þ, In this case, hei Will converge to zero before ex ; ey , then ex ; ey Will become uncontrollable. To avoid this situation, boot angle can be used in the design of the control law, that is, when ex ; ey does not converge, first control hei to be a non-zero Angle, so as to avoid the generation of control singularities. In this thesis, the boot Angle is set as follows: hd ¼ arctan

ey D

D is the boot angle parameter, D > 0, hd 2 ðp; p.

ð13Þ

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For such wheeled robots with non-integrity constraints, the following control laws 14 and 15 can be designed to ensure the stability of the system.

x¼

v ¼ k1 ex þ vr cos hei ; k1 [ 0

ð14Þ

ðD2 þ e2y Þðxr  k2 hz Þ þ Dvr sin hei Dex þ D2 þ e2y

ð15Þ

hz ¼ hd  hei is the error angle, Dvr \4k2 a ; a ¼ cos x 2 ð0; 1Þ; cos hz [ a Proof: First, for the convergence of ex ; ey , design the following Lyapunov function: 1 1 V1 ¼ e2x þ e2y 2 2

ð16Þ

Taking the derivative of Eq. 12 with the combination of Eq. 16, we can get: 0

0

0

V1 ¼ ex ex þ ey ey ¼ vex þ ex vr cos hei þ ey vr sin hei

ð17Þ

Substitute control law 14 into the above equation to obtain: 0

V1 ¼ ðk1 ex þ vr cos hei Þex þ ex vr cos hei þ ey vr sin hei ¼ k1 e2x þ ey vr sin hei ey ¼ k1 e2x þ ey vr qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D2 þ e2y

ð18Þ

vr e2y ¼ k1 e2x  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D2 þ e2y 0

k1 ; vr [ 0, so V1 \0. So we can conclude that ex ; ey converges to 0 when hei is a certain angle. Next, for the convergence of hei , design the following Lyapunov function: V2 ¼ V1 þ

1 2 h 2 z

ð19Þ ey D Þ

It can be obtained from the above definition: hz ¼ hd  hei ¼ arctanð the derivative with respect to hz : 0

hz ¼

1 1þ

e2y D2

1 0 : ð Þ : ðey Þ  ðxr  xi Þ D

Dex þ D2 þ e2y Dvr sin hei ¼ xi  2  xr 2 2 D þ ey D þ e2y

 hei , take

ð20Þ

A Multi-robot Formation Control Method

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Taking the derivative of Eq. 19: 0

0

0

V2 ¼ V1 þ hz hz

ð21Þ

Substitute Eqs. (15) and (20) into Eq. (21) to obtain: 0

0

V2 ¼V1 þ hz ð ¼

k1 e2x

Dex þ D2 þ e2y Dvr sin hei xi  2  xr Þ D2 þ e2y D þ e2y

þ ey vr sinðhd  hz Þ 

ð22Þ

k2 h2z

0

To prove that V2 is negative, we need to introduce a new variable hx 2 ð0; p2Þ. When jhz j\hx , there must be a ¼ cos hx [ 0, cos hz [ a, jhz j [ jsin hz j. Considering the last two items in Eq. (22), we can get that: ey vr sinðhd  hz Þ  k2 h2z vr e2y vr ey D ¼ k2 h2z  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cos hz  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin hz D2 þ e2y D2 þ e2y

ð23Þ

 vr D    k2 h2z  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ey hz  D2 þ e2y D2 þ e2y vr e2y

There are basic infinitives a2 þ b2  2jabj, set b [ 0, then we can get:  vr D  vr Db vr D qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ey hz   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2y þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2z 2 2 2 2 D þ ey 2 D þ ey 2b D2 þ e2y

ð24Þ

Substitute Eq. (24) into Eq. (23) to obtain: ey vr sinðhd  hz Þ  k2 h2z vr e2y vr Db vr D   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2y  k2 h2z þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2z 2 2 2 2 2 D þ ey 2b D2 þ e2y D þ ey 0 1

ð25Þ

vr vr D B C ¼  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2a  DbÞe2y  @k2  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAh2z 2 2 2 2 2b D þ ey 2 D þ ey Combining Eqs. (22) and (25), we can get: vr vr D 2 0 V2   k1 e2x  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2a  DbÞe2y  ðk2  Þh 2b z 2 D2 þ e2y

ð26Þ

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To make V2 \0, then ask



2a  Db [ 0 rD [0 k2  v2b

ð27Þ

Thus, the following equation can be obtained: 4k2 a [ Dvr

ð28Þ 0

Therefore, when the selected parameter satisfies Eq. (28), it satisfies V2 \0, that is, the system is stable, the tracking error of the robot formation approaches zero, and the formation of multi-robot formation is formed. If we want to achieve formation transformation, we only need to change the value of the constant l; r, In the following simulation experiments, I will prove that changing the value of the constant l; r can transform the formation from a triangle structure to a linear structure. 2.4

Prediction Algorithm Based on Improved Cubature Kalman Filter

Leader robot is the core of the whole system in the formation based on leader-follower control algorithm. Only the behavior and trajectory of the leader can be given to control the behavior of the whole robot swarm according to the geometric and kinematic relations between the follower and the leader. The speed and coordinates of all the follower robots are closely related to the position and posture of the leading robot. Therefore, if the attitude of the leading robot changes, the tracking of the follower robot in the system would be lost. The formation based on the leader-following control algorithm also needs to predict the next ideal position of the following robot. The adaptive Cubature Kalman Filter can predict that next motion performance of the following robot well, so that the follow robot can accurately reach the desired position and direction. Cubature Kalman Filter (CKF) is a new nonlinear filtering algorithm, which is based on the third-order spherical-radial Cubature rule and can accurately reach the third-order accuracy of Taylor expansion, and has strict theoretical derivation and proof. CKF avoids the linearization of nonlinear function by extended Kalman Filtering (EKF), so it has higher filtering precision, reduces one sampling point compared with unscented Kalman Filtering (UKF), and the sampling point weights are positive, so it has better numerical stability and computational efficiency. In this thesis, the Improved adaptive Kalman Filtering divides the state of the robot into two models. The first is to set the noise covariance matrix to a zero matrix when the system is in a stable state. The second is that when the system is in the instantaneous state, the system controls the Kalman Filtering by an adaptive Q value, and then

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judges whether the whole system is in the stable state or the instantaneous state. In the actual state model, if the measured difference component of each time step is relatively small, it is set to a stable state. When the measurement error is relatively large, it is set to the instantaneous state. The state of the system is judged by measuring the statistical model of the difference, and the state model is expressed as follow: Ho : l ¼ 0

ð29Þ

HA : l 6¼ 0 Use the large-scale data statistic model t as test statistics: t¼

Dzk;k1  l psffiffi

ð30Þ

n

Dzk;k1 —Measuring differential mean; l—The total average; n—The sampling points; S—Standard deviation of the sample The Q value of the Cubature Kalman filter is determined by the decision strategy in Table 1. The statistic t is in accordance with the normal distribution Table 1. State determination strategy t Statistics a = %5 H HA t\  ta=2 HA ta=2 \t\ta=2 Ho t [ ta=2

The system state Transient state Transient state Stable state

Kalman filter Q model Q=I Q=I Q=0

The calculation sequence of the Kalman filtering is as follows: (1) obtain the measured value and calculate the measurement deviation between them (2) calculate the measurement deviation and standard deviation (3) use the measured deviation as a sample of a test statistic and determine the value of Q (4) time update and measurement update (5) determine whether to end the cycle In this thesis, the volumetric Kalman filtering adopts two Q modes to judge whether the system is in a dynamic unstable state through statistics. Then, the volumetric Kalman filteringis used for state estimation, and the gain of Kalman filtering is updated to effectively prevent the divergence problem.

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3 Prototype and Test Results In order to verify the effectiveness of the above algorithm, four smart cars are selected to move along the Y-axis from the initial position and form a triangle formation for simulation. The initial state and motion law of the leader robot are set as: at time t = 0, the leader robot is located at the origin of the coordinate system, and the body Angle of the leader robot is p2. After the formation movement starts, the leader robot moves along the Y-axis with the reference speed vr ¼ 2. Initial state of each follower robot: position coordinate, car body Angle, formation parameter l, r are shown in Table 2 (Figs. 7 and 8).

Table 2. Initial states of robots Car type Leadinging robot Following robot one

Abscissa Ordinate Body angle l r p / / 0 0 2 5p –5 –15 10 –10 6

Following robot two –4 Following robot three 5

–13 –17

p 6 p 8

10 0 10 10

Fig. 5. Trajectory diagram of the multi-robot formation

A Multi-robot Formation Control Method

Fig. 6. Leadinging robot and following robots body angle variation diagram

Fig. 7. Following robots velocity and angular velocity variation diagram

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Fig. 8. Simulation results of adaptive Kalman filter

4 Analysis of Experimental Results After matlab simulation, and finally a robot navigation and the three following formation of the robot simulation results as shown in Figs. 5 and 6, can be seen from the figure in the initial time each smart car has a different position and Angle to the body, formed in the process of running the intelligent car with reference for leader triangle formation, and each of the intelligent car eventually converge speed and body corner, and then four smart car form a triangle formation. As can be seen from Figs. 5 and 6, the following robot’s body Angle, velocity and angular velocity gradually become stable with time, and are equal to the steering robot’s body Angle, velocity and angular velocity. And the algorithm adopted in this thesis has obvious following effect and can quickly keep up with the position change of the navigator. By adopting adaptive volumetric kalman filter, the effect of noise generated when the leader’s velocity or angular velocity changes is overcome, so that the following robot can achieve better following effect. Acknowledgments. In this thesis, an adaptive navigation-following algorithm combined with kalman filter is proposed to solve the problem of multi-agent formation. For the problem of multi-agent formation, most researches simplify each agent into a particle. Then we need to consider the formation algorithm, in fact, also need to consider the car body Angle, otherwise the final design of the formation algorithm is physically impossible to be achieved. The formation control algorithm with virtual robot tracking is proposed in this thesis, which can flexibly design

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various formation forms according to the task requirements, so that the multi-intelligent robot moves in a consistent state during formation, and the formation can be maintained stably. After the completion of theoretical proof, this thesis also gives method to further verify the robot triangle formation by matlab simulation. Aiming at the problem that the follower robot can’t keep up with the leader quickly when the running state of the leader robot changes suddenly, an Improved adaptive Cubature Kalman filter is proposed, and a good following effect is achieved between the follower and the leader by adjusting the Q value adaptively.

References 1. Author F (2016) Article title. Journal 2(5):99–110 2. Shi WX, Wang DW, Li BQ (2018) Formation control based on leader -followers for multiple mobile robots. J Tianjin Polytech Univ 37(2):72–78 (in Chinese) 3. Yang F, Liu S, Dong D (2012) Robot behavior and service-based motion behavior [7] structure design in formation control. Robot 34(1):120-128 4. Arrichiello F, Chiaverini S, Indiveri G et al (2010) The null-space-based behavioral control for mobile robots with velocity actuator saturations. Int J Robot Res 29(10):1317–1337 5. Wang BF, Zhang RL, Li S et al (2015) Formation control of vehicle based mobile robot based on trajectory tracking. Control Decis 1:176–180 (in Chinese) 6. Pang WW, Jiang DP, Pang YJ et al (2017) Formation control of multi underwater robots based on combination of artificial potential field and virtual structure. Acta Armamentarii 38 (2):326–334 (in Chinese) 7. Belta C (2007) Abstraction and control for groups of robots. IEEE Trans Robot 20(5):865– 875 8. Li Y, He K (2006) A novel obstacle avoidance and navigation method for outdoor mobile robot based on laser radar. Robot 28(3):275–278 9. Wangz L, Liuz X, Chen ZQ, et al (2014) Design of a new multi-agent navigation following formation controller. J Intell Syst 3:298–306. (in Chinese) 10. Xiong R, Sun F, Chen Z et al (2014) A data-driven multi-scale extended Kalman filtering based parameter and state estimation approach of lithium-ion olymer battery in electric vehicles. Appl Energy 113(1):463–476 11. Tian Y, Chen Z, Yin F (2015) Distributed Kalman filter-based speaker tracking in microphone array networks. Appl Acoust 89(89):71–77

Data-Driven Feedback QILC Strategy for Batch Processes Qinsheng Li1(&) and Jiafeng Yu2 1

Mrine Engineering College, Jiangsu Maritime Institute, Nanjing 211170, China [email protected] 2 Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China

Abstract. To enhance the performance of product quality tracking control of batch processes, a new control scheme, integrating quadratic criterion based iterative learning control and model-free adaptive control, is presented in this paper. An important merit is that the proposed scheme systematically integrates input-output information during the running cycle and historical information from previous batch into one uniform frame for controller design. Thus, the approach can realize two-dimension tracking control synchronously, namely a feedback control along time-axis, while the feed-forward control along batchaxis. Convergence condition is established for the proposed approach. An illustrative example is given to verify the effectiveness of the investigated approach. Keywords: Batch process
Quadratic criterion based iterative learning control
Data-driven control
Two-dimensional control

1 Introduction Batch processes constitute a very important part of industry for manufacturing of many low-volume and high-value added products such as pharmaceuticals, specialty chemicals, semiconductors, medicine, foods and metals. The main control objective in some batch processes is to meet final desired product quality at batch end. For deriving the maximum benefit from batch processes, optimal control of batch processes is very significant. The key of optimal control depends on obtaining an accurate model of batch processes, which can provide accurate predictions. Usually, developing first principle models of batch processes is time consuming and effort demanding [1]. To overcome the problems, process input–output data based models, such as neural networks and fuzzy systems have been investigated to model nonlinear processes owing to their ability to approximate a nonlinear function to any arbitrary accuracy [3, 8–10]. However, optimal control obtained from off-line process model is often suboptimal when applied to the real process because of the plant-model mismatches. Batch processes have the characteristic of repetition, which makes both technologies and applications of iterative learning control (ILC) are possible to be widely used © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 572–580, 2020. https://doi.org/10.1007/978-981-32-9698-5_63

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in the optimization control of batch processes in the past decade [1]. Exploiting the repetition of batch processes, the control law within next batch can be updated iteratively by using the results from previous batches [5–7]. Quadratic criterion based iterative learning control (QILC) is an important method for constructing an iterative learning law, in which the ILC law is derived by solving a quadratic optimization problem [2]. Norm-optimal ILC has been presented firstly by Owens [4]. Based on neuro-fuzzy model and QILC, Jia et al. have proposed an integrated ILC strategy with model identification and dynamic R-parameter to improve tracking performance and robustness for batch processes [8]. Considering the modeling complexity and the plant-model mismatches, and motivated by the model-free adaptive control (MFAC) theory [13, 14], a data-driven feedback QILC control framework for batch processes is proposed. This strategy features minimizing a quadratic objective function, which integrates time-axis information and batch-wise information into one uniform frame, to obtain the optimal control profile based on online one-step forward prediction of dynamic linearization model and online tuning of the model parameters. As a result, model uncertainties can be handled to improve the control performance and a two-dimensional optimal control scheme is built. Simulation results show that the control profile demonstrates promising tracking performance from batch to batch.

2 Problem Formulation Consider a nonlinear discrete-time single input single output (SISO) system as the discussed sampled-data batch processes, which can be described as: ð1Þ yk ðt þ 1Þ ¼ f ðyk ðtÞ;   ; yk ðt  nÞ; uk ðtÞ;   ; uk ðt  mÞÞ
 where k is the batch index. Batch length is defined as tf and t 2 0; tf is the time index within each batch. f ðÞ denotes an unknown function and m, n are the unknown orders of input uk ðtÞ and output yk ðtÞ, respectively. In this study, we suppose that the measurement of batch process output yk ðtÞ is available. The control objective is to manipulate uk ðtÞ to maximize batch-end quality output yk ðtf Þ towards the desired one yd ðtf Þ over the time interval [0, tf ]. The nonlinear system (1) is assumed to satisfy the followings [13, 14]. Assumption 1. The partial derivatives of f ðÞ with respect to control inputs uk ðtÞ are continuous. Assumption 2. System (1) is generalized Lipschitz, namely kyk ðt þ 1Þ  yk ðtÞk  bkuk ðtÞ  uk ðt  1Þk for any t and kuk ðtÞ  uk ðt  1Þk 6¼ 0 and b is a positive constant.

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3 Methodology Via partial form dynamic linearization technique [13, 14], nonlinear system (1) can be equally transformed into the following description yk ðt þ 1Þ ¼ yk ðtÞ þ /k ðtÞðuk ðtÞ  uk ðt  1ÞÞ

ð2Þ

where /k ðtÞ is called pseudo-partial derivative (PPD) [13, 14], k/k ðtÞk  b. The objective function for PPD parameter /k ðtÞ estimation is used as ^ ðtÞ  / ^ ðt  1ÞÞ2 min J1 ð/k ðtÞÞ ¼ ðDt yk ðtÞ  /k ðtÞðDt uk ðtÞÞÞ2 þ lð/ k k

ð3Þ

where Dt uk ðtÞ ¼ uk ðtÞ  uk ðt  1Þ, Dt yk ðtÞ ¼ yk ðtÞ  yk ðt  1Þ, lðl [ 0Þ is the weighted factor. 1 ð/k ðtÞÞ Let @J@/ ðtÞ ¼ 0, the PPD parameter /k ðtÞ can be estimated as k

^ ^ ðtÞ ¼ / ^ ðt  1Þ þ Dt uk ðtÞðDt yk ðtÞ  /k ðt  1ÞDt uk ðtÞÞ / k k l þ ðDt uk ðtÞÞ2

ð4Þ

^ ðtÞ instead of / ðtÞ in (2), the data based predictive model can be Next, using / k k expressed as ^ ðtÞðDt uk ðtÞÞ ^yk ðt þ 1Þ ¼ yk ðtÞ þ / k

ð5Þ

Moreover, nonlinear system (2) can be equally transformed into the following form ^ ðtÞðDt uk ðtÞÞ þ dk ðtÞ yk ðt þ 1Þ ¼ yk ðtÞ þ / k

ð6Þ

where dk ðtÞ ¼ yk ðt þ 1Þ  ^yk ðt þ 1Þ, dk ðtÞ is plant-model mismatch and it is bounded by kdk ðtÞk  dmax , dmax is a positive constant. For the control law algorithm, a weighted quadratic criterion is given by min J2 ðuk ðtÞÞ ¼ ðyd ðt þ 1Þ  ^yk ðt þ 1ÞÞ2 þ kðDt uk ðtÞÞ2

ð7Þ

Subject to ulow  uk ðtÞ  uup ylow  yk ðtÞ  yup

ð8Þ

where kðk [ 0Þ is the weighted factor, ulow and uup are the lower and upper bounds of the input trajectory. ylow and yup are the lower and upper bounds of the output trajectory. 2 ðuk ðtÞÞ ¼ 0, one can obtain the feedback conNext, substituting (5) into (7), let @J@u k ðtÞ troller as

Data-Driven Feedback QILC Strategy for Batch Processes

uk ðtÞ ¼ uk ðt  1Þ þ

^ ðtÞðyd ðt þ 1Þ  yk ðtÞÞ / k ^ ðtÞ/ ^ ðtÞ kþ/ k

575

ð9Þ

k

Similar to design feedback controller (9), for the feedback QILC control law algorithm, a weighted quadratic criterion is adopted as min J3 ðuk ðtÞÞ ¼ ðyd ðt þ 1Þ  ^yk ðt þ 1ÞÞ2 þ kðDt uk ðtÞ  ðDt uk1 ðtÞÞÞ2

ð10Þ

Subject to (8) 3 ðuk ðtÞÞ Next, substituting (5) into (10), let @J@u ¼ 0, one can derive the feedback QILC k ðtÞ controller as uk ðtÞ ¼ uk ðt  1Þ þ

^ ðtÞðyd ðt þ 1Þ  yk ðtÞÞ / kDt uk1 ðtÞ þ k ^ ^ ðtÞ ^ ^ ðtÞ/ k þ / ðtÞ/ ðtÞ kþ/ k

k

k

ð11Þ

k

In summary, we give the procedure for the algorithm of feedback QILC strategy for batch processes as follows: Step 1: At current time t within kth batch, solve Eq. (4) using the input/output (I/O) ^ ðtÞ. data {uk ðt  1Þ, yk ðtÞ}, obtaining the estimation value of PPD parameter / k ^ ðtÞ into (9), then the manipulated input uk ðtÞ is Step 2: If k = 0, substitute / k ^ ðtÞ into (11), then the manipulated input uk ðtÞ is obtained. If k  1, substitute / k obtained. Step 3: Put uk ðtÞ into the controlled plant then measure the corresponding output yk ðt þ 1Þ. Step 4: The {uk ðtÞ, yk ðt þ 1Þ} is the new I/O data at the sampling instant t + 1, and return Step 1. Step 5: If t [ tf , set t = 0, k = k + 1 and return Step 1.

4 Convergence Analysis In this section, a rigorous theorem is given to prove that the tracking error ek ðtÞ, under the proposed control law, can converge to a bound as t ! tf , k ! 1. Combining (2) and (6), the closed-loop tracking error dynamical system is derived as ek ðt þ 1Þ ¼ yd ðt þ 1Þ  yk ðt þ 1Þ ^ ^ ðtÞðkDt uk1 ðtÞ þ /k ðtÞðyd ðt þ 1Þ  yk ðtÞÞÞ  dk ðtÞ ¼ yd ðt þ 1Þ  yk ðtÞ  / k ^ ðtÞ/ ^ ðtÞ kþ/ k k ^ ¼ qðyd ðt þ 1Þ  yk ðtÞÞ  q/ ðtÞDt uk1 ðtÞ  dk ðtÞ k

¼ qðek ðtÞ þ ek1 ðt þ 1Þ  ek1 ðtÞÞ þ e ð12Þ

576

where

Q. Li and J. Yu ^

^

/k ðtÞ k q ¼ 1  k þ/k/^ðtÞðtÞ ^ ðtÞ ¼ k þ / ^ ðtÞ, ^ ðtÞ/ / k

k

k

k

It

is

obvious

that

0\q\1.

^ ðtÞÞDt uk1 ðtÞ þ dk1 ðtÞÞ  dk ðtÞ, and kek  e0 , e0 exists because ^ ðtÞ  / e ¼ qðð/ k1 k ^ the bounds of /k ðtÞ, Dt uk1 ðtÞ and dk ðtÞ exist, e0 is a positive constant. pffiffi Theorem 1. If 0\q\ 105, the tracking error ek ðt þ 1Þ in dynamical system (12) is asymptotically converge to a compact set H   2 2 H ¼ ðe2k ðtÞ; e2k1 ðt þ 1Þ; e2k1 ðtÞÞð  8q2 Þe2k ðtÞ þ ð  8q2 Þe2k1 ðt þ 1Þ 5 5 þ ð15  4q2 Þe2k1 ðtÞ  2e20 :g as t ! tf ; k ! 1: Proof. The following Lyapunov function is considered: V ¼ e2k ðt þ 1Þ The increment of Lyapunov function along both time-axis and batch-axis synchronously is calculated as 2 2 1 DV ¼ e2k ðt þ 1Þ  e2k1 ðt þ 1Þ  e2k ðtÞ  e2k1 ðtÞ 5 5 5 2 2 1 ¼ ðqðek ðtÞ þ ek1 ðt þ 1Þ  ek1 ðtÞÞ þ eÞ2  e2k1 ðt þ 1Þ  e2k ðtÞ  e2k1 ðtÞ 5 5 5 2 2 2 2 1 2 2 2 2 2  4q ð2ek ðtÞ þ 2ek1 ðt þ 1Þ þ ek1 ðtÞÞ  ek1 ðt þ 1Þ  ek ðtÞ  ek1 ðtÞ þ 2e2 5 5 5 2 2 2 2 1 2 2 2 2 2 ¼ ð8q  Þek ðtÞ þ ð8q  Þek1 ðt þ 1Þ þ ð4q  Þek1 ðtÞ þ 2e 5 5 5 pffiffi when ð4q2  15Þ\0 ,0\q\ 105 and ð25  8q2 Þe2k ðtÞ þ ð25  8q2 Þe2k1 ðt þ 1Þ þ ð15  4q2 Þ _{k - 1}^{2} (t) \ge 2\varepsilon_{0}^{2} \ge 2\varepsilon^{2}. we have DV  0. This completes the proof.

Remark. It is clear that the proposed dynamic linearization model based feedback QILC, characterized by data-driven based approximation, is a powerful tool to handle trajectory tracking control problems of nonlinear processes. Thus, a nonlinear example instead of linearization model is chosen to investigate the strategy in the sequel.

5 Example Consider a typical batch reactor process described as follow [9–11]: 8 < x_ 1 ¼ k1 expðE1 =TÞx21 x_ ¼ k2 expðE1 =TÞx21  k2 expðE2 =TÞx2 : 2 y ¼ x2

Data-Driven Feedback QILC Strategy for Batch Processes

577

where T denotes reactor temperature, x1 and x2 are the reactant dimensionless concentration respectively. The initial conditions are x1 ð0Þ ¼ 1; x2 ð0Þ ¼ 0. In nominal case, the value of parameters discussed above batch process are k1 ¼ 4:0  103 , k2 ¼ 6:2  105 , E1 ¼ 2:5  103 , E2 ¼ 5  103 . In this simulation, the reactor temperature is scaled to dimensionless value as u ¼ ðT  Tmin Þ=ðTmax  Tmin Þ, in which Tmin and Tmax are 298 (K) and 398 (K), respectively. u is the control variable, which is bounded by 0  u  1 and x2 ðtÞ ¼ yðtÞ is the output variable. The control objective is to manipulate the reactor temperature u to maximize concentration of B at the end of the batch x2 ðtf Þ ¼ yðtf Þ in the time interval [0, tf ]. The desired batch-end product quality is yd ðtf Þ ¼ 0:61. In this study, the controller parameters are chosen as k ¼ 60, l ¼ 2. The simulation ^ ð0Þ ¼ 0, / ^ ð1Þ ¼ is implemented by using the following initialization parameters: / k k 0:006, uk ð0Þ ¼ 0:6, uk ð1Þ ¼ 0:4, yk ð1Þ ¼ 0. The control performance of the proposed control strategy is tested by running 20 batches in nominal case. The input/output trajectories and batch-end output tracking error of the proposed controller systems are shown in Figs. 1, 2 and 3, respectively. Obviously, the proposed control strategy provides good performance from the 1st batch to the 20th batch. The proposed feedback QILC is compared with Yang’s method [8], traditional ILC [9] and Zhang’s method [12] as given in Table 1, which indicates that the proposed integrated control strategy have both faster convergence rate and smaller tracking error.

0.7

0.6

0.5

y

0.4

0.3

0.2 1st batch 7th batch 10th batch 20th batch

0.1

0

0

0.1

0.2

0.3

0.4

0.5 0.6 time(hour)

0.7

0.8

0.9

Fig. 1. Output trajectory of the integrated iterative learning control system

1

Q. Li and J. Yu 0.65 1st batch 7th batch 10th batch 20th batch

0.6 0.55 0.5

U

0.45 0.4 0.35 0.3 0.25 0.2

0

0.1

0.2

0.3

0.4

0.6 0.5 time(hour)

0.7

0.8

0.9

1

18

20

Fig. 2. Control trajectory of the feedback QILC system

-4

4.25

x 10

4.2 4.15 4.1

k

e (tf)

578

4.05 4 3.95 3.9 3.85

0

2

4

6

8

10 batch

12

14

16

Fig. 3. The batch-end tracking error based on the feedback QILC system

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Table 1. Batch-end output error value based on four different controller systems Methods The proposed Yang [8] ILC [9] Zhang [12]

1st batch

10th batch 15th batch

4:2  104 1:7  103 1:2  101 6:8  103

4:0  104 7:3  104 2:6  103 1:2  103

3:9  104 7:3  104 1:8  103 1:0  103

6 Conclusion In this work, a novel integrated MFAC-QILC framework is investigated, which can utilize the information of batch-axis and time-axis synchronously for controller design of batch processes to handle the model-plant mismatches. The convergence of the proposed approach is proved. Comparisons with previous presented methods show that the control performance has been improved both in convergence rate and tracking error. The results on a simulated batch reactor demonstrate the effectiveness of the proposed method. Acknowledgements. This work is partially supported by the Qing Lan Project of Jiangsu Province (No. 1602-2), Key Subject of Jiangsu Province Modern Education (No. 61980), PH.D Work Station of Jiangsu Maritime Institute (No. BS1602).

References 1. Lee JH, Lee KS (2007) Iterative learning control applied to batch processes: an overview. Control Eng Pract 15(10):1306–1318 2. Lee JH, Lee KS, Kim WC (2000) Model-based iterative learning control with a quadratic criterion for time-varying linear systems. Automatica 36(5):641–657 3. Xiong Z, Zhang J (2005) A batch-to-batch iterative optimal control strategy based on recurrent neural network models. J Process Contr. 15(11–21):19 4. Owens DH (2016) Iterative learning control an optimization paradigm. Springer, London 5. Shi J, Gao F, Wu TJ (2007) Single-cycle and multi-cycle generalized 2D model predictive iterative learning control schemes for batch processes. J Process Contr 17:715–727 6. Liu T, Gao F, Wang Y (2010) IMC-based iterative optimal control for batch processes with uncertain time delay. J Process Contr 20:173–180 7. Mo S, Wang L, Yao Y, Gao F (2012) Two-time dimensional dynamic matrix control for batch processes with convergence analysis against the 2D interval uncertainty. J Process Contr 22:899–914 8. Jia L, Yang T, Qiu M (2013) An integrated iterative learning control strategy with model identification and dynamic R-parameter for batch processes. J Process Contr 23:1332–1341 9. Jia L, Shi J, Qiu M (2012) Integrated neuro-fuzzy model and and dynamic R-parameter based quadratic criterion- iterative learning control for batch process control technique. Neurocomptuing 98:24–33 10. Xiong ZH, Zhang J, Wang X, Xu YM (2004) Run-to-run iterative optimization control of batch processes based on recurrent neural network. Adv Neural Networks 3174:97–103 11. Ray WH (1981) Advanced process control. McGraw-Hil, New York

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12. Xiong ZH, Zhang J (2003) Product quality trajectory tracking in batch processes using iterative learning control based on Time-Varying perturbation models. Am Chem Soc 42 (26):6802–6814 13. Hou ZS, Jin ST (2011) A novel data-driven control approach for a class of discrete-time nonlinear systems. IEEE Trans Control Syst Technol 19(6):1549–1558 14. Hou ZS, Jin ST (2011) Data-driven model-free adaptive control for a class of MIMO Nonlinear discrete time systems. IEEE Trans Neural Networks 22(12):2173–2188

Distributed Optimization Control for Active Distribution Networks with High Penetration of Distributed PV Units Kewang Wang(&) and Cungang Hu Anhui University, Hefei 230601, China [email protected]

Abstract. As the penetration level of distributed photovoltaic system keeps increasing in distribution networks (DNs), overvoltage caused by reverse power flow is an urgent issue to be solved. This paper proposes a distributed optimization control method by scheduling of controllable resources within each partition of DNs. In this optimization problem, the complex relationship between the power flow variables were replaced by a linear formula, and then the power flow model was transformed into a cone programming model. Afterwards, by means of partitioning a DNs into several clusters and decoupling of tie-line in adjacent clusters, the original problem is decomposed into subproblem of several clusters. According to collected local clusters data and finite boundary data exchange among adjacent clusters, the accelerated synchronous alternating direction method of multipliers (ADMM) are used to iteratively solve the optimal solution of the local clusters. After designing the synchronous ADMM, the convergence rate of synchronous ADMM is improved by the accelerated gradient method. The feasibility and effectiveness of the proposed methods are verified by the case study of the practical DNs in China. Keywords: Active distribution networks (ADNs)
Distributed optimization control
Synchronous alternating direction method of multipliers (SADMM) Second-order cone relaxation




1 Introduction With the large number of distributed power supply accessing DNs. Traditional DNs are transforming from the unidirectional power distribution network to the energy active bidirectional flow ADNs [1, 2]. The optimization of DNs has usually been settled in a centralized manner using a distribution management system (DMS). Due to the largescale integration of distributed generations (DGs) in ADNs, DMS will collect and process massive data, which will burden the subsequent communication work. In addition, in consideration of privacy issues. The centralized control method is inferior to the distributed optimal control method. So the distributed optimal control method is adopted in this paper. Many scholars have proposed a variety of convexification and linearization techniques to push complexity of the problem down. In [3], semi-definite relaxation (SDR) is applied to solve the optimal power flow (OPF) problem of power © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 581–589, 2020. https://doi.org/10.1007/978-981-32-9698-5_64

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system, which provides the initial point for searching a feasible solution by a local linear approximation of non-convex constraints. The limitation of SDR is discussed in [4] which first propose second-order conic (SoC) relaxation. The DistFlow branch equations were simplified by neglecting the quadratic term in nonlinear power flow equations in [5]. But there is a gap between the solution obtained by the way and the optimal solution. If the nonlinear and nonconvex problem involves converting into a convex and linear problem, it is relatively efficiently and easy to deal with the problem in a centralized or a distributed manner. ADMM algorithm has been widely used in distributed optimization. In [6], under the premise of reasonable partition of the ADNs, a solver was designed by using the ADMM to realize distributed reactive power optimization in the system. Reference [7] proposes double-layer distributed voltage control method, which voltage violation of intra-cluster was eliminated by the cluster autonomous optimization and the global optimal control was realized by inter-cluster coordination based on ADMM. In this paper, we use the “e-relaxation” based on the tight polyhedral representation of the conic constraints, to linearize the line-power flow equation. In this paper, an SADMM-based distributed optimization control method for the ADNs is designed by introducing reference variables.

2 Mathematical Formulation 2.1

Objective Function

The total network loss is formulated as f1 ¼

n1 X X

 2 rij Iij

i¼1 j2vðiÞ

  ref  n  X Vi  Vi  f2 ¼    DVi  i¼1

ð1Þ

Where n is the number of nodes in ADNs; rij is the resistance value of the branch (i,j); vðiÞ is the set of directed branches; Iij is the current amplitude of the branch (i,j). DVi is the difference value between the upper and lower voltage limits at bus i. 2.2

Constants

(1) Distflow branch equality constraints An example of the radial DNs is shown as Fig. 1, by which the DistFlow branch equations was illustrated (3). In the optimization model, it is a non-convex and nonlinear problem due to the existence of complex quadratic terms. In this paper, the power flow constraint is transformed into a linear equation group and a concise quadratic equation through a few of intermediate variables, and the quadratic equation is then linearized by “e-relaxation”. vi ¼ ðVi Þ2

 2 lij ¼ Iij

ð2Þ

Distributed Optimization Control for ADNs

CE

Controllable equipment

Ld

Load

PCC

l

PR, j ,QR, j

CE ,X R jl

i

Rij , X ij

Ld PD ,i , QD ,i

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j

jl

R jk , X jk

Ld PD , j , QD , j

PD ,l , QD ,l

k

Ld PD ,k , QD ,k

Fig. 1. Model of branch flow.

P 8 Pij ¼ Pk:j!k Pjk þ Pj þ lij rij > > > < Qij ¼ k:j!k Qjk þ Qj þ lij xij     2  2  vj ¼ vi  2 rij Pij þ xij Qij þ rij þ xij lij > > > : V1 ¼ V1ref

ð3Þ

The intermediate variables Vi ; lij are introduced, which are defined as (3) Where Pij , Qij are the active and reactive power on the front end of branch (i,j) respectively; Pj and Qj are the active and reactive power injected into bus j respectively. Pd;j and Qd;j are the active and reactive power from the load on bus j respectively. PCE;j and QCE;j are the injected active and reactive power from the controllable equipment on bus j respectively. Vi and Vj are the voltage amplitudes at bus i and bus j respectively and are the voltage amplitudes and reference voltages of the PCC points respectively; Iij is the amplitude of the current on the front end of branch (i,j). rij and xij are the impedance values of branch (i,j). (2) Voltage and branch current limits   Vimin  Vi  Vimax ; Iij   Iijmax

ð4Þ

where Vimin and Vimax are lower and upper limits of the bus voltage separately Iimax are upper limits of the current. (3) Pv constraints 2 2 PPV; j ¼ Pmax PV; j (QPV ; j Þ þ ðPPV ; j Þ  ðSPV ; j Þ

ð5Þ

Where PPV ; j and QPV ; j are separately the injected active and reactive power from PV on bus j. Pmax PV; j is the maximum power production on bus j. SPV ; j is the installed capacity of PV at bus j.

3 Distributed Optimization Model of ADNS Let V a and E a represent the bus set and the edge set in the cluster a, respectively. For any cluster a, it is coupled to the adjacent cluster by a certain tie-line. The upstream and downstream buses of coupling branches of the adjacent cluster are “copied” to

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opposing cluster to form a new sub-cluster [14]. The buses set of new sub-cluster is  a . Taking the simple DNs model shown in Fig. 2 as an example, the bus redefined as V set of cluster 1 is V 1 = {1-4, 12-13} and V 1 = {1-5, 12-13}, the bus set of cluster 2 is V 2 = {5-7} and V 2 = {4-8}, the bus set of cluster 3 is V 3 = {8-11, 14, 15} and V 3 = {7-11, 14, 15}.

Area1

Area2

Area3

Decoupling of cluster Area2

Area1

Area3

Fig. 2. Principle of inter-cluster decoupling.

xa;i ¼ fPa;i ; Qa;i ; Pa;ij ; Qa;ij ; va;i ; la;ij j 8j : i ! jg is defined as the state variable of bus i in the cluster a, the state variable of the boundary information is defined as Ba,ij = {Pij, Qij, vi, vj, lij| 8 j : i ! j}. Thus, Model in section II becomes decomposable as follows. min

r X

fa ðxa Þ

a¼1

s:t:

8 ga ð xa Þ  0 > > > > > < ha ð xa Þ ¼ 0

ð6Þ

> xa  xa  xa > > > > : Ba;ij ¼ Bb;ij

Where fa ðxa Þ is the objective function of the subproblem in cluster a; ga ðxa Þ is the equality constraint of the subproblem in cluster a; ha ðxa Þ is the inequality constraint of the sub-problem in cluster a; xa is the set of state variable xa , i in the cluster a;  xa and xa are the upper and lower limit.

4 ADMM-Based Solution Methodology ADMM for distributed calculations steps are: i h   q   xtaþ 1 ¼ arg min fa ðxa Þ þ kt Ba;i j  Btb;i j þ Ba;i j  Btb;i j  2 i h   q  tþ1  tþ1 B  B  B xbt þ 1 ¼ arg min fb ðxb Þ þ kt Ba;i þ   b;i j b;i j j 2 a;ij

ð7Þ ð8Þ

Distributed Optimization Control for ADNs

  tþ1 þ1 kt þ 1 ¼ kt þ q Ba;ij  Btb;ij

585

ð9Þ

Where t is the number of iterations; k is the augmented Lagrange multiplier vector; q is the penalty parameter. In order to achieve distributed optimization without the participation of the central coordinator and to improve the convergence speed, this paper proposes a synchronous ADMM algorithm based on the accelerated gradient method. By inspection of the primary and quadratic terms of the augmented Lagrange function for (29), we have 2 2 q    q  1 t   t   1 k kt k2 kt Ba;i j  Btb;ij þ Ba;i j  Btb;i j  ¼  B k  B þ a;i j b;i j 2 2 2 q 2 2q 2

ð10Þ

2

1 Let ut ¼ ð1=qÞkt , and 2q kkt k2 the constant can be omitted, then Eqs. (11), (30) and (31) can be transformed to

Bta;ij þ Btb;ij 2  2 q  t t ¼ arg min fa ðxa Þ þ Ba;i j  BKb;i j þ u  2 2   tþ1 t utaþ 1 ¼ utaþ 1 þ Ba;i j  BKb;i j tþ1 þ1 BKa;ij ¼ BtKb;ij ¼

xat þ 1

 2 q   xbt þ 1 ¼ arg min fb ðxb Þ þ Bb;ij  Btka;ij þ ut  2 2   tþ1 t utbþ 1 ¼ utb þ Bb;i j  BKa;i j xtaþ 1

2 q   t t ¼ arg min fa ðxa Þ þ Ba;i j  BKa;i j þ u  2 2

xtbþ 1

 st  1  t þ 1 ua  uta st þ 1  2 q   t t ¼ arg min fb ðxb Þ þ Bb;i j  BKb;i j þ u  2 2

ð11Þ ð12Þ ð13Þ ð14Þ ð15Þ



utaþ 1 ¼ utaþ 1 þ

utbþ 1 ¼ utbþ 1 þ

 st  1  t þ 1 ub  utb st þ 1

ð16Þ ð17Þ ð18Þ ð19Þ

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5 Numerical Results 5.1

Parameters of Test System

In order to investigate effectiveness of the proposed model and distributed optimization algorithm, a practical 10.5 kV radial feeder with high penetration of distributed PV units in China, is executed. As shown in Fig. 3, the topological structure of the feeder is divided into three clusters based on the cluster partition method in [21]. The base power was 1.0 MW, and the base voltage was 10.5 kV. The upper and lower limits of the bus voltage were given by Vimax = 1.05 and Vimin = 0.95. The set of nodes in each region is ^ B = {8-6, 26-28}, V ^ C = {18-23}. The buses 4, ^ A = {1-9, 17, 24, 25}, V respectively V 11, 13, 17, 20, 23, 25 are connected to Seven PV units. For the feeder system, three ESS were located at buses 5, 12 and 21.

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Fig. 3. The region division of IEEE 33 bus.

5.2

Analysis of Proposed Algorithm

In this part, the IPOPT and CPLEX business solvers are used to solve the centralized optimization problem. The analysis scenario is as follows: (A) the IPOPT solver is used to solve the nonlinear optimization problem in section II; (B) CPLEX solver is applied to deal with the linear optimization problem in section III; (C) The distributed optimization algorithm proposed in this paper is adopted to settle the linear optimization problem in section III. Scenario A is a traditional centralized optimization problem and the power flow constraint uses a branch flow equation without convex optimization; Scenario B uses a convex branch flow equation and is solved centrally by the CPLEX solver. Except applying the distributed solver designed in this paper, scenario C is the same as scenario B. Comparing scenario A and scenario B, it can be concluded that the calculation results after linearization are highly similar to that of the non-convex original problem. The existence of the deviation is mainly due to the acceptable error caused by polyhedron approximating of the second-order cone. The proposed distributed optimization control method is applied in this scenario C. With the iteration, the reactive power of PV is shown in Fig. 4. The communication burden between adjacent controllers is small, and the controller obtains the optimal control result of the cluster at a fast speed. Meanwhile, it is suitable for real-time control because of favorable efficiency.

Distributed Optimization Control for ADNs 70

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Fig. 4. Reactive power output of PVs.

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41 46 51 56 Time/15mi n

61 66 71

76 81 86

91 96

Fig. 5. Total active power output of load and PV

Results of Typical Daily Scenarios

Figure 5 is a comparison chart of the total active power output of distributed PV units and the total demand of the load for the typical daily scenarios in autumn. The penetration rate of distributed PV units reaches 128.52%. During the period from 8:00 to 16:00, the phenomenon that the power flow is reversed into the main grid is not conducive to local consumption of output power from distributed PV units and the operation of the distribution system (Fig. 6). -1 10

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Fig. 6. Convergence of boundary residual.

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Fig. 7. Active power of ESS.

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Fig. 8. Reactive power of ESS.

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Fig. 9. Active and reactive of PV in bus 11.

Figure 7 shows the charge and discharge power of ESS. As shown in the Fig. 12, near 9:00-16:00, since the active power of PV is difficult to be absorbed locally in the load, at this point, the ESS distributed in the three zones begin to respectively operate and store excess energy generated by PV. Near16:00-24:00, due to fluctuations in daily load and renewable energy output, it is difficult for PV to maintain the demand for load.

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The energy of ESS charged near the time from 9:00 to 16:00 in the three regions is released, which serves to stabilize power fluctuations. During the period from 21:0024:00, the discharge power of ESS2 in area B decreases gradually due to the reduce of load power demand. Figure 8 shows reactive power output of ESS in three area for all day, in which positive value represents the absorption of reactive power by the device. Since the voltage amplitude is within the redefined range in area C, the ESS3 hardly absorbed reactive power. Figure 9 shows the active power and reactive power output of PV2 located in bus 11. Near the 9:00 to 16:00 time zone, PV2 absorbs reactive power and reduces the voltage amplitude of bus 11 into a safe range. 2000

80

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Before optimi zation After optim ization

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70 Before optimi zation After optim ization

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60 500 0 -500

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11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 Time/15mi n

Fig. 10. Exchange power with main grid

0

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11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 Time/15mi n

Fig. 11. Network loss of ANDs.

In Fig. 10, the comparison of exchange power before and after optimization between the ADNs and the main grid is shown. It can be clearly seen from the Fig. 10 that after the optimization, the exchange power between the system and the main grid has significantly decreased. It implies that this strategy can effectively promote the selfconsumption of renewable energy in the system. Figure 11 shows the comparison of total network loss in the system before and after optimization for each time period. The comparison results show that the total network loss in the system is significantly reduced after distributed optimization. The total network loss of DNs decreased from 541:7220 kW
h to 217:7014 kW
h, which dropped by 62.95%. It proved that distributed optimization model of ADNs proposed in this paper can effectively reduce the network loss to improve the economic benefit of the system. From the analyses above, it is verified that the proposed method can effectively reduce the impact of short-term fluctuation of load and renewable energy on operation of DNs. Meanwhile, the method proposed allows us to optimize ADNs in a distributed way, which plays an important role in the protection of sensitive data in cluster.

6 Conclusion Based on SADMM, this paper proposes a distributed optimization model of ADNs with high penetration of distributed PV units. This method has four important characteristics: (1) By introducing the intermediate variable, the space of the solution is limited to the closed convex second-order cone and then the second-order cone is linearized by the “e-relaxation” method, which improves accuracy and optimality of the solution while speeding up the velocity of the solving problem. (2) There is no need for

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centralized controller and the independent control of each cluster protects the security of internal information in the cluster; (3) We accelerates the convergence of the algorithm by using an accelerated gradient method. (4) Compared to applying the standard ADMM algorithm, its advantage lies in that it does not require the participation of the global coordinator and the convergence speed is faster.

References 1. Xu T, Wu W, Sun H, Wang L (2017) Fully distributed multi-area dynamic economic dispatch method with second-order convergence for active distribution networks. IET Gener Transm Distrib 11:3955–3965 2. Li R, Wang W, Xia M (2018) Cooperative planning of active distribution system with renewable energy sources and energy storage systems. IEEE Access 6:5916–5926 3. Erseghe T, Tomasin S (2013) Power flow optimization for smart microgrids by SDP relaxation on linear networks. IEEE Trans Smart Grid 4:751–762 4. Andersen MS, Hansson A, Vandenberghe L (2014) Reduced-complexity semidefinite relaxations of optimal power flow problems. IEEE Trans Power Syst 29:1855–1863 5. Day-ahead Scheduling of Distribution Level Integrated Electricity and Natural Gas System Based on Fast-ADMM with Restart Algorithm. IEEE Access PP, 1 (2018) 6. Zheng W, Wenchuan W, Zhang B, Sun H, Liu Y (2016) A fully distributed reactive power optimization and control method for active distribution networks. IEEE Trans Smart Grid 7 (2):1021–1033 7. Chai Y, Guo L, Wang C, Zhao Z, Du X, Pan J (2018) Network partition and voltage coordination control for distribution networks with high penetration of distributed PV units. IEEE Trans Power Syst 33:3396–3407 8. Boyd S, Parikh N, Chu E, Peleato B (2010) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3:1–122

Research on the Improved Wavelet Threshold Denoising Method for Coriolis Mass Flowmeter Dan Feng, Qite Wang, and Yanjie Zhao(&) China Academy of Electronics and Information Technology, Beijing 100041, China [email protected] Abstract. In view of the fact that Coriolis mass flowmeter is sensitive to noise and has poor anti-jamming ability, this paper applies an improved wavelet threshold signal processing method to overcome this problem. This method can be changed with the number of decomposed layers, as it is shown flexibility in practice situation. In this paper, Signal Noise Ratio and Mean Square Error are used as the parameters to evaluate the denoising performance. The simulation results show that the improved wavelet threshold signal processing algorithm can better reduce the influence of noise and improve the quality of output signal compared with the traditional wavelet threshold processing algorithm. It lays a foundation for the accurate measurement of Coriolis mass flowmeter. Keywords: Signal processing Coriolis mass flowmeter


Wavelet threshold filtering


1 Introduction The Coriolis mass flowmeter (CMF) is a high-precision device utilized to measure the mass flow of fluid directly and has wide application in many industries, such as the petrochemical industry, food processing industry, etc. [1]. Since the CMF became commercially available in the 1970s, many significant technological improvements have been made to enhance its measurement performance [2]. However, the traditional CMF has a weak anti-jamming capability. The meter is particularly sensitive to noise because of limitations of its working principles and signal processing methods [3]. There are many kinds of industrial noise and inevitable interference. When noise produces serious influence, the CMF performance is degraded significantly and even cannot work properly [4]. Currently, most of the traditional signal processing methods is based on Fourier transform analysis method, combined with the form of filter to achieve the goal of signal denoising, but this kind of method cannot show the time-frequency characteristics of the signal, which has some limitations. To solve the aforementioned problems, an improved wavelet threshold denoising method is adopted in the CMF. This method can be changed with the number of decomposed layers, as it is shown flexibility in practice situation. In this paper, Signal © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 590–596, 2020. https://doi.org/10.1007/978-981-32-9698-5_65

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Noise Ratio (SNR) and Mean Square Error (MSE) are used as the parameters to evaluate the denoising performance. The wavelet threshold denoising method is simple and effective.

2 Wavelet Bases Selection The selection of wavelet basis can be based on the continuity of the signal. If the continuity of the signal is poor, the Haar wavelet can be selected; if the continuity and smoothness of the signal are good, the Sym8 function can be selected. The function has good continuity and symmetry, so it is more suitable to deal with the signal with good continuity and get better denoising effect. However, according to the characteristics of each wavelet basis function, it can be seen that the wavelet basis function has its own characteristics and different applicability in processing the signal, so it can be selected according to the actual signal to be processed. The results of wavelet denoising for different signals are also different. In this paper, dbN wavelet is finally used to denoise the processed signal, among which N = 6.

3 Traditional Wavelet Threshold Signal Processing 3.1

Traditional Threshold Function

After the wavelet basis function is selected, the selection of the threshold function has a decisive effect on the final effect of denoising during signal denoising processing. If the threshold value is too small, the wavelet coefficients of some noises will not be zero in the process of comparing with the absolute values of wavelet coefficients. This part of noise will be taken to the subsequent analysis and the final denoising effect of the signal will become worse. However, if the threshold selection is too large, after comparing with the absolute value of the signal wavelet coefficient, a part of the valid signal will be filtered out by error, so that the useful signal is lost. Therefore, reasonable selection of threshold function is critical to signal noise processing. At present, the traditional wavelet thresholds are mainly hard-threshold and softthreshold. They are two kinds of processing functions proposed by Donohoe D. L. and Johnstone L. M. in the 1990s. The processing method of the hard-threshold function is realized by comparing the absolute value of the wavelet coefficient with the magnitude of the threshold function, and only the portion whose threshold value is smaller than the absolute value of the wavelet coefficient is retained, and the portion whose threshold value is greater than or equal to the absolute value of the wavelet coefficient is cut off by one knife. In this way, a sudden change of the signal will occur in the wavelet domain of the signal, and a discontinuous signal will be generated at the threshold ± T, so that local jitter phenomenon occurs during the process of denoising the signal [5]. The soft-threshold function still uses the way of comparing the absolute value of wavelet coefficient with the threshold value, but the difference is that when the absolute value of wavelet coefficient is larger than the threshold value, the wavelet coefficient is

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not only reserved simply. As shown in Figs. 1 and 2, the visual effect diagrams of the soft-hard thresholds are respectively shown. It can be seen from the figure that the lines processed by the soft-threshold method have no significant mutations compared with the hard-threshold, and the obtained signals are consistent and denoised. The effect will be better, and the analysis and description of a wide range of features can be carried out, and the empirical analysis can be carried out without affecting the overall characteristics, which is closer to the practical application.

Fig. 1. The soft-threshold method

3.2

Fig. 2. The hard-threshold method

Results Analysis

The comparison result of soft-threshold method with hard-threshold method shows in Figure 3. The SNR of original CMF is 9.85. The wavelet basis function’s The original noisy signal is decomposed into three layers by the wavelet basis function db6. Analyzed by wavelet hard-threshold, the signal SNR is changed into 16.23. Similarly, analyzed by wavelet soft-threshold, the signal SNR is changed into 18.57. The analysis results verify the superiority of the soft-threshold function. However, there is always an indelible deviation between the recombined signals processed by the soft-threshold method and the original signal. Therefore, based on the analysis of the characteristics of soft and hard-threshold method, the improvement of wavelet threshold method mainly focus on the threshold function and the selected criteria of threshold, in order to select the threshold values of each layer adaptively.

4 Improved Wavelet Threshold Signal Processing In this paper, the wavelet threshold function is improved for the existing soft-threshold and the defects of the hard-threshold function. The improved wavelet threshold denoising processing method is applied to the signal denoising process of CMF. This method can not only effectively remove noise, but also reduce the loss of useful

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information. The improved wavelet threshold function applied in this paper is as follows [6]: ( Wk ¼


 sin ðW Þ jW j  eMðWT2 T 2 Þ ; jW j  T 0; jW j\T

ð1Þ

In Eq. (1), the wavelet coefficients after dimensional wavelet threshold processing, W is the wavelet coefficient after signal decomposition, and T is the obtained threshold, M = 0.2. 4.1

Selection of Threshold Function

There are four main threshold selection principles in the wavelet threshold denoising method [7]: (1) The threshold value of the sqtwolog threshold selection function is constant, fixed, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and the defined threshold is T ¼ rn 2 lnðNs Þ, rn is the standard deviation of the noise in the pending signal, Ns is the sample points for the pending signal. (2) The threshold selection of minimaxi threshold function is based on the minimax principle. Adopted this minimaxi function will eventually produce an extreme value of the minimum mean square error. (3) The rigrsure threshold function uses the unbiased likelihood estimation principle of Stein to select the adaptive threshold. And finally according to risk assessment at the threshold to select the least risky threshold. (4) The heursure threshold function is a heuristic threshold selection method, which combines the characteristics of sqtwolog and rigrsure functions, and finally uses the optimal predictor as the final selection of the threshold. Four kinds of unused threshold selection functions are applied to the processing of the original CMF signals in the same 35t/h flow state. Figure 4 shows the comparison of the denoising results of each function. Figure 3(a) is the time-domain diagram of the CMF raw signal in the 35t/h flow state, SNR = 5.53; Fig. 3(b) is the processed result of denoising the noisy signal with heursure threshold selection function, SNR = 16.7; Fig. 3(c) is the processed result of sqtwolog denoising, the signal-to-noise ratio is SNR = 11.1; Fig. 3(d) is the processed result of denoising with rigrsure for the original noisy signal, SNR = 15.9; Fig. 3(e) is the processed result of denoising with minimaxi, and the signal-to-noise ratio is SNR = 7.4. Based on the above analysis results, the “heursure” threshold function is used in the subsequent signal processing.

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4.2

Results Analysis 5

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(e) Fig. 3. The soft-threshold processing results with different threshold functions

Figure 4 is the CMF signal filtered by the improved wavelet threshold method. The SNR of original signal is 16.26. The SNR of signal filtered by the improved wavelet threshold method is 72.15, and MES is 0.40. It can be seen that the improved

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Fig. 4. The filtered spectrogram by the improved wavelet threshold method.

wavelet threshold function has stronger processing ability on CMF signal. The SNR of signal filtered by improved method is greatly improved. Meanwhile, this improved method can effectively avoid the defects of traditional wavelet threshold methods. Acknowledgments. In view of the fact that Coriolis mass flowmeter is sensitive to noise and poor in anti-interference, this paper applies an improved wavelet threshold signal processing method to denoising and filtering the original data of CMF signal collected in the field. The spectrum map before and after filtering and the performance indicators show that the improved wavelet threshold signal processing algorithm can improve the anti-interference of CMF better than the traditional wavelet threshold processing algorithm, effectively reduce the influence of noise and improve the output signal. It lays the foundation for further accurate measurement of CMF.

References 1. Zheng D, Wang S, Fan S (2009) Nonlinear vibration characteristics of coriolis mass flowmeter. Chin J Aeronaut 22:198–205 2. Wang T, Hussain Y (2010) Pressure effects on coriolis mass flowmeters. Flow Measur Instrum 21:504–510 3. Feng D, Fan S, Zheng D (2016) A time-varying signal processing method for coriolis mass flowmeter based on adaptive filter. https://doi.org/10.1177/0142331216652955 4. Clark C, Cheesewright R (2003) The influence upon Coriolis mass flow meters of external vibrations at selected frequencies. Flow Measur Instrum 14:33–42

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5. Liu H, Weida W (2018) A denoising method using the improved wavelet threshold function based on noise variance estimation. Mech Syst Sig Process 99:30–46 6. Li Q (2018) The study on signal denoising algorithm based on wavelet threshold. Xinjiang University 2013 7. Xu L (2009) Research on wavelet thresholding method for image denoising. Sci Technol Eng 9(22):1671–1819

Research on Localization System of a Permanent Magnet Based on Digital Magnetic Sensors Array Jiansheng Xu1(&), Ming Xu1, Xuan Zhao1, William Zhou2, and Xiaojian Li3 1

3

Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China [email protected] 2 Lanzhou Jiaotong University, Lanzhou, China Information and Computing Science, HuaZhong Agriculture University, Wuhan, China

Abstract. A localization system for the tracking of capsule robot with a cylindrical permanent magnet inside based on digital sensor array is introduced. The magnetic field signal of the permanent magnet is collected by 5
5 sensors array and transmitted to computer through serial port. The position and orientation parameters are calculated in MATLAB. The experimental results show that the position tracking effect is well performed and the approximate relation between average localization error and the distance is nearly linear. Keywords: Capsule robot Least square fitting

 Localization system  Sensors array 

1 Introduction With the development of modern biomedical engineering and the improvement of people’s quality of life, more and more attention has been paid to minimally invasive and non-invasive in vivo micro-diagnostic and therapeutic equipment. Medical diagnosis and treatment robot can reduce the damage to human digestive tract tissue, shorten the recovery time after surgery, reduce the area of trauma and reduce the cost, which has a very broad development prospect [1]. Capsule robot is a kind of intelligent micro-tool that can enter the human gastrointestinal tract for medical exploration and treatment, and it is a new breakthrough in medical technology of interventional examination and treatment in vivo [2]. At present, the localization research of capsule robot has made some certain progress [3]. Since the magnetic permeability of human biological tissue is close to that of air, and the effect on the static magnetic field is similar to that of air, water and other non-magnetic materials, the positioning method using static magnetic field technology has achieved high accuracy. For example, Hu et al. [4] designed a 4
4-structure 3d magnetic positioning and orientation system to track the trajectory of the wireless capsule, with an average © Springer Nature Singapore Pte Ltd. 2020 Y. Jia et al. (Eds.): CISC 2019, LNEE 594, pp. 597–604, 2020. https://doi.org/10.1007/978-981-32-9698-5_66

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positioning accuracy of 3.64 mm. Wang et al. [5] realized the bionic micro-robot positioning system based on differential magnetic localization technology. The interference of high background magnetic field was effectively removed by 8 sets of sensors, and the average distance error was 4.49 mm. Liao et al. [6] designed an in vitro magnetic tracking and positioning system based on hall sensor array, using csa-1v sensor to form a 4 x 4 sensor array, and the mean absolute error of measurement points was 4 mm. Zheng et al. [7] used an array of 16 SEN-S65 sensors which was used to measure the magnetic field generated by the permanent magnet fixed in the electronic capsule, achieving an average positioning accuracy of less than 7 mm. Yang et al. [8] designed a magnetic positioning system with 80 sensor structures based on target tracking technology, and the accuracy reached 2 mm. Wang et al. [9] designed and implemented a wearable endoscopic positioning system, using the elliptic model layout structure of 32 sensors, achieving a positioning accuracy of 0.9 mm. However, these systems are all composed of analog sensors. The system structure is complex and the stability and scalability are not high. Therefore, a magnetic positioning system based on digital sensor array is proposed.

2 Principle and Algorithm The capsule robot has a cylindrical permanent magnet fixed inside [10]. According to the position and direction of the permanent magnet, the position and direction of the capsule can be determined. The cylindrical permanent magnet used in this paper is regarded as a magnetic dipole. The triaxial component of the magnetic induction intensity of the permanent magnet at any sample point in space [11] is: n o 8 3½mðxl aÞ þ nðyl bÞ þ pðzl cÞðxl aÞ m > B ¼ k  3 lx BT 5 > rl rl > < n o 3½mðxl aÞ þ nðyl bÞ þ pðzl cÞðyl bÞ n Bly ¼ kBT  3 5 rl rl > n o > > 3½ðxl aÞ þ nðyl bÞ þ pðzl cÞðzl cÞ p : B ¼k  lz BT r3 r5 l

ð1Þ

l

And the constraint equation is 1 ¼ m 2 þ n2 þ p2

ð2Þ

Where, ðxl ; yl ; zl Þ represents the sample point coordinates; ðBlx ; Bly ; Blz Þ represents the triaxial magnetic induction intensity data of the sample point; (a, b, c) and (m, n, p) respectively represent the three position and three direction parameters of the permanent magnet; kBT is related to magnetic moment of the permanent magnet, and its unit is Gauss  cm3 under the Gaussian system of units. The above magnetic positioning equations describe the relationship between the magnetic field data of the sample points and the coordinates of the sample points. The magnetic field data of the permanent magnet measured by some fixed sensors with known coordinates can be fitted to the equation coefficients by the least square method, that is, the position and direction parameters of the permanent magnet can be obtained.

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3 System Design The proposed magnetic localization system mainly includes the hardware part of magnetic field measurement and the localization algorithm. The designed model and the real experiment set of the capsule robot localization system are shown in Fig. 1. As shown in the figure, the set is designed within a cubic area 60 cm
50 cm
50 cm, which can meet the requirements of most people’s body size. The sensors array is a two-sided structure, located on the upper and lower sides of the human body with each having 5
5 digital magnetic sensors, so that the distance between the capsule and a single sensor surface is always less than 25 cm.

Fig. 1. Model of capsule robot localization system

As the system is a two-sided symmetrical structure, in the actual experiment, the hardware part is simplified to a single-sided structure with 5
5 sensors. The experimental space is within the range of 25 cm directly above the sensors array surface. A ¢ 6 mm x 10 mm cylindrical N35 NdFeB permanent magnet is chosen as a magnetic source, and some tri-axial magnetic field sensors QMC5883L are used to collect the permanent magnet magnetic signal. The sensor arrays are arranged in a uniform distribution with spacing of 6.85 cm and 5.5 cm. The sensor data is sent to the MCU through the I2C bus for storage, and then sent to an industrial computer through the UART communication serial port. That is, the magnetic field data is received through the MATLAB serial port by interrupt mode, and the position and orientation parameters are calculated in MATLAB according to Eqs. (1) and (2). Algorithm flow chart is shown in Fig. 2.

4 Experiments and Results 4.1

Trajectory Tracking

Magnetic localization system experimental platform and trajectory tracking effect as shown in Fig. 3. Figure 3(a) is the experiment set. Experimental measurements, to

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Begin

Obtain data from UART Geomagnetic field B0 Magnet magnetic field data B-B0

ydata xdata Location algorithm

Track display

End Fig. 2. The algorithm flow chart of the algorithm

obtain the coefficient of magnetic localization system of equations. Through the sensor hardware calibration [12] to get the optimized magnetic localization algorithm. Combined with optimization algorithm to get the accurate real-time track paths display. As shown in Fig. 3, Fig. 3(b) is the tracking trajectory of letter e, Fig. 3(c) is the tracking trajectory of digital number 8, and Fig. 3(d) is the tracking trajectory of the rectangle. According to the algorithm we calculate the position and direction parameters of the permanent magnet, then compare with the real value, the position and angle error can be found among them, the position error can be represented as: DP ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Da2 þ Db2 þ Dc2

ð3Þ

When the angular deviation Dh is very small, angle error is expressed as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 180 Dh 
Dm2 þ Dn2 þ Dp2 p 

ð4Þ

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Fig. 3. Experiment platform and tracking effect of magnetic localization system. (a) Experimental set (b) Tracking trajectory of letter “e” (b) Tracking trajectory of digital number “8” (d) Tracking trajectory of “口”.

The experiment measured the 54 preset positions and orientations of permanent magnet, a total of 162 sets of data points in three direction, according to these data to determine the average precision of the magnetic localization system. The distribution of 54 points as shown in Fig. 4. Fig. 4(a) is the Top view of the points and Fig. 4(b) is the Left view of the points. It is obtained that the mean position error is 0.6692 cm after data processing, and 80% of the data point’s position deviation is less than 1 cm. While the average angle error is 5.82°, and with 62% of the data point’s angular deviation is less than 5°.

5 The Experiment Results Analysis Experiments in 162 groups of data point’s average distributed in six different plane, the error data according to the data point and the size of the distance of the sensor array z, rearrange the processing, can get the following results, as shown in Table 1. The average position errors, angular errors and the distances from the data points to sensors array are shown in Fig. 5. Form the figure we supposed that the relationship between the localization errors and the distance is approximate linear. So we deal with the data in MATLAB.

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Fig. 4. Distribution of experiment points/cm (a) Points of Top view (b) Points of Left view Table 1. Relations between average error and distance from data points to sensors array Distance/cm 7.68 10.68 13.68 16.68 19.68 22.68

Position error/cm Angular error/° 0.2297 2.2343 0.2373 2.3119 0.6012 6.4535 0.6886 6.6574 1.2631 9.7647 0.9950 7.4982

Fig. 5. Relations between the average localization error and distance z. (a) The relationship between the position error and the distance z (b) The relationship between the angular error and the distance z

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As shown in Fig. 5, the relationship formula between the system average position error e (unit: cm) and the distance from the permanent magnet to the sensor array distance z (unit: cm) is expressed as: e ¼ 0:0666z  0:3416:

ð5Þ

The fitting formula between the system average angle error ee (unit: cm) and the distance from the permanent magnet to the sensor array distance z (unit: cm) is expressed as: ee ¼ 0:4655z  1:2489:

ð6Þ

The formula reflect that the relationship between the average localization error and the distance from permanent magnet to the surface of the sensor is linear. They provide a reference for the capsule robot localization accuracy. According to the formula the different experimental areas can be obtained under the condition of approximation error.

6 Conclusions The capsule robot localization technology based on digital magnetic sensors array is thoroughly studied in this paper. Experiment results show that the localization errors increase linearly with the distance from the permanent magnet to the surface of the sensor array. And it is reasonable since this result is according with that the magnetic signal is decreases with distance. And it gives the way that we further improve the localization accuracy. We will do more work as following: (1) parameters based on the orientation angle sensor can be calculated first, simplifying the magnetic positioning equations, so as to get more accurate position parameters. (2) use higher precision of sensors, to get more accurate data of magnetic field, get a more accurate calculation results. (3) adopt a more reasonable sensor layout, reduce the average distance of the permanent magnet to the sensor, improve signal-to-noise ratio enhancement magnetic signals, reduce the interference to improve precision.

References 1. Yuan D, Shi W, Sun X, Hu L, Yang M, Li J, Ran W (2019) Analysis of the predictive factors of positive capsule endoscopy findings for obscure gastrointestin bleding. Chin J Gastroenterol Hepatol 28(4):418–421 2. Ni Z, Wang T, Liu D (2015) Survey on medical robotics. J Mech Eng 51(13):45–52 3. Xu J, Song T (2012) Differential magnetic localization method for the microrobot with two cylindrical permanent magnets. In: The 31st China control conference, pp 4798–4802 4. Hu C (2006) Localization and orientation system for robotic wireless capsule endoscope. University of Alberta 5. Wang Z, Song T, Wang J, Wang Z, Yang C (2009) Differential magnetic localization algorithm in high background. Chin J Sci Instr 30(11):2384–2389

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6. Liao Y, Jiang P, Yan G (2012) Magnet field tracking system in vitro based on the hall effect sensors array. Beijing Biomed Eng 31(5):501-506 7. Zheng X, Li J, Hou W, He J (2009) Localizing and tracking of medical capsule in human by magnetic sensor array. Opt Precis Eng 17(3):576–582 8. Yang L (2010) Design of the magnetic localization and orientation system based on magnetic sensor array. Harbin Institute of Technology 9. Wang W (2014) Capsule endoscopy localization based on embedded system. Ningbo University 10. Xu J (2013) Research on sensors arrangement for capsule endoscope microrobot magnetic localization. In: China conference on control and decision, pp 5208–5211 11. Xu M, Kong D, Ye L, et al (2017) A new localization system for tracking capsule endoscope robot based on digital 3-axis magnetic sensors array. In: Chinese intelligent systems conference. Springer, Singapore, pp 487–494 12. Li M, Song S, Hu C, et al (2009) A new calibration method for magnetic sensor array for tracking capsule endoscope. In: IEEE international conference on robotics and biomimetics. IEEE, pp 1561–1566

Weighted Multiple Support Vector Regression Models Based on Clustering Algorithm Ling Wang(&), Kang Li, and Qian Ma School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 10083, China [email protected]

Abstract. A new Weighted Multiple Support Vector Regression Models Based on Clustering Algorithm is proposed to model dynamic system. Firstly, SOM and k-means clustering algorithm is applied to partition the whole training set into several disjointed regions. Secondly, the best weighted combination of different kernel function of SVR fit each partitioned cluster. Finally, this new approach is applied to time-series prediction problems, the results show that the learning strategy has effective improvement in the generalization performance in comparison with the single SVR model. Keywords: SOM


K-means
Clustering algorithm
Weight
SVR

1 Introduction Support vector machines (SVMs) [1] is a kind of machine learning algorithm based on statistical learning theory, which show the good generalization ability in solving small sample, nonlinear, high-dimensional pattern recognition and regression estimation problems through optimum solution. SVMs have now been ap-plied in many fields such as fault diagnosis [2], classification [3], regression estimation [4], and several other applications [5]. However, it is hard for a single model including SVMs to capture such a dynamic input-output relationship inherent in the data. Furthermore, using a single model to learn the data is somewhat mismatch as there are different noise levels in different input regions—the noise in the data could lead to the over- fitting in some region or under-fitting in another region. In order to overcome the above problems, a potential solution is to use a mixture of experts (ME) architecture [6, 7]. In view of the ME architecture, this paper incorporates the ME architecture into SVMs by using a two-stage neural network architecture. First, the initial sample set is dynamically clustered by the self-organizing Map (SOM) neural network and the K-means clustering algorithm. Then, multiple sub-support vector regression (SVR) models are described for each clustered data set, and the model is obtained by weighted combination. This paper is organized as follows. An introduction of SOM and K-means clustering algorithm is given in Sect. 2. In Sect. 3, we review the use of SVMs in regression problem and present the architecture of the weighted multiple SVR model.

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In Sect. 4, experiment results are presented and discussed, finally, some conclusions are drawn in Sect. 5.

2 SOM and K-means Clustering Algorithm Self-Organizing Map Neural Network (SOM) [8] is an artificial neural network model based on unsupervised and competitive learning, which can realize the mapping from high-dimensional input space to two-dimensional grid-like neuron space. However, in the dynamic learning process, especially in the initial stage, a SOM neuron is initially clustered into one category. After a period of learning, it would be clustered into another category. If its weight vector has not been converged to a certain category, then it may be labeled as two or more category. This will inevitably make the SOM highly unstable at the initial stage and subsequent stages. In order to avoid re-learning, an online k-means clustering algorithm [9] was introduced to all winning neurons in the SOM’s competitive output layer, which is mainly used to minimize the squared distance between the input vector and the weight vector. Because the parameter of k-means clusters algorithm is very small, it can reduce the time to try parameters. After the SOM network forms multiple winning neurons at the competitive output layer, the winning neuron nodes that are close to the weight vector are obtained according to the minimum distance, the average of all the samples belonging to these nodes is looked as the initial clustering center of the K-means clustering algorithm, the input samples are re-clustered according to the minimum distance until the algorithm converges. The dynamic clustering algorithm combined SOM with k-means is described as follows: Step (1) Choose random values for the initial weights wj ð0Þ. Step (2) Find the winning neuron j at the k th iteration, using the minimumdistance Euclidean criterion

j ¼ arg minj
xj ðk Þ  wj ðkÞ
; j ¼ 1; . . .; N

ð1Þ

Where xj represents the j th input pattern, N is the total number of neurons, and k
k indicates the Euclidean norm. Step (3) Adjust the weights of the winner and its neighbors, using the following rule: wj ðk þ 1Þ ¼ wj ðkÞ þ gðkÞNj ðkÞðxj ðkÞ  wj ðk ÞÞ

ð2Þ

Where gðkÞ is a positive constant and Nj ðkÞ is the topological neighborhood function of the winner neuron at the k th iteration.  Nj ðkÞ ¼

1; disðwj ; wj Þ  rðkÞ 0; otherwise

ð3Þ

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Where disð
Þ is the distance between node j and node j , dis wj ; wj ¼
wj  wj
. Let r ðkÞ ¼ rð0Þ  ð1  k=TÞ, rð0Þ be the initial state of rðnÞ. T is the number of iterations throughout the learning. Step (4) Compute the distance between the neighboring activated neuron nodes of the SOM output layer according to Eq. (3). The two nodes with small distances can be merged into one activated neuron node uðjÞ. Step (5) Take the center of gravity of all input modes belonging to uðjÞ as the initial clustering center in k-means algorithm. C j ð 1Þ ¼

1X x ; j ¼ 1; . . .c xj 2uð jÞ j p

ð4Þ

Where, Cj ð1Þ denotes the first iteration for finding the cluster center of the j th cluster. p is the number of input modes belonging to uðjÞ, c is the number of clusters. Step (6) The new input Sample is assigned to one of the clusters according to the minimum distance between the samples with the cluster centers. Step (7) Calculate the new vector value of each cluster center. If Cj ðk þ 1Þ 6¼ Cj ðkÞ, returns to step 6, the input sample is re-clustered and repeated the iteration calculation. Otherwise, the algorithm converges and the learning process is finished.

3 Learning Strategy of Weighted Multiple Support Vector Regression Models For support vector machines, a kernel function [10] needs to be selected to solve the regression estimation problem. Although the functions satisfying the Mercer’s condition can be theoretically selected as a kernel function, for certain problems, the regression estimates obtained by different kernel functions will also be very different. Therefore, how to choose a kernel function for a particular problem is crucial. Even if a certain kind of kernel function is selected, the corresponding parameters (such as the order of the polynomial function, the radial basis parameter r) also need to be selected. In this paper, the optimized linear combination of support vector regression model is adopted by weighting the regression functions with different kernel functions. The weights are calculated by the method of MSE-OLC [11] to avoid the overfitting caused by improper kernel parameters. 3.1

Support Vector Regression

Support Vector Regression (SVR), one of the most important applications of SVMs [1]. The standard SVR is to solve the approximation problem such as f ð xÞ ¼

XN i¼1

ðai  ai ÞKðxi ; xÞ þ b

ð5Þ

Where ai and ai are lagrange multipliers. The kernel function Kðxi ; xÞ is defined as a linear dot product of the nonlinear mapping,

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K ðxi ; xÞ ¼ uðxi Þ
uðxÞ

ð6Þ

The coefficients ai and ai of Eq. (5) are obtained by minimizing the following regularized risk functional Rreg ½f , which is a combination of the model complexity and the empirical risk, for given error bound e, Xl 1 Rreg ½ f  ¼ kxk2 þ C L ðyÞ i¼1 e 2

ð7Þ

Here, kxk2 is a term which characterizes the model complexity, C is a constant determining the trade-off and the e-insensitive loss function Le ðyÞ is given by  Le ð yÞ ¼

for jf ðxÞ  yj\e 0 otherwise j f ð xÞ  y j  e

ð8Þ

The minimization of regularized risk function in Eq. (3) can be converted to the following constrained optimization problem,    1 XN XN   mina;a xða; a Þ ¼ mina;a a  a  a K ð xi ; xÞ a i j i j i¼1 j¼1 2 XN  X   N    ai  ai yi þ e ai  ai i¼1 i¼1 (P   N  i¼1 ai  ai ¼ 0 subject to a; a 2 ½0; c

ð9Þ

Where the kernel function used is Gaussian and defined as K ðxi ; xÞ ¼ expð




xi  x2
2r2

Þ

ð10Þ

Where r is a constant. 3.2

Weighted Multiple SVR Models

Based on the above clustering algorithm, we adopt the weighted combination of subsupport vector regression models formed by different kernel functions to obtain the combined output. The weighted output of each cluster set is defined as: y ¼ f ð xÞ ¼

XM k¼1

pk ðxk uk ðxÞ þ bk Þ

ð11Þ

Where M is the number of sub-support vector regression models in the cluster, and xk ; bk are the weights and thresholds of the k th sub-support vector regression model, respectively. The weight pk is determined by using the unconstrained MSE-OLC (Mean Squared error–Optical Linear Combinations) method proposed by Hashem [11],

Weighted Multiple Support Vector Regression Models

XM k¼1

pk ¼ 1; 0  pk  1; k ¼ 1; . . .; M

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ð12Þ

Similarly, according to the SVR method, the optimization problem can be described as follows: P P 2  1 min k jxk j þ C i ðni þ ni Þ 8 2 P yi  k pk ðxk uk ðxi Þ þ bk Þ  e