Proceedings of the International Conference on Aerospace System Science and Engineering 2022 9819906504, 9789819906505

Table of contents :
Preface
Contents
A Methodology for Designing the Flight Deck Windows
1 Introduction
2 Analysis of Cabin Design Standards
2.1 OST 1 00444-81
2.2 SAE ARP 4101/2
2.3 Comparison of View Diagrams
3 Comparison of View Diagrams
4 Conclusion
References
Deep Learning-Based Screen Text Detection and Recognition for Onboard Maintenance Systems
1 Introduction
2 Text Detection
2.1 Feature Extraction Network
2.2 Feature Fusion and Prediction Layer
3 Text Recognition
3.1 CRNN + CTC
3.2 Post Processing
4 Experimental Results and Analysis
4.1 Datasets and Settings
4.2 Evaluation Indicators
4.3 Experimental Comparison
5 Conclusion
References
Comprehensive Evaluation of Agile Aircraft Development Process Based on Delphi-ANP
1 Introduction
2 Evaluation Index System Determination
3 Delphi-ANP-Based Agile Aircraft Development Process Evaluation Model
4 Sample Validation
5 Conclusion
References
Effects of Gap Width on Vibration Response of Aileron-Cabin-Model Due to Acoustic-Structure Coupling
1 Introduction
2 Theoretical Method
2.1 Helmholtz Resonance Theory
2.2 Acoustic -Structure Coupling Finite Element Equation
3 Finite Element Model
4 Numerical Calculation Analysis
4.1 Cavity Modal Analysis
4.2 Structural Modal Analysis
4.3 Modal Analysis of Coupled Systems
4.4 Harmonic Response Analysis of Coupled Systems
5 Conclusion
References
Simulation of Tensile Test for Laminate Made of CFRP. Role of Different Parameters that Influence the Failure Mode Type
1 Introduction
2 Experimental Part
2.1 Material
2.2 Geometry
3 Results and Discussion
4 Conclusions
References
SysML-Based Approach for Functional Modeling of Civil Aircraft Systems
1 Introduction
2 Functional Modeling of Components
2.1 Representation of Component States
2.2 Representation of Component Behaviors
2.3 Representation of Component Action
2.4 Representation of Component Functions
3 Integration of Component Functional Models
3.1 Representation of Component States Integration
3.2 Representation of Component Behaviors Integration
3.3 Representation of Component Actions Integration
4 Case Study
4.1 Introduction of Landing Gear Systems
4.2 Functional Modeling of Components of Landing Gear Systems
4.3 Integration of Component Functional Models of Landing Gear Systems
4.4 Functional Simulation of Landing Gear Systems
5 Conclusion
References
Orientation Method of Ultralight UAV with a Rare Update of Its Location Data
1 Introduction
2 UAV Positioning Methods in Space
3 Orientation Method of Ultralight UAV with a Rare Update of Its Location Data
3.1 The Algorithm for the Movement of an Ultralight UAV Based on Previously Selected Terrain Information
3.2 Flight Optimization Algorithm
4 Conclusion
References
Optimization of Design Parameters of a Small-Sized Unmanned Aircraft with a Turbojet Engine Equipped with an Ejector Thrust Magnifier
1 Introduction
2 Requirements
3 Ejectors and Their Application in Installations with Aircraft Engines
4 Geometry and Characteristics of a Semi-rotating Wing
5 Calculation Area and Graphs
6 Analysis of the Aerodynamic Characteristics of the Aircraft
7 Calculation Results
8 Ejector Thrust Magnifier
9 Mathematical Model
10 Numerical Calculation of the Ejector Thrust Magnifier
11 Conclusions
References
Estimation of Strength Properties of Glass Fiber-Reinforced Plastics with Initial Fibre Waviness
1 Introduction
2 Materials and Models
3 Results
4 Conclusion
References
DNN and Model Combined Passive Localization and Social Distancing with Partial Inertial Aiding
1 Introduction
2 The Proposed Method
2.1 Stereo 3D Reconstruction
2.2 Coarse Pedestrian Point Cloud Extraction
2.3 Transformation from Camera Coordinate to Bird Eye View (BEV) Plane
2.4 Social Distance Measurement
3 The Experiments and Results
4 Conclusion
References
Hybrid LES/RANS Simulation of Shock/Turbulent Boundary-Layer Interactions
1 Introduction
2 Numerical Simulation Method
2.1 IDDES
2.2 Geometric Modeling and Meshing
3 Result
3.1 2D Compression Ramp
3.2 3D Compression Ramp
4 Conclusion
References
Design and Test of an Aero-Engine Inlet Distortion Screen Facility
1 Introduction
2 Test Device and Method
2.1 Test Device
2.2 Probe Settings
2.3 Basic Mesh Selection
2.4 Numerical Analysis Formula for Loss Characteristics
3 Test and Analysis of Basic Screen
4 Test and Analysis of Distortion Screen
5 Conclusion
References
Analysis of Composite Laminates Strength with Random Deviation Variables
1 Introduction
2 Hashin Criteria
3 The Establishment of Simulation Calculation Models
4 Sample and Test
4.1 Unnotched Tension/Compression
4.2 Open-Hole Compression
5 Conclusion
References
Simulink-Integrated Representation of Functional Architectures Towards Simulation of Aircraft Systems
1 Introduction
2 Function Modeling Methodology Based on SysML
2.1 Component Functional Modeling Method
2.2 Modeling Method for System Functional Architecture
3 Functional Simulation Methodology Integrating Simulink Model
4 Case Study
4.1 Functional Modeling of the Elevator System
4.2 Modelling the Dynamic Behavior of Elevator System
4.3 Integrated Simulink Model for Functional Simulation
4.4 Discussion
5 Conclusion
References
Arrangement of Sensors for Measuring Temperature in the Test of Autoclave
1 Introduction
2 Numerical Simulation and Test Experiment of Autoclave Temperature Field
2.1 Numerical Simulation
2.2 Actual Temperature Field Test Experiment
3 Typical Layout of Test Sensors
3.1 Why is the Temperature Field Test Mainly Performed on the Front and Tail Sections
3.2 Where Should the Temperature Test Sensor Be Arranged in Detail
4 What Are the Requirements for the Local Layout of the Thermocouple Measuring Junction
4.1 Numerical Simulation Analysis of the Influence of Microstructure
4.2 Actual Test Results of Microstructure Effects
4.3 Local Arrangement Requirements of Thermocouple Measuring Junction
5 Conclusion
References
Author Index

Citation preview

Lecture Notes in Electrical Engineering 1020

Zhongliang Jing Xingqun Zhan Christopher Damaren Editors

Proceedings of the International Conference on Aerospace System Science and Engineering 2022

Lecture Notes in Electrical Engineering

1020

Series Editors Leopoldo Angrisani, Dept. of Electrical and Information Technologies Engineering, University of Napoli Federico II, Napoli, Italy Marco Arteaga, Dept. de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, München, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, School of 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, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Dept. di Ingegneria dell’Informazione Palazzina 2, Sede Scientifica Università degli Studi di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Dept. of Electrical Engineering and Information Science, Technische Universität München, München, 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, Intell. Systems Lab, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, Department of Mechatronics Engineering, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, Hunan, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, 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 Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering and Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Department of Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Dept. of Intelligence Science and Technology, Kyoto University, Kyoto, Japan Luca Oneto, Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Genova, Genova, Italy Federica Pascucci, Dept. di Ingegneria, Università degli Studi Roma Tre, Roma, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, University of Stuttgart, Stuttgart, Germany Germano Veiga, FEUP Campus, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Haidian District Beijing, China Walter Zamboni, Department of Computer Engineering, Electrical Engineering and Applied Mathematics, DIEM—Università degli studi di Salerno, Fisciano, Salerno, Italy Junjie James Zhang, Charlotte, NC, USA

The book series Lecture Notes in Electrical Engineering (LNEE) publishes the latest developments in Electrical Engineering—quickly, informally and in high quality. While original research reported in proceedings and monographs has traditionally formed the core of LNEE, we also encourage authors to submit books devoted to supporting student education and professional training in the various fields and applications areas of electrical engineering. The series cover classical and emerging topics concerning: • • • • • • • • • • • •

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Zhongliang Jing · Xingqun Zhan · Christopher Damaren Editors

Proceedings of the International Conference on Aerospace System Science and Engineering 2022

Editors Zhongliang Jing School of Aeronautics and Astronautics Shanghai Jiao Tong University Shanghai, China

Xingqun Zhan School of Aeronautics and Astronautics Shanghai Jiao Tong University Shanghai, China

Christopher Damaren University of Toronto Institute for Aerospace Studies (UTIAS) University of Toronto Toronto, ON, Canada

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-99-0650-5 ISBN 978-981-99-0651-2 (eBook) https://doi.org/10.1007/978-981-99-0651-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed 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

Preface

This book presents high-quality contributions in the subject area of Aerospace System Science and Engineering, including topics such as: trans-space vehicle systems design and integration; air vehicle systems; space vehicle systems; near-space vehicle systems; opto-electronic system; aerospace robotics and unmanned system; aerospace robotics and unmanned system; communication, navigation, and surveillance; dynamics and control; intelligent sensing and information fusion; aerodynamics and aircraft design; aerospace propulsion; avionics system; air traffic management; earth observation; deep space exploration; and bionic micro-aircraft/spacecraft. The book collects selected papers presented at the 6th International Conference on Aerospace System Science and Engineering (ICASSE 2022), organized by Shanghai Jiao Tong University, hosted by University of Toronto, held on June 6–8, 2022, as virtual event due to COVID-19. It provides a forum for experts in aeronautics and astronautics to share new ideas and findings. ICASSE conferences have been organized annually since 2017 and hosted in Shanghai, Moscow, and Toronto in turn, where the three regional editors of the journal Aerospace Systems are located. December 2022

The Editors

Contents

A Methodology for Designing the Flight Deck Windows . . . . . . . . . . . . . . . . . . . . Denis Belevtsov, Pavel Klykov, Denis Legotin, and Alexander Khvan

1

Deep Learning-Based Screen Text Detection and Recognition for Onboard Maintenance Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guanrong Wu, Jiahua Ma, Runsheng Ni, and Yuanxiang Li

15

Comprehensive Evaluation of Agile Aircraft Development Process Based on Delphi-ANP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guyue Gao, Ruichang Wang, and Xinguo Ming

25

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model Due to Acoustic-Structure Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiabin Zhong, Zhefeng Yu, and Yu Ding

38

Simulation of Tensile Test for Laminate Made of CFRP. Role of Different Parameters that Influence the Failure Mode Type . . . . . . . . . . . . . . . . . . . . . . . . . . . Nikolay Turbin and Sergei Kovtunov

54

SysML-Based Approach for Functional Modeling of Civil Aircraft Systems . . . Meihui Su, Yong Chen, and Meng Zhao

65

Orientation Method of Ultralight UAV with a Rare Update of Its Location Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Naum-Leonid E. Popov and Vasilii S. Kachalin

80

Optimization of Design Parameters of a Small-Sized Unmanned Aircraft with a Turbojet Engine Equipped with an Ejector Thrust Magnifier . . . . . . . . . . . Oskirko Liubov, Alexander Khvan, and Skorohodova Ekaterina

87

Estimation of Strength Properties of Glass Fiber-Reinforced Plastics with Initial Fibre Waviness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Aliia Utiabaeva, Sergei Kovtunov, and Nikolai Turbin DNN and Model Combined Passive Localization and Social Distancing with Partial Inertial Aiding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Wenhan Yuan, Xin Zhang, Cheng Chi, and Xingqun Zhan

viii

Contents

Hybrid LES/RANS Simulation of Shock/Turbulent Boundary-Layer Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Tingkai Dai and Bo Zhang Design and Test of an Aero-Engine Inlet Distortion Screen Facility . . . . . . . . . . . 133 Yaoyao Qu and Xiaoqing Qiang Analysis of Composite Laminates Strength with Random Deviation Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Y. Y. Xu, W. B. Fan, Y. L. Hu, Y. Yu, B. Y. Yu, and W. Zhang Simulink-Integrated Representation of Functional Architectures Towards Simulation of Aircraft Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Yuyu Huo, Yong Chen, and Meihui Su Arrangement of Sensors for Measuring Temperature in the Test of Autoclave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Zhou Ma, Wei Ma, Pengfei Du, Xiaohan Liu, and Deshou Wang Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

A Methodology for Designing the Flight Deck Windows Denis Belevtsov1,2,3 , Pavel Klykov1,2,3 , Denis Legotin3 , and Alexander Khvan1(B) 1 Moscow Aviation Institute, Moscow, Russia

[email protected]

2 Shanghai Jiao Tong University, Shanghai, China 3 Engineering Center CR929, Moscow, Russia

[email protected]

Abstract. The design of glazing is one of the most important tasks in the design of the cockpit of an aircraft. Modern design technologies simplify and accelerate the process of creating and analyzing any products including the crew cabin. Keywords: Glazing design · Aircraft design · Cockpit · Flight deck · Pilot visibility · Windshield · CATIA V5

1 Introduction Visual control of the environment for a modern pilot remains as important a process as instrument control, even in the modern world. For visual control, the pilot must be provided with good visibility from the flight deck through windshield. The flight deck windshield must provide sufficient external vision to permit the pilot to perform any maneuvers within the operating limits of the aircraft safely and at the same time afford an unobstructed view of the flight instruments and other critical components and displays from the same eye position. In this paper, the design of a crew cabin designed for two pilots sitting side by side will be considered. For example, we take an administrative aircraft designed to carry 7–10 people.

2 Analysis of Cabin Design Standards In this paper, two standards will be considered: • OST 1 00444-81 used in the Russian corporation UAC [1]; • SAE ARP 4101/2 used in used in American and European aircraft manufacturing corporations [2]. Next, we will look at each standard in more detail. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 1–14, 2023. https://doi.org/10.1007/978-981-99-0651-2_1

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2.1 OST 1 00444-81 The standard provides for two pilot positions: • Point C1 the design eye point of the pilot’s position during takeoff and landing; • Point C2 the design eye point of the pilot’s position in cruising mode. Distance from C1 to C2 is 135 mm. C1 C2

Line of sight

A line simulating a head turn Axis of seat

Fig. 1. Location of points C1 and C2. (Catia V5)

Viewing angles: The forward and downward viewing angle should be such that the pilot is provided with the necessary information to make a decision on the possibility of landing in visibility conditions of 125 m (Fig. 2). 40 -85;35 -95; 35 -135;20

30 -20;20

20

10;20

30; 1540; 15

10 0 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 -10 -20;-15 -135;-15 -20 -20; -19 -30 -85;-30 -95; -30 -40 Calculated downwardsvisionangles

10 20 30 40 50 10; -15 30; -10 40; -10 10; -19

Acontourthat limitsthe viewing areaatzeropitch angle

Fig. 2. Visibility diagram [3] according to OST 1 00444-81.

A Methodology for Designing the Flight Deck Windows

3

Viewing angles (Fig. 1) relative to the longitudinal axis of the aircraft, measured in horizontal and vertical planes passing through the design position of the eyes of the left pilot at the point C1. Calculated Downwards Vision Angles See Fig. 3.

Fig. 3. Viewing angle calculation scheme

The forward and down viewing angle at zero pitch angle is determined by the formula: β = arctg

Hd + He L

where: Hd – decision height; He – eye height; L – an area of the earth’s surface invisible to the pilot, closed by a structure, equal to 125–135 m when landing an aircraft in the ICAO CAT II. The required viewing angle forward and down along the seat axis, taking into account the pitch angle when flying on a glide path, should be at least 15° and is determined by the formula: ϕ =β +υ where: v - pitch angle when flying on a glide path. Next, the construction of the over visibility diagram in Catia V5 using shape design module (Fig. 4).

4

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The surface simulating the pilot's view

C1 C2

Fig. 4. Visibility diagram constructed in Catia V5 according to OST 1 00444-81.

2.2 SAE ARP 4101/2 The standard provides only one pilot’s eye design point (Fig. 5). 40 -40; 35

-80; 35

30 20

-120; 15

20; 15

10

-130 -120 -110 -100 -90 -120; -15

-80

-70

-60

-50

-40

-30

-20

-30; -17 -30; -19

-95; -27

-70; -27

Calculated downwards vision angles

0 -10 0 -10

10 20 10; -17

-20

10; -19

-30 -40 A contour that limits the viewing area at zero pitch angle

Fig. 5. Visibility diagram according to SAE ARP 4101/2.

25; 15 20; -10 30 40 25; -10

A Methodology for Designing the Flight Deck Windows

5

In addition to the requirements, the view angle forward and down shall be sufficient to allow the pilot to see a length of approach and/or touch down zone lights which would be covered in three seconds at landing approach speed when the aircraft is: • On a 2-1/2 glide slope; • At a decision height places the lowest part of the aircraft at 30.5 above the touch-down zone; • Yawing to the left to compensate for ten knots cross wind; • Making the approach with 366 m RVR.

Calculated Downwards Vision Angles

β = arctg

Hd + He L−S

where: Hd – decision height; He – eye height; L – approach with 366 RVR. ϕ =β +υ where: v - pitch angle when flying on a glide path.

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Next, the construction of the over visibility diagram in Catia V5 using shape design module (Fig. 6).

The surface simulating the pilot's view

Eye point

Fig. 6. Visibility diagram constructed in Catia V5 according to SAE ARP 4101/2.

2.3 Comparison of View Diagrams See Fig. 7.

A Methodology for Designing the Flight Deck Windows

7

OST 1 00444-81

SAE ARP 4101/2

SAE ARP 4101/2 OST 1 00444-81

Fig. 7. SAE ARP 4101/2 visibility diagram and OST 1 00444-81 view diagram.

3 Comparison of View Diagrams The OST 1 00444-81 standard was chosen for the design of the cockpit glazing, since this standard takes into account the movement of the pilot’s head and the required viewing angle is wider (Fig. 8).

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Fig. 8. The nose part of the airpane designed in Catia V5 [4].

The visibility diagram is placed at the intended location of the left pilot’s eye (Fig. 9). Next, a projection of the diagram is built on the surface of the forward part of the aircraft (Fig. 10). Next, two lines are constructed indicating the boundaries of the windows from above and below. The lines pass through two points with maximum and minimum Y coordinates respectively (Fig. 11). According to the standard, the first post can be installed in the range from 20 to 30°. We will set the first rack at 30°. Width of the rack is 100 mm. The borders of the posts and the upper and lower borders of the posts will be connected with a rounding of 100 mm [5] (Fig. 12).

A Methodology for Designing the Flight Deck Windows

Fig. 9. Location of the view diagram.

9

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Fig. 10. Plotting a diagram projection on a surface.

A Methodology for Designing the Flight Deck Windows

Fig. 11. Lines marking the boundaries of windows.

Fig. 12. Lines marking the boundaries of windows.

11

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Next, using the split command, we remove all unnecessary geometry. As a result, we get the contours of the windows (Fig. 13).

Fig. 13. Contours of the windows.

Next, using the extrusion and split commands, we create a glazing surface (Fig. 14). The Fig. 15 shows that the designed windows of the flight deck fully satisfies the standard requirement for viewing angles [6].

A Methodology for Designing the Flight Deck Windows

Fig. 14. Windows surface.

13

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Fig. 15. Windows surface with view diagram.

4 Conclusion In this work, the front part of the aircraft was designed and built. The cockpit was built in CATIA V5 software. This program successfully built all necessary constructions, as well as Class A surfaces. Taking into account the analysis of documents on visibility diagrams, a methodology for building a visibility diagram was developed. This methodology allows to fully consider the pilot’s view from the cockpit. Taking into account the view diagrams obtained, the flight deck windows of the small aircraft was built. The presented pilot’s visibility diagram and glazing methodology can be applied to any type of passenger aircraft with a crew of two pilots.

References 1. OST 1 00444-81 Planes and helicopters. Methods for evaluating the view from the cockpit 2. SAE ARP 4101/2 Pilot visibility from the flight deck 3. A Method for Plotting Diagrams of a Real Out-of-Cabin View by an Aircraft Pilot. Helvig Mikhail Yurievich. https://www.elibrary.ru/item.asp?id=28821244 4. The forward part of the fuselage. https://patentdb.ru/patent/2403174 5. Komarov, V.A., Vyrypaev, A.A., Kuznetsov, A.S., Odintsovo, L.V.: Creating 3D Models of Aircraft Structures in the Software Package CATIA V5 6. Basov, K.: CATIA V5. Geometric modeling

Deep Learning-Based Screen Text Detection and Recognition for Onboard Maintenance Systems Guanrong Wu(B) , Jiahua Ma, Runsheng Ni, and Yuanxiang Li Shanghai Jiao Tong University, Shanghai, China {wgrrrrr,yuanxli}@sjtu.edu.cn

Abstract. Due to the numerous alarm entries and dense text on the interface of the onboard maintenance system (OMS), it is still challenging for current algorithm to achieve complete and accurate text recognition based on screen. This paper proposes a deep learning method that employs YOLOv3, CRNN and a postprocessing module. This method first uses YOLOv3 to locate some text which we really concerned; then the feature map of the positioning area is aligned and fed to the CRNN text recognition module to obtain the text detection result, and finally the text matching module based on the minimum edit distance is used to solve some hard cases. During the experiment, we also discussed the limits of each module and made some improvements. The experimental results demonstrate that the approach we proposed has an accuracy of 99.95% and a recall of 95.74%, indicating that our algorithm can solve the problems of incomplete localization and inaccurate text recognition, and can meet practical application scenarios. Keywords: Text detection · Object detection · Text recognition · Hard case promotion · Text match

1 Introduction Onboard Maintenance Systems (OMS) can monitor the health of the aircraft and diagnose problems quickly and accurately (HoneyWell 2021). By displaying alarms on the screen in real time, the crew are able to understand the working condition of avionics. However, as the complexity of the interface increases, so does the difficulty of performing manual testing at assembly, module and system level (Chen et al. 2019). Therefore, the application of machine vision technology instead of manual detection is of great importance for functional testing. The primary problem of screen text detection and recognition is to find the required text position within the visible range, and then perform text recognition on the bounding boxes containing text. So this article will be divided into two parts: text detection and text recognition. Traditional methods of text recognition mainly rely on layout processing and feature matching. Due to excessive dependence on manually extracted feature information, the accuracy of detection is low and the generalization is poor. The first © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 15–24, 2023. https://doi.org/10.1007/978-981-99-0651-2_2

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success of machine learning is greatly improving the accuracy of speech and text recognition. Researchers have done a lot of work on text localization and recognition based on machine learning. The CTPN proposed by Zhi T et al. uses the CNN network to extract high-level semantic features (Tian et al. 2016), fixed-width anchors to predict proposals, RNN to obtain classification, and merged proposal regions to form text detection results. The EAST network proposed by Zhou X et al. is an end-to-end text localization network (Zhou et al. 2017). After extracting feature information through the VGG backbone network, it fuses multi-scale features and performs box position regression to obtain the final text position. For text recognition, the representative is the CRNN network proposed by Shi et al. Since the text position is known, there is no need to perform character segmentation, and the text recognition problem is directly converted into a sequence prediction problem through a recurrent neural network. Finally, the CTC layer is used to do actual word transcriptions (Shi et al. 2016). As for researches on text detection and recognition based on screen, Wang Feng and Xiang Dao proposed a digital instrument recognition method based on CNN (Wang and Xiang 2018). First, the template matching method was used to extract the region of interest from the target image, and the region of interest was segmented. The area uses convolutional neural network for number recognition, and then uses MOSSE algorithm to perform decimal point recognition on the segmented decimal point area, and finally obtains the reading according to the recognition results of single character, positive and negative sign and decimal point. Si Pengwei and Fan Shaosheng proposed a target detection method based on similarity measurement (Si and Fan 2019). First, a FasterRCNN network was used to generate a series of candidate sets, and then feature templates were established from target regions with high confidence. The target area with low confidence is discriminated, and finally the screening result and the feature template are used as the detection result, so as to realize the identification and location of the instrument type. The latest one is the algorithm proposed by Weidong Yang et al. which used DenseNet to extract features, and the text line construction method of predicting vertex positions by region boundary elements is used (Yang et al. 2021). They also propose an improved CRNN model to reduce parameters. For airborne displays, as a screen integrates other unimportant contents such as operation tips and interactive information, the presentation varies from interface to interface, and the key information is numerous and dense, the detection effect is prone to over-detection, low efficiency and low recognition accuracy. In order to solve the above problems, we have conducted a study on batch recognition of screen text based on machine learning methods. The main work includes: (1) applying YOLOv3 flexibly to text localization, focusing on key information and adopting shared features based on Darknet53 backbone network to significantly improve detection efficiency (2) using CRNN algorithm on the basis of the extracted features for text recognition and BKTree for post-processing to bridge the bottleneck of text localization and recognition. The final architecture diagram is as follows.

Deep Learning-Based Screen Text Detection and Recognition

17

Fig. 1. The final architecture diagram

2 Text Detection 2.1 Feature Extraction Network Darknet53 is applied as the feature extraction network for the whole algorithm, and with YOLOv3’s neck structure for position regression of the desired text. The darknet53 means that there are 53 convolutional layers. Here, we excluded the last fully connected layer. 52 convolutional layers are applied to extract feature information step by step, and each convolutional layer includes one layer of convolution and one batch normalization operation. The results of the 8-fold downsampling, 16-fold downsampling and 32-fold downsampling will be used as input feature maps of the small, medium and large size prediction frames for subsequent YOLO detection (Redmon and Farhadi 2018). The number of convolutional kernels in each convolutional layer is shown in the second column of Fig. 1, and the size of the kernels is chosen to be a combination of 3 × 3, 1 × 1 with step size of 2. The activation function involved is chosen to be Leaky-ReLU, and the function expression is as follows.  if x ≥ 0 x, (1) f(x) = α(ex − 1), if x < 0 There are also residual modules between the convolutional layers, and the numbers of these modules contained in the current convolutional layer are 1, 2, 8, 8 and 4. The method of residual connections proposed by Kaiming He solves the problem of gradient disappearance caused by increasing the depth of the network (He et al. 2016). 2.2 Feature Fusion and Prediction Layer YOLOv3 not only uses the three feature maps generated by darknet53 directly, but also fuses the three feature maps, via upsampling the deeper features so that the high-level semantic features can complement the low-level texture features, which can improve detection performance. In particular, the concatenation directly joins the up-sampled features of the same dimension after the low-dimensional feature map, just deepening the depth of the feature map. After the feature maps of three sizes are obtained, the prediction of text position is started. Each grid of feature map is assigned three different sizes of prior boxes, and the network will regress and predict the offsets of the prior boxes from the grids in which they are located. The result of each prediction box includes 4-dimensional location information, 1-dimensional confidence and n-dimensional classification confidence. The size W and H of a final prediction box and the location (X, Y) are calculated as follows: W = Pw × etw

(2)

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H = Ph × eth

(3)

X = N × (σ(tx ) + Cx )

(4)

  Y = N × (σ ty ) + Cy

(5)

Pw , Ph is the size of preset anchors, σ is the Sigmoid function, which can restrict the offset within one grid, Cx , C y is the distance between preset anchor boxes and the upper left corner of the current feature map (in which grids has been normalized), tw , th , tx , ty are the parameters of the network regression and prediction, N is the scale of the current feature map compared to the original image.

3 Text Recognition On the basis of the target localization, the feature submap of the localized area is directly used as the input of text recognition. This paper uses CRNN (CNN + RNN) combined with post-processing technology for text recognition, which can be competent in the requirements of batch text detection in local areas of the airborne displays. 3.1 CRNN + CTC Shi et al. proposed CRNN (Shi et al. 2016), which is a text detection network based on images with variable length and fixed height. It can achieve the effect of end-toend training. It consists of three parts: convolutional neural network, recurrent neural network and transcription layer. (1) The convolutional neural network layer is mainly responsible for the deep semantic feature extraction of the input image. Originally, the stacked multi-layer CNN is used for feature extraction. In this paper, in order to improve the detection efficiency, we adopt a feature sharing mechanism to directly use the feature submap extracted by the backbone network, which means that the feature submap replaces the first convolution layer in CRNN. (2) The recurrent neural network layer is responsible for extracting the sequence features of the text on the basis of the convolutional features of the target area. It is composed of a bidirectional LSTM with 256 hidden units, and the size of output is W × num_class (W is the length of the feature map, and num_class is total number of word dictionaries). (3) The transcription layer defines the Loss function for the difference between label and the RNN output, and introduces the blank symbol to avoid the occurrence of “helo” for “hello”. The specific process is to obtain the alignment result of the RNN output vector, and then perform operations such as de-duplication and de-blank. The CRNN-CTC network parameters used in this experiment are as follows (Table 1):

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Table 1. CRNN-CTC network parameters Module

Kernel num

Kernel size

Stride

Convolution

256

3×3

1×1

Convolution

256

3×3

1×1

MaxPooling

-

2×1

2×1

Convolution

512

3×3

1×1

Batch normalization

-

-

-

Convolution

512

3×3

1×1

BN

-

-

-

MaxPooling

-

2×1

2×1

Convolution

512

2×1

1×1

3.2 Post Processing No matter how the deep features of images are designed, they cannot effectively utilize the semantic information such as the word structure and contextual relevance. In this paper, the smallest edit distance and context complement are cleverly used for post processing. These ways can make up for the deficiencies of upstream target detection and text recognition, and enhance the recognition accuracy. For the smallest edit distance correction method, due to the limited application background of this paper, a complete professional thesaurus can be established. By constructing the BKTree model, the error words predicted by CRNN can find the most similar words by gradually increasing the edit distance in the thesaurus. For a regular context, if there is a missing intermediate content, the smallest distance-based matching can also be performed by establishing a phrase database.

4 Experimental Results and Analysis 4.1 Datasets and Settings A proprietary data set is designed according to the application scenario. There are 581 photos of the onboard maintenance system (OMS), with the initial resolution of 2520 × 1575 and the level text as the training and test set. There are 474 screen photos of common aircraft maintenance system (CAS) with a resolution of 1680 × 1050, and the text angle is basically horizontal. For the thesaurus used for post-processing, we extracted all words involved from the sample set, with a total of 366 words and 2326 characters. The hardware environment of this experiment is configured as Intel Core i7 7800X CPU, the GPU is NVIDIA GTX 1080Ti, the memory size is 64G, the experimental software environment is Windows10 operating system, the applied machine learning framework is Tensorflow, the programming language is Python, using the Adam optimizer, the batch size is 2 and the epoch is 30.

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4.2 Evaluation Indicators The evaluation indicators for target detection are still applicable here. The accuracy and completeness of the algorithm are mainly determined by two parameters: the accuracy rate P (Precision) and the recall rate R (Recall). It is calculated as follows: Precision = Recall =

TP TP + FP

TP TP + FN

(6) (7)

Among them, TP is the predicted character and the text recognition is correct, FP is the number of texts that were not predicted, and FN is the number of false positives. 4.3 Experimental Comparison 4.3.1 Traditional Text Recognition The template matching is used to design the traditional algorithm. The prepared word picture is used as a template, and scan the entire picture to be detected. The appropriate threshold is set as the filter. Finally, the result is displayed in the interactive area through the cvui library function. A CAS alarm detection result of the validation set is shown in the following figure (Fig. 2).

Fig. 2. Result of traditional method

The experiment found that if the threshold is set too high, although the accuracy is improved, there will be too many missed detections. Therefore, in this paper, we choose to lower the threshold appropriately and vote for the final detection result of an alarm. It can also be seen from the above figure that the traditional algorithm has low discrimination for similar content, and the detection accuracy depends on the number and quality of templates, so the generalization is poor.

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4.3.2 CTPN + CRNN As mentioned above, CTPN is one of the typical algorithms for text detection. Therefore, in order to compare with the algorithm in this paper, the commonly used CTPN-CRNN algorithm are selected for text positioning and recognition. The algorithm was tested on 50 OMS samples, and the statistics were detected and the recognition accuracy (P) was about 68.3%. A picture of the detection effect is as follows. It can be seen that it detects a lot of unnecessary text content because CTPN detects all horizontal characters, which increases the workload of the algorithm. On the other hand, the text length of detection cannot be accurately controlled, it is easy to detect a long text causing the lower accuracy of CRNN (see Sect. 4.3.3 for analysis) (Fig. 3).

Fig. 3. Result of CTPN

4.3.3 YOLO + CRNN The model of this paper is applied to 581 samples of OMS. The whole research mainly analyzes and compares three points, and carries out the corresponding improvement: • The effect of text length on the accuracy of CRNN Considering the characteristics of the bidirectional recurrent neural network used by CRNN, that is, information with a long sequence length is prone to gradient disappearance during backpropagation, experiments are carried out to discuss the influence of character length on recognition accuracy in order to determine the detection unit (letter, word or phrase). Taking the Synth90k data set as a sample, 130 images are randomly selected, and the recognition accuracy statistics are carried out according to the word length. The results are as follows (Table 2).

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Length

4

8

12

16

Accuracy

0.7578

0.8342

0.7162

0.7517

0.6325

0.6411

0.3125

0.3803

ID

1

2

1

2

1

2

1

2

It can be seen that as the word length increases, the accuracy drops rapidly. Considering the characteristics of OMS samples (the length of words are fixed at 3–10 letters), this paper selects the word as the detection unit. • Image segmentation and text post-processing

Fig. 4. Comparison of detection coverage between segmentation & post-processing and nosegmentation & post-processing (a: without segmentation & post-processing b: segmentation & post-processing)

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Since YOLO performs object localization by regressing a fixed number and spacing of Bboxes on feature maps of three sizes, it is not effective in detecting dense objects and small objects. Therefore, this paper finally chooses to divide the image with the original resolution of 2520 × 1575 into sub-images for positioning and recognition, and then merge them into recognition results. The resolution of the divided image decreases, and the target increases accordingly comparing to the entire image. The size of the target increases, which also reduces the intensity of the target to a certain extent. On the other hand, the algorithm that has text post-processing also has significantly improved the accuracy of positioning and detection. Taking 100 randomly selected images of OMS, using words as units (5051 words in total), the comparison of detection coverage before and after segmentation and text post-processing is shown in the Table 3 (Fig. 4). Table 3. Comparison between with or without segmentation/post-processing Segmentation

Post-processing

Recall

Accuracy

×

× √

53.33%

99.33%

61.38%

99.47%

95.74%

99.95%

× √

√

The final result is shown in the figure below. The recognition time of one picture is about 700 ms.The recall can be higher because most of missing bboxes represent meaningless symbol like ‘-’ (Fig. 5).

Fig. 5. Local area of final result

5 Conclusion This paper discusses the method of airborne screen text detection and recognition based on deep learning. The target detection algorithm (YOLO) is cleverly used as a text localization algorithm, which improves the ratio of effective detection and can accurately control the text detection unit (using words as the detection unit); The text recognition algorithm (CRNN) is combined with post-processing technology based on edit distance, which effectively improves the accuracy of text recognition; and finally forms an end-toend airborne screen text detection and recognition algorithm. The experimental results show that the algorithm proposed in this paper has a high accuracy in the detection and recognition of text on the airborne screen, which can meet the actual needs of use.

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Acknowledgements. This work is partially supported by COMAC Shanghai Aircraft Design and Research Institute. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers.

References HoneyWell: Onboard Maintenance System. HoneyWell (2021). https://aerospace.honeywell. com.cn/cn/zh/learn/products/cockpit-systems-and-displays/onboard-maintenance-systems. Accessed 25 Jan 2022 Chen, Y., Rui, G., Yang, L.: Development, application and functional requirements of airborne maintenance system. Sci. Technol. Innov. Guide 16(28), 2 (2019) Tian, Z., Huang, W., He, T., He, P., Qiao, Y.: Detecting text in natural image with connectionist text proposal network. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9912, pp. 56–72. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46484-8_4 Zhou, X., et al.: EAST: An Efficient and Accurate Scene Text Detector. IEEE (2017) Shi, B., Xiang, B., Cong, Y.: An end-to-end trainable neural network for image-based sequence recognition and its application to scene text recognition. IEEE Trans. Pattern Anal. Mach. Intell. 39(11), 2298–2304 (2016) Wang, F., Xiang, D.: Recognition method of digital instrument based on convolutional neural network. Mech. Des. Manuf. Eng. 47(9), 63–66 (2018) Si, P., Fan, S.: Pointer meter recognition algorithm for inspection robot in power room. Inf. Technol. Netw. Secur. 38(4), 50–55 (2019) Yang, W., et al.: Research on vehicle screen text detection and recognition based on deep learning. Optoelectron. Laser 32(4), 395–402 (2021) Redmon, J., Farhadi, A.: Yolov3: an incremental improvement. arXiv e-prints (2018) He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. IEEE (2016)

Comprehensive Evaluation of Agile Aircraft Development Process Based on Delphi-ANP Guyue Gao, Ruichang Wang, and Xinguo Ming(B) Shanghai Jiao Tong University, Shanghai, China {123ggy,wang_ruichang,xgming}@sjtu.edu.cn

Abstract. In order to evaluate different agile aircraft development solutions and select a reasonable solution from them, a comprehensive evaluation index system of agile aircraft development process is constructed in this paper. Taking into account the interaction among the evaluation indicators, the evaluation model is established by using the Delphi method and analytic network process, so as to determine the comprehensive weights of each indicator in the evaluation system of agile aircraft development process based on Delphi-ANP. Keywords: Delphi method · Analytic hierarchy process · Agile aircraft development process · Comprehensive evaluation

1 Introduction In recent years, the agile development model has achieved good results in different industries [1], especially in responding quickly to customer needs and shortening the development cycle. Aircraft development is a long cycle and highly complex process, and there are significant differences between different models. Model Based Systems Engineering (MBSE) has the advantages of visualization [2], interactivity, rapid adaptation, and reusability, and is therefore often used in the design process of complex systems with long development cycles, such as large aircraft. In recent years, scholars have conducted in-depth studies on the comprehensive evaluation of agile aircraft development process. Hou et al. used a gray evaluation method to analyze the economic benefits of an aircraft model [3]. Feng et al. proposed a comprehensive sensitivity evaluation index for civil aircraft systems based on the FTA-AHP method [4]. Shang et al. proposed a stealth aircraft design evaluation index system based on the hierarchical analysis-fuzzy integrated evaluation method [5]. Thomas L. Satty, a professor at the University of Pittsburgh, USA, proposed ANP in 1996 on the basis of Analytic Hierarchy Process (AHP) [6], which is an evaluation and decision method for solving nonlinear problems of complex systems based on the existence of dependence and feedback relationships among the elements within the system [7]. Zhao et al. [8] evaluated the security capacity of airport passenger security system. Asadabadi [9] studied a customer-oriented supplier selection method using network analysis and Markov chain; Bhattacharya et al. [10] proposed a collaborative decision making method for performance evaluation of green supply chain using fuzzy ANP. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 25–37, 2023. https://doi.org/10.1007/978-981-99-0651-2_3

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At present, there are still relatively few studies on comprehensive evaluation methods for agile aircraft development process in the industry, and the evaluation system mostly adopts genetic algorithm, AHP and fuzzy comprehensive evaluation method, which are not comprehensive enough and ignore the potential relationship between different evaluation indexes and the influence of factors such as normality, reusability and visibility on the evaluation of aircraft development process. In this paper, based on literature research and expert consultation, a comprehensive evaluation index system is established for the aircraft development process based on agile system engineering, and ANP is used to determine the comprehensive weights of each evaluation index to provide a more complete and feasible evaluation method for the agile aircraft development process.

2 Evaluation Index System Determination The aircraft development process based on agile systems engineering mainly includes requirements identification phase, system development phase, system verification phase and program confirmation phase. Among them, the requirements identification phase includes agile aircraft requirements acquisition, agile system requirements definition and agile system architecture analysis and design; the system verification phase includes agile discipline development, agile subsystem discipline synthesis and agile subsystem synthesis; the system verification phase includes agile system verification and agile

Fig. 1. Aircraft development process based on Agile-MBSE

Comprehensive Evaluation of Agile Aircraft Development Process

27

system validation. In the solution validation phase, the method proposed in this paper is used to evaluate different solutions and select a reasonable solution so as to effectively guide the agile aircraft development process. The aircraft development process based on Agile-MBSE is shown in Fig. 1. The evaluation index system of aircraft development process based on Agile-MBSE is divided into 3 levels as shown in Table 1. The first level is the general objective level, which is the evaluation result of aircraft development process based on agile system engineering. The second level is the first level indicators, including the standardization, reusability, visibility, technicality and economy. The third level is the second level indicators, which mainly include business process standardization, reuse frequency, accuracy of representation and technical maturity et al. The indicators in each tier are independent of each other, and the indicators in the upper tier can govern the indicators in the lower tier. Determining the objectives and scope can clarify the system boundary of the aircraft development process. According to this boundary, the construction of the data inventory of the aircraft development process is completed. Table 1. Aircraft development evaluation index system based on Agile-MBSE. GS

i

k

Ai

Aik

Overall Goal: Comprehensive Evaluation of Agile Aircraft Development Process

1

1

Standardization

Business Process Standardization

2

3

4

2

Process Management Standardization

3

Technology Application Standardization

1

Reusability

Reuse Frequency

3

Normalization

1

Visuality

Accuracy of Presentation

2

Aesthetics of Presentation

3

Comprehensiveness of Presentation

1

Technicality

2 1

Application Prospect Technology Maturity

3 5

Reuse Costs

2

Technology Advancement Economy

Manufacturing Cost

2

Maintenance Cost

3

Design Cost

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However, the underlying evaluation indexes of the aircraft development process are not completely independent of each other, but affect and interdepend on each other, for example, the business process standardization significantly affects the degree of process standardization, and the weights of each index cannot be obtained simply based on the traditional hierarchical analysis method. Therefore, it is necessary to construct a comprehensive evaluation system by using Delphi method and ANP. When ANP is applied to analyze decision evaluation problems, the problem to be evaluated is first systematized, the factors affecting the problem are studied, then the factors are hierarchized, and finally a factor recursive hierarchy model is built. There are certain relationships among the factors, and these factors form multiple levels according to certain relationships, thus constituting a recursive hierarchy model. The factors of the next level are governed by the factors of the previous level as guidelines, that is, the factors of the next level belong to the refinement of the factors of the previous level. The Delphi method was used to determine the weights of the indicators of aircraft development evaluation based on agile systems engineering, and firstly, a questionnaire was distributed to 25 civil aircraft R&D engineers to collect the influence relationship between the indicators of aircraft development evaluation based on agile systems engineering judged by each expert. The Delphi method was used to compare the relative importance of each factor in the i-factor set by taking any factor x in the j-factor set as the benchmark, and the scale of 1–9 was used to indicate the influence degree of each index. The scale and its corresponding meaning are shown in Table 2. The weight matrix Wij was obtained by arithmetic average of 25 experts’ data. Table 2. Definition of relative importance ratio scale of primary indicators. Importance scale

Definition

1

Indicates that both elements are equally important

3

Indicates that the former of two elements is slightly more important than the latter

5

Indicates that the former of two elements is significantly more important than the latter

7

Indicates that the former of two elements is strongly more important than the latter

9

Indicates that the former of two elements is more extremely important than the latter

2,4,6,8

Indicates intermediate values between the corresponding 1–9 scales

Although the method is to get the matrix by two-by-two comparison, reducing the interference of other factors, and can more accurately reflect the relative importance of a pair of influencing factors, but after getting a complete judgment matrix, often does not meet the consistency, when the judgment matrix is not the positive and negative matrix, but the hierarchical analysis method does not require the complete satisfaction of the

Comprehensive Evaluation of Agile Aircraft Development Process

29

positive and negative matrix, but only to test the consistency. The following is the test method of consistency. Calculate the consistency index (CI): CI = (λmax − n)/(n − 1)

(1)

where n is the dimension of the matrix, λmax is the maximum eigenvalue of Wij Find the average random consistency index RI (Table 3): Table 3. Average random consistency index RI. N

1

2

3

4

5

6

7

8

9

RI

0

0

0.58

0.9

1.12

1.24

1.32

1.41

1.45

Calculate the consistency ratio (CR): CR = CI /RI

(2)

If the calculated CR value is larger than 0.1, the judgment matrix does not meet the consistency, that is, there is a contradiction in the importance of different factors in the attribute factor set, then it is necessary to refine the guidelines for expert scoring or hire more experts to participate in the importance evaluation scoring and get the average value until the judgment matrix meets the consistency test requirements. The steps of the Delphi-ANP-based agile aircraft development process evaluation are as follows. (1) Firstly, considering the mutual influence between different factor sets, the influence matrix between factor sets is constructed by taking the ith factor set as the benchmark, i.e. the weight matrix S between the first level indicators. ⎡

s11 s12 ⎢ s21 s22 ⎢ S=⎢ . ⎣ .. · · · s51 s52

... ... .. .

⎤ s15 s25 ⎥ ⎥ .. ⎥ . ⎦

(3)

... s55

(2) The judgment matrix is constructed by taking the other factors in the jth factor set respectively, and the weight matrix of the i-th factor set relative to the j-th factor set is finally obtained by finding the eigenvector corresponding to the maximum eigenvalue of each judgment matrix Wij . ⎡

⎤ ωi1 j1 ωi1 j2 ωi1 j3 Wij = ⎣ ωi2 j1 ωi2 j2 ωi2 j3 ⎦ ωi3 j1 ωi3 j2 ωi3 j3

(4)

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(3) After obtaining the weight matrix Wij super-matrix W is constructed. ⎡ W11 ⎢ W21 ⎢ W =⎢ . ⎣ ..

between each factor set, the unweighted ⎤ W12 ... W15 W22 ... W25 ⎥ ⎥ . ⎥ . · · · . . .. ⎦

(5)

W51 W52 ... W55

(4) Construct the weighted super-matrix W from the influence matrix S and the unweighted super-matrix W. ⎡ ⎤ s11 W11 s12 W12 ... s15 W15 ⎢ s21 W21 s22 W22 ... s25 W25 ⎥ ⎢ ⎥ (6) W =⎢ . .. ⎥ .. ⎣ .. . ··· . ⎦ s51 W51 s52 W52 ... s55 W55

(5) Calculate the limit of the weighted super-matrix W , i.e., calculate the eigenvector when the characteristic root of the weighted super-matrix is 1, and normalize it to obtain the weight vector of each secondary index. (6) Based on the actual evaluation values and weights of each secondary indicator, the evaluation results of the agile aircraft development process solution can be obtained by linear calculation.

3 Delphi-ANP-Based Agile Aircraft Development Process Evaluation Model The hierarchy in the ANP model can be divided into the following three parts. (1) Goal layer: The goal layer is characterized by having one and only one factor that represents the highest evaluation criterion or evaluation decision goal for the decision assessment problem. The goal level should be the highest level in the hierarchical model. (2) First-level indicator layer: This layer contains many influencing factors that affect the target of the problem, these indicators are also called criteria, each criterion does not affect each other, the weight of each criterion in the layer can be obtained by the Delphi method, the first-level indicator layer and the target layer together constitute the control layer in the comprehensive evaluation system of the aircraft development process. (3) Network layer: The network layer contains a network structure of secondary indicators underneath the primary indicators, and the interactions between the secondary indicators. The elements of the altered layer are interdependent and inter-governed, and the elements and levels are not internally independent from each other. Each criterion in the progressive hierarchy governs not a simple internally independent element, but an interdependent, feedback network structure. Establish an ANP-based aircraft development process evaluation model, as shown in Fig. 2.

Comprehensive Evaluation of Agile Aircraft Development Process

31

Fig. 2. ANP-based aircraft development process evaluation model

4 Sample Validation Based on the agile aircraft development process evaluation system proposed in this paper, a new civil aircraft development process of the same power level is analyzed with reference to the existing civil aircraft development process. Through the form of expert scoring, each judgment matrix in the index system is determined, and the judgment matrix is constructed with the standardization index factor set as an example. ⎡

W11

⎤ 142 = ⎣ 41 1 13 ⎦ 1 2 3 1

After the consistency test, it is known that the judgment matrix of the normative index is established. Similarly, the judgment matrices of reusability, visibility, technicality and economy indicators, and the judgment matrix of a single indicator set relative to other indicator sets are constructed respectively. After the consistency test, the unweighted super-matrix is obtained. By conducting a two-by-two comparison analysis of the importance of the first-level indicators, the impact matrix of the first-level indicators was obtained as follows. ⎡ ⎤ 0.211 0.286 0.286 0.286 0.273 ⎢ 0.051 0.071 0.048 0.048 0.091 ⎥ ⎢ ⎥ ⎢ ⎥ S = ⎢ 0.106 0.143 0.095 0.095 0.138 ⎥ ⎢ ⎥ ⎣ 0.211 0.071 0.19 0.19 0.273 ⎦ 0.421 0.429 0.381 0.381 0.545

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The unweighted super-matrix is shown in Table 4. Table 4. Unweighted super-matrix. A11

A12

A11 0.571 0.5

A13

A21

A22

A23

A31

A32

A33

A41

A42

A43

A51

A52

A53

0.286 0.286 0.286

0.6

0.571 0.571 0.571 0.25

0.08

0.571 0.571 0.6

0.5

A12 0.143 0.125 0.1

0.143 0.143 0.143 0.25

0.3

0.143 0.143 0.1

0.125 0.571 0.571 0.571

A13 0.286 0.375 0.3

0.286 0.286 0.286 0.5

0.62

0.286 0.286 0.3

0.375 0.143 0.143 0.143

A21 0.571 0.143 0.143 0.571 0.6

0.5

0.286 0.286 0.286 0.286 0.286 0.286 0.571 0.5

A22 0.286 0.571 0.571 0.143 0.1

0.125 0.571 0.571 0.571 0.571 0.571 0.571 0.143 0.125 0.1

0.6

A23 0.143 0.286 0.286 0.286 0.3

0.375 0.143 0.143 0.143 0.143 0.143 0.143 0.286 0.375 0.3

A31 0.286 0.143 0.143 0.143 0.143 0.143 0.286 0.286 0.286 0.286 0.286 0.286 0.286 0.286 0.286 A32 0.143 0.571 0.571 0.286 0.286 0.286 0.571 0.571 0.571 0.571 0.571 0.571 0.571 0.571 0.571 A33 0.571 0.286 0.286 0.571 0.571 0.571 0.143 0.143 0.143 0.143 0.143 0.143 0.143 0.143 0.143 A41 0.286 0.286 0.286 0.143 0.143 0.143 0.143 0.143 0.143 0.571 0.5

0.08

0.571

A42 0.571 0.571 0.571 0.286 0.286 0.286 0.286 0.286 0.286 0.143 0.125 0.125 0.25

0.3

0.143

A43 0.143 0.143 0.143 0.571 0.571 0.571 0.571 0.571 0.571 0.286 0.375 0.375 0.5

0.62

0.286

A51 0.143 0.143 0.143 0.25

0.5

0.25

0.08

0.571 0.571 0.5

0.6

0.143 0.143 0.143 0.143 0.143 0.143

A52 0.286 0.286 0.286 0.25

0.3

0.286 0.143 0.125 0.1

0.286 0.286 0.286 0.286 0.286 0.286

A53 0.571 0.571 0.571 0.5

0.62

0.143 0.286 0.375 0.3

0.571 0.571 0.571 0.571 0.571 0.571

The unweighted super-matrix of the secondary indicators and the weight matrix of the primary indicators were then calculated to obtain the weighted super-matrix of the secondary indicators, as shown in Table 5. The convergence matrix of the weighted super-matrix of the secondary index is obtained by finding the limit of the obtained weighted super-matrix, as shown in Table 6.

0.121

0.03

0.06

0.029

0.015

0.007

0.03

0.015

0.061

0.06

0.12

0.03

0.06

0.12

0.24

A11

A12

A13

A21

A22

A23

A31

A32

A33

A41

A42

A43

A51

A52

A53

ω11

0.24

0.12

0.06

0.03

0.12

0.06

0.03

0.061

0.015

0.015

0.029

0.007

0.079

0.026

0.106

ω12

0.24

0.12

0.06

0.03

0.12

0.06

0.03

0.061

0.015

0.015

0.029

0.007

0.063

0.021

0.127

ω13

0.215

0.107

0.107

0.041

0.02

0.01

0.082

0.041

0.02

0.02

0.01

0.041

0.082

0.041

0.163

ω21

0.264

0.132

0.033

0.041

0.02

0.01

0.082

0.041

0.02

0.021

0.007

0.043

0.082

0.041

0.163

ω22

0.123

0.061

0.245

0.041

0.02

0.01

0.082

0.041

0.02

0.027

0.009

0.036

0.082

0.041

0.163

ω23

0.109

0.054

0.218

0.109

0.054

0.028

0.014

0.054

0.027

0.007

0.027

0.014

0.143

0.072

0.072

ω31

0.143

0.476

0.191

0.109

0.054

0.027

0.013

0.054

0.027

0.007

0.027

0.014

0.176

0.088

0.022

ω32

0.114

0.038

0.229

0.109

0.054

0.027

0.013

0.054

0.027

0.007

0.027

0.014

0.082

0.041

0.163

ω33

Table 5. Weighted super-matrix.

0.218

0.109

0.054

0.054

0.027

0.109

0.014

0.054

0.027

0.007

0.027

0.014

0.082

0.041

0.163

ω41

0.218

0.109

0.054

0.071

0.024

0.095

0.014

0.054

0.027

0.007

0.027

0.014

0.086

0.029

0.172

ω42

0.218

0.109

0.054

0.057

0.019

0.114

0.014

0.054

0.027

0.007

0.027

0.014

0.107

0.036

0.143

ω43

0.218

0.109

0.054

0.137

0.068

0.068

0.02

0.079

0.039

0.026

0.013

0.052

0.039

0.156

0.078

ω51

0.218

0.109

0.054

0.168

0.084

0.021

0.02

0.079

0.039

0.034

0.011

0.046

0.039

0.156

0.078

ω52

0.218

0.109

0.054

0.079

0.039

0.156

0.02

0.079

0.039

0.027

0.009

0.055

0.039

0.156

0.078

ω53

Comprehensive Evaluation of Agile Aircraft Development Process 33

0.107

0.082

0.071

0.029

0.02

0.017

0.029

0.062

0.026

0.074

0.068

0.08

0.08

0.125

0.129

A11

A12

A13

A21

A22

A23

A31

A32

A33

A41

A42

A43

A51

A52

A53

ω11’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω12’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω13’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω21’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω22’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω23’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω31’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω32’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω33’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω41’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω42’

Table 6. Convergence matrix of the weighted super-matrix.

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω43’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω51’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω52’

0.129

0.125

0.08

0.08

0.068

0.074

0.026

0.062

0.029

0.017

0.02

0.029

0.071

0.082

0.107

ω53’

34 G. Gao et al.

Comprehensive Evaluation of Agile Aircraft Development Process

35

The weights of each secondary indicator in the agile system engineering-based aircraft development evaluation index system can be calculated, as shown in Table 7. By obtaining the average of the scores from experts, the score of each index was scored as 60 as the benchmark. The evaluation results are obtained as shown in Table 8. The new scheme is an agile MBSE-based aircraft development process, and the comparison scheme is an existing development process for civil aircraft of the same power level. Table 7. Weights of each secondary indicator in the Agile-MBSE aircraft development evaluation. Indicators

Weights

A11

0.107

A12

0.082

A13

0.071

A21

0.029

A22

0.02

A23

0.017

A31

0.029

A32

0.062

A33

0.026

A41

0.074

A42

0.068

A43

0.08

A51

0.08

A52

0.125

A53

0.129

The score of the new scheme under the evaluation system proposed in this paper is 68.82.

36

G. Gao et al. Table 8. Average score of indicators.

Indicators

Agile-MBSE aircraft development

original aircraft development

Business process standardization

66

60

Process management standardization

65

60

Technology application standardization

62

60

Reuse costs

68

60

Reuse frequency

71

60

Normalization

70

60

Accuracy of presentation

70

60

Aesthetics of presentation

81

60

Comprehensiveness of presentation

76

60

Application prospect

62

60

Technology maturity

58

60

Technology advancement

55

60

Manufacturing cost

62

60

Maintenance cost

61

60

Design cost

69

60

5 Conclusion In this paper, by sorting out the Agile-MBSE aircraft development process, the system boundary is determined, and an agile aircraft development process evaluation index system based on Delphi-ANP is constructed. By analyzing the interaction relationship of each secondary evaluation index and solving the comprehensive weight of each index using network analysis method, the objectivity and rationality of the evaluation system are improved from AHP. In this paper, we use Delphi method to score the agile aircraft development process, and use a sample validation of the ANP method in the evaluation of agile aircraft development process.

References 1. Wang, R., et al.: Research on the key technology of MBSE-based reliability design analysis of complex engineering systems. Aviat. Stand. Qual. (05), 42–51 (2021). https://doi.org/10. 13237/j.cnki.asq.2021.05.11 2. Zhao, J., Li, Y.: Design and simulation method of thrust management architecture for civil aircraft based on MBSE. Aviat. Comput. Technol. 51(05), 105–108+118 (2021)

Comprehensive Evaluation of Agile Aircraft Development Process

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3. Hou, P., Xu, S.: Construction and evaluation analysis of commercial aircraft economic efficiency evaluation index system. Adv. Aeronaut. Eng. 1–8 (2022). http://kns.cnki.net/kcms/ detail/61.1479.V.20210726.0838.002.html 4. Feng, Y., et al.: Comprehensive sensitivity evaluation analysis of aircraft systems based on FTA-AHP. J. Northwestern Polytech. Univ. 39(05), 971–977 (2021) 5. Shang, B., et al.: Sensitivity assessment of stealth aircraft based on hierarchical analysis-fuzzy integrated evaluation method. J. Arms Equip. Eng. 41(09), 105–110 (2020) 6. Saaty, T.L.: Decision Making with Dependence and Feedback, pp. 5–8. RWS Publication, Pittsburgh (1996) 7. Saaty, T.L.: Decision Making with the Analytic Hierarchy Process and the Analytic Network Process (2013). http://www.doc88.com/p-184634492346.html 8. Zhao, Z., Liu, F.: Evaluation method of the supporting functions of the airport passenger security inspection system based on the fuzzy analytic network progress in the study of water quality. J. Saf. Environ. 15(2), 20–24 (2015) 9. Asadabadim, M.R.: A customer based supplier selection process that combines quality function deployment, the analytic network process and a Markov chain. Eur. J. Oper. Res. 263(3), 1049–1062 (2017) 10. Bhattacharya, A., et al.: Green supply chain performance measurement using fuzzy ANP based balanced score card: a collaborative decision-making approach. Prod. Plan. Control 25(8), 698–714 (2014)

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model Due to Acoustic-Structure Coupling Jiabin Zhong, Zhefeng Yu(B) , and Yu Ding Shanghai Jiao Tong University, Shanghai, China {zjb_sjtu,yuzf}@sjtu.edu.cn

Abstract. The software ANSYS was used to perform structural model analysis, cavity acoustic modal analysis, model analysis on acoustic-structure coupled system and harmonic response analysis of an aircraft-aileron-cabin model. The resonance frequencies of cavity with a gap versus the gap width was established based on Helmholtz resonance theory. The results are roughly in agreement with the numerical simulation results obtained with ANSYS in trend. The acousticstructure coupling analysis show that there were two vibration modes when the natural frequency of cavity is approaching to that of the structure in the coupled system, and the magnitude of frequency resonance function on acoustic pressure and structural vibration are sensitive to the gap width. This study provides an effective method to analyze and design on the thin-walled cavity with gap in aircraft exposed to noise environment. Keywords: Aircraft aileron cabin · Helmholtz resonance · Acoustic-structure coupling · Structural vibration

1 Introduction When performing flight missions, aircraft are mostly in a strong noise environment. Aircraft noise is mainly composed of propulsion system noise and aerodynamic noise during flight. The noise load may damage the aircraft skin and even affect the normal operation of other equipment structures in the aircraft cabin when the aircraft surface load reaches more than 130 decibels. Noise produces dynamic alternating loads on the structure. When the frequency distribution of the alternating load intersects with or closes to the natural frequency of the structure, the noise load excites the structure to resonate, which may cause cracks or even failure of the structure (Yao and Yao 2006). Many scholars have done a lot of research on the acoustic load response of aircraft structure. Zhang Zhengping et al. proposed engineering solutions from the aspects of noise load spectrum determination, noise vibration control and acoustic fatigue design for the aircraft noise problem (Zhang et al. 2008). Zhao Xiaojian et al. applied the finite element method to study the structural response and noise distribution of the aircraft fairing under the acoustic load, and verified the reliability of the finite element method to study the response to the low-frequency acoustic load (Zhao et al. 2014). © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 38–53, 2023. https://doi.org/10.1007/978-981-99-0651-2_4

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model

39

There are a large number of cavities formed by thin-walled structures in aircraft, which are very susceptible to sound and vibration. When the cavity has a small opening, it can be regarded as a Helmholtz resonant cavity (Ma 2002). Helmholtz resonators are often used in mufflers. On the one hand, it can be excited by an external sound field to consume its energy as a sound absorber. On the other hand, the vibrations in the cavity of the Helmholtz resonator can emit sound waves through a short tube to enhance the external sound field. Many scholars have studied the mechanism of resonance generation and the calculation of the resonance frequency of Helmholtz resonators with different shapes. Rayleigh proposed the mechanical analogy method to compare the Helmholtz resonator to the mass-spring system, and the resonant frequency was calculated by circuit analogy in modern times. Chanaud obtained Helmholtz resonance frequencies of different geometric structures through experimental methods, and verified some calculation formulas of resonance frequency derived from acoustic principles (Chanaud 1997). Langfeldt and Gourdon studied the effect of the number of resonator necks (Langfeldt et al. 2019) and the shape of the neck section (Gourdon et al. 2020) on the frequency and sound absorption capacity of Helmholtz resonators, respectively. Wang Zefeng et al. studied the effect of the thickness of the elastic wall of the Helmholtz resonator cavity on the resonant frequency through theoretical and experimental studies (Wang et al. 2009). Some scholars have also conducted related research on the Helmholtz resonant cavity excited by airflow. Slaboch et al. have studied the flow-excited Helmholtz resonant cavity theoretically and experimentally, proposed a cavity pressure fluctuation prediction model based on the boundary layer method, free flow velocity and the cavity acoustic characteristics (Ma et al. 2009), and studied the influence of the upstream obstacles on the cavity (Slaboch et al. 2008). Selamet et al. found that with the increase of the air flow over the cavity mouth, the sound absorption capacity of the Helmholtz resonant cavity weakened (Selamet et al. 2011). Aiming at the acoustic-structure coupling effect in the structure cavity coupling system, Jin Guoyong et al. made in-depth theoretical research and related numerical calculations on the coupling mechanism and coupling characteristics of elastic closed cavity (Jin et al. 2007). Deng Zhaoxiang et al. conducted simulation calculations for the elastic closed cavity and analyzed the dominant characteristics of the natural frequency of the coupled system (Deng and Gao 2012). Ma Tianfei et al. established an acousticstructure coupling model of the body structure and cabin of a certain type of vehicle, and carried out modal analysis on the body structure system, cabin acoustic cavity system and acoustic-structure coupling system respectively (Ma et al. 2005). The results show that the interaction between the structure and the cavity air changes the modal frequency and mode shape of the original system, indicating that the acoustic-structure coupling system is not a simple superposition of the acoustic cavity system and the structural system. Liu Yuting et al. established an acoustic-structure coupling model of the tire and the tire cavity, and analyzed the acoustic cavity resonance and noise of the tire under different conditions (Liu et al. 2021). Ezcurra et al. established an acoustic-structure coupling finite element model of the guitar and its chamber, and studied the effect of the various parts of the guitar on the vibration effect of its resonant chamber (Ezcurra et al. 2005). Yu Yang et al. established the acoustic-structure coupling model of the traditional Chinese musical instrument Guqin, carried out the acoustic-structure coupling modal analysis of

40

J. Zhong et al.

it, and obtained the relationship between the frequency of the external excitation force and the sounding loudness of it (Yu and Xu 2016). However, there are few studies on the structural vibration response in the acoustic-structure coupling phenomenon. For some cavity structures in a strong noise environment, it should be considered that the structural vibration caused by the cavity acoustic resonance. Typical cavity structures on an aircraft include aileron cabin, flat tail trailing edge cabin and landing gear cabin. Cavity acoustic resonance will lead to a significant increase sound load near the cavity resonance frequency, and the impact of noise in this frequency band on the cavity structure will also be greatly enhanced. When the cavity resonance frequency is close to the natural frequency of the cavity structure, it may lead to structural vibrating vigorously. In view of the requirements for acoustic and vibration analysis of cavity structures in aeronautical structures, this paper studies the phenomenon that aileron cabins with gab will vibrate strongly during flight. In this study, a model similar to the acoustic and vibration characteristics of the real wing is established, the natural frequency of the structure and the cavity resonance frequency are calculated through the structural modal and cavity modal analysis. A formula for calculating the cavity resonance frequency based on Helmholtz resonance theory is proposed and the effect of the gap width on the vibration response of the model is analyzed. The research has important theoretical significance for the design of thin-walled cavity structures on aircraft that are susceptible to noise loads.

2 Theoretical Method 2.1 Helmholtz Resonance Theory The Helmholtz resonant cavity is shown in Fig. 1. The resonant cavity can be equivalent to a second-order spring damping system. The air at the orifice is regarded as the mass, and the air in the cavity is regarded as a spring, which can provide restoring force, while the sound radiation and other viscous factors are considered damping. When the pulsation of the sound pressure outside the cavity reaches a certain frequency, the pulsation of the sound pressure in the cavity increases sharply. This frequency is called the natural frequency of the Helmholtz resonant cavity. The calculation formula is  c  S (1) fhr = 2π VL

Fig. 1. Helmholtz resonator

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model

41

where fhr is the Helmholtz resonance frequency, c is the local sound velocity, S is the orifice area, V is the cavity volume, and l is the effective length of the neck. The effective length of the neck is related to the shape of the neck. When there is a flange at the orifice, it often take L = l + 0.85a; when there is no flange, it often take L = l + 0.7a. When the opening is a round hole, a is the diameter of the round hole. 2.2 Acoustic -Structure Coupling Finite Element Equation When only the structural vibration is considered, the structural response conforms to the forced vibration finite element equation of the structural dynamics multi-degree-offreedom system.     (2) [Ms ] U¨ + [Cs ] U˙ + [Ks ]{U } = {Fs } where [Ms ] is the structural mass matrix, [Cs ] is the structural damping matrix, [Ks ] is the structural stiffness matrix, {Fs } is the external excitation force of the structure and {U } is the displacement of the element node. Considering the effect of sound pressure on the structure, the finite element equation of the vibration response of the structure is       (3) [Ms ] U¨ + [Cs ] U˙ + [Ks ]{U } = {Fs } + Ff       where Ff is the force of the fluid pressure on the structure, Ff = RT {P}, [R] is the coupling matrix of the fluid and the structure, {P} is the nodal sound pressure vector. According to the Galerkin method, the finite element equation in the acoustic field is           (4) Mf P¨ + Cf P˙ + Kf {P} + [R] U¨ = 0     where Mf  is the fluid equivalent mass matrix, Cf is the fluid equivalent damping matrix, Kf is the fluid equivalent stiffness matrix. The fully coupled acoustic-structure coupling finite element equation can be obtained from Eqs. (3) and (4).





  U¨ U˙ [Cs ] 0 [Ks ] −[RT ] U Fs [Ms ] 0 (5) + + = 0 0 [Cf ] 0 [Kf ] P¨ P˙ P [R] [Mf ]

3 Finite Element Model The wind tunnel test model of the aileron cabin is divided into the wing part and the aileron part. The model has a spanwise length of 600 mm and a chord length of 800 mm. The aileron cabin model is composed of skin, ribs, front and rear beams, support beams and stringers. The front and rear beams form a cavity with the skin. There are gap on the upper surface of the connection between the wing part and the aileron part, and the gap can be considered as cavity openings. The aileron cabin structure is regarded as an

42

J. Zhong et al. Table 1. Material related parameters

Name

Parameter

Aluminum alloy

Density/(kg/m3 )

2770

Young’s Modulus/(MPa)

71000

Poisson’s Ratio

0.33

Air

Value

Shear Modulus/(MPa)

26692

Density/(kg/m3 )

1.225

Speed of Sound/(m/s)

346.25

Static Pressure/(Pa)

101325

elastic body, the material is isotropic aluminum alloy, and the acoustic medium in the cavity is air. The relevant material parameters are shown in Table 1. The aileron cabin structural 3D model was built by using the CATIA software. Done some simplification of the model that retaining important structures before simulation and calculation. Finally imported the model for calculation into ANSYS simulation software and generated meshes to get finite element model. The modeling process is shown in Fig. 2. The left part is the solid domain (model structure), and the right part

Fig. 2. Finite element modeling process

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model

43

is the fluid domain (cavity gas). The structural skin is built with shell elements, and the stringers are built with beam elements. The contact relationship of each component of the structure is defined to realize the connection of the models. The fluid domain considered the influence of the beams at the gap and ignored the influence of other beams inside the cavity. The mesh for acoustic calculation needs to meet at least 6 units at each wavelength, and the maximum size of the fluid domain mesh is set to 15 mm and the minimum size is 2 mm. When performing acoustic calculations within 1000 Hz, the sizes can met convergence requirements. When the acoustic-structure coupling calculation is performed on the model, the contact relationship between the solid and the fluid interface is defined to realize the coupling calculation.

4 Numerical Calculation Analysis 4.1 Cavity Modal Analysis Cavity acoustic mode can be calculated by using the Modal Acoustics module of the ANSYS software. The structure need to assume a rigid body during this process. So, the boundary of the acoustic computational domain can be set as a hard boundary, which does not absorb sound waves, that is, the sound pressure on the boundary along the normal direction is zero ( ∂P ∂n = 0). When there is no opening in the aileron cabin cavity, all boundaries of the cavity acoustic calculation domain are set as hard boundaries, and the first 6-order modal frequencies obtained from the calculation are shown in Table 2. When there is an opening in the cavity and the opening is a gap with a length of 570 mm and a width of 10 mm, the first 6-order modal frequencies are calculated and shown in Table 2. Table 2. First 6-order acoustic modal frequencies of aileron cabin cavity Name

1st -order 2nd -order 3rd -order 4th -order 5th -order 6th -order

Closed Cavity/Hz

304.3

472.2

561.7

608.5

770.2

895.6

Cavity with Opening/Hz 160.8

344.1

569.7

629.4

645.9

833.6

When there is an opening, the first-order mode natural frequency is 160.8 Hz, but this mode does not exist in a closed cavity. It indicates that the existence of an opening will generate a new acoustic mode in the cavity. Equation (1) is used to estimate the Helmholtz resonance frequency of the open cavity, where a is the minimum distance of the gap, and l is the distance from the edge of the skin to the edge of the stringer. The value positions are shown in Fig. 3.

44

J. Zhong et al.

Fig. 3. Model cutaway view

When the gap width is 10 mm, a = 4.7 mm, l = 15.4 mm, and the calculation result of formula (1) is 156.1 Hz, which is close to the first-order modal frequency of the open cavity. It indicates that the modal frequency is the Helmholtz resonance frequency of the acoustic cavity. Due to the irregular shape of the cavity opening and cavity, there is a certain error between the results obtained according to the calculation formula of the Helmholtz resonant cavity with a cylindrical opening and the numerical calculation results. At the same time, the natural frequencies of other modes of the acoustic cavity are changed to some extent due to the existence of the opening. Table 3. Frequency with different gap widths Gap Width/mm

Minimum gap distance/mm

Neck length/mm

First-order natural frequency/Hz

Resonance theory calculation results/Hz

4

1.3

15.4

121.3

88.9

6

2.3

15.4

138.0

115.3

8

3.4

15.4

151.1

136.6

10

4.7

15.4

160.8

156.1

12

6.1

15.4

168.5

172.7

14

7.7

15.4

174.5

187.9

16

9.2

15.4

179.2

198.8

The influences of gap width are analyzed, and the first-order modal frequency of cavity under different gap width is calculated respectively. The results are shown in Table 3. The first-order modal frequency (Helmholtz resonance frequency) of the cavity increases with the opening gap width larger. Due to the irregular section of the open neck, the calculation results of the values of a and l have a large error with the narrow gap.

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model

45

But the theoretical formula results roughly in agreement with the numerical calculation results in trend with the change of the gap width. 4.2 Structural Modal Analysis Modal module of ANSYS software is used to conduct modal analysis on the structural part of the model, and the wing ribs at both ends of the model are set as fixed support conditions. The first six natural modal frequencies calculated are shown in Table 4. Table 4. Natural modal frequency of structure (Hz) 1st -order

2nd -order

3rd -order

4th -order

5th -order

6th -order

149.5

182.5

238.4

252.7

302.6

329.4

Fig. 4. Mode shapes of model structure

46

J. Zhong et al.

Figure 4 is the structural mode shapes diagram. It can be seen from the figure that the vibration of the support beam of the aileron cabin is most obvious in the first mode. 4.3 Modal Analysis of Coupled Systems The modal analysis of the model acoustic-structure coupled system is carried out by using the ANSYS software Modal Acoustics module. The boundary conditions and meshes of the solid domain are consistent with the structural modal analysis, and the meshes of the fluid domain is consistent with the modal analysis. The boundary conditions of fluid domain are set to Fluid Solid Interface. When the opening gap width is 10 mm, the first six-order coupling modal frequencies are obtained as shown in Table 5. Table 5. Coupled-system modes Modes

Frequency/Hz

1st -order

Dominant part

132.8

Acoustic cavity

2nd -order

155.2

Structure

3rd -order

203.2

Structure

4th -order

242.2

Structure

5th -order

250.8

Structure

6th -order

302.2

Structure

The acoustic-structure coupling system is formed by the interaction between the structure and the cavity gas. On the interface between the two media, the sound pressure is equal and the normal sound particle velocity is equal. The mode of the coupled system is jointly affected by the structural vibration and the cavity sound pressure distribution. Figure 5 is the mode shapes diagram of the coupled system. It can be seen from the figure that the mode shapes of the second-order to sixth-order modes of the coupled system are similar to the first-order to fifth-order mode shapes of the structure, and the frequency changes slightly. It shows that these modes are caused by the vibration of the structure. The first-order mode shape of the coupled system cannot find the corresponding mode shape in the structural mode, and the first-order modal frequency of the coupled system is close to the first-order acoustic modal frequency of the cavity under the corresponding gap width. It indicated that the first-order mode of the coupled system is generated by the change of the cavity sound pressure.

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model

47

The first-order modal frequency of the coupling system (132.8 Hz) is 28 Hz lower than the first-order modal frequency of the cavity (160.8 Hz). This is because under the condition of acoustic-structure coupling, the acoustic boundary is no longer a hard boundary, but an elastomer. The original rigid boundary weakens at resonance, resulting in a drop in the resonance frequency. The frequencies of the second-order mode to the sixth-order mode of the coupled system is different from that of the first-order mode to the fifth-order mode of the structure. The vibration deformation of the second-order and third-order modes of the coupled system is mainly at the upper and lower skin of the cavity. Therefore, it is greatly affected by the sound pressure in the cavity. It indicates that the cavity gas produces additional stiffness to the structure which increases the natural frequencies of the structure.

Fig. 5. Mode shapes of coupled systems

The coupled system modes calculation results under different gap widths are shown in Table 6.

48

J. Zhong et al. Table 6. The first three modes of the coupled system with different gap widths

Gap Width/mm

1st -order natural frequency /Hz

2nd -order natural frequency /Hz

3rd -order natural frequency /Hz

4

106.4

151.7

195.6

6

118.7

152.7

198.2

8

127.1

153.9

200.6

10

132.8

155.2

203.2

12

136.1

157.6

205.1

14

138.3

157.7

206.6

16

140.1

158.8

208.3

With the change of gap width, the first three modal frequencies of the coupling system all increase, among which the first modal frequency increases more significantly, mainly because the first mode is generated by Helmholtz cavity resonance, so the frequency is greatly affected by the width of cavity opening. While the second and third modes are generated by the structure, so they are less affected by the size of cavity opening. The reason for the change of those frequencies is that when the gap width is different, the additional stiffness of the structure produced by the gas in the cavity is different. The first-order natural frequency changes of the cavity and structure before and after coupling are shown in Fig. 6.

Fig. 6. Natural frequency of uncoupled system and coupled system versus gap width

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model

49

4.4 Harmonic Response Analysis of Coupled Systems According to cavity acoustic modal analysis, structural modal analysis and coupled system modal analysis, the first-order modal frequency of the cavity and structure are ranging from 100 Hz to 200 Hz, the modal frequencies of the coupled system generated by these two vibration forms is still in the frequency range of 100 Hz to 200 Hz, so the harmonic response analysis of the sound pressure excitation near this frequency band is carried out for the coupled system. The meshes and boundary conditions of the cavity and structure are consistent with the modal analysis of the coupled system. The structural damping ratio is set to 1% and the frequency step is 0.5 Hz. At the same time, the external sound field is established and the sound pressure excitation is applied to the upper and lower surfaces of it. The sound pressure excitation is 63 Pa (the sound pressure level is about 130 dB). Other surfaces are set as radiation surfaces. The geometric model of acoustic-structure coupling harmonic response analysis is shown in Fig. 7.

Fig. 7. Geometric model for harmonic response analysis of acoustic-structure coupling

When the gap width varies from 4 mm to 16 mm, the frequency response calculation results of the average sound pressure level in the cavity are shown in Fig. 8. From the calculation results, it can be seen that there are three response peak frequencies in the range of 80 Hz to 210 Hz. With the increases of the gap width, the response peak frequencies also increase. The average sound pressure level response peak frequencies of the cavity under different gap widths are shown in Table 7. When the external sound field excitation frequency is close to the first peak frequency, the average sound pressure level in the cavity is around 150 dB, the sound load in the cavity is obviously enhanced and the influence of the structure by the sound load will also be enhanced. It can be seen from Table 7 that the peak frequencies under different gap widths is lower than the natural frequencies of the coupled system. Since the first-order mode is dominated by the acoustic cavity, combined with the second-order spring damping system of cavity analogy, when the outflow field exists, the effective length of the neck formed by the opening will increase and the resonant frequency of the cavity will decrease. The second-order mode and the third-order mode are dominated by the structure. The existence of the external sound field makes the air outside the cavity also

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produce additional mass to the structure, which reduces the influence of the additional stiffness produced by the air in the cavity to a certain extent, and makes the natural frequencies of the structure in the coupled system closer to the natural frequencies of the structure in the uncoupled state.

Fig. 8. Frequency response curve of cavity average sound pressure level under different gap width

Table 7. Peak frequency of cavity average sound pressure level response under different gap widths Gap First peak 1st -order Second peak width/mm frequency/Hz natural frequency/Hz frequency /Hz

2nd -order Third peak natural frequency/Hz frequency /Hz

3rd -order natural frequency /Hz

4

93.5

106.4

150

151.7

193

195.6

6

104

118.7

150.5

152.7

194.5

198.2

8

112

127.1

151

153.9

196

200.6

10

118

132.8

151.5

155.2

197.5

203.2

12

122

136.1

152.5

157.6

198

205.1

14

126

138.3

152

157.7

199.5

206.6

16

128.5

140.1

152.5

158.8

200.5

208.3

Effects of Gap Width on Vibration Response of Aileron-Cabin-Model

51

Figure 9 shows the structural displacement frequency response curve of the node in the y direction at the connection between the upper skin and the support beam. The peak frequencies of the displacement response are consistent with the peak frequencies of the average sound pressure level response of the cavity. Near the first peak frequency of the response, the node displacement response exceeds 0.5 mm. It shows that the acoustic load under the Helmholtz resonance of the open cavity will cause the cavity structure to produce a large vibration response. When there is no gap in the aileron cabin cavity, under the acoustic excitation of 80 Hz to 210 Hz, the node no longer has a large displacement response at low frequencies, but only produces a large response near the natural frequencies of the structure, and the displacement amplitude is small. It is shown that when there is no gap, the structural response is not affected by the cavity. The results show that the existence of the gap will change the acoustic and vibration characteristics of the structure, change the natural frequencies of the structure and strengthen the structure vibration under certain frequency acoustic loads.

Fig. 9. Frequency response curve of node displacement in Y direction

5 Conclusion In this paper, the modal analysis of the aileron cabin structural, the acoustic cavity and the acoustic-structure coupling system is carried out by ANSYS software, and the harmonic response analysis of the acoustic-structure coupled system is carried out. It is found that the aileron cabin gap has an important influence on the vibration response of the aileron cabin structure. The specific conclusions are as follows:

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(a) The aileron cabin with a gap can be compared to the Helmholtz resonant cavity. Since the opening of the aileron cabin is an irregular channel, it is difficult to accurately calculate the resonance frequency through a pure theoretical formula. With the change of the gap, the numerical calculation results are consistent with the change trend of the Helmholtz resonance theoretical formula. (b) In the acoustic-structure coupling analysis, the wall of the cavity is an elastic body, the cavity resonant frequency is reduced due to the coupling effect, and the natural frequencies of the structure also change due to the additional structural stiffness and mass provided by the gas. (c) With the gap becomes larger, the first-order natural frequency of the coupled system increases. The Helmholtz cavity resonance will greatly strengthen the acoustic load in the cavity. The structure will generate a larger displacement response under the action of the acoustic load at the resonance frequency. The resonant phenomenon of cavity with a gap will change the structural acoustic load response. (d) In the structural design of a cavity with a gap working in a strong noise environment, the acoustic and vibration characteristics of the cavity should be studied. The cavity structure can be optimized by the Helmholtz resonance theory, and the Helmholtz resonance frequency of the cavity should be reasonably designed to make it deviates from the frequency of the acoustic load with a large amplitude in the working environment, so as to realize the vibration reduction of the structure.

References Chanaud, R.C.: Effects of geometry on the resonance frequency of Helmholtz resonators. J. Sound Vib. 178(3), 337–348 (1997) Deng, Z.X., Gao, S.N.: Frequency coupling mechanism of structural-acoustic coupled system. J. Vibr. Shock 21(14), 11–15 (2012) Ezcurra, A., Elejabarrieta, M.J., Santamaria, C.: Fluid-structure coupling in the guitar box: numerical and experimental comparative study. Appl. Acoust. 66(4), 411–425 (2005) Gourdon, E., Savadkoohi, A.T., Cauvin, B.: Effects of shape of the neck of classical acoustical resonators on the sound absorption quality for large amplitudes: experimental results. Build. Acoust. 27(2), 169–181 (2020) Jin, G.Y., Yang, T.J., Liu, Z.G., et al.: Analysis of structural-acoustic coupling of an enclosure surrounded by flexible panel. Acta Acustica 32(2), 178–188 (2007) Langfeldt, F., Hoppen, H., Gleine, W.: Resonance frequencies and sound absorption of Helmholtz resonators with multiple necks. Appl. Acoust. 145, 314–319 (2019) Liu, Y.T., Liu, X.D., Shan, Y.C., et al.: Research on mechanism and evolution features of frequency split phenomenon of tire acoustic cavity resonance. J. Vib. Control 27(3–4), 343–355 (2021) Ma, D.Y.: Helmholtz resonator. Tech. Acoust. 21(1–2), 2–3 (2002) Ma, R.L., Slaboch, P., Morris, S.: Fluid mechanics of the flow-excited Helmholtz resonator. J. Fluid Mech. 623, 1–26 (2009) Ma, T.F., Lin, Y., Zhang, J.W.: Modal analysis for fluid-structure interaction system of car cavity. Chin. J. Mech. Eng. 41(7), 225–230 (2005) Selamet, E., Selamet, A., Iqbal, A., et al.: Effect of Flow on Helmholtz Resonator Acoustics: A Three-Dimensional Computational Study vs. Experiments. Sae Technical Papers (2011)

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Slaboch, P., Ma, R.L., Morris, S.: Vortical-acoustic interactions in a flow-excited Helmholtz resonator at low Mach numbers. In: 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference) (2008) Wang, Z.F., Hu, Y.M., Xiong, S.D., et al.: Influence of cavity wall elasticity on resonant frequency of small underwater cylindrical Helmholtz resonator. Acta Physica Sinical 58(04), 2507–2512 (2009) Yao, Q.H., Yao, J.: Vibration fatigue in engineering structures. Chin. J. Appl. Mech. 23(01), 12–15 (2006) Yu, Y., Xu, Z.Y.: Acoustic-structure coupling modal analysis of a Guqin resonator. J. Vibr. Shock 35(16), 226–230 (2016) Zhang, Z.P., Ren, F., Feng, B.C.: Noise task of aircraft-resolve in engineering. Acta Aeronautica et Astronautica Sinica 29(5), 11–15 (2008) Zhao, X.J., Lu, H., Song, Y.H., et al.: Study of structure response to acoustic load and cabin noise for a space vehicle. Missiles Space Veh. 03, 11–15 (2014)

Simulation of Tensile Test for Laminate Made of CFRP. Role of Different Parameters that Influence the Failure Mode Type Nikolay Turbin1

and Sergei Kovtunov2(B)

1 Laboratory of Polymer Composite Materials, Moscow Aviation Institute, 4 Volokolamskaya

Road, 125993 Moscow, Russian Federation 2 Shanghai Jiao Tong University, Shanghai, China

[email protected]

Abstract. The tensile test of composite material sample is a traditional mean of obtaining its strength and stiffness. The standard for conducting this experiment is ASTM D3039, where the general requirements, tooling and parameters of loading are presented. In the meantime the standard provides several modes of sample’s failure, which are likely to be met in practice. By default, the failure location in the middle of specimen is the most desirable (denoted as LGM). Other modes of failure might be treated as unacceptable result of testing, for example splitting of the material parallel to loading direction (denoted as SGM). There are many studies researching the influence of different parameters on failure mode and depending on them, the different failure modes were obtained. In current paper the attained results intersect with a results produced previously by few of other studies. The simulation via finite elements method (FEM) can become helpful instrument in assessment of sensitivity of localization and nature of failure to different parameters, such as material system used, geometry of the sample and tooling. Keywords: Tensile test · Composite material · ASTM D3039

1 Introduction Many researches of tensile testing response of different materials were made but the failure often occurred in unacceptable region. For example, at grips as in (Pyl et al. 2018), near the grips as was in study by Choudri et al. (2017) or inside grip (De Baere et al. 2011) and (Nurrul et al. 2020). Moreover, one and the same parameter variously works on failure modes of different materials. Chen et al. (2017) researched influence of thickness of specimen on failure mode of UHMWPE fibre laminates, while Ritesh Bhat studied how thickness of glass fiber reinforced isophthalic polyester composites impacts on failure mode Bhat et al. (2019). And they got different results: in Bhat’s study failure occured at grips, but in tests by Chen et al. (2017) specimen failed in the middle. This work shows a study recognizing the key aspects, that influence the appearance of failure during ASTM D3039 (2000) testing routine. The number of checked © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 54–64, 2023. https://doi.org/10.1007/978-981-99-0651-2_5

Simulation of Tensile Test for Laminate Made of CFRP

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parameters includes stiffness and strength of composite lamina, specimen and tooling configuration, thickness and compliance of adhesive layer between tooling and sample. Additionally, the impact of variables of finite element analyses are studied, namely: continuum or shell elements, oriented or non-oriented meshing and boundary conditions. The Abaqus/Explicit solver is used for processing to overcome the difficulties with convergence. Failure modes of specimens were also classified in according with ASTM D3039 recommendation. Numerical simulation was performed using ABAQUS by using the mechanical properties obtained from the experiments, in the same way as Kharghani and Guedes (2018)

Fig. 1. Finite element models of the specimens: (a) 0° unidirectional specimen; (b) 90° unidirectional specimen; (c) ±45° symmetric stacking.

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or Bak et al. (2020) modeled it but in current paper element size is 1 mm. Laminates considered in the present study consist of a number of repeating layers. The finite element models of the tension specimens are shown in Fig. 1. The geometry was discretized using C3D8R (Continuum three-dimensional eight-noded reduced) elements. The comparison was made based on the damage patterns obtained from experiments and simulations (Aswani et al. 2016).

2 Experimental Part The tensile tests were carried out in accordance with ASTM D3039. 2.1 Material Material of Specimen For current test it was used T26/Robolen 200/6.2/UMT49S-12K-EP. Its properties are shown in Table 1. Table 1. Properties of T26/Robolen 200/6.2/UMT49S-12K-EP Characteristic

Value

Longitudinal tensile strength, MPa

2200

Longitudinal compressive strength, MPa

680

Transverse tensile strength, MPa

40

Transverse compressive strength, MPa

155

Longitudinal tensile Young’s Modulus, GPa

134

Transverse tensile Young’s Modulus, GPa

7

Poisson’s Ratio

0.33

Shear Modulus, GPa

3.5

Tab Material The specimens were prepared by bonding end-tabs of E-glass fibers/epoxy laminate. Its properties are shown in Table 2. The tab material was applied at different angles to the force direction (0°, 90° and ±45°) to provide a soft introduction of load. Also steel tabs and tabs made of the same material as was being tested were used to check the tab material influence on the performance. The properties of steel are shown in Table 3. 2.2 Geometry Specimen Geometry In this work were used rectangular specimens with dimensions that are according to

Simulation of Tensile Test for Laminate Made of CFRP

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Table 2. Properties of E-glass fibers/epoxy laminate. Characteristic

Value

Longitudinal Modulus, GPa

45

Transverse Modulus, GPa

12

In-plane Poisson’s Ratio

0.19

Transverse Poisson’s Ratio

0.31

Shear Modulus, GPa

5.5

Table 3. Properties of steel. Characteristic

Value

Young’s Modulus, GPa

210

Poisson’s Ratio

0.33

ASTM D3039: 250 mm of length × 15 mm of width × 1 mm of thickness (that is recommended for 0° unidirectional specimens), 175 mm of length × 25 mm of width × 2 mm of thickness (that is recommended for 90° unidirectional specimens) and 250 mm of length × 25 mm of width × 0.175 mm of thickness (for ±45° symmetric stacking as defined by ASTM D3518 (2017). Tab Geometry Initially dimensions of specimens were chosen according to ASTM D3039: for 0° unidirectional specimens were used tabs with length 56 mm, for 90°–25 mm. Tab thickness and bevel angle also were selected in accordance with ASTM D3039, but also were varied. The specimens also were modeled by shell elements as well as in Al Abadi et al. (2018). In this study the difference is that element size was chosen to be 1 mm in place of 4 mm.

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3 Results and Discussion The samples failed when ultimate longitudinal tensile strength were achieved, that confirms that the specimens were modeled correctly. For 0° unidirectional specimen tensile stress-displacement curve is shown on Fig. 2.

Fig. 2. Tensile Stress-Displacement curve for 0° unidirectional specimen.

After the tensile tests failure regions of the specimens were received. Figure 3 shows typical specimens after failure, which present valid failure modes in accordance with ASTM D3039 (Fig. 4) (Faulstich et al. 2006). In current study the failure appeared in the middle only in 0° unidirectional specimen with tabs with bevel angle 7°, that is recommended by ASTM D3039. Tab thickness and bevel angle were varied. With the dimensions recommended in ASTM D3039 only 1,5 mm thickness provided failure in the middle. The tab plies orientation has angle 90° to the specimen orientation (which is in contrast to recommendations of ASTM D3039 where it is said that the angle is commonly 45° to the force direction). Similarly, geometry of specimen influence also was verified. The short specimens, much shorter than recommended in ASTM D3039, were tested. And they failed in acceptable region with other orientation of tabs. Result of testing depends on gage length and tab thickness (Fig. 5). Similar one was performed by Behera et al. (2019) and Wang et al. (2018). Specimen dimensions that deviated from that and from recommended in ASTM D3039 didn’t produce acceptable failure mode.

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Fig. 3. Tensile failure mechanisms of homogeneous composites: (a) 0° unidirectional specimen; (b) 90° unidirectional specimen.

Other group of tab bevel angles and orientation angles provided unacceptable results. For instance: ±45° laminate failed near the tabs, providing angled failure mode in exactly the same way as in study by Kharghani and Guedes (2018). Additionally, the 45° unidirectional lamina was modeled, with tooling and without it. Results of testing without grips is equal to (Liang et al. 2013) – the crack was angled and located at the end of specimen. With tabs – also angled crack but near the tabs as in Sun et al. (2019). Other stacking provided the results similar to Lee et al. (2014). With various values of tab thickness were obtained results close to Chevuru et al. (2020). Using of tabs oriented at angle 45° for 0° unidirectional specimen produced failure at the grips like it was obtained by Buse et al. (2020). With tabs angled at 0° specimen failed in two regions near the tabs, like in study by Abhishek et al. (2020).

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Fig. 4. Tensile test failure codes/typical modes.

Among others stacking of two laminas was modeled like in (Carmelo et al. 2017) (Padalu et al. 2020). But the failure occurred inside of tabs (not near the tabs or in the middle). It was premature failure called by delamination. Regarding material of tabs – only 0° specimen failed in the middle influenced by tab material choice. Results of shell models testing are same as in study by Al Abadi et al. (2018). All specimens failed at grips providing LAT failure mode (Fig. 4).

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Fig. 5. Short 0° unidirectional specimens.

4 Conclusions The present studied the influence of specimen and tabs geometry, material and its orientation, number of layers in stacking on the tensile failure mode of composite. Based on the executed work, following conclusions were drawn: • Only 0° unidirectional specimen fails in the middle. Other variations in number of plies and their orientation failed to repeat the result. • Tab material does not have a great impact on results of testing. 0° unidirectional specimen fails in the middle with each of tab materials used in this study. • Composite stiffness alone didn’t have essential effect on failure location. It is effective only with respect to stiffness of tab material. • By contrast, geometry of specimen and tooling works on failure mode. Dimensions recommended in ASTM standard work best for testing performance.

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For clarity the conclusive results of study are tabulated (Table 4). Table 4. Results of study. Parameter

Influence on failure mode

Number of plies and their orientation

0° unidirectional specimen fails in the middle, in other cases – in unacceptable region

Tab material

It doesn’t matter which tab material is used

Tab orientation

Tabs oriented at 90° to the specimen longitudinal direction provide accepted failure mode. The rest variations lead to unacceptable results

Composite stiffness

It is matter that the stiffness would be respectively to stiffness of tab material. Otherwise it doesn’t produce desired result

Geometry of sample and tooling

The best results achieved by dimensions recommended in ASTM standard

Mesh (oriented or non-oriented)

It doesn’t impact on failure mode. Both of this variations give identical results

Continuum or shell elements

Shell elements produce unacceptable failure mode, the specimen cracks at grips

The problem viewed in this article may be actualized in further researches. For example, more extended consideration of impact of composite stiffness on failure mode. In the current work it was shown, that values of stiffness that are essentially different from present in considered material don’t provide effect on resulting location of failure zone. The received dependencies are thought to be practical in preparation and conducting of the test program. Furthermore, the results will contribute to the quality of the computation complement of real testing of coupon and element testing blocks.

References Abhishek, K.P., Tomohiro, Y., Masahiro, I., Kazuhiro, K.: In-situ observation of tensile failure mode in cross-ply CFRP laminates using Talbot-Lau interferometry. Compos. Struct. 253, 112758 (2020). https://doi.org/10.31838/jcr.07.12.199 Behera, A., Thawre, M.M., Ballal, A.: Failure analysis of CFRP multidirectional laminates using the probabilistic weibull distribution model under static loading. Fibers Polym. 20(11), 2390– 2399 (2019). https://doi.org/10.1007/s12221-019-1194-9 ASTM D3039: Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials (ASTM International, United States) (2000). https://www.astm.org/Standards/ D3039 ASTM D3518: Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a ±45° Laminate (ASTM International, United States) (2007). https://standards.globalspec.com/std/13112493/astm-d3518-d3518m

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Aswani, K.B., Shivdayal, P., Yogesh, S., Suhail, A., Alagirusamy, R., Naresh, B.: Mechanical behavior of Kevlar/basalt reinforced polypropylene composites. Compos. A 90, 642–652 (2016). https://doi.org/10.1016/j.compositesa.2016.08.031 Bak, K.M., Raj, K.G., Ramasamy, N., Vijayanandh, R.: Experimental and numerical studies on the mechanical characterization of EPDM/ S-SBR nano clay composites. IOP Conf. Ser. Mater. Sci. Eng. 912, 052016 (2020). https://iopscience.iop.org/article/10.1088/1757-899X/912/5/052016 Bhat, R., Nanjangud, M., Sathyashankara, S., Ashu, P., Agastya, P.K., Dev, S.: Mechanical testing and microstructure characterization of glass fiber reinforced isophthalic polyester composites. J. Market. Res. 4, 3653–3661 (2019). https://doi.org/10.1016/j.jmrt.2019.06.003 Buse, Ö., Elmas, S., Mustafa, K., Ahmet, M.A.: Comparison of radome sandwich composite structures with finite element method. Mater. Today Proc. 34, 297–303 (2020). https://doi.org/ 10.1016/j.matpr.2020.03.800 Lee, B.-E., Park, E.-T., Kim, J., Kang, B.-S., Song, W.-J.: Analytical evaluation on uniaxial tensile deformation behavior of fiber metal laminate based on SRPP and its experimental confirmation. Compos. Part B Eng. 67, 154–159 (2014). https://doi.org/10.1016/j.compositesb.2014.06.031 Caggegi, C., Lanoye, E., Djama, K., Bassil, A., Gabor, A.: Tensile behaviour of a basalt TRM strengthening system: influence of mortar and reinforcing textile ratios. Compos. Part B Eng. 130, 90–102 (2017). https://doi.org/10.1016/j.compositesb.2017.07.027 Chevuru, R., Dasari, T., Subba, G.V.: Failure mode analysis for tensile S-glass fabric hexply using strain gauge method. J. Crit. Rev. 12, 2394–5125 (2020). https://doi.org/10.31838/jcr. 07.12.199 Choudri, R.V., Soni, S.C., Mathur, A.N.: Tensile fracture strength of Boron (SAE1042)/Epoxy/Aluminium (6061–t6) laminates. Mater. Today Proc. 4, 3407–3415 (2017). https://doi.org/10.1016/j.matpr.2017.02.229 De Baere, I., Van Paepegem, W., Quaresimin, M., Degrieck, J.: On the tension–tension fatigue behaviour of a carbon reinforced thermoplastic part I: limitations of the ASTM D3039/D3479 standard. Polym. Testing 30, 625–632 (2011). https://doi.org/10.1016/j.polymertesting.2011. 05.004 Al Abadi, H., Thai, H.T., Paton-Cole, V., Patel, V.I.: Elastic properties of 3D printed fibrereinforced structures. Compos. Struct. 193, 8–18 (2018). https://doi.org/10.1016/j.compstruct. 2018.03.051 Faulstich, J.M., de Paiva, S., Rezende, M.C.: Mechanical behavior of Kevlar/basalt reinforced polypropylene compo-sites. Mater. Res. 1, 83–89 (2006). https://doi.org/10.1590/S1516-143 92006000100016 Sun, J., Daliri, A., Guoxing, L., Ruan, D., Lv, Y.: Tensile failure of fibre-metal-laminates made of titanium and carbonfibre/epoxy laminates. Mater. Des. 183, 108139 (2019). https://doi.org/ 10.1016/j.matdes.2019.108139 Kharghani, N., Guedes, S.C.: Experimental, numerical and analytical study of bending of rectangular composite laminates. Eur. J. Mech. A Solids 72, 155–174 (2018). https://doi.org/10. 1016/j.euromechsol.2018.05.007 Chen, L., Zheng, K., Fang, Q.: Effect of strain rate on the dynamic tensile behaviour of UHMWPE fibre laminates. Polym. Testing 63, 54–64 (2017). https://doi.org/10.1016/j.polymertesting. 2017.07.031 Pyl, L., Kalteremidou, K.-A., Van Hemelrijck, D.: Exploration of specimen geometry and tab configuration for tensile testing exploiting the potential of 3D printing freeform shape continuous carbon fibre-reinforced nylon matrix composites. Polym. Testing 71, 318–328 (2018). https:// doi.org/10.1016/j.polymertesting.2018.09.022 Nurrul, A., Abidin, Z., Hafizi, M.Z., Jailani, M., Hussain, A.K., Mahmud, J.: Experimentalnumerical analysis of woven laminates under tension. Mater. Sci. 4, 1392–1320 (2020). https:// doi.org/10.5755/j01.ms.26.4.22898

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SysML-Based Approach for Functional Modeling of Civil Aircraft Systems Meihui Su, Yong Chen, and Meng Zhao(B) School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, China {sjtusmh,aerocy,magicmeng}@sjtu.edu.cn

Abstract. During conceptual design of complex civil aircraft systems, it is indispensable for systems engineers to establish functional architectures, which serve as the basis for subsequent detailed design. Since document-based descriptions of functional architectures tend to result in ambiguities and inconsistencies, academia has been devoted to the formal representation of functional architectures, with the aid of Model-Based Systems Engineering. However, traditional functional modeling approaches generally focus on input-output transformations, rather than state (mode) transitions of systems, which hinders the engineers from representing explicitly the functional architectures involving state-transition logic (e.g., specific signals should trigger the state of landing gear systems to change from retracted to extended, or vice versa). Furthermore, lack of formal representation of the state transitions makes the engineers rely on manual analysis to verify the functional architectures, which can be time-consuming and error-prone. To address this issue, this paper develops a SysML-based approach for functional modeling of civil aircraft systems. First, a state-integrated functional model of components is proposed; thereafter, the integration of the component functional models is proposed; Finally, the landing gear systems is employed to demonstrate the proposed approach above, followed by an illustrative case of functional simulation. Keywords: Model-based systems engineering · SysML · Conceptual design · Functional modeling · Civil aircraft system

1 Introduction With increasing product complexity, the influence of conceptual design on product performance, safety and development cost becomes more significant [1]. In conceptual design of civil aircraft system, one of the most important tasks for system engineers is to define Functional Architecture (i.e., component functions and their connections) [2], which is aimed at providing specification for detail design in different fields (e.g., mechanical engineering, electronic control, etc.). However, due to the large number of components and complex interactions of civil aircraft systems, functional architecture of the systems error-prone. For example, the result of functional integration of components of a system can be inconsistent with expected functions of the system. As a result, it will cause costly design iterations or security risk. Therefore, system engineers need to © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 65–79, 2023. https://doi.org/10.1007/978-981-99-0651-2_6

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verify [3, 4] the generated functional architecture in conceptual design stage to ensure the correctness of the functional logic. Compared with the traditional description of functional architecture based on document, the formal functional architecture based on models not only contributes to the unambiguity of the functional description, but as well provides the basis for an automated verification approach to functional architecture. Therefore, approaches for functional modeling have received considerable attention from academia and industry. There has been plenty of valuable research on functional modeling. For example, Erden et al. [5] define functional modeling as an activity of developing models of devices, objects, products and processes. Srinivasan et al. [6] review the development of functional definition and representation. Zhao et al. [7] propose a state–behavior–function model. Goel et al. [8] employ structure–behavior–function (SBF) model for automated design. Kruse et al. [9] present a new modeling approach for function and component libraries in SysML.W an et al. [10] present a novel multi-disciplinary systems engineering methodology for complex cyber physical systems. Chowdhury et al. [11] presents the concept of functional conjugacy and extends functional conjugacy to functional features. And Chowdhury et al. [12] also presents a formal representation of operational modes and states of technical devices for both discrete and continuous state transitions. Yuan [13] proposed a new hybrid method to automate the process of functional decomposition. However, the existing functional modeling approaches are mainly focused on inputoutput transformation, which neglect civil aircraft systems with multiple working states (e.g., landing gear systems and flight control systems). As a result, the schema of functional representation lacks functional logic related to state transitions (such as the logical process of extending and locking of the landing gear), resulting in that engineers cannot establish an explicit functional architecture model of the systems above. In addition, dynamic behavior modeling methods and tools (such as Simulink, Dymola, etc.) are mainly oriented to performance analysis, and it is difficult to explicitly represent abstract functional logic, so they cannot effectively support the functional architecture modeling of civil aircraft systems. Therefore, functional architectures involving system state transitions pose great challenges to the functional modeling of civil aircraft systems. As a result, system engineers have to manually analyze informal documents (or diagrams) to verify the generated functional architecture, which is time-consuming and error-prone. To address the issue above, it is urgent to carry out research on functional modeling of civil aircraft systems, which can form explicit formal representations of functional architectures, and lay the foundation for functional simulation approaches to support automated functional verification. Based on the general systems modeling language, i.e., SysML, this paper first proposes a state-integrated functional modeling approach for components, which integrates the representation of state transitions and that of inputoutput transformations; thereafter, an approach for integrating functional models of the components is proposed, which allows engineers to represent explicitly functional architectures involving state transitions; finally, the functional models of landing gear systems are demonstrated, and an illustrative functional simulation process follows, providing the basis for automated functional verification.

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2 Functional Modeling of Components 2.1 Representation of Component States A state of component refers to an abstraction of the structure of component, which is also called structural state. Considering a component can be physically decomposed into several elements, (e.g., shafts, keys, gears, etc.), the representation of Component States proposed in this study actually is a description of the elements and their physical connections attributes within the component. Take a three-position reversing valve as an example. The valve spool moves under the action of electromagnet, so that outlet ports of the three-position reversing valve are opened or closed respectively to conduct different circuits (Fig. 1).

Fig. 1. The structure sketch of three-position reversing valves

The spool of the valve has three different working positions under the action of the push rod, which respectively correspond to the three physical connections within the internal elements of the valve, namely the left position, the right position and the neutral position. Therefore, the three-position reversing valve assembly has three different component states. State Machine Diagram of SysML is a kind of behavior diagram that can be used to describe the states of the components, and the transitions between the states in response to triggering events [3]. Component states can be represented by state elements in State Machine Diagram, which are usually identified by round-angle rectangle. For example, the three-position reversing valve above is in the neutral, right and left position, then the corresponding state element will be defined as “Off", “Left” and “Right” (Fig. 2).

Fig. 2. The example of the component behaviors of three-position reversing valves

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2.2 Representation of Component Behaviors Since the component has multiple states, different trigger conditions will cause the component change from one state to another. So it is necessary to describe the transition of the component states. Therefore, Component Behaviors will be used to represent the transition of component states in this research. As shown in the figure below, when the three-position reversing valve is in the neutral position (i.e., “Off” state), the spool will move to the right position under the action of the push rod once the left coil receives an electrical signal. Then the oil circuit on the right side of the valve will be connected, which means that the valve will implement a behavior to transit its component state from “Off” to “On_Right”. If the left coil is subsequently de-energized, the spool will move from the right position to the neutral position under the action of the push rod. At the same time the valve will implement another behavior,so that the component state will be transited from “On_Right” to “OFF”. Homogeneously, there will another two component behaviors when the right coil is energized or deenergized. Based on the above analysis, the three-position reversing valve totally have four component behaviors. Component behaviors can be represented in State Machine Diagrams of SysML. It is usually identified by a solid line with an open arrow, which starts from the source vertex to the target vertex, indicating that the component switches from the initial state to the final state. In SysML, event is defined as an element in the system model, which indicates the type of event that can trigger a behavior in the actual system. The signal event represents the process of receiving the signal from the target structure of the signal instance. For example, the electrical signal received by the coil in the component behavior of the three-position reversing valve actually is a signal event. Based on the above analysis, taking the three-position reversing valve as an example, the above component behavior can be expressed as the below Fig. 3 by using State Machine Diagram of SysML.

Fig. 3. Component behaviors of the three-position reversing valve

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2.3 Representation of Component Action Component action can be regarded as the effect that a component imposes on input flows to change the output flows. The 2-tuples of “input-output flow” are widely used in existing functional modeling methods [1]. However, this method can only describe the single function of a component, and it is difficult to clearly express different transformation of input and output when the components are in different states. Component action can be represented by State Machine Diagram and Activity Diagram of SysML. In State Machine Diagram, each state element has an entry event, which can be associated with Activity Diagram. If component state in State Machine Diagram has an entry element and the category of which is Activity Diagram, the component will execute the corresponding Activity Diagram after entering this state. Activity Diagram represents the transition from input to output, so the execution of it can be regarded as the implementation procedure of component action. Therefore, multiple Activity Diagrams are used to model different states of the component, and correspond to entry elements in different component states. For example, as depicted in Fig. 4, the component action of the three-position reversing valve would be modeled as two Activity Diagrams corresponding to State Machine Diagram.

Fig. 4. Component actions of the three-position reversing valve

2.4 Representation of Component Functions To sum up, engineers can describe component states, component behaviors and component action clearly and formally, thereby establish component functional models. As shown in Fig. 5, representation of component states, component behaviors and component action can be illustrated clearly from the above model. Component states, which are generalization of all elements within the component and their physical connection attributes, determine the transition of input flow and output flow implemented by the component, so it is the basis for component functional modeling; Component behaviors, which refer to the transition of component state, reflect the expected structural change of the component, so it is one of the most important part of component functional model. Component action, which refer to the impact that the component exerts on the input to produce the expected output, is also an important part of the component functional model.

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Fig. 5. Component function model

To sum up, each attribute value in state space is the basis for the representation of the component behaviors and component action, and both the set of component behaviors and the set of component action incorporate the expected functions of the component. Therefore, for components with variable structural states, engineers can build component functional models based on SysML to fully illustrated the expected state transitions and input-output transitions.

3 Integration of Component Functional Models 3.1 Representation of Component States Integration The functional architecture scheme of complex systems should contain the corresponding rules for system states and internal component states to ensure that component state integration will keep the system in the expected state. For example, in order to control the direction of ground motion, the nose wheel steering system of aircraft has different states (i.e., “left”, “right” and “neutral”).When the system is under “left” state, the corresponding rules for internal component state are described as follows: the turning servo valve should circulate hydraulic oil to the upper chamber of the actuator, (i.e., in “On_Up” state); the swivel selector valve should remain engaged, (i.e., in “On” state);the turning actuators should be in normal working condition, (i.e., in “Norm” state); etc. Based on the above representation of component state, the constraint module of SysML can be used to express the rules for component state integration. Firstly, define different tag values for component states or system states; Secondly, use Action to update tag value in entry element of each state, so that the current component state can be recorded. On this basis, establish a constraint module, and the constraint parameters of it are bound to the current state of the system and each components. Finally, establish the corresponding relationship between system states and component states by constraint attributes. 3.2 Representation of Component Behaviors Integration In order to support the realization of system behaviors, the system functional architecture scheme should not only include the formal description of component behaviors, but also

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the formal description of component behavior integration. Since the trigger signal of component behavior is the output from other components in the system or the signal flow from the external environment of the system, component behavior integration is generally reflected in the connection between the output at component level and the control port, or the connection between the system and the control port of component. Based on the above representation of component behavior, Block Definition Diagram and Internal Block Diagram of SysML are used to express the rules for component behavior integration. Firstly, define the control ports of the system in Block Definition Diagram to receive signals from the external environment; Secondly, connect the defined system control port with the corresponding component control port in Internal Block Diagram to indicate that the signal outside the system will trigger the component behavior inside the system; Finally, connect outputs of components with control ports in Internal Block Diagram to indicate that the output of one component will trigger the behavior of another component. For example, in the nose wheel steering system of aircraft, the steering control unit triggers the behavior of the steering servo valve by sending an electrical signal. In this way, the steering control unit changes the transmission path of the hydraulic oil, which means that there is a connection between the output and the control port; at the same time, the pilot outside the system triggers the behavior of the rudder pedals inside the system through force signal, which means that there are control ports connected to the system and pedals. 3.3 Representation of Component Actions Integration In order to support the system to realize the expected input-output transformation, the system functional architecture scheme should not only include the formal description of component action, but also the formal description of component action integration. Since the energy or material flow required for component action is the output from other components in the system or the input from the external environment of the system, component action integration is generally reflected in the connection between the input at component level and the output port, or the connection between the system and the input-output port of component. Based on the above representation of component action, Block Definition Diagram and Internal Block Diagram of SysML are used to express the rules for component action integration. Firstly, define the input and output ports of the system in Block Definition Diagram to exchange material flow and energy flow with the external environment; Secondly, connect the defined system input port with the corresponding component input port in Internal Block Diagram to indicate that the material and energy outside the system will become the input of the component inside the system; Thirdly, connect the defined system output port with the corresponding component output port to indicate that the material and energy output by the internal component will reach the outside of the system; Finally, connect output ports with input ports of components in Internal Block Diagram to indicate that the output material and energy of one component will become the input of another component to implement its action. For example, in the nose wheel steering system of aircraft, the swivel selector valve can transmit the hydraulic oil to the steering servo valve to provide the energy required to implement the action, which means that the output port of the swivel selector valve is connected with the input port of

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the steering servo valve; at the same time, the input port of hydraulic energy outside the system is connected to the output port of swivel selector valve inside the system, which enables external hydraulic source to provide the input required for the swivel selector valve to implement the action.

4 Case Study 4.1 Introduction of Landing Gear Systems The landing gear system is used to support the aircraft during the process of takeoff, landing or taxiing on the ground [14]. The landing gear system of modern aircraft is usually composed of landing gear structural components (generally including nose landing gear and left/right main landing gear), actuators that drive the landing gear to retract or extend, and hydraulic control units. There are two states of the landing gear system, which are retraction and extension (Fig. 6).

Fig. 6. The different states of landing gear systems

The purpose of this research is to support engineers to represent and verify the functional architecture scheme formally. Therefore, this section will use CatiaMagic (a modeling tool for SysML) to establish a functional model of the landing gear system and its components based on the functional architecture scheme of a certain type of civil aircraft landing gear system (Fig. 7). According to the functional architecture scheme, the landing gear system obtains energy input from external hydraulic source, and uses hydraulic transmission to control the retraction and extension. During the retraction process, the selector valve transmits hydraulic oil to the up-pipeline to drive each actuator to retract the nose gear and the left/right main landing gear; during the extension process, the selector valve transfers hydraulic oil to the down-pipeline to extend gears by using the reverse movement of each actuating cylinder.

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Fig. 7. The principle of the retraction and extension of landing gears

4.2 Functional Modeling of Components of Landing Gear Systems (1) Control Lever The control lever (abbreviated as lever) has three gear positions (i.e., UP, DN and OFF) to allow pilots to control the retraction and extension of nose and main landing gears. Align with the three-position reversing valve above, the three gear positions of the lever respectively correspond to different component states, i.e., “Up”, “Dn” and “Off”. Then, the component behaviors are analyzed. For example, for the shift of the lever from OFF to UP, the initial component state is “Off”, the final component state is “Up”, and the trigger signal is a force signal named as TurnUp. Finally, the component actions are modeled. Take the UP position of the lever as an example: if the component state is “Up”, then the output flow of the component action is f_force (or ~ f_force, which means the opposite direction). In summary, the component functional model of the lever can be established with SysML Diagrams (Fig. 8).

Fig. 8. Component functional model of the control lever

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(2) Actuator The landing gear system uses a plurality of hydraulic actuators to drive the retraction and extension of each landing gear. Different from the control lever, the actuator has the unique component state (i.e., “NORM”), and no component behaviors. Regarding component action, the actuator can obtain hydraulic energy from different input ports, and then output the kinetic energy of linear motion in the opposite direction, (i.e., f_velo). Therefore, the component action of the actuator can be modeled with activity diagrams. The activity of “HydrActu” corresponds to the entry event of the state Norm, which means that if the hydraulic energy is input to the component through pi_up in the NORM state, the actuator will output kinetic energy of linear motion (or if the hydraulic energy is input through pi_dn, the actuator will output kinetic energy of reverse motion) (Fig. 9).

Fig. 9. Component functional model of the actuator

(3) Gear-up and gear-down locks and other components. If the landing gear reaches “down” position, the gear-down lock will be the “locked” state to prevent the side struts of the landing gear from collapsing; and if the landing gear begins to retract, the gear-down lock will be the “unlocked” state to allow the side struts to fold. Functional modeling of the locks and other components is omitted for conciseness. 4.3 Integration of Component Functional Models of Landing Gear Systems First, an integrated representation of the component state is established. The states of landing gear system correspond to a collection of specific component states. For example, if the state of the landing gear system is “Up”, the selection valve should output the hydraulic oil to the retracted circuit, which means that the component state is “Up”. Meanwhile, the landing gear should be in the “Up” position, and the gear-up lock is locked. Secondly, an integrated representation of component behavior is established. The components have output ports and control ports connected with each other in the landing gear system. For example, the control lever is responsible for controlling the state of the selector valve, which means that the output port of the control lever should be connected

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to the control port of the selector valve so that the force signal can trigger the behavior of the valve. In addition, the landing gear system has control ports that connect to internal components to allow signals from the external environment (such as force signals from pilot) to be transmitted to the interior of the system, as shown in Fig. 10. Finally, an integrated representation of the component action is established. The components have input ports and output ports connected with each other in the landing gear system. For example, the selector valve should output hydraulic energy to the actuator, so the output port of the former is connected to the input port of the latter. In addition, the landing gear system has input and output ports assigned to components to allow material or energy from the external environment (such as hydraulic energy, etc.) to reach the interior of the system, as shown in Fig. 10. 4.4 Functional Simulation of Landing Gear Systems In conceptual design of complex systems, it is indispensable to verify functional architectures of the systems to eliminate errors relating to functional logic. Based on the functional models above, therefore, functional simulation of the landing gear system is conducted to automatically reason about functional logical processes, which contributes to efficient verification of the functional architecture of the system. An illustrative case of the functional simulation is given as follows, which reveals that the system function of ‘retracting land gears’ can be performed as expected. Step 1, the initial state of the landing gear system is designated, allowing the computer to set the initial sates of each component. Considering the concerned function of ‘retracting land gears’, the initial state of the system is designated as ‘Dn’. Based on the integration model of the component state, the states of each component are then initialized as Fig. 10, where the main landing gear is in the state of ‘Off’ and the down position lock is ‘Locked’.

Fig. 10. Initial states of the components of landing gear systems

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Step 2, the input flows of the system are designated at specific ports, allowing the computer to deliver the flows to corresponding components. Considering the concerned function of ‘retracting land gears’, the input flows of the system include energy (e.g., hydraulic and electrical) and signals (e.g., force from pilots operating the lever). Based on the integration model of the component behaviors and actions, the input flows above are delivered to the components. For example, the actuators receive f_hydr as input energy, and the lever receives f_force as a control signal. Step 3, concerning each component, the comparison between the input signal flows acquired and those specified in component behavior models is conducted, allowing the computer to change the states of the components whose behavior can be triggered. For example, the state of the lever is changed from ‘Off’ to ‘Up’, as the force signal can trigger a state transition according to the component behavior model. Step 4, concerning each component, the comparison between the input flows acquired and those specified in component action models is conducted, allowing the computer to generate the output flows of the components whose action can be performed in the current state. For example, the lever generates f_force at the output port po_up, according to the component action model corresponding to the current state, i.e., ‘Up’. Step 5, the generated output flow of a component is delivered to another component according to the component integration models of behaviors and (or) those of actions, so that the computer can simulate the functional interaction between the components. For example, the output flow of the lever above, i.e., f_force, is delivered to the directional valve at the control port, i.e., pc_up, serving as the addition control signal of the valve. Step 6, concerning the components with additional input signals, the component behavior models are checked again, allowing the computer to determine whether subsequent state transitions occur as a result of these input signals. For example, the signal delivered to the valve above, i.e., f_force at pc_up, triggers the component behavior whose initial and final states are ‘Off’ and’Up’, respectively. Step 7, concerning the components whose states are changed, the component action models are checked again, allowing the computer to generate new output flows corresponding to the current state. For example, the valve in the state of ‘Up’ generates f_hydr at po_up, which means that hydraulic energy will be employed to retract the landing gears. At this point, it can be found that states of the lever and valve, along with the output flows of them, have been updated automatically, as shown in Fig. 11. Finally, similar to Step 5, the generated output flow of the valve is delivered to another component according to the component integration models; thereafter, the behavior and action model of this component are checked, similar to Step 6 and 7. In this way, the computer can determine the final states and output flows of each component of the landing gear system, as shown in Fig. 12.

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Fig. 11. Functional simulation process of the control lever and selector valve

The comparison between Figs. 10 and 12 reveals that the functional models of the landing gear system enable the computer to simulate the state transitions and flowtransforms of each component, as well as the interactions between the components. Furthermore, the final states and output flows of the system can be determined, which allows engineers to verify that expected function of ‘retracting landing gears’ can be fulfilled based on the system architecture.

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Fig. 12. Final states of the components of landing gear systems

5 Conclusion During conceptual design of civil aircraft systems, functional models contribute to an unambiguous representation of functional architectures, and as well provide the basis on which functional simulation can be conducted. However, traditional functional modeling approaches focused on input-output transformation fail to represent state transitions involved in functional logic of civil aircraft systems, which hinders explicit functional models of the systems. To address this issue, a SysML-based approach for functional modeling has been proposed. First, the representation of component states, behaviors and actions is proposed, which integrates state transitions and input-output transformations with state-machine and activity diagrams. Thereafter, the integration of component states, behaviors and actions is proposed, which explicitly represents state-dependent functional architectures. Finally, functional modeling of the landing gear system is employed to illustrative the proposed approach, and functional simulation is conducted to illustrative how system states and outputs can be deduced automatically. A drawback of the current work is that the approach does not consider the fact that the state transitions of systems can be subject to time changes. Therefore, in future work, a time-dependent model will be incorporated in the proposed approach. Besides, functional simulation methods that integrate dynamic models (e.g., Simulink) need to be explored to perform continuous functional simulation of civil aircraft systems. Acknowledgements. This work is partially supported by National Natural Science Foundation of China (51875346).

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Orientation Method of Ultralight UAV with a Rare Update of Its Location Data Naum-Leonid E. Popov

and Vasilii S. Kachalin(B)

Moscow Aviation Institute (National Research University), 125993 Moscow, Russian Federation [email protected]

Abstract. Recently, ultralight UAVs (unmanned aerial vehicles) have been increasingly usedto solve the tasks of exploring territories, both in the military and in the civilian sphere. The main criterion for guaranteeing the fulfillment of the task is the accuracy of its positioning in space. As a rule, the main equipment for determining the location is a GLONASS/GPS receiver, which receives a signal from satellites with interference, delays, or may be missing. The article proposes a new method of orientation of an ultralight UAV by searching for previously defined terrain landmarks when processing data from an on-board photo recorder and movement from one such object to another. The paper describes an algorithm for generating data on terrain landmarks, UAV action scenarios, and an algorithm for optimizing the movement of UAVs when moving from one landmark to another. Keywords: UAV · Navigation systems · Pattern recognition · Randomized algorithms · Optimization of movement

1 Introduction In the modern world, ultralight unmanned aerial vehicles, different in type, size and installed equipment, are increasingly being used to solve civil problems of monitoring the territory from the air. One of the main criteria for the fulfillment of the task assigned to them is their autonomous positioning in space. Military-purpose UAVs, as a rule, use an inertial system complex not only in combination with the GLONASS/GPS system, but also with a ground-based DGPS data processing system (differential GPS system), due to which the corrections to satellite data are coming on board the UAV. Due to this, the positioning accuracy of such systems can reach 5 sm. Reducing the cost of ultralight UAVs, on the one hand leads to an increase in the availability of such technological solutions, but on the other hand does not allow the installation of the entire complex of navigation equipment. Often, a GLONASS/GPS receiver and a magnetometer are installed as navigation systems on ultralight UAVs. Data from GPS satellites are updated with a frequency of 1–5 Hz, which allows the autopilot to frequently assess the course of movement and make corrections to it. Accuracy of civil GLONASS/GPS receivers are now within 5–15 m. When monitoring a territory in civilian areas, it is often necessary © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 80–86, 2023. https://doi.org/10.1007/978-981-99-0651-2_7

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to make movements at a low altitude or in a territory closed from the line of sight of satellites (for example, in mountainous terrain). Also, with the relatively low price of navigation system modules, such modules sometimes fail or lose satellites during the flight. In this regard, there is a need to develop alternative methods of orientation of ultralight UAVs based on incoming information about the terrain that will be able to clarify its location, conduct or continue the mission without a signal from the satellites of the global navigation system, make corrections to the course if accurate data on its location is not regularly updated. At the same time, such a system should not consume a lot of energy resources of an ultralight UAV and should not require the use of additional equipment. The paper proposes and describes a method for positioning UAVs without the use of satellite navigation systems, using data obtained from an on-board photo-video recorder and downloaded terrain data from it. The principle of the method is built on the actions that a person commits, focusing on the locality. The system, built on the basis of the proposed method, will allow you to build a map of the landmarks of the area that the UAV should explore, and not get lost during the next flights along the routes on the terrain that was previously flown, as well as to set the route of the emergency flight according to known landmarks. Because landmarks can be located at a considerable distance from each other, then the location update occurs irregularly, and due to the action of external processes (for example, wind) of the UAV leaves from the set course. The paper describes an algorithm for constructing a control signal (choosing the direction of movement), which partially compensates for these negative factors.

2 UAV Positioning Methods in Space Now the main method of positioning not only for UAVs, but also in other areas is the global navigation system. The receiver is installed on board the UAV and receives data from satellites. To increase the accuracy of data readings from the global system, networks of ground-based stationary towers have now been actively used. Such towers are reference points for the UAV navigation system, they determine the errors of readings global navigation systems and send corrections via the radio channel to the UAV receivers. One of the most common, at the moment, systems of this type is DGPS (differential global positioning system). There are works in which it is proposed to use stationary towers not only as correctors, but also as the main source for obtaining location data. The paper [3] describes a system and algorithm for specifying the location of a light UAV based on Kalman filtering direction-finding type measurements. A UAV positioning system is proposed based on the distances to the units of the tower network. Also, to obtain information about the position of the UAV in space, a complex of inertial systems is installed on board the UAV, in addition to GPS receivers. It includes a set of sensors, according to which the autopilot receives information about airspeed, rolls, accelerations, barometric altitude, etc. The inertial system complex may include: • A barometer with which it is possible to determine the height relative to the specified zero level. The height calculation is based on the use of a regular measurement of atmospheric pressure depending on the height of movement, relative to a certain

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level. The disadvantage of such a sensor is a relatively large measurement error (about 10–15 m). A radio-technical sensor is based on measuring the time interval between sending and receiving electromagnetic waves radiated from the surface to which the height is measured (the surface of the earth or water). Suitable for light mobile robots, the sensor has a large power consumption and at the same time works at distances up to 20–30 m, which is not enough for flying robots. Sonar is a means of sound detection of underwater objects using acoustic radiation. Suitable for light mobile robots, sonar works at distances up to 10 m, which is not enough for flying robots. LIDAR (LIDAR—light detection and distance detection)—sensors built on the technology of obtaining and processing information about remote objects using active optical systems that use the phenomena of light reflection and scattering in transparent and translucent media. The sensors have a large power consumption and a large weight, which excludes the use of such sensors in ultralight mobile robots. A complex of a three-axis gyroscope and accelerometer, which allows you to determine the angles of inclination of the UAV relative to the horizon and the acceleration of rotation. Thermal sensors in six directions, according to which the UAV microcomputer evaluates the temperature difference in different directions and draws conclusions about the angles of inclination of the UAV relative to the horizon.

In addition to the development of inertial systems for positioning UAVs, the directions of visual positioning of UAVs in space have been developing recently. Such methods use onboard sensors, photo-video recorders or a complex of such recorders and sensors, as well as software tools for processing the received data. The positioning of the UAV according to the built-in sensors in the first was used for automatic orientation of cruise missiles [1] in XX century. During the flight, the rocket microcomputer receives information from the onboard altimeter in the form of a sequence of differences in distances to the surface at a given time and in previous ones. This sequence is compared with the relief map recorded on the ground, and it is the sequences of relative heights that are compared, and not the absolute values of heights. As soon as the microcomputer detects matches the control system receives the coordinates of the route, calculates the amount of accumulated error and makes corrections to the course of movement. Such a system requires high accuracy in measuring the height, has a large weight (more than 20 kg) and a large energy consumption, which does not allow using such a method in ultralight UAVs. The paper [2] describes an algorithm for determining three-dimensional coordinates and orientation angles of a UAV without using satellite navigation signals. This approach consists in using a computer vision system to generate and process a stream of photos of the underlying terrain, as well as further comparison of the data obtained with existing maps in order to search for marker points (at least three). Due to the requirement of a large computing power resource, such a system involves processing the received data at the base station and, consequently, constant communication with the UAV. To increase the accuracy of following a given route in conditions of rare location updates (for example, flying in mountainous terrain), it becomes necessary to introduce a

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UAV microcomputer into the program code flight optimization algorithms by evaluating unknown external processes operating on the UAV. The problem of predicting the values of a random process generated by white noise passed through a linear filter is the most typical for Kalman filtering. To evaluate random processes in mobile object navigation systems the Kalman filter is used quite often and effectively, which works satisfactorily on large mobile objects with a variety of navigation equipment. For ultralight UAVs, the task of reducing the level of deviation from a given trajectory of movement remains open, since the influence of the accompanying uncertainties on them is more significant. When optimizing the movement of a single UAV and a group in real time [4, 5], there are needs for a solution in a limited time multidimensional optimization problems with noisy observations. Under such conditions, randomized recurrent stochastic optimization algorithms have proven themselves well. A monograph by O.N. Granichin etc. is devoted to a detailed analysis of the possibilities of randomized algorithms in estimation and optimization problems with arbitrary variables [7]. Also, when performing the flight of several UAVs in a group, it becomes possible to implement algorithms for optimizing the group’s flight UAV [8], positioning methods due to the transmission of current information between the group members, as well as autonomous distribution of this information during the flight of a group of UAVs with variable communication between them and noisy measurements [9, 10]. Multi-agent technologies have recently been successfully used to solve this type of tasks.

3 Orientation Method of Ultralight UAV with a Rare Update of Its Location Data Most of the above methods are already used in UAV orientation systems and successfully perform the task of specifying the location, but for ultralight UAVs such systems are either very large in size and weight, or have a large power consumption. The UAV orientation method described later in this paragraph is based on the principle of human orientation based on one’s own knowledge. The principle of human orientation on the ground, it consists in searching for objects of locality known to him (for example, rivers, fields, houses, etc.) and the movement relative to these objects. The main idea of the UAV orientation method, and the difference from the methods given in the last paragraph, is the positioning of the UAV by searching for previously allocated landmarks and terrain data that come from sensors installed on the UAV, and not by comparing all the data. As a sensor (tool) for obtaining terrain data, it is assumed to use an on-board photo and video recorder, which is the most common, installable, additional equipment. Thus, the method is based on two main processes: the formation of information about the terrain and the optimization of the UAV flight when moving from one landmark to another. 3.1 The Algorithm for the Movement of an Ultralight UAV Based on Previously Selected Terrain Information If there is a case of loss of location data (absence of a signal from the global navigation system), the system’s orientation algorithm is as follows:

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select the nearest landmark and azimuth relative to the last known location, start moving to the selected object, search for an object using a template, launch the UAV movement optimization system from the orientation to the landmark.

In order to simplify the search for a template on the received images during the flight of the UAV, each image during the flight should be oriented as well as the desired template, i.e. the top the image should be oriented to the north. Thus, in order to orient the image, it is necessary to rotate it in accordance with the magnetic azimuth. 3.2 Flight Optimization Algorithm When the UAV is moving from one object to another, it is necessary to fly to the location of the object with sufficient accuracy to fix the object template on the ground. The position of the object in the photograph depends on the accuracy of the UAV following the specified route, and the positioning accuracy depends on the position of the object in the photograph. At the same time, it is possible to increase the guarantees of hitting the object by increasing the viewing angle of the dvr, but at the same time the probability of recognition decreases due to the large distortion of the object. Also, the flight time, which is calculated based on the speed of the UAV and from the known initial external conditions, can serve as a verification parameter for reaching the established object. We will now describe the algorithm of the UAV movement in the plane from one object to another under known initial external conditions and the action of wind on it with a constant average speed, and unknown changes in its direction. We will assume that the UAV is flying in the plane at a speed and is exposed in the direction of θ the action of external disturbances (wind) with a constant average velocity b. In the case of variable wind, assume that the change in the wind direction angle is random: θt+1 = θt + wt+1 ,

(1)

where {wt } are independent, centered and equally distributed random variables:     E{wt } = 0, E w2t = σw2 < ∞, E wi , wj = 0, if i = j. Thus, with known initial wind parameters (direction and average speed), it is possible to apply a course-keeping algorithm, i.e., at the starting point of the flight, set a course for the target object, taking into account the known wind parameters. This algorithm is the simplest in the absence of location data during the flight, and this algorithm for constructing the control {ut} will give the desired accuracy, provided that the average wind change throughout the flight will be zero. Therefore, if the average wind direction is incorrectly determined or the change this value causes an error during the flight, due to which the desired object may not get on the terrain images. A randomized algorithm for estimating an unknown external parameter (wind direction) is described in [4]. Under the condition of a constant wind direction, a series of consecutive measurements will allow it to be accurately estimated for use as an amendment to the choice of course, based on the consistency of the ratio: a sin u − b sin θ = 0,

(2)

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in which the object moves from the point (xt , yt ) directly in the direction to the point (A, B), i.e. the point (xt+1 , yt+1 ) lies on a straight line connecting (xt , yt ) and (A, B). Therefore, it is easy to derive the form:   b u = arcsin sinθ (3) a To increase the guarantees of getting an object into the field of view of the photo recorder, we can distabelies the system a little by adding disturbances in the form of forming estimates for the wind direction: θt = θt−1 + wt , where {wt } is independent, centered, and equally distributed random variables. The control {ut } selection rule will have the following form:   b  ut = arcsin sinθ t a

(4)

To check the efficiency of the optimization algorithm, computer modeling was carried out, during which the measurements were carried out with a time interval of δ = 10 s. The default coordinates are x0 = 0, y0 = 0, A = 3000, B = 1000. The initial angle of the wind action is θ0 = 50 relative to the selected coordinate system. When flying ultralight UAVs, the maximum safe height of the field is 100−150 m.

4 Conclusion The article proposes a new algorithm for the orientation of an ultralight UAV in space with a rare update of its location. In the absence of a signal from the global navigation system, the presented system begins to search for predefined terrain patterns and read the azimuth map. To reduce the deviation of the UAV from the trajectory when flying from object to object, it is proposed to use a flight optimization algorithm. Further work is planned to test the proposed system for the author’s existing ultralight UAV [11], which is built on the basis of a flying wing body, has a wingspan of 2 m and a weight of 2 kg, an electric screw motor. On board, an Ardupilot autopilot and an additional microcomputer are used to work with the onboard camera, process photographic materials, generate a new flight plan and send them to the autopilot system. Acknowledgements. The authors gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

References 1. Pavlushenko, M., Evstafyev, G., Makarenko, I.: Unmanned aerial vehicles: history, application, threat of proliferation and prospects of development, 611 p. Human Rights (2005)

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2. Ardentov, A., Bescheastny, I., Mashtakov, A.: Algorithm for calculating the position and orientation of the UAV. Software Systems and Applications, pp. 23–39 (2012) 3. Amelin, K., Miller, A.: Algorithm for clarifying the location of a light UAV based on Kalman filtration of measurements of the radiation type. Inf. Process. 13(4), 338–352 (2013) 4. Amelin, K.: Randomization in the control loop of a light UAV during flight under conditions of unknown changes in wind direction. Bulletin of St. Petersburg University. Episode 10: Butt naya math. Computer science. Management Processes, no. 2, pp. 85–101 (2013) 5. Amelin, K.: Randomization in controls for the optimization of a small UAV flight under unknown arbitrary wind disturbances. Cybern. Phys. 1(2), 79–88 (2012) 6. Borichin, O.N.: Estimation of linear regression parameters with arbitrary interference. Autom. Telemech. 63(1), 25–35 (2002) 7. Granichin, O., Volkovich, Z., Toledano-Kitai, D.: Randomized Algorithms in Automatic Control and Data Mining. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-547 86-7 8. Amelin, K., Amelina, N., Granichin, O., Granichina, O., Andrievsky, B.: Randomized algorithm for UAVs group flight optimization. In: Proceedings of 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, France, pp. 205–208 (2013) 9. Amelina, N.: Application of the protocol of local voting to achieve consensus in a decentralized network of intelligent agents. Bulletin of St. Petersburg University. Series 1: Mathematics. Mechanics. Astronomy, no. 3. pp. 12–20 (2013) 10. Amelin, K.S., Amelina, N.O., Borichin, O.N., Koryavko, A.V.: Application of local voting algorithms to achieve consensus in a decentralized network of intelligent agents. Neurocomputers: Development, Application, no. 11, pp. 39–47 (2012) 11. Amelin, K.S.: Light unmanned aerial vehicle for an autonomous group. Stochastic Optim. Comput. Sci. 6, 117–126 (2010)

Optimization of Design Parameters of a Small-Sized Unmanned Aircraft with a Turbojet Engine Equipped with an Ejector Thrust Magnifier Oskirko Liubov1,2 , Alexander Khvan1(B) , and Skorohodova Ekaterina3(B) 1 Moscow Aviation Institute (National Research University), Moscow, Russia

[email protected]

2 Shanghai Jiao Tong University, Shanghai, China 3 Baltic State Technical University “Voenmeh” named after D. F. Ustinov, Saint- Petersburg,

Russian Federation [email protected] Abstract. In this article, the object of research is various layouts of unmanned aerial vehicles with a small turbojet engine using an ejector thrust magnifier. The author develops aerodynamic layouts of unmanned aerial vehicles taking into account the required size and operating speed range, determines the optimal aerodynamic scheme, performs a numerical calculation of the engine operation with an ejector thrust booster, optimizes design parameters in the XFLR5 and ANSYS software packages. Currently, unmanned aerial vehicles of various tactical and technical parameters, sizes and masses are being developed. The engines will be improved increasing efficiency and improving the characteristics: thrust, efficiency and mass. The rapid development of unmanned aerial vehicles is due to the advantages they have, for example: the absence of crew members eliminates the risk of human losses, the ability to perform maneuvers with an overload exceeding the physical capabilities of pilots, as well as the absence of a crew fatigue factor. The cost of unmanned aerial vehicles has been reduced, and lower operating costs allow for the mass production of inexpensive but efficient aircraft. The article presents graphs of changes in the aerodynamic characteristics of the considered layouts of unmanned aerial vehicles, the results of numerical calculation during the operation of the engine in flight with an ejector thrust booster, a comparison of the results obtained, as well as options for optimizing design parameters, which is the main purpose of the study in this work. Keywords: Unmanned aerial vehicle · Ejector · XFLR5 · ANSYS · Aerodynamic characteristics · Angle of attack

1 Introduction Currently, there is a rapid development of unmanned aerial vehicles of various tactical and technical parameters, sizes and masses. The cost of UAVs has been reduced, lower operating costs make it possible to mass produce inexpensive but efficient aircraft. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 87–102, 2023. https://doi.org/10.1007/978-981-99-0651-2_8

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Nowadays, there is a search for ways to improve aerodynamic layouts that will improve efficiency. Mainly - increasing the range and improving the tactical and technical parameters of unmanned aerial vehicles. When creating a UAV, an important role is played by solving problems of improving aerodynamic parameters, flight stability, controllability, efficiency, which determine the main characteristics of aircraft and its layout. One of the ways to increase the efficiency of the engine is the use of an ejector thrust booster. The principle of operation of the ejector thrust enlarger, based on the connection to a high-pressure gas jet flowing from a gas turbine engine of large masses of ambient air, makes it possible by simple means to significantly (by 40–50% or more) increase the thrust of the engine without spending additional energy. In this paper, two aerodynamic schemes are considered: normal and with a semirotating wing. As a result of the calculations, graphs were obtained, the results were analyzed and compared, options for optimizing design parameters were considered, which is the main purpose of the study in this paper.

2 Requirements When designing an unmanned aerial vehicle and an engine, it is necessary to clearly formulate and take into account all the necessary requirements. The designed aircraft and engine must meet certain operational and technical requirements, be ready for various loads, the aircraft must have sufficient stability. The technical characteristics of the structure can be classified as follows: 1) requirements arising from the purpose of the project, expressing the need for the project to meet its purpose. 2) strength requirements, expressing the need to ensure, with the least weight of the structure, its sufficient strength and rigidity, the absence of vibrations, the availability of adequate resource, reliability and survivability; 3) operational requirements aimed at ensuring simplicity and convenience of technical operation; 4) technological requirements aimed at ensuring the simplicity and cheapness of the manufacture and repair of the structure, the use of non-scarce materials in its manufacture. When installing the engine on the aircraft, it is necessary to meet the following requirements: 1) to ensure the minimum increment of the mass and aerodynamic drag of the aircraft; 2) the engine must be conveniently located for installation, disassembly and easily accessible for technical inspection and maintenance.; 3) provide the possibility of localization and rapid extinguishing of a fire that has arisen in the engine.

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The more fully all requirements are fulfilled, the higher the quality of the aircraft design, the fewer defects and failures occur and the more economical the operation of the aircraft.

3 Ejectors and Their Application in Installations with Aircraft Engines An ejector is a device in which the total pressure of one (ejected) flow increases by mixing it with another (ejecting) flow having a higher total pressure. It is of great importance that when using the ejector there are no moving and rubbing parts, which is essential when working with hot or aggressive media. A valuable quality is the ease of manufacture and installation. The rear part of the nacelle can be equipped with an ejector, which will cool the combustion products, as well as increase engine thrust. The main source of the increase in thrust is the mass of erectionmale flow of external air (1): P = (G1 − G2 )w4 − G2 wn

(1)

where G1 is the active flow rate; G2 is the passive flow rate; w4 is the flow rate of the mixture from the ejector diffuser; wn is the velocity of the incoming flow.

4 Geometry and Characteristics of a Semi-rotating Wing The main purpose of the work is to develop an aerodynamic layout of the UAV taking into account the required size, range of operational speeds and optimization of these design parameters. The analysis of the variable characteristics and parameters of the aircraft layout is performed. The calculation of aerodynamic characteristics is performed in the XFLR5 program. The data obtained will allow us to judge the main characteristics and advantages of the considered layouts. As the main element of the developed aircraft is an unmanned aerial vehicle with a so-called "semi-rotating" wing. The rotary part means the deflected 2/3 of the wing relative to the root part. At the first stage, the aerodynamic characteristics of a trapezoidal wing are considered. The proposed aerodynamic layout of a small-span wing is shown in Figs. 1, 2, 3.

Fig. 1. Front view

Fig. 2. Side view

The wing has a trapezoidal shape in the figure is the rotating part of the wing, they are marked “2”, under the numbers “1” to the root of the wing, applied steel profile NACA 1410. Parameters of the wing: a wing Span of 1500 mm., wing area– 24.5 sq. DM., root chord– 180 mm, lines length– 180 mm, mean aerodynamic chord – 165 mm.

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Fig. 3. Top view

5 Calculation Area and Graphs To create control moments, control rudders are installed on the aircraft. The deviation of these rudders from the normal position creates additional forces acting from the incoming flow. These forces create control moments that set the direction of movement of the body. Also, to create stability when moving, stabilizers are added to the aircraft, they create moments that compensate for moments that take the body out of the equilibrium position. Since the steering wheels and stabilizers perform absolutely opposite tasks, it is necessary to solve the problem of their optimal interaction. The body should be both controllable and its movement should be stable. The layout considered in the work does not have rudders. Only the rotary part of the wing is involved in pitch and roll control, which gives an advantage over the usual aerodynamic scheme. To determine the aerodynamic characteristics in the XFLR5 program, the parameters of the layout of the wing in question are introduced. The calculation results are shown in the graphs below (Figs. 4, 5, 6 and 7).

Fig. 4. Dependence of the lift coefficient on the drag coefficient

Fig. 5. Dependence of the wing lift coefficient on the angle of attack

Then these results will be used for further calculations. The advantage of the layout of the aircraft with the rotary part of the wing is that the air intake of the turbojet is streamlined at zero angle of attack during takeoff and landing, however, the disadvantage is the large force that falls on the wing, since the wing is attached to the fuselage only on one axis, there are no other fastening elements, such an effort to the wing is limited, therefore, such an arrangement is applicable only at low speeds on a small aircraft. As a consequence of the fact that the classical aerodynamic scheme of aircraft has a disadvantage called “balancing losses”, the aerodynamic layout “canard” is used in the work. When using this layout, the horizontal tail does not create a negative lifting force, therefore, in horizontal flight, to create an angle of attack of the carrier wing, the stabilizer does not lower the tail section of the aircraft, while the lifting force of the

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Fig. 6. Dependence of the longitudinal damping moment on the angle of attack

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Fig. 7. The dependence of the quality of the wing profile on the angle of attack

aircraft does not decrease by the amount of the lowering force of the horizontal tail, as it happens in the traditional layout. In the “canard” scheme, the angle of attack is controlled without loss of lifting force for balancing. To create an advantageous angle of attack of the wing, the tail lifts the front of the aircraft, the lifting forces of the wing and tail are folded, directed in the same direction. Therefore, aircraft made according to this scheme have an important advantage—less load per unit area of the wing. The area of the stabilizer plane is also a carrier. Another important advantage of the “canard” scheme is the almost complete absence of stall, that is, it is practically impossible for an aircraft to enter an uncontrolled flat spin. This is explained by the fact that with a loss of speed or a large angle of attack, the disruption of the air flow occurs first on the front horizontal tail, and the aircraft slightly lowers the nose, thereby preventing the disruption of the flow on the main wing and putting the aircraft into a controlled dive mode. The “canard” scheme provides pitch control without loss of lifting force for balancing. Therefore, aircraft built according to this scheme have the best characteristics of carrying capacity per unit area of the wing and maneuverability in pitch. These properties of the aerodynamic scheme allow us to count on obtaining higher load-bearing properties and higher aerodynamic quality of the aircraft. The disadvantage of the “canard” scheme is that airplanes have a tendency, which in one case is an advantage, and in the other is a serious disadvantage, which is called the “pecking tendency”. “Pecking” is observed at large angles of attack of the front horizontal tail, close to critical. Due to the bevel of the flow behind the front horizontal tail, the angle of attack on the wing is less than on the front horizontal tail. As a result, as the angle of attack increases, the flow disruption begins first on the front horizontal tail. This dramatically reduces the lifting force on the front horizontal tail, which is accompanied by a spontaneous lowering of the nose of the aircraft - a “peck”, which prevents stall at altitude, but is very dangerous during takeoff and landing. With the use of an electric control system, all the positions of the front horizontal tail in different flight modes, leading to a “peck”, are limited to a computer, regardless of the pilot’s control actions on the aircraft controls. The “canard” scheme was chosen, in which, unlike the traditional wing, the wing is semi-rotating, due to this there is no need to set the angle of attack for the entire aircraft, it is enough to deploy the rotary part of the wing at a certain angle.

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Next, a comparison is made of the aerodynamic traditional layout, where the angle of flow of the wing depends on the angle of attack set by all aircraft, and the layout, where you can set this angle separately. Further, we call the normal aerodynamic layout AIRCRAFT without a rotary wing. At the second stage, the aerodynamic characteristics of the UAV of the traditional layout and the layout with a semi-rotating wing are considered. The advantage of this approach is that the air intake of the turbojet is streamlined at zero angle of attack during takeoff and landing, however, the disadvantage is the large force that falls on the wing, since the wing is attached to the fuselage only on one axis, there are no other fastening elements, such force to the wing is limited, therefore, this arrangement is applicable only at low speeds on a small aircraft. A comparison is made between the aerodynamic traditional layout, where the angle of the wing flow depends on the angle of attack set by all aircraft, and the layout, where this angle can be set separately. The proposed aerodynamic layout of the aircraft of the meter size range is shown in Figs. 8, 9, 10.

Fig. 8. Front view

Fig. 9. Side view

Fig. 10. Top view

The wing has a trapezoidal shape, the areas of the rotary part of the wing are marked in the figure, they are indicated by the numbers “2”, under the numbers “1” the root part of the wing, the asymmetrical profile of NACA 1410. Wing parameters: wingspan - 1500 mm., wing area - 24.5 sq. dm., root chord 180 mm, end chord - 180 mm, average aerodynamic chord - 165 mm. Horizontal tail: Root chord - 180 mm; end chord - 100 mm; span - 500 mm; profile NACA 1410; located with an offset - 100 mm back. Vertical tail: Root chord - 180 mm; end chord - 100 mm; span - 360 mm; profile NACA 1410; located with an offset - 400 mm back. The choice of the area of the horizontal tail is made by determining the coefficient of Cg.o cro =

cro fro S12 l1

+

S22 l2

(2)

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Here Sg.o is the area of the horizontal tail, ƒg.o is the shoulder of the horizontal tail relative to the aircraft’s center, S is the wing area, l is the wingspan. To determine the aerodynamic characteristics, the XFLR5 program introduced the layout parameters of the aircraft in question. The calculation results are shown in the graphs below (Figs. 11, 12, 13 and 14).

Fig. 11. Dependence of the lift coefficient on the drag coefficient

Fig. 13. Dependence of the longitudinal damping moment on the angle of attack

Fig. 12. Dependence of the wing lift coefficient on the angle of attack

Fig. 14. The dependence of the quality of the wing profile on the angle of attack

Then these results will be used to calculate.

6 Analysis of the Aerodynamic Characteristics of the Aircraft Next, the aerodynamic characteristics of the UAV are analyzed, in which the angle of deviation of the rotary part of the wing changes by 5, 10 and 15°. The results of the analysis are shown in the graphs below (Figs. 15, 16, 17 and 18).

Fig. 15. Dependence of the lift coefficient on Fig. 16. Dependence of the wing lift the drag coefficient coefficient on the angle of attack

The graphs showed that the UAV of the traditional layout has better performance than the UAV with a semi-rotating wing.

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Fig. 17. Dependence of the longitudinal damping moment on the angle of attack

Fig. 18. The dependence of the quality of the wing profile on the angle of attack

Let’s analyze the aerodynamic characteristics: according to the results obtained, it can be concluded that when the angle of attack changes by the value of α, the aerodynamic force R applied at the center of pressure changes. The longitudinal balancing of the aircraft is not disturbed, the aerodynamic pitch moment MZ is balanced, which does not cause the aircraft to rotate relative to the 0Z axis, as it happens with the aircraft of the classical layout. Also, a change in the angle of attack does not cause a change in the position of the center of pressure. The UAV of the canard aerodynamic scheme manages to reduce the air friction resistance to the limit by reducing the area of the washed surface of the projectile. Canard allows you to eliminate balancing losses. Therefore, it is necessary to investigate and optimize canard.

7 Calculation Results A series of calculations was carried out to study a number of aerodynamic characteristics of UAVs of traditional layout and layout with a semi-rotating wing. The variable α was set at angles from −2 to 14° in increments of 0.5. The speed of the aircraft is 100 km/h. UAVs of traditional layout and with a semi-rotating wing with a specified speed parameter of 100 km/h. As can be seen in the graphs, the lifting force of a traditional UAV layout is better than that of a twisted one. It can be seen from the graphs that the coefficient of lift with an equal coefficient of drag is better for UAVs of traditional layout. Further, the graphs show that the coefficient of lift from the angle of attack is higher for a UAV of a traditional layout, therefore, a UAV with a semi-rotating wing is less stable than a UAV of a traditional layout. Further on the graph shows that the coefficient of lift from the angle of attack is higher for a UAV of a traditional layout than for a UAV with a semi-rotating wing deviating by 5, 10, 15°, therefore, such aircraft are more stable. In the program used, it is not possible to calculate the parameters of a UAV with a turbojet engine, below is a diagram of the finished aircraft. The parameters of the turbojet engine were considered in the Ansys Fluent program (Fig. 19).

8 Ejector Thrust Magnifier The ejector is used for various purposes, it can act as a pump in a wind tunnel or it is used as a fan to maintain a continuous flow of air in a channel or room. The ejector is

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Fig. 19. UAV with turbojet engine

used to create a reduced pressure in a certain volume and thus performs the role of an extractor. The use of ejectors in gas collection networks is also important. In this paper, another possible area of use of the ejector properties is considered, namely, an increase in jet thrust by mixing external air with a jet of gas flowing from the jet engine nozzle. The Plotnikov V.A. patent [1] describes an ejector for a multi-plane layout, which allows to increase the thrust more than twice while maintaining fuel consumption. In this patent, the channel profile is important, the scheme considered in it is shown in Fig. 20.

Fig. 20. The scheme of the ejector thrust amplifier for a multi-nozzle layout

The  patent [1] shows the following ratios of geometric parameters: Fex = (6, 5 − 40) F0 , where Fex is the cross–sectional area at the outlet of the mixing chamber;  F0 is the sum of the areas of the outlet sections of the nozzles. The output section of the displacement chamber should be located at a certain distance from the nozzle section: L = (0, 35 − 1, 4)Dex , where L is the average distance from the nozzle section to the output section of the mixing chamber, Dex is the diameter of the output section of the mixing chamber, and the angle of inclination of the inner wall in the mixing area to its axis is α = (5−17)o. The use of these ratios together make it possible to provide a high coefficient of increase in engine thrust without exaggerating fuel consumption. If the angle of the mixing chamber wall solution is increased by  more than 17o, the area of the mixing chamber outlet section is assigned FBbIX > 40 F0 and this section is located at a distance from the nozzle section of less than 0.35 of its diameter, then the discharge on the inner surface of the mixing chamber area decreases. This leads to the fact that the resultant pressure forces (external and internal axial component) on the wall of the mixing area decreases. This means that there is no increase in thrust or it has an insignificant value. When performing the area of the output section of the mixing chamber with  the following ratio to the areas of the output sections of the nozzles: FBbIX > 6, 5 F0 , the size of this section will not be sufficient for the output of combustion products. If the outlet section is located at a distance from the nozzle section that is more than 1.4 of its diameter, the channel length will be too large. In this case, the solution angle of the mixing chamber wall should be made less than 5o, then the air flow rate will decrease,

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which will also lead to a decrease in the discharge on the inner surface of the mixing chamber section and, as in the previous case, to a decrease to insignificant values of additional thrust. The purpose of using an ejector magnifier is to increase traction. This increase is possible only when the flight speed is less than the flow rate from the engine nozzle. 4 The ejection coefficient n, the velocity ratio w w1 and the thrust increase coefficient δ are monotone functions of the geometric parameters α and f. The dependence of the parameters of a reactive system with an ejector on the geometric parameter of the ejector α and f = 1 is shown in Fig. 21, and the dependence of the same parameters on the degree of expansion of the diffuser f and α = 0.3 is shown in Fig. 22.

Fig. 21. Dependence of the parameters of a Fig. 22. The parameters of a reactive system reactive system with an ejector on the with an ejector depend on the degree of geometric parameter of the ejector α and f = expansion of the diffuser f and α = 0.3 1

From the analysis of Figs. 21 and 22, it follows that an ejector with a large α value, i.e. with a relatively small chamber area, is high-pressure, but cannot work with large ejection coefficients. An ejector with a small α allows you to suck a large amount of gas, but it does not increase its pressure much.

9 Mathematical Model Navier-Stokes equations and turbulence models. In the case of an incompressible fluid, the Reynolds equation can be derived from the Navier-Stokes equations using Reynolds averaging [2]: f(t) =

1 2T



t+T

f(t)dτ

(3)

t−T

where the period of averaging 2T is assumed to be large compared to the time scales of all turbulent inhomogeneities present in the considered period, and small enough compared to the characteristic time scale averaged current, a f is an averaged function; Averaging will be performed as follows: −

−

f + g= f + g; c = c; cf = cf ; ∂f /∂s= ∂f /∂s

(4)

where f and g are arbitrary functions which can be represented as the sum of average and fluctuation variables f = f + f  and g = g + g  , s is a space coordinate or time, c is a constant.

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In the case of a compressible gas, averaging occurs according to Favre, in which the density ρ and pressure p are averaged according to Reynolds, and weighted averages are introduced for other variables: ρf f˜ = ρ

(5)

The averaged Navier-Stokes equations for a compressible perfect gas (the averaging signs are omitted) are presented in the system of Eqs. 4 (for an incompressible one, the energy equation is excluded, ρ = const and consist of the equations of conservation of mass, momentum and energy. It is also necessary to consider the equation of state: ⎧ ∂ρ − → ∂t +∇·(ρ u )=0; ⎨ → ∂ (ρ − u) − → − → (6) +∇·(ρ u u )=−∇p+∇·(τm +τt ); ∂t  

 − − − ⎩ ∂(ρE) → → − → → ; + ∇ · ρ u H = ∇ · u · + τ + q + q (τ ) m t m t ∂t pm ρ= RT − → ,τ +τ Here u is the velocity vector of the averaged flow with components m

t

_ are the molecular and turbulent components of the viscous stress tensor, E = Cv T + 0, 5(u2 +v2 +w2 ) is the total energy of the gas, H = E + ρp = C T +0, 5(u2 +v2 +w2 ) p → → q __t are the molecular and turbulent components of the is its total enthalpy, − q +− m

t

vector heat flux densities, T is temperature, Cv = (Cp − R/m) is the specific heat of the gas at constant volume, Cv = (Cp − R/m) is the specific heat of the gas at constant pressure, m is the molar mass of the gas, R = 8, 31434 is the universal gas constant. The magnitude of the molecular components of the stress tensor and the vector of heat flux density in the system of 4 equations are determined, respectively, using rheological Newton’s law and Fourier law: 1 → u) τm = 2μ(T )(S − I ∇ · − 3

(7)

t → → where S = 21 (∇ − u + [∇ − u ] ) is the tensor of strain rates, I is the identity tensor, μ(T ) i λ(T ) are the coefficients of the molecular dynamic viscosity and thermal conductivity. The system of Eqs. 4 is open-ended, since the relationship between the turbulent → q t with the parameters components of the stress tensor τt and the heat flux density vector − of the averaged flow, which are the main variables of the system, is unknown and is determined using additional relations that make up the turbulence model. In this paper, we consider the k-kl-omega turbulence model with three differential equations.

10 Numerical Calculation of the Ejector Thrust Magnifier The aircraft that the author is considering has a Jet 100 turbojet engine with a maximum thrust of 10 kg (100 N), the engine is shown in Fig. 23. The flight speed of the aircraft is 100 m/s, and the gas flow rate from the turbojet nozzle is 500 m/s.

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Fig. 23. Jet 100 Engine

Since the flight speed is less than the flow rate from the nozzle of a turbojet engine, the nacelle is equipped with an ejector thrust magnifier. The purpose of this research part is to test the effectiveness of the ejector thrust magnifier. To solve this problem, the ANSYS software package is used. The Workbench module was used for numerical research. The dimensions of the ejector thrust booster were selected based on the ratios [1], observing the dimensions of the turbojet nozzle. Special attention is paid to the ejector profile. In the scheme, the profile of the ejector mixing chamber is important for increasing the thrust of the system. The distribution of static pressure along the length of the ejector nozzle is shown in Fig. 25. The largest corresponds to the cross section of the entrance to the amount of rarefaction mixing chamber of the ejector thrust booster. Further along the length of the chamber, gradually increases and at the outlet of the ejector becomes the static pressure . The discharge at the entrance to the chamber equal to the atmospheric pressure leads to an increase in the ejection coefficient and an increase in the flow rate of the mixture from the ejector. For numerical calculation in the XFLR 5 program, the ejector thrust booster profile was selected, it is shown in Fig. 25 (Fig. 24).

Fig. 24. Static pressure distribution

Fig. 25. Profile of the ejector thrust booster

The engine nozzle is equipped with a central body and is shown in Fig. 26. The geometric characteristics of the nozzle part are shown in Fig. 27.

Fig. 26. Engine nozzle

Fig. 27. Geometric characteristics

The problem is solved in a two-dimensional stationary formulation. The calculated grid is structured and contains 51631 cell elements, the grid is thickened (cells in this

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area have a smaller size) in the inlet of the nozzle and ejector, the central body and the inner part of the ejector. The problem is solved in Ansys Fluet using the following boundary conditions: • The velocity of the incoming flow at the outer boundary of the computational domain is set by the “velocity-inlet” condition. The value varied depending on the engine operating mode from 0 m/s when working on site and up to 100 m/s in flight, atmospheric pressure p = 0 (101325 Pa), the flow is directed along the x axis, the direction of the velocity vector in the xy plane, the flow temperature T = 300K; • The flow rate from the nozzle is set by the condition “velocity-inlet” has a value of 500 m/s, atmospheric pressure p = 50000 (151325 Pa), the flow is directed along the x axis, the direction of the velocity vector in the xy plane. Expiration temperature T = 1000K; • The “pressure-outlet” condition is indicated at the exit from the calculated area, atmospheric pressure p = 0 (101325 Pa). • On the surface of the ejector, the central body and the nozzle body, the “wall” wall hardness conditions are set, including the conditions of adhesion and non-leakage. When the engine is running at an incoming flow velocity w = 50 m/s, the results have the following values (see Fig. 28).

Fig. 28. Results of numerical calculation when the engine is operating in flight with an ejector thrust booster

If the engine is running in place (the incoming flow velocity is zero w = 0 m/s), the results are shown in Fig. 29.

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Fig. 29. Results of numerical calculation when the engine is running in place with an ejector thrust booster

The thrust of the engine was calculated in two sections (see Fig. 30): the first, on the nozzle section, is highlighted in blue, and the second at the outlet of their ejector, is highlighted in red.

Fig. 30. Calculated cross sections

The thrust force F is calculated by the following formula:  F = (ρw2 + pe )dS

(8)

where pe is the overpressure. Provided that the aircraft was moving at a speed of 50 m/s, the thrust force at the output of the ejector thrust booster was. F = 140.2 N Analyzing the obtained values, it can be concluded that when using an ejector thrust booster at low flight speeds, the thrust force increases by 1.4 times.

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11 Conclusions The study and comparison of the aerodynamic characteristics of different aircraft layout schemes were carried out, various dependencies were obtained that affect the wing layouts in question in the plan. Taking into account these dependencies, it is possible to judge the nature of the further movement of the body in the flow. The advantages of semi-rotating wings include the absence of a keel, which will make the aircraft less weighty, the functions of the keel are performed by the deviating parts of the wing. The graphs below show the dependence of the aerodynamic quality on the angle of attack of the aircraft of the classical layout and the layout with a semi-rotating wing, comparing these schemes it can be seen that the aircraft of the classical layout has a higher aerodynamic quality (Fig. 31).

Fig. 31. Dependence of aerodynamic quality on the angle of attack

The green color shows the traditional layout of the aircraft, pink - the aircraft with a semi-rotating wing deviating by an angle of 5°, blue - the aircraft with a semi-rotating wing deviating by an angle of 10°, red - the aircraft with a semi-rotating wing deviating by an angle of 15°. The graphs below show the moment of damping from the angle of attack for the aircraft of the classical layout and the layout with a semi-rotating wing. Comparing these results, it is clear that the aircraft of the classical layout is stable, compared with the aircraft with a semi-rotating wing (Fig. 32).

Fig. 32. The moment of damping from the angle of attack

The green color shows the traditional layout of the aircraft, pink - the aircraft with a semi-rotating wing, deviating by an angle of 5°, blue - the aircraft with a semi-rotating

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wing, deviating by an angle of 10°, red - the aircraft with a semi-rotating wing, deviating by an angle of 15°. The conducted research has shown that the semi-rotating wing has no advantages over the traditional one. However, there is no significant deterioration in aerodynamics. The use of this layout is justified, because it has a number of advantages: the turbojet is streamlined at zero angle of attack; the absence of rudders, since the rotary part of the wing can be effectively controlled by roll, pitch and yaw; the absence of rudders will make the aircraft less weighty, the functions of the rudders are performed by the deviating parts of the wing. In this paper, an ejector thrust magnifier was also considered, as a result of numerical calculation of which the efficiency of the engine operation in terms of increasing thrust reaches a value of δ = 1.4 at a speed of w = 50 m/s. The goals set in this work have been fully fulfilled. As a result, all the tasks identified at the initial stage of work were solved.

References 1. Arepyev, A.: Questions of designing light aircraft. Selection of the scheme and parameters (2001) 2. Afanasyev, P.: Unmanned aerial vehicles. Fundamentals of the device and operation (2009) 3. Baidakov, V., Klumov. A.: Aerodynamics and flight dynamics of aircraft (1979) 4. Boldyrev, A., Komarov, V.: Design of aircraft wings using 3D models of variable density (2011) 5. Bondaryuk, M., Ilyashenko, S.: Ramjet engines (1958) 6. Gorbatenko, S.: Calculation and analysis of the movement of aircraft (1979) 7. Krasilshchikov, M., Serebryakova, G.: Control and guidance of UAVs based on modern information technologies (2003) 8. Mitin, M., Nikolsky, D.: Scientific article (2006) 9. Ostoslavsky, I.: Aeroplane aerodynamics (1957) 10. Ostoslavsky, I., Strazheva, I.: Dynamics of flight (trajectory of aircraft) (1969) 11. Pavlushenko, M., Evstafyev, G., Makarenko, I.: Unmanned aerial vehicles: history, application, threat of proliferation and development prospects (2005) 12. Podkur, M.: Virtual wind tunnel XFLR5 from scratch step by step (2009) 13. Strelets, D., Serebryansky, S., Shkurin, M.: Research of the possibility of improving the traction and economic characteristics of a supersonic passenger aircraft engine through minimal modifications to the high-pressure compressor (2021) 14. Sukhachev, A.: Unmanned aerial vehicles. State and prospects of development (2007)

Estimation of Strength Properties of Glass Fiber-Reinforced Plastics with Initial Fibre Waviness Aliia Utiabaeva1(B)

, Sergei Kovtunov2

, and Nikolai Turbin2

1 Shanghai Jiao Tong University, Shanghai, China

[email protected] 2 Moscow Aviation Institute, Moscow, Russia

Abstract. The paper compares the strength of fiber-reinforced composites with and without fabrication defects. The influence of the initial waviness of the fibers on the behavior of the material during longitudinal compression is revealed. The samples are modeled using Python and then imported into Simulia Abaqus. The analysis is carried out by means of computational micromechanics using representative volume element (RVE). A two-dimensional deformable RVE with a volumetric fiber content of 50% is modeled. There are no initial stresses in the material. The input data for modeling are the elastoplastic and strength properties of the components, the geometry and the size of the RVE. A mesh in the form of triangular elements was superimposed on the sample. Post-processing includes an assessment of the strength of micromechanical samples with straight and initially wavy fibers. The data obtained can be used in the preparation and implementation of a test program for composite materials and also in understanding of influence of fabrication defects on theirs strength properties. Keywords: Fiber kinking · Computational micromechanics · Representative volume element · Longitudinal compression

1 Introduction In recent years, composite materials reinforced with unidirectional fibers have been widely used in the aviation industry. They have become indispensable due to the fact that they can significantly lighten the weight of the structure compared to metals. Nevertheless, there are a number of problems caused by the heterogeneity of the structure and anisotropy of the properties of composite materials. The heterogeneous structure of composite materials leads to the complexity of the mechanisms of destruction under various loads applied to the lamina. Computational micromechanics (CM) is a convenient tool for studying the failure mechanisms of composite materials at the level of individual components: fiber, matrix and interface. In this paper, the strength of composite materials reinforced with carbon fibers under longitudinal compression load is evaluated by means of CM. The influence of such a © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 103–107, 2023. https://doi.org/10.1007/978-981-99-0651-2_9

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technological defect as the initial waviness of the fibers on the material behavior under compressive load is considered. The initial fiber misalignment is taken into account in the work of Sebaey et al. (2020). In their work 3D RVEs generated in the form of cubes are used. Authors considered fibers as linear elastic orthotropic and matrix is modelled using damage plasticity model. In this paper we consider damage plasticity model for both matrix and fibers. Naya et al. (2017) investigated the longitudinal compression of continuous fibers with different angles of waviness. In this paper we also consider difference of the angle of curvature that repeats fibres form. Also in our work the RVE with straight fibers is considered. A qualitative assessment of the results of calculating the longitudinal compressive strength is carried out for models with and without manufacturing defects.

2 Materials and Models All micromechanical samples (Fig. 1) are modeled as follows: – a fiber is created in the form of a rectangle with a given width and length in micrometers (in the case of a curved fiber, this is a spline with a given angle of curvature); – a matrix is created that repeats the shape of the fiber, since the volume fraction adopted by us in the article is 50%; – fiber and matrix are combined into one part; – using the “Array” tool, the created part is multiplied; – the resulting part is cut by an auxiliary part to obtain the required dimensions.

Fig. 1. The samples: a – with straight fibers, b – angle of waviness is 1°, c – angle of waviness is 3°, d – angle of waviness is 5°

The radius of the fiber adopted by us in the article is 6 μm. The sample length is 4000 μm. Four samples were created, one of them with straight fibers, the other three with curvature angles of 1, 3 and 5°, respectively. The angle of waviness was chosen optimal from the permissible values from 0 to 5°, since it follows from the article (Naya 2017) that at large angles the fibers lose their basic strength characteristics.

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The damage plasticity model is assigned for both matrix and fiber. The input properties are listed in the Table 1 and Table 2. Table 1. Mechanical properties of glass-fibers (Soden 2004). Fibre type

E-glass 21 K43 Gevetex

Longitudinal modulus Ef1 GPa

80

Poisson’s ratio υm

0.2

Longitudinal compressive strength XfC MPa

1450

Density g/mm3

2.5·10–3

Table 2. Mechanical properties of matrice (Soden 2004). Matrix type

LY556/HT907/DY063 epoxy

Modulus Em Gpa

3.35

Poisson’s ratio υm

0.35

Compressive strength YmC MPa

120

Density g/mm3

1.2·10–3

The bond between fibers and matrix is idealized, there is no contact. The surface-based coupling is used in the analysis as shown in the Fig. 2. Defining a coupling constraint requires the specification of the reference node (also called the constraint control point), the coupling nodes, and the constraint type. The coupling constraint associates the reference node with the coupling nodes. The constraint is imposed by eliminating almost all degrees of freedom, both translational and rotational.

Fig. 2. Coupling.

The load is set as a non-zero displacement that assigned to the reference point. Also a zero displacement is assigned in x and y-direction as shown below (Fig. 3).

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Fig. 3. Loads.

The mesh is superimposed in the form of triangular elements (Fig. 4). The global seed size adopted in our article is 2 μ. This size is enough to achieve the convergence of results.

Fig. 4. Mesh

Processing of the calculation involves converting the obtained dependence between the reaction force RF and the displacement U into a stress-strain dependence (Turbin 2020). The stress is found from the equation: σ =

RF a2

(1)

where RF is the reaction force, a is the length of the fiber. The strain is calculated using the equation: ε= where u is the assigned displacement.

u a

(2)

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3 Results All representative volume elements are modeled as mentioned earlier with an ideal and rigid interface, a plastic damaged matrix, so that the possibility for destruction is not only the rupture of the fiber during compression, but also the formation of a crack in the matrix itself. The obtained values of strength are presented on the Table 3. Table 3. Results Sample

σc

Straight fibers

591

1° of waviness

617

3° of waviness

625

5° of waviness

620

It can be seen from the table that the initial waviness of fibers leads to the improving of the strength properties of the material.

4 Conclusion The work was carried out to compare the strength characteristics of micromechanical samples with straight fibers and with fibers with initial waviness. The micromechanical sample model is simplified, which allows to significantly reduce the calculation time and at the same time obtain the convergence of the results. It can be concluded that computational micromechanics is a convenient tool for calculating the strength characteristics of a material. In the future, this will significantly reduce the cost of conducting experiments on elementary samples and, accordingly, simplify the process of calculating the strength of the structure.

References Naya, F., Herraez, M., Lopes, C.S., Gonzalez, C., Van der Veen, S., Pons, F.: Computational micromechanics of fiber kinking in unidirectional FRP under different environmental conditions. Compos. Sci. Technol. 144, 26–35 (2017). https://doi.org/10.1016/j.compscitech.2017. 03.014 Sebaey, T.A., Catalanotti, G., Lopese, C.S., O’Dowd, N.: Computational micromechanics of the effect of fibre misalignment on the longitudinal compression and shear properties of UD fibrereinforced plastics. Compos. Struct. 248, 112487 (2020). https://doi.org/10.1016/j.compstruct. 2020.112487 Soden, P.D., Hinton, M.J., Kaddour, A.S.: Lamina properties, lay-up configurations and loading conditions for a range of fibre reinforced composite laminates. In: Failure Criteria in Fibre-Reinforced-Polymer Composites, pp. 30–51 (2004). https://doi.org/10.1016/B978-008 044475-8/50003-2 Turbin, N., Kalutskiy, N.: Determination of the composite’s representative volume for longitudinal tensile test simulations (2020)

DNN and Model Combined Passive Localization and Social Distancing with Partial Inertial Aiding Wenhan Yuan, Xin Zhang(B) , Cheng Chi, and Xingqun Zhan School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China [email protected]

Abstract. At the outbreak of COVID-19, researchers worldwide are seeking approaches to containing this disease. It is necessary to monitor social distance in enclosed public areas, such as subways or shopping malls. Passive localization, such as surveillance cameras, is a natural candidate for this issue, which is meaningful for rapid response to finding the infected suspect. However, the latest surveillance camera system is rotatable, even movable. And it is impossible for professionals to regularly calibrate the extrinsic parameters in a large-scale application, like COVID-19 suspect monitoring. We propose an inertial-aided passive localization method using surveillance camera for social distance measurement without the necessity to obtain extrinsic parameters. Moreover, the hardware modification cost of the off-the-shelf commercial camera is low, which suits the immediate application. The method uses SGBM (Semi-Global Block Matching) for 3D reconstruction and combines YOLOv3 and Gaussian Mixture Model (GMM) clustering algorithm to extract pedestrian point clouds in real time. Combining the 2D DNN-based and model-based methods makes a better balance between the computational load and the detection accuracy than end-to-end 3D DNN-based method. The inertial sensor provides an extra observation for the coordinate transformation from the camera frame into the world ground frame. Results show we can get a decimeter-level social distancing accuracy under noisy background and foreground environments at a low cost, which is promising for urgent COVID-19 public area monitoring. Keywords: Surveillance system · Human detection · Localization · Social distancing monitoring

1 Introduction COVID-19 is an exceptionally infectious disease, the outbreaks of which have already occurred worldwide. Before any trustable vaccine is present, the most effective way to suppress the pandemic is to rapidly and effectively quarantine the confirmed, and suspected patients (Prem et al. 2020). Social distance monitoring or social distancing is one of the key technologies for real-time close contact determination and identification, which will greatly enhance the efficiency of discriminating suspected patients. The © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 108–122, 2023. https://doi.org/10.1007/978-981-99-0651-2_10

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most commonly used localization sensor, global navigation satellite system (GNSS), is already providing certifiable meter level accuracy positioning under open sky (Marais et al. 2017). However, high accuracy positioning is still a challenge in an obstructed environment, which entails non-line-of-sight (NLOS) signals featured in urban canyons and indoors. In the past decades, researchers have tried utilizing multitudes of sensor modalities to solve this problem, such as camera, WiFi, Bluetooth, 5G signals, LiDAR, and IMUs (Brena et al. 2017). However, there is still not a consent to the solution. Among these choices, passive localization outstands due to its non-intrusive features (Shinde et al. 2018; Saeed et al. 2014). It does not need any extra sensor installed on the pedestrian, leading to easy implementation for large-scale pedestrian monitoring. Surveillance camera-based passive localization is one of the most promising techniques within the category because of the rapid breakthrough in deep neural network (DNN) (Krizhevsky et al. 2017; Girshick et al. 2014). Its powerful representation ability significantly promotes the adaptability of this method to the real-world environment. The main drawback of the DNN-based localization algorithm is the high computational load. Moreover, the surveillance camera usually needs carefully calibrated extrinsic parameters for world coordinate calculation when they moved. In this paper, we mainly focus on these two issues. Generally, there are two modules in a surveillance camera-based pedestrian social distancing monitoring system: 3D information reconstruction, 3D pedestrian detection. LiDAR is the most accurate and straightforward device for 3D information, but it is too expensive for large-scale applications, and the vertical resolution is limited (Wang et al. 2019). Camera is much cheaper with bunches of existing algorithms and applications. With recent DNN-based stereo matching and depth perception algorithms, camera can provide pseudo point clouds as accurate as LiDAR in a relatively close range (You et al. 2020; Weng and Kitani 2019). The core procedure of 3D reconstruction for the stereo camera is to get the disparity map. The traditional way (Xu et al. 2019) follows a four-step procedure (Hirschmuller 2005), which tries to find the matching pixel pairs between the left and right images. Most researchers recently focus on an end-to-end DNN (Scharstein et al. 2001) for matching cost calculation after the Deep Siamese Network is proved useful for stereo matching. The DNN-based method provides a more accurate matching result and higher computational load than the traditional cost function. PSMNet (Chang and Chen 2018), one of the top-ranking algorithms on the KITTI dataset, needs an expensive GPU to achieve real-time matching. Due to the complex contours of the pedestrian, they are usually matched easily. In order to reduce the system computational load, the Semi-global Block Matching (SGBM) (Hirschmuller 2005) algorithm is used for stereo matching in this paper. Most of the algorithms on 3D object detection operate on LiDAR point clouds (Zhou and Tuzel 2018), and some others choose to use RGB-D (Qi et al. 2018) or camera (Weng and Kitani 2019). The 3D convolution or the 3D search has a very high computation complexity, which is o(n3 ), with respect to the image resolution and becomes too expensive for a large scene. Multi-view 2D object detection can also achieve 3D detection and saves a lot of computing resources (Chen et al. 2017; Saeidi and Ahmadi 2020). One of the 2D object detection, YOLOv3, can perform around 3/15FPS on a Jetson TX2

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at a high/low image resolution, which is much cheaper and fast enough for real-time pedestrian localization. Hence, we combine the front-view 2D image object detection and sparse pseudo point clouds extracted from images for indoor pedestrian localization in this paper. This way, the algorithm can be more suitable for commercial embedded equipment. There are plenty of works on 2D object detection. Traditional feature extraction methods, such as Integrate Channel Features (ICF) (Dollár et al. 2009), is not flexible enough to deal with the complex real-world indoor scenarios. Because it usually needs a huge amount of training data to adapt itself to various scenarios, which always leads to poor performance using traditional machine learning. Faster-RCNN\(Ren et al. 2017), SSD (Liu et al. 2016), YOLO (Redmon et al. 2016), YOLOv3 (Redmon and Farhadi 2018), Mask-RCNN (He et al. 2017), are the most common DNNs for this task. There are also some algorithms designed especially for pedestrian (Saeidi and Ahmadi 2020; Li et al. 2019). The two-stage methods (Ren et al. 2017; He et al. 2017) are more accurate and can even achieve pixel-level pedestrian extraction but bring about a tremendous amount of computing, limiting its application. One-stage methods (Liu et al. 2016; Redmon et al. 2016; Redmon and Farhadi 2018) do the regression and classification straightly on the image, which is much faster and has shown remarkable results in real-world use. The main drawback of these one-stage methods for pedestrian localization is that the detection bounding box contains too much foreground and background pixels (Seo and Kim 2016). These extra clusters may deteriorate the positioning accuracy or even cause failure in the stereo surveillance localization system. Some previous works use CNN to eliminate these extra points on a Bird-Eye View (BEV) image (Supreeth and Patil 2018). However, they need a massive amount of training data with extraordinarily laborintensive and time-consuming pixel-level labeling, especially for pedestrian tracking. Hence, a principled/model-based way is preferred to extract the point cloud in this paper. K-means clustering (Viola and Jones 2003) is easily implemented and saves computation resources. However, it is sensitive to the initial parameters and tends to cluster into a sphere shape, while the point cloud cluster within the bounding box is often irregular. Density-Based Spatial Clustering (DBSCAN) (Schubert et al. 2017) has a better performance in adapting itself to all kinds of cluster shapes. However, it also has two tricky parameters to tune, and it is very likely to aliasing the adjacent clusters when the parameters are not suitable. GMM (Zhou and Zhang 2005) via the EM-algorithm tends to cluster into elliptical shapes, which fits the experimental observation. Moreover, it could provide a more robust result than KNN and DBSCAN. The above methods output the pedestrian locations in camera coordinate, but the social distancing is defined in real-world coordinate. It usually needs extrinsic parameters to get the real-world coordinate, which is labor-intensive for large-scale monitoring and hard to maintain. In this paper, 1) we propose an accelerometer-aided algorithm to utilize the direction of gravity to recover the pedestrian distance in the camera coordinate into the earth ground, which could lift off this limitation. 2) we propose a method that uses an integration of DNN and model-based algorithms to achieve finer-grained pedestrian point cloud extraction, which can be used for high accuracy positioning. 3) we integrated all the combined proposed methods on ROS and tested this system under

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two typical scenarios in real indoor environments. The results show that the accuracy of inter-pedestrian distances is at the decimeter level in real-time, which is suitable for monitoring social distancing at a low cost.

2 The Proposed Method A general algorithm overview is depicted in Fig. 1. It consists of three components: 1) 3D reconstruction using the stereo camera, 2) pedestrian point cloud extraction and 3) inter-pedestrians distancing measurement. The inertial measurement unit (IMU) should be implemented on the rigid body of the stereo camera. In this paper, we only need the accelerometer in the IMU for inter-pedestrian measurement. We choose the Kalibr (Joern et al. 2016) for the accelerometer and stereo camera calibration for convenience. This method also needs a gyroscope. However, some other calibration methods may not need a gyroscope, so only the accelerometer is necessary.

Fig. 1. Arithmetic flow

First of all, a stereo camera should be implemented where the camera field-of-view is unobstructed. Because the optical positioning system only works within line of sights (LOS). The positioning information can only be acquired under the LOS environment to one of the surveillance cameras. During the localization phase, we take the pedestrian bounding box parameters and the depth image as inputs. The depth image is then converted into a 3D point cloud and combined with the bounding box information to extract the point cloud within the pedestrian’s detected window. Then GMM is utilized to separate the points belong to the different objects in the BEV/Top-down view. The next step is finding the pedestrian clusters and extracting the geometric center of these point clusters as the pedestrian’s position in the camera coordinate. The last step is finding the normal vector of the ground plane. The social distance is then the inter-pedestrian distance in camera coordinate projected onto the ground plane.

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2.1 Stereo 3D Reconstruction The 3d reconstruction using a stereo camera has two steps: 1) the stereo camera calibration, 2) the calculation of the disparity map and 3D reconstruction. Stereo Camera and Accelerometer Calibration: The 3D reconstruction using the surveillance stereo camera needs a two-step calibration. The checkerboard calibration method (Zhang 2000) is often used to remove lens distortion from a raw image. The camera model we use here is a radial tangential model. We use Kalibr (Joern et al. 2016) to acquire the intrinsic parameters of the stereo camera and the rotation, transformation matrix from the accelerometer to the left camera. 3D Reconstruction Using Disparity Map: In the Binocular Vision System (BVS), the 3D coordinates can be calculated through visual disparity.

Fig. 2. The geometrical principles of stereo vision system

The 3D reconstruction using the stereo camera follows a geometric principle depicted in Fig. 2. We assume that the optical axes of the two cameras are in parallel. b is the interocular distance of the stereo camera. PL and PR are the corresponding pixels between the left and right cameras. The 3D coordinate of every pixel can be calculated using the disparity. The key part of this module is to find the matching pixels. Recently, researchers focus on using CNN to get an accurate matching cost and optimize it in a semi-global way. In this paper, we utilize the SGBM algorithm, which is implemented in OpenCV, to find the corresponding pixels.

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2.2 Coarse Pedestrian Point Cloud Extraction YOLOv3 is the most seminal improved version of You Only Look Once, which could locate the objects and distinguish their categories in a one-stage neural network. The details of the network structure are described in (Redmon and Farhadi 2018). The bounding box detected from YOLOv3 tends to include every part of the human body. Hence, the width and length are usually determined by the widest and longest parts of the body exposed under the line-of-sight (LOS) of the camera. As shown in Fig. 3(a) and (b), this preference can bring in a lot of background and foreground object pixels, which contaminate the pedestrian localization result. In order to overcome the negative effects of the background points, some researchers suggest using the foot points, which is usually considered the lower part of the points within the bounding box. However, this only works when there is no obstacle in front of the feet. Hence, we need a method to handle this situation. A more detailed segmentation is needed to extract pedestrian points for localization. Some (Xu et al. 2019) proposes to use foot pixels or head pixels for localization, but the pixel-level DNN-based segmentation is too computationally intensive. In this paper, we propose a 2D GMM clustering algorithm using point clouds information to calculate the pedestrian localization in a plane, which is parallel to the ground earth.

Fig. 3. (a) The detected pedestrian; (b) Point cloud in camera coordinate; (c) Point cloud in real-world coordinate

2.3 Transformation from Camera Coordinate to Bird Eye View (BEV) Plane The segmentation of the pedestrian in pixel level is cumbersome in the 3D world coordinate. However, it is usually linearly separable in the bird-eye-view (BEV) plane of real-world coordinate, depicted in Fig. 3(c). The intuition behind this assumption is that the objects can be considered to have no overlap between each other in the BEV, and the point clouds belong to the same object clustered together, so they are usually linearly separable. In Fig. 3(b) and (c), we can find that all the points are tightly clustered. So

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a clustering model, such as GMM, can be utilized to describe the probability density function. The point clouds circled by a red ellipse are the pedestrian point clouds, which usually has the largest number of the point clouds among all the clusters in the pedestrian detection bounding box. This can be modeled by the largest weight Gaussian distribution in GMM, Social distancing is defined as the inter-pedestrian distance in world coordinate, which can be simplified to the distance on a 2D earth plane. Hence, the pedestrian position on the BEV plane (db in Fig. 4) is equal to the simplified social distance. We define the BEV plane (plane Yb Zb ) is parallel to the earth’s ground, which is considered as the Xw Yw plane of the world coordinate. We define the X-axis of the BEV coordinate Xb is the direction of the gravity. Hence, the rotation matrix Rcb from camera coordinate to a BEV coordinate is depicted in Fig. 4.

Fig. 4. The geometrical principles of inter-pedestrian distance

 T The x-axis of the camera coordinate is 1 0 0 . The x-axis of the BEV coordinate  T is the gravity direction, which is obtained from the accelerometer xa ya za . Hence, we can get the angle θ from the x axis of the camera coordinate to the x axis of the BEV coordinate. θ = arccos

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2.4 Social Distance Measurement The Gaussian mixture model (GMM) is a classic but useful method for clustering. Its mathematical expression is as follows. p(x) =

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where N indicates a Gaussian distribution, μl and Σl are the parameters means and covariance of the GMM, αl is the weights assigned to each Gaussian distribution, and k is the number of clusters. To find the best μl and Σl to describe the data rapidly and adequately, it equals to calculate the maximum likelihood expectation (MLE) of GMM. let  = {μ1 , Σ1 , α1 , μ2 , Σ2 , α2 , ..., μk , Σk , αk } MLE = argmaxθ (L(θ )) This is a typical incomplete-data problem, and an iterative way is the only way to approximate the solution. In this paper, we use the Expectation-Maximization (EM) algorithm to solve this issue. Let us assume a time series of  = θ (1) , θ (2) , ..., θ (t) . l+1 = argmaxθ ( log(p(X , Z|θ ))p(Z|X , l ))dz Z

where Z is the latent variable, and it means the cluster index in GMM. The EM algorithm is sensitive to the initial parameters, especially the number of clusters k. Bayesian Information Criterion (BIC) is often used to measure the performance on different k. We test the performance of our system exhaustively, and find that k = 3 or 4 is the fine-tuned parameter for this system. The details are provided in the next section. The initial parameters for EM do affect the clustering result, but the changes are always on the background and foreground clusters. The pedestrian extraction is often much more stable. We will also show this result in the next section. The GMM model is substituted into the above formula, and its parameters are optimized. Because the points data are within the pedestrian detected bounding box, the pedestrian is always the cluster with the highest weights. The pedestrian point cloud cluster can be easily extracted. The geometric center of these point clouds is considered as the pedestrian position. The social distancing measurement is the Euclidean distance between the pedestrian positions.

3 The Experiments and Results The experiment site is in a residential room. First, we evaluate the accuracy when the extrinsic parameters are given. A camera test shot, the camera installation, and the realworld coordinate are shown and defined in Fig. 5. The stereo camera is installed in the ceiling corner. We directly connect the camera with a PC to process the input data. The

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Fig. 5. Experiment equipment and site (a) Camera; (b) Experiment trace

room is filled with all kinds of furniture to simulate complicated background. A chest is used as an obstacle so that we can simulate partial obstacles and the complicated background. MYNTEYE camera is used as the surveillance camera, which continuously capturing the video frame, and transmitting the image into the server. Image resolution is 740×468. The PC server we use is running Ubuntu 18.04.4 LTS with Intel i5 CPU and NVIDIA GTX 2060. The server inputs the left image of the stereo pairs into YOLOv3 and monitors if there is a pedestrian. When a user asked for his/her position, the server starts the pedestrian extraction algorithm and output the position. We use the two classic clustering algorithms to find the most appropriate one for our task and test their positioning accuracy.

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Fig. 6. The process of 3D reconstruction using stereo camera. (a) The distorted raw Image; (b) The corresponding undistorted image; (c) The disparity map; (d) The point clouds

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Initialization and Calibration: In the experiment, we first calibrate the stereo camera and get the extrinsic parameters using a chessboard. The results are shown in Fig. 6(a) and (b), which shows a test scene image before and after calibration. Then we input the stereo images into the proposed algorithm in Sect. 2 to get the 3D point cloud in view, as shown in Fig. 6(c) and (d). Next, we need to find out the pedestrian pixels to extract pedestrian point cloud information. Pedestrian Extraction: First, we evaluate the clustering performance under partial occlusion and noisy background scenarios. Figure 7(a) and (c) depict the pedestrian detection result from YOLOv3. The ground truths of the pedestrian points are shown as the ellipses in Fig. 7(b) and (d). The clustering method is utilized to extract the pedestrian points further. There are mainly two kinds of initial parameters for K-means and GMM, the amount of clusters k and the initial iteration parameters of the EM. We use BIC to evaluate the performance of different k. When the k is selected correctly, the initial model parameters will have smaller effects on the pedestrian point extraction. As shown in Fig. 8(a), the BIC indices show that k = 4 is the best choice for both scenarios. The positioning performance reduction is evident when the k is not appropriately selected, as depicted in Fig. 8(b) and (c) and Table 1.

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Fig. 8. Experiment results. (a) BIC of position1; (b) Positioning error CDF, position1, k = 4; (c) Positioning error CDF, position1, k = 3; (d) BIC of position2; (e) Positioning error CDF, position2, k = 4; (f) Positioning error CDF, position2, k = 3

The final pedestrian point clustering is also shown in Fig. 9 In general, GMM performs better than K-means, while K-means is more likely to fail, just like the clustering result in Fig. 9(b). Moreover, our system achieves a 10 cm point positioning accuracy under partial occlusion and noisy background, as shown in Table 1. Social Distance Monitoring: In order to further verify the performance of our algorithm, we test it on a video in the lab of SJTU-GNC. Figure 10 depicts the performance of the accelerometer-aided algorithm. We did not calibrate the extrinsic parameters this time and only use the intrinsic calibrated by Kalibr. The result shows that the accuracy of the inter-pedestrian measurement is also at decimeter level. This result is comparable to

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the above experiment, which needs careful calibration for extrinsic parameters and this proves that our proposed method can adapt to the scenario where the surveillance cameras are non-static and large-scale application without extra camera extrinsic calibration workload. Table 1. Positioning error GMM [cm]

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4 Conclusion In this paper, we propose an easily implemented system for social distancing monitoring, leveraging a surveillance stereo camera to extract the pedestrian clusters from all the

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points within the detected bounding box. This method is built on YOLOv3 and GMM to quickly adapt to a real-world environment without any extra data training and can be utilized for high-accuracy passive vision-based positioning. We conduct a comprehensive experiment in a real indoor environment, which reveals that our system can achieve decimeter level accuracy even when the pedestrian is half-occluded or under a noisy background. Due to its easy implementation, robustness, and low computational complexity, this method could be a suitable candidate for detecting potential infection and pandemic control in a public health event like COVID-19. We will continue by solving the NLOS issue using sensor-fusion algorithms with commercial off-the-shelf sensors in future work.

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Girshick, R., Donahue, J., Darrell, T., Malik, J.: Rich feature hierarchies for accurate object detection and semantic segmentation. In: CVPR 2014: Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition, pp. 580–587 (2014) Wang, Y., Chao, W.L., Garg, D., Hariharan, B., Campbell, M., Weinberger, K.Q.: Pseudo-LiDAR from visual depth estimation: bridging the gap in 3D object detection for autonomous driving. In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 8445–8453 (2019) You, Y., Wang, Y., Chao, W.L., Garg, D., Pleiss, G., Hariharan, B., et al.: Pseudo-LiDAR++: accurate depth for 3D object detection in autonomous driving. In: ICLR 2020: Eighth International Conference on Learning Representations (2020) Weng, X., Kitani, K.: Monocular 3D object detection with pseudo-LiDAR point cloud. In: 2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW), pp. 857–866 (2019) Xu, J., Chen, H., Qian, K., Dong, E., Sun, M., Wu, C., et al.: iVR: integrated vision and radio localization with zero human effort. Proc. ACM Interact. Mob. Wearable Ubiquit. Technol. Arch. 3(3), 114 (2019) Hirschmuller, H.: Accurate and efficient stereo processing by semi-global matching and mutual information. In: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2005), vol. 2, pp. 807–814 (2005) Scharstein, D., Szeliski, R., Zabih, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. In: Proceedings IEEE Workshop on Stereo and Multi-Baseline Vision (SMBV 2001), vol. 47, pp. 7–42 (2001) Chang, J.R., Chen, Y.S.: Pyramid stereo matching network. In: 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 5410–5418 (2018) Zhou, Y., Tuzel, O.: VoxelNet: end-to-end learning for point cloud based 3D object detection. In: 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4490–4499 (2018) Qi, C.R., Liu, W., Wu, C., Su, H., Guibas, L.J.: Frustum PointNets for 3D object detection from RGB-D data. In: 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 918–927 (2018) Chen, X., Ma, H., Wan, J., Li, B., Xia, T.: Multi-view 3D object detection network for autonomous driving. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 6526–6534 (2017) Saeidi, M., Ahmadi, A.: A novel approach for deep pedestrian detection based on changes in camera viewing angle. Sig. Image Video Process. 14, 1273–1281 (2020). https://doi.org/10. 1007/s11760-020-01662-y Dollár, P., Tu, Z., Perona, P., Belongie, S.J.: Integral channel features. In: British Machine Vision Conference 2009, pp. 1–11 (2009) Ren, S., He, K., Girshick, R., Sun, J.: Faster R-CNN: towards real-time object detection with region proposal networks. IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1137–1149 (2017) Liu, W., et al.: SSD: single shot multibox detector. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9905, pp. 21–37. Springer, Cham (2016). https://doi.org/10. 1007/978-3-319-46448-0_2 Redmon, J., Divvala, S., Girshick, R., Farhadi, A.: You only look once: unified, real-time object detection. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 779–788 (2016) Redmon, J., Farhadi, A.: YOLOv3: an incremental improvement. ArXiv Preprint arXiv:1804. 02767 (2018) He, K., Gkioxari, G., Dollar, P., Girshick, R.: Mask R-CNN. In: 2017 IEEE International Conference on Computer Vision (ICCV), pp. 2980–2988 (2017)

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Hybrid LES/RANS Simulation of Shock/Turbulent Boundary-Layer Interactions Tingkai Dai(B) and Bo Zhang Shanghai Jiao Tong University, Shanghai, China {jayddkt,bozhang}@sjtu.edu.cn

Abstract. In order to reduce the computational cost of Large Eddy Simulation method at high Reynolds number, the hybrid LES/RANS model-Improved Delayed Detached Eddy Simulation (IDDES) method based on k-ω SST turbulence model is used to simulate a 2.84 Mach number flow of the 24° compression ramp. The effects of two kinds of inlet boundary conditions which includes fixed inlet and turbulent inlet were investigated. The numerical simulation reproduces the phenomena of boundary layer separation, shock separation and reattachment. The results show that the length of simulated separation region under the fixed boundary condition is significantly larger than the experimental result, and the length of the separation region under the turbulent inlet decreases with the increase of turbulent intensity, which is gradually close to the experimental results. The results show that the IDDES hybrid model is very dependent on the turbulence of the incoming flow. Keywords: Hybrid LES/RANS method · Shock/turbulent boundary-layer interactions · Turbulent inlet

1 Introduction Shock Wave/Turbulent Boundary Layer Interaction is a common flow phenomenon caused by the Interaction between Shock waves and wall turbulent boundary. The interaction between shock wave and boundary layer is one of the important physical phenomena in the external and internal flows of various high-speed aircraft, which contains very complex aerodynamic and thermodynamic characteristics. In the outflow, the heat exchange situation may be changed significantly and the unsteady pressure load will be generated, which will shorten the structure life greatly. The internal flow can induce large scale unsteady separation flow, increase the total pressure loss and produce flow field distortion. The SBLI have the following harm: sudden drop in velocity; flow separation; sudden rise in temperature significant drag and efficiency reductions. Looking back over the past 70 years, SBLI is still one of the most important issues in aerospace research [1]. Compressed ramp shock/boundary interaction (CR-SBLI) is the most common simplified model for shock/boundary layer interaction. Its overall flow structure is relatively © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 123–132, 2023. https://doi.org/10.1007/978-981-99-0651-2_11

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simple, which helps researchers to peel off typical flow structures and deepen their understanding of mechanical problems. When the supersonic flow passes through the compression corner, an oblique shock wave is generated, and the pressure behind the wave increases. Under the action of the adverse pressure gradient, the flow equilibrium state is destroyed, which thickens the boundary layer at the front of the compression corner. Under the influence of boundary layer distortion, a series of oblique compression waves are generated in front of the corner. The boundary layer behind the oblique shock wave is often separated near the inflection point due to its inability to withstand strong adverse pressure gradient, forming a separation region. After the supersonic flow through the separation region, a series of compression wave systems are generated under the compression action of the downstream inclined plane [2]. SBLI was first to study through the experiment, the main research methods include schlieren, oil flow and sensors, etc. [3–7], over time, due to the laser measurement technology, image processing and analysis technology, the rapid development of high-speed camera and particle imaging technology, also by PIV, NPLS of shock wave boundary layer interference were studied [8, 9]. The characteristics obtained from the experimental study of shock boundary layer interference are mainly in three aspects: the first is the two-dimensional macroscopic structure and flow parameter characteristics, the second is its unsteady characteristics, and the third is the three-dimensional structure of gottle-like vortex in the flow. With the development of computers, the application of computational fluid dynamics in the study of shock/boundary layer interference shows a strong momentum of development, including RANS, LES, DNS three types of shock boundary layer interference simulation. However, the RANS method based on the traditional turbulence model can better predict the time-mean wall pressure and heat flow, as well as the initial separation position of weak interference, but cannot accurately predict the pressure, heat flow, topological structure of flow field and unsteady characteristics of wave system and separation region downstream of the interference region and strong interference flow field. In contrast, LES and DNS can better reflect the physical nature of the flow field and have unique advantages in predicting some flow parameters dominated by unsteady phenomena. However, the multi-wall surface leads to more complex multi-boundary layer/multi-wave system interference flow field, and the description of such complex flow field by the sub-lattice model also has some defects. Secondly, the calculation amount is still large, even for medium Reynolds number and small calculation area, the number of grids can easily reach tens of millions of magnitudes [10–12]. The object of the paper is to reduce the computational cost of Large Eddy Simulation method at high Reynolds number and get more accurate simulation results than RANS for CR-SBLI. So, the hybrid LES/RANS model-Improved Delayed Detached Eddy Simulation (IDDES) method based on k-ω SST turbulence model is used to simulate a 2.84 Mach number flow of the 24° compression ramp.

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2 Numerical Simulation Method 2.1 IDDES Detached eddy Simulation (DES) is the common hybrid RANS/LES. Spalart et al. [13] proposed the SA-DES (DES97) method by reforming the Spalart-Allmaras (SA) model. However, this method would judge the boundary layer region that should be solved by RANS as LES region when the grid near the wall is not arranged properly. The transition to LES mode is premature, and the grid is insufficient to support LES computation. This would reduce the vorticity viscosity and cause the Reynolds stress imbalance of the model, which is known as model stress depletion (MSD). SPALART et al. [14] also proposed delayed detached- Eddy Simulation (DDES) method based on SA model by modifying the definition of d˜ , thus solving the MSD problem. MENTER et al. [15] also proposed the DES method based on (Sheared Stress Transport (SST)) model, and solved grid-induced separation (GIS) caused by MSD problems. Then, improved delayed detached Eddy Simulation (IDDES) was proposed [16]. IDDES method contains more upstream information and turbulence information, so its flow field distribution is more reasonable. Moreover, more near-wall information is involved in the scale structure, which can prevent excessive Reynolds stress drop and log-layer Mismatch at the junction of RANS and LES, and improve the solution quality of near-wall turbulence, which can effectively simulate large separated flows. For incompressible viscous fluid, the continuity equation and momentum equation after filtration can be expressed as: ∂ui ∂xi

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lh in k equation is the turbulence length scale, which is the switch that controls the solution of LES or RANS. For the SST-DDES model, the turbulence length scale lDDES is defined as follows: lDDES = lRANS − fd max(0; lRANS − lLES )

(7)

Here, lDES = CDES × , and Maximum mesh size = max( x, y, z), CDES is the DES constant, fd is the shielding function, which is equal to 0 near the wall and 1 in the distance to ensure that RANS simulation is used near the wall and LES simulation is used in the distance. For the SST-IDDES model, the turbulence length scale lIDDES is defined as follows:   lIDDES = fˆd (1 + fe )lRANS + 1 − fˆd lDES (8) In the formula, grid scale is different from DDES model and is defined as = min[max(cw max ; cw dw ; min ); max ]

(9)

Here, max is the maximum size of the grid, and min is the minimum size of the grid, cw is a constant, and dw is the shortest distance from the wall surface. When fe = 0,   lIDDES = fˆd lRANS + 1 − fˆd lDES (10) 

Here, IDDES become the DDES, the function fˆd = max (1 − fdt ); fB ], it contains fluid (1 − fdt ) and the geometry fB two parts. When fe > 0 and fˆd = fB , lIDDES = lWMLES = fB (1 + fe )lRANS + (1 − fB )lLES

(11)

Here, IDDES become WMLES. IDDES model was a mixture of DDES and Wall-model LES (WMLES). As can be seen from the comparison of Formulas (7) and (8), IDDES improves the definition of and makes it includes the distance from the wall surface rather than just the grid size, thus helping to solve the Reynolds stress. Secondly, the problem of logarithmic boundary layer mismatch is solved by improving the empirical function fˆd . 2.2 Geometric Modeling and Meshing The flow problem at the compression ramp is shown in Fig. 1. In order to compare the simulated results with the classical experimental results of Settle, all the conditions are corresponding to the experimental conditions of Settle. As shown in Fig. 1, the inflection point of the compression ramp is X = 0, and the upstream and downstream X coordinates of the ramp are measured along the wall surface. The upstream X coordinate is negative, the downstream X coordinate is positive, and the Y coordinate is always perpendicular to the wall surface. Experimental flow parameters measured at X = −10 mm are given in the literature as shown in Table 1.

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Table 1. Flow parameters at X = −10 mm. Ma

P∞ (Pa)

Tt (K)

U∞ (m/s)

δ∞ (mm)

2.84

23900

278

586

23

Fig. 1. Compression ramp in Settle’s experiment

The two-dimensional geometric model is consistent with Fig. 1, with a size of 100 mm in the Y direction, and the three-dimensional geometric model is expanded in the Z direction with a size of 50 mm. The number of grids is 251 × 200 × 50, and the grids are evenly distributed along the flow direction. The mesh is refined in the Y direction near the wall to ensure y+ < 1 for the first layer of grids away from the wall in the Y direction. The wall surface is the non-slip adiabatic condition, the upper boundary is the supersonic far field boundary condition, and the outlet boundary is the InletOutlet boundary condition of OpenFoam. For 3D cases, the front and back are the cyclic boundary which is the periodic boundary condition. So, The boundary layer is not affected by the boundary conditions of the front and back surfaces. In order to reduce the number of grids and save computing resources, boundary conditions with a certain boundary layer thickness should be used at the inlet. The same simulation and grid are used to simulate the boundary layer of the plate. When the boundary layer parameters are consistent with the experiment results, the boundary layer parameters at this time are taken as the inlet parameters. The RANS flow field simulated by SST model is initialized. Because large eddy simulation is sensitive to turbulent boundary conditions at the inlet, two types of turbulent boundary conditions at the inlet are adopted here: (1) no turbulence is given, that is, the same boundary conditions are simulated as RANS; (2) A velocity inlet boundary condition based on a synthetic eddy current for generating a synthetic turbulent like time series from a given set of turbulence statistics.

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3 Result 3.1 2D Compression Ramp 2D Compression ramps of the angle-24° are simulated, the length of the separation area is larger than the experiment result. The K-Omega SST turbulence model was used for two-dimensional simulation. Figure 2 is the Pressure of 2D compression ramp. From the figure we can see that the boundary layer thickness of the incoming flow, the separation and attachment of shock waves have been obviously simulated. From the perspective of structure, the wave system structure simulated in 2D is consistent with the experiment.

Fig. 2. Pressure of 24° 2D compression ramp simulation

Figure 3 is the wall pressure of the different turbulent model simulation. The simulation of turbulent model, the basic will produce a pressure step after the separation zone, which is not found in the experimental data, the separation point will be top than it really is a lot, but in the end pressure is consistent, the BSL model is also the most close to the experimental data; Because the viscosity of the turbulence vortex given is much lower than that of the turbulence model, the boundary layer cannot get enough energy from the mainstream, and no turbulence pulsation information is added to the inlet, so there is no turbulence pulsation energy. This makes the boundary layer less able to withstand the pressure gradient, so the calculated separation zone is much larger than the experimental value. The coordinates of separation points Xs of different turbulence models are shown in Table 2. The simulation results of BSL model on wall pressure are closest to the experiment results. This shows that the simulation of BSL model on the wall is the best.

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Fig. 3 Wall pressure of 24° 2D compression ramp simulation

Table 2. Separation points Xs of different turbulence models EXP

k-omega BSL

Transition SST

Reynolds stress BSL

k-omega SST

Standard k-omega

−1.99

−2.45

−4.29

−4.77

−5.50

−8.72

3.2 3D Compression Ramp In this paper, turbulentDFSEMInlet inlet conditions in OpenFoam are used to generate turbulence. This turbulent inlet condition is a velocity inlet boundary condition based on synthetic eddy-currents for generating synthetic turbulent like time series from a given set of turbulence statistics for LES and hybrid RANS-LES calculations. This boundary inlet requires a front-end boundary layer velocity data to be used as boundary layer inlet thickness, and the generated initial field should contain as much information as possible in the turbulent fitting structure. The two-dimensional simulations are used to become part of the inlet condition. Given different turbulence intensities, we can obtain the turbulence statistics at the corresponding turbulence intensities. Figure 4 is the instantaneous velocity and mean pressure of 24° 3D compression ramp simulation. For 3D simulation, the unsteady property can be clearly seen for this figure(a). The turbulent boundary layer with a certain thickness can be clearly seen from the figure. In order to better compare with the experiment data, the simulation results are averaged over time. Figure 4(b) is the mean pressure simulation results, the separation and attachment of shock are also simulated.

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(a)

(b) Fig. 4. (a) Instantaneous velocity (b) mean pressure of 24° 3D compression ramp simulation

Figure 5 is the wall pressure of 24° 3D compression ramp simulation. When n = 9, the separation point is at −2.63 which is 31.4% larger than the experiment result. When n = 6, the separation point is at −2.23 which is 11.5% larger than the experiment result. And when n = 9, the separation point is at −2.06 and the error become 2.6%. As can be seen from the figure, as n decreases, the turbulent intensity at the entrance increases, the length of the separation zone gradually decreases and approaches the experimental value, and the pressure platform also gradually decreases until it finally disappears.

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Fig. 5. Wall pressure of 24° 3D compression ramp simulation

4 Conclusion Hybrid LES/RANS simulations are carried out for 24° compression ramp shock/turbulent boundary layer interaction flow. The results are compared and analyzed under two boundary conditions: fixed inlet and turbulent inlet. The simulation results show that the main shock wave, separated shock wave, boundary layer separation and reattachment phenomena can be obtained. However, the length of simulated separation zone under fixed inlet condition is significantly larger than the experimental results, and the simulated results do not reflect the unsteady characteristics of the turbulent boundary layer. According to the analysis, this is because the mixing function will switch to LES mode after separating the shock wave, which greatly reduces the vortex-viscosity coefficient of the boundary layer and weakens the ability of the boundary layer to withstand the pressure gradient, and further increases the separation zone. In the turbulence inlet, with the increase of artificially added turbulence, the separation gradually decreases to the experimental value, and the pressure platform also decreases or even disappears. The results show that the IDDES hybrid model is very dependent on the turbulence of the incoming flow. This indicates that the hybrid LES/RANS simulation is sensitive to the degree of turbulence at the inlet and requires us to provide sufficient turbulence pulsation energy to resist the adverse pressure gradient. In the further study, it is necessary to establish the inlet boundary condition which can reflect the characteristics of turbulent boundary layer more accurately.

References 1. Gaitonde, D.V.: Progress in shock wave/boundary layer interactions. Prog. Aerosp. Sci. 72, 80–99 (2015)

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2. Babinsky, H., Harvey, J.K.: Shock Wave-Boundary-Layer Interactions Cambridge Aerospace Series. Cambridge University Press, Cambridge (2011) 3. Selig, M.S., et al.: Turbulence structure in a shock wave/turbulent boundary-layer interaction. AIAA J. 27(7), 862–869 (1989) 4. Settles, G., Vas, I., Bogdonoff, S.: Shock wave-turbulent boundary layer interaction at a high Reynolds number, including separation and flowfield measurements. In: 14th Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics (1976) 5. Settles, G.S., Fitzpatrick, T.J., Bogdonoff, S.M.: Detailed study of attached and separated compression corner flowfields in high Reynolds number supersonic flow. AIAA J. 17(6), 579–585 (1979) 6. Settles, G.S., Vas, I.E., Bogdonoff, S.M.: Details of a shock-separated turbulent boundary layer at a compression corner. AIAA J. 14(12), 1709–1715 (1976) 7. Smits, A.J., Muck, K.-C.: Experimental study of three shock wave/turbulent boundary layer interactions. J. Fluid Mech. 182, 291–314 (1987) 8. Ganapathisubramani, B., Clemens, N.T., Dolling, D.S.: Effects of upstream boundary layer on the unsteadiness of shock-induced separation. J. Fluid Mech. 585, 369–394 (2007) 9. Ganapathisubramani, B., Clemens, N.T., Dolling, D.S.: Low-frequency dynamics of shockinduced separation in a compression ramp interaction. J. Fluid Mech. 636, 397–425 (2009) 10. Loginov, M.S., Adams, N.A., Zheltovodov, A.A.: Large-eddy simulation of shockwave/turbulent-boundary-layer interaction. J. Fluid Mech. 565, 135–169 (2006) 11. Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994) 12. Pirozzoli, S., Grasso, F.: Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M = 2.25. Phys. Fluids 18(6), 065113 (2006) 13. Spalart, P., et al.: Comments on the feasibility of LES for winds, and on a hybrid RANS/LES approach, vol. 1, pp. 4–8 (1997) 14. Spalart, P.R., et al.: A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20(3), 181–195 (2006). https://doi.org/10.1007/s00162006-0015-0 15. Menter, F.R., Kuntz, M., Langtry, R.: Ten years of industrial experience with the SST turbulence model. Turbulence Heat Mass Transfer 4(1), 625–632 (2003) 16. Gritskevich, M.S., et al.: Development of DDES and IDDES formulations for the k-ω shear stress transport model. Flow Turbul. Combust. 88(3), 431–449 (2012)

Design and Test of an Aero-Engine Inlet Distortion Screen Facility Yaoyao Qu and Xiaoqing Qiang(B) Shanghai Jiao Tong University, Shanghai, China {yaoyao_qu,qiangxiaoqing}@sjtu.edu.cn

Abstract. To design and invent a new type of reliable inlet distortion screen facility plays an important part in the current flight compliance certification. In order to achieve the design as well as analyzing and verifying the outlet distortion flow field, this paper relied on the existing equipment of the Shanghai Jiao Tong University Aero Engine Research Institute, designed and processed a new inlet distortion screen facility. In the small wind tunnel, the facility was installed to achieve inlet distortion conditions, and 30 sets of basic meshes were selected to operate wind tunneling test under wind speed of different Mach number. Through the finishing of the test data, the experiment acquired the resistance coefficient and loss characteristics of the 30 sets of basic meshes, and summarized the test data according to its geometric parameters. Then the test selected distortion meshes from the former basic meshes, and operated followed-up wind tunneling test. The simulation achieved inlet distortion conditions. With analyzing of the data acquired by the pressure sensor, the test obtained the loss characteristic curve and the surface pressure distribution of the distortion screen facility. The results showed that the designed distortion screen facility was well simulated the flow field characteristics of different distortion angles under the Airworthiness requirements, which proves the feasibility of the method. The distortion device can also provide familiar flow field distortion assessment for the same type of aero engine. Keywords: Inlet · Distortion screen · Aerodynamic loss

1 Introduction Inlet and engine matching problem has always been one of the most important issues that restrict the development of aero engine. The flow field quality provided by the inlet passage directly affects the performance of the engine. The inlet distortion is the main factor affecting the matching of inlet and engine. As one of the most important distortion types, the total pressure distortion is mainly due to the inhalation of the fuselage boundary layer as well as the aircraft in the air-attack angle, when the air flow separates from the airway inlet and causes the uneven of the engine inlet total pressure distribution [1]. This phenomenon is inclined to induce a series of problems such as irradiation of compressor, blade fibril, stall and severely restrict the improvement of engine performance and expansion of the aircraft flight wrapper [2]. In order to evaluate this impact, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 133–146, 2023. https://doi.org/10.1007/978-981-99-0651-2_12

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a large number of inlet airway tests has been operated domestically and abroad. Engine component test (usually a compressor test) and whole-engine test, are used to analyze the performance of inlet and engine compatibility, Effect of gas total pressure distortion against the compressor and the performance of the whole machine. Inlet tests are usually carried out in the wind tunnel, generally there are two forms: one is to set a small proportion model of the inlet passage and the front bodies, and put it into a large wind tunnel, with changing of the fuselage pitch angle and side slip angle, the real distortion environment of inlet passage is simulated. The universities, air force and navy of United States and NASA laboratory have carried out a large number of airways and comprehensive wind tunnels in front of the front fuselage for different models. For example, DAVE Beale et al. proposed a direct connection turbine engine test method [3]. The other is to install a distortion generator in a small wind tunnel to achieve inlet distortion conditions, this kind of method is mainly for the design of new distortion generators and the research of outlet distortion flow characteristics, as well as the test verification programs [4]. According to the “Transportation Aircraft Airworthiness Standard” (CCAR-25-R4), “Aviation Engine Airworthiness regulations” (CCAR-33-R2), and the “Aircraft Model Qualified Approval Procedure” (AP-21-AA-2011-03-R4), The engine development process should be applied to the field of distortion test methods and in accordance with the flow field distortion assessment to the airworthiness field. With the continuous improvement of Chinese airworthiness management system, Li Zhiping et al. introduced a parallel compressor model into the airworthiness engineering field, developing aero engine stall and asthmatic airworthiness verification procedure under distortion conditions caused by different flying angles (AOA) and side wind [5, 6]. Qi Lei et al. combined pneumatic thermal basic theory and airworthiness, they developed a rapid estimation method for aero engine surge margin under multiple influencing factors [7]. However, with the advancement of Chinese large aircraft projects and its demand for airborne proof, the compliance verification method for aerospace surge and stall is not sufficient, which leaves an urgent need to carry out further research work.

2 Test Device and Method For the inlet total pressure experiments of the compressor and the whole machine, the engine machine test bench and the compressor test bench are generally connected to the air supply pipeline [8]. In the import or internal of the air supply pipe, there are installed with distortion generators such as filter mesh, simulation plate and the support plate [4, 9]. A series of tests were performed in AIP (Aerodynamic Interface Plane) and other cross-section, in order to analyze the total pressure recovery and distortion of AIP and the influence of inlet total pressure distortion against the stability of compressor and engine. In the inlet total pressure distortion test, the probe comb can be used to measure the steady and dynamic total pressure and speed field, which can draw distortion maps of total pressure, static pressure, Mach number and turbulence. These distortion maps under relative methods can visually show characteristics of distortion flow field [10].

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Based on the design of the classic airfoil, this test analyzes the numerical characteristics under different distortion screen angles, which gives the pressure loss test results. The support plate used a size ratio as 1 to 10, and selected 8 blade of 250 mm in diameter. The plate was fixed to the inlet low speed stream field. For the basic meshes covering the entire section, the test selected materials of stainless steel, different wire diameters and hole diameters, and the distortion screen gives a symmetrical, where there is a certain angle design to simulate the actual distortion flow field. 2.1 Test Device The wind source equipment used in this test is shown in Fig. 1. The gas source adopted by the test is provided by 2 Roots Blowers with power of 500 kW and 132 kW, and the default increasing pressure is 68.6 kPa. The power of blowers is determined according to the desired inlet total pressure. The fan catheter export is divided into 2 channels, each connected to the expansion segment and the regulator box, and the regulator has a diameter of ϕ800 mm, with 3-channel damping net and 1 honeycomb rectifier grille. This test uses the pipeline below, which is connected to the distortion screen facility after the regulator box. The pressure collecting portion contains 8 PSI 9116 acquisition modules with a total of 128 stable pressure channels.

Fig. 1. Top view of wind source equipment

The distortion screen facility is shown in Fig. 2. During the test, the basic mesh and the distortion screen can be replaced at the inlet. The profile of cross-sectional view is shown in Fig. 3. In order to reduce the influence of the branch stream, there is a pilot cap in front of the plate. The support plate is used to provide support for the distortion screen, to prevent it from deformed under high-speed airflow. It consists of eight brackets, which are connected at the center, as well as connected to the outer wall at the casing. The branch section is rectangular, with 4 mm support thickness and 45 mm for the length. The test preparation has correlated numerical simulation on the strength of the support plate, to ensure that the support rack intensity meets the requirements in the actual test.

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Fig. 2. Overall view of distortion screen tester

Fig. 3. Sectional view of distortion screen tester

This test totally consists of 3 parts: (1) Loss characteristics test for the support plate. (Excluding the basic mesh and distortion screen); (2) Basic mesh loss characteristics test. (Total of 30 sets of different specifications); (3) According to the selected basic mesh and distortion screen, the distortion screen loss characteristic test is performed according to the design angle.

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In the test, after completing the working conditions of a single test object in different Mach numbers, disassemble and change the meshes and complete the follow-up test without cutting down the power of wind tunnel. 2.2 Probe Settings Commonly used distortion generator probe setting includes a 40-probe scorpion for measuring the total pressure distortion of steady state and time-varying state [3]. Usually, 8 thorny scorpions put the probe in 5 rings [11]. In this test, because the angle of probe can be adjusted by physically rotating the probe relative to the distortion screen, so only a row of 9 points total pressure comb probes was set. In the test, the inlet total pressure was measured in the regulator section. The probe used was a single-point sleeve total pressure probe, which has a good direction sensitivity. The inlet total temperature was also measured in the regulator section, the temperature probe employed the PT100 thermal resistance with an accuracy of ±0.5 °C. In the barrel wall surface in front of the foundation, 1 mm small hole is opened to measure the wall static pressure. In the tester outlet, the radial direction distribution is measured by 9point total pressure comb probe. The probe is designed according to the equipped area to ensure the average accuracy of the test data. Also, the comb probe can be rotated circumferentially by a planar bearing to collect a total pressure distribution of different phases. 2.3 Basic Mesh Selection Table 1 lists the data of 30 sets designed and processed basic meshes. For different wire diameters, the void ratios are evenly changed. Between meshes of different wire diameter, the void ratio is also kept similar, in order to analyzing the lateral contrast. 2.4 Numerical Analysis Formula for Loss Characteristics The inlet drag coefficient ω and the total pressure recovery coefficient σ ∗ are defined as follows: σ∗ =

∗ Pout ∗ Pin

(1)

∗ is the average total pressure in the outlet section of inlet, and P ∗ is the total Pout in pressure of the coming free flow.

ω=

∗ − P∗ Pin out ∗ −P Pin in

Pin is the static pressure at the inlet pipeline.

(2)

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Set Diameter (mm) Mesh length (mm) Hole length (mm) Void ratio Clogging degree 1

3.0

40.0

37.0

0.8556

0.1444

2

3.0

35.0

32.0

0.8359

0.1641

3

3.0

30.0

27.0

0.8100

0.1900

4

3.0

25.0

22.0

0.7744

0.2256

5

3.0

23.0

20.0

0.7561

0.2439

6

3.0

20.0

17.0

0.7225

0.2775

7

3.0

18.0

15.0

0.6944

0.3056

8

2.0

28.0

26.0

0.8622

0.1378

9

2.0

25.0

23.0

0.8464

0.1536

10

2.0

22.5

20.0

0.8301

0.1699

11

2.0

20.0

18.0

0.8100

0.1900

12

2.0

17.5

15.0

0.7845

0.2155

13

2.0

15.0

13.0

0.7511

0.2489

14

2.0

12.5

10.5

0.7056

0.2944

15

2.0

10.0

8.0

0.6400

0.3600

16

1.7

19.0

17.3

0.8291

0.1709

17

1.5

25.0

23.5

0.8836

0.1164

18

1.5

21.5

20.0

0.8653

0.1347

19

1.5

17.5

16.0

0.8359

0.1641

20

1.5

15.0

13.5

0.8100

0.1900

21

1.5

12.0

10.5

0.7656

0.2344

22

1.5

10.5

9.0

0.7347

0.2653

23

1.5

8.0

6.5

0.6602

0.3398

24

1.0

13.0

12.0

0.8521

0.1479

25

1.0

11.0

10.0

0.8264

0.1736

26

1.0

9.0

8.0

0.7901

0.2099

27

1.0

7.0

6.0

0.7347

0.2653

28

1.0

5.0

4.0

0.6400

0.3600

29

0.8

10.0

9.2

0.8464

0.1536

30

0.8

6.0

5.2

0.7511

0.2489

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3 Test and Analysis of Basic Screen In the measuring of basic meshes, the total rotation angle is 1 and 4 circumference (90°) according to the symmetry principle. For each step of rotation, rotating angle  = 5°, which leads to the total data points as 19. The sensor data acquisition time is 5 s. In each wind tunnel test, record the total pressure and wall static pressure both at inlet and outlet.

Fig. 4. Overall performance of the basic mesh

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Fig. 4. (continued)

After the collected data were processed, the resistance coefficient of the basic mesh and the total pressure recovery coefficient of different wire diameters were drawn as shown in Fig. 4 (due to too little data of the same type of wire mesh, the results of 1.7 mm wire diameter were not drawn out). As for the same wire diameter, it can be seen clearly in fitting map of different Mach number and clogging degree that, with the increase of Mach number, the resistance coefficient is constantly elevated. Especially when the clogging degree gets lower, the resistance coefficient rises faster and has an indexed rising. When the clogging is less than 0.15, the resistance coefficient of all the different wires have exceeded 1before Mach number reaches 0.35 and when the clogging degree is higher than 0.3, the resistance coefficient of the test wire mesh is slowly approaching to 0.75 with Mach number reaches 0.5. And the larger the wire diameter, the faster the increase of resistance coefficient. For the basic mesh with same wire diameter and different Mach number and clogging degree, the fitting curve is distinguished in the Fig. 4, which shows the spread distribution of the base wire mesh is more typical. As the number of Mach is increased, the low energy fluid in the nacelle inlet is constantly accumulating, causing the AIP partial total pressure recovery coefficient to decrease, for the basic mesh has wire diameter less than 1.5 mm, when the clogging is close or greater than 0.25, the total pressure recovery coefficient decreases more obvious.

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4 Test and Analysis of Distortion Screen In order to better reflect the test results of different grids, the test selected 2 # basic mesh as the foundation of the distortion screen, and the other 5 sets of wire mesh as a subsequent distortion screen, this choice is based on the different void ratio and wire diameter, for the purpose of obtaining a more average, general test data. The selected mesh numbers are 11 #, 26 #, 27 #, 28 #, 29 #. Select the test method and measure 2 + 11 #, 2 + 26 #, 2 + 27 #, 2 + 28 #, 2 + 29 #, a total of five sets of distortion screen data. This step is similar to the method of the third chapter, but more details. Since the angle of the probe can be changed by manually rotating the airway device, we measured distortion data at distortion screen angle of 90°, 120°, 150°, 180°, and 360°. The specific test method is as follows. The starting point of the test is the symmetrical center in the inlet (as angle 0°), each step the rotation angle 1 = 5°, when approaching the edge of the distortion screen, change rotation angle 2 = 15° until the circumference 180°. The sensor data acquisition time is 5 s. (360° distortion screen only measured 1and4 round surface, each step the rotation angle 1 = 5°). Total four sets of data in Mach number 0.2, 0.3, 0.4, 0.5 each time. Figure 5 shows the actual map of the installation angle.

Fig. 5. Distortion screen installation angle

The total pressure recovery coefficient and resistance coefficient of the resulting data were consolidated. Figure 6 draws fitting map of loss characteristics for distortion screen 26 # in different angles and Mach numbers.

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Fig. 6. Overall performance of the distortion screen (26#)

It can be seen from Fig. 6, under the same Mach number, with the increase of the angle of the distortion degree, the resistance coefficient keeps rising. The airflow in the wind tunnel gradually blocks. When the angle of the distortion degree is 360°, the Mach number of Roots Blowers could not increase to 0.5. To this end, we have chosen the blow data of 0.4 Mach for subsequent analyzing of loss characteristics in the loop. For easy viewing, Fig. 7 and 8 gives the resistance coefficient cloud map and total pressure recovery coefficient cloud map of distortion screen 26 # under the same Mach number (which is 0.4), but with different distortion angles. The experiment uses simple, fixed geometric elements to explore the distortions that result from changes in wedge angle, porosity, Mach number, and Reynolds number. Elements change geometric parameters through physical exchange. During data collection, only the data within a 180° range was collected according to the principle of symmetry, and mirroring was performed when the cloud map was drawn. Since the distortion screen is supported by 8 blades, the influence of the strut can be clearly seen from Fig. 7 and 8. At the same flight Mach number, with the increase of the screen angle, the low-energy fluid inside the nacelle air inlet keeps accumulating, resulting in an increase in the local drag coefficient of the AIP and a decrease in the total pressure recovery coefficient, resulting in a “crescent-shaped” distortion zone in the AIP, and the scope and magnitude continue to increase. The value of the total pressure loss coefficient is lower at the position closer to the center of symmetry, and the drag coefficient is opposite. The extrema of the two appear at the edge of the torus where the mesh is arranged. At a flight Mach number of 0.4, the distortion region exhibited by AIP is not asymmetric, but has a certain circumferential movement in the clockwise direction.

Design and Test of an Aero-Engine Inlet Distortion Screen Facility

Fig. 7. Cloud map of drag coefficient (#26, Ma = 0.4)

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Fig. 8. Cloud map of total pressure recovery coefficient (#26, Ma = 0.4)

5 Conclusion In this paper, the design of the distortion screen facility combined the distortion test method used in the engine stability assessment and the engineering practice in the airworthiness compliance verification. And the aerodynamic test model is designed based on the similar principle to verify its reliability. By corresponding relationship between

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engine surge margin and different mesh angles and distortion degree, a method for verifying the airworthiness compliance of engine surge and stall characteristics under intake distortion conditions is developed. By comparing the aerodynamic design scheme of the distortion screen device and the performance parameters and flow field characteristics of the inlet under different mesh angles obtained from experiments, the results show that the designed distortion screen device can better simulate the distorted flow under the conditions of different angles of attack in the climbing stage. The characteristics of the flow field prove the feasibility of the method. The distortion screen facility can provide a reference for the evaluation of flow field distortion for the same type of engine. In this test, the variation law and corresponding relationship of the inlet loss characteristics of the different distortion angle schemes are obtained, so as to verify the compliance of the fan, compressor or engine to the surge and stall characteristics in CCAR-33-R2 under the distortion condition [12]. In the task stage of aircraft type certification, the airworthiness regulations of aero-engines can be taken into account when evaluating the flow field distortion during the development and modification of the same type of engine and components, and then in the realization of engine or compression on the basis of the stability evaluation of the components, the compliance with the surge and stall airworthiness clause can be met at the same time, which can provide methods and data reference for later verification of high-altitude compliance, flight test verification, and guarantee for passing the final type certification.

References 1. Yusoof, M.S., Sivapragasam, M., Deshpande, M.: Strip distortion generator for simulating inlet flow distortion in gas turbine engine ground test facilities. Propul. Power Res. 5(4), 287–301 (2016) 2. Lee, K., et al.: Inlet distortion test with gas turbine engine in the altitude engine test facility. In: 27th AIAA Aerodynamic Measurement Technology and Ground Testing Conference (2010) 3. Beale, D., et al.: Demonstration of a transient total pressure distortion generator for simulating aircraft inlet distortion in turbine engine ground tests. In: Turbo Expo: Power for Land, Sea, and Air (2007) 4. Lucas, J.R.: Effect of BLI-type inlet distortion on turbofan engine performance. Virginia Tech. (2013) 5. 李志平等: 侧风影响下航空发动机失速 and 喘振适航审定方法. 航空动力学报 35(07), 1549–1558 (2020) 6. 李志平, 王孟琦: 进气畸变下航空发动机失速 and 喘振适航审定方法. 航空学报 36(09), 2947–2957 (2015) 7. 綦蕾等: 航空发动机适航审定喘振与失速影响因素. 航空动力学报 35(08), 1724–1734 (2020) 8. Arshad, A., et al.: Effects of inlet radial distortion on the type of stall precursor in low-speed axial compressor. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 232(1), 55–67 (2018) 9. 杜军, 韩伟: 进气压力畸变试验中面平均紊流度的计算. 燃气涡轮试验与研究 32(03), 53–57 (2019) 10. 钟亚飞等: 航空发动机进气总压畸变地面试验测试技术进展. 航空发动机 46(06), 62–77 (2020)

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11. Vouros, S.V., et al.: Effects of rotor-speed-ratio and crosswind inlet distortion on off-design performance of contra-rotating propelling unit. In: Turbo Expo: Power for Land, Sea, and Air. American Society of Mechanical Engineers (2016) 12. 郭重佳等: 畸变条件下航空发动机喘振 and 失速适航符合性方法. 航空动力学报 1–13 (2022)

Analysis of Composite Laminates Strength with Random Deviation Variables Y. Y. Xu, W. B. Fan, Y. L. Hu, Y. Yu(B) , B. Y. Yu, and W. Zhang Aerospace Structure Research Center, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China {xyy_654321,fwbzyx,yilehu,yuyin,boyi98224, zifengzhang156}@sjtu.edu.cn

Abstract. Due to the large dispersion of composite materials, in order to obtain statistical value of the strength of composite laminates, the current method relies on a large number of experiments, which requires extremely high labor, time, and costs. This paper proposes a new parametric modeling method to cover the effects of random deviation variables (material properties, layup angle and laminates thickness) on strength of composite laminates. The Monte-Carlo method is used to generate a large number of laminates models with random variation of composite material properties. The model is established and revised by tensile and compression tests of 0° and 90° laminates. Then the method is validated by open-hole compression tests of composite laminates with four different layers. The errors of average and coefficient of variation between simulation and test results are compared. The modeling method with random deviation variables in this paper can be used to reduce the allowable value test of composite laminates. Keywords: Composite laminates · Normal distribution · Compression · Dispersion

1 Introduction The composite material has a series of advantages such as high specific strength, high specific stiffness, corrosion resistance, fatigue resistance, etc., which can meet the special and performance requirements of aerospace technology. However, one of the disadvantages of composite materials is the large dispersion. Manufacturing process, operating environment, material batch, defect, load and so on will affect the mechanical properties of composite structures. Compared with metal structures, composite structures lack mature analysis methods and sufficient experience in design and application, and rely more on multi-level building block verification tests than metal structures. In the process of building block verification, a large number of component-level tests are needed, and the number of tests is particularly large (tens of thousands) and of various types. The simulation method can shorten the development period and reduce the test cost, but the traditional simulation method input fixed parameters, which cannot accurately simulate the real situation caused by the dispersion of composite materials. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 147–169, 2023. https://doi.org/10.1007/978-981-99-0651-2_13

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In this paper, a new calculation method is proposed. Using computer simulation technology, it is considered that the change of material properties of composite singlelaminate plate is in normal distribution. Then Monte-Carlo algorithm is used to generate multiple simulation samples to study the results and dispersion of composite material test performance. Change of material properties of composite single-laminate consider Angle of the laminate and laminate thickness, transverse tensile elastic modulus, transverse compressive elastic modulus, the longitudinal tensile elastic modulus, longitudinal compressive elastic modulus, Poisson’s ratio, shear modulus and transverse tensile strength, transverse compression strength, longitudinal tensile strength, longitudinal compression strength, transverse shear strength, the longitudinal shear strength. The simulation sample of this paper is based on the two-dimensional Hashin [1– 4] damage evolution theory, using the secondary development function of ABAQUS software, To generate a set of experiment used for automatic calculation of composite material allowable value (Unnotched tension/compression and Open– hole compression) calculation models, automatically generated by the input information of multiple laminate structure of the calculations of the dispersion simulation samples. Finally, the statistical data of material properties are obtained by using mathematical statistics method.

2 Hashin Criteria The simulation samples in this paper are based on the two-dimensional Hashin damage evolution theory, which is expressed as follows. Fiber tensile failure:   2  τ12 2 σ1 + 1 σ1 0 (1) Xt S12 Fiber compression fracture: 

σ1 Xc

2 1 σ1 0

(2)

Matrix tensile or shear failure: 

σ2 Y1

2

 +

τ12 S12

2 1 σ2 0

(3)

1 σ2 0

(4)

Matrix compression or shear failure: 

σ2 Ye

2

 +

τ12 S12

2

where, Xt and Xc are longitudinal tensile strength and longitudinal compressive strength of laminates; Yt and Yc are transverse tensile strength and transverse compressive strength of laminates; S12 is the shear strength in the 1–2 direction.

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3 The Establishment of Simulation Calculation Models The Object Structure of Abaqus Mdb (Model Database) is shown in Fig. 1. In this paper, the process of establishing the simulation calculation models using the secondary development function of ABAQUS is shown in Fig. 2, in which the steps of generating the discrete simulation calculation models include: 1) establishing the composite laminates geometric models and fitting the laminates to facilitate the subsequent mesh optimization and improve the accuracy of simulation calculation results; 2) Divide the mesh. If there are round holes in the models, optimize the mesh at round holes with bias ratio function and specify the cell type; 3) Create materials and assign material properties, and take Hashin failure criterion as the failure criterion of materials; 4) Create layup information; 5) Create an analysis step and select the required output variables. This paper takes the failure load of the composite laminates specimens as the research object; 6) Add the load, combine the load loading point with the side of the specimens using the MPC function in Constraint, and select Beam as the MPC type; 7) Submit analysis, which can be submitted continuously through batch processing. Experiments in this paper, calculation of composite material allowable value (Unnotched tension/compression and Open–hole compression) simulation of the models reference standard are shown in Table 1.Generally, when conducting the allowable value test, N1 = Nb × Ncf × Nn × Nc × NL is used for the number of test parts at the same temperature (Nb is the batch of material, Ncf is the batch of curing furnace, Nn refers to the number of samples, Nc is the number of different working conditions, NL is the number of laminates), a total of N1 samples. In other words, for the same working condition, the number of test samples corresponding to each laminates at the same temperature should be N2 = Nb × Ncf × Nn , N2 samples in total. Embodied in the change of angle of the laminate and laminate thickness, transverse tensile elastic modulus, transverse compressive elastic modulus, the longitudinal tensile elastic modulus, longitudinal compressive elastic modulus, Poisson’s ratio, shear modulus and transverse tensile strength, transverse compression strength, longitudinal tensile strength, longitudinal compression strength, transverse shear strength, the longitudinal shear strength [5–18]. In the process of Monte-Carlo algorithm to generate multiple simulation samples, every change of random variables are independent, performance in the simulation calculation models, random offset variables each specimen is different, and the performance in the program, which corresponds to each sample of each input parameter on the single conducted a normal change about the mean and standard deviation, Also in order to simulate the real test, we considered the laminate in the random offset variables angle error, it is also subject to its mean and standard deviation of the normal change, but different from the rest of the single plate material parameters, laminate angle in the process of actual production and processing belongs to the maximum offset controllable parameters, In this paper, the maximum offset angle of single-laminate plate is 0.5°, that is, the maximum offset threshold is added to the program. When the difference angle between the value after normal change and the ideal value is greater than 0.5°, the program will generate a new value with a difference Angle less than 0.5° from the ideal value for the calculation of the simulation models.

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Fig. 1. Mdb (model database) object structure

Fig. 2. The process of establish the simulation calculation models Table 1. List of allowable value tests for composite materials. Case

Test item

Abbreviation

Reference

1

0° tensile test

LTM

ASTMD3039

2

0° compression test

LCM

SACMASRM1

3

90° tensile test

TTM

ASTMD3039

4

90° compression test

TCM

SACMASRM1

5

Open-hole compression test

OHC

ASTM D6484

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In this paper, the function of RSG (Really Simple GUI) Dialog Builder of Abaqus is adopted, and the Abaqus Plug-in is developed by Python. Through the plug-in, the parameters used in the models can be directly input, and the working module of Abaqus is used. Generate a large number of computational simulation models automatically.

4 Sample and Test 4.1 Unnotched Tension/Compression For the Unnotched tension/compression test, when the lamina orientation angle is 0°, the tensile strength is Xt , the compressive strength is Xc . When the lamina orientation angle is 90°, the tensile strength is Yt , the compressive strength is Yc . Material A is selected from the references to process the composite laminates. Make rectangular stretching and compression samples in the direction of 0° and 90° according to ASTMD3039 and SACMASRM1. The properties of material A are shown in Table 2. The Coefficient of variation (CV) in the table is the ratio of the standard deviation of the sample to the mean value The dimensions of test parts are shown in Fig. 3 and Table 3. Table 2. Material properties Material properties

Value

Coefficient of variation /%

E1t/MPa

169000

5.7

E2t/MPa

7100

4.2

E1c/MPa

153000

3.2

E2c/MPa

8295

2.7

Nu12/MPa

0.32

5.0

G12/MPa

4370

3.3

G13/MPa

4370

3.3

G23 /MPa

3428

3.3

XT/MPa

2737

3.5

XC/MPa

1602

2.2

YT/MPa

86.4

4.3

YC/MPa

212.8

5.0

S12/MPa

111.9

1.7

S13/MPa

111.9

1.7

The plug-in interface of Unnotched Tension/Compression is shown in Fig. 4. After parameters are entered in the plug-in, the analysis model is shown in Fig. 5.

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Fig. 3. Unnotched tension/compression drawing Table 3. Dimensions of specimens Laminates

Layup

L/mm

W/mm

t/mm

A-1-A-10

(0)6

250

15

1.11

B-1-B-10

(0)6

80

12.7

1.11

C-1-C-10

(90)12

175

D-1-D-10

(90)12

80

25

2.22

12.7

2.22

Fig. 4. Unnotched tension/compression plug-in operation interface

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Fig. 5. Unnotched tension/compression model

4.1.1 0° Tensile Simulation Calculation Model A tensile simulation calculation model with A layup angle of 0° for specimens was established. For A total of 10 specimens from A-1 to A-10, the comparison of the material parameters in the simulation calculation model with the original material parameters is shown in Table 4.The third column in the form of Coefficient of variation of Original material properties is measured by experiment, form the fifth column shows that the simulation calculation model of material parameters is a certain discreteness, It is through Original material properties after about its mean and standard deviation of normal after the change, can real actual simulation test of the discrete situation. The simulation calculation model is submitted and compared with the test results. Figure 6 shows the comparison between the simulation calculation results and the test Table 4. Material properties of A1 ~ A10 Material properties

Original material properties

The average of input after processing

Error

Material properties

CV/%

The average of simulation model

CV/%

Difference/%

CV/%

E1/MPa

169000

5.7%

168014.23

5.40%

−0.58%

−0.3%

E2/MPa

7100

4.2%

7144.84

3.44%

0.63%

−0.8%

Nu12/MPa

0.32

5.0%

0.32

4.20%

0.43%

−0.8%

G12/MPa

4370

3.3%

4376.35

2.43%

0.15%

−0.9%

G13/MPa

4370

3.3%

4349.67

3.46%

−0.47%

0.2%

G23/MPa

3428

3.3%

3383.70

5.52%

−1.29%

2.2%

XT/MPa

2737

3.5%

2800.31

3.73%

2.31%

0.2%

XC/MPa

1602

2.2%

1640.77

2.22%

2.42%

0.0%

YT/MPa

86.4

4.3%

86.41

4.12%

0.01%

−0.2%

YC/MPa

212.8

5.0%

213.98

3.02%

0.55%

−2.0%

S12/MPa

111.9

1.7%

114.21

1.53%

2.07%

−0.2%

S13/MPa

111.9

1.7%

112.97

1.25%

0.96%

−0.4%

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results. The horizontal lines in the figure are the average of the test results, and the comparison results are shown in Table 5. The tensile simulation calculation model established by this calculation method measured an error of −2.7% in the mean value of A and B, and an error of 0.5% in the dispersion coefficient.

Fig. 6. 0°Tensile simulation calculation model Table 5. Comparison of simulation and test results Simulation

Test

The average value (N) CV/%

The average value (N) CV/% The average value CV /%

2663.85

4.59% 2737

Error 4.1%

−2.7%

0.5%

4.1.2 0° Compressive Simulation Calculation Model A compression simulation calculation model with a layup angle of 0° was established for the specimens, and compared with the test results. For B-1 to B-10 specimens, the comparison between the material parameters in the simulation calculation model and the original material parameters is shown in Table 6. The simulation calculation model is submitted and compared with the test results. Figure 7 shows the comparison between the simulation calculation results and the test

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Table 6. Material properties of B1 ~ B10 Material properties

Original material properties

The average of input after processing

Error

Material properties

CV/%

The average of simulation model

CV/%

Difference /%

CV/%

E1/MPa

153000

3.2%

139261.19

2.75%

−8.98%

−0.5%

E2/MPa

8295

2.7%

9921.41

6.19%

19.61%

3.5%

Nu12/MPa

0.32

5.0%

0.32

3.62%

−0.60%

−1.4%

G12/MPa

4370

3.3%

4371.56

3.56%

0.04%

0.3%

G13/MPa

4370

3.3%

4415.23

3.86%

1.03%

0.6%

G23/MPa

3428

3.3%

3447.43

3.76%

0.57%

0.5%

XT/MPa

2737

3.5%

2754.50

5.28%

0.64%

1.8%

XC/MPa

1602

2.2%

1639.69

2.54%

2.35%

0.3%

YT/MPa

86.4

4.3%

90.68

−1.75%

4.96%

−6.1%

YC/MPa

212.8

5.0%

214.66

4.24%

0.88%

−0.8%

S12/MPa

111.9

1.7%

111.81

1.84%

-0.08%

0.1%

S13/MPa

111.9

1.7%

111.99

0.93%

0.08%

−0.8%

results. The horizontal lines in the figure are the average of the test results, and the comparison results are shown in Table 7. The tensile simulation calculation model established by this calculation method measured an error of −1.5% in the mean value of A and B, and an error of −0.1% in the dispersion coefficient. Table 7. Comparison of simulation and test results Simulation

Test

The average value (N) CV/% 1577.81

Error

The average value (N) CV/% The average value CV/%

2.12% 1602

2.2%

−1.5%

−0.1%

4.1.3 90° Tensile Simulation Calculation Model A tensile simulation calculation model with a layup angle of 90° was established for the specimens and compared with the test results. For C-1 to C-10 specimens, the comparison between the material parameters in the simulation calculation model and the original material parameters is shown in Table 8. The simulation calculation model is submitted and compared with the test results. Figure 8 shows the comparison between the simulation calculation results and the test

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Fig. 7. 0° compressive simulation calculation model

results. The horizontal lines in the figure are the average of the test results, and the comparison results are shown in Table 9. The tensile simulation calculation model established by this calculation method measured an error of −6.9% in the mean value of A and B, and an error of −0.8% in the dispersion coefficient.

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Table 8. Material properties of C1 ~ C10 Material properties

Original material properties

The average of input after processing

Error

Material properties

CV/%

The average of simulation model

CV/%

Difference/%

CV/%

E1/MPa

169000

5.7%

168954.29

6.66%

−0.03%

1.0%

E2/MPa

7100

4.2%

6995.41

4.24%

−1.47%

0.0%

Nu12/MPa

0.32

5.0%

0.32

7.99%

0.22%

3.0%

G12/MPa

4370

3.3%

4352.28

3.07%

−0.41%

−0.2%

G13/MPa

4370

3.3%

4369.60

2.99%

−0.01%

−0.3%

G23/MPa

3428

3.3%

3433.76

3.20%

0.17%

−0.1%

XT/MPa

2737

3.5%

2737.62

2.12%

0.02%

−1.4%

XC/MPa

1602

2.2%

1610.08

1.38%

0.50%

−0.8%

YT/MPa

86.4

4.3%

92.18

3.63%

6.69%

−0.7%

YC/MPa

212.8

5.0%

208.99

6.17%

−1.79%

1.2%

S12/MPa

111.9

1.7%

111.71

1.44%

−0.17%

−0.3%

S13/MPa

111.9

1.7%

113.47

1.39%

1.40%

−0.3%

Fig. 8. 90° tensile simulation calculation model

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Simulation

Test

The average value (N) CV/%

The average value (N) CV/% The average value CV/%

98.51

Error

2.84% 92.18

3.6%

6.9%

−0.8%

4.1.4 90° Compressive Simulation Calculation Model A compressive simulation calculation model with a layup angle of 90° was established for the specimens, and compared with the test results. For D-1 to D-10 specimens, the comparison between the material parameters in the simulation calculation model and the original material parameters is shown in Table 10. Table 10. Material properties of D1 ~ D10 Material properties

Original material properties

The average of input after processing

Error

Material properties

CV/%

The average of simulation model

CV/%

Difference /%

CV/%

E1/MPa

153000

3.2%

140711.87

2.85%

−8.03%

−0.3%

E2/MPa

8295

2.7%

10133.05

7.99%

22.16%

5.3%

Nu12/MPa

0.32

5.0%

0.32

4.89%

−0.08%

−0.1%

G12/MPa

4370

3.3%

4382.82

3.14%

0.29%

−0.2%

G13/MPa

4370

3.3%

4345.43

3.26%

−0.56%

0.0%

G23/MPa

3428

3.3%

3401.99

4.27%

−0.76%

1.0%

XT/MPa

2737

3.5%

2727.23

3.60%

−0.36%

0.1%

XC/MPa

1602

2.2%

1559.64

2.24%

−2.64%

0.0%

YT/MPa

86.4

4.3%

87.69

−0.42%

1.49%

−4.7%

YC/MPa

212.8

5.0%

213.64

6.16%

0.39%

1.2%

S12/MPa

111.9

1.7%

111.54

0.98%

−0.32%

−0.7%

S13 /MPa

111.9

1.7%

111.42

1.75%

−0.43%

0.1%

The simulation calculation model is submitted and compared with the test results. Figure 9 shows the comparison between the simulation calculation results and the test results. The horizontal lines in the figure are the average of the test results, and the comparison results are shown in Table 11. The tensile simulation calculation model established by this calculation method measured an error of −1.6% in the mean value of A and B, and an error of 1.1% in the dispersion coefficient.

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Fig. 9. 90° Compressive simulation calculation model

Table 11. Comparison of simulation and test results Simulation

Test

The average value (N) CV/%

The average value (N) CV/% The average value CV/%

209.44

6.05% 212.8

Error 5.0%

−1.6%

1.1%

Is the above four kinds of working condition, it can be concluded that: in the case of four Unnotched tension/compression, this algorithm can be used to simulate the real situation of test, and relatively accurate results are obtained. 4.2 Open-Hole Compression A composite laminate, with four layup A, B, C and D, was selected to make A rectangular compression sample according to ASTMD6484. The plug-in interface of this working condition is shown in Fig. 10. After parameters are input in the plug-in, the specimens obtained after grid partition are shown in Fig. 11.

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Fig. 10. Open-hole compression Plug-in operation interface

Fig. 11. Open-hole compression mesh model

As the research sample sizes during the process of sampling the results, the influence of the mesh fineness under the same conditions, by Open-hole compression simulation calculation model based on random deviation variables of laminates A, B, C, D, respectively study sample sizes of 5, 10 and 20 respectively, the statistical results of CV, the calculation results are obtained as shown in Table 12.

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Table 12. Comparison of simulation and test results Laminates

Simulation result (N)

Test result (N)

A

48748

43008

A

48261

A

48139

B

61846

B

60713

B

60851

C

52670

C

51917

C

51900

D

48354

D

47545

D

47651

1.98%

62023

53177

46727

Error

CV of simulation

CV of test

Error

Sample sizes

13.35%

5.06%

10.64%

−5.58%

5

12.21%

5.08%

10.64%

−5.56%

10

11.93%

5.01%

10.64%

−5.63%

20

−0.29%

3.80%

7.31%

−3.51%

5

−2.11%

4.42%

7.31%

−2.89%

10

−1.89%

4.56%

7.31%

−2.75%

20

−0.95%

3.07%

8.49%

−5.42%

5

−2.37%

3.17%

8.49%

−5.32%

10

−2.40%

3.16%

8.49%

−5.33%

20

3.48%

9.01%

15.75%

−6.74%

5

1.75%

8.99%

15.75%

−6.76%

10

8.97%

15.75%

−6.78%

20

In order to study the influence of mesh fineness on the results, under the condition that the number of samples is 10, we have established three simulation calculation models of mesh fineness of different degrees for each layup, and the calculation results are shown in Table 13. Table 13. Comparison of simulation and test results Laminates

Simulation result (N)

Test result (N)

A

54663

43008

A

48261

A

43492

B

65546

B B C

56447

C C D

53166

D D

Error

CV of simulation

CV of test

Error

Mesh fineness

27.10%

5.39%

10.64%

−5.25%

Fine

12.21%

5.08%

10.64%

−5.56%

Middle

1.12%

5.29%

10.64%

−5.35%

Rough

5.68%

5.97%

7.31%

−1.34%

FIne

60713

−2.11%

4.42%

7.31%

−2.89%

middle

58031

−6.44%

4.45%

7.31%

−2.86%

Rough

6.15%

3.07%

8.49%

−5.42%

Fine

51917

−2.37%

3.17%

8.49%

−5.32%

Middle

47608

−10.47%

3.18%

8.49%

−5.31%

Rough

13.78%

9.21%

15.75%

−6.54%

Fine

47545

1.75%

8.99%

15.75%

−6.76%

Middle

43310

−7.31%

7.29%

15.75%

−8.46%

Rough

62023

53177

46727

According to the results, the accuracy of middle mesh is the highest for A, B, C and D layup with different precision. For different sampling methods with the same mesh

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precision, the error of CV changes little more. For different mesh accuracies with the same sample number, the same result can be obtained. So mesh fineness and sampling method have limited influence on the error of Coefficient of variation. When considering the discreteness of thickness, the thickness variances of A, B, C and D can be obtained by measuring the specimens, and the variances represent the total error of the composite laminates, and the variances of single laminate can be calculated by the transfer formula of error. As shown in Eq. (5). S 2 = n × Sc2

(5)

where parameter S is the variance of composite laminates thickness, n is the number of laminate, Sc is the variance of composite single laminate thickness Control group 1 and control group 2 were added and compared with the results by the error transfer formula. Control group 1: The Variance of composite laminate thickness is directly equal to Variance of composite laminates thickness without calculation in Eq. (5). Control group 2: Laminates thickness is discretized by the measured Variance of composite laminate thickness and each laminate thickness of laminates is considered to be the same. The calculation results of control group 1 and control group 2 are shown in Table 14 and Table 15. Table 14. The control group 1 Laminates

Simulation result (N)

Test result (N)

Error

CV of simulation

A

68113

63098

7.95%

4.16%

B

40759

41177

−1.02%

2.97%

C

66630

71655

−7.01%

2.33%

D

56240

57675

−2.49%

9.81%

CV of s

Error

Sample sizes

10.64%

−6.48%

10

7.31%

−4.34%

10

8.49%

−6.16%

10

15.75%

−5.94%

10

Table 15. The control group 2 Laminates Simulation Test result Error result (N) (N)

CV of CV of test Error simulation

A

67691

63098

7.28%

5.10%

B

40599

41177

C

66445

D

59352

Sample sizes

10.64%

−5.54% 10

−1.40% 4.07%

7.31%

−3.24% 10

71655

−7.27% 3.11%

8.49%

−5.38% 10

57675

2.91%

15.75%

−0.18% 10

15.57%

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After Variance of composite single laminate thickness is added, the calculation results are shown in Table 16 and Table 17. Figures 12, 13, 14, and 15 shows the hash in failure in the damaged area. Displacement load curve of middle mesh fineness are shown in Figs. 16, 17, 18 and 19. Table 16. Dispersion of sample thickness Laminates CV of laminates thickness CV of laminates thickness Error of test /% of simulation /%

Sample sizes

A

5.18%

5.11%

0.07%

10

B

2.57%

2.59%

−0.02% 10

C

2.83%

2.95%

−0.12% 10

D

15.58%

15.64%

−0.06% 10

A

5.18%

5.70%

−0.52% 20

B

2.57%

2.58%

−0.01% 20

C

2.83%

2.66%

0.17%

D

15.58%

17.07%

−1.49% 20

A

5.18%

5.26%

−0.08% 30

B

2.57%

2.66%

−0.09% 30

C

2.83%

2.67%

0.17%

D

15.58%

16.91%

−1.33% 30

20

30

Where, Xt and Xc are longitudinal tensile strength and longitudinal compressive strength of laminates; Yt and Yc are transverse tensile strength and transverse compressive strength of laminates; S12 is the shear strength in the direction 1–2 of laminates.

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Laminates

Simulation result (N)

Test result (N)

Error

CV of simulation

CV of test

Error

Sample sizes

A

44973

43008

4.57%

7.24%

10.64%

−3.40%

10

B

59244

62023

−4.48%

5.53%

7.31%

−1.78%

10

C

47984

53177

−9.77%

2.89%

8.49%

−5.60%

10

D

45575

46727

−2.47%

19.98%

15.75%

4.23%

10

A

45167

43008

5.02%

6.79%

10.64%

−3.85%

20

B

59283

62023

−4.42%

5.26%

7.31%

−2.05%

20

C

48660

53177

−8.50%

3.35%

8.49%

−5.14%

20

D

41966

46727

−10.19%

21.29%

15.75%

5.54%

20

A

45102

43008

4.87%

6.95%

10.64%

−3.69%

30

B

59270

62023

−4.44%

5.35%

7.31%

−1.96%

30

C

48434

53177

−8.92%

3.30%

8.49%

−5.19%

30

D

43169

46727

−7.61%

21.35%

15.75%

5.60%

30

HSNFCCRT

(b) HSNFTCRT

(c) HSNMCCRT

(d) HSNMTCRT

(a)

Fig. 12. Hashin failure in the damaged area of laminates A

Analysis of Composite Laminates Strength with Random Deviation Variables

Fig. 13. Hashin failure in the damaged area of laminates B

HSNFCCRT

(b) HSNFTCRT

(c) HSNMCCRT

(d) HSNMTCRT

(a)

Fig. 14. Hashin failure in the damaged area of laminates C

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HSNFCCRT

(b) HSNFTCRT

(c) HSNMCCRT

(d) HSNMTCRT

(a)

Fig. 15. Hashin failure in the damaged area of laminates D

Fig. 16. Displacement load curve of laminates A

Analysis of Composite Laminates Strength with Random Deviation Variables

Fig. 17. Displacement load curve of laminates B

Fig. 18. Displacement load curve of laminates C

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Fig. 19. Displacement load curve of laminates D

5 Conclusion In order to explain the influence of deviation variables on composite properties, numerical simulation was carried out on commercial software Abaqus, and detailed analysis method was given. In unnotched tension/compression, the analysis models with deviation variables are more accurate in the calculation of mean value and coefficient of variation. It can effectively simulate the real experiment. For the experiments of openhole compression, the sampling number and mesh fineness have little influence on the coefficient of variation, while the dispersion of thickness has the greatest influence on the dispersion of experimental results. When the dispersion of thickness increases, the dispersion of experimental results will also increase. In the case of constant mean, the discretization of random variables has little influence on the mean of output results. When the dispersion of thickness is large, the thickness may be less than zero when the normal distribution is directly used in calculation. How to ensure the accuracy of this condition, add constraints or try different distribution methods will be studied in future research work. Acknowledgements. This work is supported by School of Aeronautic and Astronautic, Shanghai Jiao Tong University. Thanks for the detailed instruction from my tutors Dr. Hu and Dr. Yu. Their insightful suggestions always light me in the lost. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

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References 1. Gao, X.G., Song, Y.D., Sun, Z.G.: Study on the dispersion of composite properties caused by random fiber size. J. Mater. Sci. Eng. 23(3), 335–340 (2005) 2. Feng, X., Lu, Z.X.: Modulus dispersion of composite single-layer plates based on random field. Mech. Strength 32(4), 622–626 (2010) 3. Reifsnider, K.L., Jamison, R.: Fracture of fatigue-loaded composite laminates. Int. J. Fatigue 4(4), 187–197 (1982) 4. Hashin, Z., Rotem, A.: A fatigue failure criterion for fiber - reinforced materials. J. Compos. Mater. 7(4), 448–464 (1973) 5. Liu, Y., Chen, S.J., Gao, X., et al.: Progressive failure analysis of single-layer plate based on Hashin criterion. Equipment Environ. Eng. 7(1), 34–39 (2010) 6. Dalmaz, A., Ducret, D., Guerjouma, R.E., et al.: Elastic moduli of a 2.5D C f /SiC composite: experimental and theoretical estimates. Compos. Sci. Technol. 60(6), 913–925 (2000) 7. Prewo, K.M.: Tension and flexural strength of silicon carbide fibre-reinforced glass ceramics. J. Mater. Sci. 21(10), 3590–3600 (1986) 8. Tan, S.C., et al.: Progressive failure of laminated composites with a hole under compressive loading. J. Reinf. Plast. Compos. 12(10), 1043–1057 (1993) 9. Karandikar, P., Chou, T.W.: Characterization and modeling of microcracking and elastic moduli changes in Nicalon–CAS composites. Compos. Sci. Technol. 46(3), 253–263 (1993) 10. Matzenmiller, A., Lubliner, J., et al.: A constitutive model for anisotropic damage in fibercomposites. Mech. Mater. 20(2), 125–152 (1995) 11. Okabe, T., Komotori, J., Shimizu, M., et al.: Mechanical behavior of SiC fiber reinforced brittle-matrix composites. J. Mater. Sci. 34(14), 3405–3412 (1999) 12. Pryce, A.W., et al.: Behaviour of unidirectional and crossply ceramic matrix composites under quasistatic tensile loading. J. Mater. Sci. 27(10), 2695–2704 (1992) 13. Ekvall, J.C., Griffin, C.F.: Errata: design allowables for T300/5208 Graphite/Epoxy composite materials. J. Aircr. 20(6), 576–576 (1983) 14. Guynn, E.G., Ochoa, O.O., Bradley, W.L.: A parametric study of variables that affect fiber microbuckling initiation in composite laminates. I - Analyses. II - Experiments. J. Compos. Mater. 26(11), 1594–1616 (1992) 15. Budiansky, B., Fleck, N.A.: Compressive failure of fibre composites. J. Mech. Phys. Solids 41(1), 183–211 (1993) 16. Jelf, P.M., et al.: Compression failure mechanisms in unidirectional composites. J. Compos. Mater. 26(18), 2706–2726 (1992) 17. Bansemir, H., Haider, O.: Fibre composite structures for space applications—recent and future developments. Cryogenics 38(1), 51–59 (1998) 18. Han, X.: Normalized B-basis of the space of trigonometric polynomials and curve design. Appl. Math. Comput. 251(C), 336–348 (2015)

Simulink-Integrated Representation of Functional Architectures Towards Simulation of Aircraft Systems Yuyu Huo, Yong Chen, and Meihui Su(B) School of Aeronautics and Astronautics, Shanghai Jiao Tong, University, Shanghai, China {hyy.0077,aerocy,sjtusmh}@sjtu.edu.cn

Abstract. Recently, system functional simulation mostly uses discrete functional logic models, and it is difficult to simulate the impact of continuous behavioral parameter changes on functional logic. To remedy the addressed issue, a functional simulation method integrating a discrete functional model and continuous behavior model is proposed to help engineers analyze the correctness of functional design efficiently. Firstly, a component functional modeling and a system functional architecture modeling method are established based on state machine; secondly, a model integration simulation method based on FMI is established to integrate discrete function models and continuous behavior models of components or systems; Finally, this paper takes the aircraft elevator system as an example to verify the application of functional modeling and simulation methods. The application results show that the functional modeling and the simulation method which integrates dynamic behavior can simulate the continuous behavior and the system function execution effectively. Thereby, the engineers can ensure the correctness of the system design with this method. Keywords: Functional models · State machine · FMI · Simulink · Integrated simulation

1 Introduction In the conceptual design process of complex products and systems such as the main flight control system of civil aircraft, engineers often need to establish a systematic function model: On the one hand, functional models are direct expressions of product design intent, and provide a common communication basis for engineers from different fields; On the other hand, the functional models can support the functional simulation in the conceptual design process, improving design efficiency and reducing design costs by verifying the validity of design scheme before the product hardware is realized with the help of computers. However, it is difficult to satisfy the stakeholders’ needs for verification of system behavior through functional models only. Engineers always use different simulation tools (e.g. Mathworks Simulink or Modelica Dymola) to analyze the system behavior. Therefore, it needs to investigate methods for integrating continuous behavior © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 170–190, 2023. https://doi.org/10.1007/978-981-99-0651-2_14

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models with discrete functional models for the simulation verification of solutions in the design phase. At present, a lot of research has been carried out on functional modeling methods. According to the analysis of technical systems (factories, equipment, machines, equipment, assemblies, or components) by Pahl et al. [1], it is proposed that all systems involve the conversion of energy, materials, and signals, defining the functional model in terms of the conversion of physical quantities from a system perspective. In terms of functional expression, the Function-Behavior-Structure (FBS) model proposed by Umeda et al. [2], the Function-Behavior-State (FBS) model proposed by Goel et al. [3], Guo Gang et al. [4] proposed an ontology-based functional modeling method. In terms of the integration of functional models and behavioral models, there have been many experiments to integrate MATLAB/Simulink tools (usually used to model the dynamic behavior of systems) with UML/SysML simulation tools to achieve cosimulation. For example, Vanderperren et al. [5] proposed two different approaches to UML and Simulink coupling: (1) model-in-the-loop co-simulation via an intermediate coupled bus, allowing the two simulations (Simulink and UML simulation) to communicate, and (2) object-based implementation code-in-the-loop co-simulation in a language (usually C++ or MATLAB/ code itself) as the common execution language for both models. Similar to the second approach proposed by Vanderperren et al., Bombino and Scandurra [6] propose a co-simulation solution based on (C++) code, that is generated by the Simulink component, called Real-Time Workshop (RTW), and an Artisan Studio tool, called Automatic Code Synchronizer (ACS)—code generation from SysML state diagrams. In [7], an approach for establishing the mapping of structure and behavior when using UML and MATLAB/Simulink at the same time is presented. For structure mapping, the Simulink model is converted into UML composite structure and activity models, and for behavior mapping, the MATLAB/Simulink simulation behavior is captured as UML activity diagrams. In this paper, we propose a state-based component/system functional modeling approach and a functional simulation approach integrating dynamic behavior models. Firstly, based on finite state machine, the functional modeling method is studied at two levels, component and system, and the component functional modeling and system functional architecture modeling are carried out by using System Modelling Language (SysML). Based on this, the functional simulation method of integrated dynamic behavior is studied by integrating the continuous behavior model (Simulink model) of the component/system through the Functional Mock-up Unit (FMU). Finally, an example of the elevator control system in civil aircraft flight control system is applied for verification.

2 Function Modeling Methodology Based on SysML In design science, the function is expressed as an abstraction of objective action, which is the action of an objective object (e.g., system, subsystem, component, etc.) on the external environment to bring about the desired change to satisfy a specific requirement [8]. According to the above, a function can be expressed as the transformation from input to output, i.e., a function can be modeled by “Input/Output Flow”. In the functional modeling of complex systems, there are different levels of objects such as systems,

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subsystems, components, etc. Most of the objects perform different functions in different situations, and it is necessary to combine the states of the objects in the functional modeling. SysML [9] is a graphical modeling language for the system engineering field, which can structurally model the requirements, behaviors, structures, parameters, etc. involved in the system design process. In this paper, we mainly apply SysML state machine diagrams and activity diagrams in functional modeling of components, and SysML module definition diagrams and internal module diagrams in functional architecture modeling of systems, which will be described in detail below. 2.1 Component Functional Modeling Method In the functional modeling of components, single-state components can be functionally modeled with input-output flow transitions; for multi-state components, different functions are implemented in different states. Therefore, it is also necessary to consider the states of the component and the state transitions in functional modeling, and this can be achieved with the help of state machines. Finite state machine (FSM), or state machine for short, is an abstract model of things in the real world [10]. It has a finite number of states, is in one of the states at a given time, and can trigger an Action or a Transition from one state to another based on some Event. The event that causes a state transition is called a Trigger Event, or Trigger for short. In the functional modeling of multi-state components, the component is abstractly expressed as a state machine with a finite number of states, and the functions performed by the component in different states (if they exist) can be represented by the actions performed by the state machine in the states. The following will be analyzed in the terms of component states, state transition conditions, and functional expressions (i.e., actions in the state machine). (1) Component state The component state in functional modeling is the state that is functionally relevant and is expected by the engineer and is generally reversible. For example, in kinematic subsets, i.e. movable connections where the components are in direct contact with each other and make relative movements, irreversible changes such as wear are likely to occur, but this state is not expected by the engineer and is not reversible, so it is not considered in our study. However, when irreversible component state changes occur as the desired function, it is something that needs to be considered in the research process. For example, in the field of communication power supplies, there is often a need for overload protection, and a fuse can fulfill this function. It can only be used once and this change of state, although irreversible, is a component state that engineers expect. This particular component state is also considered in our research. In addition, there is a class of component state that engineers expect, but in which the component does not perform a set of actions, i.e. it does not have functionality, but it is also necessary for the component to exist. In this regard, we consider this state when modeling the component state, but do not model.

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(2) State transition conditions The trigger conditions of component state transition are divided into three categories. (1) The discrete functional flow from external objects, can be divided into three categories: material, energy, and signals. Mostly, the trigger condition from external is signal flow, such as the rudder state transition triggered by the current signal from the power control device received by the civil aircraft elevator rudder motion device. (2) The trigger event based on time. Time is a special trigger condition that does not depend on the change of external objects and is not affected by the internal changes of the component. For example, the timing switch triggers the state transition after some time. (3) The continuous behavioral parameters inside the component. For example, the continuously changing parameters, such as the motion speed and temperature of the component trigger the state transition. (3) Representation of the function of a component in a certain state Multi-state components can be represented functionally in the form of “state + function”, where a specific function can be described by a transformation from the input flow to the output flow of the object, as described above. Thus, the function of the component in a given state can be expressed as: F(c) =< state, In, Out >

(1)

where, F represents a function. c represents the component. state is a formal description of the current state of the component. In, Out is a formal description of the input and output flows, respectively. The description of the component state is an objective description of the key characteristics of the component at that moment in time and should be by conventional cognitive conventions. For example, the key feature of a flow control valve is the opening and closing of the valve, at which point the state can be described as Open according to conventional cognitive conventions, i.e. state(Value) = Open, indicating that the current state of the valve is “open”. The types of input and output flows are classified as energy, material, and signal. The normalized description of input and output flows in Eq. (1) is carried out in the way of “stream type + stream property + property value”. For example, the common component flow control valve in the aircraft cockpit loop control system has two states, “Open” and “Close”. In the “Open” state, the component achieves the regulation of airflow, so that the output gas reaches the standard pressure, the valve’s input is air m_air (m represents the material flow, air represents the air in the material flow), the output is also m_air, but the input and output are not the same, so according to the needs of the current function, the air can be added to the properties of pressure and property values to more accurately describe the function of the valve. Such as the output flow in the valve open state is expressed as < m_air, pressure, 101Kpa >. From the analysis of the above study, all states of the component that need to be considered should be analyzed first when modeling the function of the component.

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Distinguish whether the state switching condition is a discrete functional flow from an external object, a time-based trigger condition, or a continuous behavioral parameter change inside the component, and perform the expression of the component function in terms of the input and output flow of the component under the state, the conceptual diagram is shown in Fig. 1.

Fig. 1. Conceptual diagram of state-based functional representation of components

From the above, to meet the needs of component function expression, this paper chooses the combination of state machine diagram and activity diagram in SysML for component function modeling. A state machine diagram in SysML can usually express a component, with a rounded rectangle identifying different states of the component and a solid line with an open arrow identifying the state switching of the component. Component state transition conditions can be expressed in terms of three types of information that can be specified in the state machine diagram: Trigger, Guard, and Effect. Trigger conditions are modeled using signal events defined in SysML to represent discrete functional flows from external objects, time events to represent time-based trigger conditions, and change events to represent continuous behavioral parameter trigger conditions within a component. The formal representation of the input and output flows of a component function in a given state is modeled using activity diagrams. The component function is decomposed into multiple consecutive actions, with object flows identifying the types and properties of the input and output flows and control flows identifying the sequence of execution between actions. Basic actions are expressed as verb phrases and avoid putting multiple verb phrases in a single action, instead of breaking it down into multiple actions. For example, “enter and save data” is an irregular representation of action and two consecutive actions should be created: “enter data” and “save data”. After representing the function of the component in the current state as an activity diagram, it is written into the executable internal behavior - entry behavior - defined by

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the state machine diagram. During functional simulation, when a trigger condition is met, a transition of the component state is triggered and the entry behavior is executed after entering the new state, i.e. the function in the current state of the component is achieved and waiting for the next trigger event to occur. 2.2 Modeling Method for System Functional Architecture The function of the system can be regarded as the abstraction of the objective working which is imposed on the input of the system in a certain state, to produce the output that meets the expectations of the engineer. The realization of the system function means that there is at least one exchange of energy, materials, or signals between the system and the external environment [11]. The realization of the system function depends on the realization of the function of internal components, which can be understood as the result that the internal components of the system realize their respective functions in a certain order. System functional architecture modeling consists of representations of the architecture of system components and single (or multiple) functions of the system. From the analysis in the previous section, for the function modeling of a single component, this study adopts the expression of the input-output flow of the component function based on an integrated state; for function modeling of the system which is composed of multiple components, the state of the system is the state collection of each component within the system. The functional architecture modeling in the system state should include the functional expression in the component state corresponding to the system state and the functional connection relationship between components and components or between components and the external environment of the system. The latter only considers the connection relationship related to the system function, which can be represented by flow and port. The functional connection relationship between system components can be divided into energy flow, material flow, and signal flow. When expressing the flow between components in the system function, the outgoing/incoming object, the class, and the properties of the flow should be considered. For example, the flow of 28 V electrical energy from component 1 to component 2 can be expressed as: Flow1 (com1 → com2 ) = e_voltage, 28V 

(2)

In practical cases, the functional connection relationship between two components may have multiple flows of the same type. The input and output of different functional connection relationships can be represented in the form of component’s ports in order to express the flow between components more clearly. Therefore, Eq. (2) can be refined into the following form: Flow1 (com1 → com2 ) = porto1 , porti1 , e_voltage, 28V 

(3)

where, portO1 represents the output port of the component; porti1 represents the input port of the component;e represents the energy flow (s represents the signal flow and m represents material flow);voltage represents that the flow property is 28V.

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To express the transfer relationship of the functional flow between components more clearly, component ports and system ports are introduced as shown in Fig. 2. System ports express the interaction point between the system and the external environment; component ports express the interaction point between components or between the component and the outside of the system, where S is the description of the state of the system, and s is the description of the state of the component.

Fig. 2. Diagram of the functional integration of the internal components of the system

Based on the above analysis of system functional architecture modeling, the Block Definition Diagram (i.e., BDD) of SysML is used to define the information of system structure, including different types of model elements such as internal components of the system and the project flow; Internal Block Diagram (i.e., IBD) of SysML is used to describe the internal components of the system and the interface and connection relationships of the components, which indicates how the internal components realize the functions of the system. In addition, there are energy flow, material flow, and signal flow in the functional modeling mentioned above. In the process of functional modeling, a single function flow can be represented by the category, attributes, and attribute values of the flow. In SysML, the expression of different types of flows required in the system is established by defining Flow Specification in BDD. To sum up, the application of diagrams of SysML in component function modeling and system function architecture modeling is shown in Table 1.

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Table 1. Application of SysML in functional modeling SysML type chart

Application scenarios

Application description

State Machine Diagram

Functional modeling of component integration states

• Component state representation • Component state transition event modeling • Component functional representation (entry activity)

Activity Diagram

Block Definition Diagram

Internal Block Diagram

• Dividing component functions into simple actions • Modeling of functions done in the component state, linked to entry activities in the state machine System functional architecture modeling

• Modules describe objects such as systems, components, external environments, etc • Hierarchical description of the internal structural components of the system • Establishing interactions and ports between modules • Establishing ports for components to interact with the outside • Establishing functional flow transfer between components or between components and the external environment

3 Functional Simulation Methodology Integrating Simulink Model The SysML-based component and system functional model is a qualitative, discrete functional logic model that expresses the functional architecture of the system at each level and the discrete functional logic, but for complex systems, the functional model contains not only discrete logic signals but also continuous behavioral parameters, such as velocity, height, etc. Therefore, the dynamic behavior model of the system needs to be supplemented in functional simulation. In this paper, Matlab/Simulink is used as the system dynamic behavior modeling tool, and the Simulink model is integrated into the discrete SysML model for functional simulation.

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System functional modeling is divided into functional architecture modeling and state-based component functional modeling. Correspondingly, when modeling the dynamic behavior of the system, the functional objects at different levels are represented by employing modular division, subsystem creation, and encapsulation, and the function realization process of components or systems in different states is established by enabling modules and switch modules. The Functional Mock-up Interface (FMI) standard provides an interface standard for the interaction of different functional and performance models to support model exchange and co-simulation of dynamic models, FMI defines an interface that can be implemented by an executable file called FMU. Traditional model co-simulation relies on users to develop co-simulation interfaces between different simulation tools on demand, which requires a lot of development effort. The co-simulation methodology [12] in the FMI standard is further optimized on the traditional method and provides a unified standard for each simulation software interface. For the software supporting the FMI standard, the FMU file exported by any other tool can be imported into its software platform, and the XML file (model description file) in it can be automatically parsed, and the association between its solver and dynamic library can be established after some simple parameter settings by the user and applied to the subsequent solution process. The functional model unit (FMU) in the form of simulation is imported into the functional simulation platform supporting the FMI standard for integrated simulation. For simulation, the exported Simulink model can be launched after the simulation environment detects the required license file, provided that the same version of MATLAB tools is available locally. In the process of model integration simulation, the interaction between the discrete functional logic model and the continuous behavior model is the interaction of data [13]. The discrete logic model outputs discrete instructions or state values of components (Systems) as the state parameters of the continuous behavior model, which are used to start different continuous behavior models. The continuous parameters in the execution process of the continuous behavior model are transmitted to the discrete logic model in real-time as feedback, to wait for the execution of the discrete logic model and the next output. Figure 3 is a schematic diagram of the model integration simulation method taking the main flight control system of civil aircraft as an example. Based on the cosimulation interface standard in FMI, the joint simulation of the functional logic model and behavior model can be realized through the interaction of parameters.

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Fig. 3. Co-Simulation of tool coupling method

4 Case Study From the above component functional modeling, system functional architecture modeling and model integration simulation methods, this section takes ARJ21’s elevator system as an example for application verification. The structure of the elevator system is shown in Fig. 4, which mainly contains the actuator control electronic (ACE), power control unit (PCU), and rudder motion unit components.

Fig. 4. Schematic diagram of the composition of the elevator system of a civilian aircraft

4.1 Functional Modeling of the Elevator System During the operation of the rudder system, ACE receives rudder position command signals from the cockpit and enhanced commands related to the rudder control system

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from the FCM, compares them with the position signals from the PCU, and generates current command signals to the PCU through control law calculations. After receiving the signal, the PCU controls the actuator through the electro-hydraulic servo valve (EHSV) to drive the rudder to the specified position. The position of the actuator cartridge is detected by an LVDT and fed back to the ACE in the form of a current signal. The following is a detailed introduction to component functional modeling using ACE as an example, and to system functional architecture modeling using the elevator system as an example. (1) Functional model of ACE ACE is an analog processor unit that is the direct control path between the cockpit control sensors and the electro-hydraulic actuator. It is the primary connection used in rudder systems to replace the mechanical system in conventional aircraft control. ACE has three modes: normal mode, direct mode, and DNR mode, and combined with its turn-on state, there are six working states: normal-turn-on, normal-standby, direct-on, direct-standby, DNR-turn-on, DNR-standby and the OFF state before power-on. The state definition is made in the state machine with a rounded rectangular box, and the functions accomplished by ACE under the state are written in the form of an activity diagram in the entry behavior, as shown in Fig. 5.

Fig. 5. State-based functional model of ACE

The transition event between states is defined by the trigger, make the transition from OFF state to Direct-UnCapEngage state as an example, as shown in Fig. 5. The transition condition between the OFF state and Direct-UnCapEngage state is “when (ElecVol > 0)”, the trigger indicates that when the value of ElecVol is greater than 0, i.e., when power is applied, ACE will transfer from the OFF state to Direct-UnCapEngage

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state. In addition, it is possible to create a guard for a state transition to achieve the definition of necessary conditions in state transition other than the trigger. As shown in “[xlaneebge = = 1 & & selactact = = 0 & & drctsw = = 0]” in the transition conditions from direct uncappengage state to DNR uncappengage state in the figure. The guard indicates the trigger: “NormModeCap = = 1” can trigger the state switch provided that the FCC mode command is “Main-Standby “, the neighboring ACE is on and the direct mode switch is not on. (2) Functional architecture model of the elevator system The internal components of the rudder system are represented by the module definition diagram, as shown in Fig. 6. The elevator control system consists of two ACE units called “Ele.L.PACE.OB” and “Ele.L.PACE.IB”, two actuators called “Ele.L.PCU.OB” and “Ele.L.PCU.IB”, an elevator rudder surface named “ Ele.L “ and an elevator actuator behavior module. To distinguish the functional logic model parameters from the dynamic behavioral model parameters during the modeling process, two modules, Controller and Behavior, have been created for each component.

Fig. 6. Block definition diagram of the elevator system

The functional flow relationships between the internal modules of the rudder control system are represented in the IBD, as shown in Fig. 8. The value attributes and port connection relationships for each module can be defined in the IBD.

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As shown in Fig. 7(a), the binding relationship between the “isPrior” signal and the “pSigEngPrior” port of “Ele.L.PACE.OB” in the IBD of the elevator control system shows that the “isPrior” signal always passes through the “pSigEngPrior” port flows into “Ele.L.PACE.OB”. Figure 7(b) The ACE IBD contains the ACE STM and ACE Behavior modules and a series of ports, showing the port mapping between the ports in the ACE and the two modules and the interaction between the value attributes within the ACE Behavior module and the ACE external system. Figure 7(c) The internal PCU module diagram sums up the actuator functions in the PCU Controller module, the Buffer value attribute, and the associated ports. The PCU Controller module is mainly concerned with the state transition information of the PCU, therefore it is associated with the PCU STM state machine diagram. The PCU state machine receives the incoming voltage signal (SOVL) from outside the module, which is used to judge the state switching conditions in the state machine, and outputs the PCU state information to the outside of the module through the port, while there is rudder surface The PCU also interacts with the external system via the port for the parameters of the motion commands.

(a)

(b)

(c)

Fig. 7. Internal block diagram of the elevator system

4.2 Modelling the Dynamic Behavior of Elevator System The behavior of the rudder system is modeled by first building a component behavior model and then integrating it into a system behavior model. In addition, a civil aircraft

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model is built as the elevator system simulation environment. ACE is used as an example to demonstrate component behavior modeling. (2) Dynamic behavioral model of the ACE When modeling the continuous behavior of ACE, two states of ace are considered: normal mode and direct mode. In normal mode, the elevator actuator electronic controller uses the enhanced command, proportional gain, and limit command transmitted from FCM through the CAN bus. The adjustment offset of the sensor signal is not considered here. According to the look-up table, the position signal of the joystick is shaped to obtain the command degree of the rudder surface. ACE receives the electronic counterweight input from FCM and adds it to the feedforward loop signal. It multiplies the elevator gain value calculated from FCM to obtain the elevator command signal. The command signal is compared with the elevator surface deflection feedback value. The difference between the two is converted into an electrical signal and output to the EHSV, as shown in Fig. 8 below. 1 1-D T(u)

PositionFeedback

PositionCommand

ColumnShaping

Bobweight 2

2-D T(u) u1

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Flap0 1-D T(u) 6

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CAS Flap25

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Fig. 8. ACE behavior model in normal mode

In direct mode, ACE uses local proportional gain and signal limit. The direct mode gain is a function of the discrete signal of the slat from the FSECU. At this time, when the pilot makes the aircraft pitch by manipulating the joystick, the elevator surface command signal is obtained through the integer of the joystick position signal in the ACE of the elevator system, multiplied by the proportional gain calculated in the ACE, the elevator surface feedback signal is compared with the command signal, and the difference between the two is converted into an electrical signal and output to EHSV. The ACE in direct mode is shown in Fig. 9.

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1 ColumnPosition

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1 CurrentSignal(mA)

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Fig. 9. ACE behavior model in direct mode

(3) Dynamic behavioral model of the elevator system Since the modes between the components can affect each other, for example, two PCUs in one rudder surface in the elevator system, if one of them is in failure mode, the other PCU has another actuator cylinder damping in addition to the external load, which needs to be integrated into the system-level model analysis, and the continuous dynamic behavior model of the elevator system is shown in Fig. 10.

Fig. 10. Continuous dynamic behavior model of the elevator system

(4) System simulation environment model The aircraft attitude information, velocity, etc. are often used as inputs to the model during the modeling of the rudder system and component behavior. Therefore, to facilitate the subsequent integration simulation, this paper builds the whole aircraft model with the disclosed aircraft structural parameters and aerodynamic coefficients, and integrates the elevator system model into the actuators module (Actuators), as shown in Fig. 11.

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Fig. 11. Elevator rudder surface motion unit behavior model

4.3 Integrated Simulink Model for Functional Simulation Export the Simulink model into an FMU document based on the FMI standard and integrate it into a BDD in the SysML model. A block is created in the BDD diagram that defines a port with the same parameter name as the FMU module input and output ports but does not contain a specific implementation, and the FMU is imported with a generalized relationship to this block as its realization. As shown in Fig. 12.

Fig. 12. Schematic diagram of model integration

The parameter interaction between the FMU generated from the Simulink model and the SysML model is shown in Fig. 13.

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Fig. 13. Parameter diagram of model integration

During the functional simulation, the value attributes “ColPos”, “Nz”, “SlatPos”, etc. are set to 0 to simulate the initialization state of the system, as shown in Fig. 14. Both FCM channels are in the “NormUncap-ActRev” state, waiting for the change of the “isFCMValid” signal, as shown in Fig. 14(b); both ACEs are in the “ OFF” state, waiting for the power-on signal, as shown in Fig. 14(a); both PCUs are in the “NotEngaged” state, waiting for the change of the “SOVL” and “SOVH” signals, as shown in Fig. 14(c); the elevator surface is in the “retracted” state, waiting for the “curpos” signal to change, as shown in Fig. 14(d). When simulating the normal flight of the aircraft, the pilot performs rudder control activities during normal flight, when FCM is in effect, the rudder column position changes, the input parameter “ColPos” is set to 5, and the system component state is shown in Fig. 15. The FCM switches to the “NormCap-ActAct” state, as shown in Fig. 15(b); after the ACE is powered on, it finally enters the “Normal-On” state according to the initial input conditions, and sets “SOVL = 0”, “SOVH = 28”, “isNorm = LaneEngage = 1” and “LaneDrct = 0” through the entry activity “setNCap”, as shown in Fig. 15(a). The PCU switches to the “Engaged” state with the change of “SOVL” and “SOVH”, as shown in Fig. 15(c); the elevator rudder surface then enters the “Negative Partial Extended” state, as shown in Fig. 15(d).

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(d) Fig. 14. Elevator system initialization state

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(d) Fig. 15. System state transition of the elevator system

This section shows the functional simulation process of the system with the elevator system in the initial state and the functional execution of the system when the control commands and parameters are changed as an example. With the help of the state machine diagram and activity diagram, the system transition between different modes (states) and the functional logic in each state can be effectively simulated, and the continuous parameters in the behavioral model provide the basis for the functional model to judge

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the state transition logic. This section systematically demonstrates the application of the integrated functional-behavioral modeling approach to component and system functional simulation. 4.4 Discussion Existing functional modeling methods mostly focus on functional representation and functional decomposition, which are difficult to express clearly for common multi-state functional objects in complex systems. The functional and behavioral model established in this paper can not only clearly express the functional logic of the system in multiple states, but also support the computer to reason out the system state changes triggered by the control signals and activate different behavioral models, to completely simulate the system functional realization process. Compared with existing functional modeling methods, the proposed method in this paper is based on known system architecture solutions and is more applicable to the analysis stage of complex product design.

5 Conclusion Based on the state machine theory, this paper studies the functional modeling method from two levels, component and system. Build the component functional model by the state machine and activity diagram in SysML, and build the system, functional architecture model, by IBD and BDD. On this basis, carry out the function-behavior integrated simulation based on the behavior model (Simulink model) of the FMI integrated component/system. And use the civil aircraft elevator system as an example for application verification. The result shows that the functional modeling method of the integrated state and the functional simulation method of integrated behavior proposed in this paper can not only support the engineers to express the functional architecture of the system clearly but also support the functional realization of the computer simulation system during the continuous processes, which can help the engineers to ensure whether the system function design scheme is correct. However, the following issues still need further research: how to integrate the functional state machine model of multi-level objects, and how to integrate sequential logic in the functional simulation model. Acknowledgments. This paper is sponsored by the National Natural Science Foundation of China (51875346).

References 1. Pahl, G., Beitz, W., Feldhusen, J., et al.: Engineering Design: A Systematic Approach. Springer-Verlag, London (2007) 2. Umeda, Y., Ishii, M., Yoshioka, M., Shimomura, Y., Tomiyama, T.: Supporting conceptual design based on the function-behavior-state modeler. Artif. Intell. Eng. Des. Anal. Manuf. 10(4), 275–288 (1996). https://doi.org/10.1017/S0890060400001621

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3. Goel, A., Rugaber, S., Vattam, S.: Structure, behavior, and function of complex systems: the structure, behavior, and function modeling language. Artif. Intell. Eng. Des. Anal. Manuf. 23(1), 23–35 (2009). https://doi.org/10.1017/S0890060409000080 4. Guo, G., Tang, H.M., Luo, Y.: Semantic-based product functional formal modeling. Comput. Integr. Manuf. Syst. 17(6), 1171–1177 (2011). https://doi.org/10.1080/17415993.2010. 547197 5. Vanderperren, Y., Dehaene, W.: From UML/SysML to Matlab/Simulink: current state and future perspectives. In: Proceedings of the Design Automation & Test in Europe Conference, vol. 1, p. 1. IEEE (2006). https://doi.org/10.1109/DATE.2006.244002 6. Bombino, M., Scandurra, P.: A model-driven co-simulation environment for heterogeneous systems. Int. J. Softw. Tools Technol. Transfer 15(4), 363–374 (2012). https://doi.org/10. 1007/s10009-012-0230-5 7. Sjöstedt, C.J., Shi, J., Törngren, M., Servat, D., Chen, D., Ahlsten, V., Lönn, H.: Mapping Simulink to UML in the design of embedded systems: Investigating scenarios and transformations. In: OMER4 Post-Proceedings, pp. 137–160 (2008) 8. Xie, Y.: Some basic concepts in modern design theory. Chinese J. Mech. Eng. 43(11), 10 (2007). https://doi.org/10.3321/j.issn:0577-6686.2007.11.002 9. Parrott, E.: SysML Distilled: A Brief Guide to the Systems Modeling Language. INSIGHT (2015). https://doi.org/10.1002/inst.201417263 10. Mavridou, A., Laszka, A.: Designing secure ethereum smart contracts: a finite state machinebased approach. In: Financial Cryptography and Data Security, pp. 523–540 (2008). https:// doi.org/10.48550/arXiv.1711.09327 11. Erden, M.S., Komoto, H., Beek, T.J.V., D’Amelio, V., Echavarria, E., Tomiyama, T.: A review of function modeling: approaches and applications. Artif. Intell. Eng. Des. Anal. Manuf. 22(2), 147–169 (2008). https://doi.org/10.1017/S0890060408000103 12. Hong, T., Sun, H., Chen, Y., Taylor-Lange, S.C., Da, Y.: An occupant behavior modeling tool for co-simulation. Energy Build. 117, 272–281 (2015). https://doi.org/10.1016/j.enbuild. 2015.10.033 13. Azizi, M., Rahman A., Mizukawa, M.: Model-based development and simulation for robotic systems with sysML, simulink and simscape profiles regular paper. Int. J. Adv. Robot. Syst. 10(2) (2007). https://doi.org/10.5772/55533

Arrangement of Sensors for Measuring Temperature in the Test of Autoclave Zhou Ma1,2(B) , Wei Ma1 , Pengfei Du3 , Xiaohan Liu1 , and Deshou Wang4 1 Shanghai Aircraft Manufacturing Co., Ltd., Shanghai, China

[email protected], [email protected], [email protected] 2 Shanghai Jiao Tong University, Shanghai, China 3 China Jiliang University, Hangzhou, China [email protected] 4 Beijing Seekbest Technology Co., Ltd., Beijing, China [email protected]

Abstract. The test of the autoclave temperature field is very important for the quality control of the civil aircraft composite material manufacturing. The existing test methods mainly arrange thermocouples on the front and tail sections and geometric center of the autoclave for multi-point distributed measurement. However, the reason why temperature tests are mainly carried out on the front and tail sections, the detailed sensor arrangements, as well as the requirements for the local layout of the thermocouple measuring junctions are still unclear. A threedimensional steady-state numerical simulation of the autoclave temperature field is performed in this article. The discrete distribution tests showed that the actual temperature distribution is consistent with the numerical simulation results with the effects of the front and rear rectifier plates considered. The low-temperature area was observed in the tank door and top, whereas the high-temperature area was distributed in the tank tail and bottom. The flow field near the rectifier plates on both sides was more complicated as compared with that in other regions. The microstructure did not significantly affect the overall temperature field in the tank, whereas it exerted a greater effect on the local temperature field. The temperature distribution of the entire autoclave can be represented by the typical measurement points. Additionally, local layout requirements of test sensors are proposed, which can provide a basis for determining the point for the autoclave temperature field test. Keywords: Autoclave · Numerical simulation · Temperature field test · Test point

1 Introduction The autoclave forming process is one of the most widely used methods for the manufacturing of civil aircraft composite material components [1]. As a specific process that cannot pass the post-manufacturing destructive test for quality inspection, its temperature field distribution is uneven, and its temperature control ability is inferior. Hence, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, pp. 191–201, 2023. https://doi.org/10.1007/978-981-99-0651-2_15

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residual stresses will be generated, thereby affecting the strength, shape, and surface accuracy of the component [2]. To ensure the quality of product curing, Sectthe spatial distribution of the autoclave in the temperature field must be reasonable, and the temperature field of the autoclave must be tested periodically before and during use. The test method of the autoclave is mainly to place thermocouples on the two end sections and the geometric center of the cylindrical tank for multi-point distributed measurement, but the distribution of sensor points is not consistent among different manufacturers. Some researchers [2] believe that the temperature field performance of the autoclave is excellent and can be benchmarked for engineering acceptance; but the corresponding identification methods are summed up in traditional practical test experience, lacking theoretical explanation and data support. At present, civil aircraft composite material manufacturers mainly refer to the heat treatment equipment standard for the test of the temperature field of the autoclave [3–5]. However, they differ from the autoclave in objective conditions such as equipment shape and structure, thermal insulation, radiation and convection mode, and pressure state. Whether the point distribution of the sensors is suitable for the test of the autoclave has not been systematically verified. The main direction of research through computational fluid dynamics is the temperature field of composite components and frame molds [6–10], and the overall simplification of complex components such as front and rear fairing plates that seriously affect the heat transfer in the tank [11–15], few studies have applied the numerical simulation of the inherent temperature field of the autoclave to the test method of the temperature field. As a conclusion, issues that are still unclear and need to be further investigated: 1 Why is the temperature field test mainly carried out on the front and tail sections? 2 Where should the temperature test sensor be arranged in detail? 3 What are the requirements for the local layout of the thermocouple measuring junctions? The main purpose of this paper is to answer the above-mentioned questions. The structure of the paper is as follows: In Sect. 2, numerical simulation and practical test of temperature field are carried out. In Sect. 3, the temperature field distribution characteristics of the autoclave are studied, and a typical point arrangement scheme is given. In Sect. 4, the local layout requirements for the measuring junctions of the sensor are discussed. Finally, conclusions are given in Sect. 5.

2 Numerical Simulation and Test Experiment of Autoclave Temperature Field 2.1 Numerical Simulation The research object was a typical 4.5 m × 11.0 m autoclave suitable for the manufacture of composite materials for civil aircraft, which is a cylindrical structure with a symmetrical longitudinal boundary. The front and rear rectifier plates can make the gas flow in the autoclave more uniform, improve the heat exchange efficiency, and ensure more uniform

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heat transfer in the tank. Because the rectifier plates exerted a significant effect on the flow field and temperature field of the autoclave, it was investigated comprehensively. The grid opening of the front rectifier plate increased gradually from top to bottom, in the following order: 0°, 14°, 24°, 43°, and 90°; meanwhile, the rear rectifier plate was positioned at the center of the plate with the smallest opening, and it opened outward gradually in an increasing manner, as follows: 7.8°, 14.8°, 18.6°, and 90°. The autoclave used in this study was a large airtight pressure vessel; however, its wall panels, clapboards, and other structures were only a few millimeters thick and had a large span. Using local grid densification, the thin plate structure, rectification grid, and key areas were refined, and a coarser grid was used for the tank space. After defining the grid as shown in Fig. 1.

(a) External volume grid (b) Volume grid perspective

(c) Front rectifier board body grid map (d) Rear rectifier board body grid map Fig. 1. Autoclaved tank grid diagram

Convection and conduction are the primary heat transport methods of the autoclave, with a limited degree of heat radiation under high-temperature settings. To enable easier calculations, the following were assumed [16]: A uniform air volume at the fan’s air outlet, no internal heat source, an incompressible fluid, no diffusion between the solid interfaces, fully developed flow and heat transfer, and non-consideration of the increase in the heat transfer area of small structures and energy transfer loss.

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Based on the operating conditions of the autoclave, the initial load and boundary conditions were set as follows: the temperature was set to 250 °C, and the pressure in the tank was set to 350 kPa, the position of the rectifier plate was the interface, the Reynolds number corresponded to a turbulent fluid flow, the air inlet port was set as the velocity inlet, the velocity was 5 m/s, the air outlet and the ambient temperature were 25 °C, the wall material was stainless steel, the emissivity was 0.85, and the tank was filled with nitrogen. Other flow and thermophysical parameters are presented in Table 1. Table 1. Material fluid and thermophysical parameters Material

Density (kg·m−3 )

Dynamic viscosity (Pa·s)

Heat capacity (J·kg−1 ·k−1 )

Thermal conductivity (W·m−1 ·k−1 )

Nitrogen

1.1453

1.789

1040.76

1.0 × 10–4

Stainless steel

7832

/

434.0

63.9

2.2 Actual Temperature Field Test Experiment To verify the simulation results, the working area of the autoclave is equally divided into 8 sections, with 4 points arranged at the edge of each section at 90°, one point at the center, and two points near the controlling thermocouples, the numbers are (1–42), a total of 42 conventional points. Five points are arranged on the cross section of the rectifier plate at tank tail, one point is arranged at each junction of the tank wall and clapboard of the four sections of E, D, C, and A, and (8)-attached to the clapboard, (9)—hanging and unobstructed, (15)—attached to the tank wall, 16—hanging and unobstructed„ and (10)—shading by the lampshade are added, the numbers are ((1)–(17)), a total of 17 specific locations. A distributed temperature test experiment was carried out at a interval of 2 min for 20 consecutive times.

Fig. 2. Temperature test point layout diagram

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3 Typical Layout of Test Sensors 3.1 Why is the Temperature Field Test Mainly Performed on the Front and Tail Sections Figure 2(a) depicts the total temperature field from the outside. The high-temperature area was distributed in the heating unit under the clapboard, the low-temperature area was distributed near the tank end and bottom, and the heat concentration area was near the tank door and top area. Because the area below the bottom clapboard did not constitute the autoclave’s effective operating area, only the temperature distribution above the clapboard was considered.

(a) External manipulative temperature (b) Middle section of velocity vector

(c) Tank door temperature; (d) Intermediate section temperature field;(e) Tank tail section temperature field

Fig. 3. Simulated temperature field and velocity field of autoclave

Figure 3(b) shows the velocity vector diagram of the middle longitudinal section. The flow field was more uniform in the operating area of the tank, whereas it was more complicated near the rectifier plates on both sides because of multi-opening structures and different opening angles. Although the gas flow can be made more uniform, the flow vortex also causes the pressure gradient to have a greater impact on the local heat transfer, which resulted in an unstable temperature field distribution. The analysis of the temperature field of sections (c), (d), and (e) in Fig. 3 shows that the low-temperature area was distributed at the top of each section, the high temperature was distributed at the symmetrical corner position where the lower clapboard and tank wall were connected, and the median temperature was distributed at the green isothermal line.

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The test results at conventional locations show that the minimum actual temperature of the autoclave was at point 26 (as shown in Fig. 1), and the maximum was at point 3. The K-means clustering analysis of the test results and the initial segmentation provided the minimum temperature, maximum temperature, and set temperature. The high-temperature points were 3, 5, 7, 8, 9, 13, 13, 15, 17, 18, 19, 20, 24, 29, 32, 33, 34, 37, 38, 39, and 40, which were primarily distributed in the lower section and at the end of the autoclave; the low-temperature points were 1, 2, 4, 22, 26, 31, 32, 35, 36, 37, and 46, which were primarily distributed in the upper section of the tank door and the middle of the tank. The average values of measured temperatures at specific locations on the A, C, and O cross-sections are compared with the numerical simulation temperature after normalization, as shown in Fig. 4(a). The distribution and fluctuation of different test points are compared by calculating the average values of the standard deviations of the O, A, B, C, D, and E cross-section test results, as shown in Fig. 4(b). Figure 4(a) shows that in different cross-sections, the measured values at each point have the same distribution trend as the simulation results. Figure 4(b) shows that the standard deviations of the temperature distribution of the tank tail and the tank door are significantly larger than that of other sections, and the tank door fluctuation is significantly larger than that of other sections, which is consistent with the results of the flow field analysis of the autoclave. The standard deviation of the fluctuation of each cross-section shows a decreasing trend in the order of E-D-C-B-A-O, but the difference between the fluctuation of the tank tail and other cross-sections is small. This is because the tank door section is the air outlet of the autoclave, which is directly affected by the heating and cooling system. The tank tail is the air return port, and the gas temperature is stable when the circulating air from the tank door flows through the entire autoclave to the end of the tank. Therefore, even if the return air flow field from the tank tail is complicated, its fluctuation is still small. The actual test results are basically consistent with the numerical simulation calculation results, so the numerical simulation results can be used to predict the temperature field of the autoclave. 3.2 Where Should the Temperature Test Sensor Be Arranged in Detail Therefore, when setting the temperature field test points, more points should be set near the rectifier plates on both sides, that is, the tank door and tank tail, and the sparser points should be set in the middle area. As shown in Fig. 2, to ensure that the highest and lowest limit values of the temperature field in the operating area can be tested, when setting the test points, the highest temperature points ((6) and (7)) and lowest temperature point (1) should be included. However, the difference between the maximum and minimum temperatures of different sections was insignificant. The maximum and minimum temperature points of the entire autoclave may change during the regular test. Therefore, other maximum temperature points of the section ((13) (14) (16) and (17)) and the lowest temperature points (16 and 36) should be included. Because the highest and lowest temperatures of the middle section were both within the highest and lowest temperature ranges of the two ends, high temperature ((13) and (14)) and low temperature (16) test points need not be specified in the middle section. To allow the interpolation and evaluation of the overall temperature field distribution when required, a point can be

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specified at the middle temperature of each section. To render the test more standardized and operable, the geometric center of each Section (5,20 and 40) can be selected. The point layout of the autoclave temperature field test is shown in Fig. 3(b), where the minimum points were 1,(6) and (7), the general points were 1,(16),(17),5,20,36,(6),(7) and 40.

4 What Are the Requirements for the Local Layout of the Thermocouple Measuring Junction The air passage of the autoclave is relatively simple in the approximate cylindrical cavity and is generally simplified to a symmetrical thin-walled cylindrical structure. However, the actual autoclave wall and clapboards are composed of small microstructures, such as wire hanging grooves, rail guide grooves, lampshades, limiters, and temperature measuring racks. These microstructures are extremely small compared with the size of the autoclave and may not significantly affect the overall temperature field of the autoclave. However, their effect on the local temperature field should not be disregarded. In the temperature field test, the test thermocouples were installed near the microstructures. Because the measurement was less than 1 mm, they were affected easily by the micro cycle, and the test results could not reflect the overall temperature field performance of the autoclave. 4.1 Numerical Simulation Analysis of the Influence of Microstructure The microstructure in the tank comprised many types and shapes; therefore, an aluminum alloy plate was placed in the center of the autoclave to simulate the microstructure in the tank. The temperature of the autoclave was set as 200 °C, the pressure as 683 kPa, the wind speed as 5 m/s, and the initial temperature of the aluminum alloy plate as 196 °C; additionally, a non-steady-state analysis was adopted in the numerical analysis . As shown in Fig. 4(a), the aluminum alloy plate only affected the temperature field along the flow direction and did not significantly affect the overall temperature field of the autoclave. Owing to the ambient flow, a temperature gradient of 3 °C was formed on the back edge of the board, and a low-temperature thin layer area with a thickness of approximately 2 cm was formed around the board. As shown in Fig. 4(b), the low- and high-temperature areas on the middle plate was distributed on the leeward and windward positions, respectively. The overall plate temperature was approximately 3.5 °C lower than the gas temperature in the tank (Fig. 5).

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(a) Longitudinal section temperature field (b) Aluminum alloy plate temperature field Fig. 5. Overall temperature field map of autoclave and alloy plate at 1289.6 s

4.2 Actual Test Results of Microstructure Effects The standard deviations, differences and averages of temperature fluctuations at points of (8), (9), (15), 16, and (10) are calculated, as shown in Table 2: Table 2. Influence of microstructure on test results Calculation results (°C)

(8)

(9)

(15)

16

(10)

Fluctuation standard deviation

0.06

0.12

0.09

0.16

0.32

Fluctuation difference

0.20

0.50

0.30

0.70

1.60

183.08

182.26

180.73

182.76

181.56

Average value

The temperature of the thermocouple attached to the clapboard is slightly higher than that of the hanging and unobstructed thermocouple, but the temperature of the thermocouple attached to the tank wall is slightly lower than that of the hanging and unobstructed thermocouple. This is because the clapboard is directly heated by the heating unit’s radiation and conduction, so the temperature is higher than the gas temperature, but the heat of the tank wall comes from the gas convection, so the temperature is lower than the gas temperature, which is consistent with the numerical simulation results. The standard deviation and difference of the temperature fluctuation at the shaded position of the lampshade are the largest, and the actual temperature value is the smallest, which is caused by the large changes in the local microcirculation caused by the turbulent flow of the gas medium in the shaded area of the lampshade. 4.3 Local Arrangement Requirements of Thermocouple Measuring Junction Therefore, the effect of the local microstructure on the overall temperature field is negligible when performing the autoclave temperature field test; however, the measuring junction of the test sensor should be avoided when it is placed near the microstructure, particularly for the 2 cm thin layer range and the leeward surface. If other metal components are connected to the measuring junction of sensors, the measured temperature

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cannot effectively characterize the temperature field of the autoclave; hence, this should be avoided in the actual test.

5 Conclusion Firstly, combining the numerical simulation of the temperature field of the autoclave and the analysis of the actual test results, the inherent temperature field characteristics of the autoclave can be obtained., it was concluded that the high-temperature area in the autoclave was distributed in the tank tail and bottom, whereas the low-temperature area was distributed in the tank door and upper area. Secondly, When setting the temperature field test points, more points should be set near the rectifier plates on both sides, and sparse points should be set in the middle area. At the tank door and tank tail sections, the test points were symmetrically located at the intersection of the bottom clapboard and the tank wall, and a point was set at the geometric center of each portion. Thirdly, The effect of the microstructure was negligible; however, the sensor measurement end should not be placed near complicated microstructures or connected to tank walls or other metal components. Acknowledgement. This work is supported by the Civil Aircraft Scientific Research Project (Project No.: MJ-2017-J-85).

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Author Index

B Belevtsov, Denis

N Ni, Runsheng 15

1

C Chen, Yong 65, 170 Chi, Cheng 108

P Popov, Naum-Leonid E. 80 Q Qiang, Xiaoqing 133 Qu, Yaoyao 133

D Dai, Tingkai 123 Ding, Yu 38 Du, Pengfei 191 E Ekaterina, Skorohodova

S Su, Meihui 65, 170 87

F Fan, W. B. 147 G Gao, Guyue

25

H Hu, Y. L. 147 Huo, Yuyu 170 K Kachalin, Vasilii S. 80 Khvan, Alexander 1, 87 Klykov, Pavel 1 Kovtunov, Sergei 54, 103 L Legotin, Denis 1 Li, Yuanxiang 15 Liu, Xiaohan 191 Liubov, Oskirko 87 M Ma, Jiahua 15 Ma, Wei 191 Ma, Zhou 191 Ming, Xinguo 25

T Turbin, Nikolai 103 Turbin, Nikolay 54 U Utiabaeva, Aliia

103

W Wang, Deshou 191 Wang, Ruichang 25 Wu, Guanrong 15 X Xu, Y. Y.

147

Y Yu, B. Y. 147 Yu, Y. 147 Yu, Zhefeng 38 Yuan, Wenhan 108 Z Zhan, Xingqun 108 Zhang, Bo 123 Zhang, W. 147 Zhang, Xin 108 Zhao, Meng 65 Zhong, Jiabin 38

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Jing et al. (Eds.): ICASSE 2022, LNEE 1020, p. 203, 2023. https://doi.org/10.1007/978-981-99-0651-2