Advances in Computer Science for Engineering and Manufacturing (Lecture Notes in Networks and Systems, 463) 9783031038761, 9783031038778, 3031038762

Table of contents :
Preface
Contents
Computer Science for Manage of Natural and Engineering Processes
Analysis of Virtual Promotion of a Product
1 Introduction and Related Works
2 Problem Statement
3 Proposed Approach
4 Summary and Conclusion
References
Conditions of Non-uniform Fluidization in an Auto-oscillating Mode
1 Introduction
2 Physical Model of Non-uniform Jet-Pulsating Fluidization in an Auto-oscillating Mode
3 Determination of Main Parameters of the Non-uniform Jet-Pulsating Fluidization in an Auto-oscillating Mode
3.1 Determination the Speed of Movement of the Mass Center of Bed of Solids
3.2 Determination of the Hydrodynamics Quality
3.3 Determining the Conditions for Ensuring High-Quality Hydrodynamic Mode of Fluidization
3.4 Flow Simulation in SolidWorks
3.5 Explanation of Determining the Gas Velocity in Slits of GDD
4 Experimental Study of the Influence of the Height of the Bed of Granular Material on the Size of the Formed Gas
5 Summary and Conclusion
References
The Heat Exchange in the Process of Granulation with Non-uniform Fluidization
1 Introduction
2 Physical Model of Non-uniform Fluidization in the Granulator Chamber
3 Mathematical Model of Heat Exchange in a Fluidized Bed During Granulation of Liquid Systems
3.1 Determination of Temperature in the Vicinity of the Dispersant
3.2 Heat Balance Equation for Gas Coolant and Fluidized Bed
4 Results and Discussion
5 Conclusions
References
An Approach Towards Vacuum Forming Process Using PostScript for Making Braille
1 Introduction
2 Software System for Plate Manufacturing
2.1 The PostScript File Creation for Test Plate Manufacturing
2.2 The PostScript File Creation for Plate Manufacturing to Produce Final Goods
3 Conclusion
References
Investigation of Anomalous Situations in the Machine-Building Industry Using Phase Trajectories Method
1 Introduction
2 Phase Space Method for the Study of Technological Processes
3 The Projections of Varieties of Phase n - Dimensional Spaces
4 Summary and Conclusion
References
Prediction of Magnetic Remanence of Sm-Co Magnets Using Machine Learning Algorithms
1 Introduction
2 Materials and Methods
2.1 Dataset Collection
2.2 Machine Learning Algorithms
2.3 Performance Evaluation
3 Modeling and Results
4 Comparison and Discussion
5 Summary and Conclusion
References
The Wind Generator’ Power Effective Forecast Method Based on Modified One-Dimensional Convolutional Neural Network and Metaheuristics
1 Introduction
2 Research Background
3 Research Methodology
3.1 The Forecast Model Based on a Modified One-Dimensional Convolutional Neural Network Creation
3.2 The Criterion Selection for the Suggested Model’ Effectiveness Evaluating
3.3 The Method Development for Suggested Model’ Parametric Identification Based on Local Search
3.4 The Method Development for Suggested Model’ Parametric Identification Based on Metaheuristic Search
4 Numerical Research
5 Research Results
6 Conclusion
References
Determination of Geometric Parameters of Piezoceramic Plates of Bimorph Screw Linear Piezo Motor for Liquid Fertilizer Dispenser
1 Introduction
2 Literature Review
3 Materials and Methods
4 Experiments and Results
5 Conclusions
References
Ensuring Safety of Navigation in the Aspect of Reducing Environmental Impact
1 Introduction
2 Materials and Methods
3 Results and Discussion
4 Summary and Conclusion
References
Synthesis of the Algorithm for Determining the Film Thickness Based on the Obtained Data of the White Light Interferogram
1 Introduction
1.1 Literature Review
2 Methodology and Methods
3 Results
4 Conclusion
References
Model for a Direct Torque Control System of an Alternating Current Electric Drive for Urban Transport Rolling Stock Tasks
1 Introduction. Analysis of Literary Sources and Statement of the Problem
2 Basic Material of the Research
3 Conclusions
References
Method for Determining the Generating Capacity of the Waste Heat Recovery System of Main Engines
1 Introduction
2 Energy Efficiency Design Index of Vehicle Power Plant
3 Method for Determining of the Waste Heat Recovery System Efficiency
4 Conclusions
References
Computer Science for Education, Robotics and Biology
Research into the Parameters of a Robotic Platform for Harvesting Apples
1 Introduction
2 Literature Review
3 Research Methodology
4 Theoretical Aspects of a Research
5 Practical Implementation
6 Conclusions
References
Virtual Laboratory Works in Teaching Practical Circuit Design and Development of Responsibility Component of Students’ Academic Integrity
1 Introduction
2 Methodology
3 Results and Discussion
4 Summary and Conclusion
References
Adaptation of Distilling Knowledge Method in Natural Language Processing for Sentiment Analysis
1 Introduction
2 Related Work
3 Approach
3.1 Overview of the Offered Solution
3.2 Data Overview
3.3 BERT
3.4 FastText
4 Experiments
4.1 Datasets Overview
4.2 Implementation Details
4.3 Results
5 Conclusions
References
Designing Intelligent Multi-agent Ontology-Based Training Systems: The Case of State University of Infrastructure and Technology
1 Introduction
2 Modeling of Training Processes
2.1 Modeling of Students’ Training
2.2 Modeling of Student Knowledge Control
3 Intelligent Multi-agent Training System
4 Modeling the Behavior of an Intelligent Software Agent
5 Summary and Conclusion
References
Security Access Using Simple RFID Reader and Arduino UNO: A Study Case
1 Introduction
2 Theoretical Aspects
3 Programming and Circuit Realization
4 Conclusion
References
Investigation of the Bifurcation Properties of the Dynamics of a Biological Population Based on a Logistic Model
1 Introduction
2 Mathematical Model of Subpopulations Dynamics with a Logistic Function as a Basic One
3 Experimental Research and Applied Use of the Developed Model
4 Discussion and Conclusions
References
The Applying of Second Order Frequency-Dependent Components in Signal Processing of Autonomous Mobile Robotic Platforms
1 Introduction
2 The Low Order Frequency-Dependent Components Definition
3 The Low Order Frequency-Dependent Components Models
3.1 The Second Order LF and HF Butterworth Filter
3.2 The Second Order LF and HF Chebyshev I Filter
3.3 The Second Order LF and HF Chebyshev II Filter
3.4 The Second Order LF and HF Cauer Filter
4 The Transfer Function Coefficients Calculation
4.1 The Butterworth Transfer Function Coefficients Calculation
4.2 The Chebyshev I Transfer Function Coefficients Calculation
4.3 The Chebyshev II Transfer Function Coefficients Calculation
4.4 The Cauer Transfer Function Coefficients Calculation
4.5 The Computation Costs Reducing
5 The Additional Conveniences in Using the Low Order Filters
6 Conclusions
References
Stochastic Algorithms for Optimization of the Path of Robotic Systems
1 Introduction
2 References Analysis and Formulation of the Problem
3 Ant Colony Method
4 Genetic Algorithm
5 The Results of the Demo Program
6 Conclusion
References
Veterinary Self-protected Cone-Beam Computed Tomography Scanner
1 Introduction
2 Materials and Methods
3 Measurements and Discussion
4 Summary and Conclusion
References
Optimization of Deep Learning Neural Network by Analysis of Cross-Validated Metrics with and Without Data Augmentation
1 Introduction
2 State of the Art
3 Dataset, Models, and Problems
4 Experimental Results
5 Discussion and Conclusions
References
Mathematic and Technological Achievements for Various Applications
Residual Stresses Occurring During Laser Shock Processing Technology of High-Load Units of Agricultural Machinery
1 Introduction
2 Studded Material
3 Numerical Calculations by the Finite Element Method
4 Constitutive Relation
5 Analysis of the Occurrence of Anisotropy of Residual Stresses Arising in the Process of LSP
5.1 Residual Stresses Arising After the “Shot” By a Single Laser Pulse
5.2 Study of the Residual Stress After the End of the First Column of “Shots”
5.3 Study of Residual Stress After the Beginning of the Second and Subsequent Columns of “Shots”
5.4 Reducing the Anisotropy of Residual Stresses By Applying Random Scanning
6 Conclusion
References
Strengthening of Agricultural Machinery Parts by Cryogenic Laser Shock Processing Technology
1 Instruction
2 CLSP Technology Modeling
3 Defining Relation
4 Theoretical Background
5 The Obtained Results and Discussion
5.1 Surface Residual Stresses Analysis
5.2 Microhardness Distribution by Depth
6 Conclusion
References
Method of Reducing Friction in the Plow Moldboard with Soil During Cultivation Due to the Implementation of Ultrasonic Vibrations
1 Introduction
2 Formal Problem Statement
3 Literature Review
4 Materials and Methods
5 Experiments and Results
6 Conclusions
References
Ways to Reduce Negative Impacts from the Use of Rapeseed Oil as a Fuel for Diesel Engines
1 Introduction
2 Materials and Methods
3 Results
3.1 Bench Tests to Determine the Amount of Rapeseed Oil in the Crankcase
3.2 Data Fusion Simulation Experiment
4 Discussion
5 Closing Comments
References
Brand Management of Archives in Ukraine: Raising the Issue
1 Introduction
2 Topic Development Status. Brand Management Characteristics
2.1 Sources and Bibliography
2.2 Conceptual Apparatus of the Research
2.3 Objective Characteristics of a Brand
3 Research Methods
4 Types of Corporate Brand Management and Brand Identity
5 A Model for Creating and Developing Brand Identity and Its Extrapolation to the Sphere of Archives
6 The Results of the Statistical Research and Comments on Them
7 Conclusions
References
Combined Approach to Solving the Neumann Problem for a Parametric Quasilinear Elliptic Equation
1 Introduction
1.1 Analysis of the Last Publications
2 Methods and Materials
2.1 Preliminaries
2.2 Problem Statement
2.3 FD Approximation of the Differential Model
2.4 Projection-Iteration Implementation of the Newton-Like Method and Its Modifications
3 Summary and Conclusion
References
Influence of Hadamard Matrices Canonicity on Image Processing
1 Introduction
2 Related Research
3 Theoretical Foundations of the Study
4 Experimental Studies
4.1 The Image Processing Method Using Three Types of Hadamard Matrices
4.2 The Results of Experimental Evaluation the Quality of the Restored Images
5 Conclusion
References
Investigation of Reading Convenience Factors Based on Graph Theory and Systems Analysis
1 Introduction
1.1 The Basic Concepts of Computer Fonts
2 Research Methods
3 Modeling and Results
4 Comparison and Discussion
5 Summary and Conclusion
References
The Generalized Chaotic System in the Hyper-complex Form and Its Transformations
1 Introduction
2 Method
2.1 Coordinate Transformation for the Generalized Chaotic System
2.2 Transformed Generalized Chaotic System Modeling
3 Results and Discussion
3.1 The Lorenz System in the Quaternion Form
3.2 Linear Coordinate Transformation for the Lorenz System
4 Summary and Conclusion
References
The Impact of Connecting a Wind Power Plant on Emergency Modes of a Traction Substation of an AC Traction System
1 Introduction
2 Methods
2.1 Modern Approaches to Modeling the Short-Circuit Modes in Electric Power Networks
2.2 General Structure and Peculiarities of Subsystems of the Electricl-Engineering Complex “Wind Power Plant - AC Traction Substation”
2.3 Development of Computational Equivalent Circuits
2.4 Short-Circuit Current Analysis
3 Results and Discussion
4 Summary and Conclusion
References
Air Quality Assessment Based on the Selection of Fitting Anomaly Detection Methods
1 Introduction
2 Problem Statement
3 Detection Anomalies in Data
4 Final Comparison
5 Summary and Conclusion
References
Author Index

Citation preview

Lecture Notes in Networks and Systems 463

Zhengbing Hu Sergey Petoukhov Felix Yanovsky Matthew He   Editors

Advances in Computer Science for Engineering and Manufacturing

Lecture Notes in Networks and Systems Volume 463

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Advisory Editors Fernando Gomide, Department of Computer Engineering and Automation—DCA, School of Electrical and Computer Engineering—FEEC, University of Campinas— UNICAMP, São Paulo, Brazil Okyay Kaynak, Department of Electrical and Electronic Engineering, Bogazici University, Istanbul, Turkey Derong Liu, Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, USA Institute of Automation, Chinese Academy of Sciences, Beijing, China Witold Pedrycz, Department of Electrical and Computer Engineering, University of Alberta, Alberta, Canada Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Marios M. Polycarpou, Department of Electrical and Computer Engineering, KIOS Research Center for Intelligent Systems and Networks, University of Cyprus, Nicosia, Cyprus Imre J. Rudas, Óbuda University, Budapest, Hungary Jun Wang, Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

The series “Lecture Notes in Networks and Systems” publishes the latest developments in Networks and Systems—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNNS. Volumes published in LNNS embrace all aspects and subfields of, as well as new challenges in, Networks and Systems. The series contains proceedings and edited volumes in systems and networks, spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. The series covers the theory, applications, and perspectives on the state of the art and future developments relevant to systems and networks, decision making, control, complex processes and related areas, as embedded in the fields of interdisciplinary and applied sciences, engineering, computer science, physics, economics, social, and life sciences, as well as the paradigms and methodologies behind them. Indexed by SCOPUS, INSPEC, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science. For proposals from Asia please contact Aninda Bose ([email protected]).

More information about this series at https://link.springer.com/bookseries/15179

Zhengbing Hu Sergey Petoukhov Felix Yanovsky Matthew He •

•

•

Editors

Advances in Computer Science for Engineering and Manufacturing

123

Editors Zhengbing Hu Faculty of Applied Mathematics National Technical University of Ukraine Kyiv, Ukraine Felix Yanovsky Department of Electronics, Robotics, Monitoring and IoT Technologies National Aviation University Kyiv, Ukraine

Sergey Petoukhov Mechanical Engineering Research Institute of Russian Academy of Sciences Moscow, Russia Matthew He Halmos College of Arts and Sciences Nova Southeastern University Fort Lauderdale, FL, USA

ISSN 2367-3370 ISSN 2367-3389 (electronic) Lecture Notes in Networks and Systems ISBN 978-3-031-03876-1 ISBN 978-3-031-03877-8 (eBook) https://doi.org/10.1007/978-3-031-03877-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The development of artificial intelligence systems and their applications in various fields belongs to the most urgent tasks of modern science and technology. One of these areas is engineering and manufacturing, whose development is aimed at increasing the life support of the world’s population, including the tasks of developing industry, agriculture, medicine, transport, etc. The rapid development of artificial intelligence systems requires the intensification of training of a growing number of relevant specialists. At the same time, artificial intelligence systems have significant perspectives of their application inside education technologies themselves for improving the quality of training of specialists taking into account personal characteristics of such specialists and also the emergence of new computer devices. The International Symposium on Engineering and Manufacturing (December 24–26, 2021, Kyiv, Ukraine) has its purpose to present new thematic approaches, methods, and achievements of mathematicians, physicians, biologists, and technologists and also to attract the additional interest of different specialists to this perspective theme. Its proceedings additionally includes articles on specific tasks in various fields, where artificial intelligence systems can be applied in the future with great benefit. The Symposium is organized jointly by the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” National Aviation University, Kyiv National University of Construction and Architecture, Hubei University of Technology, Polish Operational and Systems Society, and International Research Association of Modern Education and Computer Science. The best contributions to the conference were selected by the programed committee for inclusion in this book out of all submissions. Zhengbing Hu Sergey Petoukhov Felix Yanovsky Matthew He

v

Contents

Computer Science for Manage of Natural and Engineering Processes Analysis of Virtual Promotion of a Product . . . . . . . . . . . . . . . . . . . . . . Sergey Orekhov

3

Conditions of Non-uniform Fluidization in an Auto-oscillating Mode . . . Bogdan Korniyenko, Yaroslav Kornienko, Serhii Haidai, Andrii Liubeka, and Serhii Huliienko

14

The Heat Exchange in the Process of Granulation with Non-uniform Fluidization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bogdan Korniyenko, Yaroslav Kornienko, Serhii Haidai, and Andrii Liubeka An Approach Towards Vacuum Forming Process Using PostScript for Making Braille . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volodymyr Mayik, Taras Dudok, Lyudmyla Mayik, Nataliia Lotoshynska, Ivan Izonin, and Jacek Kusmierczyk

28

38

Investigation of Anomalous Situations in the Machine-Building Industry Using Phase Trajectories Method . . . . . . . . . . . . . . . . . . . . . . Solomiya Liaskovska, Ivan Izonin, and Yevgen Martyn

49

Prediction of Magnetic Remanence of Sm-Co Magnets Using Machine Learning Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrii Trostianchyn, Ivan Izonin, Roman Tkachenko, and Zoia Duriahina

60

The Wind Generator’ Power Effective Forecast Method Based on Modified One-Dimensional Convolutional Neural Network and Metaheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eugene Fedorov, Maryna Leshchenko, Serhii Rudnytskyi, Vitalii Duduk, and Nataliia Lada

69

vii

viii

Contents

Determination of Geometric Parameters of Piezoceramic Plates of Bimorph Screw Linear Piezo Motor for Liquid Fertilizer Dispenser . . . Constantine Bazilo, Sergey Filimonov, Nadiia Filimonova, and Dmytro Bacherikov Ensuring Safety of Navigation in the Aspect of Reducing Environmental Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oleksiy Melnyk and Svitlana Onyshchenko

84

95

Synthesis of the Algorithm for Determining the Film Thickness Based on the Obtained Data of the White Light Interferogram . . . . . . . . . . . . 104 Yurii Kryvenchuk, Maryana Zakharchuk, Olha Sencovych, Yulia Malynovska, Nataliia Topylko, and Yurii Novytskyi Model for a Direct Torque Control System of an Alternating Current Electric Drive for Urban Transport Rolling Stock Tasks . . . . . . . . . . . . 120 Vasyl Stopkin, Mykola Tryputen, Anatoliy Nikolenko, Vitaliy Kuznetsov, and Maksym Tryputen Method for Determining the Generating Capacity of the Waste Heat Recovery System of Main Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Alexander Rak, Victor Busher, Oksana Glazeva, Oleksii Chornyi, Yurii Kachan, and Vitaliy Kuznetsov Computer Science for Education, Robotics and Biology Research into the Parameters of a Robotic Platform for Harvesting Apples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 D. O. Khort, A. I. Kutyrev, and I. G. Smirnov Virtual Laboratory Works in Teaching Practical Circuit Design and Development of Responsibility Component of Students’ Academic Integrity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Valerii Borodai, Lada Berdnyk, Vitaliy Kuznetsov, Dmyro Tsyplenkov, and Alvina Havrylova Adaptation of Distilling Knowledge Method in Natural Language Processing for Sentiment Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Oleksandr Korovii and Andrii Petrashenko Designing Intelligent Multi-agent Ontology-Based Training Systems: The Case of State University of Infrastructure and Technology . . . . . . . 181 Tkachenko Olha, Tkachenko Kostiantyn, and Tkachenko Oleksandr Security Access Using Simple RFID Reader and Arduino UNO: A Study Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Volodymyr Rusyn, Aceng Sambas, and Christos H. Skiadas

Contents

ix

Investigation of the Bifurcation Properties of the Dynamics of a Biological Population Based on a Logistic Model . . . . . . . . . . . . . . . . . . 203 Victor Busher, Oleksii Chornyi, Oleksandr Kuzenkov, Mykola Tryputen, Vitaliy Kuznetsov, and Vladislav Rumiantsev The Applying of Second Order Frequency-Dependent Components in Signal Processing of Autonomous Mobile Robotic Platforms . . . . . . . . . 213 Ivan Afanasyev, Valery Sytnikov, Oleg Streltsov, Pavel Stupen, and Volodymyr Kudria Stochastic Algorithms for Optimization of the Path of Robotic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Anatolii Pashko, Tetiana Oleshko, and Svitlana Biesiedina Veterinary Self-protected Cone-Beam Computed Tomography Scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Oleksandra Miroshnychenko, Sergii Miroshnychenko, Boris Goldberg, Sergey Guzeev, Andrii Nevgasymyi, and Yurii Khobta Optimization of Deep Learning Neural Network by Analysis of Cross-Validated Metrics with and Without Data Augmentation . . . . 248 Yuri Gordienko, Mariia Ladonia, and Sergii Stirenko Mathematic and Technological Achievements for Various Applications Residual Stresses Occurring During Laser Shock Processing Technology of High-Load Units of Agricultural Machinery . . . . . . . . . . 263 Gerontiy Zhorovich Sakhvadze Strengthening of Agricultural Machinery Parts by Cryogenic Laser Shock Processing Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Gerontiy Zhorovich Sakhvadze and Dinara Usmanovna Khasyanova Method of Reducing Friction in the Plow Moldboard with Soil During Cultivation Due to the Implementation of Ultrasonic Vibrations . . . . . . 281 Constantine Bazilo, Sergey Filimonov, Nadiia Filimonova, and Sergei Yashchenko Ways to Reduce Negative Impacts from the Use of Rapeseed Oil as a Fuel for Diesel Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 Ovchinnikov Evgeniy, Uyutov Sergey, Fedotkin Roman, and Kryuchkov Vitaliy Brand Management of Archives in Ukraine: Raising the Issue . . . . . . . 302 Valentyna Bezdrabko, Oleksandr Garanin, Viacheslav Hryhoriev, Oksana Matviienko, Lesia Kovalska, and Кateryna Klymova

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Contents

Combined Approach to Solving the Neumann Problem for a Parametric Quasilinear Elliptic Equation . . . . . . . . . . . . . . . . . . . . . . . . 316 Liudmyla Hart Influence of Hadamard Matrices Canonicity on Image Processing . . . . . 329 Khrystyna Kulchytska, Mariia Semeniv, Bohdan Kovalskyi, Nadiya Pysanchyn, and Zoryana Selmenska Investigation of Reading Convenience Factors Based on Graph Theory and Systems Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Zoryana Selmenska, Bohdana Havrysh, Tetyana Holubnyk, Bohdan Kovalskyi, and Orest Khamula The Generalized Chaotic System in the Hyper-complex Form and Its Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 Roman Voliansky, Nina Volianska, Vitaliy Kuznetsov, Mykola Tryputen, Alisa Kuznetsova, and Maksym Tryputen The Impact of Connecting a Wind Power Plant on Emergency Modes of a Traction Substation of an AC Traction System . . . . . . . . . . . . . . . . 360 Yurii Kachan, Vitaliy Kuznetsov, and Oleh Bondar Air Quality Assessment Based on the Selection of Fitting Anomaly Detection Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 Valerii Bagaveev and Rustam Latypov Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

Computer Science for Manage of Natural and Engineering Processes

Analysis of Virtual Promotion of a Product Sergey Orekhov(B) Computer Science and Software Engineering Department, Kharkov Polytechnical Institute, National Technical University, Kharkiv 61002, Ukraine [email protected]

Abstract. Over the past ten years, our scientific team has completed more than thirty projects in the field of search engine optimization. The results of these projects indicate the existence of a new branch of marketing - virtual promotion. Therefore, the purpose of this work was to describe a new control object. The work formulates the definition, purpose, structure and metrics for evaluating the effectiveness of virtual promotion of a product. The object includes two channels: knowledge distribution and marketing. One plays role of logistics of knowledge about a product in virtual space, but another controls this process on-line. On the basis of this, a diagram of the business process of virtual promotion is proposed. A new approach to the management of this object is also proposed through the solution of four problems: structural parameter synthesis, coordination, generation of a semantic kernel, and performance evaluation. As a result, a new scheme of the business process of virtual promotion was proposed. The schema is based on the new idea that the knowledge about a product is being presented as knowledge unit named semantic kernel of web content. Keywords: Virtual promotion · Business process · IDEF framework

1 Introduction and Related Works The classic definition of a marketing channel speaks of the interaction of the manufacturer, buyer and intermediary in order to benefit from the maximum satisfaction of a given need. There are three main functions of such a channel. The first is to satisfy the consumer’s request. The second is to stimulate demand. And the third – after sales service. The paper focuses on the second function – stimulating demand. But the work explores a new form of marketing channel – virtual promotion. The main goal of virtual promotion is to increase the level of sales of goods or services due to technologies that exist in cyberspace. Virtual promotion has the same nature as the logistics channel [1]. We will assume that virtual promotion is a system where there are two channels (sub-systems). The first sub-system has the function of distributing knowledge. The second is the marketing of knowledge about a product or service. The first channel forms the technology of information transfer (knowledge) about the product in cyberspace. It concentrates actions on transportation, storage and retrieval of information about a product depending on the needs of a potential buyer. To simplify, we © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 3–13, 2022. https://doi.org/10.1007/978-3-031-03877-8_1

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S. Orekhov

assume that there are two functions: the transfer and storage of information (knowledge) about the product. The search function is implemented through a search server. The distribution of knowledge about the product is formed on the basis of the URI of web resources and web services. This is a set of IP addresses that obey the OSI model [2]. In other words, it is a set of software components that are located on the Internet at specified IP addresses. Each component performs either the function of transmitting or storing information (knowledge) about the product or service. Another channel is a network of websites, channel telegrams, marketplaces and video blogs. In other words, the marketing channel is formed by real firms that buy and sell information or knowledge about goods or services in cyberspace. The moment of uploading information to the web resource will be considered a transformation or transfer of knowledge about the product in cyberspace. Thus, the distribution channel sets the configuration of virtual promotion, and the marketing channel - the organizational structure. We will consider a virtual promotion successful when a potential buyer has downloaded the product to their web resource or made a request to obtain information about our product or service from one of the specified IP addresses. As a result, a two-level system is formed, where levels actively interact. The level of marketing is the manager, and the distribution channel plays the role of the object of management. In addition, it can be argued that virtual promotion is the formation of an organizational system for managing the channel of knowledge dissemination in cyberspace. We will call this organizational structure of market card management. This map shows the two levels at which knowledge about a product or service is transported, stored and transferred to a potential buyer. Let’s try to classify the channel of knowledge dissemination on the basis of known analogues in the field of logistics. At the moment, there are two main logistics concepts: “on time” or “quick response” and the range or “continuous replenishment”. The first concept is based on the assessment of demand for the product. In our case, this approach is not used, because virtual promotion as an innovator forms future channels of communication with potential customers. Of course, it is possible to form any value of the prediction, for example, on the basis of probability theory, but such predictions will be ineffective. The second concept assumes that product knowledge must be placed at specified points in cyberspace and wait until they are activated by potential buyers. This option is closer to our situation. In this case, we perform three actions: consolidation or concentration, adjustment and scattering. The first operation means concentrating knowledge about a product or service on a corporate website, telegram channel or video blog. At the same time, these software components must be configured to transfer knowledge on demand over the Internet as quickly as possible. The second operation means processing knowledge depending on the nature of the request. It is necessary to form a combination of knowledge, we sort them into certain groups or sets. That is, the transformation of knowledge depending on external requests for their receipt. In other words, they need to be reformatted into a form acceptable to the potential buyer to encourage him to buy.

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The third operation of “scattering” involves the transfer of knowledge about the product to other storage nodes in these formats. In other words, knowledge on the Internet is duplicated. We will assume that such duplication is also accompanied by reformatting, as we work in an environment of anti-plagiarism programs and components [3]. We will call this channel of knowledge dissemination intensive, because the number of consumers is huge and potentially unlimited. A new marketing channel is a distributed system for disseminating knowledge about a product or service, which consists of the following sequence of steps – Fig. 1 [4]. Knowledge about a product

Product description Consolidation of knowledge about the product in cyberspace A0

Formats

Knowledge processing and representation A0

Software and Web services Knowledge of the product in a given form

Inquiries for the purchase of goods

Client localization Dissemination of knowledge in response to a request A0

Product localization

Virtual promotion metrics Marketing strategy Evaluation of the effectiveness of the operation of knowledge dissemination A0

Fig. 1. Modern schema of business process of virtual promotion of a product

The standard product description should be transformed into a form that is convenient for distribution in cyberspace. The transformation takes place in two stages. Initially, the text description of the product or service is uploaded to the so-called nodes (hubs). Next, these nodes perform word processing operations in order to present knowledge in the form necessary for further scattering on the Internet. This operation is performed taking

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into account the localization of the potential customer’s profile and the localization of the product itself. The result of the channel is a request to purchase a given product or service. Feedback within the channel allows you to get the values of virtual promotion metrics based on the analysis of goals within the marketing strategy of the enterprise and the actual number of sales of goods or services. The main question remains, what is knowledge about the product. We will assume that knowledge about the product is an algorithm that describes how with the help of this product you can meet a given need for something. To describe this algorithm to cover a specific need, the user uses a search server (technology), which in a given format performs a search in response to a query in the form of a set of keywords. This set of keywords describes both the user’s request and a specific marketing message that directs the business to cyberspace. The task is to establish in a minimum of time a connection between the user who wants to meet their needs, with a given product and the company that has this product. In other words, the user searches the network for instructions (algorithm) on how to close a certain need for the product. The search is performed using a search engine, content management system, social network, by watching a video or reading a blogger. The task of the marketing service is to lay out in a given format in the virtual space algorithm to cover the needs of the user. Features of virtual space impose the following restrictions or requirements on the actions of the enterprise: 1) Product description is a set of keywords that are scanned by a search engine. The server generates responses according to a certain algorithm. The answer can consist of a large number of positions. The user usually inspects only the first positions [5–9]. Therefore, an important marketing factor is to be first in response or at least on the first page. 2) HTML product presentation format allows you to select keywords, to which the search server responds when generating responses. 3) The search server registers the number of links to the web page and keywords highlighted in the text. 4) Users register en masse in social networks that have a technological connection with the search server or have built-in search algorithms. 5) Search servers learn to extract keywords from video and audio files. 6) Businesses integrate their information systems with search engines, content management systems and social networks. 7) Mobile applications are widely used to connect with social networks, which allow you to collect data on the real needs of users to cover a particular need. The above description of virtual promotion as a marketing channel allows us to identify the following research objectives.

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2 Problem Statement To highlight the tasks of virtual promotion, you need to determine the class of the object of study (management) in the first approximation, indicate its main properties. This also allows you to give a first estimate of the model type of this object. The main purpose of the object of study (virtual promotion) is to attract buyers of goods or services. Quantitative assessment of the goal is to determine the number of customers of the product and the income they provide to the company. The function of virtual promotion is to form a marketing channel at two levels: the distribution of knowledge about the product and management (governing body). The distribution is responsible for downloading, moving and finding knowledge about the product, binding to the level of TCP/IP, URI, URL. That is, to the level of specific placement of knowledge on the Internet. Management is about determining where in the network and for how long you should place knowledge about a product or service. That is, a promotion map is formed: a list of Internet sites where knowledge about the product is placed to attract a potential buyer. A promotion map is a virtual promotion map that consists of links to URLs and links to each other. In the literature there is an analogue of such a map - a map of the client’s travels on the Internet (customer journey map) [6]. The second level determines the form and presentation of this knowledge. That is, the level of management forms the message about the product, which encourages the customer to buy the product. We will call this message the semantic core. According to the classical definition, it is a set of keywords with which the user searches for the desired product on the Internet [6–9]. Next, the control level issues control to perform operations on loading knowledgemessage (semantic core) about the product to each node of the virtual promotion map. Then the distribution channel nodes work independently as separate agents. Also, the second level is responsible for the analysis of promotion, i.e. forms an assessment of its effectiveness. Promotion efficiency is quantified in the form of enterprise income due to cyberspace. Thus, we can draw the following conclusions about the object of study (virtual promotion) and the conditions of its existence: 1) The object of research includes two levels: logistics of knowledge and management. 2) The level of management forms the semantic core and the map of virtual promotion. 3) The control level sends a signal to load the kernel to the Internet nodes described in the map and monitors the feedback signals about user behavior. 4) Logistics level includes Internet nodes: profiles in social networks; mobile applications connected to the network; messenger channels; video blogger channels; corporate websites and marketplaces. 5) Each node of the logistics level works separately. But it is possible to load the semantic kernel to the node, display the semantic kernel for scanning by the search server and it is guaranteed to find through the search server the semantic kernel that was downloaded earlier. That is, the node performs the three basic functions mentioned above.

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6) Each node of the second level is an autonomous system, but all nodes are connected hierarchically according to the map of virtual advancement. Thus, analyzing the above conclusions regarding the two-level system of virtual promotion, we can talk about the existence of a distributed hierarchical system, which is a composition of two separate hierarchical subsystems. At first glance, we have the task of coordinating two levels, where the level of marketing plays the role of the management system, and the level of distribution of the object of management. Moreover, the marketing and logistics levels have different goals. In addition, at the logistical level, the goals of individual elements are also different. Further, our marketing subsystem of the enterprise has a goal that differs from the goals of similar systems at the marketing level. Thus, on the first and on the second levels we have network systems, where our management system interacts with other marketing systems and with their reflection at the logistical level.

Structural

and

parametric

Coordination of local management

identification of a two-level

actions at the logistical level to

system

ensure a global optimum at the marketing level

А

B

D

C

Evaluation of the effective-

Formation of control impulses at

ness of a two-tier system

the marketing level to activate the distribution channel of knowledge about the product or service

Fig. 2. Task tree of business process of virtual promotion of a product

Therefore, our future technology must form a management system based on the company’s existing marketing service on the Internet. In other words, it is necessary to form a network of management systems at the marketing level and a network of management facilities at the logistics level (Fig. 2). Thus, the first main task is the structural-parametric identification of two channels (levels) [10–14]. The next task is to coordinate the two levels. Since the goals of the first and second level systems may be different, we will talk about different types of coordination.

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1. Coordination of the problem to be solved in the subsystem of the marketing level. In this case, for some selected control influence, as a result of solving the top-level problem, each subsystem of the logistics level will have such local control influences, in which the criterion of the top-level problem reaches its global optimum. 2. Coordination of tasks to be solved in each of the subsystems of the two-level system. For this variant of coordination, the local control actions of the lower-level tasks provide a global optimum in the upper-level task. 3. Coordination on the compromise value of the objective functions of the subsystems of the two-level system. This situation is typical in the presence of conflict both between subsystems of one level and between subsystems of different levels. If the conflict is not antagonistic in nature, then the choice of control influence is reduced to decision-making on many criteria of individual subsystems. Our coordination task has the second type, when the global result is provided by control actions on performance of tasks at logistic level.

3 Proposed Approach The next task is to form control actions from the marketing level to the logistics level, when there are three main types of such actions at the second level: consolidation (loading), processing and scattering of knowledge. The main issue in solving this problem (Fig. 3) is to determine the form of knowledge about the product that should be accumulated and processed at the distribution level. In the literature on search engine optimization on the Internet [5–9] the term semantic kernel of web content is most often used. Therefore, we will call the form of presentation of knowledge about a product or service that must be loaded into the logistics network of the second level - the semantic kernel. The semantic kernel is not a static object, but can change over time. This change needs to be tracked. The last task (Fig. 2) is to determine the optimization criteria for assessing the effectiveness of a two-tier system (marketing and logistics of knowledge about the product). This criterion will determine the quality of virtual promotion of goods at the enterprise level. Thus, the paper will consider the methodology of virtual promotion of goods or services through the solution of four main tasks: 1. Structural and parametric synthesis of the marketing channel of virtual promotion as a two-level system. The first level is the management system. It generates control signals and analyzes the effectiveness of the second level - the level of distribution of knowledge about the product or service. Thus, the first task is to generate input and output signals in the channel, build a channel model, determine the criteria for channel efficiency, propose algorithms for identifying elements of a two-tier system and choose criteria and methods for verifying the channel model.

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S. Orekhov Algorithms for presenting knowledge Product description

Semantic kernel Presentation of knowledge about the product A0

Software

Kernel processing at the logistic level

Promotion metrics

A0 Analysis of the effectiveness of the semantic kernel

Web services

The cost of attracting a client

A0

Fig. 3. New schema of business process of virtual promotion of a product

2. Coordination of the functioning of the knowledge distribution channel in order to achieve a given level of efficiency of the channel as a whole. Solving this problem means the formation of control signals for the logistics channel in order to provide a global optimum criterion for the effectiveness of the marketing channel of virtual promotion. 3. Formation of the semantic kernel of web content as a control impulse for the logistics level of the marketing channel. The semantic core is a message that is formed in the channel in order to encourage a potential customer to buy a given product or service. 4. Verification of the constructed two-level system consists in the confirmed efficiency of the offered model. According to the classical definition, the purpose of product promotion is to increase the efficiency of sales, sales and demand [15, 16]. However, the essence of promotion is any form of communication that is used to inform potential customers about the product, packaging, brand, advertising exhibitions, demonstrations, business and more. Then the effectiveness of sales depends on the effectiveness of the message about the product to a potential customer. That is, the effectiveness of promotion is determined by the effectiveness of the communication channel between the company and customers. There are two types of communication channels: personal and impersonal. Virtual promotion has a second type.

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Conceptually, promotion can be represented in the form of four stages: 1) 2) 3) 4)

Defining the goals of promotion. Defining the target audience. Choice of promotion tools. Determining the promotion budget.

On the other hand, sales efficiency is determined by the concept of profitability of sales. This is a percentage of the share of profit from each earned hryvnia. Or it is the ratio of net income to the amount received from the sale of products, which is expressed as a percentage [15, 16]. Then the impact of promotion is determined by the costs that the company makes on the formation of the communication channel and the message itself. Profitability can also be affected by the number of customers involved through the message and the communication channel. Thus, you should determine the metrics and criteria that describe the effectiveness of the channel and the message. On the one hand, we need criteria that indicate the reduction of costs for the formation of the communication and communication channel, and on the other hand, we need metrics that determine the number of customers involved through the channel and communication. The message includes the following information for the potential customer: 1) 2) 3) 4) 5)

Description of the product or service and its characteristics. Place of receipt of goods or method of delivery. Information about the packaging of the goods. Justification of the price of the goods. Payment procedure.

Currently, the main indicator that can describe the effectiveness of the channel and the message on the Internet will be traffic [6, 7]. This metric describes the number of unique users who read messages on the channel per unit time. Channels are also becoming more typical. There are the following types of channels where a message about a product or service is placed on the Internet: search engine promotion, contextual advertising, banner advertising and social media marketing. Each channel is characterized by the budget and the traffic it generates. Thus, you can enter the conditional efficiency of the channel and the message based on the classical theory of marketing [15] and search engine optimization [17–20]: E=

T2 B

(1)

B T

(2)

where T – traffic, B – budget of a channel. P=

where P – the price of attracting one customer of goods through this channel. A modern communication channel must meet four conditions: uniqueness, urgency, specificity and usefulness.

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The message should be formed from the standpoint of content marketing [17–20]. That is, the so-called “ladies” must be formed. The classic indicator of channel efficiency is the rate of return on investment in the communication channel [17]: ROI =

Pr −Ex Ex

(3)

where Pr – profit, Ex- expenses on channel formation. Another important indicator is the conversion (4). It reflects the achievement of the main goal - to attract the required number of buyers of goods. K=

Q N

(4)

where Q – the number of customers attracted by the promotion channel, and N is the total number of channel visitors [18]. All of the above indicators correspond to one of seven categories, namely: traffic, bounce rate, conversion, the cost of attracting one buyer, the average check, return on investment, repeat visits. But these indicators are only metrics, unfortunately, the criterion of effectiveness among them is not identified. Modern theory of Internet promotion is based only on the metric approach. Thus, there is an urgent problem of formulating a criterion for the effectiveness of virtual promotion. This criterion should describe the benefit of the message in the promotion channel and the benefit of the channel itself. And since virtual promotion is a two-tier system, the benefits must be determined at two levels coordinated in time.

4 Summary and Conclusion The above description of a new control object - virtual promotion of a product allows us to formulate the following conclusions: 1) The main goal of managing this object is to increase the sales of the product. 2) The object of management is complex and includes two channels: logistics and marketing. The first channel performs the function of distributing knowledge from node to node, and the second channel controls this transformation. The logistics channel forms the configuration of the system, and the marketing channel forms its organizational structure. 3) The article presents a modern diagram of the business process of virtual promotion within the framework of the IDEF0 methodology. The study of this scheme allowed us to form a set of four tasks. This is a new approach, a new vision of the problem of virtual promotion of a product. 4) The approach proposed in the article is based on solving the problem of structuralparametric synthesis, the problem of coordinating the functioning of two channels, the problem of forming a semantic kernel, as well as the problem of evaluating efficiency based on a new criterion of optimality.

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5) The analysis of metrics for evaluating the effectiveness of virtual promotion was carried out and it was revealed that there is no criterion of optimality. The direction of further research should be considered the problem of forming a criterion for the optimality of virtual promotion. This criterion should include constraints and metrics for the seven identified areas.

References 1. Lambert, D.M.: Fundamentals of Logistics Management, 622 p. McGrow Hill, New York (1998) 2. Alani, M.M.: Guide to OSI and TCP/IP Models, pp. 1–50. Springer, Cham (2014). https:// doi.org/10.1007/978-3-319-05152-9 3. Christopher, M.: Logistics & Supply Chain Management, 288 p. Prentice Hall, Upper Saddle River (2011) 4. IFEF0: Integration Definition for Function Modeling, 128 p.. National Institute of Standards and Technology, Gaithersburg (1993) 5. Godlevsky, M.D., Orekhov, S.V.: Theoretical fundamentals of search engine optimization based on machine learning. CEUS-WS 1844, 23–32 (2017) 6. Kelsey, T.: Introduction to Search Engine Optimization, 126 p. Apress, Berkeley (2017) 7. Veglis, A., Giomelakis, D.: Search Engine Optimization, 104 p. Future Internet (2021) 8. Orekhov, S.V., Malyhon, H.V.: Virtual promotion knowledge management technology. Bull. Natl. Tech. Univ. “KhPI”. Ser. Syst. Anal. Control Inf. Technol. NTU «KhPI» 1(3), 74–79 (2020) 9. Hashimova, K.K.: Analysis method of internet advertising-marketing information’s dynamic changes. Int. J. Inf. Eng. Electron. Bus. 5, 28–33 (2017) 10. Alvin, K.F., Robertson, A.N., Reich, G.W., Park, K.C.: Structural system identification: from reality to models. Comput. Struct. 81, 1149–1176 (2003) 11. Lei, J.: Static structural system identification using observability method. A Doctoral thesis Submitted to UniversitatPolitècnica de Catalunya, 180 p. (2018) 12. Subbotin, S.A.: Structural-parameter identification fuzzy neural models for diagnostics. Bionika Intellect. KNURE 2(71), 118–122 (2009). (in Russian) 13. Karabutov, N.: Structural identifiability of nonlinear dynamic systems under uncertainty. Int. J. Intell. Syst. Appl. 1, 12–22 (2020) 14. Karabutov, N.: Geometrical framework application directions in identification systems. Review. Int. J. Intell. Syst. Appl. 2, 1–20 (2021) 15. Kotler, P., Armstrong, G., Saunders, J., Wong, V.: Principles of Marketing, 1036 p. Prentice Hall Europe, Upper Saddle River (1999) 16. Kotler, P., Keller, K.: Marketing Management, 812 p. Prentice Hall, Upper Saddle River (2012) 17. Kamala, H.: Development of an effective method of data collection for advertising and marketing on the internet. Int. J. Math. Sci. Comput. (IJMSC) 7(3), 1–11 (2021). https://doi.org/ 10.5815/ijmsc.2021.03.01 18. Rowley, J.: Understanding digital content marketing. J. Mark. Manag. 24(5–6), 517–540 (2008) 19. Sihare, S.R.: Roles of e-content for e-business: analysis. Int. J. Inf. Eng. Electron. Bus. 1, 24–30 (2018) 20. Bendle, N., Farris, P., Pfeifer, P., Reibstein, D.: Marketing metrics. In: The Manager’s Guide to Measuring Marketing Performance, 456 p. Pearson Education, Inc., Boston (2016)

Conditions of Non-uniform Fluidization in an Auto-oscillating Mode Bogdan Korniyenko(B) , Yaroslav Kornienko, Serhii Haidai, Andrii Liubeka, and Serhii Huliienko National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Kyiv 03056, Ukraine [email protected]

Abstract. The use of fluidization technique provides high efficiency in diffusioncontrolled processes. However, the efficiency and intensity of the application of the fluidization technique significantly depends on the hydrodynamic mode of fluidization and the height of the bed of solid granular material. To solve this problem in this work is proposed to apply non-uniform fluidization in an autooscillating mode at a height of the bed of solid material, which is four times higher than the breakdown height of the gas jet. In this work is presented the physical model of non-uniform jet-pulsating fluidization in an auto-oscillating mode at the ratio of the height of the initial bed of solid granular material to the breakdown height of the gas jet zf /H 0 = 0.33 and zf /H 0 ≤ 0.25. The influence of the rate of supplying of the gas liquefying agent on the quality of hydrodynamics as well as on the formation of the gas bubble is analyzed. The conditions under which the absence of stagnant zones on the working surfaces of the gas distribution device is ensured, which is very important when supplying the coolant with a temperature exceeding the melting point of components of the granular material which are sensitive to temperature. Keywords: Granulation · Fluidized bed · Non-uniform fluidization

1 Introduction The use of fluidization techniques in heat and mass transfer processes ensures their implementation with a heat utilization rate of more than 50% [1–11]. This is especially important when carrying out granulation processes of liquid systems in a fluidized bed. The economic feasibility of such processes is achieved through the use of a coolant with a high temperature, however, there is a risk of formation of stagnant zones with subsequent melting of the material on the working surfaces of the gas distribution device (GDD) [12–20]. The rate of transfer processes in dispersed media in the presence of a phase transition is determined by the thickness of the diffusion sublayer. In order to further increase the efficiency of diffusion-controlled processes in recent years in published works [12–20] it is proposed to use non-uniform fluidization in an © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 14–27, 2022. https://doi.org/10.1007/978-3-031-03877-8_2

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auto-oscillating mode. As a result of the implementation of such a hydrodynamic mode of fluidization, it is possible to slightly reduce the thickness of the diffusion sublayer located near the surface of solid particles and, accordingly, to increase the intensity of the transfer processes. Typically, a mechanical device (pulsator) was used for pulsating coolant supply [21]. However, with this method of supplying the heated coolant there is a cyclic temporary cessation of its supply. There is a certain time interval when the granular material is stationary on the surface of the gas distribution device (GDD). In the case of dehydration and granulation processes in the presence of materials which are sensitive to temperature, this method of implementing inhomogeneous fluidization is unacceptable. The essence of the technical solution to eliminate this shortcoming is to create a hydrodynamic regime, which provides active volumetric circulation of granular material in the layer with minimizing the volume and residence time of the granules on the working heated surfaces of the gas distribution device (GDD) having a high temperature [22–48].

2 Physical Model of Non-uniform Jet-Pulsating Fluidization in an Auto-oscillating Mode A method of implementing non-uniform fluidization in an auto-oscillating mode without the use of a mechanical pulsator was investigated in works [12–20].

a) =0 state of equilibrium

b) = 1 gas bubble formation

c) = 1+ 2 rise of a gas bubble, removal of solid material

d) = 1+ 2+ 3 the shift of solid material layer to reach state of equilibrium

Fig. 1. Physical model of non-uniform jet-pulsating fluidization in an auto-oscillating mode at H 0 /A = 1; zf /H 0 = 0.33; Z.I. – zone of intensive heat and mass transfer; I.Z. – irrigation zone; M.Z. – the movement zone of granular material

The auto-oscillating non-uniform jet-pulsation mode of fluidization, Fig. 1, a detailed description of which is given by the authors [15–20] is provided by two-level asymmetric

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introduction of the liquefying agent into the granulator chamber and takes place in several stages: 1 – gas bubble formation – τ1 , Fig. 1 a, b; 2 – inertial ejection of granular material from zones II and III into the space upper the bed of solids and its redirection to the relaxation zone I – τ2 , Fig. 1 c; 3 – intensive movement of granular material from zone I to the formed cavities in zones II and III with the return of the bed of solids to equilibrium – τ3 , Fig. 1 d. The total duration of the cycle of one pulsation, s: τcycle = τ1 + τ2 + τ3 .

(1)

The proposed model of non-uniform fluidization allows to realize three-dimensional mixing of granules (solid particles) in the apparatus with passage through all technological zones, providing active renewal of the contact surface of the phases, which is confirmed by research results in [12–20] at the height of the fixed bed of solid material H 0 /A≈1.

3 Determination of Main Parameters of the Non-uniform Jet-Pulsating Fluidization in an Auto-oscillating Mode 3.1 Determination the Speed of Movement of the Mass Center of Bed of Solids The conditional scheme of movement of the center of mass of the bed of granular material is shown in the Fig. 2. In the general case, the motion of the mass center is complex, so it is proposed to determine the chord between the initial A0 and extreme upper position of the center of mass at point Amax . The deviation of the position of the center of mass along the z and x axes was determined by the values of z and x. It is assumed that the movement of mass center along the axis y is absent and y = 0 m. With this in mind, the length of the segment A0 Amax can be determined from the expression, m:  |A0 Amax | = zi2 + xi2 . (2) The average speed of movement of mass center of bed of solids can be defined as, m/s:  zi2 + xi2 wmass center (τi ) = . (3) τi With this at the beginning of the pulsation cycle at τi = 0 s the bed of solid granular material is in state of equilibrium, its mass center occupies the initial position A0 (z0 ; x 0 ), Fig. 2, and the value of average speed of its movement is wmass center = 0 m/s.

Conditions of Non-uniform Fluidization in an Auto-oscillating Mode

17

c) τі =τ1+τ2

a) τі =0 state of equilibrium at the beginning of the cycle

b) τі =τ1+τ2 maximum displacement of solid material

d) τі = τ3

Fig. 2. Conditional scheme of movement of mass center of solid material bed at realization of non-uniform jet-pulsating fluidization in an auto-oscillating mode in the case when H 0(1) /A = 1

According to the physical model, the maximum value of the displacement of the mass center at point Amax is achieved during the second stage of the pulsation (τ1 + τ2 ), and the return at point A0 in the third stage (τ3 ). Then the speed of movement of the mass center from A0 to Amax (wmass center(↑) ) and, accordingly, in the opposite direction from Amax to A0 (wmass center(↓) ) can be defined as, m/s:  2 2 zmax + xmax . (4) wmass center(↑) = τ1 + τ2  2 2 zmax + xmax . (5) wmass center(↓) = τ3 The average value of the speed at the extreme positions of the mass center of bed of solids for stage 3 can also be written as, m/s:  wmass center(↓) = 2gzmax . (6) The value of the speed of movement of the mass center to the point Amax is derived from the expression: wmass center(↑) τ1 + τ2 = = Km.c. . (7) wmass center(↓) τ3 Whence: wmass center(↑) = wmass center(↓) Km.c. . where Km.c. < 1, and values of τ1 , τ2 and τ3 are determined experimentally.

(8)

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3.2 Determination of the Hydrodynamics Quality Thus, the hydrostatic pressure at point p, Fig. 3, which is determined by the height of the bed of solid granular material in zone I will increase 2 times compared to the initial state at τ = 0 when H bed = H 0 , Fig. 1 a. That is, at this point in zone D, Fig. 3, there may be a stationary zone or low moving speed of solid granular material on the working surface of the gas distribution device with size δ.

Fig. 3. Scheme for determining the quality of the mode of fluidization

To do this, the dependence of the porosity in the specified zone D – εD(i) = f (τ) was determined by video recording and compared with the allowable set point [εD ] = 0.85…0.95. To quantify the quality of hydrodynamics, the Taguti method is used, which allows to calculate the loss of quality of hydrodynamics [18–20]:    2 [δ] − δ(i) 2 , (9) LD = K1 [εD ] − εD(i) + K2 l where K1 = 0.3 and K2 = 0.7 – are the coefficients of proportionality; εD(i) – experimentally determined the current value of porosity in zone D; [δ] = 0.01l, m; l – chord length of GDD plate, m. Hydrodynamics quality index [18–20]: Ya = 1 − LD .

(10)

The area of satisfactory quality is achieved when the value of the quality index of hydrodynamics is 0.9 ≤ Y a ≤ 1. The maximum value of the quality of hydrodynamics

Conditions of Non-uniform Fluidization in an Auto-oscillating Mode

19

Y a = 1 will be achieved when the value of the loss of quality L D → 0 [18–20]. The final satisfactory value of the quality of hydrodynamics will be determined experimentally. 3.3 Determining the Conditions for Ensuring High-Quality Hydrodynamic Mode of Fluidization The technical concept of the slit-type gas distribution device is that such a kinetic energy can be locally introduced into the bed of solid granular material, which with a frequency f = 1.5… 2 Hz would increase the potential energy of the fluidized bed by almost 2 times. Energy consumption to increase the potential energy of the fluidized bed: Ep =

Mbed (H0 + hI )g. τ1 + τ2

(11)

With this the condition E k > E p must be fulfilled: Ek =

2 (m1 + m2 )wslits . 2

(12)

where m1 + m2 – the total mass consumption of the liquefying agent, kg/s; wslits – gas velocity in the slits of gas distribution device, m/s (assume that wslits = wslit(1) = wslit(2) ). Ensuring conditions for the quality of hydrodynamics in zone D, Fig. 3, is achieved solely by the influence of gas velocity in the slits, which depends on the coefficient of GDD cross section – ϕ. wslit(1) =

Vs , ϕAB

(13)

where V s – the total volumetric liquefying agent consumption at the given temperature calculated from the mass transfer conditions, m3 /s; A, B – geometric dimensions of the device in cross section of GDD, m; ϕ – coefficient of GDD cross section, %. 3.4 Flow Simulation in SolidWorks For the slit-type gas distributing device with different values of the cross section coefficient [22–24] For the slit-type gas distributing device with different values of the cross section coefficient [22–24] using the SolidWorks plots of the velocities of the gas coolant near the working surfaces of gas distributing device (GDD) were obtained, Fig. 4 a, b. The obtained simulation results confirm that when using a gas distribution device of type 2 with a cross-section coefficient ϕ 2 = 4.9% the value of the gas velocity at the exit from the slit of the GDD is 1.72 times higher than when using GDD of type 1.

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а) GDD type 1(

1=6%)

b) GDD type 2 (

2=4.9%)

Fig. 4. Diagrams of liquefying agent velocities for two types of GDD at V s = 0.03736 m3 /s (SolidWorks)

3.5 Explanation of Determining the Gas Velocity in Slits of GDD The presence of a local increase in gas velocity by 1.8 times at the outlet of slit 1 of the gas distribution device (GDD) type 2 allowed to increase the kinetic energy of the jet by 3.24 times, which meets the requirements of the physical model to the gas distribution device.

Fig. 5. Scheme of force distribution in the area of introduction of the liquefying agent

To ensure the quality index of hydrodynamics Ya ≥ 0.9, the velocity in the slit of the gas distribution device at the level of the point p must be wslits ≥ 35 m/s, Fig. 5. The force of hydrodynamic pressure of the gas F gas must be greater than the total counteraction force τ counteraction on the surface of GDD arising from hydrostatic pressure: Fgas ≥ τcounteraction

(14)

Fgas = Pgas fslits ,

(15)

where Pgas – gas pressure at point p, Pa:  2 2, Pgas = ρgas wslits

(16)

Conditions of Non-uniform Fluidization in an Auto-oscillating Mode

21

where f slits – the area of the slit at point p, m2 : fslits = h1 B1 ,

(17)

where h1 and B1 – height and width of the slit at point p, m. τ counteraction – the total force of counteraction, N: τcounteraction = Phydrostatic Kτ fGDD ,

(18)

where Phydrostatic – hydrostatic pressure of the layer of granular material at point p, Pa: Phydrostatic = H0 (1 − ε0 )ρsolids g,

(19)

where ε0 – porosity (proportion of voids) of a tightly packed bed of solids (ε0 = 0.4); ρ solids – density of solid granules, ρ solids = 1450 kg/m3 ; g – acceleration of gravity, g = 9.81 m/s2 ; Kτ – transformation coefficient; h1 and B1 – height and width of the slit at point p; f GDD – the working surface area of the gas distribution device (trapezoids with bases B1 and B2 and height l), m2 :

fGDD =

B1 + B2 l. 2

(20)

Then after substitution (15) and (18) into (14): Pgas fslits = Phydrostatic Kτ fGDD .

(21)

For the case H 0 = 0.32 m the transformation coefficient is determined by the expression: Kτ =

Pgas fslits . Phydrostatic fGDD

(22)

For all other cases, it is possible to calculate the gas velocity in the slits, which provides an index of hydrodynamic quality Y a ≥ 0.9 by expression:  wslits =

2H0∗ (1 − ε0 )ρsolids gfGDD Kτ ρgas fslits

0.5 ,

where H 0 * – the given value of the total height of fixed bed of solids, m.

(23)

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4 Experimental Study of the Influence of the Height of the Bed of Granular Material on the Size of the Formed Gas For a slit type gas distributing device, the formation of a gas bubble at a height yf = zf +  takes place in the form of a cylinder with a horizontal axis. In this case, the diameter of the bubble underlying this cylinder is calculated by the proposed expression [16–20]:   H0 − zf +  dbubble = . (24) 1+π 4 The calculation of the diameter of the gas bubble depending on the height of the fixed bed of solids is given in the Table 1. Thus, when doubling the initial height of the bed of solids H 0 = 2 A the estimated size of the diameter of the gas bubble is almost equal to the width d bubble = 0.986 A, Fig. 6. Since the axis of formation of the gas bubble is shifted by 2/3 relative to the width – the bubble begins to move vertically closer to the right side, Fig. 6. There is some deformation of the shape of the gas bubble, Fig. 6, as well as a partial shift of the material from zone II to zone III. This creates the conditions for the formation of a second, smaller gas bubble. At this moment in zone III, condition H residual ≤ zf +  is satisfied. Table 1. The diameter of the gas bubble depending on the initial height of the bed H 0 H0 , mm

H0 /d bubble

H 0 , mm

H 0 /A

d bubble , mm

d bubble /A

320

1.00

112

0.370

88

0.780

420

1.40

168

0.560

132

0.785

520

1.73

224

0.746

176

0.785

620

2.06

280

0.950

214

0.764

650

2.16

296

0.986

234

0.790

In this phase, the height of the bed of solid granular material in zone I increase by 2 times, which causes an adequate increase in hydrostatic pressure at point p of the base slit, Fig. 6. This leads to a short-term adequate reduction of gas coolant flow through the base slit at the point p and leads to the formation of a local zone with a slow moving granular material. For the case when H 0 = 320 mm at a pulsation frequency f = 1.8…2.0 Hz for d e = 4.35 mm the material ejection time is τ 2 = 0.25τ c = 0.25·0.58 = 0.145 s.

Conditions of Non-uniform Fluidization in an Auto-oscillating Mode

a) =0 formation of the first gas bubble

b) = 1 formation of a second gas bubble

c) = 1+ 2 merging of gas bubbles and lifting with removal of material

23

d) = 1+ 2+ 3 shift of the material layer to reach state of equilibrium

Fig. 6. Physical model of non-uniform jet-pulsating fluidization in an auto-oscillating mode at H 0 = 2 A; zf /H 0 ≤ 0.25; Z.I. – zone of intensive heat and mass transfer; I.Z. – irrigation zone; M.Z. – the movement zone of granular material

5 Summary and Conclusion The use of pulsating injection of the liquefying agent into the fluidized bed allows increasing the efficiency of diffusion-controlled processes. However, the provision of pulsations due to the use of mechanical devices is inefficient, energy consuming, and makes it impossible to supply coolant with a temperature exceeding the temperature of destruction of components which are sensitive to temperature in the processes of granulation of organic-mineral fertilizers, since stagnant zones are formed on the working surfaces of the gas distribution device. A method of implementing non-uniform jetpulsating mode of fluidization in an auto-oscillating mode without the use of mechanical pulsators is presented in this paper and the definition of the main parameters that provide high-quality of fluidization hydrodynamics is proposed: 1) In this work is presented the physical model of non-uniform jet-pulsating fluidization in an auto-oscillating mode at the ratio of the height of the initial bed of solid granular material to the breakdown height of the gas jet zf /H 0 = 0.33.

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2) Non-uniform fluidization in an auto-oscillating mode depends on the pulsation transfer of the mass center of the bed of solids along the horizontal and vertical axes. 3) The index of quality of hydrodynamics is provided by porosity of a bed of solids near a surface of the gas-distributing device (GDD) [εD ] = 0.85…0.95 and also in the absence of stagnant zones on plates of GDD. The hydrodynamic mode of fluidization is considered qualitative when the value of the quality index of hydrodynamics is 0.9 ≤ Y a ≤ 1. 4) The obtained results of the flow simulation in SolidWorks confirm that when using a gas distribution device of type 2 with a cross-section coefficient ϕ 2 = 4.9% the value of the gas velocity at the exit from the slit of the GDD is 1.72 times higher than when using GDD of type 1. 5) Is established an expression of calculating the gas velocity in the slits of GDD that provides an index of hydrodynamic quality Ya ≥ 0.9 depending on height of initial bed of solids and parameters of GDD. 6) Is presented the physical model of non-uniform jet-pulsating fluidization in an autooscillating mode at the ratio of the height of the initial bed of solid granular material to the breakdown height of the gas jet zf /H 0 ≤ 0.25 based on the results of visual and video analysys of experimental studies.

References 1. Kornienko, Y., Raida, V., Sachok, R., Tsepkalo, O.: Mathematical modelling of continuous formation of multilayer humic-mineral solid components. Chem. Chem. Technol. 3(4), 335– 338 (2009) 2. Kornienko, Y., Raida, V., Sachok, R.: Complex assessment of the efficiency of granulation process in dispersed systems. Chem. Chem. Technol. 2(3), 217–220 (2008) 3. Kornienko, Y.M.: Technical methods of granulation, 128 p. IZMM (1997). (Ukr.) 4. Kornienko, Y.M.: The efficiency of the formation of multilayer solid composites. Naukovipraci Odes’koi’ nacional’noi’ akademii’ harchovyh tehnologij. Sci. Works Odessa Natl. Acad. Food Technol. 32, 97–99 (2008). (Ukr.) 5. Kornienko, Y.M.: Utilization of industrial waste through the creation of technology for the production of new fertilizers for environmentally friendly agriculture. Abstract of the dissertation for the degree of Doctor of Technical Sciences, C. 29 (2003). (Ukr.) 6. Kornienko, Y.M.: Research of processes of formation of complex crystalline-amorphous structures from industrial waste for protection and ecologically safe development of environment. NTUU «KPI»221 (2009). http://ela.kpi.ua/handle/123456789/1609/. (Ukr.) 7. Kornienko, Y., Haidai, S., Martyniuk, O.: Improved process to obtain granular humic fertilizers. NTUU «KPI», 349. NTUU «KPI», Kyiv (2014). http://ela.kpi.ua/handle/123456789/ 11943/ 8. Kornienko, Y.M., Semenenko, D.S., Haidai, S.S.: The process of obtaining modified granular humic-mineral fertilizers, p. 167. National Technical University of Ukraine «Kyiv Polytechnic Institute», Kyiv (2015) http://ela.kpi.ua/handle/123456789/11944. (Ukr.) 9. Kornienko, Y.M., Lubeka, A.M., Haidai, S.S.: The process of obtaining modified granular humic-mineral fertilizers, 210 p. National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Kyiv (2017). http://ela.kpi.ua/handle/123456789/21268/. (Ukr.)

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10. Kornienko, Y.M., Sachok, R.V., Gaidai, S.S., Martyniuk, O.V., Kurinovsky, O.V., Lubeka, A.M.: Kinetics of the process of creating organo-mineral humic fertilizers. Naukovipraci Odes’koi’ nacional’noi’ akademii’ harchovyh tehnologij. Sci. Works Odessa Natl. Acad. Food Technol. 47(1), 167–170 (2015). (Ukr.) 11. Kornienko, Y., Hayday, S., Liubeka, A., Martynyuk, O.: Kinetic laws of the process of obtaining complex humic-organic-mineral fertilizers in the fluidized bed granulator. Ukrainian Food J. 5(1), 144–154 (2016) 12. Kornienko, Y.M., Sachok, R.V., Haidai, S.S.: Simulation of non-uniform fluidization in an auto-oscillating mode.Int. Sci. J. «Internauka» 4(66), 63–67 (2019). https://ela.kpi.ua/bitstr eam/123456789/31088/3/Modeling_of_inhomogeneous_luidizing.pdf. (Ukr.) 13. Kornienko, Y.M., Gaidai, S.S., Denisenko, V.R., Shevchenko, Y.M.: Hydrodynamics of nonuniform fluidization. Proc. NTUU “Igor Sikorsky KPI”. Ser. Chem. Eng. Ecol. Resour. Saving 1, 13–17 (2019). https://doi.org/10.20535/2617-9741.1.2019.170880. (Ukr.) 14. Artemiev, V.K., Kornienko Y.N.: Numerical modeling of influence non-monotonic profile of gas content on a distribution of velocity and temperature in a two-phase bubbly flow. In: Proceedings of the 3rd Russian National Conference, pp. 41–44 (2002) 15. Kornienko, Y.M., Gaidai, S.S., Lubeka, A.M., Turko, S.O.: Hydrodynamics of jet-pulsation mode of fluidization with directional circulation. Mizhnarodnyjnaukovyj zhurnal. [Int. Sci. J.] 2(5), 101–106 (2016). (Ukr.) 16. Kornienko, Y., Haidai, S.: Non-uniform fluidization in auto-oscillating mode. Ukrainian Food J. 6(3), 562–576 (2017) 17. Korniyenko, Y., Haidai, S., Liubeka, A., Turko, S., Martynyuk, O.: Modelling of pulsating mode of fluidization when obtaining organic-mineral fertilizers. Ukrainian Food J. 5(4), 781– 794 (2016) 18. Haidai, S.S.: Hydrodynamics in granulators with a fluidized bed when obtaining organicmineral fertilizers. Abstract of the dissertation of the candidate of technical sciences, p. 24. National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» (2018). https://ela.kpi.ua/bitstream/123456789/25455/1/Haidai_diss.pdf. (Ukr.) 19. Haidai, S.S.: Hydrodynamics in granulators with a fluidized bed when obtaining organicmineral fertilizers. Dissertation of the candidate of technical science, p. 253. National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» (2018). https://ela. kpi.ua/bitstream/123456789/25455/1/Haidai_diss.pdf. (Ukr.) 20. Tuponogov, V., Rizhkov, A., Baskakov, A., Obozhin, O.: Relaxation auto-oscillations in a fluidized bed. Thermophys. Aeromech. 15(4), 603–616 (2008) 21. Shevchenko, Y.M., Kornienko, Y.M., Haidai, S.S., Denisenko, V.R.: Gas distributing device of the apparatus of fluidized bed. Patent UA 136196 U Ukraine, IPC B01J 8/44, 18 February 2019, Bulletin № 15 (Ukr.) 22. Turko, S.O., Kornienko, Y.M., Haidai, S.S., Martyniuk, O.V., Liubeka, A.M.: Gas distributing device of the apparatus of the fluidized bed. Patent № 109509 Ukraine, IPC (2006.01) B01J 8/44. 25 August 2016, Bulletin № 16/2016 (Ukr.) 23. Denisenko, V.R., Kornienko, Y.M., Haidai, S.S., Shevchenko, Y.M.: Apparatus for nonuniform fluidized bed in auto-oscillating mode. Patent № 133308 Ukraine, IPC (2006) B01J 8/44 (2006.01) B01J 8/00, 25 March 2019, Bulletin № 6/2019 (Ukr.) 24. Kornienko, Y.M., Sachok, R., Tsepkalo, O.V.: Modelling of multifactor processes while obtaining multilayer humic-mineral solid composites. Chemistry 20(3), E19–E26 (2011) 25. Kornienko, Ya.N., Podmogilnyi, N.V., Silvestrov, A.N., Khotyachuk, R.F.: Current control of product granulometric composition in apparatus with fluidized layer. J. Autom. Inf. Sci. 31(12), 97–106 (1999)

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26. Korniyenko, B., Ladieva, L.: Mathematical modeling dynamics of the process dehydration and granulation in the fluidized bed. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds.) ICCSEEA 2020. AISC, vol. 1247, pp. 18–30. Springer, Cham (2021). https://doi.org/10. 1007/978-3-030-55506-1_2 27. Korniyenko, B., Ladieva, L., Galata, L.: Control system for the production of mineral fertilizers in a granulator with a fluidized bed. In: ATIT 2020 - Proceedings: 2020 2nd IEEE International Conference on Advanced Trends in Information Theory, № 9349344, pp. 307–310 (2020). https://doi.org/10.1109/ATIT50783.2020.9349344 28. Ladieva, L., Kozanevych, Z., Klusta, T., Korniyenko, B.: System of control of the process of alkylation of benzene with peripene in the liquid phase. In: ATIT 2020 - Proceedings: 2020 2nd IEEE International Conference on Advanced Trends in Information Theory, № 9349330, pp. 311–314 (2020). https://doi.org/10.1109/ATIT50783.2020.9349330 29. Galata, L., Korniyenko, B.: Research of the training ground for the protection of critical information resources by iRisk method. In: Zawi´slak, S., Rysi´nski, J. (eds.) Engineer of the XXI Century. MMS, vol. 70, pp. 227–237. Springer, Cham (2020). https://doi.org/10.1007/ 978-3-030-13321-4_21 30. Kornienko, Y.M., Haidai, S.S., Sachok, R.V., Liubeka, A.M., Korniyenko, B.Y.: Increasing of the heat and mass transfer processes efficiency with the application of non-uniform fluidization. ARPN J. Eng. Appl. Sci. 15(7), 890–900 (2020) 31. Korniyenko, B., Galata, L., Ladieva, L.: Research of information protection system of corporate network based on GNS3. In: 2019 IEEE International Conference on Advanced Trends in Information Theory, ATIT 2019 - Proceedings, № 9030472, pp. 244–248 (2019). https:// doi.org/10.1109/ATIT49449.2019.9030472 32. Korniyenko, B., Galata, L.: Implementation of the information resources protection based on the CentOS operating system. In: 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering, UKRCON 2019 - Proceedings, № 8879981, pp. 1007–1011 (2019). https://doi.org/10.1109/UKRCON.2019.8879981 33. Korniyenko, B., Galata, L., Ladieva, L.: Mathematical model of threats resistance in the critical information resources protection system. In: CEUR Workshop Proceedings, vol. 2577, pp. 281–291 (2019) 34. Zhulynskyi, A.A., Ladieva, L.R., Korniyenko, B.Y.: Parametric identification of the process of contact membrane distillation. ARPN J. Eng. Appl. Sci. 14(17), 3108–3112 (2019) 35. Korniyenko, B.Y., Borzenkova, S.V., Ladieva, L.R.: Research of three-phase mathematical model of dehydration and granulation process in the fluidized bed. ARPN J. Eng. Appl. Sci. 14(12), 2329–2332 (2019) 36. Kornienko, Y.M., Liubeka, A.M., Sachok, R.V., Korniyenko, B.Y.: Modeling of heat exchangement in fluidized bed with mechanical liquid distribution. ARPN J. Eng. Appl. Sci. 14(12), 2203–2210 (2019) 37. Korniyenko, B.Y., Osipa, L.V.: Identification of the granulation process in the fluidized bed. ARPN J. Eng. Appl. Sci. 13(14), 4365–4370 (2018) 38. Korniyenko, B., Galata, L., Ladieva, L.: Security estimation of the simulation polygon for the protection of critical information resources. In: CEUR Workshop Proceedings, vol. 2318, pp. 176–187 (2018) 39. Galata, L.P., Korniyenko, B.Y., Yudin, A.K.: Research of the simulation polygon for the protection of critical information resources. In: CEUR Workshop Proceedings, vol. 2067, pp. 23–31 (2017) 40. Kravets, P., Shymkovych, V.: Hardware implementation neural network controller on FPGA for stability ball on the platform. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds.) ICCSEEA 2019. AISC, vol. 938, pp. 247–256. Springer, Cham (2020). https://doi.org/10.1007/978-3030-16621-2_23

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41. Deka, K.: Modeling of air temperature using ANFIS by wavelet refined parameters. Int. J. Intell. Syst. Appl. (IJISA) 8(1), 25–34 (2016). https://doi.org/10.5815/ijisa.2016.01.04 42. Ghiasi-Freez, J., Hatampour, A., Parvasi, P.: Application of optimized neural network models for prediction of nuclear magnetic resonance parameters in carbonate reservoir rocks. Int. J. Intell. Syst. Appl. (IJISA) 7(6), 21–32 (2015). https://doi.org/10.5815/ijisa.2015.06.02 43. Malekzadeh, M., Khosravi, A., Noei, A.R., Ghaderi, R.: Application of adaptive neural network observer in chaotic systems. Int. J. Intell. Syst. Appl. (IJISA) 6(2), 37–43 (2014). https:// doi.org/10.5815/ijisa.2014.02.05 44. Bhagawati, K., Bhagawati, R., Jini, D.: Intelligence and its application in agriculture: techniques to deal with variations and uncertainties. Int. J. Intell. Syst. Appl. (IJISA) 8(9), 56–61 (2016). https://doi.org/10.5815/ijisa.2016.09.07 45. Wang, W., Cui, L., Li, Z.: Theoretical design and computational fluid dynamic analysis of projectile intake. Int. J. Intell. Syst. Appl. (IJISA) 3(5), 56–63 (2011). https://doi.org/10.5815/ ijisa.2011.05.08 46. Patnaik, P., Das, D.P., Mishra, S.K.: Adaptive inverse model of nonlinear systems. Int. J. Intell. Syst. Appl. (IJISA) 7(5), 40–47 (2015). https://doi.org/10.5815/ijisa.2015.05.06 47. Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M.: Methods and models for information data analysis. In: Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M. (eds.) Diagnostic Systems for Energy Equipments. Studies in Systems, Decision and Control, vol. 281, pp. 23–70. Springer, Cham (2021). https://doi. org/10.1007/978-3-030-44443-3_2 48. Babak, V., Shchepetov, V., Nedaiborshch, S.: Wear resistance of nanocomposite coatings with dry lubricant under vacuum. Sci. Bull. Natl. Min. Univ. Issue 1, 47–52 (2016)

The Heat Exchange in the Process of Granulation with Non-uniform Fluidization Bogdan Korniyenko(B) , Yaroslav Kornienko, Serhii Haidai, and Andrii Liubeka National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Kyiv 03056, Ukraine [email protected]

Abstract. In modern conditions, widely used technologies for the approval of solid compositions with given power structures that correspond to the morphological, which ensures the uniform distribution of mineral and organic components in all parts of the solid fertilizers. The stability of the kinetics of multifactorial processes during granulation significantly depends on the heat exchange in the middle of the fluidized bed. A mathematical model for the calculation of the temperature field by high devices for the processes of granulation of liquid systems in devices with fluidized bed in the self-oscillating mode using the conical design of a mechanical dispersant with an extended growth zone is proposed. The technique research of a temperature field in the process of granulation humic and mineral fertilizers is offered, development the map of thermocouples for definition change of temperature on height of the device. The adequacy of the application of this method of modeling has been experimentally achieved and can be used for tested processes that perform a phase transition. Keywords: Granulation · Fluidized bed · Non-uniform fluidization

1 Introduction In the context of the aggravation of the global food crisis, Ukraine occupies a prominent place among agricultural producers. This is especially true for the production of sunflower oil. However, the degree of plowing of soils in Ukraine reaches 57%, which is twice as high as for EU soils. Such intensity of exploitation of agricultural lands leads to rapid depletion. In the world practice of agriculture, the movement for the introduction of organic farming as a development of the paradigm of “sustainable development” began to spread intensively. This direction emerged as an alternative to excessive use of only mineral fertilizers to preserve soil fertility [1, 2]. In accordance with the recommendations of the Ukrainian Academy of Agrarian Sciences (UAAS), the authors [3] developed a method of obtaining granular humicmineral fertilizers that contain macroquantities of minerals of mineral and organic origin, deoxidizing components and microquantities of humates and other elements. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 28–37, 2022. https://doi.org/10.1007/978-3-031-03877-8_3

The Heat Exchange in the Process of Granulation with Non-uniform Fluidization

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Moreover, the content of nutrients, stimulants and deoxidizing substances must meet the agro-climatic conditions of the region of their use, which will help preserve the ecological balance. One of the main requirements for granular humic and mineral fertilizers is the uniform distribution of nutrients and stimulating components throughout the volume of the granules. The authors [4] theoretically substantiated and experimentally proved that in order to fulfill these requirements it is expedient to apply the technique of dehydration of multicomponent liquid systems in a fluidized bed. It is known that the use of fluidization technique allows the heat transfer process with a heat utilization factor η ≥ 50%. Experimental studies [4–8] have shown that ensuring the uniformity of distribution of components in the granule can be achieved only with a layered granulation mechanism. Given that the process of dehydration and granulation is accompanied by phase transitions and is diffusion-controlled, to implement a layered mechanism, it is advisable to increase the intensity of transfer processes and activate the change of phase contact surfaces in the fluidized bed [11–35]. To solve this technical problem, the authors [5–8] proposed to use inhomogeneous fluidization in self-oscillating mode without the use of mechanical devices.

2 Physical Model of Non-uniform Fluidization in the Granulator Chamber The essence of the process of non-uniform fluidization is that the liquefying agent is introduced into the granulator chamber in the horizontal and vertical directions by means of a special gas distribution device (FGD), Fig. 1.

Fig. 1. Physical model of non-uniform fluidization

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At a certain height, the two jets merge and result in the formation of a combined gas flare, the top of which begins to form a gas bubble, provided that the filtration rate around its perimeter is much lower than the rate of gas phase supply. After reaching the critical size, the bubble moves vertically, which causes the inertial release of a significant mass of material into the superlayer space? When interacting with the guide distributor, the solid particles move to the surface of zone I, Fig. 1. The transferred material is rapidly returned to the voids formed in zones II and III to the initial equilibrium state, the cycle is repeated many times. In addition, in zone I, the direction of movement of the granular material with a porosity ε = 0.4 Fig. 2 is opposite to the direction of movement of the coolant. Thus, inhomogeneous jet-pulsation fluidization in self-oscillating mode is realized without the use of mechanical pulsators. 0.79 0.75 0.71 0.67 0.63 0.59 0.55 0.51 0.47 0.43 0.39

εp

τ, s 0

0.08

0.16

τ1+τ2

0.24

0.32

τ3

0.4

Fig. 2. Dynamics of changes in porosity in different zones; d e = 2,5 mm, wp(pr) = 1,60 m/s, K w = 2,05

To maintain the stable kinetics of the process with a granulation coefficient of ψ ≥ 90%, one of the important factors is the method of applying heat to the film of the liquid phase on the granule in a fluidized bed. Previous studies have shown that in the process of granulation the temperature of the fluidized bed can not exceed 98 °C, otherwise there is a significant extraction of ammonia from the granules, which leads to a significant increase in the acidity of the granules. When lowering the temperature of the layer to 80 °C and below is accompanied by an increase in dust removal, which causes a decrease in the coefficient of granulation to 75–80% [4–8].

3 Mathematical Model of Heat Exchange in a Fluidized Bed During Granulation of Liquid Systems 3.1 Determination of Temperature in the Vicinity of the Dispersant The introduction of the liquid phase into the fluidized bed using a mechanical dispersant of conical type with a perforated surface allows to increase the size of the spray zone

The Heat Exchange in the Process of Granulation with Non-uniform Fluidization

31

by 5–6 times compared to the disk disperser (static irrigation zone) and create intensive circulation of granules through the inner bowl of the disperser (dynamic zone which intensifies the process of mixing granular material. As a result of intensive mixing, the risk of agglomeration formation and formation of local waterlogging zones is practically eliminated. To measure the temperatures in the working chamber of the granulator are placed conditional planes, which pass in the middle of the hydrodynamic zones I, II, III, in which the tracks of thermocouples, Fig. 3. The mathematical model of heat transfer is based on the authors equation [3], supplemented by energy consumption for heating the liquid phase and evaporation of the solvent, also taking into account the increase in heat transfer coefficient α associated with the use of jet-pulsation fluidization.

a)

b)

c)

Fig. 3. Location of thermocouple tracks: a) general view of the camera; b) placement of thermocouple tracks in the vicinity of the dispersant PL.2; c) placement of thermocouple tracks in the vicinity of the dispersant PL.4

Given that the dry matter content of the liquid phase, which is fed during granulation, contains a large amount of ammonium sulfate, which is a thermolabile substance, it is necessary to determine the temperature of the layer to solve the system of Eq. (1). We assume that all the moisture from the film of liquid falling on the granule evaporates due to the heat coming from the heated granule, while its temperature decreases to the temperature of a wet bulb thermometer.

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3.2 Heat Balance Equation for Gas Coolant and Fluidized Bed The heat balance equation for a gas coolant is written as: ∂ 2 Tg ∂(Tg · ε) ∂(Tg · ε) + Wg · Cg ε · ρg · =ε·a· − α · F · (Tinlet − Tpart ) ∂t ∂x ∂y2 + Gp · (1 − xp ) · (r + Cp · Tpart ); (1)

ρg · Cg ·

and accordingly for granules: ∂(Tp · εT ) ∂(Tp · εT ) − WT · ρp · = α · F · (Tinlet − Tpart ) ∂t ∂x − Gp · (1 − xp ) · (r + Cp · Tpart ) + Gp · xp · q.

ρp · Cp ·

(2)

where ε is the porosity of the layer (gas fraction); ρg - gas density, kg/m3 ; ρp - density of granules, kg/m3 ; wg - gas velocity, m/s; Cr - heat capacity of gas, KJ/(kg · K); λg - thermal conductivity of gas, W/(kg · K); F - specific surface of the granules in the layer at a given height, m2 /m3 ; de - equivalent particle diameter in the layer, mm; yi - mass part of i fraction; di - average size of the i-th fraction, mm Gp - mass load of the layer of granular material, according to the working solution, kg/(s · m3 ); xp - mass fraction of dry matter in the solution supplied to the granulator, % (mass); Tinlet , Tprt - coolant inlet to the granulator and the temperature in the layer, °C; Wed - heat capacity of the working solution supplied to the device, J/(kg · deg); q - specific heat of crystallization, kJ/kg; r - heat of vaporization, kJ/kg; wt - velocity of solid particles, m/s; α - heat transfer coefficient from the gas to the surface of the granules, W/(m2 ·K); a - thermal conductivity, m2 /s; Therefore, given that the maximum amount of ammonium sulfate solution, which provides a layered granulation mechanism, is: Mfluid = 0, 1Mpart

(3)

The Heat Exchange in the Process of Granulation with Non-uniform Fluidization

33

where Mpart - mass of granules, kg. Then the amount of water - solvent in solution on the surface of the granules is: Mfluid = 0, 1Mpart (1 − xp )

(4)

where is the mass fraction of dry matter in the working solution. Determining the amount of heat to evaporate a given amount of solution: Qext = Mfluid · r

(5)

where r is the specific heat of vaporization at t = 20 °C, r = 2448 kJ/kg. Therefore, the amount of heat supplied conductively from the pellet: Qpart = Mpart · (Cp )part · (Tpart − TM )

(6)

where Cp is the heat capacity of the granules of ammonium sulfate, TM is the temperature of the wet bulb thermometer. Equating the right-hand sides of Eqs. (5) and (6), we obtain: Mpart · r = Mpart · (Cp )part · (Tpart − TM )

(7)

Hence, taking into account (3), (4) we obtain the basic value of the layer temperature: Tpart ·

0, 05 · r · (1 − xp ) + TM (Cp )part

(8)

As previous studies have shown [4–9], to ensure a stable granulation process with a layered mechanism, the layer temperature at a height of 180 mm in the fracturing must be maintained at 98 ± 2 °C. Another feature of the granulation process with inhomogeneous jet-pulsation mode is the cyclic change of porosity in three conditionally selected technological zones, Fig. 1 with a frequency of 1.1–1.8 Hz. Therefore, the calculation of the temperature change along the height of the layer was performed for each zone. According to the method of the authors [10], the dependence of the porosity ε on the time of the inhomogeneous fluidization process in a fixed volume of the apparatus (by zones and average) was determined: (9) (10) (11) (12) Taking into account Eqs. (6)–(9), and substituting them to the system (1) for the appropriate time in order to take into account the effect of the porosity of the granules on the temperature, the system was solved by the grid method using Python.

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4 Results and Discussion According to the method of the authors [10], the change in temperature depending on the velocity of the granules in the respective zone was taken into account. Figure 4 shows the results of calculations for different layer heights.

Fig. 4. The increase in the temperature of the heat by the height of the ball during the granulation process for the skin of the three zones; H0 - the hanging of an unstable ball, Hd – the height of the rotary disperser with the horizontal head of the wrapping

Deficiency of fallowness to show the change in temperature rise along the height of the ball in the amount of fallowness in the amount of porosity, Fig. 4. for the first zone ε1 = const, the line of temperature change is unambiguous for the other ε2 and the third ε3 are displayed on the graph of the line mean value, Table 1. So, for the first ε1 and other zones and ε2 , the main temperature difference (Tinl – Tpart ) is realized at a height of 100 mm. For overhead flow - zone III → ε3 , the main temperature drop at the height is 240 mm. At the height of the unruly ball. H0 = 320 mm, the temperature in all zones is filled with practically the same value. The increase in the size of the zone and the reduction of the crumbling power by the heat and mass exchange is explained by the peculiarities of the hydrodynamic non-uniform pseudo-vision in the flow-pulsation mode.

The Heat Exchange in the Process of Granulation with Non-uniform Fluidization

35

Table 1. Values of temperatures in hydrodynamic zones H, mm

Zone 1

Zone 2

Zone 3

ε1 = 0,4

ε2 = 0,5 ÷ 0,8

ε3 = 0,5 ÷ 0,8

40

138

140

165

80

98

110

150

120

84

92

138

160

85

91

120

200

89

95

106

240

90

98

95

280

90

96

92

320

91

95

93

360

91

93

91

5 Conclusions The principles of introduction of a liquid heterogeneous phase into a fluidized bed for realization of the layer-by-layer granulation mechanism are formulated. The device with self-oscillating inhomogeneous jet-pulsation fluidization in which three technological zones are formed in the granulator chamber, is substantiated. The proposed mathematical model of heat transfer in the fluidized bed adequately describes the process with an average deviation of less than 3% and can be used to calculate the temperature dependence of the fluidized bed on the height of the apparatus in self-oscillating fluidization mode to calculate the industrial apparatus. Achieving high quality distribution of the liquid phase in the fluidized bed is confirmed by a mathematical model of the granulation process, which describes the change in temperature along the height of the layer when using jet-pulsation fluidization for three hydrodynamic zones in the granulator chamber.

References 1. Korniienko, Y.: Zvit pro naukovo-doslidnu robotu Rozrobka efektyvnykh metodiv zberezhennia gruntiv u vidpovidnosti z paradyhmoiu staloho rozvytku, 295 p. (2011) 2. Korniienko, Y.: Osoblyvosti vprovadzhennia pryntsypiv staloho rozvytku. In: Korniienko, Ya.M., Stepaniuk, A.R., Sachok, R.V. (eds.) Naukovo-tekhnichnyi rozvytok: ekonomika, tekhnolohii, upravlinnia: KhI mizhnarodna naukovo-praktychna konferentsiia (Kyiv, 21—24 kvitnia 2010r.) zb. tez dop.—K.: NTUU «KPI», S. 75 (2010) 3. Korniienko, Y., Zahrai, Y., Budzherak, A.: Zasady tekhnohennoi bezpeky v ahropromyslovomu kompleksi Ukrainy. Naukovi visti NTUU “KPI”, №3, pp. 129–135 (2001) 4. Kornienko, Y., Gaidai, S., Martyniuk, O.: Improved process to obtain granular humic fertilizers (2014). http://ela.kpi.ua/handle/123456789/11943 5. Kornienko, Y., Sememenko, D., Martyniuk, O. Gaidai, S.: The process of composite liquid systems dehydration in a fluidized bed using mechanical dispersant (2015). http://ela.kpi.ua/ handle/123456789/11944

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6. Kornienko, Y., Sachok, R., Rayda, V., Tsepkalo, O.: Mathematical modeling of continuous formation of multibed humic-mineral solid composites. Chem. Chem. Technol. 3(4), 335–338 (2009) 7. Kornienko, Y., Haidai, S., Liubeka, A., Martynyuk O.: Kinetic laws of the process of obtaining complex humic-organic-mineral fertilizers in the fluidized bed granulator. Ukrainian Food J. 5(1), 144–154 (2016) 8. Kornienko, Y., Haidai, S., Liubeka, A., Martynyuk, O.: Modelling of pulsating mode of fluidization when obtaining organic-mineral fertilizers. Ukrainian Food J. 5(4), 781–794 (2016) 9. Korniienko, Y.: Pidvyshchennia efektyvnosti protsesu oderzhannia hranulovanykh huminovomineralnykh dobryv. In: Korniienko, Y., Haidai, S., Martyniuk, O. (eds.) NTUU «KPI». – Kyiv: NTUU «KPI», 349 S (2014) 10. Kornienko, Y., Haidai, S., Liubeka, A., Martynyuk, O.: Kinetic laws of the process of obtaining complex humic-organic-mineral fertilizers in the fluidized bed granulator. Ukrainian Food J. 5(1), 144–154 (2016) 11. Kornienko, Y.M., Sachok, R., Tsepkalo, O.V.: Modelling of multifactor processes while obtaining multilayer humic-mineral solid composites. Chemistry 20(3), E19–E26 (2011) 12. Kornienko, Ya.N., Podmogilnyi, N.V., Silvestrov, A.N., Khotyachuk, R.F.: Current control of product granulometric composition in apparatus with fluidized layer. J. Autom. Inf. Sci. 31(12), 97–106 (1999) 13. Korniyenko, B., Ladieva, L.: Mathematical modeling dynamics of the process dehydration and granulation in the fluidized bed. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds.) ICCSEEA 2020. AISC, vol. 1247, pp. 18–30. Springer, Cham (2021). https://doi.org/10. 1007/978-3-030-55506-1_2 14. Korniyenko, B., Ladieva, L., Galata, L.: Control system for the production of mineral fertilizers in a granulator with a fluidized bed. In: ATIT 2020 - Proceedings: 2020 2nd IEEE International Conference on Advanced Trends in Information Theory, № 9349344, pp. 307–310 (2020). https://doi.org/10.1109/ATIT50783.2020.9349344 15. Ladieva, L., Kozanevych, Z., Klusta, T., Korniyenko, B.: System of control of the process of alkylation of benzene with peripene in the liquid phase. In: ATIT 2020 - Proceedings: 2020 2nd IEEE International Conference on Advanced Trends in Information Theory, № 9349330, pp. 311–314 (2020). https://doi.org/10.1109/ATIT50783.2020.9349330 16. Galata, L., Korniyenko, B.: Research of the training ground for the protection of critical information resources by iRisk method. In: Zawi´slak, S., Rysi´nski, J. (eds.) Engineer of the XXI Century. MMS, vol. 70, pp. 227–237. Springer, Cham (2020). https://doi.org/10.1007/ 978-3-030-13321-4_21 17. Kornienko, Y.M., Haidai, S.S., Sachok, R.V., Liubeka, A.M., Korniyenko, B.Y.: Increasing of the heat and mass transfer processes efficiency with the application of non-uniform fluidization. ARPN J. Eng. Appl. Sci. 15(7), 890–900 (2020) 18. Korniyenko, B., Galata, L., Ladieva, L.: Research of information protection system of corporate network based on GNS3. In: 2019 IEEE International Conference on Advanced Trends in Information Theory, ATIT 2019 - Proceedings, № 9030472, pp. 244–248 (2019). https:// doi.org/10.1109/ATIT49449.2019.9030472 19. Korniyenko, B., Galata, L.: Implementation of the information resources protection based on the CentOS operating system. In: 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering, UKRCON 2019 - Proceedings, № 8879981, pp. 1007–1011 (2019). https://doi.org/10.1109/UKRCON.2019.8879981 20. Korniyenko, B., Galata, L., Ladieva, L.: Mathematical model of threats resistance in the critical information resources protection system. In: CEUR Workshop Proceedings, vol. 2577, pp. 281–291 (2019)

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21. Zhulynskyi, A.A., Ladieva, L.R., Korniyenko, B.Y.: Parametric identification of the process of contact membrane distillation. ARPN J. Eng. Appl. Sci. 14(17), 3108–3112 (2019) 22. Korniyenko, B.Y., Borzenkova, S.V., Ladieva, L.R.: Research of three-phase mathematical model of dehydration and granulation process in the fluidized bed. ARPN J. Eng. Appl. Sci. 14(12), 2329–2332 (2019) 23. Kornienko, Y.M., Liubeka, A.M., Sachok, R.V., Korniyenko, B.Y.: Modeling of heat exchangement in fluidized bed with mechanical liquid distribution. ARPN J. Eng. Appl. Sci. 14(12), 2203–2210 (2019) 24. Korniyenko, B.Y., Osipa, L.V.: Identification of the granulation process in the fluidized bed. ARPN J. Eng. Appl. Sci. 13(14), 4365–4370 (2018) 25. Korniyenko, B., Galata, L., Ladieva, L.: Security estimation of the simulation polygon for the protection of critical information resources. In: CEUR Workshop Proceedings, vol. 2318, pp. 176–187 (2018) 26. Galata, L.P., Korniyenko, B.Y., Yudin, A.K.: Research of the simulation polygon for the protection of critical information resources. In: CEUR Workshop Proceedings, vol. 2067, pp. 23–31 (2017) 27. Kravets, P., Shymkovych, V.: Hardware implementation neural network controller on FPGA for stability ball on the platform. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds.) ICCSEEA 2019. AISC, vol. 938, pp. 247–256. Springer, Cham (2020). https://doi.org/10.1007/978-3030-16621-2_23 28. Deka, K.: Modeling of air temperature using ANFIS by wavelet refined parameters. Int. J. Intell. Syst. Appl. (IJISA) 8(1), 25–34 (2016). https://doi.org/10.5815/ijisa.2016.01.04 29. Ghiasi-Freez, J., Hatampour, A., Parvasi, P.: Application of optimized neural network models for prediction of nuclear magnetic resonance parameters in carbonate reservoir rocks. Int. J. Intell. Syst. Appl. (IJISA) 7(6), 21–32 (2015). https://doi.org/10.5815/ijisa.2015.06.02 30. Malekzadeh, M., Khosravi, A., Noei, A.R., Ghaderi, R.: Application of adaptive neural network observer in chaotic systems. Int. J. Intell. Syst. Appl. (IJISA) 6(2), 37–43 (2014). https:// doi.org/10.5815/ijisa.2014.02.05 31. Bhagawati, K., Bhagawati, R., Jini, D.: Intelligence and its application in agriculture: techniques to deal with variations and uncertainties. Int. J. Intell. Syst. Appl. (IJISA) 8(9), 56–61 (2016). https://doi.org/10.5815/ijisa.2016.09.07 32. Wang, W., Cui, L., Li, Z.: Theoretical design and computational fluid dynamic analysis of projectile intake. Int. J. Intell. Syst. Appl. (IJISA) 3(5), 56–63 (2011). https://doi.org/10.5815/ ijisa.2011.05.08 33. Patnaik, P., Das, D.P., Mishra, S.K.: Adaptive inverse model of nonlinear systems. Int. J. Intell. Syst. Appl. (IJISA) 7(5), 40–47 (2015). https://doi.org/10.5815/ijisa.2015.05.06 34. Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M.: Methods and models for information data analysis. In: Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M. (eds.) Diagnostic Systems for Energy Equipments. Studies in Systems Decision and Control, vol. 281, pp. 23–70. Springer, Cham (2021). https://doi. org/10.1007/978-3-030-44443-3_2 35. Babak, V., Shchepetov, V., Nedaiborshch, S.: Wear resistance of nanocomposite coatings with dry lubricant under vacuum. Sci. Bull. Natl. Min. Univ. Issue 1, 47–52 (2016)

An Approach Towards Vacuum Forming Process Using PostScript for Making Braille Volodymyr Mayik1 , Taras Dudok2 , Lyudmyla Mayik1 , Nataliia Lotoshynska3 , Ivan Izonin3(B) , and Jacek Kusmierczyk4 1 Ukrainian Academy of Printing, 19, Pid Holoskom Street, 79020 Lviv, Ukraine 2 Vlokh Institute of Physical Optics, 23, Dragomanov Street, 79005 Lviv, Ukraine 3 Lviv Polytechnic National University, 28a, Stepan Bandera Street, 79013 Lviv, Ukraine

[email protected], [email protected] 4 Polish Guild of Gutenberg Knights, 34E, Marywilska Street, 03-228 Warsaw, Poland

Abstract. This study aims to present a simple approach to the PostScript language usage for plate manufacturing with the help of vacuum forming technology. In addition, the calibration process method has been described as calibration sometimes is a necessary procedure to meet requirements for Braille geometric parameters. The article contains the research of the synthesis method of the PostScript file for plate manufacturing of text products. Such a PostScript file analytically describes the movement trajectory of the output device working part in test and working plate making. The advantage of such an approach is multiplatform. The plates for vacuum forming technology have been made with laser engraving (cutting). Keywords: Software · PostScript language · ASCII codes · Braille · Laser engraving · Vacuum forming · Plate making processes

1 Introduction The vacuum forming technology is widely used in educational and methodological publications for people with visual impairments, packaging, and advertising [1, 2]. Braille parameters [3, 4] have to comply with the defined standards (national standards and rules, industry requirements or recommendations for drug labeling, button marking in elevator cabins, etc.) [4–6]. Unlike the general process of Braille making [7, 8], proposed in this paper, the technology consists of the following procedures: text input, calibration (if necessary), converting text into Braille in the vector format within PostScript standards, preparation of image output for devices, plate manufacturing, finished goods production (Braille application), and quality control. PostScript is used in our technology as it is a language of the page layout and is exploited in printing systems [9, 10]. PostScript interpreters (software or hardware components) for document output are introduced in almost every modern computer system. PostScript is based on a text (or images) representation model on a blank page. For example, when the page is ready, it is printed, and the reproduction of the next page © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 38–48, 2022. https://doi.org/10.1007/978-3-031-03877-8_4

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39

starts. Hence, in our case, the PostScript document is equivalent to the program that represents text and images on printing equipment (a laser graver or laser cutter). In the beginning, special attention should be paid to the periodical calibrating process of technological operations [11, 12]. In our case, plate manufacturing is happening with the help of laser engraving (laser cutting) technology. If the vacuum forming of plate manufacturing is implemented, diameter of the laser beam and its power, speed of the laser beam about the plate material and its properties during the combustion process, and possibly hardware and software peculiarities of laser engraver lead to the distortion of the diameter of the hole, which corresponds to the Braille element. It should be noted that the deviation between the actual (final) value and a required value can increase up to 0,2 mm. That fact is unacceptable for our technology. The calibration process consists of the following procedures: 1. Input of initial parameters (the minimum and maximum allowable values of the Braille elements’ base diameter on the plate, horizontal and vertical spacing between plate elements, character, and line spacing); 2. The test file creation in the vector format within PostScript standards; 3. The test plate manufacturing; 4. The measurement (control) of the plate elements’ sizes; 5. The calculation of the initial parameters for the distortion correction; 6. The control plate manufacturing (if necessary). Consequently, plate manufacturing requires a test image creation. In our case, the test image is a set of holes that correspond to Braille parameters (the base elements’ diameter in Braille, horizontal and vertical spacing between font elements, character, and line spacing). In general, the preparation stages are fully described in our previous study [10], and this paper contains detailed research of the PostScript language usage for making the Braille elements. This paper aims to present a developed by authors, simple and effective method for plate manufacturing via vacuum forming technology using PostScript standard usage.

2 Software System for Plate Manufacturing The fact calibration causes the necessity of software development [13, 14] is a two-stage process: calibration of the plate making process (laser cutting) and calibration of the product manufacturing process (vacuum forming). Both these technological operations can generate some distortions [15, 16]. Considering the plate specifics (significant quantity of the same type objects, located in the fixed dimensional grid), the manual process of the test image creation is long-lasting and disorderly. Usually, there is the necessity of the test plate re-manufacturing, and as a result, the calibrating time is increasing. One more aspect of paying attention to is that a dimensional grid can be different. For example, it can be smaller for children (the smaller tactile contact area). There has been developed a unique software solution using all requirements [17, 18] for the plate making designed for the production of samples containing Braille:

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– Software for the synthesis of a PostScript file and the analytical description of Braille elements (and the corresponding distances between the components) with various base element diameters in Braille. The aim is to calibrate the product manufacturing technological process with the vacuum forming technology for data import into the arbitrary software environment supporting PostScript language. – Software for the translation of the text in ASCII codes into the Braille text, and the synthesis of the appropriate PostScript file with the Braille elements’ analytical description with the fixed diameter of the Braille element base. Such software is developed for the data import into the arbitrary software environment supporting the PostScript language. 2.1 The PostScript File Creation for Test Plate Manufacturing Software for the PostScript file synthesis to make a test plate for calibration of the Braille making process with the vacuum forming technology is located in a separate folder and contains the following files: 1. BRL_TST.EXE is the executable file. 2. shkala_t.txt – Braille element numbers to be reproduced on the form. 3. shkala_t.ini – the file with input Braille parameters. The output (resulting) file is “SHKALA_T.PRN.” The algorithm of the software for the PostScript file synthesis to make a test plate for the Braille making process calibration with the vacuum forming method is as follows: 4. 5. 6. 7.

Reading of the file with input data “shkala_t.ini.” Reading of the file “shkala_t.txt.” Creating a PostScript file title. Calculating the necessary (X and Y) Braille element centers’ position and center diameters. 8. Recording the calculation results in the PostScript file with the PostScript syntax compliance. 9. Finalizing the PostScript file and its closing. The structure of the “shkala_t.ini” file is: The first line contains the minimum diameter of the Braille element base. The second line includes the maximum diameter of the Braille element base. The third line consists of the distance between Braille element centers horizontally. The fourth line contains the distance between Braille element centers vertically. The fifth line has Braille character spacing. The sixth line includes Braille line spacing. See the example below for a better understanding of how it works. Software synthesizes ten versions of symbols with different hole diameters for the Braille base (10 lines). The base diameter changes evenly from the minimum value indicated in the “shkala_t.ini” file to the maximum value with the identical step.

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“shkala_t.txt” is a file containing data placed in a column for the Braille elements’ synthesis in a line. Here is an example: 126 means the synthesis of such font elements as “1”, “2”, and “6”. 0 represents the space. 16 indicates the synthesis of such font elements as “1” and “6”. The following scale synthesis is provided with PostScript means [11–13]: the input “SHKALA_T.PRN” PostScript file is created containing data about holes to be cut with laser equipment. The peculiarity of such an approach is that PostScript enables the analytical description of the objects (in our case, holes in the plate for vacuum forming) without reference to other software (Table 1). Table 1. Parameters and their description A parameter in a line

Parameter description

1.4

The minimum diameter of the Braille element base equals 1.4 mm

1.8

The maximum diameter of the Braille element base equals 1.8 mm

2.5

The distance between Braille elements’ centers horizontally equals 2.5 mm

2.5

The distance between Braille elements’ centers vertically equals 2.5 mm

6

The Braille character spacing equals 6.0 mm

12

The Braille line spacing equals 12 mm

The standard formula of the area of the circle in PostScript is used: “new path X Y RAD A0 A1 arc stroke.” where X is the position of the element center vertically. Y is a position of the element center horizontally. RAD is the element radius, A0 is the initial angle, A0 is the ending angle, and “new path”, “arc”, “stroke” are the reserved words in the PostScript language [11]. Here is an example of the hole diameters’ setting in the PostScript file: newpath 0.0 0.0 0.75 0 360 arc stroke. newpath 2.5 0.0 0.75 0 360 arc stroke. That example (with the file titles according to the PostScript standard) visualizes two circles with the 2 * 0,75 mm diameter and the distance between centers equal to 2,5 mm as a result of importing to the CorelDraw environment. It should be admitted that PostScript usage is a powerful tool for image creation that consists of the same type of elements.

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Figure 1 demonstrates the image of the test plate received by the import of the “SHKALA_T.PRN” input file in the “CoralDraw 7” environment and the following export in jpeg format for meaning in this text.

Fig. 1. Parameters of the “shkala_t.txt” file: 12345678, 56, 146, 456, 0, 123456, 56, 146, 456, 0, 123456, 56, 146, 456 (placed in a column)

The test scale presented in Fig. 1 has been made with a laser engraver. The fragment of the finished plate is presented in Fig. 2.

Fig. 2. The plate made with the LaserPro 180II laser engraver; a – the plate fragment, b – the scaled-up view of one of the plate holes, c – the hole cut, the slope of the hole side is clearly defined as a peculiarity of laser beam focusing

2.2 The PostScript File Creation for Plate Manufacturing to Produce Final Goods Software for translating the text in ASCII codes into the Braille text has been developed with the same approach, namely the synthesis of the PostScript file and the analytical description of Braille elements’ placing. The key peculiarity of this software is a transforming possibility of the text in ASCII codes into the Braille text. The Braille geometric parameters as the base diameter, the distance between Braille elements’ centers horizontally and vertically, Braille character, and line spacing are fixed for the whole text.

An Approach Towards Vacuum Forming Process Using PostScript

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The software algorithm for the translation of the text in ASCII codes into the Braille text and the synthesis of the PostScript file: 1. 2. 3. 4. 5. 6.

Reading of the “b0.ini” file with input data. Reading of the “b1. Fnt” font file. Creating the PostScript file title. Byte reading of the “b1.txt” input file in ASCII codes. Calculating the required Braille elements (X and Y) placing and their diameters. Recording the calculation results with the saved PostScript syntax in the PostScript file until the byte reading of the input file in ASCII “b1.txt” is completed. 7. Finalizing the PostScript file and its closing. The software comprises the following parts: 1. 2. 3. 4. 5.

“BRL_EDX.EXE” is the executable file; “b1.txt” is the input file in ASCII codes; “b0.ini” is the file with input Braille elements data; “b1.fnt” is the font file; “b1.PRN” is the output (resulting) file.

The “b0.ini” file structure is: The first line contains the Braille element base diameter. The second line has the distance between Braille elements’ centers horizontally. The third line includes the space between Braille elements’ centers vertically. The fourth line contains Braille character spacing. The fifth line includes Braille line spacing. The “b1.fnt” file contains input font data, namely, numbers of Braille symbol elements are clearly indicated. For example, the Ukrainian lowercase letter “a” in ASCII codes equals “0224”; meanwhile, only one Braille element is being used to indicate this letter. Similarly, the Ukrainian lowercase letter “” in ASCII codes equals “0230”, and Braille elements in “2”, “4”, and “5” positions are used to indicate this letter (Table 2). The Ukrainian uppercase letter “” in ASCII codes equals “0198”, and we need the same Braille elements as for the lowercase letter “” indicating, however, it requires a reserved symbol “The next symbol is an uppercase letter” (the “6” element) before the main letter symbols. Also, the reserved Braille symbol “The next symbols are numbers” (the “3”, “4”, “5”, and “6” elements) are used. As follows, the “b1.fnt” file has a simple structure as every line contains data with a similar design as in the “shkala_t.txt” file from the previous “BRL_TST.EXE” software. The line number is simultaneously an ASCII code, including Braille elements’ numbers required for reproduction.

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Table 2. ASCII codes, font symbols corresponding to them, Braille reserved symbols and Braille symbols

ASCII Symbol Braille Braille code reserved symbol symbol

ASCII code

Symbol

‘ ’ “ ” • – — ˜ ™ љ › њ ќ ћ џ

0032 0033 0034 0035 0036 0037 0038 0039 0040

! " # $ % & ' (

3 2356

0145 0146 0147 0148 0149 0150 0151 0152 0153

0041 0042 0043 0044 0045 0046 0047 0048 0049 0050 0051 0052 0053 0054 0055 0056 0057

) * + , . / 0 1 2 3 4 5 6 7 8 9

2356 236 235 2 36 256 256 245 1 12 14 145 15 124 1245 125 24

0154 0155 0156 0157 0158 0159 0160 0161 0162 0163 0164 0165 0166 0167 0168 0169 0170

0058 0059 0060 0061 0062 0063 0064

: ; < = > ? @

25 23 236 2356 356 26

0171 0172 0173 0174 0175 0176 0177

235 236

3456 3456 3456 3456 3456 3456 3456 3456 3456 3456

Braille reserved symbol

Braille symbol 3 3 236 236 36 36

Ў ў Ј ¤ Ґ ¦ § Ё © Є « ¬ ® Ї ° ± (continued)

An Approach Towards Vacuum Forming Process Using PostScript

45

Table 2. (continued) 0065 0066

A B

6 6

1 12

0178 0179

І і

13456

0067

C

6

14

0180

ґ

12456

0068 0069

D E

6 6

145 15

0181 0182

μ ¶

0070 0071

F G

6 6

124 1245

0183 0184

· ё

0072 0073

H I

6 6

125 24

0185 0186

№ є

0074

J

6

245

0187

»

0075 0076

K L

6 6

13 123

0188 0189

ј Ѕ

0077 0078 0079

M N O

6 6 6

134 1345 135

0190 0191 0192

ѕ ї А

6

1456 1

0080 0081

P Q

6 6

1234 12345

0193 0194

Б В

6 6

12 2456

0082 0083 0084

R S T

6 6 6

1235 234 2345

0195 0196 0197

Г Д Е

6 6 6

1245 145 15

0085 0086 0087

U V W

6 6 6

136 1236 2456

0198 0199 0200

Ж З И

6 6 6

245 1356 24

0088

X

6

1346

0201

Й

6

12346

0089 0090 0091 0092

Y Z [ \

6 6

13456 1356 246 1256

0202 0203 0204 0205

К Л М Н

6 6 6 6

13 123 134 1345

0093

]

12456

0206

О

6

135

0094 0095 0096

^ _ `

45 456 3

0207 0208 0209

П Р С

6 6 6

1234 1235 234

`

0097

a

1

0210

Т

6

2345

0098 0099 0100 0101 0102

b c d e f

12 14 145 15 124

0211 0212 0213 0214 0215

У Ф Х Ц Ч

6 6 6 6 6

136 124 125 14 12345

0103

g

1245

0216

Ш

6

156

0104

h

125

0217

Щ

6

1346

(continued)

46

V. Mayik et al. Table 2. (continued) 0105 0106

i j

24 245

0218 0219

0107 0108

Ъ Ы

k

13

0220

Ь

6

l

123

0221

Э

6

0109 0110

m n

134 1345

0222 0223

Ю Я

6 6

0111

o

135

0224

а

1

0112 0113 0114 0115

p q r s

1234 12345 1235 234

0225 0226 0227 0228

б в г д

12 2456 1245 145

0116 0117 0118 0119

t u v w

2345 136 1236 2456

0229 0230 0231 0232

е ж з и

15 245 1356 24

0120

x

1346

0233

й

12346

0121 0122 0123 0124

y z { |

13456 1356

0234 0235 0236 0237

к л м н

13 123 134 1345

0125 0126 0127 0128 0129 0130

} ~ Ђ Ѓ ‚

0238 0239 0240 0241 0242 0243

о п р с т у

135 1234 1235 234 2345 136

0131 0132

ѓ „

0244 0245

ф х

124 125

0133 0134 0135 0136

… † ‡ €

0246 0247 0248 0249

ц ч ш щ

14 12345 156 1346

0137 0138

‰ Љ

0250 0251

ъ ы

0139 0140 0141

‹ Њ Ќ

0252 0253 0254

ь э ю

23456

0142 0143 0144

Ћ Џ ђ

0255

я

1246

23456 1256 1246

1256

An Approach Towards Vacuum Forming Process Using PostScript

47

Here is the working software algorithm. The byte reading of the “b1.txt” input file enables the equivalence of the symbol code with the corresponding line from the “b1.fnt” file. In the next moment, the executable “BRL_EDX.EXE” file records the necessary cable in the PostScript format to the resulting file considering the “b0.ini” file data with geometric input parameters of Braille elements. The letter “” in the output PostScript file fragment is encoded as: newpath 2.5 0.0 0.750 0 360 arc stroke (the “2” Braille element – the element center position – vertically – 2,5 mm, horizontally – 0 mm). newpath 0.0 2.5 0.750 0 360 arc stroke (the “4” Braille element – the element center position – vertically – 0 mm, horizontally – 2,5 mm). newpath 2.5 2.5 0.750 0 360 arc stroke (the “5” Braille element – the element center position – vertically and horizontally – 2,5 mm). The “0.75” parameter is the radius of Braille elements; the “0” and “360” parameter groups are the common circle area in PostScript (the arc is equal from 0 to 360°). As shown, the file structure is quite simple. In addition, one should not forget about the file title and the PostScript file finalizing. For example, the label indicates such parameters as line thickness, line colors (many laser engravers set the specific cutting speed and laser beam power for the particular color line), drive marks, etc. The PostScript file finalizing includes the command for the whole page output/

3 Conclusion The paper proposed applying a simple and effective method for plate manufacturing with the help of vacuum forming technology using PostScript standard usage. Taking into consideration the PostScript expansion in printing systems, our approach is straightforward for employees to implement. There exist some complications in taking control of the Braille production process by printing company employees. That is why the proposed approach is rational to implement. The other fact, our approach can be easily used with any other method of Braille text synthesis.

References 1. Throne, J.L.: Understanding Thermoforming, 2nd edn, p. 269. Carl Hanser Verlag, Munich (2008) 2. Maik, V.Z., Dudok, T.H.: Investigation of the quality of image reproduction by vacuum forming in the manufacture of information carriers for the blind. Sci. Rep. 3(48), 82–85 (2014). (in Ukrainian) 3. Ali, H.S., Assabie, Y.: Recognition of double sided amharic braille documents. Int. J. Image Graph. Sig. Process. (IJIGSP) 9(4), 1–9 (2017) 4. Venugopal-Wairagade, G.A.: Braille recognition using a camera-enabled smartphone. Int. J. Eng. Manuf. (IJEM) 6(4), 32–39 (2016) 5. Size and Spacing of Braille Characters: Standards for Braille Embossed on Paper. Standards for Braille Signage. American National Standard, vol. 4 (2003) 6. Norton,R., et al.: Specification 800:2014 Braille Book and Pamphlets. Library of Congress, USA (1994)

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7. World Braille Usage: Perkins International Council on English Braille National Library Service for the Blind and Physically Handicapped Library of Congress, 3rd edn. UNESCO, Washington (2013) 8. Mayik, V.Z., et al.: A research of technology of Braille vacuum forming method. In: Proceedings of 21st International Conference MECHANIKA, pp. 186–189. Baltic Association of Mechanical Engineering, Lithuania (2016) 9. PostScript Language Reference Manual, 3rd edn, p. 962. Adobe Systems Incorporated: Addison-Wesley Publishing Company (1999) 10. Shariat, Z., et al.: Research and compare standards of e-learning management system: a survey. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 2, 52–57 (2014) 11. Liu, W., Du, J., Wang, B., Jia, X., Liu, S., Jia, Z.: Field calibration method of camera for measuring the dimensions of large forging. In: Liu, H., Ding, H., Xiong, Z., Zhu, X. (eds.) ICIRA 2010. LNCS (LNAI), vol. 6425, pp. 285–295. Springer, Heidelberg (2010). https:// doi.org/10.1007/978-3-642-16587-0_26 12. Avrutov, V.V.: Scalar diagnostics of the inertial measurement unit. Int. J. Intell. Syst. Appl. (IJISA) 7(11), 1–9 (2015) 13. Piletskiy, P., Chumachenko, D., Meniailov, I.: Development and analysis of intelligent recommendation system using machine learning approach. Adv. Intell. Syst. Comput. 1113, 186–197 (2020) 14. Peleshko, D., Rak, T., Izonin, I.: Image superresolution via divergence matrix and automatic detection of crossover. Int. J. Intell. Syst. Appl. (IJISA) 8(12), 1–8 (2016) 15. Li, G., et al.: The calibration algorithm of a 3D color measurement system based on the line feature. Int. J. Image Graph. Sig. Process. (IJIGSP) 1, 17–24 (2009) 16. Tsizh, B.R., Marusenkova, T.A.: A potrace-based tracing algorithm for prescribing twodimensional trajectories in inertial sensors simulation software. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 13(4), 42–54 (2021) 17. Hovorushchenko, T., et al.: Development of an intelligent agent for analysis of nonfunctional characteristics in specifications of software requirements. EEJET 2(97), 6–17 (2019) 18. Babichev, S., et al.: Technology of gene expression profiles filtering based on wavelet analysis. Int. J. Intell. Syst. Appl. (IJISA) 10(4), 1–7 (2018)

Investigation of Anomalous Situations in the Machine-Building Industry Using Phase Trajectories Method Solomiya Liaskovska1 , Ivan Izonin2(B) , and Yevgen Martyn3 1 Department of Designing and Operation of Machines, Lviv Polytechnic National University,

Kniazia Romana Street, 5, Lviv 79905, Ukraine 2 Department of Artificial Intelligence, Lviv Polytechnic National University, Kniazia Romana

Street, 5, Lviv 79905, Ukraine [email protected] 3 Department of Project Management, Information Technologies and Telecommunications, Lviv State University of Life Safety, Kleparivska Street, 35, Lviv 79007, Ukraine

Abstract. The use of phase trajectories is an effective method for studying specific situations in production. They represent effective manuals for learning the behavior of nonlinear technical systems in phase planes, interaction with the number of parts of differential levels and describing their arguments’ analytical functions. We have adopted the technological process as a multiparameter technical system. The operation of such a system is influenced by many parameters: the reliability of the components, the number of elements, the impact of the environment, etc. The dynamics of systems described by higher-order differential equations can be studied by involving the geometry of multidimensional phase spaces. The dimension of a space is determined by the number of differential equations or the order of the generalized differential equation of the technical system. Phase trajectories belong to the methods of qualitative theory of differential equations, which are used in practice in the study of a wide range of nonlinear technical systems. Keywords: A multiparameter technical system · Phase trajectories · Differential equations

1 Introduction Analysis of the average technological production process, particularly in mechanical engineering, especially in the manufacture of metal products, indicates the real presence of risks of dangerous situations. The level of such events, the probability of their occurrence is proportional to the quality of the technological process. Such an event may or may not occur at a particular, unexpected time in most cases. Note that the probability of danger exists mainly in the implementation of the technological process. Thus, dangerous situations are likely for any technological process, regardless of its level of perfection [1]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 49–59, 2022. https://doi.org/10.1007/978-3-031-03877-8_5

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Analysis of the evolution of technological improvement indicates that the desire of engineers - designers to create more sophisticated and functional products leads to an increase in the likelihood of increasing threats. Such dangers are especially great at the beginning of the introduction and use of technological processes in production. The subsequent stages of service are appropriate for providing the possibility of hazards or their elimination from such a technological process [2–5]. Note that if the formation of the first simple technological processes, the level of danger was reduced mainly to harm the health of a small number of service personnel, the flaw in the modern technological process, which uses the latest computer technology, is high. It can create problems both at the place of production and constitute a global catastrophe. The scale of probable hazards from errors in the design of the technological process or its operation requires the project team to consider effective scientific organizational and design tools and measures to minimize the likelihood of danger in the operation of technological processes in mechanical engineering. It is impossible to eliminate the probability of danger both at the design level and during the operation of technological processes. Therefore, success in minimizing the occurrence of such hazards can be achieved in two stages: • in the process of creating a technological process; • the development of practically expedient organizational measures of its functioning. Identifying problems and, consequently, the causes of hazards can be effective the stage of creating a technological process, where it is essential to consider the specific risks of the expected in the process of operation of the technological hazard [6]. Next, its practical aspects should be formulated as a basis for developing effective measures to minimize the likelihood of risks. The dangers posed by the technological process are different: human casualties, injuries, and - other material collections. In the context of the technological process regarding the mechanical engineering level, the hazards determine the probability of reviewing or achieving a specific situation in one of its stages and their combination. Thus, the technological process is inherently a probable cause of danger. Its level and probability of occurrence are directly proportional to the difference of perfection of technological process, involvement in its creation of modern technologies. Danger threatens the maintenance of the technological process of personnel and the premises in which this technological process is implemented. Let’s also emphasize such a technological process can start that: even a small element in its system that has failed can lead to the breaking of many parts and the installation from which it will become. The main thing in the design of the technological process is to create appropriate conditions for its operation. The probability of danger, its significant percentage, can be eliminated at the stage of its creation. The variety of elements, blocks, equipment as components of the technological process is proportional to the number of possible hazards arising from the technological process. Its elements as sources of hazards determine varieties of hazards from the technological process. Factors of danger from the operation of technological processes can be the human factor, technical reasons.

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The use of phase tractors is effective for studying specific situations in production. They show effective tools for studying the behavior of nonlinear technical systems in phase planes that affect actions when parts of differential levels represent their arguments’ analytical functions. In practice, phase planes are used to study nonlinear technical systems, which are described by two differential levels [10]. The dynamics of systems described by higher-order differential equations can be studied by involving the geometry of multidimensional phase spaces. It is known that the dimension of space is determined by the number of differential equations or the order of the generalized differential equation of the technical system. Phase trajectories belong to the methods of qualitative theory of differential equations, which are used in practice in the study of a wide range of nonlinear technical systems [11–13]. N first-order differential equations describe the behavior of the variables of the technical system αi (

dxi , xi , t) = 0, i = 0, 1, . . . n dt

(1)

where t – time, which are usually considered with respect to derivatives: dxi = fi (xi , t). dt

(2)

The specialty of studying nonlinear technical systems involves tracking the relationships of nonlinear differential levels from the initial conditions. Therefore, the method of the phase space method is widely used to analyze the state of the system; its partial case is the phase plane in which the phase trajectories of two nonlinear differential levels with two changes in the parameters x, y: dx = f (x, t) dt dy = φ(x, t). dt

(3)

where the analytic functions of their arguments can represent the right sides, ie decomposed into series by powers of x and y. Studies of the dynamics of systems represented by higher-order equations require the use of multidimensional phase spaces.

2 Phase Space Method for the Study of Technological Processes The main factor that is dominant in determining the level of danger is the system’s stability, i.e. the technological process. Considering many independent parameters, including the reliability of the constituent elements and their number and the impact of the environment, it is stability that is directly related to reliability, and hence the possibility of danger [7]. Given the parameters of the process, the time component, it is the stability that covers their relationship with differential equations. Depending on the level of detail of the technological process, the number of parameters may be different. But always for a stable system, which is a technological process, the solution tends to the set value. The

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technological process can often be reduced to a system of two first-order differential equations with the original determinants x, y, and constant a, A, b, B, R, c, D parameters dy 1 = (A − Ry − cx) dt a 1 dx = (By − D) dt b

(4)

It is a basic mathematical model of many multiparameter systems for various purposes. To study such systems, we use phase trajectories. Let us construct a phase trajectory with a stable diacritic node. Parameters b and c belong to area 2; assume b = c = 4. The characteristic equation has the form: k 2 + 4k + 4 = 0.

(5)

This equation corresponds to a second-order differential equation: d 2x dx + 4 + 4x = 0 dt 2 dt

(6)

Let’s demonstrate (6) as a system of differential equations of the first order: dy = x; dt dx = −4x − 4y. dt

(7)

We used expressions (6), (7) and visualized in the Matlab environment phase trajectories for initial conditions, for example, y0 = 50; x0 = 100. The phase portrait is a stable node Fig. 1. The study of the system’s stability, which includes the technological process, is necessary but insufficient conditions for calculating the possibility of danger [8–10]. Such risk factors as the impact on one or a group of staff of time characteristics, the case of danger, their frequency, local or large-scale destruction, the level of economic damage, in our opinion, should be investigated and calculated at the design stage of the technological process. The main steps to increase the level of safety in the implementation of the project operation of the technological process [11]: Case 1: Research of input elements of technological process on their reliability for reduction of danger; Case 2: Research of input elements of technological process on their reliability for reduction of danger; Case 3: Study of the influence of environmental parameters on the operation of the technological process (external parameters); Case 4: Development of requirements for the level of professionalism of service personnel (external factors); Case 5: Development of requirements for utilizing the technological process (external and internal factors).

Investigation of Anomalous Situations in the Machine-Building Industry

53

Fig. 1. Phase trajectory with stable node

We can see that abnormal situations in the technological process can be described as a multiparameter system. It can highlight the relationships between different parameters. We have proposed a research method for the use of phase trajectories for multiparameter systems. The stability of solutions of differential equations of technical systems is determined by the free component of the transition process. We research the case when the righthand side of the differential equation is zero. Instead of a variable parameter for the case of Euclidean n - measurable space, we take its derivative, and its constant value A is taken as zero. We fix the value of the derivative of the variable parameter [12, 13]: dy = 0. (8) dt The manifold that reflects the solution of such dependence is a line y = const parallel to the axis Ot of the plane Otu. As in the case of the formation of hypersurfaces of the lowest dimension, the phase space is a two-dimensional plane. Therefore, we write this equality in the form: d 2 y dy = 0. + dt 2 dt and we present it by a system of two first-order differential equations: y1 =

(9)

dy ; dt

dy1 + y1 = 0. (10) dt obtain a one-dimensional manifold - a phase trajectory - a two-dimensional phase space. We present (9) in the form: d 3 y d 2 y dy = 0, + 2 + dt 3 dt dt

(11)

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Fig. 2. Phase three-dimensional space of the system (12)

By lowering its order, we form a system of three equations: dy d 2y , y3 = 2 ; dt dt d 3y dy1 dy2 dy3 = y2 ; = y3 ; = = −y3 − y2 . dt dt dt dt

y1 = y, y2 =

(12)

The system (12) contains four variable parameters y1 , y2 , y3 t, for which the phase space is three-dimensional. Thus, the trajectory can be formed immediately in threedimensional phase space Oy1 y2 y3 , the measurements of which correspond to all three variable parameters of the generalized technological process in Fig. 2. The above phase portrait is both a visual representation of the phase trajectory of the three-dimensional phase space.

3 The Projections of Varieties of Phase n - Dimensional Spaces Here is a generalization of the construction of projections of varieties of phase n-dimensional spaces on the example of five-dimensional space: d 5 y d 4 y d 3 y d 2 y dy =0 + 4 + 3 + 2 + dt dt dt dt dt 5

(13)

When we lower the order, we get: dy d 2y d 3y d4 y ; y3 = 2 ; y4 = 3 ; y5 = 4 ; dt dt dt dt dy1 dy2 dy3 dy4 dy5 = y2 ; = y3 ; = y4 ; = y5 ; = −y5 − y4 − y3 − y2 . dt dt dt dt dt

y1 = y; y2 =

(14)

Projections of phase trajectories in three-dimensional subspaces are given in Fig. 3.

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55

Fig. 3. Phase three-dimensional planes of the system (13)

Figure 4 shows projections of these phase trajectories in all two-dimensional planes.

Fig. 4. Phase two-dimensional planes of the system (13)

The smallest number of projections of phase trajectories of the technological process requires three-phase planes, for example Oy1 y2 , Oy3 y4 and Oy1 y5 . When we are researching and designing multiparameter technical systems, the problem of choosing such values of link parameters that ensure its proper performance is often solved. There is a need to analyze such transients at the values of the parameters belonging to the relevant area. To analyze the free component of the transition process, also use phase trajectories, the nature of which is determined by the selected parameters of the system under the given initial conditions of the studied process. The nature of the phase trajectories of the second-order system: d 2 x bdx + cx = 0. + dt 2 dt

(15)

The nature of the phase trajectories of the second-order system: k 2 + bk + c = 0.

(16)

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For a given pair of values of the coefficients b, c of the characteristic equation, the location of the phase trajectory in the plane takes place. Known tools involve determining the roots for the selected coefficients b and c, which do not always correspond to the desired type of phase trajectory. By analyzing the coefficients of the characteristic equation, it is possible to determine the necessary and sufficient conditions for the negativeness of the real parts of its roots and, consequently, to divide the trajectories into two classes corresponding to a stable or unstable transient process. Complex plane Opiq has roots k with a negative and positive real part. For selected values b and c these roots determine the sets of phase trajectories corresponding to stable and unstable rest points. The stable point, node, above. The roots of the characteristic equation k = ±iq determine the phase trajectories in the form of closed curves. Parameter area b and c, we find the plane Obc by substituting the value k = ±iq in (16) and p(k) = 0: q2 + c ± ibq = 0.

(17)

The expression (16) value equals zero if its real and imaginary components are equal to zero; we receive b = 0, c = q2 . For the roots to be imaginary, the condition must be met c > 0. The area of parameters b, c for the required phase trajectories in closed curves is the positive half-axis Oc of the plane of parameters Obc (Fig. 5).

Fig. 5. System parameter areas

Let’s take the area of parameters b and c, the values of which provide similar phase trajectories with a stable focus. Take the roots of the characteristic equation k12 = −p ± qi, for which Eq. (16) has the form: (−p ± qi)2 + b(−p ± qi) + c = 0.

(18)

Equating to zero the real and imaginary part, we obtain p2 −q2 −bp+c = 0; ∓2ipq = 0. For the partial value q = 0, we obtain a special case of equality of roots k1 = k2 = −p < 0. For the partial value q = 0, we obtain a special case of equality of roots k1 = k2 = −p representing the arc of the curve c = b2 /4 and c > 0 i b > 0.

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57

For positive root values k1 = k2 = p > 0 expression (18) has the form: p2 − q2 + bp + c = 0; ∓2ipq ± ibq = 0. The range of parameters for similar phase trajectories with an unstable node with the same roots of the characteristic equation k1 = k2 = p > 0 is the arc of the curve c = b2 /4 with c > 0 and b < 0. The complex equations k12 = −p ± qi and k12 = p ± qi the characteristic equation is obtained for the values of the parameters of the phase trajectories in the region bounded by the arc of the curve c > b2 /4 and half-axis, respectively b > 0 (area 4) and b < 0 (area 5). For straight  lines given by segments with an unstable rest point of phase trajectories 2

k12 = − 2b ± b4 − c = 0. After the transformations, we obtain the range of values b = c = 0. For the segments of straight lines with a stable rest point of the phase trajectories defined by the roots, the transformation of the expression gives the range of parameters k1 = 0, k2 < 0, the transformation of the expression gives k12 the range of parameters c = 0, b > 0. Phase trajectories are represented by segments of lines with an unstable rest point, for the values of the roots form the parameters in the region 8: c = 0, b < 0. A necessary condition for determining the negative roots in the presence of both positive parameters b and c: b > 0 and c > 0. By transforming the expression k12 , the expression forms a region 9 of parameters b and c of phase node. For the trajectories with a stable 2

2

case of positive roots, for example k1 = − 2b + b4 − c > 0; k2 = − 2b − b4 − c > 0, we obtain the range of parameters b and c of phase trajectories with an unstable node, bounded south b < 0 and curve arc c < b2 /4 with the meanings c > 0. Atdifferent signs of the roots  of the characteristic equation, for example k1 = 2

2

− 2b + b4 − c > 0; k2 = − 2b − b4 − c < 0, we obtain phase trajectories with a point of calm in the form of a saddle. The parameters b and c are determined from the lower half-plane of the plane of the parameters Obc. The research results are summarized in Table 1. Table 1. Areas of the plane Obc parameters of phase trajectories #

The roots of the equation

Area of parameters

Point of the calm

±qi

c>0

Center

2

−p

c = b2 /4, c > 0, b > 0

Diacritical stable node

3

p

c = b2 /4, c > 0, b < 0

Diacritic unstable node

−p ± qi

c = b2 /4, b > 0

Steady focus

5

p ± qi

c = b2 /4, b < 0

Unstable focus

6

0

b=c=0

Unstable point of the calm

7

0

c = 0, b > 0

Stable point of the calm

k1 1

4

k2

0

c = 0, b < 0

Unstable point of the calm

0, b > 0

Stable node

10

>0

c < b2 /4, c > 0, b < 0

Unstable node

11

>0

−∞ ≤ b ≤ ∞, c < 0

Saddle

9

ε, then go to the block 2. If E < ε, then it is end. To increase the probability of hitting the global extremum, a second method of parametric identification is further proposed. 3.4 The Method Development for Suggested Model’ Parametric Identification Based on Metaheuristic Search The parametric identification method for the proposed model based on Adaptive Cat Swarm Optimization (ACSO) are proposed in this research. The ACSO method allows finding a quasi-optimal vector of parameter values for the proposed model and consists of the following blocks.

The Wind Generator’ Power Effective Forecast Method

77

Block 1 – Initialization: – – – –

setting the number of the current iteration n to one; setting the maximum number of iterations N ; setting the size of the swarm K; setting the dimension of the cats’ position M (corresponds to the number of proposed model’ parameters); – setting the number of cat’s position copies L; – setting the probability of the search mode psearch ; – position initialization xk (corresponds to the vector of proposed model’ parameters)  xk = (xk1 , . . . , xkM ), xij = xjmax − xjmin U (0, 1) + xjmin , k ∈ 1, K, where xjmin , xjmax – minimum and maximum value, U (0, 1) – the function that provides the calculation of a uniformly distributed random variable on a segment [0,1]; – speed initialization vk : vk = (vk1 , . . . , vkM ), vij = 0, k ∈ 1, K – setting an initial swarm of cats: Q = {(xk , vk )} – the current population’ cat with the best position determination (corresponds to the vector of the proposed model’ parameters with the best goal function) k ∗ = arg min F(xk ), x∗ = xk ∗ k ∈ 1,K

Block 2 – Search mode (the cat is at rest, but looks around to move to a new position) – coping of each cat’s position:  x˜ klj = xkj + δ(n) xjmax − xjmin (−1 + 2U (0, 1), k ∈ 1, K, l ∈ 1, L, j ∈ 1, M δ(n) = NN+1−n +1 , ⎧ min min x , x ˜ klj ≤ xj ⎪ ⎨ j  x˜ klj = x˜ klj , x˜ klj ∈ xjmax , xjmin , ⎪ ⎩ max x˜ klj ≥ xjmax xj , k ∈ 1, K, l ∈ 1, L, j ∈ 1, M

where δ(n) – parameter that controls the generation of the cat’ new position on iteration n.

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The adaptability of the parameter δ(n) makes it possible to establish an inverse relationship between δ(n) and the iteration number, so the search is global in the first iterations, and in the last iterations, the search becomes local. The parameter adaptation δ(n) satisfies the condition δ(n) ∈ (0, 1). – calculating the probability for a copy of each cat’s position: max F(˜xkm ) − F(˜xkl )

pkl =

m∈1,L

max F(˜xkm ) − min F(˜xkm )

m∈1,L

, k ∈ 1, K, l ∈ 1, L

m∈1,L

– changing the position of each cat: rk = U (0, 1), k ∈ 1, K, ⎧ ⎨ x˜ c , rk ∈ c−1 pkl , c pkl l=1   , k ∈ 1, K l=1 xk =

c c−1 ⎩ xk , rk ∈ / l=1 pkl l=1 pkl , Block 3 – Tracking mode (cat looking for target) – modifying the speed of each cat using simulated annealing: vk = w(n)vk + α(n)(xk ∗ − xk )U (0, 1), −n w(n) = 0.4 + 0.5 N N −1 , N −n ⎧ α(n) = 4 N −1 ,  ⎨ vkj , vkj ∈ xmin , xmax j , j vkj = min ⎩ 0, vkj ∈ / xj , xjmax k ∈ 1, K, j ∈ 1, M , where w(n) – parameter governing the contribution of the previous speed to the cat’ speed during the iteration n. α(n) – parameter governing the contribution of the component (xk ∗ − xk ) to the cat’s speed at iteration n. The adaptability of the parameters w(n) and α(n), introduced in this research, makes it possible to establish an inverse relationship between w(n) and α(n) and the iteration number, so in the first iterations, the search is global, and in the last iterations, the search becomes local. Adaptation of parameters w(n) and α(n) satisfies the condition w(n) ∈ [0.4, 0.9]α(n) ∈ [0, 4]. – modification of the position of each cat according to the speed:

x k = xk + vk , k ∈ 1, K, ⎧ min x˜ kj ≤ xjmin ⎪ xj , ⎨  x˜ kj , x˜ kj ∈ xjmax , xjmin , x˜ kj = ⎪ ⎩ max x˜ kj ≥ xjmax xj , k ∈ 1, K, j ∈ 1, M ,

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Block 4 – Setting a new population: rk = U (0, 1), k ∈ 1, K,  x , r ≥ psearch , k ∈ 1, K xk = k k x k , rk < psearch Block 5 – Determining the current cat’ population with the best position: k ∗ = arg min F(xk ) k∈1,K

Block 6 – Determining the global best position: If F(xk ∗ ) < F(x∗ ), then x∗ = xk ∗ . Block 7 – Stop condition. If n < N , then increase the iteration number n by one and go to block 2.

4 Numerical Research The neural network forecast of the wind generator’ power was carried out according to such characteristics as: wind speed, humidity and air temperature. The structural representation of the forecast model based on a modified onedimensional convolutional neural network (1D CNN) (Fig. 1). The first block (from top to bottom) corresponds to the input layer (the data type and form of the layer’ input and output are indicated). The second block corresponds to the convolutional layer (the data type and form of the layer’ entry and exit are indicated). The third block corresponds to the pooling (subsampling) layer (the data type and form of the layer’ input and output are indicated). The fourth block corresponds to a flattening layer (the data type and form of the layer’ input and output are indicated); it converts the planes set into a vector. The fifth block corresponds to a dense (fully connected) layer (the data type and form of the layer’ input and output are indicated), The sixth block corresponds to the output layer (the data type and form of the layer’ input and output are indicated). For an effective experiment, training and test implementations were obtained from a wind generator WINDER T12 (1.2 kW, 48 V). Parametric identification of the modified 1D CNN model was carried out on Q = 10000 training implementations based on the proposed metaheuristic search. The following parameters were chosen: the maximum number of iterations N = 100, the size of the swarm K = 100, the number of copies of the cat’s position L = 100, the probability of the search mode psearch = 0.5. Table 1 shows the prediction accuracy obtained for 1000 test implementations based on the proposed modified 1D CNN model and traditional models of artificial neural networks.

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Fig. 1. Structural representation of a prediction model based on a modified one-dimensional convolutional neural network (1D CNN) Table 1. Forecast accuracy Different Network/criterion

ENN (SRN)

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0.80

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5 Research Results According to the Table 1, 1D CNN gives the best results in terms of forecast accuracy. Increasing the forecast accuracy for the modified 1D CNN model became possible by increasing the number of the convolutional and pooling layer planes depending on the number of features and time delay, which allows more accurate feature extraction, as well as through the use of metaheuristic determination of the parameters of the modified 1D CNN model. The learning rate increase of the modified 1D CNN model became possible due to the use of the batch mode (in the case of using the CUDA parallel information processing technology, the outputs of all neurons in the layer are calculated simultaneously, and the calculation of thresholds and synaptic weights is based on parallel reduction and

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requires the number of iterations log2 Q, where Q is the length of the time series), which is difficult in the case of recurrent networks. Thus, the goal of the study was achieved. The efficiency increasing of the wind generator’ power forecast based on modified one-dimensional convolutional neural network and metaheuristics. The practical contribution of this work lies in the fact that it makes possible to predict the power of a wind generator by means of an artificial neural network, which is trained on the proposed metaheuristic basis, which makes it possible to increase the forecast accuracy.

6 Conclusion To solve the problem of insufficient quality analysis of the wind generator’ power, the corresponding neural network forecasting methods were investigated. To improve the efficiency of training neural networks, metaheuristic methods have been investigated. The model of the modified one-dimensional convolutional neural network by automatically calculating the convolution, pooling (subsampling) and dense (fully connected) layers’ number and sizes allows to extract the most significant features, which increases the forecast accuracy. The method of suggested neural network model parametric identification due to the lack of recurrent links allows the use of a batch training mode, which increases the training speed. The method of proposed neural network model parametric identification based on the adaptive optimization of a swarm of cats through the use of simulated annealing makes possible to make the search global at the first iterations, and to make the search local at the last iterations, which increases the forecast accuracy. The method for predicting of the wind generator’ power based on a modified onedimensional convolutional neural network can be used in various intelligent systems for analyzing the characteristics of high-dynamics technical objects.

References 1. Du, W., Wang, H., Bu, S.: Small-Signal Stability Analysis of Power Systems Integrated with Variable Speed Wind Generators. Springer, Cham (2018). https://doi.org/10.1007/978-3-31994168-4 2. Luo, N., Vidal, Y., Acho, L.: Wind Turbine Control and Monitoring. Springer, Charm (2018). https://doi.org/10.1007/978-3-319-08413-8 3. Bianchi, F.D., de Battista, H., Mantz, R.J.: Wind Turbine Control Systems Principles, Model and Gain Scheduling Design. Springer, London (2007) 4. Du, K.-L., Swamy, M.N.S.: Neural Networks and Statistical Learning, pp. 299–335. Springer, London (2014). https://doi.org/10.1007/978-1-4471-5571-3_10 5. Aggarwal, C.C.: Neural Networks and Deep Learning: A Textbook. Springer, Charm (2018). https://doi.org/10.1007/978-3-319-94463-0 6. Sivanandam, S.N., Sumathi, S., Deepa, S.N.: Introduction to Neural Networks Using MATLAB 6.0. The McGraw-Hill Comp., Inc., New Delhi (2006)

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7. Mikolov, T., Karafiát, M., Burget, L., Cernocký, J., Khudanpur, S.: Recurrent neural network based language model. In: Interspeech, vol. 2, p. 3 (2010) 8. Sutskever, I., Martens, J., Hinton, G.E.: Generating text with recurrent neural networks. In: Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 1017– 1024 (2011) 9. Berglund, M., Raiko, T., Honkala, M., Kärkkäinen, L., Vetek, A., Karhunen, J.T.: Bidirectional recurrent neural networks as generative models. In: Cortes, C., Lawrence, N. D., Lee, D. D., Sugiyama, M., Garnett, R., (eds.) Advances in Neural Information Processing Systems, vol. 28, pp. 856−864. Curran Associates, Inc., Red Hook (2015) 10. Sundermeyer, M., et al.: Translation modeling with bidirectional recurrent neural networks. In: Proceedings of the Conference on Empirical Methods on Natural Language Processing, October 2014 11. Chung, J., Gulcehre, C., Cho, K., Bengio, Y.: Empirical evaluation of gated recurrent neural networks on sequence modelling. arXiv preprint arXiv:1412.3555 (2014) 12. Dey, R., Salem, F.M.: Gate-variants of gated recurrent unit (GRU) neural networks (2017). arXiv:1701.05923 13. Fedorov, E., Nechyporenko, O., Utkina, T.: Forecast method for natural language constructions based on a modified gated recursive block. In: CEUR Workshop Proceedings, vol. 2604, pp. 199–214 (2020) 14. Yu, C., Wang, S., Guo, J.: Learning Chinese word segmentation based on bidirectional GRUCRF and CNN network model. IJTHI 15, 47–62 (2019) 15. Fan, T., Zhu, J., Cheng, Y., Li, Q., Xue, D., Munnoch, R.: A new direct heart sound segmentation approach using bi-directional GRU. In: Proceedings of the 2018 24th International Conference on Automation and Computing, Newcastle, UK, 6–7 September 2018, pp. 1–5 (2018) 16. Potash, P., Romanov, A., Rumshisky, A.: Ghostwriter: using an LSTM for automatic rap lyric generation. In: Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pp. 1919–1924 (2015) 17. Sundermeyer, M., Schluter, R., Ney, H.: LSTM neural networks for language modelling. In: Thirteenth Annual Conference of the International Speech Communication Association (2012) 18. Graves, A., Schmidhuber, J.: Framewise phoneme classification with bidirectional LSTM and other neural network architectures. Neural Netw. 18(5), 602–610 (2005) 19. Kiperwasser, E., Goldberg, Y.: Simple and accurate dependency parsing using bidirectional LSTM feature representations. Trans. Assoc. Comput. Linguist. 4, 313–327 (2016) 20. Bazaz, T., Zafar, S.: A neoteric optimization methodology for cloud networks. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 6, 27–34 (2018) 21. Talbi, El.-G.: Metaheuristics: From Design to Implementation. Wiley, Hoboken (2009) 22. Loshchilov, I.: CMA-ES with restarts for solving CEC 2013 benchmark problems. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2013), Cancun, Mexico, 2013 June, pp. 369–376 (2013) 23. Mahdad, B., Srairi, K.: Optimal power flow improvement using a hybrid teaching-learningbased optimization and pattern search. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 3, 55–70 (2018) 24. Alawad, N.A., Rahman, N.G.: Design of (FPID) controller for automatic voltage regulator using differential evolution algorithm. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 12, 21–28 (2019) 25. Yuen, S.Y., Chow, C.K.: Agenetic algorithm that adaptively mutates and never revisits. IEEE Trans. Evol. Comput. 13(2): 454–72 (2009)

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Determination of Geometric Parameters of Piezoceramic Plates of Bimorph Screw Linear Piezo Motor for Liquid Fertilizer Dispenser Constantine Bazilo(B) , Sergey Filimonov, Nadiia Filimonova, and Dmytro Bacherikov Cherkasy State Technological University, Shevchenko blvd, 460, Cherkasy 18006, Ukraine [email protected], {s.filimonov,n.filimonova}@chdtu.edu.ua

Abstract. Agriculture today is at the forefront of development and is one of the main industries in the country. To control the dosage of pouring out liquid fertilizers, special dispensers are used. The main element of the dosing and pouring unit is a control system using electric motors and solenoid valves. The paper proposes and mathematically calculates the design of a piezoelectric motor based on bimorph piezoelectric elements for use in order to accurately dose fertilizers. To study the vibration amplitude of one of the plates of a piezoelectric motor with bimorph piezoelectric elements a simulation was carried out in COMSOL Multiphysics. The paper defines the relationship between the geometric dimensions of the piezoelectric element of the bimorph element. On the basis of these data the rational dimensions of a piezoelectric element on a metal plate are determined. Mathematical dependences are given for determining the rational ratios of the piezoelectric element. The study of the amplitude frequency characteristics of experimental sample was carried out. The obtained results confirmed the adequacy of the Comsol Multiphysics simulation. In addition, the vibration amplitude of the bimorph piezoelectric element is determined for various sizes of the piezoelectric element. Keywords: Precision farming · Dispenser · Linear piezoelectric motor · Bimorph piezoelectric element · Agrosphere

1 Introduction Modern agriculture is based on digital data, and the latest technologies used to manage and optimize crop production. Thanks to the automation and modernization of farming methods, this industry is at the forefront of development, and is one of the main industries in the country. In addition, software platforms for managing, monitoring, analysing and collecting data on the farm in real time are rapidly developing [1–6]. Despite the development, one of the important stages for obtaining a good harvest is spraying and applying liquid fertilizers. In the last 10 years alone in Ukraine, the volume of application of liquid complex fertilizers, micronutrient fertilizers, nitrogen fertilizers and preparations has quadrupled. This means that spraying and applying are widely © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 84–94, 2022. https://doi.org/10.1007/978-3-031-03877-8_8

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used not only by large agricultural holdings, but also by small farms. The direction of precision farming which is currently technically developed in systems for pouring out and accurate dosage and compliance with specified standards, which does not lead to overruns of fertilizers and the budget, is becoming relevant. Thus, the development and implementation of priority areas of precision farming will contribute to an increase in the profitability of agricultural production, an increase in labour productivity and a decrease in environmental pollution. To control the dosage of pouring out liquid fertilizers, special dispensers are used. The main element of the dosing and pouring unit is the control system. It is based on control using dampers, calibrated holes, regulation using electric motors and solenoid valves, which are widely used in precision farming systems [7]. The main disadvantages of existing control systems are inaccurate positioning, excessive consumption of electric current due to maintaining a constant position, and as a result, overheating and discalibrating occurs. Recently piezo motors have been actively developing as a modern alternative to DC motors. They are also known as vibrating motors based on the piezoelectric effect. The advantages of such motors are high positioning accuracy, speed and power with small overall dimensions. They also do not require reduction gear to change the speed [8]. One of the varieties of piezoelectric motors is a piezomotor based on bimorph piezoelectric elements. It has low power consumption and a larger vibration amplitude. When designing bimorph piezoelectric motors, there is practically no theoretical basis for their design. Namely, the choice of the size of the piezoelectric plates of the bimorph piezoelectric element to create the maximum vibration amplitude. The aim of this work is to determine the influence of the geometric parameters of piezoceramic plates on the amplitude characteristic of piezoelectric motor. The paper proposes to determine and obtain the dependences of the rational dimensions of a piezoceramic element located on a metal plate using specialized software based on the finite element method. This makes it possible to obtain results comparable to the experimental ones.

2 Literature Review A significant number of designs of such motors are known [9–11], in particular, designs of piezoelectric motors of companies New Scale Technologies (NST) and Physik Instrumente (PI) [12, 13]. The designs of New Scale Technologies SQL series and Physik Instrumente (PI) motors are distinguished by their complexity and technical characteristics. They are derived from the amplitude of vibration of the resonant system of the motor, where the movement is created by variable deformation caused at the frequency of the mechanical resonance of the device by an alternating electric field. The design of the New Scale Technologies SQL series piezoelectric motor is shown in Fig. 1. According to the authors, it is the most relevant design for use in order to accurately dose fertilizers. The main elements of this piezo motor are a four-sided metal profile (made of nonmagnetic material) with an internal thread, a shaft (worm) and four piezoceramic plates.

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Piezoceramic plates are attached to the edges of the metal profile; the worm is twisted into the metal profile.

Fig. 1. The design of the New Scale Technologies SQL series piezoelectric motor

The principle of operation is as follows. When a two-phase voltage is applied to opposite pairs of piezoceramic plates, mechanical vibrations occur, which are transmitted to the metal profile. As a result, the shaft rotates and moves linearly in relation to the metal profile. By changing the phase shift by 90°, one can change the direction of the shaft movement. Depending on their size, these piezo motors operate at frequencies of 30–200 kHz. The key disadvantage of this design is the following. When moving from one face to another, long stiffeners be formed, which negatively affect the characteristics of the structure, namely, the amplitude of oscillations of the edges of the metal profile of the motor decreases. This leads to an increase in the amplitude of the control voltage, etc. This results in additional force, which opposes the operation of the piezo motor. To solve this problem, the paper proposes a design of a screw linear piezoelectric motor based on bimorph piezoelectric elements (Fig. 2).

Fig. 2. The design of the developed linear piezoelectric motor

The main features of this design are the use of bimorph piezoelectric elements of a special shape to reduce the influence of a stiffener in a piezoelectric motor, which made it possible to increase the vibration amplitude, the maximum torque on the shaft, and to reduce the amplitude of the control signal.

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However, to obtain the maximum characteristics of the proposed motor, it is necessary to know the rational dimensions of the metal plate and the piezoceramic element of the bimorph plates. The works [14–20] present mathematical calculation formulas for piezoceramic elements and in particular for bimorph piezoelectric elements. Analysis of these sources showed the absence of design formulas for a bimorph rectangular piezoelectric element fixed on both sides. In addition, the use of calculated mathematical formulas basically allows one of the parameters to be calculated, which is not always justified and accurately describes the required parameter, and besides, it cannot be presented visually in 3D, as well as obtain a multivariate result in one calculation. To obtain the maximum vibration amplitudes, it is necessary to have theoretical foundations such as calculation formulas for the dependencies of geometric parameters. Thus, the use of theoretical dependences to determine the rational geometric dimensions of bimorph piezoelectric elements is an urgent problem.

3 Materials and Methods The main component of the developed screw piezoceramic motor (Fig. 2) is a bimorph piezoelectric element. Figure 3 shows an axonometric model of one of the plates of a piezoelectric motor using bimorph piezoelectric elements.

Fig. 3. Axonometric model of one of the plates of a piezoelectric motor with bimorph piezoelectric elements: 1 – piezoelectric element; 2 – brass plate; 3–8 plate attachment point; A, B – dimensions of the piezoelectric element that will be changed at the modelling stage

Considering the technical features of piezoelectric motors and all the difficulties arising in their manufacture, the optimal solution is to use numerical calculation methods implemented by special CAD systems [21–23]. To study the vibration amplitude, a numerical simulation of the operation of one of the plates of piezoelectric motor using bimorph piezoelectric elements is carried out in the COMSOL Multiphysics 3.5. The analysis of the piezoceramic motor is carried out in the Frequency response mode. The computational mesh of finite elements in the “Mesh” item is chosen to be

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orthogonal (Normal). The mesh is constructed by tetragonal subdivision, and the studied three-dimensional models are presented by a set of more than a thousand elements each. Direct is used as a solver, in which the numerical SPOOLES method is chosen for solving systems of linear equations with sparse matrices. The following limiting conditions are adopted: piezoelectric element 1 together with brass plate 2 (bimorph piezoelectric element) have the type of boundary conditions Fixed at the edges and faces 3–8, electric voltage (Electric potential) of 100 V is applied to piezoelectric element 2, and the Ground is applied to the brass plate 1 on the opposite side (Fig. 3). Piezoceramics PZT-5H was used as a material for modelling a piezoelectric motor. The thickness of the piezoelectric element 0.4 mm together with the dimensions of the brass plate 36 × 12 × 0.1 remained unchanged throughout the entire research cycle. The dependence of the geometric dimensions of the piezoceramic plate was represented by the coefficient K = b/a (the ratio of the base width b to the length a). The coefficient K a varied from 0.20 to 0.85 with a step of 1 mm at the first stage of modelling, while the width b remained unchanged (b = 6 mm), and only the length a changed. The influence of the geometric dimensions of the width b on the amplitude of vibrations of a piezoceramic plate at a constant length a (a = 30 mm) was investigated at the second stage of modelling, the coefficient K b changed similarly to the first stage.

4 Experiments and Results When carrying out numerical simulations in the COMSOL Multiphysics software package in the Eigenfrequency mode, the vibration amplitudes of the bimorph piezoelectric element were determined when its geometric dimensions were changed. The first step to get reliable results is to build a mesh (“Mesh”), the breakdown of which significantly affects the obtained data (Fig. 4). From Fig. 4 it is seen that the division of the mesh for solving the problem is satisfactory, the number of cells in the division is 35010. Some results of numerical simulation of a bimorph piezoelectric element in the process of changing the length of the piezoelectric element with its constant width is shown in Fig. 5. Figure 5 shows the dynamics of changes in the vibration amplitude of the bimorph piezoelectric element depending on the change in geometric dimensions. So in Fig. 5,a the amplitude is 0.6 µm at K = 0.20, and in Fig. 5,b the amplitude is 9.6 µm at K = 0.85. Figure 6 shows the obtained results of numerical simulation in the form of the dependence of the vibration amplitude δ on the coefficient K = b/a. The maximum vibration amplitude of 9.6 µm of a bimorph piezoelectric element corresponds to the coefficient K a = 0.66. The graphical dependence obtained as a result of numerical simulation for the amplitude of oscillations of the actuator was approximated using a quadratic function δ = a + bx + cx2

(1)

where δ is the amplitude of the actuator oscillations; x is the coefficient K; a, b, c are the coefficients of the Eq. (1) (a = 75.393852; b = 668.16983; c = −1849.8358 respectively).

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Fig. 4. Computational mesh “Mesh”

Fig. 5. Results of modelling a bimorph piezoelectric element with different values of the coefficient K a at a constant width of the bimorph piezoelectric element: a) K a = 0.20; b) K a = 0.85

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12 10 8 6 4

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Fig. 6. The dependence of the amplitude of oscillations δ of a bimorph piezoelectric element at a constant width and with different values of the coefficient K a

The next step was to determine the vibration amplitude δ when changing the width b of the piezoelectric plate at a constant value of the length a = 30 mm. Width b varied from 6 to 1 mm with a step of 1 mm. Some of the numerical simulation results are shown in Fig. 7. Figure 8 shows the results of numerical modelling the dependence of the vibration amplitude δ of a bimorph piezoelectric element with different values of the coefficient K at a constant length. The dependence obtained as a result of numerical simulation for the vibration frequency was approximated using a quadratic function (1), where coefficients a = 0.010979675; b = 129.82668; c = −2230.3525. Thus, it was found that with a constant length of the piezoelectric element and only changing its width, there will be a quadratic increase in the amplitude of oscillations in the interval K from 0.2 to 0.03. The maximum vibration amplitude in this case is 2.07 µm at K = 0.03, which corresponds to a plate width of 1 mm, and the minimum vibration amplitude is 0.59 µm at K = 0.2, which corresponds to a width of 6 mm. To check the validity of the results of the Comsol Multiphysics simulation a comparative experiment was carried out. It was based on the measuring the amplitudefrequency characteristic of a rectangular bimorph piezoceramic element fixed on both sides in width. The dimensions of the experimental sample corresponded to the size of the model in Comsol Multiphysics shown in Fig. 7, a. Figure 9 shows the amplitude frequency characteristics obtained using Comsol Multiphysics and experimentally. Figure 9 shows that the resonant frequency of the bimorph piezoceramic plate obtained using Comsol Multiphysics is 855 Hz, and the experimental one is 850 Hz. The error is 0.6%. This means that the results obtained using Comsol Multiphysics are adequate.

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Amplitude of oscillaons, δ μm

Fig. 7. Results of modelling a bimorph piezoelectric element with a constant length a with different coefficients K b : a) K b = 0.2; b) K b = 0.03

2.5 2 1.5 1 0.5 0 0.2

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Fig. 8. The dependence of the amplitude of oscillations δ of a bimorph piezoelectric element at a constant length a with different values of the coefficient K b

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Fig. 9. The amplitude frequency characteristics of bimorph piezoceramic plate obtained using Comsol Multiphysics (dash line) and experimentally (solid line)

5 Conclusions By means of numerical simulation, the main results of the study of a bimorph piezoelectric element were obtained in the process of changing the length of the piezoelectric element at its constant width, and changing the width at a constant length. The influence of the geometric parameters of the bimorph piezoelectric element on its amplitude characteristics was determined, graphical and analytical dependencies were established for the choice of their rational ratios. The maximum vibration amplitude of 9.6 µm of a bimorph piezoelectric element corresponds to the coefficient K a = 0.66. The study of the amplitude frequency characteristics of experimental sample was carried out. The obtained results confirmed the adequacy of the Comsol Multiphysics simulation, while the error was 0.6%. The obtained mathematical dependences will help to predict the change in the frequency and amplitude of oscillations of the bimorph piezoelectric element, depending on the geometric dimensions of the plates. The research results can be used to design piezoceramic linear motors. Further research will be aimed at increasing the power characteristics of a linear screw piezoelectric motor based on bimorph piezoelectric elements.

References 1. Torikov, V.E., Osipov, A.A.: The main directions of digital technologies in the system of precision farming. In: Conference Proceedings: New Information Technologies in Education and the Agricultural Sector of the Economy, Bryansk, pp. 4–16 (2019). (in Russian) 2. Lyashynskyy, V.B.: Ecological and economic principles of formation of non-conventional land use in Ukraine. Agrosvit 7–8, 131–138 (2021). https://doi.org/10.32702/2306-6792.2021.78.131. (in Ukrainian) 3. Basavaraj, S., Anami, N.N.M., Surendra, P.: Automated paddy variety recognition from colorrelated plant agro-morphological characteristics. Int. J. Image Graph. Sig. Process. (IJIGSP) 1, 12–22 (2019). https://doi.org/10.5815/ijigsp.2019.01.02

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4. Bansal, B., Sidhu, J.S., Jyoti, K.: A review of image restoration based image defogging algorithms. Int. J. Image Graph. Sig. Process. (IJIGSP) 11, 62–74 (2017). https://doi.org/10. 5815/ijigsp.2017.11.07 5. Kumar, K.A., Aju, D.: An internet of thing based Agribot (IOT- Agribot) for precision agriculture and farm monitoring. Int. J. Educ. Manag. Eng. (IJEME) 4, 33–39 (2020). https://doi. org/10.5815/ijeme.2020.04.04 6. Arakeri, M.P., Arun, M., Padmini, R.K.: Analysis of late blight disease in tomato leaf using image processing techniques. Int. J. Eng. Manuf. (IJEM) 4, 12–22 (2015). https://doi.org/10. 5815/ijem.2015.04.02 7. Shpaar, D., Zakharchenko, A.V., Yakushev, V.P. (eds.): Precision Agriculture. Pushkin, St. Petersburg (2009). (in Russian) 8. Panich, A.E., Zhukov, S.N.: Piezoelectric Instrument Making, vol. 4. Piezoelectric Actuators, Rostov-on-Don (2008). (in Russian) 9. Spanner, K., Burhanettin, K: Piezoelectric motors, an overview. Actuators 5, 6 (2016). https:// doi.org/10.3390/act5010006 10. Mojallali, H., Amini, R., Zamanabadi, R.I., Jalali, A.A.: Systematic modeling for free stators of rotary piezoelectric ultrasonic motors. IEEE/ASME Trans. Mechatron. 12(2), 219–223 (2007). https://doi.org/10.1109/TMECH.2007.892829 11. Ryndzionek, R., Sienkiewicz, Ł, Michna, M., Kutt, F.: Design and experiments of a piezoelectric motor using three rotating mode actuators. Sensors 19, 5184 (2019). https://doi.org/ 10.3390/s19235184 12. Henderson, D., Schaertl, L.: Piezoelectric motors move miniaturization forward. New Scale Technologies. https://www.newscaletech.com/wp-content/uploads/PiezoMotors_Ele ctrProd_reprint_1006.pdf 13. Spanner, K., Vyshnevskyy, O., Wischnewskiy, W.: New linear ultrasonic micro motors for precision mechatronic systems. In: Proceedings of the 10th International Conference on New Actuators, pp. 439–443 (2006) 14. Bazilo, C.: Modelling of bimorph piezoelectric elements for biomedical devices. In: Hu, Z., Petoukhov, S., He, M. (eds.) AIMEE 2019. AISC, vol. 1126, pp. 151–160. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-39162-1_14 15. Li, J.: Design of active vibration control system for piezoelectric intelligent structures. Int. J. Educ. Manag. Eng. (IJEME) 2(7), 22–28 (2012). https://doi.org/10.5815/ijeme.2012.07.04 16. Sharapov, V.: Piezoceramic Sensors, pp. 1–500. Springer, NewYork (2011). https://doi.org/ 10.1007/978-3-642-15311-2 17. Smirnov, A.B.: Mechatronics and Robotics. Micro displacement systems with piezoelectric drives. St. Petersburg (2003). (in Russian) 18. Mukhanov, A., et al.: Development of a design tool for optimization of voltage generation from a bimorph piezoelectric cantilever beam. In: Materials Today: Proceedings, vol. 4, no. 3, Part A, 4477–4490 (2017). https://doi.org/10.1016/j.matpr.2017.04.020 19. Sarafraz, A.A., Roknizadeh, S.A.S.: Shape and geometrical parameter effects of a bimorph piezoelectric beam on energy harvesting performance. J. Appl. Comput. Mech. 3(2), 92–102 (2017). https://doi.org/10.22055/jacm.2017.21610.1111 20. Zhukov, S.N.: Piezoelectric Ceramics: Principles and Applications. Minsk, FUAuinform (2003). (in Russian) 21. Halchenko, V.Y., Bondarenko, Y.Y., Filimonov, S.A., Filimonova, N.V.: Determination of influence of geometric parameters of piezoceramic plate on amplitude characteristics of linear piezomotor. Electr. Eng. Electromech. (1), 17–22 (2019). https://doi.org/10.20998/2074272X.2019.1.03 22. Halchenko, V.Ya., Filimonov, S.A., Batrachenko, A.V., Filimonova, N.V.: Increase the efficiency of the linear piezoelectric motor. J. Nano-Electron. Phys. 10(4), 04025 (5p.) (2018). https://doi.org/10.21272/jnep.10(4).04025

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Ensuring Safety of Navigation in the Aspect of Reducing Environmental Impact Oleksiy Melnyk(B) and Svitlana Onyshchenko Odesa National Maritime University, Odesa 65029, Ukraine [email protected]

Abstract. The main areas of environmental pollution from ships, during their operation, are sewage, garbage and oil spills during accidents. The environment is also harmed by power plant exhaust gases from ships, which contain black carbon and components of incomplete combustion, ballast water discharge, noise pollution, and mammalian collisions with ships. A modern merchant ship is equipped with a great variety of equipment, instruments, devices and tools by means of which the ship’s navigating staff carries out the navigation process. Shipboard technical means and navigation systems, which the modern vessel is equipped with, enable to solve the tasks of ship navigation and handling, and therefore ensure safe navigation process and minimize the risks of emergencies and environmental pollution threats. This article offers a study of the relationship between maritime safety and environmental protection as well as degree of dependence of ship safety, particularly, failure of navigation equipment and systems and related causes of shipping accidents affecting environmental maritime safety. Keywords: Navigation safety · Navigation systems · Environment protection

1 Introduction Modern development of water transport and waterways puts more and more pressure on safety issues. Safety of human life, vessel, port infrastructure and environment is always among the priority tasks and involves the application of a whole set of measures and methods, to which the works of the following authors are devoted. Thus in sources [1–3] analysis of emissions from ships and statistical data on accident rates in the merchant fleet is given. Investigation of marine pollution caused by ship operations, measures for preventing pollution from ships studied in [4–6, 8, 14]. In [7] recycling marine used oil using green ship conversion technique highlighted. Specific evaluation of emissions from shipping including assessment and impact of maritime transport emissions on coastal air quality in [9–12]. Systems of automatic control of ship movement and safety of the process of ship navigation and ship operation reviewed in [13–18]. The papers [19–22] devoted on study of Gis-based emergency management system on abrupt environmental pollution accidents, air quality prediction and safety data modelling and information analysis and decision-making. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 95–103, 2022. https://doi.org/10.1007/978-3-031-03877-8_9

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Thus, this paper proposes a review of the issues of navigational safety, achieved through the analysis of methods of forecasting failure of navigation equipment in the process of navigation. Particularly attention require navigation systems, in order to establish a relationship between providing accident-free navigation process and environmental protection to improve safety standards, accuracy and reliability of ship’s navigation, which ultimately is a guarantee of environmental safety. Therefore, aims to focus on two important topics, navigational safety and marine environmental protection, to consider issues such as the failure of navigational equipment and systems and related causes affecting environmental safety.

2 Materials and Methods Any economic activity at sea has a significant impact on marine ecosystems and their components. Shipping is no exception. Every year a large number of ships crossing ocean trade routes, burn more than two billion barrels of fuel oil. Heavy fuel oil, a byproduct of crude oil, contains concentrations of sulfur that have a profound effect on the intensity of global warming. Serious and decisive action on the part of the global community required to combat air pollutants and to reduce greenhouse gases in order to avoid the situation developing to catastrophic proportions. A schematic of shipping impacts on marine ecosystems shown in (Fig. 1).

Fig. 1. Negative impacts on marine ecosystems from shipping

The International Maritime Organization (IMO) estimates that the average annual emissions of carbon dioxide from maritime transport amount to more than 3% of global emissions, and are expected to increase by at least 50% by 2050 compared to the current period. This aspect is especially important for the European Straits, one of the busiest shipping routes in the world. The actual increase will depend on future socioeconomic conditions. However, under all scenarios, emissions from ships expected to increase steadily. As greenhouse gas emissions from other sectors decline, shipping will contribute an increasing share of global pollution.

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The impact of ships on the environment occurs in several trends at once: greenhouse gas emissions, pollution of the biosphere by operational waste, as well as pollution because of accidents, during which toxic cargo is released (mostly oil and petroleum products) a special place belongs to collisions and ship sinking, which cause enormous damage to the environment (Fig. 2).

Fig. 2. Main areas of environmental pollution impact

3 Results and Discussion Achievement of the general purpose of navigation safety means the implementation of ways to reduce the impact of the human factor and the number of accidents, which occur because of failure of navigational equipment or its inadequate functioning. The use of methods for predicting the failure of ship navigation equipment, a result of the development of information technology and its implementation on board modern ships. It allows carrying out process of integration of existing ship navigation systems and new ones, which are aimed at increase of efficiency and safety of ship operation in conditions of failure of standard systems and occurrence of risk accident. Reliable operation of the ship’s navigational equipment is required when navigating in confined waters, areas with high traffic density, especially in restricted visibility conditions. However, in the event of failure of primary devices and systems, to prevent loss of control over the ship’s position, heading and to maintain her on a given course requires a transition to the use of alternative sources to ensure the safety of navigation. Therefore, the study of the principles of functioning, the development of methods for predicting the causes and probabilities of failure of such equipment, a review of prospective ideas for the use of such methods among the actual tasks. The main threats to safety of navigation are accidents. One of the causes of accidents is incorrect or inaccurate navigation information. According to the world’s statistics, 2/3

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of all accidents in the fleet are navigational accidents. Of these, 85% occur at a distance of about five miles from the shore, including 30% in harbor waters. The same situation is typical for other modes of transport: takeoff and landing of aircrafts, especially with vertical takeoff, docking of spacecrafts, parking of vehicles (in particular, large-size ones). Adequate technical condition of the ship, availability of necessary rescue equipment, concluded insurance contracts, verified routes, as well as careful study of meteorological conditions during the passage minimize the risks associated with shipping and ensure the safety of maritime transport. The international shipping industry is responsible for transporting about 90% of global trade, so ship safety is critical. The sector has continued its long-term positive safety trend, with the number of reported total ship losses over 100 GRT remaining stable compared to a year earlier. This means that annual ship losses have halved over the past decade, although 2020 was the first year in five years when losses have not declined, suggesting that total losses may stabilize near the minimum level achievable. The accident rate of seagoing ships depends on the design features, type of transported cargoes, navigation areas and a number of other factors. The main cause of marine accidents is breakdowns, damage, or failure of engines and equipment. More than a third (9,334) of the 26,000 incidents in the last decade were caused by equipment damage or malfunction. This is also the reason why the most expensive insurance claims arise 10 billion USD over the past five years (data based on an analysis of 230,000 insurance claims in the maritime industry involving AGCS (Allianz Global Corporate & Specialty) and other insurance companies from July 2013 to July 2021. Collision is the next most common occurrence, with total ship losses again up from last year, reaching a four-year high. One-third of all ship fatalities are cargo ships. The most common cause of loss is sinking. In 10 years, 551 vessels out of 1,036 were lost for this reason. In 2018, there were 30 incidents of shipwrecks. The total number of vessel incidents in 2018 was 2,700. In addition, the number of fire-related incidents is increasing. Of greatest concern, car carriers and container ships - on board them, fires occur on average every 60 days. Therefore, by identifying the main causes of accidents on ships, this study will establish how the level of reliability of navigational equipment affects the safety of navigation and consequently, environmental safety. The research of ecological threats from shipping activities is carried out by analogy with already existing projects. Within the framework of it, methodical approaches on an estimation of ecological transparency for an estimation of activity of the shipping companies and their influence on environment were already tested firstly. However, the actual problem comes directly from the ships themselves as a result of technical malfunctions during their operation. Technical failure is a state of a technical device when at least one of its main or additional parameters does not meet the requirements stipulated in the technical documentation. The device enters a faulty state due to failure or damage. Failure causes the device to become inoperable because at least one of the main parameters does not meet the technical requirements for the device. Thus main causes of accidents on ships shown in Fig. 3. Classification by types of hazards (types of emergencies) is based on such ship conditions, which pose a real threat to its safety or loss of seaworthiness, and then six main types of hazards can be classified as those, namely:

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15% sunk / submerger

11%

wrecked / stranded

54% 20%

fire / explosion others

Fig. 3. Main causes of accidents on ships

– damage to the hull and destruction of its integrity due to external extreme operational loads (excessive wave loads, heavy ice conditions, contact with submerged floating objects); – capsizing of the vessel or its excessive heeling, which does not allow to continue the voyage, caused by incorrect loading, shifting of cargo and damage of its securing means, icing; – ship sinking (loss of buoyancy) due to hull watertightness failure, not directly connected with exposure to extreme operating loads, at corrosion or similar damages; – loss of motion and controllability due to failure of main propulsion unit or propellerrudder complex; – contact with external objects (navigational AS): collision, grounding due to forcemajeure circumstances, navigator’s mistakes, failure of navigational equipment, pilot or ship control system errors, impact of another ship or moving object, insufficiency of navigational and cartographic support, including unmarked on the chart shallows and submerged objects; – fire or explosion in the vessel compartments caused by electrical short circuit or ignition of electrical equipment, negligent handling of fire, welding works, fuel getting in contact with hot surfaces of the running engine or explosion of oil vapors in the crankcase, spontaneous ignition of cargo or other flammable materials. In view of the above reasons, it is necessary to detail navigation emergencies and consider problems of navigation equipment and systems failure and the reasons related to it. Navigational equipment and systems are a mandatory element of any ship’s equipment to ensure safe navigation. The requirements for equipping ships with navigation systems and devices are presented in Regulation 19, Chapter 5 of the International Convention for the Safety of Life at Sea (SOLAS), which is the fundamental document of international

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maritime law establishing mandatory requirements for the design and equipment of ships and other methods and means of ensuring safety at sea. Chapter 5 “Safety of Navigation” establishes requirements for navigational equipment of seagoing ships, the navigation bridge construction, as well as for shore services and organizational measures to ensure safety of navigation. Let us consider some basic systems ensuring the process of navigation itself. Virtually the vast majority of merchant ships are equipped with these navigational instruments, which provide information about the surrounding environment or perform operations in the process of ship handling (Table 1). Table 1. Navigation systems and its components Navigation systems

Components

1. Course indicating systems

Gyro, magnetic, satellite compasses

2. Ship radar system

ARPA & Radar

3. Automatic ship course keeping control system

Ships steering system

4. Devices for recording speed and distance

Log & echo sounder

5. Electronic chart display and information system

ECDIS

6. Automatic identification system

AIS

7. Voyage data recorders

VDR

8. Navigation satellite positioning systems

GPS

9. Light and sound system

Navigation lights

10. Ship’s information

Pilot card

Modern trends in ensuring navigational safety impose the conditions of using the “redundancy principle” of the most important ship instruments and systems, and therefore the large-capacity vessels equipped with navigation equipment and systems, as a rule, in two or even three duplicates, which can operate both independently and simultaneously. Figure 4 shows the division of the safety level of the ship navigation process into sublevels depending on the degree of ensuring the operational condition of the navigational equipment. Every ship navigation system that ensures safety of navigation can be in one of three conditions ((normal, inoperative (failure), transient)), which can be observed with different probability that is determined by system manufacturer, its age, conditions of its operation, crew qualification, etc. Thus, the inoperative condition of one or even several systems may not lead to critical condition in terms of navigational safety of a vessel. It is determined, firstly, by possibility of return transition to working (normal) condition with certain probability; secondly, by possibility of switching (duplication) of functions of some systems to others. Dependence of navigational safety on ship’s systems operational condition is shown on Fig. 5, which is, simulates the process of transition of each system into different

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Fig. 4. Navigation safety level chart

operational states and allows estimating the effect of different combinations of system states on the resulting state of navigational safety of the vessel. Thus, combination of various conditions of navigation systems defines one of five major ship’ conditions with regard to navigational safety. The interest for research of navigational safety problem is the study of process of transition of each system into various conditions and estimation of influence of various state combinations of systems on a final condition of a ship’s navigational safety. Base for similar researches is at theoretical level - description of corresponding probabilistic process, and also the analysis of static data for numerical estimation of probability of those or other states of a ship navigation system, as the first stage in management system of ecological safety of ship operation.

Fig. 5. Dependence of navigational safety on ship’s systems condition

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4 Summary and Conclusion The results from the present study indicating that reliability of ship navigation process is of great importance for both safety of ship operation and the effectiveness of environmental disaster prevention. It should be emphasized that measures to prevent emergencies include high-precision control of the ship position, which is of special importance when navigating in the coastal zone, approaches, narrow waters, canals and ports, where the consequences of a ship accident are associated with the risk of environmental pollution, damage to coastal infrastructure and human casualties. Despite availability of up-to-date electronic navigation aids, satellite systems, electronic charts and other equipment, the standard navigation aids are still irreplaceable and kept in use. The use of combinations of various navigation systems makes it possible to improve accuracy of information as well as ship navigation safety and, as a consequence, to ensure ecological safety. Therefore, to meet modern requirements to shipping safety, qualitatively new means and systems to be introduced, but the issues of ensuring the reliability of navigation, including the development of ways and methods of forecasting equipment failure, are also remain among the priority tasks. Also based on an expert assessment of the degree of threats, taking into account the international environmental regulation of shipping, it is necessary to develop criteria for environmental openness of shipping companies, which will assess their activities to reduce environmental risks, as well as strengthen cooperation with all stakeholders to reduce the impact on the environment.

References 1. Report Shipping on Arctic-2020. https://www.ra-national.ru/sites/default/files/Report_Shi pping%20on%20Arctic_NRA_WWF_October%202020.pdf. Accessed 25 Oct 2021 2. Marine Environment. https://www.imo.org/en/OurWork/Environment/Pages/Default.aspx. Accessed 25 Oct 2021 3. Review of maritime transport – 2020. https://unctad.org/system/files/official-document/rmt 2020_en.pdf. Accessed 20 Oct 2021 4. Özdemir, O., Yılmaz, H., Ba¸sar, E.: Investigation of marine pollution caused by ship operations with DEMATEL method. TransNav, Int. J. Mar. Navig. Saf. Sea Transp. 10, 315–320 (2016). https://doi.org/10.12716/1001.10.02.14 5. Mazzoccoli, M., Altosole, M., Vigna, V., Bosio, B., Arato, E.: Marine pollution mitigation by waste oils recycling onboard ships: technical feasibility and need for new policy and regulations. Front. Mar. Sci. 7, 566363 (2020). https://doi.org/10.3389/fmars.2020.566363 6. European Maritime Safety Agency: Preventing Pollution from Ships. European Maritime Safety Agency, Lisboa (2008) 7. Eslam, M.: Recycling marine used oil using green ship conversion technique. In: Proceedings of the SPE Gas and Oil Technology Showcase and Conference, Dubai (2019) 8. Mueller, D., Uibel, S., Takemura, M.: Ships, ports and particulate air pollution - an analysis of recent studies. J. Occup. Med. Toxicol. 6(31) (2011). https://doi.org/10.1186/1745-66736-31 9. Viana, M., et al.: Impact of maritime transport emissions on coastal air quality in Europe. Atmos. Environ. 90, 96–105 (2014). https://doi.org/10.1016/j.atmosenv.2014.03.046 10. Corbett, J., Winebrake, J., Green, E., Kasibhatla, P., Eyring, V., Lauer, A.: Mortality from ship emissions: a global assessment. Environ. Sci. Technol. 41, 8512–8518 (2007)

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11. Campling, P., Janssen, L., Vanherle, K., Cofala, J., Heyes, C., Sander, R.: Specific evaluation of emissions from shipping including assessment for the establishment of possible new emission control areas in European Seas. Flemish Institute for Technological Research (VITO), Mol, BE, p. 395 (2013) 12. Viana, M., et al.: Chemical tracers of particulate emissions from commercial shipping. Environ. Sci. Technol. 43(19), 7472–7477 (2009) 13. Vaguschenko, L., Tsymbal, N.: Automatic Ship Motion Control Systems, 3rd edn, 328 p. Odesa (2007). (in Rissian) 14. Kartamysheva, E., Ivanchenko, D., Beketova, E.: Ship as a source of environmental pollution. Young Sci. 25(211) 12–15 (2018). (in Russian) 15. Mironov, A.: Methods for optimizing the parameters of functioning of laser range beacon systems to ensure the safety of navigation in cramped navigation conditions. Thesis abstract, 21 p. (2011). (in Russian) 16. Onyshchenko, S., Shibaev, O., Melnyk, O.: Assessment of potential negative impact of the system of factors on the ship’s operational condition during transportation of oversized and heavy cargoes’. Trans. Mar Sci. 10(01), 126–134 (2021) 17. Onyshchenko, S., Melnyk, O.: Modelling of changes in ship’s operational condition during transportation of oversized and heavy cargo (December 31, 2020). Technol. Audit Prod. Reserves 6(2(56)), 66–70 (2020). https://doi.org/10.15587/2706-5448.2020.221653 18. Melnyk, O., Bychkovsky, Y.: Modern assessment methods of ship safety level and ways of its improvement. Transp. Dev. 2(9), 37–46 (2021). https://doi.org/10.33082/td.2021.2-9.03. (in Ukrainian) 19. Zhang, H., Liu, M.: GIS-based emergency management system on abrupt environmental pollution accidents in counties of China. Int. J. Educ. Manag. Eng. (IJEME) 2(8), 31–38 (2012). https://doi.org/10.5815/ijeme.2012.08.06 20. Rao, K.S., Devi, G.L., Ramesh, N.: Air quality prediction in Visakhapatnam with LSTM based recurrent neural networks. Int. J. Intell. Syst. Appl. (IJISA) 11(2), 18–24 (2019). https://doi. org/10.5815/ijisa.2019.02.03 21. Anda, I., Rabiu, I.O., Aminu, E.F.: A safety data model for data analysis and decision making. Int. J. Inf. Eng. Electron. Bus. (IJIEEB) 9(4), 21–30 (2017). https://doi.org/10.5815/ijieeb. 2017.04.04 22. Aanandh, S.B., Kar, C., Siddiqqui, N.: Safety information modeling: smart safety devices & internet of everything. Int. J. Intell. Syst. Appl. (IJISA) 7(2), 41–49 (2015). https://doi.org/ 10.5815/ijisa.2015.02.06

Synthesis of the Algorithm for Determining the Film Thickness Based on the Obtained Data of the White Light Interferogram Yurii Kryvenchuk(B) , Maryana Zakharchuk, Olha Sencovych, Yulia Malynovska, Nataliia Topylko, and Yurii Novytskyi Lviv Polytechnic National University, 12 Bandera Street, 79013 Lviv, Ukraine [email protected]

Abstract. In many fields of science and technology there is a problem of measuring the surface parameters of various objects, such as profile, roughness, etc. With the improvement of technologies and miniaturization of products, the requirements for the accuracy and speed of measuring the parameters of technological processes increase. In recent years, there is considerable interest white light interferometry, the advantages of this technology include the lack of contact with the object under study, high resolution, the ability to control surfaces with sharp differences and slopes, where traditional monochromatic interferometry does not give reliable results. The use of a broadband light source instead of traditional laser radiation makes it possible to measure not only relative displacements but also their absolute values with high accuracy. The article considers the concept of creating an algorithm for determining the film thickness and its change using white light interferometry for measurements in the nanoscale range. The solution of this problem is realized by processing the interferogram of white light and determining with its help the studied parameters of the film. In addition, during the development and testing of the algorithm, a number of filters were selected and developed to improve the processing and analysis of interferograms. Keywords: Interferometry · Algorithm · Film thickness determination · Mathematical model · Interferogram · Filters

1 Introduction White light interferometry plays an essential role in science and technology, in particular it is used to study thin films, determine the length and study the surface topology. Using this phenomenon, it is possible to perform measurements in the micrometric range, with a reasonably good resolution (μm - x and y axes, and nm - z axis). The advantage of using interferometry is its high speed and wide range of measurements. White light interferometry is widely used in such engineering fields as biomechanics, chemistry, semiconductor engineering, medicine, 3D systems for nanopositioning, control and research of applied hardening coatings. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 104–119, 2022. https://doi.org/10.1007/978-3-031-03877-8_10

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At present, as was already mentioned, with the help of interferometers, which are widely used in science and industry, it is possible to study the displacement of small dimensions, the topology of the surface, the instability of the refractive index of the medium. Interferograms are available with fairly high accuracy with the help of interferometers. In this case, it is very important to have an interference pattern to study thin films, because in this study, it is necessary to compare two or more interferograms, which is impossible with insufficient resolution. The article analyzes the methods of spectral noise reduction, on the basis of research of which it is possible to quickly choose the necessary method and means depending on the requirements. 1.1 Literature Review Light that has a clearly stated frequency is defined as monochromatic. Two monochromatic waves that have a phase difference constant in time are called coherent. There is a distinction between temporal and spatial coherence [1, 2]. Monochromatic light can be obtained by using either a monochromator for a polychromatic light beam or a point light source [2, 3]. In contrast to monochromatic light, which is characterized by a constant frequency, white light is characterized by variable values of amplitude and frequency at any given time [1]. Since the measuring set uses an IR diode as a light source, it is possible to consider the function of density of its distribution; as a rule, this is the function of the normal distribution [3] (Fig. 1).

Fig. 1. Spectral function of distribution density

This function can be described as follows: 1 ν − ν0 2 ) ] S(ν) = √ · exp[−( ν π · λ where: ν0 – central frequency of white light signal; v – spectral bandwidth;

(1)

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v – frequency. The central wavelength ν0 corresponds to the average λ0 wavelength value, and the spectral bandwidth ν0 corresponds to the wavelength range (spectrum width) λ. Coherence time is a period of time during which the maximum lag from each other is possible, but they are still mutually coherent. The distance travelled by the wave during this time is called the coherent distance [4]. Coherence time is equal to: Ik =

λ2 λ

(2)

For the white light, overlapping of time-varying parameters of amplitude and frequency means the formation of interference pattern only in the segment of coherence length. The phenomenon of interference occurs as a result of the superposition of several light waves. In the simplest case, this can be described by the following equation:  A = A21 + A22 + 2A1 A2 α (3) where A1 and A2 —the amplitudes of the corresponding waves, α—the phase difference of these waves. As a result, a redistribution of intensity occurs and there are peak and minimum intensity points, and the resulting image is an interference pattern [6]. In Fig. 2 an example of a simulated interferogram is provided.

Fig. 2. Simulated interferogram

When heated, the film between the plates of the interferometer changes its parameters, and, in the general case, this is considered as the incidence of the beam of parallel light on a wedge-shaped plate. The beams are reflected from both the upper and lower faces (Fig. 3). At almost perpendicular incidence of the light beam and a very small wedge angle, the optical path difference can be described using the following formula: =2·d ·n·



n2 − sin2 (ε) ·

λ λ ≈2·d ·n· 2 2

(4)

When the following conditions are met: 1 = 2 · d1 · n −

λ λ = m · λ, 2 = 2 · d2 · n − = (m + 1) · λ, 2 2

(5)

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Fig. 3. Interference on the wedge, the interference pattern formation

then two adjacent intensity peak points correspond to the thickness d1 and d2. And the internal path difference is equal to: 2 − 1 = 2 · n · (d2 − d1 ) = λ

(6)

And the expression 2 − 1 = l · tan(ε) allows determining the distance between intensity peaks: l=

λ 2 · n · tan(ε)

(7)

L·λ 2·n·l

(8)

d=

where, d – film thickness (maximum value); d1 , d2 – local values of film thickness; n – refraction index of the medium; λ – central wavelength value; ε – wedge-shaped plate angle; m – interference order; l – distance between intensity peaks; L – region of interference pattern formation. Fabry-Perot interferometer is an interference spectral device with high resolution, the principle of operation of which is based on the phenomenon of multibeam interference (Fig. 4).

Fig. 4. Operation principle of Fabry-Perot interferometer

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The most common applications of Fabry-Perot interferometer are the separation of the structure of spectral lines (splitting interference fringes with simultaneous irradiation of the interferometer with the waves of approximate wavelength values) [9]; measuring small deviations of wavelength changes in the optical spectra, comparison of wavelengths (determination of the light beam wavelength, which illuminates the interferometer, as well as a reference beam with a known wavelength). Basically, Fabry-Perot interferometer is an air layer (d) formed between two parallelsided plates, usually made of quartz or glass, with polished inner surfaces, with a high reflection coefficient coating and illuminated from the outside. The outer surfaces of the plate can form a small angle with the inner ones to eliminate the influence of light gleams on the process of observing the interference pattern. When the plates are placed in parallel (constant distance value between them), the interference pattern is formed in the focal plane of the lens and has the form of rings of equal inclination (due to the formation of the light beam from a wide radiation source). As previously stated, the interferometer operation principle is based on the phenomenon of multibeam interference, i.e. the beam entering through the outer surface of the plate (appropriateness of illumination) is repeatedly reflected from the inner surfaces and partially passes on [10]. As a result, coherent waves that differ in amplitude and phase are formed. The amplitudes of the reflected waves can be described by the following equations: Amplitudes of transmitted waves: A1 = (1 − R)A0 , A2 = R(1 − R)A0 , A3 = R2 (1 − R)A0

(9)

R – coefficient of reflection; A0 – initial amplitude. Amplitudes of reflected waves: √ √ √ A1 = RA0 , A2 = − R(1 − R)A0 , A3 = − RR(1 − R)A0 ,

(10)

Using the “-” sign, it is possible to take into account the loss of half-wave during reflection. Path difference  between two adjacent beams and the phase difference are equal to:  = 2dncosθ  = k

(11)

k – wave number. Therefore, based on the above formulas, the resulting amplitudes of the reflected wave and the wave are as follows:   Ad = A0 (1 − R) 1 + Re−iφ + R2 e−2iφ + ... (12) Ar =

  √ √ RA0 − R(1 − R)A0 e−iφ 1 + Re−iφ + R2 e−2iφ + ...

where i – imaginary unit.

(13)

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If the plate is long enough, then the amplitudes can be written as the sum of infinite descending geometric progressions: Ad =

Ar =

(1 − R) A0 1 − Re−iφ

   R 1 − e−iφ 1 − Re−iφ

(14)

A0

(15)

It is also worth mentioning that the order of interference and resolution are mixed in compliance with the increase in the diameter of the interferogram ring.

2 Methodology and Methods It is worth considering the the experiment set for a better understanding of the process of obtaining interferometric data, which is presented schematically in Fig. 5 and as a hardware in Fig. 6. The scheme (Fig. 6) of the measuring set consists of: a radiating source (1), the role of which is played by the IR diode, as it can be used to obtain a good stable signal; stabilized output for it (2) (to avoid ripple, which allows getting a clearer interference pattern); collimator (3) for the formation of a parallel beam of radiation, because there is a spherical wave at ints input; a miniature Fabry-Perot interferometer (4) with nonparallel plates and a Peltier element (5) for heating the film under study applied between the interferometer plates; a converging lens (6) for forming an interference pattern and a CCD camera that captures the fully formed interferogram and transmits its data via USB port to a computer connected to the given set. Light

output device

Fabry-Perot Collimator

Lens

CCD-camera

interferometer

Fig. 5. Schematic representation of the measuring set

for computer

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Fig. 6. Hardware image of the real measuring set

Such data transfer from the CCD camera lens to the PC via USB port can be carried out by means of the built-in software package tools “MatLab” Data Acquisition Toolbox, which does not require extra settings or scripting. The following algorithms will be tested on the given set. Visual problem statement as well as the principle of its solution may be presented so that we could understand the suggested method better (Fig. 7).

Fig. 7. Visual image of the task and the principle of its solution

The suggested algorithm concept can be described by the following steps: • uploading measured or simulated interferometric data; selecting the working area of processing; receiving informative signals of interferograms; determining the values of film thicknesses of each interferogram by determining the distance between the intensity peaks; comparison and analysis of results obtained by processing simulated and real data.

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For the purposes of comparison and analysis, two interferograms obtained at different temperatures of the heated film are required. For the comparison, the concept of the algorithm will be tested on simulated and real data. Data simulation is conditioned by the need to evaluate the method and the results obtained, respectively, and the real data are difficult to process immediately, because they also contain non-informative signal parameters, such as noisiness, which can complicate their processing. Furthermore, for the processing of a real interferogram, it is best to choose the study area not as a whole picture, but one of the central fragments (to simplify processing). According to the size, the study areas of the simulated interferograms were selected. Interferogram simulation is carried out in the MatLab software package. To begin with, it is necessary to describe the mathematical model of the white light interferogram: I (T ) = I0 + IM · E(T ) · C(T )

(16)



2 · π 2 · (T )2 · λ2 E(T ) = IM · exp − (Envelope) λ4 

4·π · (T ) (Carrier) C(T ) = cos λC

(17) (18)

I0 – constant component of the signal; IM – modulation amplitude; T – optical phase difference; λc – central wavelength; λ – deviation of wavelengths. Interferogram simulation was performed applying formulas 17–19. The following form for the interferometer plates (Fig. 8) and the simulated interferogram (Fig. 2) have been obtained.

Fig. 8. Graphical representation of interferometer plates

The simulation parameters were as follows: constant signal component I0 = 0, modulation amplitude IM = 2, central value of the wavelength λC = 830, nm, spectrum width λ = 80, nm, wedge angle e1 = π 620, (for the first interferogram shown in the figure), rad.

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To approximate the simulated data to the real ones, an interferogram as big as 3000 * 3000 points was obtained, but in the future only the area identical in size to the realm of the real interferogram analysis area will be analyzed. Moreover, when simulating interferograms to approximate them to real data, the formula of the coefficient of thermal expansion was applied (to change the film thickness, or the distance between the plates, the simulated data analogous to the adhesive film heating): T

d = α · d0 · T

(19)

d – change of film thickness when exposed to temperature; d0 – the initial value of the film thickness; T – variation of temperature, which corresponds to the change in film thickness by time; α – coefficient of thermal expansion of the material (tabular value). As it was already mentioned, it is necessary to choose one of the central fragments to process real interferogram, which is presented in the figure below (Fig. 9).

Fig. 9. Selection of a rectangular interferogram fragment

The obtained fragment is processed using the Image Processing Toolbox. To obtain a sufficiently informative and clear signal, it is possible to find the arithmetic mean of each column of the image matrix with the help of the built-in function mean(*) [6] and graphical display of the resulting array.

Fig. 10. Graphical representation of interferometer plates

However, the received signal is uninformative, as it does not allow determining unambiguously its peaks that appear in the actual signal (Fig. 10) and, consequently,

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the distances between them. Therefore, it is reasonable to apply a filter to eliminate the noise present in the interferogram pattern. Several filters have been selected for this purpose, including the median filter, the Gaussian filter, the average filter, the Wiener filter, and the so-called “smoothing” filter. In Fig. 11. the graph of the real data signal of interferograms received at temperatures of 20 °C and 50 °C without filtering is presented.

Fig. 11. Graphic representation of the real data signal of the interferogram without filtering

Therefore, to improve the obtained real data, it was decided to carry out median filtering, which belongs to nonlinear filters. Median filtering of the image matrix in two directions is taking place by means of it. The function medfilt2 (*) [4, 6] is used to apply this filter. Figure 12 shows the graph of the filtered signal.

Fig. 12. Graphic representation of the real data signal of the interferogram after median filtering

As shown by the graphical representation, the received signal already has certain well-pronounced peaks, but this is not enough, so it is advisable to use other filters to achieve high quality filtering. The next step in the extraction of the quality signal is the use of a Gaussian Filter, calling the imspecial(*) function. When forming the filter, the

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following parameters were used for its characteristics: a matrix of 5:5 size, with a value of rσ = 1. Figure 13 presents the signal filtered by the Gaussian filter. As can be seen, the filtering result is still unsatisfactory, as it is impossible to unambiguously determine the number of peaks.

Fig. 13. Graphic representation of the real data signal of the interferogram after applying the Gaussian filter

The next filter to select the peaks is the average filter, which uses the technique of smoothing time dependencies, i.e. smoothing of data series. To apply the given filter, one can use the same imspecial(*) function as in the case of the Gaussian filter, also using 5:5 square matrix. Graphic representation of the signal filtered by the average filter is shown in Fig. 14.

Fig. 14. Graphic representation of the real data signal of the interferogram after applying the average filter

As can be seen from the graph, this filter is quite effective, as the signal is much better smoothed. However, as in previous cases, it is still impossible to achieve the same number

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of segments between the peaks of the signals. Therefore, the next stage of filtering was the use of the Wiener filter. This is a special noise-suppressing filter designed for image processing. The filtering condition assumes that the signal and additive noise are the same stochastic processes with the known spectral distribution and circular correlation. The filtering result is presented in Fig. 15.

Fig. 15. Graphic representation of the real data signal of the interferogram after applying the Wiener filter

Since even the latest filtering results are unsatisfactory, a smoothing filter can be applied. In this method, the curve fits into the new curve as accurately as possible, with the smallest possible deviation. In this case, a polynomial of lower order approximation is used, which satisfies the smoothing condition. Filtering by applying this method can be obtained using the smooth (*) function. The filtering results are presented in Fig. 16.

Fig. 16. Graphic representation of the real data signal of the interferogram after “smoothing” filtering

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3 Results The obtained results allow testing the concept method on both real and simulated data. The first step, i.e. the selection of the interferogram study area, can be taken using the ordinary function, simply by specifying in brackets the name of the image and the coordinates for selecting a particular area; this applies to both simulated and real interferograms (Fig. 7): IM11 = IM110(327:606,399:898,:); where IM110 is the original interferogram pattern. To obtain an informative signal of the simulated interferogram, it is sufficient to represent it graphically using the plot (*) function. An example: Figure; plot(I1_2); grid;xlabel(‘Pixels’); ylabel(‘Intensity’); where I1_2 is an arbitrary row of interferogram matrix (in this case, all the rows are duplicated). Obtaining an informative signal of the real interferogram is described above. Figure 17 illustrates the differences in the signals.

Fig. 17. Simulated interference patterns and their signals

Upon receipt of the signals, it is possible to calculate the local distance between the interference peaks of the graph (using formula 8). Since we have different measuring units (pixels and nanometers), we introduce the pixel coefficient: pixel_coef = (5 * lambda0)./1000; The results obtained are presented in Fig. 18.

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b) real

Fig. 18. Film thickness value for interferograms

Figure 19 shows a graphical comparison of the film thickness values for the simulated and real interferograms (the temperatures of their reception are most closely approximate). Real interferogram

Real intergferogram

Simulated interferogram Simulated interferogram

Fig. 19. Graphical representation of film thickness values determined for summed and real interferograms (at 20 °C)

But the task was to determine the change in film thickness. The results are presented in Fig. 20.

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Real interferogram

Simulated interferogram

Fig. 20. Change in the film thickness when heated for simulated and real interferograms

4 Conclusion This paper studies a concept-method of creating an algorithm for high-precision determination of the change in film thickness using white light interferometry, based on the processing of white light interferograms. Simulation and processing of interferometric data for further comparison of the results obtained with their help was carried out. The algorithm was tested on simulated and real interferometric data. Central fragments of two interferograms (one for each type) were chosen as the basis for comparison. To approximate the simulated data to the actual measured during the simulation, the coefficient of thermal expansion was also taken into account. To improve the processing of real measured data and obtain their informative signals, a number of filters designed for image processing were developed and applied. The best results were shown by the so-called “smoothing filter”. To some extent, the technique can be considered as “rough”, because no amendments or corrections of calculated data were introduced in the calculations. However, according to the calculations, the obtained results showed that the values of the set thickness are mainly within the range of several micrometers, which indicates certain efficiency and relevance of the calculations and experimental findings, taking into account inaccuracies and errors. The value of the film thickness change is within the nanoscale range, which indicates fairly good efficiency of the technique under investigation. In the future it is planned to test the method taking into account heat losses that affect the expansion of the smelting, as well as various related influencing factors.

References 1. Perdrotti, F., Pedrotti, L., Bausch, W., Schmidt, H.: Optik für Ingeniere, Grundlagen, vol. 3, pp. 23–37. Springer, Heidelberg (2007). https://doi.org/10.1007/b139018 2. Zinth, W., Zinth, U.: Lichtstrahlen-Wellen-Photonen, 4 Auflage, pp. 118–131, Münschen (2013) 3. http://www.polytec.com/fileadmin/user_uploads/Solutions/Surface_Profiling/Documents/ OM_AN_IF0207_E_Basics_WLI.pdf

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4. Rao, Y., Jackson, D.: Recent progress in fiber optical low-coherence interferometry. Meas. Sci. Technol. 7, 981 (1996) 5. Yuan, L., Zhou, L., Jin, W.: Recent progress of white light interferometric fiber optical strain sensing techniques. Rev. Sci. Instrum. 12(71), 46–48 (2000) 6. Fedushko, S., Syerov, Y., Kolos, S.: Hashtag as a Way of archiving and distributing information on the internet. In: CEUR Workshop Proceedings, vol. 2386, pp. 274–286 (2019) 7. Yuan, L., Ansari, F.: White light interferometric fiber optical distribution strain sensing system. Sens. Actuators 63, 177 (1997) 8. Manojlovi´c, L.: High-resolution wide-dynamic range electronically scanned white-light interferometry. Appl. Opt. 53(15), 3341–3346 (2014) 9. Yu, Z., Weng, Y.: Spatial distribution of carrier-envelope phase for femtosecond pulsed laser beam profile determined by asymmetric spectral interferometry. Opt. Lett. 35(13), 2275–2277 (2010) 10. Schmidt, M., Fürstenau, N.: Fiber-optic extrinsic Fabry–Pérot interferometer sensors with three-wavelength digital phase demodulation. Opt. Lett. 24(9, 599–601 (1999) 11. Qi, B.: Novel data processing techniques for dispersivewhite light interferometer. Opt. Eng. 42, 3165–3171 (2003) 12. Ding, W., Jiang, Y., Gao, R., Liu, Y.: High-temperature fiber-optic Fabry-Perot interferometric sensors. Rev. Sci. Instrum. 86, 104–109 (2015) 13. Shah, D., Bera, K., Joshi, S.: Software Implementation of CCSDS recommended hyperspectral lossless image compression. Int. J. Image Graph. Sig. Process. (IJIGSP) 4, 35–41 (2015) 14. Migiraneza, J., Sinha, A.: Analogue wavelet transform based the solution of the parabolic equation. Int. J. Image Graph. Sig. Process. (IJIGSP) 7, 1–20 (2012) 15. Migiraneza, J.: Quantum wavelet transforms generated by the product of the sine polynomial and the Gaussian envelope on the tetrahedral graph. Int. J. Image Graph. Sig. Process. (IJIGSP) 7, 11–24 (2018)

Model for a Direct Torque Control System of an Alternating Current Electric Drive for Urban Transport Rolling Stock Tasks Vasyl Stopkin1 , Mykola Tryputen2 , Anatoliy Nikolenko1 , Vitaliy Kuznetsov1(B) , and Maksym Tryputen3 1 Electric Engineering Department, National Metallurgical Academy of Ukraine, Gagarina

Avenue, 4, Dnipro, Ukraine [email protected] 2 Department of Automation and Instrumentation, Dnipro University of Technology, Avenue Dmytra Yavornytskoho, 19, Dnipro, Ukraine 3 Department of Calculating Mathematics and Mathematical Cybernetics, Oles Honchar Dnipro National University, 35, D. Yavornitsky Avenue, 4 Building of DNU , Dnipro, Ukraine

Abstract. A mathematical model has been developed in the paper of the direct torque control (DTC) system of an alternating current (AC) electric drive for the tasks of the urban electric transport rolling stock, as an alternative to the existing types of frequency control of an induction motor, taking into account its relevance, principles of operation and causes of occurrence. During the research on the mathematical model of direct torque control of an induction motor on the MATLAB platform, its main disadvantages have been revealed, which limit the scope of its application. The main task of the DTC system is to identify the stator flux linkage, which is solved by integration with a certain accumulation of errors. The source of accumulated errors is the inaccuracy when determining the stator active resistance and its change during the induction motor operation. The DTC system is characterized by the disadvantage of torque pulsation occurrence and rotor speed fluctuations at low loads. The main advantage of the DTC system has been determined – high static and dynamic speed accuracy. The results of mathematical modeling and the presented sequence of studies are of practical value in the development and adjustment of complete electric drives with a DTC control system for railway transport mechanisms. New is a technical solution that acts as an alternative to a complex vector control system - this is the use of the DTC system for the tasks of the rolling stock of urban transport. Keywords: Induction motor · Frequency converter · Voltage inverter · Direct torque control · Torque controller · Flux regulator · Observer

1 Introduction. Analysis of Literary Sources and Statement of the Problem For the first time, the method of an induction motor direct torque control (DTC) was patented by ABB (Asea Brown Boveri Ltd) Company. The implementation of the method © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 120–133, 2022. https://doi.org/10.1007/978-3-031-03877-8_11

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in industry became possible in the mid-1990s with the advent of high-precision and quick-operating microprocessor technology proposed by ABB Company. In 1995, ABB Company introduced the first ACS600 frequency converter with the new DTC system [1]. DTC systems are relevant for electric drives generating electromagnetic torque. Currently, direct torque control is a modern way to control a frequency-controlled inductionmotor drive with significant advantages – no need for feedback in speed and position of the motor [2]; quick operation of the system due to the optimal controllers of torque and flux linkage; high static and dynamic speed accuracy; stable functioning in the presence of data errors of the controlled object observed parameters [3]; optimal switching of transistors for each control cycle and compliance of the drive with the requirements of the controlled load; stability of functioning under various disturbances in the process of regulation of the controlled object coordinates [4]. The DTC system, in comparison with vector control systems, does not require in its structure cross-coupling compensation elements, coordinate transformation, separate controllers for each component of the stator current. But at present, for DTC systems, including for railway transport mechanisms, the algorithms for controlling the process of switching the inverter power modules, taking into account the mechanics of the electric drive, have not been sufficiently developed [5–8]. In order to reduce the electromagnetic torque pulsations of induction machine with direct control, there is an improved direct control with algorithms for predicting the changes in the electromagnetic torque and the value of the stator magnetic flux for each vector of the output voltage [9–12]. A comparative analysis of predictive algorithms to control the DTC systems with conventional DTC systems is presented in works [13, 14]. In works [15–20], a scheme to control the linearization of the speed feedback is proposed for the DTC system, in order to reduce the torque pulsations. There is a system of fuzzy torque control of an induction motor [21] using fuzzy controllers to generate the amplitude and angle of the reference voltage, which is used by the space vector modulator to generate the inverter switching state. In work [22], in order to optimally select the voltages in the DTC system, an induction motor model is used to predict the estimates of control variables. In work [23], a comparative analysis of three DTC systems is performed, using the MATLAB program: conventional DTC system with hysteresis controllers; direct control using space vector modulation with predictive controllers; simplified spatial vector modulation of direct torque control using the concept of an imaginary switching time. In work [24], a method is proposed for assessing the torque in the DTC system in each stator tooth, using the measured magnetic induction of the tooth. In work [25], the parameters of the PI speed controller in the DTC system are optimized using a genetic algorithm in accordance with speed fluctuations within the predicted and reference ones, which in turn improves the torque determination. For a traction electric drive of railway transport mechanisms, quick operation with highly dynamic control of the stator flux linkage and the induction motor torque is an important factor for developing the control systems with an induction electric drive. In traction electric drive, AC drives are widely used instead of the traditional commutator motor with series excitation [26–29].

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The use of the DTC system also enables energy efficient optimization of the flux linkage loop in order to reduce the stator current consumption by the criterion of its minimum. Until the end of the XX century, a direct current (DC) electric drive with a relaycontactor control system was used on the rolling stock of urban electric transport (tram, trolleybus, metro) on the territory of the USSR, and is still used in the cities of Ukraine. This drive has known disadvantages: the presence of a collector in DC motors, the need to maintain the collector-brush assembly unit, the need to protect against moisture ingress during operation; the use of starting-braking rheostats to control the speed, which leads to an increase in losses during this control, especially at low speeds; the necessity of using a large number of contact elements; the lag of the current protection systems did not allow limiting the currents in emergency modes. Since 2001, the Tatra-Yug Company in Ukraine has been producing tram-cars of the K-1 type with Ukrainian-made units based on an AC electric drive. The traction electric drive with AD931U2 induction motors has a converter based on modern powerful IGBT transistors, which provides separate control of the tram-cars. The reversing of the traction electric drive is ensured by means of power transistors at zero switching current. Such tram-cars are operated in Zaporizhia, Kryvyi Rih, Mariupol, Kyiv, Odessa, Mykolayiv. The traction motor power is 4x40 kW, and depends on the car modification. For example, all trams that operate in Odessa have a KPTT-2 transistor control system of traction electric drive manufactured in Zaporizhia, and traction electric drives are manufactured at JSC PLANT Electrotyazhmash (Kharkiv). In works [1–29], the options for using the DTC system for electric drives of rolling stock were not considered. As shown by the analytical review, direct torque control of an AC drive has proven itself quite well for various mechanisms. The task of developing a methodology for constructing a model for such a drive is a really urgent direction.

2 Basic Material of the Research This paper proposes a methodology for compiling a mathematical model of an electric drive with a direct torque control system for rolling stock. The model was developed using the building blocks of the Simulink and Simscape libraries in MATLAB 2016a. The mechanics of the electric drive was simulated using a simplified technique using MATLAB building blocks. In this paper, the direct torque control (DTC) system of an induction motor is modelled as an alternative universal control in contrast to the existing ones. A well-known method of control is a vector one, which ensures precise maintenance of the electromagnetic torque and stable operation of the electric drive over the entire speed range. The main types of vector control systems are sensor and sensorless systems. Moreover, the absence of a speed sensor increases the volume of calculations in the control system and leads to its complication. The DTC system may be an alternative type. The mathematical model of an induction motor direct torque control (DTC) system has been developed on typical MATLAB blocks.

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The parameters of the AD931U2 induction motor at a network frequency of 50 Hz are taken as the initial data: rated power is Pr = 54 kW; rated voltage Ur = 380 V; shaft torque Mn = 290 Nm; efficiency coefficient – 0.93; stator active resistance R1 = 19.23 m; total active rotor resistance R‘2 = 13.45 m, stator inductance L1 = 0.25 mH; rotor inductance L‘2 = 0.25 mH, motor torque of inertia Jdv = 2.3 kg · m2 . The DTC system is based on the vector control principles. The difference from the systems with field orientation is the absence of control loops of the stator current projections, which determine the electromagnetic torque and flux. The flux and torque control loops are internal. The idea of control is to determine at each step of calculating the optimal voltage inverter state, such that can cause a change in the torque and flux of the stator in the required direction in order to reduce to zero the error between the set and actual value of the regulated variable [26]. This is the case where a link of the pulse-width modulator becomes unnecessary. The state of the inverter switches does not change at every step – there is hysteresis control with the support of regulated variables within the specified limits. The state of the inverter changes when the threshold value of the error module for torque or flux is exceeded. The larger this margin, the lower the switching frequency of the valves and the worse the regulation quality. The principle of DTC control implementation is studied using the example of a fixed coordinate system. The correspondence of voltage sectors and vectors in a fixed coordinate system is shown in Fig. 1.

Fig. 1. Correspondence of voltage sectors and vectors in a fixed coordinate system

The electromagnetic torque of an induction motor is determined through the vector product of the stator and rotor flux linkages: Me =

p · Lm 3 · · ψs · ψr · sin γ , 2 Ls · Lr − L2m

(1)

where Ls – stator inductance; Lr – rotor inductance; γ – the angle between the vectors of the stator and rotor fluxes.

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The stator flux module is maintained at a constant level. The rotor flux module changes more slowly than the stator flux module due to the large rotor time constant. The torque control is performed by acting on the angle between the two vectors. The possibility of such control follows from the formula: dψs = Us − Is · Rs , dt

(2)

where Us – stator voltage; Is – stator current; Rs – stator active resistance. Formula (2) is simplified by neglecting the voltage drop in the stator winding of the motor. This is permissible, since only the direction of vector ψs change is considered, which has the same direction as the stator voltage vector Us . The optimal vector is selected in the following way. The plane is divided into six equal sectors (Fig. 1). One of them is studied. If the stator vector is in Sector 1 and it is necessary to increase the torque, then one of the advance vectors U2 or U3 should be used. These two vectors will increase the angle γ and, as a consequence, the torque will increase. The first vector is used when the stator flux module increases, and the second vector is used when it decreases. To reduce the torque, one of the zero vectors U0 or U7 is used. A zero voltage vector causes the stator flux vector to stop. In this case, the rotor flux continues to rotate, catching up with the stator flux, which leads to a decrease in torque. At low motor rotational frequency, the rotor flux moves slowly, and in this case it is not possible to quickly reduce the torque using the zero voltage vector. In such cases, a lagging voltage vector U5 or U6 is used. Table 1 shows the algorithm for selecting the voltage vector. Table 1. Algorithm for selecting the voltage vector Sector number in which 1 the stator flux vector is located

2

3

4

5

6

>ψs M

2

3

4

5

6

1

M

3

4

5

6

1

2

DumpInfo and upload the code. This code will be available in the Arduino IDE (after installing the RFID library). Then, open the serial monitor. We should see something like the Fig. 5:

Fig. 5. Serial monitor

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Approximate the RFID card or the keychain to the reader. Let the reader and the tag closer until all the information is displayed (Fig. 6).

Fig. 6. Information from RFID reader

We have 1024 bytes of data storage divided into 16 sectors and each sector is protected by two different keys, A and B. Write down your UID card because we’ll need it later. Upload the Arduino code that has been suffixed here. Sketch for Arduino shown below:

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#include #include #define SS_PIN 10 #define RST_PIN 9 MFRC522 mfrc522(SS_PIN, RST_PIN); // Create MFRC522 instance. void setup() { Serial.begin(9600); // Initiate a serial communication SPI.begin(); // Initiate SPI bus mfrc522.PCD_Init(); // Initiate MFRC522 Serial.println("Approximate your card to the reader..."); Serial.println(); } void loop() { // Look for new cards if ( ! mfrc522.PICC_IsNewCardPresent()) { return; } // Select one of the cards if ( ! mfrc522.PICC_ReadCardSerial()) { return; } //Show UID on serial monitor Serial.print("UID tag :"); String content= ""; byte letter; for (byte i = 0; i < mfrc522.uid.size; i++) { Serial.print(mfrc522.uid.uidByte[i] < 0x10 ? " 0" : " "); Serial.print(mfrc522.uid.uidByte[i], HEX); content.concat(String(mfrc522.uid.uidByte[i] < 0x10 ? " 0" : " ")); content.concat(String(mfrc522.uid.uidByte[i], HEX)); } Serial.println(); Serial.print("Message : "); content.toUpperCase(); if (content.substring(1) == "BD 31 15 2B") //change here the UID of the card/cards that you want to give access {

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Serial.println("Authorized access"); Serial.println(); delay(3000);

else { Serial.println(" Access denied"); delay(3000); }

In the piece of code above you need to change the if (content.substring(1) = = “REPLACE WITH YOUR UID”) and type the UID card we’ve written previously.

4 Conclusion The simple RFID reader for security system that can be used for individual or different commercial security as example personal data, based on the RFID-RC522 module and Arduino Uno. The Arduino was connected to a computer through the USB port and programmed using a language similar to C++. Programming code (sketch) was uploaded into Arduino using program software ArduinoIDE. Connection scheme is also presented. All theoretical, programming and practical details of the simple RFID security access system can be used for education of the students that studying in cybersecurity specialty.

References 1. Farooq, U., ul Hasan, M., Amar, M., et al.: RFID based security and access control system. IACSIT Int. J. Eng. Technol. 6(4), 309–314 (2014) 2. Weinstein, R.: RFID: A technical overview and its application to the enterprise. IT Profess. 7(3), 27–33 (2005) 3. Adole, P., Mom, J.M., Igwue, G.A.: RFID based security access control system with GSM technology. Am. J. Eng. Res. 5(7), 236–242 (2016) 4. Kulkarni, A.M., Tawaresachin, S.: Embedded security system using RFID and GSM. Int. J. Comput. Technol. Electron. Eng. 2(1), 164–168 (2013) 5. Rusyn, V., Subbotin, S., Sambas, A.: Analysis and experimental realization of the logistic map using Arduino Pro Mini. CEUR Workshop Proc. 2608, 300–310 (2020) 6. Rusyn, V., Subbotin, S., Sambas, A.: Simple autonomous security system based on Arduino UNO platform and fingerprint scanner module: a study case. CEUR Workshop Proc. 2864, 262–271 (2021) 7. Santhosh, S., Sanihosh, K.K.: campus access control system RFID based. Int. J. Electron. Comput. Sci. Eng. 1(3), 1439–1445 (2013) 8. Ambati, P., Singamsetti, M.: A new approach for RFID tag data reading in FPGA by using UART and FIFO. Int. J. Eng. Manuf. (IJEM) 8(2), 33–44 (2018) 9. Chikouche, N., Cherif, F., Cayrel, P.-L., Benmohammed, M.: A secure code-based authentication scheme for RFID systems. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 7(9), 1–9 (2015)

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10. Dhal, S., Gupta, I.S.: Object authentication using RFID technology: a multi-tag approach. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 7(4), 44–53 (2015) 11. Dhal, S., Gupta, I.S.: Managing authentication and detection probability in multi-tag RFID system. J. Inf. Assur. Secur. 9(6), 316–328 (2014) 12. Kumar, V.K.N., Srinivasan, B.: Design and development of biometrics secure person detection system for E-passport using cryptographic security protocols. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 5(12), 80–90 (2013) 13. Rizomiliotis, P., Rekleitis, E., Gritzalis, S.: Security analysis of the song-mitchell authentication protocol for low-cost RFID tags. Commun. Lett. 13(4), 274–276 (2009) 14. Rajeshwari, G., Daniel, V.D.M.J.: FPGA realization of RFID tag data reading enhancement mechanism by using parallel processing. Middle-East J. Sci. Res. 24(4), 1330–1334 (2016) 15. Kumar, V.N., Srinivasan, B.: Biometric passport validation scheme using radio frequency identification. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 5(4), 30–39 (2013)

Investigation of the Bifurcation Properties of the Dynamics of a Biological Population Based on a Logistic Model Victor Busher1 , Oleksii Chornyi2 , Oleksandr Kuzenkov3 , Mykola Tryputen4 , Vitaliy Kuznetsov5(B) , and Vladislav Rumiantsev6 1 National University “Odessa Maritime Academy”, Odessa 65029, Ukraine 2 Kremenchuk Mykhailo Ostrohradskyi National University, Kremenchuk, Ukraine 3 Oles Honchar Dnipro National University, Dnipro 49000, Ukraine 4 Dnipro University of Technology, av. Dmytra Yavornytskoho 19, Dnipro, Ukraine 5 National Metallurgical Academy of Ukraine, Dnipro 49000, Ukraine

[email protected] 6 Zaporizhzhia National University, Zaporizhia 69600, Ukraine

Abstract. The paper substantiates the structure of the model that describes the dynamics of subpopulations in the general ecological niche. Based on the theory of bifurcations, the results of experimental studies of the effect of excess electromagnetic radiation of worn out or repaired electromechanical equipment on biological objects are analyzed. Analysis of phenotypic changes in the biological test object of Drosophila melanogaster, identified over three generations, based on the bifurcation model, made it possible to identify trends in long-term forecasts, which are in good agreement with the known results of population development in unfavorable conditions. Keywords: Logistic model · Subpopulation · Theory of bifurcation · Electromagnetic field · Biological test-object · Teratogen · Anthropogenic factor · Phenotype

1 Introduction Anthropogenic pressure leads not only to a global deterioration of the ecology of the environment, but also to an increase in the number of pathologies of biological objects (a decrease in the level of immunity, a deterioration in reproductive function, etc.). Under conditions of instability of environmental factors, mosaic nature of species ranges, the genetic heterogeneity of species and separate populations increases significantly. The specificity of such a situation must be taken into account during planning nature conservation measures, conducting environmental monitoring, and solving problems of predicting the future state of populations. It is extremely important to study the level of genetic heterogeneity of the human population. The accumulation of pathological recessive genes can be latent for a long time, and from a certain moment it can reveal in the form of a rapid increase in the incidence of certain hereditary diseases. The © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 203–212, 2022. https://doi.org/10.1007/978-3-031-03877-8_18

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use of mathematical models, computer simulation of the dynamics of these or other factors make it possible to identify general trends efficiently, with minimal expenditure of time and material resources [1]. The same applies to the dynamics of heterogeneous populations, where computer simulation allows predicting the state of the system and the possible consequences of artificial intervention in the process, predicting the spread of genetic abnormalities.

2 Mathematical Model of Subpopulations Dynamics with a Logistic Function as a Basic One The study is based on the idea of the population as a set of individuals, which can be divided into n subpopulations, which are genetically more or less homogeneous, but differ significantly [2]. They are not reproductively isolated, and there is a certain probability that the offspring of the individual from the i-th subpopulation to the j-th subpopulation. The differential model of the system can be written in general as follows:  dxj Aji fi (x) , j = 1, n , = dt n

(1)

i=1

N

j where xj = Nmax – the relative number of the j-th subpopulation Nj to the maximum possible ecological capacity of the environment Nmax ; fi (x) – a function that describes the total reproductive capacity of the i-th subpopulation; of descendants of the i-th subpopulation that falls to the j-th. Aji – the proportion  Aji = 1 for any i. The function fi (x) corresponds to the well-known Assume that

j

logistical law:  fi (x) = ai xi 1 −

n 

 xl ,

(2)

l=1

where ai – reflects the reproductive capabilities of the i-th subpopulation. According to (1), (2) the increase of a subpopulation approaches zero in the case when its number approaches zero or when the total number of all subpopulations approaches the maximum possible ecological capacity of the environment Nmax . System (1), (2) is not Voltairean in the sense that its trajectories can intersect the coordinate axes and, for example, the local behavior of the system near the origin is determined by its properties not only in the first quarter [3]. To study the equilibrium points of system (1), (2) we use the standard Lyapunov analysis. It is easy to see that one of the equilibrium points is the zero point (origin). In addition, there are an infinite number of equilibrium points that lie on the plane:  xi = 1. (3) i

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The location of equilibrium points is quite natural from an ecological point of view. Of course, in the complete absence of individuals of this species, they can not arise from nothing. If subpopulations occupy the same ecological niche and do not differ in the resources they consume, their arbitrary distribution by number in this niche is equilibrium. In the case of n = 1, system (1) is transformed into equation: dx1 = a1 x1 (1 − x1 ), dt the solution of which, depending on the coefficient of reproduction, is displayed by the classical bifurcation diagram (Fig. 1, a). In the case n = 2, system (1) can be represented as follows: ⎧ dx 1 ⎪ = (λ1 a1 x1 + (1 − λ2 )a2 x2 )(1 − (x1 + x2 )) ⎨ dt (4) ⎪ ⎩ dx2 = (λ a x + (1 − λ )a x )(1 − (x + x )). 2 2 2 1 1 1 1 2 dt For system (4), a parameter λi = Aii is introduced that reflects part of the increase in the subpopulation with an index i that belongs to the parent by its phenotypic properties. n ___  Aij , j = 1, n. According to the condition of closed system parameters λi = 1 − i=1,i=j

Further analysis is based on two theorems proved by one of the authors of this article in [4] by analyzing the Jacobi matrix in a neighborhood of points of the fixed line x1 + x2 = 1 of system (4). These theorems prove that systems (1), (2) are degenerate in a neighborhood of singular points of the stationary hyperplane (3). Besides, the degenerate stationary line x1 + x2 = 1 of system (4) consists of points of attracting beam (attractor) of general form x1 (a2 − a1 ) − a2 < 0 and points of repulsive beam (repeller) of general 0. The point connecting the attractor and repeller beam has form x1 (a2 −

a1 ) − a2 >  a2 a1 coordinates a2 −a1 , a1 −a2 , and the characteristic equation of the Jacobi matrix at this point has zero multiplicity root 2. Subpopulations may differ in reproduction coefficients ai , initial number and transition coefficients λi (part of the growth of the subpopulation, which according to its phenotypic characteristics belongs to the “parent”). A sample of the phase portrait in the two-dimensional case is shown in Fig. 1, b. For environmental reasons, we are only interested in the first quarter, where subpopulations are positive. In Fig. 1, b the origin is an unstable node, all points of the line are attractive. This behavior is characteristic to the system under normal conditions, when two subpopulations, developing, complement each other with a certain part of their offspring and thus increase the system-wide biomass of the population. When the total number of individuals reaches the maximum allowable limit Nmax , the growth of subpopulations stops in the sense that the number of newborns is equal to the number of deaths. This case is realistic from a practical point of view, because if the first subpopulation has a zero coefficient of reproductive potential, its individuals appear only due to the growth of the second subpopulation. In this case, the part of individuals of the subpopulation

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a)

b) Fig. 1. Phase portraits of system n = 1–(a); n = 2, a1 = 0.1, a2 = 0.3, λ1 = λ2 = 0.95–(b)

x2 , whose phenotypic properties belong to the parent, is equal λ2 , and part of the offspring belonging to x1 , respectively (1 − λ2 ). It is obvious that in this case the ratio of the number of two subpopulations will be constant, i.e. the phase trajectories will be straight lines [5]. Based on the mathematical properties of bifurcation systems, it can be concluded that the system-wide dynamics of subpopulation processes depends not only on the reproductive potential of subpopulations, but also on the intrasystem dynamics that objectively occur in such systems. One of the determinants in the system of interaction of several subpopulations is the parameter that determines the mass fraction of individuals that exchange the presented subpopulations.

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3 Experimental Research and Applied Use of the Developed Model Electrical appliances, especially electrical machines, are the source of various types of anthropogenic radiation. These are acoustic noise, vibrations [6], electromagnetic radiation. Let us consider an example based on the results of experimental studies of the effect of the magnetic field of the industrial frequency of electromechanical energy converters on biological objects for which the magnetic field is a teratogen (mutagen). The statement of the problem is based on the fact that the environment around us has always been under the influence of magnetic and electromagnetic fields (MF and EMF) [7–9]. These fields are background radiation because they are naturally occurring. However, with the development of science and technology, background radiation has increased significantly, the intensity of anthropogenic electromagnetic fields significantly exceeds the natural background, that makes them a dangerous environmental factor. In 1995, the World Health Organization coined the term “global electromagnetic pollution of the environment”. Currently, the maximum permissible level (MPL) standards for assessing the impact of EMF on biogeocenoses (ecosystems) as a whole have not been developed in any country. There are scattered data from individual studies of the impact of EMF on some components of ecosystems in the literature. The most developed and implemented in many states are the standards for the remote control of electromagnetic radiation (EMR) for humans. EMR levels of industrial frequency are most fully taken into account now only in the design of electrical facilities associated with safe for the environment and personnel transmission, transportation of electrical energy [10, 11]. Standards for high frequency EMR are also being developed [12]. Accordingly, measures to compensate for excess EMR are being developed [13]. However, the EMR values do not exceed the limit only for electric motors, the parameters and characteristics of which correspond to the passport ones. Meanwhile, the majority of the electric motors fleet consists of engines that have been in operation for a long time, have gone through various stages of repair with various deviations in design or parameters. Any acquired deviations make the electric motors an essentially nonlinear system and lead to the appearance of non-sinusoidal currents. Complex energy exchange processes, which lead to the appearance of external electromagnetic fields with a complex spatial structure are formed. In most cases of assessing the magnitude of electromagnetic pollution as a whole, the authors use simplified mathematical models [14], which make it possible to approximately calculate the field strength on the surface of an object and at a certain distance from it. Of course, the impact of such fields on biological systems becomes different [15]. However, the actual effect of the field on biological systems can only be estimated experimentally. For this purpose, measurements of the magnetic field induction were taken for two new identical induction motors (IM), in one of which a parametric asymmetry was artificially created. The power supply of the IM with a power of 0.4 kW was implemented from a three-phase source of 380 V. The results were recorded directly on the motor housing and at a distance of up to 0.5 m every 0.1 m using an electromagnetic field tester TES1394 with the following parameters: measurement range 2… 200 μT; operating frequency of measurement 30… 300 Hz; error ± 3% in the range 50… 60 Hz [16].

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Researches of the phenotypic changes in the biological test object Drosophila Melanogaster Meigen caused by a magnetic field were conducted by placing test tubes with the population of the object in the field of induction motors with acquired parametric asymmetry and physical deterioration. The results were compared with a control group, which was exposed to the magnetic field of serviceable symmetrical motors. The use of fruit flies is due not only to a convenient life cycle for the experiment, but also to the adequate reactivity of these insects to EMF. In our opinion, the extension of the postulates of Hans Selye’s theory of stress to the results of original research makes it possible to extrapolate them in relation to human health and psychoemotional sphere. Both groups were constantly exposed to EMF during their development (growth and reproduction) for three generations (30 days), which is considered sufficient for assessing population dynamics [17, 18]. At the same time, all phenotypic changes caused mainly by teratogenic mutations in each of the observed generations of the test object were recorded, and healthy (normal) and mutated (defective) flies were counted in each generation. After the appearance of the larvae, the old insects moved out to avoid interbreeding between generations, and after the individuals grew up, we inspected them, but the individuals of the same generation continued to coexist in the same environment. Thus, we obtained a generation that was born, raised and gave the next generation under the influence of EMF. According to the results of an external inspection of the first generation, in addition Table 1. The ratio of phenotypic forms of hybrids of three generations Asymmetric induction motor Phenotypic groups

Photo

Symmetrical induction motor

F1

F2

F3

F1

F2

F3

%

%

%

%

%

%

3

4

5

6

7

8

wingless

3.8

3.3

–

–

0.8

–

reduced wings

7.1

6.6

–

1.4

–

–

deformed abdomen

7.8

8.1

–

2.1

4.7

–

disproportionate body parts

6.9

21.2

41.1

28.2

29.4

36

Total:

25.6

39.2

41.1

31.7

34.9

36.0

no anomalies

74.4

60.8

58.9

68.3

65.1

64.0

100 1937

100 3899

100 6240

100 3845

100 7740

100 12386

1

Total:

2

% amount

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to individuals without anomalies, four phenotypic forms of teratologies were recorded, apparently caused by certain mutations: 1) wingless; 2) with reduced (underdeveloped) wings; 3) with a deformed abdomen; 4) with disproportionate body parts. The results of the studied and control populations are shown in Table 1. Based on the data obtained, it was determined that 74.4% first generation flies F1 are healthy, and 25.6% have developmental disabilities, which corresponds to the second law of Gregor Mendel. As a result of studies of second generation flies F2 , it was found that a large percentage of insects have disproportionate body parts. Few wingless forms and insects with reduced wings, and individuals with a deformed abdomen, were found. In addition, in comparison with the control group of fruit flies, which were not affected by external factors in the process of their development and reproduction, a noticeably smaller number of offspring was obtained. The main feature of the third generation flies F3 is that wingless individuals, individuals with reduced wings and a deformed abdomen have not been identified. Healthy flies prevailed, as well as individuals with disproportionate body parts. Based on the data obtained, it is possible to analyze the development of subpopulations. Then the bifurcation equation is reduced to the following form: xi = axi−1 (1 − xi−1 ),

(5)

where a – the bifurcation coefficient; xi−1 , xi – the relative population size of the previous and current generations. This equation can be rewritten as:

Ni−1 Ni Ni−1 1− , (6) =a Nmax Nmax Nmax where Ni−1 , Ni – the population size of the previous and current generations, Nmax – the maximum possible population size. Based on the data obtained on the development of populations over three generations, a system of equations was compiled, which allows determining the parameters of the bifurcation Eq. (7):

⎧ N1 N2 N1 ⎪ ⎪ 1− =a ⎨ Nmax Nmax Nmax

(7) ⎪ N2 N N ⎪ ⎩ 3 =a 2 1− , Nmax Nmax Nmax Dividing the 1st equation by the 2nd, we get the ones Nmax of interest to us for each group: Nmax =

N21 N3 − N32 N1 N3 − N22

.

(8)

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Based on the obtained values of population capacity, it is possible to compose a system of algebraic equations, now counting healthy and defective individuals of subpopulations:  x1i = (λ1 a1 x1i−1 + a2 x2i−1 − λ2 a2 x2i−1 )(1 − x1i−1 − x2i−1 ) x2i = (λ2 a2 x2i−1 + a1 x1i−1 − λ1 a1 x1i−1 )(1 − x1i−1 − x2i−1 ). Based on data on three generations for two pairs of subpopulations, we obtain 4 equations each with four unknown parameters a1 , a2 , λ1 , λ2 , that makes it possible to find an exact solution: a1 = 2.686, a2 = 0.870, λ1 = 0.634, λ2 = 0.626 for a population under conditions of increased EMF, a1 = 2.484, a2 = 2.269, λ1 = 0.757, λ2 = 0.598 for a control population and predict their development (Fig. 2).

Fig. 2. Forecast of the development of subpopulations of healthy and defective individuals under normal conditions (Nnormal, Ndefect) and under the effect of excessive EMF (Nnormal_emf , Ndefect_emf )

4 Discussion and Conclusions Differences in the bifurcation coefficients reflect significant differences in the development of populations. First, it can be seen that the control population develops faster, reaching the established number 2…3 generations earlier. In addition, in the control population, the relative number of defective individuals is less (58%) than in the population exposed to EMF (71%). Although the experiments ended in the third generation, the variety of types and significant fluctuations in the number of defective individuals of different phenotypes are signs of genetic disorders in the future. In addition, a seemingly strange feature should be noted: in a population under unfavorable conditions, there are fewer defective individuals than in the control group. The reason is that in the control population, even defective individuals are capable of producing offspring. Many defective individuals in the studied population turn out to be unviable.

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Thus, a study of the bifurcation properties of subpopulation dynamics was conducted, which are necessary for obtaining and evaluating the results of modeling. Mathematical bifurcation properties of the considered systems have a clear applied biological interpretation. An example of searching for the parameters of a bifurcation model with two subpopulations based on the results of population development over three generations is given. By the bifurcation analysis, we assessed the effect of worn out or undergoing repair electromechanical equipment on biological objects. The maps of the electromagnetic field obtained as a result of measurements around damaged induction motors have a pronounced unevenness, which, on the one hand, carries information about the technical condition of the engine, and on the other hand, it cannot but have a local effect on biological objects. This is confirmed by experimentally proven phenotypic changes caused by excess electromagnetic radiation, which is a teratogen (mutagen) for the biological test object Drosophila melanogaster. And the bifurcation model of population development made it possible to identify trends in long-term forecasts, which are in good agreement with the known results of population development in unfavorable conditions.

References 1. Holmes, J., Hassini, S.: Discrete-time Markov chain modelling of the ontario air quality health index. Water Air Soil Pollut. 232(4), 1–13 (2021). https://doi.org/10.1007/s11270-021-050 96-1 2. Kuzenkov, O., Serdiuk, T., Kuznetsova, A., Tryputen, M., Kuznetsov, V., Kuznetsova, Y.: Mathematical model of dynamics of homomorphic objects. CEUR Workshop Proc. 2516, 190–205 (2019) 3. Kiseleva, E., Hart, L., Prytomanova, O., Kuzenkov, O.: An algorithm to construct generalized voronoi diagrams with fuzzy parameters based on the theory of optimal partitioning and neuro-fuzzy technologies. CEUR Workshop Proc. 2386, 148–162 (2019) 4. Chernyshenko, S.V., Kuzenkov, O.O.: Bifurcation effects in a degenerate differential model of subpopulation dynamics. In: Proceedings - 8th EUROSIM Congress on Modelling and Simulation, EUROSIM 2013, pp. 108–111 (2015). https://doi.org/10.1109/EUROSIM.201 3.29 5. Chernyshenko, S.V., Kuzenkov, O.O.: Bifurcation effects in degenerate differential models of subpopulation dynamics. In: Proceedings - 27th European Conference on Modelling and Simulation, ECMS 2013, pp. 130–135 (2013). https://doi.org/10.7148/2013-0130 6. Ya˘gcilar, Ç., Yardimci, M.: Effects of 432 Hz and 440 Hz sound frequencies on the heart rate, egg number, and survival parameters in water flea (Daphnia magna). J. Ecol. Eng. 22(4), 119–125. https://doi.org/10.12911/22998993/134038 7. Kayode, A., Ayodeji, A., Oluseye, O., Theophilus, E.: Alternative device for non-ionizing radiation detection. Int. J. Eng. Manuf. (IJEM) 9(5), 23–33 (2019). https://doi.org/10.5815/ ijem.2019.05.02 8. Osaci, M.: Numerical simulation methods of electromagnetic field in higher education: didactic application with graphical interface for FDTD method. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 10(8), 1 (2018). https://doi.org/10.5815/ijmecs.2018.08.01 9. Mashud, M.A.A., Hossain, M.S., Islam, M.N., Islam, M.S.: Design and development of PC based data acquisition system for radiation measurement. Int. J. Image, Graph. Sign. Process. (IJIGSP) 5(7) 34–40 (2013). https://doi.org/10.5815/ijigsp.2013.07.05

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10. CEU: Commission of the European Communities, amended proposal for a council directive on minimum requirements for the protection of workers from harmful physical agents. Off. J. EC 37, 115 (1994) 11. The hygienic standard GN 2.1.8/2.2.4.2262–07. Maximum allowable levels of magnetic fields with a frequency of 50 Hz for residential and public premises and habitable territories. (in Russian) 12. Lin, J.C.: A new IEEE standard for safety levels with respect to human exposure to radiofrequency radiation – IEEE Antennas and Propagation Magazine – ieeexplore.ieee.org (2006) 13. Kuznetsov, B.I., Nikitina, T.B., Bovdui, I.V.: Active shielding of magnetic field of overhead power line with phase conductors of triangle arrangement”. Tekhnichna elektrodynamika. Institute of Electrodynamics National Academy of Science of Ukraine, No 4 (July/August), pp. 25–28 (2020). https://doi.org/10.15407/techned2020.04.025 14. Zagirnyak, M., Nykyforov, V., Sakun, O., Chorna, O.: The industrial electrical equipment screened magnetic fields effect on model organisms. In: Proceedings of the International Conference on Modern Electrical and Energy Systems, MEES 2017, 2018-January, pp. 380– 383 (2017). https://doi.org/10.1109/MEES.2017.8248938 15. Vanderstraeten, J.: Health effects of extremely low-frequency magnetic fields: reconsidering the melatonin hypothesis in the light of current data on magnetoreception. In: Vanderstraeten, J., Verschaeve, L., Burda, H., Bouland, C., Brouwe, C. (eds.) J. Appl. Toxicol. 32(12), 952–958 (2012) 16. Zagirnyak, M., Chornyi, O., Nykyforov, V., Sakun, O., Panchenko, K.: Experimental research of electromechanical and biological systems compatibility. Przeglad Elektrotechniczny 92(1), 128–131 (2016). https://doi.org/10.15199/48.2016.01.31 17. Godlewska, A., Becher, M.: The effect of waste materials on the content of some macroelements in test plants. J. Ecol. Eng. 2021 22(4), 167–174 (2021). https://doi.org/10.12911/229 98993/134046 18. Kuzenkov, O., Kuznetsov, V., Tryputen, N.: Analysis of phase trajectories of the third Order dynamic objects. In: 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering, UKRCON 2019 - Proceedings, pp. 1235–1243 (2019). https://doi.org/10.1109/ UKRCON.2019.8879819

The Applying of Second Order Frequency-Dependent Components in Signal Processing of Autonomous Mobile Robotic Platforms Ivan Afanasyev(B) , Valery Sytnikov, Oleg Streltsov, Pavel Stupen, and Volodymyr Kudria Odesa National Polytechnic University, Odesa, Ukraine [email protected], [email protected]

Abstract. The paper presents the use of rebuildable frequency-dependent components usage in cognitive computing systems using digital filters as an example. They can be included in data processing paths and adaptive blocks of cognitive computing system. The models for these components are presented. Based on models the equations system for transfer function coefficients calculation are represented with an approach for reducing computational costs are presented. Moreover, the cascade connection issues are considered for resolving increasing a same type component order and reduce costs for rebuilding and processing data. These approaches give it opportunity to increase efficiency of cognitive computing system. Keywords: Cognitive computing · Adaptivity · Frequency dependent components · Adaptive filter · Digital filters

1 Introduction The automatic mobile robotic systems modern development in general defined by Industry 4.0 conception. The requirements for computer system components and for their software mean the need to modernize already known components, to create new. They are responsible for mobility criteria, flexibility, adaptivity and fitting in to their operation conditions [1]. Collecting, processing, decision making based on incoming information handled by specialize computer systems that contains adaptive elements. The role of staff in these cases reduced to platform monitoring. The staff intervention is necessary in emergency and critical situations [2, 3]. These tasks are encountered through using variable mobile platforms and specialized computer systems, also in systems for resolving critical situations [4–8]. The artificial intelligence usage and attached training directions of technical systems are the main direction in automatic mobile systems development. The one of direction in artificial intelligence is a development of cognitive computer systems [9]. The direction © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 213–226, 2022. https://doi.org/10.1007/978-3-031-03877-8_19

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based on cognitive computing which centered on technical artificial intelligence and signal processing. These systems usually represent human brain simulation which realizes cognition, that is the possibility to relate events in time, and also to build interactive spacetime models [10]. The technical realization approach requires a development specialized algorithms, software and hardware based on neurophysiological models. The opportunities created on models could be used efficiently for cognitive components development and structures based on this. They are capable to realize behavior processes that implement human behavior. The cognitive systems are perfectly applicable in big data analysis, speech recognition, sentiment analysis, risk assessment, fraud detection. All these themes are united by having uncertainty and uncontrollability the situations that could happens. Being in certain circumstances, the specialized cognitive computer system should have context defining skills in special domain, obtaining new experience, adapting to changing operation conditions. Based on allocated skills they could be decomposed on domains which should have according names. Domain that is responsible for adaptation should react on incoming information in system through change parameters of system yourself [10– 12]. The uncertain behavior requires using stochastic models and using fuzzy values [13]. The implementations which works with stochastic models are realized usually in a swarm [14]. During the cognitive system adaptive module realization, the opportunity of realization using adaptive signal processing is appears. It also important in situations when the frequency-dependent components are used. The adaptation happens by transfer function coefficients adjustment by incoming criteria which allows to stand out a useful signal, digitalize him and handle some operation using him [13]. Much stricter requirements for signal stand outing lead to using the more higher order components. The system components similar to these are hard to manage. They require much more resources through realization and they are complex through development process. The low order frequency-dependent components are a best solution for resolving these tasks. Considering the functionality conditions of autonomous mobile systems and their restrictions in power supply and computing resources, this solution is efficient. Indeed, the rebuilding does not require a lot of resources, it could be handled with limited computing resources. Based on this, the opportunity for building a flexible system is appears. Each component could be configured by necessary conditions or the full system could be rebuilt. The article contains the using of low order frequency-dependent components through handling sensors signals in autonomous mobile robotic platforms. Should be notices, the frequency-dependent components could be divided on filters and typical components of automatic control systems [15, 16].

2 The Low Order Frequency-Dependent Components Definition The source analysis for development and reconstruction of frequency-dependent components [4–6, 15, 17–19] showed a ways, algorithms and procedures of direct rebuilding

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methods with partial transformation are complex for use in real-time systems. For implementation considered methods needs a large number of operations and computational costs which complicates their applying. The using of low order frequency-dependent components in autonomous mobile robotic platforms is reviewed in second order digital filters example. For the second order filter could be attributed low pass filters (LF) and high pass filters (HF) Butterworth, Chebyshev I, Chebyshev II, Cauer (Elliptic). However, the transfer function for each type have unique features. The transfer functions for second order filters have following form: H2 (z) =

a0 + a1 z −1 + a2 z −2 . 1 + b1 z −1 + b2 z −2

(1)

where, a0 , a1 , a2 , b1 , b2 – real coefficients for numerator and denominator. Through research process of second order transfer functions have been detected that two numerator coefficients are equal [18]. a0 = a2 ,

(2)

using (2), the transfer function (1) can have following form: H (z) = where, a =

a1 −1 + z −2 a0 z a0 1 + b1 z −1 + b2 z −1

1+

= a0

1 + az −1 + z −2 , 1 + b1 z −1 + b2 z −2

(3)

a1 a0 .

3 The Low Order Frequency-Dependent Components Models Based on components definition and phase response analysis of LF and HF a math model can be built. Using them, the possibility for second order digital filter building is appears and, if it necessary, reconstruct a component. The future models will have common features in frequency and phase responses independency from cut frequency but at the same time they will have dependency from ripple level on those models where it is present. Based on models, the opportunity for every filter types coefficients definition is appears. Based on obtained coefficient models it is easy to develop modules that allow represent filter as component. The component will be able to rebuilding. The components will have pool of input parameters and will process output digital filter characteristics. These abstractions can be structured in certain cascades of same type components. 3.1 The Second Order LF and HF Butterworth Filter The Butterworth filter has the one of simplest model for filter design, but has monotone and low frequency discrimination in transition band between bandwidth and stopband.

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This is a reason to say that a usage sometime is not efficient [14]. After mapping from (3), a math model for second order LF of Butterworth will have following form: ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

a1 = 2a0 , a2 = a0 ,

16a02 = 1, (1−b2 1 +2)(b1 +2b2 ) 2 4a0 (1+cos(ωc )) (1−b2 )2 +(b1 +2 cos(ωc ))(b1 +2b2 cos(ωc ))

(4)

)2 +(b

=

c2 ,

b1 = −(1 + b2 ) cos(ωc ).

where, ωc – cut frequency, c – cut frequency definition level The HF Butterworth model has following form: ⎧ a1 = −2a0 , ⎪ ⎪ ⎪ ⎪ ⎪ a2 = a0 , ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 16a02 ⎨ = 1, (1 − b2 )2 + (b1 − 2)(b1 − 2b2 ) ⎪ ⎪ ⎪ ⎪ 4a0 (1 − cos(ωc ))2 ⎪ ⎪ = c2 , ⎪ 2 ⎪ ⎪ + + 2 cos(ω + 2b cos(ω − b (b (1 ) ))(b )) 2 1 c 1 2 c ⎪ ⎪ ⎩ b1 = −(1 + b2 ) cos(ωc ).

(5)

3.2 The Second Order LF and HF Chebyshev I Filter For more efficient frequency suppression through low order filter usage, usually a Chebyshev filter is used. This type helps to provide necessary characteristics for phase response, namely much more rapid frequency discrimination in transition band. However, for this type, an additional parameter is introduced – ripple level. Because of this, the characteristic becomes uneven in bandwidth or stopband [18]. Chebyshev type I has ripple level influence for bandwidth. Math model for second order LF has following form: ⎧ a1 = 2a0 , ⎪ ⎪ ⎪ ⎪ ⎪ a2 = a0 , ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 16a02 ⎪ ⎪ = 1, ⎨ (1 − b2 )2 + (b1 + 2)(b1 + 2b2 ) (6) ⎪ 2 ⎪ 4a + cos(ω (1 )) 0 c ⎪ 2 ⎪ = cp , ⎪ ⎪ ⎪ (1 − b2 )2 + (b1 + 2 cos(ωc ))(b1 + 2b2 cos(ωc )) ⎪ ⎪ ⎪ ⎪ (b2 − 1) sin(ωc ) ⎪ ⎪ = tgθ (cp). ⎩ (b2 + 1) cos(ωc ) + b1 where, cp– ripple level in bandpass, tgθ (cp) – phase response

The Applying of Second Order Frequency-Dependent Components

Analogically, math model for HF: ⎧ a1 = −2a0 , ⎪ ⎪ ⎪ ⎪ ⎪ a2 = a0 , ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 16a02 ⎪ ⎪ = 1, ⎨ (1 − b2 )2 + (b1 − 2)(b1 − 2b2 ) ⎪ ⎪ 4a0 (1 − cos(ωc ))2 ⎪ ⎪ = cp2 , ⎪ ⎪ 2 ⎪ + + 2 cos(ω + 2b cos(ω − b (b (1 ) ))(b )) 2 1 c 1 2 c ⎪ ⎪ ⎪ ⎪ − 1) sin(ω (b ) ⎪ 2 c ⎪ = tgθ (cp). ⎩ (b2 + 1) cos(ωc ) + b1

217

(7)

3.3 The Second Order LF and HF Chebyshev II Filter The Chebyshev type II is used less often than Chebyshev type I. The reason is less frequency discrimination of frequency response. The difference between first type and second is that a last does not have ripple level in bandwidth. The ripple level passes to stopband. Like for a first type, a second type is processed using a same rule [18]. Math model for second order LF will has following form: ⎧ a2 = a0 , ⎪ ⎪ ⎪ ⎪ ⎪ (a1 + 2a0 )2 ⎪ ⎪ ⎪ = 1, ⎪ ⎪ (b1 + (1 + b2 ))2 ⎪ ⎪ ⎪ ⎪ ⎪ (a1 + 2a0 cos(ωc ))2 ⎨ = cs2 , 2 2 + 2b (1 + b ) cos(ω ) + 4b cos2 (ω ) (8) + b − b (1 ) 2 1 2 c 2 c 1 ⎪ ⎪ ⎪ ⎪ ⎪ (a1 − 2a0 )2 ⎪ ⎪ = cs2 , ⎪ ⎪ ⎪ (b1 − (1 + b2 ))2 ⎪ ⎪ ⎪ ⎪ (1 − b2 ) sin(ωc )(a1 + 2a0 cos(ωc )) ⎪ ⎩ = tgθ (cs). a1 b1 + (2a0 b1 + a1 (1 + b2 )) cos(ωc ) + 2a0 (1 + b2 ) cos2 (ωc ) where, cs – ripple level in bandpass, tgθ (cs) – phase response Analogically, math model for Chebyshev type II HF: ⎧ a2 = a0 , ⎪ ⎪ ⎪ ⎪ 2 ⎪ ⎪ ⎪ (a1 + 2a0 ) ⎪ = cs2 , ⎪ 2 ⎪ + + b (1 (b )) ⎪ 1 2 ⎪ ⎪ ⎪ 2 ⎪ ⎨ (a1 − 2a0 ) = 1, (b1 − (1 + b2 ))2 ⎪ ⎪ ⎪ ⎪ (a1 + 2a0 cos(ωc ))2 ⎪ ⎪ = cs2 , ⎪ ⎪ 2 2 2 (ω ) ⎪ + b + 2b cos − b + b cos(ω + 4b (1 ) (1 ) ) ⎪ 2 1 2 c 2 c 1 ⎪ ⎪ ⎪ ⎪ − b + 2a cos(ω sin(ω (1 ) )(a )) 2 c 1 0 c ⎪ ⎩− = tgθ (cs). a1 b1 + (2a0 b1 + a1 (1 + b2 )) cos(ωc ) + 2a0 (1 + b2 ) cos2 (ωc )

(9)

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3.4 The Second Order LF and HF Cauer Filter The Cauer filter model requires usage of both ripple level parameters in bandwidth and stopband. Using them, this filter type has very rapid frequency discrimination for frequency response. It is more efficient filter type for frequency suppression [18]. The most complete math model of second order LF elliptic filter has following form: ⎧ a2 = a0 , ⎪ ⎪ ⎪ ⎪ ⎪ (a1 + 2a0 )2 ⎪ ⎪ = cp2 , ⎪ ⎪ 2 ⎪ + + b (1 (b )) ⎪ 1 2 ⎪ ⎪ ⎪ ⎪ (a1 + 2a0 cos(ωc ))2 ⎨ = cp2 , 2 2 + 2b (1 + b ) cos(ω ) + 4b cos2 (ω ) (10) + b − b (1 ) 2 1 2 c 2 c 1 ⎪ ⎪ ⎪ ⎪ ⎪ (a1 − 2a0 )2 ⎪ ⎪ = cs2 , ⎪ 2 ⎪ ⎪ − + b (1 (b )) 1 2 ⎪ ⎪ ⎪ ⎪ (1 − b2 ) sin(ωc )(a1 + 2a0 cos(ωc )) ⎪ ⎩− = tgθ (cp). a1 b1 + (2a0 b1 + a1 (1 + b2 )) cos(ωc ) + 2a0 (1 + b2 ) cos2 (ωc ) Analogically, math model for elliptic type second order HF: ⎧ a2 = a0 , ⎪ ⎪ ⎪ ⎪ ⎪ (a1 + 2a0 )2 ⎪ ⎪ ⎪ = cs2 , ⎪ 2 ⎪ + + b (1 (b )) ⎪ 1 2 ⎪ ⎪ ⎪ 2 ⎪ ⎨ (a1 − 2a0 ) = cp2 , 2 (11) − + b (1 (b )) 1 2 ⎪ ⎪ ⎪ ⎪ (a1 + 2a0 cos(ωc ))2 ⎪ ⎪ = cp2 , ⎪ ⎪ 2 2 2 ⎪ ⎪ ⎪ (1 − b2 ) + b1 + 2b1 (1 + b2 ) cos(ωc ) + 4b2 cos (ωc ) ⎪ ⎪ ⎪ (1 − b2 ) sin(ωc )(a1 + 2a0 cos(ωc )) ⎪ ⎩ − = tgθ (cp). a1 b1 + (2a0 b1 + a1 (1 + b2 )) cos(ωc ) + 2a0 (1 + b2 ) cos2 (ωc ) Obtained math data models allow processing calculation of necessary coefficients for organization a characteristics reconstruction these components in dependency from operating conditions. According to models, it can be defined that they have dependency from ripple level and that means that certain coefficients also will have this dependency [17].

4 The Transfer Function Coefficients Calculation For passing a filter models to general view needs to allocate abstractions from obtained models. It will lead to applying a filter general entity, interface for rebuilding, coefficients calculation.

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4.1 The Butterworth Transfer Function Coefficients Calculation For definition a transfer function coefficients of Butterworth LF processed research have showed that based on model (4), the values accordingly equal: √ ⎧ 2 − sin ωc ⎪ ⎪ ⎪ b2 = √ , ⎪ ⎪ 2 + sin ωc ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ b1 = −(1 + b2 ) cos(ωc ), (12) (1 + b2 ) 2 ωc ⎪ sin , ⎪ ⎪ a0 = ⎪ 2 2 ⎪ ⎪ ⎪ ⎪ a1 = 2a0 , ⎪ ⎪ ⎩ a2 = a0 . And Butterworth HF based on model (5) has following form: √ ⎧ 2 − sin ωc ⎪ ⎪ ⎪ b2 = √ , ⎪ ⎪ 2 + sin ωc ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ b1 = −(1 + b2 ) cos(ωc ), ωc (1 + b2 ) ⎪ cos2 , a0 = ⎪ ⎪ ⎪ 2 2 ⎪ ⎪ ⎪ ⎪ a1 = −2a0 , ⎪ ⎪ ⎩ a2 = a0 .

(13)

From relations (12) and (13) follows that general calculated formulas are equal except coefficient a1 . 4.2 The Chebyshev I Transfer Function Coefficients Calculation For definition transfer function coefficients of Chebyshev HF, analogically based on math model (6), it can be obtained accordingly formulas. The model has dependency from ripple level which expressed through phase response. In the coefficient’s models themselves, the value tgϕ(cp) is much more convenient represent like tgϕ(cp) = φ. Using this, models will have following form: ⎧  ⎪ 2 1 + φ 2 + (1 + cos(ωc )) − φ sin(ωc ) ⎪ ⎪ b2 =  , ⎪ ⎪ ⎪ 2 1 + φ 2 + (1 + cos(ωc )) + φ sin(ωc ) ⎪ ⎪   ⎪ ⎪ ⎪ (1 − b2 ) ⎪ ⎪ , sin(ω b = − cos(ω + + b ) ) ) (1 1 2 c c ⎨ φ (14)   ⎪ cp (1 − b2 ) ⎪ ⎪ a0 = sin(ωc ) , (1 + b2 )(1 − cos(ωc )) − ⎪ ⎪ ⎪ 4 φ ⎪ ⎪ ⎪ ⎪ ⎪ a1 = 2a0 , ⎪ ⎪ ⎩ a2 = a0 .

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Transfer function coefficient of Chebyshev type I HF based on model (7) will have next definition: ⎧  ⎪ 2 1 + φ 2 + (1 − cos(ωc )) + φ sin(ωc ) ⎪ ⎪ , ⎪ b2 =  ⎪ 2 + (1 − cos(ω )) − φ sin(ω ) ⎪ 2 1 + φ c c ⎪ ⎪   ⎪ ⎪ ⎪ (1 − b2 ) ⎪ ⎪ sin(ωc ) , ⎨ b1 = − (1 + b2 ) cos(ωc ) + φ (15)   ⎪ cp (1 − b2 ) ⎪ ⎪ a0 = sin(ωc ) , (1 + b2 )(1 + cos(ωc )) − ⎪ ⎪ ⎪ 4 φ ⎪ ⎪ ⎪ ⎪ ⎪ a1 = −2a0 , ⎪ ⎪ ⎩ a2 = a0 . In this case, it is much more differences but coefficient b1 from (14) and (15) are same. 4.3 The Chebyshev II Transfer Function Coefficients Calculation The transfer function coefficients of Chebyshev type II based on (8) model can be calculated as: ⎧  ⎪ 2cs 1 + φ 2 + (1 + cs) − (1 − cs) cos(ωc ) + φ(1 − cs) sin(ωc ) ⎪ ⎪  b2 = , ⎪ ⎪ 2 − (1 + cs) − (1 − cs) cos(ω ) − φ(1 − cs) sin(ω ) ⎪ 2cs 1 + φ c c ⎪ ⎪ ⎪ ⎪ (1 − b2 ) sin(ωc ) + (1 + b2 )φ cos(ωc ) ⎪ ⎪ ⎪ , b =− ⎪ ⎨ 1 φ (16) b1 (1 − cs) + (1 + b2 )(1 + cs) ⎪ ⎪ , a0 = ⎪ ⎪ 4 ⎪ ⎪ ⎪ ⎪ b1 (1 + cs) + (1 + b2 )(1 − cs) ⎪ ⎪ , a1 = ⎪ ⎪ 2 ⎪ ⎪ ⎩ a2 = a0 . The transfer function coefficients of Chebyshev type II based on math model (9) will be defined as: ⎧  ⎪ −2cs 1 + φ 2 + (1 + cs) − (1 − cs) cos(ωc ) + φ(1 − cs) sin(ωc ) ⎪ ⎪  b2 = , ⎪ ⎪ 2 − (1 + cs) + (1 − cs) cos(ω ) + φ(1 − cs) sin(ω ) ⎪ 2cs 1 + φ c c ⎪ ⎪ ⎪ ⎪ (1 − b2 ) sin(ωc ) + (1 + b2 )φ cos(ωc ) ⎪ ⎪ ⎪ , b =− ⎪ ⎨ 1 φ (17) −b1 (1 − cs) + (1 + b2 )(1 + cs) ⎪ ⎪ , a0 = ⎪ ⎪ 4 ⎪ ⎪ ⎪ ⎪ b + cs) − + b2 )(1 − cs) (1 (1 1 ⎪a = ⎪ , ⎪ 1 ⎪ 2 ⎪ ⎪ ⎩ a2 = a0 . The Chebyshev type II has the same results with Chebyshev type I.

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4.4 The Cauer Transfer Function Coefficients Calculation Based on math model (10) the Cauer LF transfer function coefficients can be calculated as: ⎧  ⎪ 2cs 1 + φ 2 + (cp + cs) + (cp − cs) cos(ωc ) − φ(cp − cs) sin(ωc ) ⎪ ⎪  b2 = , ⎪ ⎪ 2 + (cp + cs) + (cp − cs) cos(ω ) + φ(cp − cs) sin(ω ) ⎪ 2cs 1 + φ c c ⎪ ⎪ ⎪ ⎪ (1 − b2 ) sin(ωc ) + (1 + b2 )φ cos(ωc ) ⎪ ⎪ ⎪ , b =− ⎪ ⎨ 1 φ (18) b1 (cp − cs) + (1 + b2 )(cp + cs) ⎪ ⎪ a0 = , ⎪ ⎪ 4 ⎪ ⎪ ⎪ ⎪ b1 (cp + cs) + (1 + b2 )(cp − cs) ⎪ ⎪ a1 = ⎪ ⎪ 2 ⎪ ⎪ ⎩ a2 = a0 . Based on model (11), Cauer HF: ⎧  ⎪ 2cs 1 + φ 2 − (cp + cs) + (cp − cs) cos(ωc ) − φ(cp − cs) sin(ωc ) ⎪ ⎪  b2 = , ⎪ ⎪ 2 − (cp + cs) + (cp − cs) cos(ω ) + φ(cp − cs) sin(ω ) ⎪ 2cs 1 + φ c c ⎪ ⎪ ⎪ ⎪ (1 − b2 ) sin(ωc ) + (1 + b2 )φ cos(ωc ) ⎪ ⎪ ⎪ b =− , ⎪ ⎨ 1 φ b1 (cp − cs) + (1 + b2 )(cp + cs) ⎪ ⎪ , a0 = ⎪ ⎪ 4 ⎪ ⎪ ⎪ ⎪ b1 (cp + cs) − (1 + b2 )(cp − cs) ⎪ ⎪ , a1 = ⎪ ⎪ 2 ⎪ ⎪ ⎩ a2 = a0 .

(19)

4.5 The Computation Costs Reducing Should be noticed, for reduce a computation costs for Chebyshev type I filters processing it is expedient, accordingly with formulas (14) and (15), to lead into constants the values  φ, φ1 , 2 1 + φ 2 and ripple level cp. These values should be calculated in advance at the development step and written into memory. After this, these formulas could be introduced in new notation. ⎧ ⎪ A = φ, ⎪ ⎪ ⎨ B = φ1 ,  (20) ⎪ D = 2 1 + φ2, ⎪ ⎪ ⎩ E = cp 4.

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 For Chebyshev type II it is expedient to lead φ, φ1 , 2cs 1 + φ 2 and (1 + cs), (1 − cs) values. After this, new notation will have following form: ⎧ A = φ, ⎪ ⎪ ⎪ ⎪ B = φ1 , ⎪ ⎪  ⎪ ⎪ ⎪ ⎨ D = 2cs 1 + φ 2 (21) E = (1 + cs), ⎪ ⎪ ⎪ F = (1 − cs), ⎪ ⎪ ⎪ ⎪ G = D − E. ⎪ ⎪ ⎩ L = AF  For Cauer filter it is expedient to lead φ, φ1 , 2cp 1 + φ 2 and (cp + cs), (cp − cs) values. After this, new notation will have following form: ⎧ A = φ, ⎪ ⎪ ⎪ ⎪ B = φ1 , ⎪ ⎪  ⎪ ⎪ 2 ⎪ ⎪ ⎪ D = 2cp 1 + φ , ⎨ E = (cp + cs), (22) ⎪ F = (cp − cs), ⎪ ⎪ ⎪ ⎪ Gp = D + E, ⎪ ⎪ ⎪ ⎪ ⎪ Gm = D − E, ⎪ ⎩ L = AF. These notations give it opportunity to develop and reconstruct second order digital filters more conveniently. Obtained views led to reducing a computation amount by 27%. It means, a duration for calculation and duration for rebuilding reduced proportionally. This test was executed on platform Intel NUC for mobile platform [20].

5 The Additional Conveniences in Using the Low Order Filters During the digital side construction of handling sensors signals on autonomous mobile robotic platforms, it is necessary to resolve a task for change the cut frequency and also for increase the filter discrimination of frequency response. Since the construction of high order filter is a complex process, it is important to have cascade connection of same type low order filters [15]. It Is known that the transfer functions of cascade chain are multiplying, Fig. 1. n Hi (p) (23) H (p) = i=1

where, H (p), Hi (p)-final and current transfer function. During transfer functions multiplying, the frequency response contracts and with it the cut frequency is shifted in low frequency area for LF, but for BF – shifted into central frequency area. Should be noticed, a frequency response discrimination grows. For analyzing the construction features of digital path processing a base LF and BF have reviewed.

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Fig. 1. The same type frequency-dependent components sequence chain

During research, the cascade connection of ten same type base filters is done. For Butterworth filter this dependency has good approximation by following equation: F = F0 N −0.27

(24)

where,F0 – cut frequency of base low order filter (1000 Hz), F– cut frequency with N cascade chain count Based on Eq. (19), it is possible to find a relation that allows to define base filter cut frequency using the cut frequency F0 from N connections for low order digital filters. F = F0 N 0.27

(25)

Based on obtained result, it is possible to notice that the cascade chain of same type filters requires usage of base filters with flat frequency response in bandwidth. The Butterworth and Chebyshev filters fall within these types. Should be noticed that all extracted equations have following view: F0 = FN b

(26)

Realization of this formula in mobile and specialized systems with limited computing resources is impossible. Therefore, the relation N b , where N – integer, and 0 < b < 1 will be has following view [21]: N b = eblnN

(27)

The expand for this equation with exponential function and logarithm into power serials will has following forms [20]: x2 x3 x4 xn x + + + + ... + (28) 1! 2! 3! 4! n!

   N −1 1 N −1 3 1 N −1 5 N − 1 2n+1 1 + lnN = 2 + + + ... + N +1 3 N +1 5 N +1 (2n + 1) N + 1 (29) ex = 1 +

It is necessary to use obtained series in practice in most cases because it speeds up work for mobile platform (Fig. 2).

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Fig. 2. The graph of normalized bandwidth dependency from cascade connection count for digital bandpass Butterworth filters

6 Conclusions In results of handled research, it is possible to say that the using of low order frequencydependent components through sensors signal processing in autonomous mobile robotic platform allows resolving an adaptation tasks for components in cases when the difficult hindrance environment exists with limited resources. Indeed, to calculate the source equations are complex and require much more advance microprocessor. By the way, obtained relations after transformation is not easy in calculations due to large number of simple functions. During the construction and commutation in digital path processing, the same type filters should be pre-calculated using strict environment and locate them in RAM for rapid rebuilding. This variant of pre-calculation is much more convenient. Should be notices that with cascade chain connection of same type digital filters the using of Butterworth and Chebyshev filters makes sense which provides good growth for frequency response discrimination and provides an expected value for cut frequency. Obtained models can be used on practice in adaptive rebuilding modules. These modules receive setting parameters on input which allow calculate transfer function coefficients. After this, the filter rebuilding is happens using new coefficients. Existing the difference filter types give a opportunity to lead all filters for one general interface and apply this with each type, generate coefficients and characteristics. The disadvantage of this approach is accuracy of obtained models, coefficients based on these models. For development modules will exist the requirement related with error level for characteristics.

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Stochastic Algorithms for Optimization of the Path of Robotic Systems Anatolii Pashko1(B) , Tetiana Oleshko2 , and Svitlana Biesiedina3 1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

[email protected]

2 National Aviation University, Kyiv, Ukraine 3 Bohdan Khmelnytsky National University of Cherkasy, Cherkasy, Ukraine

Abstract. The development of modern information technologies and artificial intelligence systems has led to the development of non-traditional methods for solving problems. Metaheuristic optimization methods have been developed. Among them are algorithms for ant colonies, bee swarm optimization algorithm, genetic algorithms, random search methods, simulated annealing, and others. Pathfinding is a non-trivial mathematical problem of finding the optimal route between two or more points using algorithmic methods. The paper considers the application of the ant colony algorithm and the genetic algorithm for solving the traveling salesman problem. The ant colony algorithm is used to train the robot to choose the optimal path when moving through the territory of an automated warehouse. Keywords: Ant colony method · Genetic algorithms · Minimum path · Path on the graph

1 Introduction Interest in heuristic methods and technologies began to develop rapidly at the end of the last century. It was then that a successful solution was found for many different practical complex optimization problems. Heuristic algorithms, based on the ideas of artificial intelligence, are used to solve a wide range of problems in various industries, including statistics, engineering, mathematical programming and operational research. One of the directions of development of heuristic optimization methods is the methods of “swarm intelligence”. Developed in the early 90s, these methods continue to actively develop, including due to the possibility of their application in parallel computing systems. Solving of complex optimization problems often consists in finding and determining the most suitable solution for optimization (finding the minimum or maximum) of the objective function from a discrete set of possible solutions. In this paper, we investigate the ant colony optimization method and genetic algorithms for finding the robot path in an automated warehouse. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 227–236, 2022. https://doi.org/10.1007/978-3-031-03877-8_20

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Modern software makes it possible not only to easily manage such a powerful system as automated warehouse systems, but also: to monitor, find out the load of shelves and the availability of goods, control cargo flows and much more. As a form of probabilistic search methods, ant colony algorithms and genetic algorithms aim to find the best, not the optimal, solution to a problem. First of all, this is due to the fact that for a complex problem it is often required to find some satisfactory solution, while the problem of reaching the optimum fades into the background. At the same time, other methods focused on finding a strictly optimal solution become generally unacceptable due to the dependence of the solution time on the dimension of the problem, which led to the emergence, active development and growth of popularity of evolutionary optimization methods.

2 References Analysis and Formulation of the Problem The shortest path problem is one of the main routing problems solved in graph theory. This task arises in the analysis of web structures, in the creation of navigation systems, traffic modeling and logistics optimization. In the problem, the shortest path is found between two given vertices of the original directed graph G and the sum of the weights of the arcs that make up this path is minimized. Traditionally, the problem is solved using Dijkstra’s algorithm, which works by assigning labels to the vertices of the graph G and uniformly expanding the solution search space, starting from the starting vertex s and up to the target vertex t of this graph [1, 2]. Over the past decades, metaheuristic algorithms have become very popular in solving optimization problems. This led to the emergence of new optimization methods and the use of these algorithms in applied problems. Among these algorithms, one can distinguish ant colonies algorithms [3, 4], bee swarm optimization algorithm [3, 5], genetic algorithms [3, 6–8], random search algorithms [3], algorithms for simulating annealing [9]. Among the various problems where heuristic algorithms are used, one can distinguish the problems of multicasting [10], image segmentation [11]. The ant colony is used in the tasks of multi-stream data transfer [12]. The proposed algorithm uses the smells of pheromones of the path, constantly updates the correctness of the choice of a particular path. Another problem where ant colonies are successfully used is the problem of classifying intrusions in communication networks [13]. The bee swarm is used in social network analysis tasks. So, in [14] it is used to detect the maximum clique (Clique). Considering the NP-complexity of the problem, the bee swarm algorithm gives good results. The bee swarm is also effectively used in problems of scheduling tasks in a cloud computing environment [15]. In addition to optimization problems [3], genetic algorithms are also used in classification problems, for example, to determine the centers of clusters in the problem of ensuring the minimum energy consumption in networks [16]. A feature of genetic algorithms is the variety of crossover and mutation algorithms. A new crossover scheme for solving the traveling salesman problem with a genetic algorithm is presented in [17]. This approach increases the likelihood of getting the best offspring, makes the computational process easier and faster.

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The considered areas of application of metaheuristic algorithms are caused by an increase in the number of dynamic problems, the current level of development of information technologies and artificial intelligence systems. In connection with the above, important tasks in the field of artificial intelligence are tasks related to control in robotic systems, solving the problems of choosing the optimal path in the traveling salesman problem, and applying the results in practice. Among such tasks is the use of metaheuristic algorithms to control a family of mobile robots, optimization of settings, and routes choice [18]. Traditional approaches in such problems are not preferable due to the high computational complexity. The paper discusses the problem of constructing routes for a mobile robot using the example of the movement of a robot in an automated warehouse. The robot serves the delivery of goods, it needs to visit several points and return to the starting point. Robot movement is a traveling salesman problem. As the main methods for solving the problem, it is proposed to use the ant colony method in several modifications, genetic algorithms and random search algorithms.

3 Ant Colony Method The idea of a heuristic algorithm based on the use of analogs of the ant system and its variations is presented in [19–21]. The ant colony method is based on the use of many agents with the same properties, the collective behavior of which is regulated by positive feedback. The most important differences between artificial ants and their natural counterparts is the use of memory, which stores the already traveled part of the path, discrete time, and the ability to assess the attractiveness of the path ahead. The most significant characteristics of the methods used that affect the quality of the solution for the ant colony method are: 1. Pheromone level. Pheromone is a substance left by each ant along its route. This substance is perceived by other ants and thus regulates their behavior. In this case, the presence of a pheromone on the path serves as an indicator that a certain number of ants have already passed along this section of the path. The more pheromone is on the path, the more ants will choose this path (positive feedback effect). In our case, a real number acts as a pheromone, which each ant “lays” on the way between two points. When calculating the pheromone value, the length of the shortest path found since the start of the search, the evaporation coefficient and the coefficient of pheromone addition are taken into account, which allows you to control the choice of the path. In the general case the change in the value of the pheromone can be expressed by the formula τij (t + 1) = (1 − ρ)τij (t) + τij , where ρ is evaporation coefficient (0 < ρ ≤ 1), τij is the amount of pheromone placed by the ants on the arc connecting points i and j. The amount of pheromone is calculated by the formula. τij =

m  k=1

τijk ,

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where τijk is the amount of pheromone placed by the k-th ant on the arc connecting points i and j. This value is equal to zero if the ant did not pass along the arc (i, j), and is functionally dependent on the total length of the route traversed by the k-th ant, otherwise, for example, it is inversely proportional. 2. Visibility of the path. This is the reciprocal of the distance between the starting point and the ending point of the path segment. When using this parameter as a defining one, the algorithm is reduced to the “greed principle”: as the next step, we select the point that is at the minimum distance from the current one. In general, the visibility of point j from point i is determined by. ηij = f (dij ), where dij is distance between points. 3. The number of ants and the initial distribution of ants, for example, uniform, that is, an equal number of ants at each point, or arbitrary. To study the parameters of the algorithms, the following were chosen: the time of obtaining a solution close to the optimal one, the stability of the solution obtained, the level of knowledge use, the level of pheromone on the arc in the ant colony algorithm. Suppose we use m ants to solve the problem. At the beginning of each iteration, the ants are randomly located at n points, and at the end of the iteration, the ants “die”. Each ant during one iteration must make (n-1) moves in order to build a complete path. An ant’s move can be described by the following rules: – the ant chooses a point to move to, with a probability which is a function of the distance between the current point and the chosen one, as well as the amount of pheromone along the way; – to control the correctness of the solution found by the ant, a list of already visited points is used (ant memory). The ant chooses the direction of movement only among the points it has not yet visited; – at the end of the iteration, the ant puts the pheromone on the arcs along which it went in search of the found solution. Initially, all arcs are covered with some amount of pheromone. This is a fairly small number. Let τij (t) be the pheromone intensity on the path between points i and j at the t-th iteration. At the end of each iteration, the pheromone is updated: a certain amount of pheromone evaporates from all arcs. And to those arcs along which the ant passed, a certain amount of it is added. Let us determine the probability of the ant moving from point i to point j at the t-th iteration: ⎧ α β ⎪ ⎨ (τij (t)) (ηαij ) β , j ∈ Alk (t)) (τ (η im ) pijk (t) = m∈Alk im ⎪ ⎩ 0, j ∈ / Alk

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where Alk is the list of points not yet traversed by the k-th ant, ηij is path visibility, α and β are parameters that control the relative priority of the pheromone along the path or visibility of the next point. Each artificial ant has its own memory. In this memory, the ant stores the so-called “prohibitions” list. This is a list of the points that it has passed (tbk ). Thus, Alk = n−tbk . The parameters α and β determine the importance of the pheromone and the visibility of the path. If α = 0, then the pheromone does not play any role, and only the visibility of the path affects the probability of choosing the next point (the nearby points are selected with a higher probability). If β = 0, then only the pheromone is used to select the next step. As the best solution, we use the path with the shortest length min(Lk ). To display it, we will use the “prohibitions” list of the ant that found this solution. Since the prohibitions list is filled with points in the order they are visited, it contains the correct path. The role of pheromone and path visibility can be briefly described as follows. At the first stages of the solution, when the amount of pheromone on the arcs is insignificant, the visibility of the path determines the direction of the search for a solution or some global solution. In the future, the best local solution is formed on the basis of the pheromone.

4 Genetic Algorithm Genetic algorithms arose as a result of observation of natural processes occurring in the world of living things, and consist in the organization of an evolutionary process, the purpose of which is to optimize the solution [22]. From a mathematical point of view, genetic algorithms are random search algorithms used mainly for solving optimization problems. They use analogs of the mechanism of genetic inheritance (creation of the next generation) and natural selection (operations of crossing and mutation), as well as definitions borrowed from biology [22]. During operation, the algorithm forms generations of individuals according to several rules, which imply a gradual improvement in the result or preservation of the previous level of fitness [22]. There are three main types of rules: • Selection rules. According to these rules, individual parents are selected that form part of the next generation using the crossing over process. • Crossing rules. According to these rules, it is determined what exactly the descendant from two specific parents will be. • Mutation rules decide exactly how a particular individual will be changed for the next generation. The classical genetic algorithm (also called elementary or simple genetic algorithm) consists of the following steps [22]: 1. Initialization or selection of the initial population of chromosomes. 2. Assessment of the fitness of chromosomes in the population. 3. Checking the condition for stopping the algorithm.

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Selection of chromosomes. Application of genetic operators (crossing, mutation). Formation of a new population. Choosing the “best” chromosome.

As part of the adaptation of the genetic algorithm to the path optimization problem, it is necessary to compare the concepts of the genetic algorithm and the problem: 1. Individual is a variant of the route between the start and end points, set P = (v1 , v2 , ..., vn , v1 ). The peculiarity of the route is that the first and last vertices coincide. 2. Crossing is the process of forming a new route from two ready ones. 3. Descendant is a route resulting from crossing or mutation. 4. Gene is a separate vertex of the route P, vi . 5. Population is a set of different routes. When adapting the applied genetic algorithm, a set of potential vertices is used, which is supplemented during the algorithm’s operation and to which all the vertices of the population routes must belong. New vertices can be taken for the mutation operation from this set. The initial set is formed when a set of visibility points is obtained and is further supplemented with the help of mutation operations and the formation of new vertices during the crossing operation. Separately, it is necessary to characterize the operations of crossing and mutation: 1. Vertex mutation - a random selection and small displacement of the vertex coordinate used in one of the routes of the population along the border of the zone of heterogeneity. Adding the modified vertex to the set of potential vertices. 2. Route mutation - replacement of a random route vertex with one of the nearest vertices belonging to the set of potential vertices. 3. Crossing routes - is the replacement of a random part of one parent route with a random part of the route of the other parent. It is necessary to take into account the peculiarity that the first and last vertices in the route coincide. In this case, the number of vertices in the route can change: Parent 1 is P1 = (v1 , v2 , v3 , v4 , v5 , vm v1 ). Parent 2 is P2 = (v1 , v6 , v7 , v8 , v9 , vm , v1 ). Descendant is P3 = (v1 , v2 , v7 , v8 , v4 , v5 , vm , v1 ). In the classical genetic algorithm, the initial population is formed randomly, but even when using the vertices obtained using the mechanism of points of view, the generation of the initial population will take a long time. To solve this problem, it is proposed to use classical pathfinding algorithms to form part of the initial population. Thus, part of the routes will be created using, for example, a greedy algorithm and the other part at random, which allows you to quickly get an initial population of sufficient size.

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5 The Results of the Demo Program A mobile robot moves through an automated warehouse to deliver goods. A genetic algorithm is used to construct an initial route. The mobile robot moves along the developed routes for a certain time and learns at the same time. Robot learning algorithm: 1. The same amount of pheromone is deposited on the route, which is built using the genetic algorithm. 2. The amount of pheromone deposited on the constructed route is summed up with the amount of pheromone that is already on the routes. 3. The robot moves along the specified route, but at the same time it is possible to correct the route of movement. Correction conditions are either set by external traffic conditions (the passage is closed, obstacle on the way), or randomly. 4. When the robot moves, it simulates the work of an ant in the ant colony algorithm, while a certain amount of pheromone is deposited along the route. After completing the movement, the amount of pheromone will be remembered. The new movement begins with the indication of points of visit and the construction of a new route by a genetic algorithm. Let the robot serve some warehouse. The warehouse plan is shown in Fig. 1. It is assumed that the robot can only move parallel to the racks. To determine the route of movement, a graph was built, which has 348 vertices, including the initial R (reception). An ant colony algorithm was used to determine the path of the robot.

Fig. 1. Plan of automated warehouse

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Fig. 2. Robot route

The robot needs to visit three points. In Fig. 1 these points are shown in red. The robot’s movement route obtained using the ant algorithm is shown in Fig. 2. The program is written in the C++ programming language. The result of the program is a sequence of graph vertices.

6 Conclusion The paper presents an algorithm for training a mobile robot to find the best route from the starting point to destinations in the workspace of an automated warehouse. For training, an ant colony algorithm is used, where a mobile robot simulates the work of an ant. A genetic algorithm is used to create an initial pathway. The use of the ant colony method for training the robot allows the robot to correct the route obtained by the genetic algorithm. Correction occurs either randomly, or when the robot encounters an obstacle on its way. The training results show the efficiency of the proposed algorithm. The use of the algorithm allows minimizing the travel time of the robot through the most frequently visited points. In the future, it is planned to improve the genetic algorithm, as well as to use random search algorithms and an annealing simulation algorithm instead of the genetic algorithm for constructing the initial path. In the future, it is planned to optimize the movement of a family of mobile robots, to develop methods of swarm intelligence. Acknowledgment. This project is supported by Key Projects of China Southern Power Gird (GZ2014-2-0049).

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References 1. Kormen, T., Leyzerson, C.H., Rivest, R., Shtayn, K.: Algoritmy. Plotting and Analysis. M.: Vil’yams,1328 (2013). (in Russian) 2. Rassel, S., Norving, P.: Artificial Intelligence: modern approach. M.: Vil’yams, 2006: 1408(in Russian) 3. Karpenko, A.P.: Modern algorithms of search optimization. Algorithms inspired by nature, Moscow: Publishing house MGGU im. N.E. Bauman, p. 446 (2017). (in Russian) 4. Escario, J.B., Jimenez, J.F., Giron-Sierra, J.M.: Ant colony extended: experiments on the travelling salesman problem. Expert Syst. Appl. 42, 390–410 (2015) 5. Zhan, S.-H., Lin, J., Zhang, Z.-J., Zhong, Y.-W.: List-based simulated annealing algorithm for traveling salesman problem. Comput. Intell. Neurosci. 2016, 1–8 (2016) 6. Bhattacharyya, M., Bandyopadhyay, A.K.: Comparative study of some solution methods for traveling salesman problem using genetic algorithms. Cybern. Syst. 40, 1–24 (2008) 7. Nagata, Y., Soler, D.: A new genetic algorithm for the asymmetric traveling salesman problem. Expert Syst. Appl. 39, 8947–8953 (2012) 8. Hussain, A., Muhammad, Y.S., Muhammad, N.S., Hussain, I., Mohamd, S.A., Gani, S.: Genetic algorithm for traveling salesman problem with modified cycle crossover operator. Comput. Intell. Neurosci. 2017, 1–7 (2017) 9. Gunduz, M., Kiran, M.S., Ozceylan, E.: A hierarchic approach based on swarm intelligence to solve the traveling salesman problem. Turk. J. Electr. Eng. Comput. Sci. 23, 103–117 (2015) 10. Sahana, S.K., AL-Fayoumi, M., Mahanti, P.K.: Application of modified ant colony optimization (MACO) for multicast routing problem. Int. J. Intell. Syst. Appl. (IJISA) 8(4), 43–48 (2016). https://doi.org/10.5815/ijisa.2016.04.05 11. Ye, Z., Wang, M., Jin, H., Liu, W., Lai, X.: An image thresholding approach based on ant colony optimization algorithm combined with genetic algorithm. Int. J. Intell. Syst. Appl. (IJISA) 7(5), 8–15 (2015). https://doi.org/10.5815/ijisa.2015.05.02 12. Maity, D.S., Goswami, S.: Multipath data transmission with minimization of congestion using ant colony optimization for MTSP and total queue length. IJCNIS 7(3), 26–34 (2015).https:// doi.org/10.5815/ijcnis.2015.03.04 13. Sharma, R., Chaurasia, S.: An integrated perceptron kernel classifier for intrusion detection system. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 10(12), 11–20 (2018). https://doi.org/10. 5815/ijcnis.2018.12.02 14. Fotoohi, S., Saeidi, S.: Discovering the maximum clique in social networks using artificial bee colony optimization method. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 11(10), 1–11 (2019). https://doi.org/10.5815/ijitcs.2019.10.01 15. Sethi, N., Singh, S., Singh, G.: Multiobjective artificial bee colony based job scheduling for cloud computing environment. Int. J. Math. Sci. Comput. (IJMSC) 4(1), 41–55 (2018). https:// doi.org/10.5815/ijmsc.2018.01.03 16. Kheireddine, M., Abdellatif, R., Ferrari, G.: Genetic centralized dynamic clustering in wireless sensor networks. IJCNIS 7(8), 1–8 (2015). https://doi.org/10.5815/ijcnis.2015.08.01 17. ul-Haq, E., Hussain, A., Ahmad, I.: Development a new crossover scheme for traveling salesman problem by aid of genetic algorithm. Int. J. Intell. Syst. Appl. (IJISA) 11(12), 46–52 (2019). https://doi.org/10.5815/ijisa.2019.12.05 18. Marie, M.J., Mahdi, S.S., Tarkan, E.Y.: Intelligent control for a swarm of two wheel mobile robot with presence of external disturbance. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 11(11), 7–12 (2019). https://doi.org/10.5815/ijmecs.2019.11.02 19. Dorigo, M., Gambardella, L.M.: Ant – Q: a reinforcement learning approach to the traveling salesman problem. In: Proceedings of ML–95. Twelfth International Conference on Machine Learning, pp. 252–260. Morgan Kaifmann (1995)

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Veterinary Self-protected Cone-Beam Computed Tomography Scanner Oleksandra Miroshnychenko1(B) , Sergii Miroshnychenko2 , Boris Goldberg3 , Sergey Guzeev3 , Andrii Nevgasymyi2 , and Yurii Khobta2 1 National Aviation University, 1 Liubomyra Huzara ave., Kyiv, Ukraine

[email protected]

2 Teleoptika, SPA, 20-a Borovkova str., v. Pidhirtsi, Obukhiv Dist., Kyiv, Ukraine 3 Orimtech Ltd., 1611 Barclay Blvd., Buffalo Grove, IL 60089, USA

Abstract. Cone-beam computed tomography is a new method of obtaining 3D Xray images in medicine and veterinary. Most of such devices not entirely protected from radiation and mechanical hazards. To solve this problem the self-shielded cone-beam computed tomography scanner for veterinary medicine had developed and it implementation has presented in this paper. The tomography devices case was developed in such way to protect staff form the both radiation and mechanical hazards. The main performance characteristics of the proposed product are presented. The width of the central tomography area in lateral was extended from 14 cm up to 21 cm by implementing the corresponding software without significant loss of image quality. The resolution of the tomographic image in the central and extended area of the tomography is enough for diagnosis. Keywords: Cone-beam computed tomography · X-ray protection · Veterinary medicine · Tomography area · Spatial resolution

1 Introduction The high efficiency of tomographic examinations of animals in veterinary medicine is well known today. In orthopedics and traumatology, dental research, and many other uses, X-ray computed tomography (CT) is a practically unalterable method of diagnosis in veterinary medicine, despite the active development of other diagnostic methods [1]. However, there are significant obstacles to the widespread use of CT in conventional clinical practice: 1) high cost of medical CT, which determines the long-term return on investment in tomography equipment; 2) limited life-time of tomographic X-ray tubes, which determines the major risk of purchasing used tomography scanners and significant cost of tomographic examinations; 3) large dimensions and weight of medical X-ray CT, which requires it installation on solid foundations, and determines the increased cost of construction and installation work; © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 237–247, 2022. https://doi.org/10.1007/978-3-031-03877-8_21

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4) significant electricity consumption and radiation loads on clinic staff in adjacent premises, which determines the prohibition of installing tomographic equipment near human habitation and the need to use costly X-ray protection; 5) low resolution of medical CT for examination of small and medium animals, due to the anthropometric parameters of the human adult population and the desire to reduce the its absorbed dose. These restrictions apply together with a wide range of dimensions and weights of animals examined in clinics. Thus, up to 90–95% of clinic patients are usually rodents, cats, small dogs (up to 30 kg) or dental examinations of large dogs. The use of medical CT with a typical voxel size of 400–500 µm (resolution about 1.0 lp/mm), the size of the tomography area of 50–70 cm and the multislice principle of tomographic imaging do not meet the anthropometry of the examined vet patients and the requirements for diagnostic images detail [3, 4]. Using of cone-beam computed tomography (CBCT) scanners allowed to solve most of these problems. The characteristics of the veterinary CBCT scanners on the market were analyzed before the start of the work [5–20]. The parameters of the most promising devices are presented in Table 1. Table 1. Parameters of the best veterinary CBCT scanners on the market Name

MyVet CT i3D

Verity VET

NewTom 5G XL

VetCAT

Vimago

Company

Rayence & Myvet Inc

Planmed

Cefla s.c

Xoran

Epica

Gentry hole, cm

58

40

58

63

60

3D FOV, cm

30 × 7,5 30 × 12 30 × 41

16 × 13 16 × 20

21 × 19 18 × 16

22 × 14

32 × 7,8

Voxel size, µm

400*

200

200–300

300–800

>90

Scan Time, s

20–60

18–35

18

20–45

–

Ua, kV

50–120

80–96

–

120–140

40–120

Ia, mA

10

2,4–12

–

10–15

10–120

P, kW

1,2

1,0

–

2,0

10*

Length

120

180

170

120

230

Width

270

70

360

80

85

Height

157

140

180

152

165

Weight, kg

–

350

660

217

600

Dimensions, cm

Unfortunately, most of implementations of this device use open design that lead to scattered radiation and mechanical hazards for staff.

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These discrepancies make the development of light-weight, easy-to-operate and relatively inexpensive self-shielded cone-beam computed tomography (CBCT) scanner with high detail diagnostic images relevant. One of the tasks in the development process of a CBCT scanner is to reduce the influence of artifacts in the resulting images. The following types of artifacts occur most frequently during diagnostics: – movement artifacts; – artifacts from metal objects; – irradiation inhomogeneity artifacts Movement artifacts occur in the case of movement of the examined part of the animal during the 60s of scanning. Most often, motion artifacts are present when examining the lungs and movable internal organs: heart, diaphragm, etc. The artifacts appear in the form of increased noise, additional contours, areas with sharp drops in X-ray density and loss of image clarity in the images of tomographic slices. It is necessary to perform the correct positioning of the animal and use radiolucent clamps to eliminate motion artifacts. Artifacts from metal objects occur when objects with a high X-ray density and sharp boundaries enter the tomography area. This situation occurs when observing the results of surgical operations using fixing screws, metal bars, etc. To suppress artifacts from metal objects, the MAR (Metal Artifacts Reduction) software package is used. Artifacts of irradiation inhomogeneity can occur when the animal is not properly positioned, when a part of it (for example, a limb) goes beyond the tomography zone. From the point of view of reconstruction, this situation is equivalent to inhomogeneous X-ray irradiation. As a result, characteristic artifacts appear on the image. To exclude artifacts of irradiation inhomogeneity, the placement of the animal should be performed strictly within the cylindrical tomography zone inscribed in the concave tomography table. When necessary, during installation, vet doctor should use X-ray transparent fixation clips. Software of the device uses mathematical apparatus that available in many others medical image processing implementations [21–25]. The purpose of this work is to present developed veterinary CBCTs scanner ETS2.

2 Materials and Methods The general concept of the self-shielded veterinary CBCT ETS2 is based on the use of an outer X-ray shielded casing (Fig. 1), which closes the scanning mechanism on all sides - the gentry and the small animal whole body or zone of interest of large animal under the study. Thus the animal is immersed into a medical sleep and is put on a table deck that has a semi-cylindrical form with open bases.

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Fig. 1. Design of self-shielded CBCT scanner ETS2 for veterinary purpose.

The lightweight open design of the tomography scanner provides the convenience of placing the animal on the concave tomography table and selecting the examination area. The safety guards are closed during the examination. A longitudinally moving carriage is located under the plane of the table, on which a rotating wheel with a 60° cut - gantry is fixed. A microfocus X-ray generator is attached to the gantry incision on one side. On the opposite side, a high-detail X-ray receiver is installed. The carriage is set to the “0” position, which provides free access through the incision on the gantry to the table for laying the vet patient. The animal can be placed on the table by parallel movement, as well as longitudinal - shift into the hole, as is usually done in tomography scanners. The tomography area on the table is selected by the longitudinal controlled movement of the carriage. This complex includes software that uses a variety of mathematical tools for image processing. Additionally, software packages are supplied to reduce the noise level, reduce the effect of scattered radiation and artifacts from metal elements in the tomography area. The requirements for self-protection of X-ray devices for different countries and regions are slightly different, but in most cases they are limited to not exceeding the flux density G < 10 µSv/hour at a distance of 10 cm from the outer casing of the tomography scanner during exposure. The modeling stand with an X-ray generator, a digital dynamic receiver and security elements was created to verify the fulfillment of this requirement. The operator’s console was located in the remote control room. In the casing of the tomography scanner were identified two areas of protection (see Fig. 2): – protection against direct radiation with a thickness up to Pb = 1 mm - on the butt walls; – protection against scattered radiation with a thickness up to Pb = 0.5 mm - on the side walls.

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Fig. 2. Area of protection against direct rays (a) and against scattered radiation (b)

Direct radiation protection was provided by sheet lead, and scattered radiation protection was provided by a combination of lead sheet and soft lead-containing plastic blinds. The requirement of self-protection imposes very strict restrictions on the choice of parameters of the X-ray emitter. At the modeling stand, the requirement of self-protection was satisfied (see Table 1) at voltages on the X-ray tube up to 80 kV, tube current up to 08, mA and X-ray generator power up to 50 W. The technical parameters of ETS2 CBCT scanner are presented in Table 2. Table 2. The technical parameters of ETS2 CBCT scanner Parameter

Value

X-ray protection

Self-protection

Average added dose load per staff, not more than µSv/day

0,15

Gentry hole, cm

40

X-ray generator power, W

99%) were demonstrated on the MNIST dataset [12] of handwritten digits by convolutional neural networks [13]. At the moment, most work on character recognition has concentrated on pen-on-paper or similar systems [14]. In all cases, the methods were based on significant preprocessing actions, which provides high accuracy, but preprocessing requires a priori knowledge about the entire glyph, and here is a first problem, the CGCL datasets are not

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available at the moment as open source databases except for some cases of their publications [7, 8]. The recent progress in computer vision and machine learning methods allows to apply some of them to improve the current recognition, identification, localization, semantic segmentation, and interpretation of such historical graffiti of various origin from different regions and cultures, including Europe (ancient Ukrainian graffiti from Kyivan Rus) [7], Middle East and Africa (Safaitic graffiti) [6], Asia (Chinese hieroglyphs) [15], and other. Moreover, the progress of diverse mediums in the recent decades determined the need for many more alphabets and methods of their recognition for different use cases, such as controlling computers using touchpads, mouse gestures or eye tracking cameras. It is an especially important topic for elderly care applications [16] on the basis of the newly available information and communication technologies based on multimodal interaction through human-computer interfaces like wearable computing, brain-computing interfaces [17], etc. Results of tSNE analysis of CGCL and notMNIST datasets show that CGCL can hardly be differentiated by dimensionality reduction methods, which is because of worse letter representation and quality [22]. This means that the dataset quality needs to be improved either by data extension or by improving sample quality and the dataset structure. Result of MLR model demonstrated the AUC values for ROC are not lower than 0.92 and 0.60 for notMNIST and CGCL. Usages subset of CGCL, which contained glyphs of A and H (two-letter classification) for training 2D CNN model with lossy data augmentation demonstrated the AUC values more than 0.9 [22].

3 Dataset, Models, and Problems Currently, more than 7000 graffiti of St. Sophia Cathedral of Kyiv are identified, studied, preprocessed, and classified [18–20]. They contain the cathedral inscriptions-graffiti dated back to 1018–1022, which reliably confirmed the foundation of the St. Sophia Cathedral in 1011. Recently, the image dataset of these carved Glagolitic and Cyrillic letters (CGCL) from graffiti of St. Sophia Cathedral of Kyiv was assembled and preprocessed to provide glyphs (Fig. 1) for recognition and classification by multinomial logistic regression (MLR) and deep neural networks [21, 22]. The new version of the dataset which was created for this research includes Slavic, Latin, and Greek alphabets and is based on a new structure, with labels named not in accordance with their spelling, as was in previous version [22]. In this version, labels correspond to letters from the relevant alphabet in accordance with ISO 15924. For the Latin alphabet, letter labels were assigned in accordance with letter names in classical Latin alphabet as defined by Latn, 215, ISO 15924. For the Greek alphabet, letter labels were assigned in accordance with letters name as defined by Grek, 200, ISO 15924. For the Slavic alphabet, letter labels are transliterated name in accordance with the Cyrs, 221 alphabet as defined ISO 15924. All other letters which do not correspond to any labels of the structure were labeled as ‘Strange’. The implementation of this label also can be used for labeling unclean data in the future. Other graffiti groups were labeled ‘All’. At the moment, the entire dataset consists of more than 5000 images for more than 90 types (classes) of letters (Fig. 1), but is continuously enlarged by new contributions. Research was focused on Slavic letters as on the most represented group.

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Fig. 1. Examples of Slavic glyphs from the CGCL dataset obtained from graffiti of St. Sophia Cathedral of Kyiv with their transliterated name in accordance with the Cyrs, 221 alphabet as defined by ISO 15924

In this work, 2D convolutional neural networks (CNNs), both standard (like MobileNetV2, EfficientNetB0, VGG16, DenseNet121, NASNetLarge, NASNetMobile, Xception) and custom ones, were applied to check the feasibility of CNN application for a dataset as small as CGCL to recognize letters from their glyphs. Custom CNNs had a pyramid VGG-like architecture with 5 convolutional/max-pooling layers, different numbers of convolutional filters (channels) inside and the correspondent different numbers of trainable parameters, rectified linear unit (ReLU) activation functions, categorical cross-entropy as a loss function, and made use of the Adam optimizer. Letter classification problems were defined for the following cases: (i) for the two most representative letters (classes), namely AZU (341 images) and ONU (285 images), and (ii) for all available letters that were represented by at least 6 images, or, in other words, 29 classes total with 2824 images. Both problems were considered with and without data augmentation to highlight its importance. Data augmentation included approaches random horizontal and vertical flips, random rotations (up to 45 degrees), width shifts (up to 20%), height shifts (up to 20%), shear (up to 20%), and zoom (up to 20%) of the original images. To determine the basic statistical properties of the metrics obtained (accuracy, loss, area under ROC-curve - AUC), stratified k-fold cross-validation was applied (k = 6) where the folds were created by preserving the percentage of samples for each class. The initial studies have shown that for both classification problems stated above the relatively small customized VGG-like CNNs on datasets of this size have demonstrated much better performance results than standard CNNs both trained from

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scratch (randomized initial weights) and after pretraining on the ImageNet dataset [23]. The well-known observation is that large CNNs (like the standard ones mentioned above) with millions of trainable parameters after several training epochs immediately memorize small datasets and tend to be over-trained leading to low performance on the validation subset of the dataset. To explore the relative influence and importance of CNN complexity, data augmentation, and dataset size, the following procedure was used. Custom CNNs were created with a pyramid VGG-like architecture with 5 convolutional/max-pooling layers with the constant number (F) of convolutional filters (channels) in each layer. Various variants of CNNs with F = 2n , where n in the range 1–8 were investigated. After each fold training, the validation AUC value was calculated on the validation subset of the dataset (obtained as a result of the stratified k-fold) with the model that demonstrated the highest validation AUC-value during 30 epochs of the current fold training. Then the mean and standard deviation of AUC were calculated on the basis of the separate AUC values obtained after training on 6 folds.

4 Experimental Results Two-Letter Classification Problem. Results of explores of different models are shown in Table 1, calculated the generalization (measured as the difference AUC LOSSY AUC NODA ) for each model. And here was observation is related to the correspondence between the correlated growth of performance (AUC) and generalization, the new hypothesis is formulated as ‘the accuracy limit of the model is reaching by generalization tend to zero’. As an example of each fold training in Fig. 2 the history plots of mean accuracy (Fig. 2a) and mean loss (Fig. 2b) with the confidence intervals for the standard deviations are shown for the customized VGG-like model with F const = 32 and lossy data augmentation. The correspondent confusion matrix (Fig. 2c) and ROC-curve with mean AUC values (Fig. 2d) demonstrate high performance for a model this small. To bring to light the impact of data augmentation a new type of the data augmentation correspondence plot, namely “no data augmentation versus lossy data augmentation” (NO DA vs. LOSSY DA) plot, was proposed (Fig. 3), where performance metric values obtained without data augmentation (NO DA) were plotted versus the ones obtained with lossy data augmentation (LOSSY DA). Here the mean AUC values after cross-validation were used as the performance metrics. Table 1. AUC and generalization (as the difference AUC LOSSY –AUC NODA ) values. Model

AUC_mean (NODA)

AUC_mean (LOSSY)

Generalization

Custom, F = 1

0.7748

0.6686

−0.1062

Custom, F = 2

0.8550

0.69

−0.165

Custom, F = 4

0.9123

0.7449

−0.1674

Custom, F = 8

0.9196

0.8621

−0.0575 (continued)

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Table 1. (continued) Model

AUC_mean (NODA)

AUC_mean (LOSSY)

Generalization

Custom, F = 16

0.9434

0.8958

−0.0476

Custom, F = 32

0.9408

0.9196

−0.0212

Custom, F = 64

0.9408

0.9336

−0.0072

Custom, F = 128

0.9371

0.9399

0.0028

Custom, F = 256

0.9427

0.9471

0.0044

Custom, F = 512

0.953

0.905

−0.048

Xception

0.4881

0.4881

0

DenseNet121

0.5852

0.5868

0.0016

MobileNetV2

0.9123

0.9123

0

NASNetMobile

0.5065

0.5861

0.0796

EfficientNetB0

0.4803

0.5262

0.0459

EfficientNetB7

0.512

0.519

0.007

Fig. 2. History plots of mean accuracy (a) and mean loss (b) with the correspondent confusion matrix (c) and ROC-curve with mean AUC values (d) for the 2-class (AZU-ONU letters) classification task after training the customized VGG-like model (F const = 32) with lossy data augmentation. All plots contain the mean and standard deviation values denoted by ± sign and the correspondent intervals calculated after 6-fold stratified cross-validation.

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The following main parts of the NO DA vs. LOSSY DA correspondence plot (Fig. 3) should be mentioned. The lower left corner titled as “Low Performance” corresponds to (AUC LOSSY ; AUC NODA ) = (0.5; 0.5) values of AUC which are characteristic for random predictions. The upper right corner titled as “High Performance” corresponds to (AUC LOSSY ; AUC NODA ) = (1.0; 1.0) values of AUC which are characteristic for perfectly accurate models and predictions. The upper left corner titled as “Low Generalization” corresponds to (AUC LOSSY ; AUC NODA ) = (1.0; 0.5) values of AUC which are characteristic for the models with perfectly accurate predictions made on data without any distortions, but also with absolutely unusable predictions on distorted data which is characteristic for the badly generalized models. The dash line from (0.5; 0.5) to (1.0; 1.0) titled as “High Generalization” denotes the dividing line between nicely and badly generalized models, i.e., the closer model is to it, the more generalizable the model is.

Fig. 3. AUC macro values for the 2-class (AZU-ONU letters) classification task after training with lossy data augmentation (LOSSY DA, AUC macro LOSSY ) and without data augmentation (NO DA, AUC macro NODA ), plotted with the numbers of the trained filters F (denoted by the figures) with mean and standard deviation error bars.

The increase of the number of filters F in each layer of the customized VGG-like model is followed by the increase of the performance (mean AUC values in the limits of their standard deviations) from F = 1 up to F = 128 and then decrease from F = 128 up to F = 512 (Fig. 3). The generalization grows from F = 4 up to F = 32 and then decreases from F = 128 up to F = 512. The relatively small customized VGG-like CNNs on such small dataset have demonstrated much better performance results than standard CNNs both trained from scratch (randomized initial weights) and after pretraining on the ImageNet dataset (Fig. 4a), even in the range of the measured standard deviations (if the error bar are not shown in Fig. 4b, that means that they are smaller than symbol sizes).

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Fig. 4. AUC macro values for the 2-class (AZU-ONU letters) classification task after training with data augmentation (LOSSY DA, AUC macro LOSSY ) and without data augmentation (NO DA, AUC macro NODA ), plotted with the numbers of the trained parameters P denoted by figures in thousands and the relative sizes of blue circles (a) and with mean and standard deviation error bars (b).

Multi-letter (Multiclass) Classification Problem. For that problem was used custom CNNs with a pyramid VGG-like architecture with 5 convolutional/max-pooling layers with the constant number (F) of convolutional filters (channels) in each layer and with increasing numbers of filters in each next layers, where total number calculated FILTERS + A*n, where n from 0 to 4. Various variants of CNNs with F = 2n , where n in the range 1–8 were explored, and some variants of A, result are shown in Table 2. The increase of the number of filters F in each layer of the customized VGG-like model is followed by

Fig. 5. AUC macro values for the multiclass letter classification task after training with lossy data augmentation (LOSSY DA, AUC macro LOSSY ) and without data augmentation (NO DA, AUC macro NODA ) with the numbers of the filters (F) denoted by the figures and relative sizes of circles.

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the increase in performance (mean AUC values in the limits of their standard deviations) from F = 1 up to F = 128 and then decrease from F = 128 up to F = 256 (Fig. 5), but the location of maximum cannot be supported statistically, as the data for both filter values overlap in the limits of standard deviation (Fig. 6b). The generalization (AUC LOSSY −AUC NODA ) grows from F = 4 up to F = 32 and then decreases from F = 128 up to F = 512 (Fig. 5). Was also verified the standard CNNs models for multi-letter classification. The small customized VGG-like CNNs on small dataset have also demonstrated much better performance results than standard CNNs both trained from scratch (randomized initial weights) and after pretraining on ImageNet dataset (Fig. 6a), but again it cannot be supported statistically, because the data for both filter values overlap in the limits of standard deviation (Fig. 6b). Table 2. Dependence of accuracy on Generalization parameter as observed. Models

AUC macro NODA

AUC macro LOSSY

Generalization

Custom, F = 16

0.727

0.614

−0.113

Custom, F = 16, A = 8

0.745

0.692

−0.053

Custom, F = 16, A = 16

0.735

0.718

−0.017

Custom, F = 16, A = 32

0.709

0.765

0.056

Custom, F = 32

0.727

0.655

−0.072

Custom, F = 32, A = 8

0.71

0.665

−0.045

Custom, F = 32, A = 24

0.669

0.565

−0.104

Custom, F = 64

0.626

0.65

Custom, F = 128

0.75

0.628

−0.122

Custom, F = 256

0.732

0.67

−0.062

0.024

5 Discussion and Conclusions For both classification problems, training histories of accuracy and loss (Fig. 2 and Fig. 5) demonstrate a steady learning behavior without early overfitting which was characteristic for standard models considered here. In comparison to 2-letter classification problem, the multi-letter classification one demonstrates much lower values of accuracy, higher loss, and lower AUC values. The correspondent confusion matrix (Fig. 2c) and ROC-curve with the mean AUC values (Fig. 2d) also demonstrate at worse performance for the multiletter classification problem in comparison to the previous 2-letter classification one. This phenomenon can be explained by a much more complicated dataset (more classes) with low representation of some classes. Unfortunately, the current standard CNN models demonstrate even worse performance. An intriguing observation is (consists in) the feasibility to tune the architecture of the custom CNN (VGG-like here) and improve performance significantly.

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Fig. 6. AUC macro values for the multiclass letter classification task after training with lossy data augmentation (LOSSY DA, AUC macro LOSSY ) and without data augmentation (NO DA, AUC macro NODA ) with the numbers of the parameters (P) denoted by figures (in thousands) the relative sizes of blue circles (a) and with mean and standard deviation error bars (b).

Comparing results of standard CNN models and customized VGG-like small CNN show that small VGG-like CNN have higher performance on dataset with low representation of data. Small VGG-like CNN can be used for the historical graffiti recognition, with high performance by the proper selection of F (the number of trainable parameters P), leading to higher performance (AUC), and better generalization (AUC LOSSY -AUC NODA ). Usually, grid search of the better model by the gradual changes of the architecture parameters (like F that could be different in different convolutional layers in the same CNN) can be very resource and time demanding. That is why additional criteria like reaching the value of generalization (AUC LOSSY –AUC NODA ) that is equal or lower than the correspondent standard deviation of AUC LOSSY and AUC NODA after intensive data augmentation can be very helpful. In general, it can be important for applications with low datasets where the complicated modern CNNs cannot be applied directly due to very fast overfitting. That is why additional methods for data-driven optimization of CNNs will be of great interest. As to the future, even in such relatively simple architecture like the presented custom VGG-like CNN with the fixed number of CNN layers (n = const = 5) and the constant number of filters (F i = const) per layer (I), the additional improvements can be obtained by tuning distribution of filters among layers F i = f (i), and the number of layers (n = const). The usage of other DNN types could also be very promising in the view of similar optimizations, for example, by usage of capsule-based deep neural networks that were recently proposed and demonstrated on the MNIST dataset [24], and notMNIST and CGCL datasets [25]. Better solutions of letter classification problems can be reached by extension of data, especially increasing variety of data for unrepresented letters (few images).

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In conclusion, the improved version of the image dataset with the carved Glagolitic and Cyrillic letters (CGCL) was prepared and several standard and custom CNNs were trained and tested for letter recognition in two-letter and multi-letter classification problems. The dataset was published as an open source resource for the data science community. The results of different models for both classification problems, which was examined in this research work and a data augmentation correspondence plot (NO DA vs. LOSSY DA plot) formed the basis, was proposed new criterion for the search of a better CNN architecture that can be formulated as reaching the value of generalization (AUC LOSSY –AUC NODA ) that is equal or lower than the correspondent standard deviation of AUC LOSSY and AUC NODA after intensive data augmentation.

References 1. Mascardi, V., et al.: A holonic multi-agent system for sketch, image and text interpretation in the rock art domain. IJICIC 10(1), 81–99 (2014) 2. Zeppelzauer, M., et al.: Interactive 3D segmentation of rock-art by enhanced depth maps and gradient preserving regularization. J. Comput. Cult. Heritage (JOCCH) 9(4), 1–30 (2016) 3. Leong, G., Brolly, M.: Towards a neural network approach for automated recognition of lichen-covered prehistoric carvings at Stonehenge, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020–10701 (2020) 4. Burt, D.: The Online Corpus of the Inscriptions from Ancient North Arabia (OCIANA). http:// krc2.orient.ox.ac.uk/ociana 5. Ancelet, J.: The history of graffiti. University of Central London (2006) 6. Alzate, J.R., Tabares, M.S., Vallejo, P.: Graffiti and government in smart cities: a Deep Learning approach applied to Medellín City, Colombia. In International Conference on Data Science, E-learning and Information Systems 2021, April 2021, pp. 160–165. https://doi.org/10. 1145/3460620.3460749 7. Nikitenko, N., Kornienko, V.: Drevneishie Graffiti Sofiiskogosobora v Kieve i Vremya Ego Sozdaniya (Old Graffiti in the St. Sofia Cathedral in Kiev and Time of Its Creation), Mykhailo Hrushevsky Institute of Ukrainian Archeography and Source Studies, Kiev (2012). (in Russian) 8. Vysotskii, S.A.: Drevnerusskie Nadpisi Sofii Kievskoi XI-XIV vv. (Old Russian Inscriptions in the St. Sofia Cathedral in Kiev, 11th-14th Centuries) Kiev: Naukova Dumka (1966). (in Russian) 9. Nazarenko, T.: East slavic visual writing: the inception of tradition. Canadian Slavonic Papers 43(2–3), 209–225 (2001) 10. Drobysheva, M.: The Difficulties of Reading and Interpretation of Old Rus Graffiti (the Inscription Vys. 1 as Example). Istoriya, 6(6 (39)), 10–20 (2015) 11. Pritsak, O.: An Eleventh-Century Turkic bilingual (Turko-Slavic) Graffito from the St. Sophia Cathedral in Kiev. Harvard Ukrainian Stud. 6(2), 152–166 (1982) 12. LeCun, Y., Cortes, C., Burges, C.J.: MNIST Handwritten Digit Database. AT&T Labs. http:// yann.lecun.com/exdb/mnist. Accessed 30 Aug 2018 13. LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. In: Proceedings of the IEEE, vol. 86(11), pp. 2278–2324. IEEE (1998) 14. Hafemann, L.G., Sabourin, R., Oliveira, L.S.: Offline handwritten signature verification— literature review. In: 2017 Seventh International Conference on Image Processing Theory, Tools and Applications, pp. 1–8. IEEE (2017) 15. Winter, J.: Preliminary Investigations on Chinese Ink in Far Eastern Paintings, Archaeological Chemistry, pp. 207–225(1974)

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16. Gang, P., et al.: User-driven intelligent interface on the basis of multimodal augmented reality and brain-computer interaction for people with functional disabilities. In: Proceedings of the Future of Information and Communication Conference, 5–6 April 2018, pp. 322–331. IEEE, Singapore (2018) 17. Gordienko, Y., et al.: Augmented coaching ecosystem for non-obtrusive adaptive personalized elderly care on the basis of cloud-fog-dew computing paradigm. In: Proceedings of the IEEE 40th International Convention on Information and Communication Technology, Electronics and Microelectronics, pp. 387–392, IEEE, Opatija, Croatia (2017) 18. Nikitenko, N., Kornienko, V.: Drevneishie Graffiti Sofiiskogosobora v Kieve i Ego Datirovka (The Ancient Graffiti of St. Sophia Cathedral in Kiev and Its Dating). Byzantinoslavica 68(1), 205–240 (2010). (in Russian) 19. Kornienko, V.V.: Korpus Hrafiti Sofii Kyivskoi, XI – pochatok XVIII_st, chastyny I-III (The Collection of Graffiti of St. Sophia of Kyiv, 11th-17th centuries), Parts I-III, Mykhailo Hrushevsky Institute of Ukrainian Archeography and Source Studies, Kiev (in Ukrainian) (2010–2011) 20. Sinkevic, N., Kornienko, V.: NoweZrodla do Historii Kosciolaunickiego w Kijowie: Graffiti w Absydzie Glownego Oltarza Katedry Sw. Zofii, Studia Zrodloznawcze, 50 (2012) 21. Glyphs of Graffiti in St. Sophia Cathedral of Kyiv. https://www.kaggle.com/yoctoman/gra ffiti-st-sophia-cathedral-kyiv 22. Gordienko, N., et al.: Open source dataset and machine learning techniques for automatic recognition of historical graffiti. In International Conference on Neural Information Processing, pp. 414–424. Springer, Cham, December 2018. https://doi.org/10.1007/978-3-03004221-9_37 23. Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., Fei-Fei, L.: ImageNet: a large-scale hierarchical image database. In: 2009 IEEE Conference On Computer Vision and Pattern Recognition, pp. 248–255. IEEE, June 2009 24. Sabour, S., Frosst, N., Hinton, G.E.: Dynamic routing between capsules. In: Advances in Neural Information Processing Systems, pp. 3856–3866 (2017) 25. Gordienko, N., Kochura, Y., Taran, V., Peng, G., Gordienko, Y., Stirenko, S.: Capsule deep neural network for recognition of historical Graffiti handwriting. arXiv preprint arXiv:1809. 06693 (2018) 26. Petrovska, B., Stojanovic, I.: Tatjana Atanasova-Pacemska, classification of small sets of images with pre-trained neural networks. Int. J. Eng. Manuf. (IJEM) 8(4), 40–55 (2018). https://doi.org/10.5815/ijem.2018.04.05 27. Sadique, M.F., Haque, S.M.R.: Content-based image retrieval using color layout descriptor, gray-level co-occurrence matrix and K-nearest neighbors. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 12(3), 19–25 (2020). https://doi.org/10.5815/ijitcs.2020.03.03 28. Shwetha, S.V., Dharmanna, L.: An automatic recognition, identification and classification of mitotic cells for the diagnosis of breast cancer stages. Int. J. Image Graph. Sign. Process. (IJIGSP) 13(6), 1–11 (2021). https://doi.org/10.5815/ijigsp.2021.06.01 29. Zaman, S., Sheikh, M.: Rabiul Islam, classification of FNIRS Using Wigner-ville Distribution and CNN. Int. J. Image Graph. Sign. Process. (IJIGSP) 13(5), 1–13 (2021). https://doi.org/ 10.5815/ijigsp.2021.05.01

Mathematic and Technological Achievements for Various Applications

Residual Stresses Occurring During Laser Shock Processing Technology of High-Load Units of Agricultural Machinery Gerontiy Zhorovich Sakhvadze(B) Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4, M. Kharitonyevskiy Pereulok, 101000 Moscow, Russian Federation [email protected]

Abstract. To increase the reliability and lifetime of high-load agricultural machinery units, it is very important to apply various strengthening technologies to them. Laser shock processing (LSP) is an innovative technology for hardening materials and is considered as an alternative to the well-known shot peening. The work investigates the aluminum alloy 2024-T351. The technology is based on the occurrence of compressive residual stresses in the near-surface layers of processed metal alloys. In order to completely cover the surface to be treated, the surface is usually scanned in a zigzag scheme. Such a zigzag scan is the simplest and easiest to carry out, but it has one significant side effect - the resulting residual stresses have a pronounced anisotropy. The purpose of this work is to develop a numerical model that allowed describing and explaining the influence of the scanning direction on the residual stress. To reduce the above-mentioned anisotropy of residual stresses, it is proposed to use surface scanning using a random scheme instead of the traditional zigzag scheme. Keywords: Agricultural machinery · Laser shock processing · Anisotropy of residual stresses · Finite element method · Random scanning scheme · Zigzag scanning scheme · 2024-T351 aluminum alloy

1 Introduction To increase the reliability and lifetime of high-load agricultural machinery units, it is very important to apply various strengthening technologies to them. Laser shock processing (LSP) is an innovative technology for surface treatment of highly loaded machine units, which initiates powerful fields of compressive residual stresses (CRS) in the nearsurface layers of processed metal alloys. These CRS, in turn, significantly increase their main mechanical characteristics, such as fatigue strength, as well as corrosion and wear resistance [1–3]. The LSP technology is based on scanning a metal surface under investigation with high-intensity laser pulses with an intensity (>1 GW/cm2 ) and a duration of several nanoseconds [4]. The shock wave in the near-surface region initiates the occurrence of plastic deformation, as well as compressive residual stresses, which improve © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 263–271, 2022. https://doi.org/10.1007/978-3-031-03877-8_23

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the surface properties of the material. In the LSP scheme, a transparent confining layer (usually water) is used to increase the pressure in the generated plasma. Since each laser pulse in LSP covers only a small part of the treated surface (usually 1–25 mm2 ), in order to completely cover the entire surface under study, laser pulses usually overlap each other (with varying degrees of overlap) and scanning occurs in a zigzag scheme (Fig. 1) [5, 6]. Such a zigzag scan is the simplest and easiest to carry out, but it has one significant side effect - the resulting residual stresses have a pronounced anisotropy.

Fig. 1. Scanning the investigated surface with laser pulses in a zigzag scheme

Significant differences between the values of the residual stresses after the LSP in the direction x (σx ) and in the direction y (σy ) have been recorded in many works, but until now the explanation of such anisotropy of residual stresses remained an open question. Only recently in [7] was the effect of LSP on the generation of dislocations, the nature of displacement of dislocations, and grain refinement in depth studied, and it was suggested that all this could be related to the anisotropy of residual stresses. However, the authors of [7] also recommend more systematic studies to explain the anisotropy of residual stresses. This paper explains the influence of various scanning schemes on the components of residual stresses σx and σy . To achieve this goal, the author have developed a threedimensional numerical model using the finite element method (FEM), which makes it possible to simulate the LSP technology using surface scanning both in a zigzag scheme and in a random scheme.

2 Studded Material The material for the study was 2024-T351 aluminum alloy. This is a high-strength material with fairly good machinability, which is successfully used in a wide variety of areas: from rocketry and aircraft fuselage to gears, shafts, pistons, and various fasteners. Its chemical composition is shown in Table 1, mechanical properties - in Table 2 [8].

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Table 1. Chemical composition of aluminum alloy 2024-T351 Element

Cu

Mg

Si

Fe

Mn

Zn

Cr

Ti

Al

(%)

3.8–4.9

1.2–1.8

0.5

0.5

0.3–0.9

0.25

0.10

0.15

Rest

Table 2. Mechanical properties of aluminum alloy 2024-T351 [8]. Material

Young’s modulus (GPa)

Yield strength (MPa)

Ultimate strength (MPa)

Elongation

2024-T351

72

360

481

19

3 Numerical Calculations by the Finite Element Method For 3D finite element modeling of the LSP technology, the Abaqus/Explicit package was used. It solves the physical problem of the propagation of a shock wave in a solid, taking into account the special elastoplastic behavior of the material [6, 9]. From a geometric point of view, a fully three-dimensional configuration is considered, where the strategy of sequential overlap of the investigated surfaces with laser pulses is implemented. Finite elements in the form of eight-node prisms, namely C3D8R, are used in the area processed by LSP. The element size is 100 × 100 × 25 μm3 , which is the maximum element size that allows the convergence of calculations to be maintained. In the rest, where there are no applied loads, the finite elements are simpler six-node prisms, namely the C3D6T, which successfully mate with the C3D8R elements. The features of the application of the finite element method in LSP problems are presented in more detail in [10–12].

4 Constitutive Relation The constitutive relation describes the plastic behavior of the material and includes the functional dependence of the dynamic yield stress σ on the equivalent plastic deformation ε, strain rates ε˙ and temperature T. Usually, the constitutive relations are obtained on the basis of processing a set of strain curves obtained by tensile (compression) tests and/or shift by various methods. The constitutive relations are based on a number of assumptions caused by the complexity of the real functional relationships between the ongoing processes, and describe the behavior of the material with satisfactory accuracy in a wide range of deformations, strain rates and temperatures. The success of applying a particular model depends on how effectively they describe the internal connections of the phenomenon under consideration. The most widespread are empirical and, more recently, semi-empirical dependencies. Among them, for fast dynamic processes, the most successful were the Johnson-Cook [13] and Zerilli-Armstrong [14] models. Due to their simplicity (a small number of constants) and the ability to describe the form of deformation curves in a sufficiently high quality manner in a wide range of temperatures and strain rates, these

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equations are widely used in practical calculations for numerical modeling, in particular, in the study of shock-wave processes in the materials under study [15, 16]. The model of Johnson-cook, which is used for the analysis of LSP, is an empirical dependence of the dynamic yield stress from the equivalent plastic strain, strain rate (von Mises) and temperature [13]:   m   ∗ (1) σ = A + Bεn 1 + C ε˙ [1 − T∗ ], ∗ ˙ ε˙ 0 – where σ is the equivalent von Mises stress, ε is the equivalent plastic strain, (ε) ε˙ = ε/ −1 ˙ dimensionless equivalent strain rate (ε0 = 1.0 s ), T* - homologous temperature, whose connection with the absolute temperature T is defined as follows:

T ∗ = (T − T0 )/(Tm − T0 ), where T 0 is the room temperature, and T m is the melting point of the sample material. Equation (1) contains five material constants, which are determined empirically: A is the static yield strength, B is the modulus of strain hardening, n is the exponent in the law of strain hardening, C is the coefficient of strain rate, m is the exponent in the law of temperature softening. It should be noted that when the melting point is reached (T * = 1), the yield strength tends to zero for all deformations and strain rates. Table 3 shows the parameters in the Johnson-Cook model for the D16 aluminum alloy. Table 3. Parameters in the Johnson-Cook model for aluminum alloy 2024-T351 [15] A (MPa)

B (MPa)

C

n

m

369

684

0.0083

0.73

1.70

There are several other models of constitutive relations, for example, the ZerilliArmstrong model, which is based on the theory of dislocations, which potentially makes it preferable to other empirical relations. Moreover, it is assumed that each type of microstructure of the material (HCC, BCC) has its own dependence. On the other hand, a more complex form of the relation implies a more complex way of obtaining these constants. In our work, the Johnson-Cook model will be used.

5 Analysis of the Occurrence of Anisotropy of Residual Stresses Arising in the Process of LSP 5.1 Residual Stresses Arising After the “Shot” By a Single Laser Pulse Before analyzing the situation with respect to residual stresses arising from multiple laser pulses, it is necessary to study in detail the features of the appearance of residual stresses σx and σy after the “shot” by a single laser pulse. The results of this simulation are shown in Fig. 2a. Inside the laser spot, the residual stresses σx and σy are almost the same. However, outside of the spot, these values differ significantly from each other.

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Namely, for σx , the compressive residual stresses (CRS) occur in the upper and lower regions of the laser spot (with values of σx ≈ −130 MPa), and the tensile residual stresses (TRS) occur in the left and right regions of the spot (σx ≈ 180 MPa). For σy , we have the opposite picture: the CRS occurs in the left and right parts of the spot (σy ≈ −130 MPa), and the TRS occurs in the upper and lower regions (σy = 180 MPa). The residual stresses that occur in this case are the same in absolute values, but have different signs.

Fig. 2. The occurrence of residual stresses σx and σy after “shots” with 1 pulse (a), 11 (b) and 16 (c) pulses with a zigzag scanning scheme. 1 - hardening zone (compressive residual stresses increase), 2 - softening zone (compressive residual stresses decrease)

5.2 Study of the Residual Stress After the End of the First Column of “Shots” In Fig. 2b shows the distributions of surface residual stresses for σx and σy after the “shot” on the sample with 11 pulses, at which the first column of pulses ends, after which the second column immediately begins. It is seen that the resulting compressive residual stresses along the x-axis (σx ) are greater than along the y-axis (σy ). It should be noted that in this case, each new pulse adds compressive residual stresses to σx , thereby strengthening the material (stress drop σx ≈ −100 MPa), and in σy , each new pulse reduces compressive stresses, softening it (σy ≈ 170 MPa). This is due to the superposition of residual stresses occurring outside the spot (see Fig. 2a).

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5.3 Study of Residual Stress After the Beginning of the Second and Subsequent Columns of “Shots” The properties of the behavior of the residual stress fields change significantly with the beginning of the second column of “shots» (see Fig. 2c, which shows the picture after 16 pulses). For example, for residual stresses on the x-axis (σx ), each new pulse from the second column reduces CRS (σx = 245 MPa), and in σy , on the contrary, each new pulse increases CRS (σy = −185 MPa). Obviously, the decrease in σx is associated with the addition of tensile stresses created by the second column of “shots” on the left and right sides of the laser spot. Naturally, the increase in σy is associated with the addition of compressive stresses generated by the second column of “shots” on its upper and lower parts. Note that in this case, the character of the distribution of residual stresses in the vicinity of each laser spot remains the same as after a single pulse (see Fig. 2a). In Fig. 3 shows the distributions of residual stress fields after 100 and 286 pulses, respectively. It can be seen that the trend appearing in Fig. 2 is preserved: the compressive residual stresses arising in the zigzag scanning scheme in the scanning direction (σy ) are greater than in the perpendicular direction (σx ). These features of the distribution of residual stresses are the main reason for the occurrence of significant anisotropy of residual stresses in a zigzag scanning scheme.

Fig. 3. Residual stresses σx and σy after 100 (a) and 286 (b) pulses with a zigzag scanning scheme. 1 - Hardening zone (compressive residual stresses increase), 2 - Softening zone (compressive residual stresses decrease)

5.4 Reducing the Anisotropy of Residual Stresses By Applying Random Scanning The obtained numerical results show that the method of choosing the scanning direction has a strong influence on the anisotropy of residual stresses. In particular, it was found that with a zigzag scanning scheme the CRS in the scanning direction is much greater than in the perpendicular direction. Therefore, the choice of the scanning direction is an important separate task that should be solved before using LSP to optimize the resulting residual stress fields. If the laser pulses in the LSP are not directed according to a predetermined scheme (for example, shown in Fig. 3, where the zigzag scanning scheme was initially chosen), but are triggered in a random sequence, then the difference in residual stresses between

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σx and σy decreases noticeably. This is clearly seen from Fig. 4, where it is seen that the distribution pattern of residual stresses σx and σy after the application of 286 pulses fired in a random sequence are very similar (Fig. 4b). A random sequence of pulses for numerical analysis was programmed and implemented using the VDLOAD subroutine, available from the Abaqus finite element package.

Fig. 4. Distributions of residual stresses σx and σy after the “shot” of 16 (a) and 286 (b) pulses when scanning according to the random scheme

The difference between zigzag and random scan schemes can be visualized more clearly if the changes in residual stresses σx and σy are graphically represented over depth. In Fig. 5 shows the above comparison. As you can see, the difference between σx and σy (σx ,an = |σx − σy |), which is indicated in the figure in gray, after scanning according to a zigzag scheme is much greater than when scanning according to a random scheme (σx ,an = 150 ÷ 275 MPa in the first case and σx ,an = 50 ÷ 100 MPa - in the second case). This means that with a random scanning scheme, the anisotropy of residual stresses decreases by ≈100 ÷ 175 MPa.

Fig. 5. Comparison between the residual stress anisotropies (σRES ) induced by zigzag (a) and random (b) scanning schemes. 1 - σx , 2 - σy

Analyzing the results obtained, the main conclusion can be drawn that the random scheme of scanning by laser pulses in LSP is an effective solution to the problem of reducing the anisotropy of residual stresses. The results obtained show that the resulting

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anisotropy of residual stresses is a consequence of the use of a zigzag sequence of pulses, and that it is due to the natural mutual equilibrium of the residual stresses. Some important features of obtaining and generalizing data using neural networks are given in the works [17–21].

6 Conclusion 1. A 3D finite element model has been developed that makes it possible to simulate the technologies of laser-shock-wave processing (LSP) according to various scanning schemes. 2. It is shown that in a number of cases, the anisotropy of residual stresses can be a big problem, and in such cases, it is necessary to achieve almost the same distribution of residual stresses σx and σy . It was found that the superposition of residual stresses in the outer zones of the laser spot during scanning in a zigzag scheme leads to significant differences between the values of σx and σy (anisotropy of residual stresses) in the treated area. 3. Recommendations have been developed according to which, in order to reduce the anisotropy of residual stresses, the scanning of the investigated surface with laser pulses should be performed not in a zigzag scheme, but in a random scheme.

References 1. Peng, L., Siyu, S., Hu, J.: Effect of laser shock peening on the microstructure and corrosion resistance in the surface of weld nugget zone and heat-affected zone of FSW joints of 7050 A1 alloy. Opt. Laser Technol. 112, 1 (2019) 2. Lin, L., Jiaojiao, W., Jianzhong, Z.: Characterization and analysis on microhardness and microstructure evolution of brass subjected to laser shock peening. Opt. Laser Technol. 115, 325 (2019) 3. Su, C., Zhou, J.Z., Meng, X.K., et al.: Improvement in fatigue performance of aluminum alloy welded joints by laser shock peening in a dynamic strain aging temperature regime. Materials 9, 799 (2016) 4. Morales, M., Ocaña, J.L., Molpeceres, C., Porro, J.A., García-Beltrán, A.: Model based optimization criteria for the generation of deep compressive residual stress fields in high elastic limit metallic alloys by ns-laser shock processing. Surf. Coat. Technol. 202(11), 2257 (2008) 5. Sano, Y., Masaki, K., Gushi, T., Sano, T.: Improvement in fatigue performance of friction stir welded A6061-T6 aluminium alloy by laser peening without coating. Mater. Des. 36, 809 (2012) 6. Hfaiedh, N., Peyre, P., Song, H., Popa, I., Ji, V., Vignal, V.: Finite element analysis of laser shock peening of 2050-T8 aluminium alloy. Int. J. Fatigue 70, 480 (2015). https://doi.org/10. 1016/j.ijfatigue.2014.05.015 7. Trdan, U., Skarba, M., Grum, J.: Laser shock peening effect on the dislocation transitions and grain refinement of Al-Mg-Si alloy. Materials 97, 57 (2014) 8. Dorman, M., Toparli, M.B., Smyth, N., Cini, A., Fitzpatrick, M.E., Irving, P.E.: Effect of laser shock peening on residual stress and fatigue life of clad 2024 aluminum sheet containing scribe defects. Mater. Sci. Eng. A Struct. 548, 142 (2012)

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9. Zhou, Z., Gill, A.S., Qian, M.S.D., Langer, K., Wen, Y., Vasudevan, V.K.: A finite element study of thermal relaxation of residual stress in laser shock peened IN718 superalloy. Int. J. Impact Eng. 38(7), 590 (2011) 10. Sakhvadze, G.: Enhancement of material crack resistance using laser shock processing. J. Mach. Manuf. Reliab. 49(4), 335 (2020). https://doi.org/10.3103/S1052618820040123 11. Sakhvadze, G., Sakhvadze, G.G., Kavtaradze, R.Z.: Increasing the crack resistance of materials by means of laser shock waves. Russ. Eng. Res. 41(1), 27 (2021). https://doi.org/10.3103/ S1068798X21010202 12. Sakhvadze, G., Kikvidze, O.G.: The role of laser shock processing treatment in the growth dynamics of fatigue cracks in specimens of Ti-6Al-4V titanium alloys damaged by foreign objects. J. Mach. Manuf. Reliab. 49(10), 836 (2020). https://doi.org/10.3103/S10526188201 00088 13. Johnson, G.R., Cook, W.H.: A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th International Symposium on Ballistics, p. 541 (1983) 14. Zerilli, F.J., Armstrong, R.W.: Dislocation mechanics-based constitutive relation for material dynamics calculations. J. Appl. Phys. 12, 1816 (1987) 15. Flores-Johnson, E.A., Muránsky, O., Hamelin, C.J., Bendeich, P.J., Edwards, L.: Numerical analysis of the effect of weld-induced residual stress and plastic damage on the ballistic performance of welded steel plate. Comput. Mater. Sci. 58, 131 (2012) 16. Ocaña, J.L., Molpeceres, C., Gómez, G., Porro, J.A., Morales, M.: Experimental assessment of materials treatment by laser shock processing. Appl. Surf. Sci. 238, 501 (2004) 17. Karande, A.M., Kalbande, D.R.: Weight assignment algorithms for designing fully connected neural network. Int. J. Intell. Syst. Appl. (IJISA) 6, 68–76 (2018) 18. Dharmajee Rao, D.T.V., Ramana, K.V.: Winograd’s inequality: effectiveness for efficient training of deep neural networks. Int. J. Intell. Syst. Appl. (IJISA) 6, 49–58 (2018) 19. Hu, Z., Tereykovskiy, I.A., Tereykovska, L.O., Pogorelov, V.V.: Determination of structural parameters of multilayer perceptron designed to estimate parameters of technical systems. Int. J. Intell. Syst. Appl. (IJISA) 10, 57–62 (2017) 20. Awadalla, M.H.A.: Spiking neural network and bull genetic algorithm for active vibration control. Int. J. Intell. Syst. Appl. (IJISA) 10(2), 17–26 (2018) 21. Abuljadayel, A., Wedyan, F.: An approach for the generation of higher order mutants using genetic algorithms. Int. J. Intell. Syst. Appl. (IJISA) 10(1), 34–35 (2018)

Strengthening of Agricultural Machinery Parts by Cryogenic Laser Shock Processing Technology Gerontiy Zhorovich Sakhvadze(B) and Dinara Usmanovna Khasyanova Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4, M. Kharitonyevskiy Pereulok, 101000 Moscow, Russian Federation [email protected]

Abstract. The influence of a new combined technology of material processing cryogenic laser shock processing (CLSP) on the residual stresses and microhardness that occur in aluminum alloys 2024-T351, is investigated. Parts from this alloy are widely used in agricultural engineering. The residual stresses that occur in the test sample when using various treatment technologies were studied. The results obtained showed that cryogenic treatment (CT) can improve the strengthening effect obtained by classical laser shock processing (LSP). It is shown that the combined processing technology - preliminary 4-h cryogenic treatment (CT) of the test material, and then LSP (the so-called CLSP-4 technology) provides a higher microhardness of the surface, as well as creates stronger fields of compressive residual stresses. It is shown that the surface microhardness and compressive residual stresses of the sample at CLSP-4 were increased by 22.84% and 34.81%, respectively, in comparison with the classical LSP. Keywords: Laser shock processing · Cryogenic laser shock processing · Residual stresses · Finite element method · Aluminum alloy 2024-T351

1 Instruction Aluminum alloy 2024-T351 is using in the production of critical high-load components of machines and structures, especially in the agricultural, aviation and aerospace fields, due to its high strength, ductility and good workability [1]. Unfortunately, the harsh and aggressive operating conditions where these units operate sometimes lead to failures due to the formation of various types of damage in them, such as corrosion, wear from friction, fatigue, cracks and even destruction. Therefore, it is necessary to further improve the quality of the surfaces of these units, as well as to increase their fatigue strength [2]. In recent years, many methods have been applied to change the microstructure of aerospace aluminum alloys in order to improve their complex mechanical properties [3, 4]. Laser shock processing technology (LSP) is an innovative and effective hardening technology that creates compressive residual stresses and a favorable microstructure in the surface layer, which leads to an improvement in the basic mechanical properties of materials [5–7]. Previous studies have shown that although (LSP) can increase the tensile strength © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 272–280, 2022. https://doi.org/10.1007/978-3-031-03877-8_24

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and fatigue properties of materials, however it cannot significantly improve the ductility of processed materials [8]. In addition, the compressive residual stresses and improved microstructure (grain grinding) created by the LSP at normal temperature relax at a high rate under the influence of external loads and with increasing temperature, which reduces the stability of the mechanical properties of structural materials [9]. It is known that cryogenic treatment (CT) is a specific technological process at materials are placed in a tank with a temperature range from −196 °C to −130 °C, and this process is used to improve mechanical characteristics and their stability [10, 11]. Particularly, in [12], it was studied the influence of CT on the strength properties and microstructure of the aluminum alloy 2024-T351 and it was shown that after CT, the grains become finer. It is worth noting that the holding time of the CT has a great influence on the hardening effect, and a properly selected cryogenic holding time can simultaneously increase both the strength and ductility of the processed materials. In addition, theoretical analysis and numerical simulation results shown the synergistic strengthening effect of plastic deformation and cryogenic temperature can provide higher mechanical characteristics of structural materials [13–15]. According to recent studies, under certain conditions, can achieve a synchronous improvement in both strength and ductility by changing the microstructure compared to LSP at normal temperature. However, the effect of the optimal cryogenic holding time on the strengthening effect of CLSP has not been previously researched. In this paper, we investigate this issue and study the mechanical properties of the aluminum alloy 2024-T351.

2 CLSP Technology Modeling It was carried numerical simulation of the CLSP technology out in the Abaqus finite element package. The features of such modeling are described in [9, 11, 12]. To represent the simulated processes, Fig. 1 shows a diagram of a similar experiment from [12]. The material under study is aluminum alloy 2024-T351 (position 7 in Fig. 1). The laser wavelength is 1064 nm, the pulse duration is 8 ns, the laser energy in the pulse is 1.8 J, the laser spot diameter is 1 mm, and the laser spot overlap factor is 50%. The transparent and absorbing layers are K9 glass with a thickness of 3 mm (position 5) and aluminum foil with a thickness of 120 microns (position 6), respectively. When exposed to laser radiation with the test sample, a plasma is formed (position 13), with the expansion of which a shock wave propagates in the material (position 14). For more information about the processes occurring with CLSP, see [13–15]. It was used liquid nitrogen as the refrigerant. The ultra-low temperature is transmitted to the sample through a well-heatconducting base (position 8) mounted to the sample, provides the sample temperature in the range (−130 ± 2)°C. The sample temperature was controlling by an ultra-low thermometer (position 12). The CLSP begins when the sample reaches a stable cryogenic temperature.

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Fig. 1. Schematization of CLSP technology. 1-laser complex, 2-laser beam, 3-reflecting mirror, 4-focusing lens, 5-transparent layer (K9 glass), 6-absorbing layer (aluminium foil), 7-test sample (2024-T351), 8 – heat-conducting base, 9-cryogenic tank, 10 – liquid nitrogen, 11-funnel, 12temperature measurement and control system, 13-plasma, 14 - shock wave

3 Defining Relation The researched material is the aluminum alloy 2024-T351 with elastic-plastic homogeneous isotropic material without initial stresses. During of LSP, due to the influence of large and short-term pressure, the strain rates in the material under study reach values of 106 c-1 or more, so it was used the Zerilli-Armstrong model in the calculations of the stress-strain state, which will be used later in the analysis of cryogenic laser shock wave processing (CLSP), based on the dislocation theory, that potentially makes it preferable to other empirical relations. Moreover, it was assumed that each type of material microstructure (HCC, BCC lattice) has its own dependence. On the other hand, a more complex form of the relation implies a more complex way of obtaining constants. The Zerilli-Armstrong model for HCC metals, which include the researched 2024T351 alloy, has the form [16]: σ = C0 + C0 ε1/2 · exp[−C3 + C4 ln(˙ε)]T ,

(1)

where C0 , C2 , C3 , C4 are material constants. Wherein, the initial value of the dynamic yield strength C0 does not depend on the strain rate and temperature, but depends on the grain size: C0 = σa + kH d −1/2 ,

(2)

where σa - the thermal component of the dynamic yield strength connected with the initial microstructure of the material and showing the contribution to the yield strength of solutes and the initial density of dislocations; d - average grain diameter; kH - Hall-Petch coefficient, which depends on the intensity of microstructural stresses. The values of the constants in the Zerilli-Armstrong model for the researched 2024T351 alloy (HCC lattice) shown in Table 1 [16].

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Table 1. Constants in the Zerilli-Armstrong model Material

C 0 MPa C 1 MPa C 2 MPa C 3 K−1 · 10−3 C 4 K−1 · 10–4 C 5 MPa n

Aluminum 292.2 alloy 2024-T351 (HCC lattice)

–

11.82

13.7

2.44

–

–

4 Theoretical Background During the CLSP-4 process, the effect of volumetric shrinkage of the material lattice occurs in an environment with ultra-low temperatures. Below are the Eqs. (3)–(7), which describe the relation between the change in temperature and the change in the volume of the material and their relation with the resulting average stress. The effect of volumetric shrinkage can be described by the equations [10]:   ∂V , (3) αV = V −1 ∂T p VT = V0 eαV (T −T0 ) ,

(4)

where αV - volume expansion coefficient (the relative change in volume when the temperature changes by one Kelvin at constant pressure), V – volume of the material, V0 initial volume, VT - volume of materials after processing, T - cryogenic temperature„ T0 - initial temperature. The change in the volume of the material V can be shown as:   V = VT − V0 = V0 eαV (T −T0 ) − 1 . (5) Therefore, the contraction coefficient of the material volume θ can be shown as: θ=

V = eαV (T −T0 ) − 1. V0

(6)

Assuming that the volume shrinkage is a volume strain, the corresponding average stress can be obtained according to Hooke’s law. Thus,   (7) σm = Kθ = K eαV (T −T0 ) − 1 , where K is the compression modulus, K = E/[3(1−2μ)]; E and μ - Young’s longitudinal elastic modulus and Poisson’s ratio, respectively; σm - average stress. From the above analysis, it follows that a decrease in the volume of the material leads to the appearance of compression stresses, which contribute to the spread of dislocations. However, it is known that dislocation structures scattered throughout the volume. As the CT time increases, the density of dislocations increases even more, then these dislocations intertwine with each other and are fixed at the grain boundaries, that contributes to an increase in the microhardness and strength of the matrix of processed materials

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[17]. Meanwhile, in comparison with the treatment of LSP at normal temperature, the cryogenic environment at CLSP-4 causes partial closure and collapse of existing internal defects of materials, as well as the dissolution of some existing impurities, that reduces the stress concentration during loading [18]. Consequently, the materials will withstand greater deformation before breaking, which at the macroscopic level means increased ductility.

5 The Obtained Results and Discussion 5.1 Surface Residual Stresses Analysis Notoriously that the effectiveness of the use of CT and LSP technologies is largely determined by the arisen residual stresses. The features of the distribution of surface residual stresses in different processing technologies are shown in Fig. 2. We see that both in the case of CT and LSP, compressive residual stresses (CRS) occur in the aluminum alloy 2024-T351. In the initial (untreated) sample are observed small technological tensile residual stresses (TRS - line 1 in Fig. 2). The CT process effectively removes these TRS and even induces a slight CRS (line 2). In addition, CT before LSP (CLSP-4) results in CRS with higher peak values (line 4) compared to the classic LSP technology (line 3). If we compare the quantitative indicators, the average sleep caused by CLSP-4 and LSP is about −245 MPa and −180 MPa, respectively. The increase is about 34.81%.

Fig. 2. Features of the distribution of surface residual stresses (along the x-axis) at different processing technologies of the 2024-T351 alloy. 1 – The sample is in its original state; 2 – after processing by CT technology; 3 – after processing by LSP technology; 4 – after processing according to the CLSP-4 technology

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During CT, the plastic deformation caused by the bulk shrinkage effect of the material increases its density, which causes various defects, such as vacancies and dislocations, to move inside the materials. At the same time, it was shredded the grain. After CT, during the temperature increase from cryogenic to normal temperature, additional compressive residual stresses occur in the surface layer because of natural differences in the thermal expansion coefficients of various elements. Meanwhile, the high-intensity shock wave caused by LSP causes severe plastic deformations on the surface of the materials, which leads to further dislocation propagation and grain grinding. It is known that uneven deformation of grains and/or subgrains and additional formation of defects, such as dislocations leads to an increase in compressive residual stresses in the surface layer [18]. Consequently, the combined treatment of CT and LSP (CLSP) creates more powerful fields of compressive residual stresses on the surface of the 2024-T351 aluminum alloy than a separate LSP technology. 5.2 Microhardness Distribution by Depth There are a number of assumptions for establishing quantitative relationships between residual stresses and hardness. In this paper, we consider the Larson-Carlson model proposed in [19]: H=

H0 , 1 − (σR /3σT )

(8)

where H - hardness in the presence of residual stresses, H0 - initial hardness (in the absence of residual stresses), σR - residual stress, σT – yield strength of the material. The formula obtained for the case of a flat homogeneous stress state. Some features of obtaining and generalizing data using neural networks are given in the works [20–24]. Figure 3 shows the distribution of microhardness over depth at different surface treatment technologies of the 2024-T351 alloy. It can be seen that in the initial state of the sample (before treatment), it was observed a uniform distribution of microhardness over depth. Analysis of their distribution after various treatments showed that in all cases, the microhardness gradually decreases with increasing depth from the upper surface (recall that LSP (line 2) and CLSP (line 3) are LSP tests performed at room and cryogenic temperatures, respectively, CLSP-4 (line 4) – exposure to cryogenic temperature for 4 h followed by LSP). If we evaluate the ongoing processes quantitatively, we have the following picture: the microhardness of the initial untreated sample on the surface is about 132 HV, and its value after LSP is about 165 HV, which is 25% higher than that of the sample in the initial state. Thus, we see that when processing the surface using the CLSP technology, it was obtained a higher surface microhardness than with LSP, and this value increases even more with an increase in the holding time of the CT to 4 h. The microhardness on the surface at CLSP and CLSP-4 reach values of 173 HV and 197 HV, respectively, which is 14.85% and 22.84% higher than that of the sample with LSP. However, it should be noted that the increase in microhardness in depth at CLSP (i.e., LSP at cryogenic temperature) was higher than the microhardness obtained at LSP (i.e., at room temperature), and the best hardening effect, as expected, is achieved by holding the CT for 4 h followed by

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Fig. 3. Features of the distribution of microhardness over the depth of the sample at different processing technologies of alloy 2024-T351. 1-the sample in its initial state; 2-after processing by the LSP technology; 3-after processing by the CLSP technology; 4-after processing by the CLSP-4 technology;

LSP (i.e., at CLSP-4 mode). Due to the volume shrinkage effect caused by cryogenic temperature, the microhardness of the matrix of samples (at a depth of about 1 mm) treated with CLSP was greater than the microhardness of the original sample and the sample with LSP. In particular, the microhardness of the matrix of the CLSP-4 sample is about 150 HV, which is 13.64% better than that of the sample in the initial state. In the near future, it is planned to conduct similar studies for titanium alloys.

6 Conclusion In this article, the influence of cryogenic treatment (CT) and laser shock processing (LSP) technologies, both individually and in a combined form, on the residual stresses and microhardness of the 2024-T351 aluminum alloy is investigated, from which the following main conclusions can be drawn: 1. It is shown that both CT and LSP technologies produce compressive residual stresses in the surface layer of the aluminum alloy 2024-T351. However, the amplitude of the surface compressive residual stresses and the microhardness induced by CLSP are significantly greater than in CT or LSP separately. 2. It is shown that the strengthening mechanism of the fatigue properties in the 2024T351 alloy is promoted by the resulting synergistic effect from the superposition of the processes occurring at CT and LSP, which induces more powerful and more stable compressive residual stresses. At CLSP, apparently, a favorable evolution of the microstructure is observed in the material, which is expressed in additional grain

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grinding, the spread of more dislocations, which plays a key role in improving the mechanical properties of the aluminum alloy 2024-T351. 3. In comparison with the classical LSP, the microhardness of the surface and the compressive residual stresses of the sample at CLSP-4 were increased by 22.84% and 34.81%, respectively.

References 1. Peng, L., Siyu, S., Hu, J.: Effect of laser shock peening on the microstructure and corrosion resistance in the surface of weld nugget zone and heat-affected zone of FSW joints of 7050 A1 alloy. Opt. Laser Technol. 112, 1 (2019) 2. Lin, L., Jiaojiao, W., Jianzhong, Z.: Characterization and analysis on microhardness and microstructure evolution of brass subjected to laser shock peening. Opt. Laser Technol. 115, 325 (2019) 3. Su, C., Zhou, J.Z., Meng, X.K., et al.: Improvement in fatigue performance of aluminum alloy welded joints by laser shock peening in a dynamic strain aging temperature regime. Materials 9, 799 (2016) 4. Morales, M., Ocaña, J.L., Molpeceres, C., Porro, J.A., García-Beltrán, A.: Model based optimization criteria for the generation of deep compressive residual stress fields in high elastic limit metallic alloys by ns-laser shock processing. Surf. Coat. Technol. 202(11), 2257 (2008) 5. Sano, Y., Masaki, K., Gushi, T., Sano, T.: Improvement in fatigue performance of friction stir welded A6061-T6 aluminium alloy by laser peening without coating. Mater. Des. 36, 809 (2012) 6. Hfaiedh, N., Peyre, P., Song, H., Popa, I., Ji, V., Vignal, V.: Finite element analysis of laser shock peening of 2050-T8 aluminium alloy. Int. J. Fatigue 70, 480 (2015). https://doi.org/10. 1016/j.ijfatigue.2014.05.015 7. Trdan, U., Skarba, M., Grum, J.: Laser shock peening effect on the dislocation transitions and grain refinement of Al-Mg-Si alloy. Materials 97, 57 (2014) 8. Dorman, M., Toparli, M.B., Smyth, N., Cini, A., Fitzpatrick, M.E., Irving, P.E.: Effect of laser shock peening on residual stress and fatigue life of clad 2024 aluminum sheet containing scribe defects. Mater. Sci. Eng. A: Struct. 548, 142 (2012) 9. Zhou, Z., Gill, A.S., Qian, M.S.D., Langer, K., Wen, Y., Vasudevan, V.K.: A finite element study of thermal relaxation of residual stress in laser shock peened IN718 superalloy. Int. J. Impact Eng. 38(7), 590 (2011) 10. Li, J., et al.: Effects of cryogenic treatment on mechanical properties and microstructures of IN718 super-alloy. Mater. Sci. Eng. A 707, 612 (2017) 11. Xu, L.Y., Zhu, J., Jing, H.Y., Zhao, L., Lv, X.Q., Han, Y.D.: Effects of deep cryogenic treatment on the residual stress and mechanical properties of electron-beam-welded Ti-6A1-4V joints. Mater. Sd. Eng. A 673, 503 (2016) 12. Zhou, J., et al.: Tensile properties and microstructures of a 2024-T351 aluminium alloy subjected to cryogenic treatment. Metals 6, 279 (2016) 13. Sakhvadze, G.Zh.: Enhancement of material crack resistance using laser shock processing. J. Mach. Manuf. Reliab. 49(4), 335 (2020). https://doi.org/10.3103/S1052618820040123 14. Sakhvadze, G.Zh., Sakhvadze, G.G., Kavtaradze, R.Z.: Increasing the crack resistance of materials by means of laser shock waves. Russ. Eng. Res. 41(1), 27 (2021). https://doi.org/ 10.3103/S1068798X21010202

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15. Sakhvadze, G.Zh., Kikvidze, O.G.: The role of laser shock processing treatment in the growth dynamics of fatigue cracks in specimens of Ti-6Al-4V titanium alloys damaged by foreign objects. J. Mach. Manuf. Reliab. 49(10), 836 (2020). https://doi.org/10.3103/S10526188201 00088 16. Zerilli, F.J., Armstrong, R.W.: Dislocation mechanics-based constitutive relation for material dynamics calculations. J. Appl. Phys. 12, 1816 (1987) 17. Flores-Johnson, E.A., Muránsky, O., Hamelin, C.J., Bendeich, P.J., Edwards, L.: Numerical analysis of the effect of weld-induced residual stress and plastic damage on the ballistic performance of welded steel plate. Comput. Mater. Sci. 58, 131 (2012) 18. Ocaña, J.L., Molpeceres, C., Gómez, G., Porro, J.A., Morales, M.: Experimental assessment of materials treatment by laser shock processing. Appl. Surf. Sci. 238, 501 (2004) 19. Carlsson, S., Larsson, P.L.: On the determination of residual stress and strain fields by sharp indentation testing. Part 1: theoretical and numerical analysis. Acta Mater. 49, 2179 (2001) 20. Karande, A.M., Kalbande, D.R.: Weight assignment algorithms for designing fully connected neural network. Int. J. Intell. Syst. Appl. (IJISA) 10(6), 68–76 (2018) 21. Dharmajee Rao, D.T.V., Ramana, K.V.: Winograd’s inequality: effectiveness for efficient training of deep neural networks. Int. J. Intell. Syst. Appl. (IJISA) 10(6), 49–58 (2018) 22. Hu, Z., Tereykovskiy, I.A., Tereykovska, L.O., Pogorelov, V.V.: Determination of structural parameters of multilayer perceptron designed to estimate parameters of technical systems. Int. J. Intell. Syst. Appl. (IJISA) 9(10), 57–62 (2017) 23. Awadalla, M.H.A.: Spiking neural network and bull genetic algorithm for active vibration control. Int. J. Intell. Syst. Appl. (IJISA) 10(2), 17–26 (2018) 24. Abuljadayel, A., Wedyan, F.: An approach for the generation of higher order mutants using genetic algorithms. Int. J. Intell. Syst. Appl. (IJISA) 10(1), 34–35 (2018)

Method of Reducing Friction in the Plow Moldboard with Soil During Cultivation Due to the Implementation of Ultrasonic Vibrations Constantine Bazilo(B) , Sergey Filimonov, Nadiia Filimonova, and Sergei Yashchenko Cherkasy State Technological University, Shevchenko blvd, 460, Cherkasy 18006, Ukraine [email protected], {s.filimonov,n.filimonova}@chdtu.edu.ua

Abstract. Agriculture is one of the leading sectors of the production sector, which is engaged in the cultivation of agricultural crops. The main task of agriculture is to provide the population with food and the supply of raw materials for industry. One of the main problems in agriculture is the complexity and efficiency of ground cultivation. The main tool for tillage is the plow. The analysis of modern plows is carried out and their characteristics are analyzed. To reduce friction, a method is proposed and substantiated, as well as a model of a plow with a piezoelectric actuator. To determine the reduction of the friction of the plow moldboard with the soil, an improved Goryachkin’s formula is proposed. Calculations are made to determine the forces that act on the plow during plowing. To determine the vibrations in the plow blade, a numerical simulation of the process is carried out using the COMSOL Multiphysics software package. Keywords: Vibratory plow · COMSOL Multiphysics · Automation · Vibration technology · Piezoelectric actuator · Friction

1 Introduction Agriculture is one of the most important industries, providing the population with food and raw materials for a number of industries. The food security of the state and its citizens depends on the state of agriculture. The emergence of resource-saving technologies has changed the attitude of farmers to field cultivation. Many of them refuse to use a plow, not wanting to disrupt the natural structure of the soil, which has been developing over the years. Nevertheless, a significant part of agricultural producers is sure that in no case should we completely abandon the use of the plow, since it loosens the soil, helps fight weeds and improves the quality of the soil as a whole [1, 2]. Plowing is a method of soil cultivation, which consists in trimming the processed slice, lifting it with loosening and rotation by 130–180% and laying it on the bottom of a previously opened furrow. This method is characterized by complete cleansing of the field surface from after harvest residues (by 95–100%), incorporation of organic, mineral fertilizers, weeds into the soil, a significant decrease in the density of the arable layer and an increase in its porosity [3, 4]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 281–289, 2022. https://doi.org/10.1007/978-3-031-03877-8_25

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2 Formal Problem Statement One of the main problems in agriculture is the complexity and efficiency of ground cultivation. The process of loosening the soil is one of the most common ways to improve its properties [5]. Plowing is accompanied by deformation, destruction and movement of the soil layer. Soil cultivation is the most energy-intensive operation in the technological process of growing crops [6]. Loosening the ground is created by using conventional plows. The main disadvantage of this plow is the high resistance (friction) that occurs when plowing the soil, while there is a high-energy consumption, faster wear of the material and its failure [7].

3 Literature Review The main tool for cultivating soil in agriculture is the plow. Two main components of the plow are a plowshare and a moldboard. The plow moldboard is one of the working parts of the plow. Its main task is to cut from the wall of the soil layer, crumbling it and turning it over. That is, in many respects, the quality of the moldboard depends on how well the soil will be prepared. The plowshare is a part of the plow that cuts the soil layer, and it is along this that the cut soil layer rises and falls on the moldboard. The main advantages of the plow are its ease of manufacture and relatively low price. The main disadvantage of such a plow is the high resistance (friction) that occurs when plowing the soil, while the energy consumption is significantly increased. Today, there is such an alternative to a conventional plow as a vibratory plow. It has been experimentally established that when using vibrations in the plow, sliding friction by the soil is significantly reduced, it is the main component in the total value of traction resistance. The sticking of the working bodies is also reduced [8]. In [9], a decrease in friction between two surfaces of bodies under the action of ultrasonic vibrations is presented and experimentally proved. In this regard, many designs of plows with vibrating working bodies have recently appeared [10, 11]. Figure 1 shows a functional diagram of a vibratory plow. The vibratory plow consists of a body 1, a body stand 2, which is connected to the frame 3 by means of a hinge 4. On the plow frame 3, at a variable angle α, a vibrator 5 is fixed, which is connected by a rod 6 to the body stand 2. Vibrator 5 consists of a piston 7, made together with a rod 6, and a spool 8. The cavity of the vibrator 5 is connected to the hydraulic system of the tractor. The throttle 9 provides regulation of the vibration frequency of the vibrator 5 [11]. These improvements have a number of disadvantages such as an increase in the weight of the working body, a decrease in the operating time of the vibration unit, an increase in the complexity of maintenance and product manufacturing, etc. The work [12] presents the design of a vibratory plow, in which a mechanical system with an offset eccentric is used to create vibrations. The disadvantage of such a vibratory plow is the complexity of the design and the limited power of vibrations.

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Fig. 1. Functional diagram of a vibratory plow

An example of using a hydraulic drive to create vibrations in a plow is described in [13]. One of the disadvantages of using this design in the agrosphere is the low speed. Thus, with the addition of extra mechanical devices, their characteristics and disadvantages are superimposed on the organ of tillage itself (plow). In practice, it is the mechanical parts of devices that most often fail, and the more there are, the higher the risk of failure of one of these parts. Especially when the device or body that is involved in this case in the cultivation of the ground, must withstand high physical activity. This factor increases the risks of reducing the wear resistance of materials. So, the use of vibration [14, 15] technologies in soil cultivation would significantly reduce material costs, but the developed structures, due to their complex design, have not found wide application in the modern agricultural sector.

4 Materials and Methods The aim of the work is to develop a method for reducing the friction of the plow when plowing the ground and reducing sticking of working bodies by using vibration principles based on a piezoceramic actuator. The COMSOL Multiphysics software package is used to determine the deformation distribution of a plow moldboard with a piezoceramic actuator. COMSOL Multiphysics is an integrated modelling platform that includes all the steps from creating geometry, defining material properties and describing physical phenomena, to customizing the solution and post-processing, for accurate and reliable results [7, 16, 17]. The analysis of the piezoceramic element of the plow moldboard is carried out in the Frequency response mode. The computational mesh of finite elements in the “Mesh” item is chosen to be orthogonalized (Normal). The mesh is built by a tetragonal partition, and the studied three-dimensional models are represented by a set of more than a thousand elements each. Direct is used as a solver, in which the numerical SPOOLES method is chosen for solving systems of linear equations with sparse matrices. When carrying out numerical simulations in the COMSOL Multiphysics software package, the resonance frequency at which the piezoceramic element entered the resonant oscillation mode is first determined. Then, its maximum amplitude of oscillations at certain frequencies and the type of oscillation is determined.

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To determine the reduction of friction of the plow moldboard with the ground, an improved formula of Goryachkin is proposed.

5 Experiments and Results Friction is a mechanical resistance arising tangentially to the touching surface of two contacting bodies during their relative displacement. The resistance force F directed opposite to the relative displacement of a given body is called the friction force. It depends on the dry friction coefficient μ of the force P with which one body is pressed against another and other factors. Some work is spent on overcoming the friction force. If in any way in one of the contacting bodies to cause ultrasonic vibrations with frequency f , then the friction force will decrease. Accordingly, due to ultrasonic vibrations, the work to overcome friction is also reduced. Figure 2 schematically shows the creation of oscillations in the plow, namely in the plow blade, when the oscillatory displacements ξ are oriented perpendicular to the plane of contact of the soil, and, consequently, the direction of the speed of their relative movement [18, 19].

Fig. 2. Diagram illustrating the direction of movement of the plow and the orientation of ultrasonic vibrations ξ, top view

With an increase in the amplitude of ultrasonic vibrations ξm , the amplitude of the vibrational acceleration (2πF)2 ξm (where F is a frequency of ultrasonic vibrations) increases, as well as the vibrational force PA . If the value of PA exceeds the force Px (force required to pull the plow, i.e. soil resistance), then there is a periodic separation of the contacting bodies from each other. In this case, the friction force does not act all the time, but only in those fractions of the oscillation period T = 1/F, when the bodies touch. We can assume that under these conditions there is an effective friction force P0 . If PA >> Px then the friction force tends to zero [18, 19]. Thus, the force of counteracting the friction of the plow by the soil is equal to PA = (2π F)2 ξm · mp , where mp is a plow mass.

(1)

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To calculate the force required to pull the plow P0 when creating ultrasonic vibrations in it, you must first determine the force required to pull the plow in the classic version. To determine the force required to pull the plow, the founder of agricultural mechanics, Academician Goryachkin, proposed a formula that reveals the patterns and physical connection between the main factors of the plow’s working process and the total resistance that arises during its work. These dependencies are written in a rational form, hence the formula, called rational, has the form [20, 21]. Px = f · G + (k · a + ε · a · b · v2 ) · n,

(2)

where f is a coefficient similar to the coefficient of friction; G is a gravity of the plow, N; k is a soil resistivity coefficient, Pa; a and b are the dimensions of the cross section of the formation, m; ε is a dimensionless coefficient dependent on the shape of the blade and the soil properties; υ is a speed, m/s; n is a number of plow bodies. The efficiency of the plow is determined by the formula η=

(k · a · b + ε · a · b · υ 2 )n . fG + (k · a · b + ε · a · b · υ 2 )n

(3)

The coefficients f , k, and ε of the rational Goryachkin formula are determined by the formulas (4–6) [22] P1 , G

(4)

k=

q·l−m·r , n · l − m2

(5)

ε=

n·r−q·m . n · l − m2

(6)

f =

Based on Goryachkin’s formulas (2–6), the forces required for traction of a singlebody plow n = 1 are determined. The following data were used for calculations: plow gravity G = 47 N; dimensions of the cross section of the formation a = 0.2 m, b = 0.35 m; speed υ = 1.5 m/s; m = 4.7 kg, P1 = 235 N, l = 0.43, n = 1. According to the formula (4), the coefficient of friction is calculated f = 0.5. The coefficient of resistivity is taken from the table [8] k = 41000 N/m2 (light, sandy loam, compacted, gristly soil). According to the formula (2), we calculate the force required to pull the plow Px = 3.2 kN [22, 23]. Thus, if we subtract the force that the ultrasonic piezoceramic actuator PA can create from the force required for traction of the plow PX , then we can find out the effective friction force P0 when ultrasonic vibrations are created in it P0 = PX − PA .

(7)

Figure 3 shows a 3D model of a plow structure with a piezoceramic actuator based on the proposed method. The basis of which is the creation of vibrations due to the reverse piezoelectric effect.

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a)

b)

Fig. 3. 3D plow design with piezoelectric actuator: a) front view; b) back view; 1 – moldboard, 2 – plowshare, 3 – body stand, 4 – piezoelectric actuator in the form of a disk, 5 –shoe

The essence of the proposed method is as follows. Piezoceramic actuator [24, 25] tightly located on the surface of the plow moldboard. Due to the presence of a reverse piezoelectric effect in a piezoceramic element, it can be used as an actuator (vibrator). When an alternating electric voltage is supplied oscillations arise in the piezoelectric element and are transmitted to the plow moldboard. Thus, vibration occurs in the plow, which helps to reduce the frictional force of the plow with the soil. Figure 4 shows the dimensions of the plow moldboard structure using a piezoceramic actuator. To study the effect of vibrations of a piezoceramic actuator on the plow moldboard, numerical simulation was carried out using the COMSOL Multiphysics 3.5 software package.

Fig. 4. Plow moldboard with piezoceramic actuator: 1 – moldboard; 2 – piezoelectric actuator

The COMSOL Piezoelectric Device Interface combines COMSOL Solid Mechanics and Electrostatics module modelling functionality into one piezoelectric material modelling tool. Modelling piezoelectric devices in COMSOL Multiphysics 3.5 is done using the Piezoelectric Effects module. Since the operation of piezoelectric actuators is based

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on the inverse piezoelectric effect, therefore, the Stress-Charge Form mode is selected in the Piezoelectric Effects module [26, 27]. A piezoelectric element is characterized by a relationship between deformation and an electric field, which is determined by material and constitutive ratios [28–31]. Lagrange finite elements with elementary basic functions of the second order Lagrange-Quadratic are used for modelling. The analysis of the piezoelectric actuator in interaction with the plow moldboard is carried out in the Frequency response mode. The computational mesh of finite elements in the “Mesh” item is selected as orthogonalized (Normal). The investigated threedimensional model is represented by a set of elements obtained as a result of constructing a mesh with a tetragonal partition. Direct is used as a solver, in which the numerical SPOOLES method is chosen for solving systems of linear equations with sparse matrices. The boundary conditions for a model of plow moldboard with a piezoceramic actuator in the form of a disk 60 mm in diameter and 5 mm thick are follows: Electric potential of 100 V is applied to the diametrical electrode, and Ground is applied to the electrode on the opposite side. The dimensions of the plow moldboard correspond to the drawing shown in Fig. 4. PZT-5H piezoceramics is used as a material for modelling a piezoceramic moldboard. Copper is used as the material for modelling the metal part of the plow moldboard. The simulation results are shown in Fig. 5. The obtained spectral characteristics (Fig. 5) show the maximum influence of the piezoelectric actuator on the creation of vibrations in the plow moldboard.

Fig. 5. Results of simulation of a vibratory plow based on a piezoelectric actuator

6 Conclusions Thus, a decrease in the friction of the plow with the ground during plowing can be achieved as a result of a decrease in contact in the plow moldboard due to vibrations. The design features of modern models of vibratory plows were analyzed. Their advantages and disadvantages were identified. A method for reducing the friction of the

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cultivation body using ultrasonic vibrations created by a piezoelectric actuator was proposed. The proposed plow design with a vibrating body has a higher vibration frequency and force, smaller dimensions and, as a result, lower cost. Based on the simulation performed in the COMSOL Multiphysics program, the maximum effect of the piezoelectric actuator on the creation of vibrations in the plow moldboard was determined. Proposed and derived formulas for calculating the reduction of traction resistance in a plow moldboard using ultrasonic piezoelectric actuator. The results can be used in the design of vibratory plows. In the future, it is planned to conduct studies with the proposed plow design to determine the reduction in fuel consumption during soil cultivation. Acknowledgements. The research leading to these results was made within the framework of a state budgetary research topic “Development of highly efficient intellectual complex for creation and research of piezoelectric components for instrumentation, medicine and robotics”.

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Ways to Reduce Negative Impacts from the Use of Rapeseed Oil as a Fuel for Diesel Engines Ovchinnikov Evgeniy(B) , Uyutov Sergey, Fedotkin Roman, and Kryuchkov Vitaliy Federal Scientific Agroengineering Center VIM, 1-y Institutsky proezd 5, Moscow 109428, Russian Federation [email protected], [email protected], [email protected], [email protected] Abstract. The study authors conducted tests and further analysis to assess performance characteristics of a tractor diesel engine bifuel system when running on pure rapeseed oil. A test brake bench for up to 154 kW engines was used as a load, with a D-440 four-cylinder diesel engine with indicated efficiency of 68kW and operating time 50-engine-hours manufactured by the Al-tai Motor Plant mounted on it. The research methodology program included evaluating the efficiency of a bifuel system regarding the ways pure rapeseed oil-based fuel affected the lubrication system, the fuel equipment and the cylinder-piston group, as well as studying the process of carbon formation on the working surfaces of the combustion chamber and the atomizer nozzles. During the tests, the engine loading was performed in stepwise 16-h cycles as foreseen in its operation manual. After each of the rapeseed oil test cycles, the engine was disassembled to analyze the condition of the cylinder-piston group parts and the fuel equipment. The results showed that this system allows replacing up to 90% of the diesel fuel in a compression-powered engine with pure rapeseed oil while maintaining its general technical and technoeconomic characteristics. It is noteworthy that equipping the engine with a bifuel system of this sort did not require any significant changes to its design. Besides, with added 0.01–0.02% of nano-composites to rapeseed oil, both the combustion chamber and the atomizer nozzles have been proved to self-clean, which in turn leads to significant reduction of labor costs while enhancing the feasibility of the combustion chamber and the atomizer nozzle components. Keywords: Bifuel system · Carbon formations · Diesel engine · Diesel fuel · Lubrication system · Rapeseed oil

1 Introduction Over the recent years, the use of renewable alternative fuels for internal combustion engines has become increasingly relevant [1–3] due to both the environmental situation on the planet and the fossil fuel prices through-out the world [4, 5]. Diesel fuel is the most common fuel used in agricultural machinery, its main alternative being vegetable oil fuel in pure form as well as in the form of various additives. In fact, one of the first specimens of internal combustion engines worked on vegetable oil-based fuel [6]. The idea of using vegetable oils as a fuel dates back to the end of the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 290–301, 2022. https://doi.org/10.1007/978-3-031-03877-8_26

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XIXth century [7]. Use of vegetable oil-based motor fuels is especially relevant in the light of environmental safety of the engine itself in terms of reducing the concentration of harmful emissions in exhaust gases and efficiency resulting from fuel costs reduction. However, there’s still a number of problems that need to be addressed in regards to achieving higher efficiency - particularly, when using rapeseed oil, it is necessary to ensure that it is supplied to the diesel cylinders in optimal amounts, its combustion is complete, and all probability of it getting into the engine crankcase is excluded [8]. Another necessity lies in preventing the formation of solid film of rapeseed oil on any of the parts of the fuel system, as well as of carbon formations on the working surfaces of the combustion chamber and atomizer nozzles. The latter leads to a decrease in the effective flow area of the nozzle openings, adversely affecting the overall operation of the fuel equipment [9–13]. To solve these problems, the authors propose methods and technical solu-tions for operating a diesel engine using rapeseed oil as the fuel in a bifuel system that allows up to 90% replacement of diesel fuel with alternative fuel, while preserving the engine’s technical characteristics, and leaving com-bustion chambers and atomizer nozzles free of carbon formations.

2 Materials and Methods In the tests represented here, the team used the D-440 engine manufactured by the Altai Motor Plant for agricultural tractors, combines and road-building machinery. The choice of this engine was conditioned by its wide application in self-propelled agricultural machinery in Russia. Its main characteristics are outlined in Table 1. Table 1. D-440 technical description Description

Unit

Specifications

Manufacturer, type

–

Altai Motor Plant D-440, turbocharged, with direct injection

Cylinders, configuration

Nr

4, straight and vertical

Bore, stroke

mm, mm 130, 140

Total displacement

cm3

Volumetric compression ratio –

7430 16:1

Nominal power

kW

68

Nominal engine speed

Rpm

1750

Cold-pressed rapeseed oil and a nano-dispersed powder consisting of silicon dioxide, aluminum trioxide and thermally dispersed acid-intercalated graphite, with particles averaging 14 nm in size at the most, were used as the fuel mixture. The fuel mixture was prepared by adding the nano-dispersed powder to pure rapeseed oil in the amount

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between 0.01% and 0.02% of the total volume of the fuel, with the mixture being heating to a minimum viscosity temperature (80–90 °C) and stirring. The efficiency of rapeseed oil as a fuel was tested on a typical 154 kW GPF 17b brake stand with a load brake manufactured by Elbtalwerk Heidenau GmbH fully equipped for testing internal combustion engines. The authors propose a method to reduce carbon formation in combustion chambers and atomizer nozzles by adding nano-dispersed powder to rapeseed oil. The authors have designed technical documentation for, and further implemented, a method of engine adaptation for bifuel systems with fuel heating. Engine adaptation for using rapeseed oil fuel requires an additional rapeseed oil tank, a second low-pressure line with fuel heating, and an automatic or manual fuel switching system that utilizes electromagnetic valves the high-pressure fuel pump, electrical sensors, and a system control unit. To determine the amount of rapeseed oil getting into the crankcase, bench tests were performed in idle mode at various engine speeds for eight hours. The test modes are shown in Table 2. Table 2. Test modes to determine the amount of rapeseed oil in the crankcase Mode #

Engine speed

Load, %

Time, minutes

1

850

0

15

2

1150

0

15

3

1450

0

15

4

1750

0

15

Modes 1–4 ran 8 times accordingly

Before the tests, we heated the engine and subsequently drained the crankcase oil (in the course of 3 h). Then, the required volume (21 L) of M-10DM SAE 30 mineral oil was poured into the crankcase in accord-ance with the manufacturer’s recommendations, the Altai Motor Plant. After 8 h in idle mode, the crankcase oil was completely drained (also in the course of 3 h). Then, the volume of the drained motor oil was measured, revealing the presence of rapeseed oil that had gotten into the oil sump by the cylinder walls. Analysis of carbon formation in the combustion chamber and the atomizer nozzles when using rapeseed oil fuel was based on 16 h of bench tests performed in cyclic step modes simulating the engine’s normal operat-ing conditions (as shown in Table 3). In the event of operating solely on die-sel fuel, as in 2, 3 and 19, no tests were performed. The atomizer nozzles were weighed on a Sartorius LA 230S laboratory scale with a measurement error of 0.2 mg after having been completely dried in a Memmert UFB 400–500 multi-purpose heating cabinet at a temperature of 105 °C. Carbon formations on the working surfaces of the combustion chamber and pistons were assessed visually.

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Table 3. Test modes to assess carbonization in the combustion chamber and on atomizer nozzles for various types of fuel Step #

Load, %

Nominal rotation frequency, % of nr.s

Duration of the operation in minutes

1. Engine heating (using diesel fuel)

5

ni.s.min

20

2. Taking regulator parameters (using diesel fuel)

0–100

ni.s.max

90

3. Switching to tested fuel 10

ni.s.min

25

4. Taking regulator parameters (using tested fuel)

0–100

ni.s.max

110

5. Mode 1

17,5

50

3

6. Mode 2

60

75

6

7. Mode 3

17,5

50

3

8. Mode 4

80

87,5

6

9. Mode 5

17,5

50

3

10. Mode 6

100

100

9

11. Mode 7

12,5

37,5

3

12. Mode 8

100

75

6

13. Mode 9

12,5

37,5

3

14. Mode 10

100

50

9

15. Mode 11

12,5

37,5

3

16. Mode 12

100

100

6

Total, on Modes 5–16

60

17. Stopping the engine to weigh the atomizer nozzles

60

18. Heating the engine using diesel fuel

20

Modes 5–16 repeated eleven times 19. Taking regulator parameters

0–100

Maximal idle mode frequency, ni.s.max

110

20. Switching to diesel fuel

10

Minimal idle mode frequency, ni.s.min

25

21. Taking regulator parameters (running on diesel fuel)

0–100

Maximal idle mode frequency, ni.s.max

90

(continued)

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O. Evgeniy et al. Table 3. (continued)

Step #

Load, %

Nominal rotation frequency, % of nr.s

Duration of the operation in minutes

22. Engine stoppage

0

Minimal idle mode frequency, ni.s.min

10

Total, running on:

Rapeseed oil

960

Diesel fuel

240

3 Results 3.1 Bench Tests to Determine the Amount of Rapeseed Oil in the Crankcase The measurement of the volume of the drained oil revealed a total 4.21 L of rapeseed oil in the crankcase (disregarding the crankcase oil fumes). In the idle mode, part of unburned rapeseed oil got into the discharge manifold. Thus, we were able to confirm our hypothesis that when using rapeseed oil in a diesel engine, due to incomplete combustion of the fuel charge, the rapeseed oil gets into the crankcase by the walls of the cylinder. This occurs because the self-ignition temperature of rapeseed oil is 320 °C which is 50 °C higher than that of diesel fuel. To solve this problem, we designed an automated system that would switch fuels from rapeseed to diesel and vice versa. The automated system switched to diesel fuel with an unheated engine and a less than 20% load, and, when the engine heated to 75 °C and the load superseded 20%, to rapeseed oil, which was observed when performing idle mode engine tests. After the tests had been completed, the crankcase oil was drained within 3 h. The volume of the drained oil after 56 h of tests constituted 20.39 L. According to the burning oil consumption rate of 0.84 L claimed by the manufacturer, the resulting volume of the drained oil should have constituted 20.16 L. Thus, after 56 test hours, we had about 0.23 ml of rapeseed oil in the crankcase. 3.2 Data Fusion Simulation Experiment Figure 1 shows the nozzles of the engine (with cylinder numbering) when working on pure rapeseed oil (a) and when working on rapeseed oil with a nano-dispersed additive (b) in a concentration of 0.01–0.02%. The tests continued for sixteen hours in cyclic step-by-step modes simulating the engine’s operating conditions. As can be seen in Fig. 1, the nano-dispersed powder causes carbon formations to peel from the working surfaces of the nozzles.

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a

b Fig. 1. Carbon formations on nozzles following sixteen hour tests: a - pure rapeseed oil; b rapeseed oil with a nano-dispersed additive.

Figure 2 shows carbon formations on the ignition side of the combustion chamber when using pure rapeseed oil; when using rapeseed oil with a nano-dispersed additive, carbon formations are practically absent. Valve plates are also clean. Insignificant carbonization on the head of cylinder 4 can be accounted for by insufficient tightness of the gasket under the nozzle.

a

b Fig. 2. D-440 diesel engine cylinder head following the test: a - using pure rapeseed oil without nano-dispersed additives; b - using rapeseed oil with nano-dispersed additives

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Figure 3 shows the puncher surface with soot traces after working on pure rapeseed oil (a), as well as after working on rapeseed oil using nano-dispersed powder (b). Figure 3 (b) shows an insignificant presence of soot. When assessing it, we found that the piston rings had retained their elasticity and mobility in the annular grooves.

a

b Fig. 3. The D-440 engine piston after working on pure rapeseed oil: a - without nano-dispersed additives; b - with nano-dispersed additives

Table 4 presents the results of assessing carbon formations on atomizer nozzles with the D-440 engine using diesel fuel, pure rapeseed oil and rapeseed oil with a nano-dispersed additive. Table 4. Atomizer nozzles’ weighing results Fuel

Weighing conditions

Weight (grams) 1

Diesel fuel 100%

Test time, in hours

Cylinder # 2

3

4

Nozzle weight prior testing (in grams)

118,40

115,06

117,47

115,35

0

Nozzle weight following the test (in grams)

118,64

115,46

117,70

115,63

16

(continued)

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Table 4. (continued) Fuel

Weighing conditions

Weight (grams) Cylinder # 1

Rapeseed oil 100%

Rapeseed oil 100%, with nano-dispersed additives

2

Soot mass (in grams)

0,25

Average soot mass, average (in grams)

0,26

Atomizer nozzles, mass before testing (in grams)

Test time, in hours

118,19

3

0,27

4 0,23

0,27

16 16

115,88

117,43

113,15

0

Atomizer nozzles, mass after the test (in grams)

118,65

116,60

118,03

113,87

16

Soot mass, in grams

0,45

0,72

0,60

0,72

16

Average soot mass, in grams, after the test

0,62

16

118,25

114,87

117,32

112,65

0

Atomizer nozzle weight after the test, in grams

118,54

115,19

117,62

112,96

16

Soot mass (in grams)

0,29

0,32

0,30

0,31

16

Average soot mass, in grams

0,30

16

The average amount of soot on the atomizer nozzles when operating on diesel fuel was 0.26 g, on pure rapeseed oil - 0.62 g, on rapeseed oil with the nano-dispersed additive - 0.30 g. As can be seen from the results, when using nano-dispersed additives in rapeseed oil, the resulting amount of soot on the nozzles will be similar to that resulting from using diesel fuel. Without nano-dispersed additives in rapeseed oil, the amount of soot increases by 2 times.

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4 Discussion We started the tests with determining the amount of rapeseed oil getting into the engine’s crankcase. For this purpose, we conducted an eight-hour idle mode test at various engine speeds ranging between 850 and 1750 min. Having measured the amount of oil getting into the crankcase, we changed the lubricating oil and began testing our automated system that switched between fuels: from diesel to rapeseed oil and vice versa. Once the engine had been started and heated, the system began receiving signals from sensors mounted on the engine, namely, fuel temperature sensors, coolant temperature, and the position of the rail of the high-pressure fuel pump. With all conditions in place (namely: minimum engine temperature of 75 °C and high-pressure fuel pump rail position corresponding to at least 20% of the engine load) the control module of the automated system sends signals to an addi-tional fuel pump on the rapeseed oil fuel supply line and solenoid valves of a normally closed type, restricting and opening the supply of each type of fuel. A diagram of the two fuel systems is shown in Fig. 4. The proposed automated fuel system adapted for operating on rapeseed oil, is dualfuel, and comprised of two tanks and two lines of fuel supply equipment that delivers fuel from the tank to the high pressure fuel pump. The line designed for the supply of

Fig. 4. Dual-fuel engine system for diesel fuel and rapeseed oil fuel: 1 - rapeseed oil tank; 2 - heater; 3 - coarse rapeseed oil filter; 4 - fuel priming pump; 5 - fine rapeseed oil filter; 6* three-way fuel-supply solenoid valve; 7 - high pressure fuel pump; 8 - nozzle; 9 - three-way fuel drain solenoid valve (when using three-way valves); 10 - pressure reduction valve (2 bar); 11 diesel fuel tank; 12 - coarse diesel fuel filter; 13 - electric fuel priming pump; 14 - fine diesel fuel filter; 15 - safety valve (3 bar); 16 - fuel temperature sensor; 17 - fuel pressure sensor; 18 - temperature sensor coolant; 19 - high pressure fuel pump lath position sensor; 20 - switch; 21 - control module; 22 - tee connector; 23 - normally-open solenoid valve (when using two-way valves); 24 - normally-closed solenoid valve (when using two-way valves); 25 - valve unit (when using two-way valves); 26 - indicator light; 27 - engine cooling system; 28 - air filter

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diesel fuel is standard with respect to the type and model of the engine, except a smaller tank holding 10–30% of the fuel supply required for the equipment to operate. Normally, such lines consist of a diesel tank, a coarse filter, a fuel priming pump, a fine filter, and a high pressure fuel pump. To supply rapeseed oil, the standard fuel supply equipment line is duplicated, with an additional fine filter and two heaters in the fuel intake zone in the tank and fine filters integrated into it. The rapeseed oil tank that holds 70–90% of the fuel supply required for the equipment to operate. Thus, the oil line is comprised of a tank, a heater, a coarse filter, a fuel priming pump, and two fine filters. The two lines are connected to a highpressure fuel pump via an electromagnetic valve. The drain tubes are connected to the electromagnetic valve and then, depending on the type of the fuel used, into one of the tanks. Fuel switching is performed automatically by a module controlling the solenoid valves and the electric fuel pump, receiving data from the fuel temperature sensors, the coolant temperature sensor, the fuel pressure sensor and the fuel supply sensor. Manual fuel switching is foreseen for forced operation running on rapeseed oil or on diesel fuel. The type of fuel in use is displayed on the dashboard. A filter clogging indicator is foreseen as well. During operation, the tractor runs on diesel fuel in the following modes: in unheated engine mode ( 0 ˜ n be Fréchet differentiable on a set and L > 0, respectively. Let operators T˜ n and Q ˜ ˜ ˜ ˜ n ⊂ Xn , and let their derivatives T n (˜un ) and Q n (˜un ) satisfy the Lipschitz condition with constants K˜ > 0 and L˜ > 0, respectively (n ≥ N ). In addition, let the proximity conditions (5)–(7) be satisfied for all n ≥ N . Assume that there exists the inverse operator (0) [T (u)]−1 such that ||[T (u)]−1 || ≤ b and ||[Q (u)]−1 || ≤ ν, u ∈ S(uN , R), at that σ ≡  2 ˜ n there exist the inverse b |μ|ν(K + |μ|L) (1 − b|μ|ν) < 1, as well as for all u˜ n ∈  −1 −1 ˜ ˜ ˜ operators [T n (˜un )] such that ||[T n (˜un )] Q n (˜un )|| ≤ ν˜ n , ν˜ n → 0 as n → ∞. Let ˜ N be a solution to the equation T˜ N u˜ N = f˜N (i.e. A˜ N u˜ (0) (0) ≡ an element u˜ N(0) ∈  N (0) (0) ˜ N u˜ (0) || ˜ ≤ ζ˜ (0) and the parameter μ T˜ N u˜ N = f˜N ). If u˜ N satisfies the condition ||Q N XN N value is such that ˜ N ≤ R; |μ|bν < 1, |μ|˜νn < 1 (n ≥ N ); r˜N = b˜ N |μ|ζ˜N(0) G    (0) ˜ b˜ N ζ˜ (0) + 2ν˜ N (1 − |μ|˜νN ) < 2, h˜ N = b˜ N |μ|(K˜ + |μ|L) N ˜N where G

=

H˜ N +

∞  m=N

(h˜ 0N /2)Sm < 2H˜ N , HN

=

1/(1 − h˜ 0N /2), sm

=

 (kn − 1), b˜ N = b/(1 − bρ˜N − σ ), ρ˜N = α˜ 1,N + β˜ 1,N +|μ| α˜ 2,N + β˜ 2,N + n=N  ˜ νN /(1 − |μ|˜νN ) , then Eq. (3) has a solution u∗ ≡ u∗ (μ) in the ball (K˜ + |μ|L)˜ S(uN(0) , r˜N ) ⊂ X of radius r˜N centered at the point uN(0) = −1 ˜ N(0) , and the process N u m 

Combined Approach to Solving the Neumann Problem

321

(k )

of successive approximations {−1 ˜ n n (μ)}∞ n u n=N defined by formulas (9) converges to u∗ with the error estimate  (0) (0) ˜ n(kn ) (μ) − u∗ ||X ≤ b˜ N |μ|ζ˜N V˜ n (h˜ N 2)Sn , n ≥ N , ||−1 n u where V˜ n = H˜ N +

∞  m=n+1

(0)

(h˜ N



2)Sm −Sn < 2H˜ N .

The proof of this theorem is based on the results of [19]. 2.2 Problem Statement Let the equation



Lu(μ) ≡ u + μ

∂ ∂ (pF) + (qF) = −f (x, y), ∂x ∂y

(x, y) ∈ G

(10)

be given in the square G = G ∪ = {(x, y) : 0 ≤ x, y ≤ π } under the second kind boundary condition  ∂u  = 0, (11) ∂ n (x, y)∈ where is the Laplace differential operator, μ is a numerical parameter; F ≡ F(x, y, u, p, q) and f (x, y) are given functions for (x, y) ∈ G; u ≡ u(μ) = u(x, y; μ) is ∂u a sought function on G, p = ∂u  is the outer normal to the boundary . Let ∂x , q = ∂y ; n F(x, y, u, p, q) be continuous and bounded ˜ with the second order partial derivatives in its domain, and let f (x, y) be such that f (x, y) dxdy = 0. Note that the well-known G

minimal surface equation and equations arising in plastic torsion problems have the form (10) [15]. The direct expansion of the expression on the left-hand side of Eq. (10) gives   2 2 ˜ y, u, p, q) ∂ u + μ B(x, ˜ y, u, p, q) ∂ u Lu(μ) ≡ 1 + μ A(x, 2 ∂x ∂x∂y   ∂ 2u ˜ ˜ + D(x, y, u, p, q), (x, y) ∈ G. + 1 + μC(x, y, u, p, q) ∂y2 where ∂F ∂F ∂F ∂F ˜ = ∂F p + ∂F q + ∂F (p2 + q2 ). p, B˜ = p+ q, C˜ = F + q, D A˜ = F + ∂p ∂q ∂p ∂q ∂x ∂y ∂u Assume that the inequality B˜ 2 − 4 A˜ C˜ < 0 holds for all (x, y) ∈ G, that is, L is a quasilinear elliptic differential operator. Let us rewrite Eq. (10) in the operator form (3): Au(μ) ≡ Tu + μ Qu = f , where

∂ ∂ Au = −Lu, Tu = − u, Qu = − (pF) + (qF) , (x, y) ∈ G. (12) ∂x ∂y

322

L. Hart ◦

We will consider Eq. (3) in the space X = L(G) consisting of functions u(x, y) ∈ 2 ˜ L2 (G), which satisfy the boundary condition (11) and the condition u(x, y) dxdy = 0, G ˜ with the norm ||u||X = u2 (x, y) dxdy, and we will assume that the domain D(A) ⊂ G

◦

X of A is the set of functions u(x, y) ∈ L(G) having summable generalized partial 2

derivatives up to the second order inclusive on G. Let us investigate the question of the existence, location and approximate finding of a solution u∗ ≡ u∗ (x, y; μ) to problem (10), (11) (if an approximate solution u(0) (x, y; 0), (x, y) ∈ G is already known) using a combined approach based on the finite difference method and a Newton-like method in accordance with the projection-iteration principle considered in Sect. 2.1. 2.3 FD Approximation of the Differential Model The finite difference method is the most commonly used numerical method for solving boundary value problems for elliptic differential equations due to its versatility and efficiency. The versatility lies in the possibility of using this method for both linear and nonlinear boundary value problems, problems of different dimensions, and for domains of complex (non-canonical) shape [20–22]. We approximate the differential Eq. (10) (or, which is the same, (3), (12)) with a sequence of finite-difference equations n uij + μ n uij = −f (xi , yj ),

(xi , yj ) ∈ ωn , n = 1, 2, ...,

(13)

which are specified on a set of rectangular uniform refining grids (meaning that a finer grid is overlaid on the coarse one): ωn = ωn ∪ γn = {(xi , yj ) ∈ G :  (n) (n) h1 = π N1 ,

(n)

(n)

xi = ih1 , i = 0, N1 ;  (n) (n) h2 = π N2 ,

(n)

(n)

yj = jh2 , j = 0, N2 }, (n)

(n)

hn = (h1 , h2 );

N1(n+1) ≥ N1(n) , N2(n+1) ≥ N2(n) , n = 1, 2, ...;

N1(1) > 0, N2(1) > 0.

We consider the system of finite-difference Eqs. (13) for each n = 1, 2, ... in the ◦ space X˜ n = Hhn consisting of grid functions u˜ n = {uij }, uij ≈ u(xi , yj ), which are defined on the grid ωn and satisfy the conditions  Bn uij (x ,y )∈γ = 0, (14) i

j

n

Combined Approach to Solving the Neumann Problem (n)

and

(n)

N1−1 N2−1 i=0

j=0

(n) uij h(n) un ||X˜ n 1 h2 = 0, with the norm ||˜

323

 (n) N1−1 N2(n) −1 2 (n) (n) =  uij h1 h2 . i=0

j=0

Here Bn is the difference analogue of the operator of differentiation along the normal in (11). Following the notation of [20], for each n = 1, 2, ... we can write: n uij = (uij )xx + (uij )yy , (xi , yj ) ∈ ωn ; n uij =

(15)

 1  ˜ ˜ i , yj , uij , (uij )x , (uij )y ) (uij )xx A(xi , yj , uij , (uij )x , (uij )y ) + A(x 2   ˜ i , yj , uij , (uij )x , (uij )y ) (uij )xy ˜ i , yj , uij , (uij )x , (uij )y ) + B(x + B(x   ˜ i , yj , uij , (uij )x , (uij )y ) + C(x ˜ i , yj , uij , (uij )x , (uij )y ) (uij )yy + C(x   ˜ i , yj , uij , (uij )x , (uij )y ) , (xi , yj ) ∈ ωn ; ˜ i , yj , uij , (uij )x , (uij )y ) + D(x + D(x

⎧  (n) (n) ⎪ (u − 4u + 3u ) (2h2 ) = 0, 0 ≤ i ≤ N1 ; ⎪ i2 i1 i0 ⎪ ⎪  ⎪ ⎪ ⎨ (u (n) − 4u (n) + 3u (n) ) (2h(n) ) = 0, 0 ≤ i ≤ N (n) ; 2 1 i,N2 −2 i,N2  −1 i,N2 Bn uij = (n) ⎪ 0 < j < N2(n) ; (u2j − 4u1j + 3u0j ) (2h1 ) = 0, ⎪ ⎪ ⎪  ⎪ ⎪ (n) (n) ⎩ (u (n) − 4uN (n) −1,j + 3uN (n) ,j ) (2h1 ) = 0, 0 < j < N2 , N −2,j 1

where (uij )x =

ui+1,j −uij (n)

h1

1

, (uij )x =

1

uij −ui−1,j (n)

h1

, (uij )y =

ui,j+1 −uij (n)

h2

, (uij )y =

uij −ui,j−1 (n)

h2

. As

shown in [23], the finite-difference scheme (13), (14) in the general case has the first ◦

order of approximation on a solution of problem (10), (11). Subspaces Xn ⊂ L2 (G), ◦ which are isomorphic to the spaces X˜ n = Hhn , can be defined as the spaces of the piecewise constant functions (n)

(n)

N1 −1 N2 −1

un (x, y) =





i=0

j=0

(n)

uij χij (x, y), (x, y) ∈ G,

(16)

(n)

where χij (x, y) is the characteristic function of the cell (n)

Gij = {(x, y) ∈ G : xi ≤ x < xi+1 , yj ≤ y < yj+1 } ⊂ ωn . (n)

Function (16) is obviously equal to uij at all points of the cell Gij . It is easy to see that ||un ||X = ||˜un || ˜ , that is, the spaces Xn and X˜ n are isometric (n = 1, 2, ...). Xn

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2.4 Projection-Iteration Implementation of the Newton-Like Method and Its Modifications To solve the quasilinear elliptic boundary value problem (10), (11), depending on a numerical parameter, under the formulated assumptions about the problem initial data, projection-iteration processes of the form (8) and (9) can be used. It is easy to show based on the theorem in Sect. 2.1 that the finite difference method for solving problem (10), (11) is a method of projection type, and to construct its projection-iteration modifications. Following formulas (8), we apply Newton’s method to solving each of the “ap(k) (k) proximate” problems (13), (14), constructing only a few approximations u˜ n = {uij }, k = 1, 2, ..., kn , and take the last of them, using piecewise linear interpolation (16), as the initial approximation for the next “approximate” problem:   (k+1) (k) (k) (k) uij (μ) = uij (μ) − [n + μn (uij )]−1 (n + μn )uij (μ) + f (xi , yj ) , (17) (xi , yj ) ∈ ωn ,k = 0, 1, ..., kn − 1;   (k) Bn uij (μ)

(0)

(xi ,yj )∈γn (n)

uij(0) (μ)

(18)

(n)

N1 −1 N2 −1

=

(0)

= 0, k = 0, 1, ..., kn ; uij (μ) = uij , (xi , yj ) ∈ ω1 ;





l=0

m=0

(kn ) (n) ulm (μ) χlm (xi , yj ), (xi , yj ) ∈ ωn+1 ,n = 1, 2, ...

(19)

The feasibility and convergence of the projection-iteration process (17)–(19) for problem (10), (11) are substantiated in [23]. In particular, since a solution to problem (10), (11) exists for μ = 0, then it can be guaranteed for all sufficiently small values of μ specified in [23]. Thus, each step of the projection-iteration process (17)–(19) is reduced to solving the linear finite-difference elliptic problem     (k) (k+1) (k) (k) (μ) = μ n (uij ) − n uij (μ) − f (xi , yj ), (20) n + μn (uij ) uij (xi , yj ) ∈ ωn ,k = 0, 1, ..., kn − 1 (0)

(0)

◦

under conditions (18), (19), where the initial approximation u˜ 1 = {uij } ∈ Hh1 at the first step (n = 1) is a solution to the corresponding finite-difference problem (13), (14)  with μ = 0: 1 uij = −f (xi , yj ), (xi , yj ) ∈ ω1 ; B1 uij (x ,y )∈γ = 0. 1 i j Note that although Newton’s method has the quadratic convergence rate, the implementation of scheme (20), (18), (19), which implies the construction of the operator (k) n + μn (uij ) and its inversion at each iteration, is not always successful in practice and requires significant expenditure of labor and time. It is much easier to implement process (9) based on the Newton-like method, which at each step reduces to solving the finite-difference problem for the Poisson equation   (k+1) (k) (μ) = − μ n uij (μ) + f (xi , yj ) , (xi , yj ) ∈ ωn ,k = 0, 1, ..., kn − 1 (21) n uij

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under conditions (18), (19). In this case, similarly to [23], the existence and location of a solution u∗ ≡ u∗ (x, y; μ) to the original boundary value problem (10), (11), as well as the convergence of the sequence {un(kn ) (x, y; μ)}∞ n=1 , (x, y) ∈ G of piecewise linear interpolants of the form (16) are established using the theorem in Sect. 2.1. Note that the numbers kn (n = 1, 2, ...) in the projection-iteration processes (20) and (21) under conditions (18), (19) can be chosen in different ways described, for example, in [16, 18, 19, 24, 25]. To analyze the effectiveness of the proposed projection-iteration schemes, their software implementation and testing were performed using the example of solving several model problems of the form (10), (11), one of which had the form: 2 2

∂u ∂u 2 = 4(x2 + y2 + 1), (x, y) ∈ G; + 2u Lu ≡ u + μ u u + 2u ∂x ∂y     ∂u  ∂u  ∂u  ∂u  = = −2, = = 2, ∂x (−1,y)∈ ∂y (x,−1)∈ ∂x (1,y)∈ ∂y (x,1)∈  G = G ∪ = {(x, y) : −1 ≤ x, y ≤ 1 }, μ = 1 3. When implementing projection-iteration algorithm (9), the set of nested grids (1) (1) ωhn (n = 1, 2, ..., m) was determined by the order N1 = N2 = 5 of the primary partition of the square G, and to obtain an approximate solution to the problem with the accuracy ε = 10−4 , it turned out to be composed of m = 5 grids with the last (m) (m) discretization order N1 = N2 = 80. The number kn of approximations at the n-th step of the algorithm was determined as the smallest integer k satisfying the inequality ||˜un(0) − u˜ n(kn ) ||Hhn < εn , in which εn > 0 was chosen in accordance with the order of the grid approximation of the original boundary value problem; the criterion for the end of the projection-iteration process was the condition εn ≤ ε. In particular, with the (0) (0) initial approximation u˜ 1 = {uij } ∈ Hh1 , which was specified at the first step of the projection-iterative algorithm as the solution to the corresponding Neumann problem for the Poisson equation (at μ = 0), an approximate solution to the original problem was m  kn = 2 + 3 + 4 + 3 + 4 = 16 iterations; the counting time was 11.48 s; obtained in n=1

for the norm of error, a value of 0.00019 was obtained. When solving the same boundary value problem by the usual FD method, using the Newton-like method on one last grid with N1 = N2 = 80, the calculation accuracy ε = 10−4 and the indicated initial approximation, an approximate solution to the problem was found in 28 iterations, which took 80.27 s; for the norm of error, a value of 0.00249 was obtained. Graphic images of the obtained approximate solutions for this model problem are shown in Fig. 1, 2.

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Fig. 1. Approximate solution of a model problem using the projection-iteration method

Fig. 2. Approximate solution of the model problem using the conventional FD method

3 Summary and Conclusion The paper is devoted to the application of projection-iteration methods to solving the second boundary value problem for quasilinear parametric equations of elliptic type, which are of great applied and scientific importance. As is known, iterative methods, despite the exponential convergence rate and simple computational schemes, have a limited area of application. In turn, projection methods, which have a wide range of applications, are characterized by a power-law convergence rate (sometimes rather slow) and computational instability. Therefore, the effective synthesis of projection and iterative methods in order to eliminate their inherent disadvantages, as well as the theoretical substantiation and analysis of the corresponding numerical algorithms, constitute an important direction in the development of the modern theory of algorithms and computations.

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In this paper, to solve a quasilinear second-order elliptic equation, depending on a numerical parameter, under Neumann boundary conditions, an effective computational scheme of the projection-iteration method is proposed based on the finite-difference method and a Newton-like method (with the replacement of the inverse operator to the derivative by an operator close to it at each point of the process). The results of study showed that the application of the Newton-like method not to the original problem, but to simpler approximate (FD) problems allows the simplest construction of a sequence of approximations to a solution. Moreover, the problem of choosing an initial approximation is greatly simplified, since the verification of the sufficient conditions imposed on the choice of an initial approximation should be carried out only for the first approximate (FD) problem, which is the simplest. This ensures the feasibility of similar conditions for the consequent approximate problems. This property of the projection-iteration method is extremely important, since the choice of an appropriate initial approximation is one of the most difficult moments when solving nonlinear problems by iterative methods. In addition, the practical implementation of the proposed approach shows that projection-iteration computational schemes have certain advantages over projection type conventional algorithms both in the quality of obtained approximate solutions and in the computational costs, a significant part of which is associated with solving approximate problems of low dimension. Along with the fact that the software implementation of algorithms of both types requires approximately the same computing power from the computer (since in the projection-iterative algorithm only repeatedly uses the classical one), the estimation of the number of necessary arithmetic operations and computation time confirms the effectiveness of the projection-iteration approach.

References 1. Lubyshev, V.: Precise range of the existence of positive solutions of a nonlinear, indefinite in sign Neumann problem. Commun. Pure Appl. Anal. 8, 999–1018 (2009) 2. Kuzenkov O., et al.: Mathematical model of dynamics of homomorphic objects. In: CEUR Workshop Proceedings, vol. 2516, pp. 190–205 (2019) 3. Tryputen, M., Kuznetsov, V., Kuznetsova, A., Tryputen, M., Kuznetsova, Y., Serdiuk, T.: Improving the reliability of simulating the operation of an induction motor in solving the technical and economic problem. Adv. Intell. Syst. Comput. 1247, 143–152 (2021) 4. Kiseleva, E.M., Kadochnikova, Ya.E.: Solving a continuous single-product problem of optimal partitioning with additional conditions. J. Autom. Inf. Sci. 41(7), 48–63 (2009) 5. Hart, E.L., Hart, L.L.: Application of the projection-iterative method to the study of the stressstrain state of a plate with a hole. Visnik Donetsk Univ.: Ser. A. Nat. Sci. 2, 54–58 (2002). (in Russian) 6. Li, Y., Wang, X.: Existence of solution for a quasilinear elliptic Neumann problem involving multiple critical exponents. Boundary Value Probl. 2020(1), 1–16 (2020). https://doi.org/10. 1186/s13661-020-01353-0 7. Wu, R., Li, J.: Boundary value problem for a fully nonlinear elliptic equation. J. Phys. Conf. Ser. 1978(012028) (2021) 8. Hart, L.L., Dovgay, P.O., Selishchev, V.L.: Grid algorithms for solving a problem of optimal control of an elliptic system. Probl. Appl. Math. Math. Model. 17, 42–53 (2017). (in Ukrainian)

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9. Kiseleva, E.M.: The emergence and formation of the theory of optimal set partitioning for sets of the n-dimensional Euclidean space. Theory and application. J. Autom. Inf. Sci. 50(9), 1–24 (2018) 10. Tryputen, N., Kuznetsov, V., Kuznetsova, Y.: About the possibility of researching the optimal automatic control system on a physical model of a thermal object. In: IEEE 2nd Ukraine Conference on Electrical and Computer Engineering, UKRCON 2019 - Proceedings, (8879830), pp. 1244–1248 (2019) 11. Tryputen, M., et al.: One approach to quasi-optimal control of direct current motor. In: IEEE 5th International Conference Actual Problems of Unmanned Aerial Vehicles Developments, APUAVD 2019 - Proceedings, pp. 190–193 (2019) 12. Wang, Q., Fu, F.: Variational iteration method for solving differential equations with piecewise constant arguments. Int. J. Eng. Manuf. 2(2), 36–43 (2012). https://doi.org/10.5815/ijem. 2012.02.06 13. Falade, K.I., Tiamiyu, A.T.: Numerical solution of partial differential equations with fractional variable coefficients using new iterative method. Int. J. Math. Sci. Comput. 6(3), 12–21 (2020). https://doi.org/10.5815/ijmsc.2020.03.02 14. Islam, N.: Concepts of Bezier polynomials and its application in odd higher order non-linear boundary value problems by Galerkin WRM. Int. J. Math. Sci. Comput. 7(1), 11–19 (2021). https://doi.org/10.5815/ijmsc.2021.01.02 15. Faragó, I., Karatson, J.: Numerical Solution of Nonlinear Elliptic Problems via Preconditioning Operators. Theory and Applications. Nova Science Pub Inc., UK (2002) 16. Hart, L.L.: Projection-iteration methods for solving operator equations and infinitedimensional optimization problems, thesis … Doctor’s degree in phys.-math. sciences, 01.05.01, Ministry of education and science of Ukraine, Dnipro, DNU (2016). (in Ukrainian) 17. Kantorovich, L.V., Akilov, G.P.: Functional Analysis, 2nd edn. Elsevier (1982) 18. Hart, L.L.: Projection-Iteration realization of a Newton-like method for solving nonlinear operator equations. J. Optim. Diff. Eqn. Appl. 27(1), 58–68 (2019) 19. Hart, L.L.: Combined approach to solving nonlinear operator equations based on a Newtonlike method. In: Recent Studies in Mathematics and Its Applications, pp. 73–103. IKSAD Publishing House, Ankara (2021) 20. Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker Inc., New York (2001) 21. Rodrigues, T.N.: An implementation of the finite differences method for the two-dimensional rectangular cooling fin problem. Int. J. Inf. Technol. Comput. Science (IJITCS), 11(8), 1–8 (2019). https://doi.org/10.5815/ijitcs.2019.08.01 22. Kumar, V., Sen, S., Roy, S.S., Das, S.K., Shome, S.N.: Inverse kinematics of redundant manipulator using interval Newton method. Int. J. Eng. Manuf. (IJEM) 5(2), 19–29 (2015). https://doi.org/10.5815/ijem.2015.02.03 23. Hart, L.L.: Substantiation of the projection-iteration approach to solving the Neumann problem for a quasilinear elliptic equation with a parameter. Probl. Appl. Math. Math. Model. 21, 34–50 (2021). (in Ukrainian) 24. Hart, L.L.: The application of projection-iteration methods to solving optimal control problems for systems of ordinary differential equations. Hamburger Beiträge zur Angewandten Mathematik. Institut für Angewandten Mathematik der Universität Hamburg, Reihe A (152), 1–17 (2000) 25. Hart, L.L.: Calculating the optimum two-link robot arm with respect to movement time. J. Math. Sci. 107(6), 4458–4463 (2001)

Influence of Hadamard Matrices Canonicity on Image Processing Khrystyna Kulchytska(B) , Mariia Semeniv, Bohdan Kovalskyi, Nadiya Pysanchyn, and Zoryana Selmenska Ukrainian Academy of Printing, Lviv, Ukraine [email protected]

Abstract. The Hadamard matrices and Hadamard transform are widely used in different scientific disciplines and technologies, such as communication systems, signal and image processing. In this paper, we propose an image processing method using Hadamard matrices for the encryption. In addition, we have used three different types of Hadamard matrices that are differ in the number of negative and positive elements. We investigate the influence of the structure of Hadamard matrices of canonical, semicanonical and noncanonical type on the quality of restored images. An application for image processing using a new method has been developed for research. Based on experiments, we show that the result of encrypting images with a noncanonical Hadamard matrix is visually different from the other two types. We discussed Peak Signal to Noise Ratio (PSNR) values, color differences and histograms of brightness of restored images as visual quality metrics. The PSNR values of the processed images with a noncanonical Hadamard matrix exceed ones with other two types of Hadamard matrix. The calculation of brightness differences in model CIE Lab has been performed. The obtained histograms show that the quality of restored images depends on tone range of the original images. Experimental results confirm outperforms of using a noncanonical Hadamard matrix for image processing, in particular encryption. Keywords: Hadamard matrices · Encryption · Image processing · Restored image · Application · Image noise

1 Introduction The Hadamard matrix and Hadamard transform are fundamental problem-solving tools. They are used in communication systems, signal and image processing (signal representation, coding, filtering, recognition, and watermarking), and digital logic (Boolean function analysis and synthesis, and fault-tolerant system design). The Hadamard matrix and Hadamard transform are a constituent part of modern information technology. In communication, the most important applications include error-correcting codes, spreading sequences, and cryptography [1]. With the rise of digital computer technology, one can notice the rise in interest towards studying the unique properties of orthogonal Hadamard matrices, their systematization, and searching for new areas of practical use. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 329–338, 2022. https://doi.org/10.1007/978-3-031-03877-8_29

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Discrete orthogonal Walsh-Hadamard transformation is constructed using Hadamard matrices as a basis. It is widely used for digital image processing, discrete signal and image spectral analysis, cryptography. The concept of coding is based on the principle of global substitution of the graphic image by the ordered nonperiodic structures, constructed using orthogonal Hadamard matrices as a basis, without any possibility of decoding the image with one key.

2 Related Research The compression of images using Hadamard matrices was studied in [2]. In [3], encoding and decoding are performed with and without additional noise. Some modifications were proposed that can be used for any type of image, but the greatest benefits are achieved when using images that clearly distinguish the contours. The discrete orthogonal Walsh-Hadamard transformation was studied in [4, 5]. Image encryption algorithms based on chaotic pixel permutation have also been developed [6]. In [7], the simulation results show that higher quality compression can be achieved for images using Discrete Rajan Transform, which is a variant of Hadamard Transform in comparison with other popular transforms like Discrete Cosine Transform, and Discrete Wavelet Transform. Multiple-image encryption method based on Hadamard basis patterns and RSA public key cryptography has been proposed in [8]. This method solves the problem of low quality of traditional random illumination patterns and increases the security of the system [8]. This paper proposes an encryption method based on encoding and spreading techniques with Hadamard code applied to color image. The color image to be encrypted is first separated into three color channels: red (R), green (G), and blue (B). Numerical simulations have been demonstrated that the proposed scheme has considerably high security level and certain robustness against data loss [9]. On balance, the considered scientific works conclude that Hadamard matrices and orthogonal Hadamard transform are often used for image encryption and provide minimal information loss during recovery. The classification of the whole set of all orthogonal Hadamard matrices with dimension 4 × 4 was performed in paper [10]. It was established that 384 matrices are belonging to six different classes. Each class of similar Hadamard matrices, which is characterized by a spectrum of eigenvalues, contains a different number of matrices of three types – canonical, noncanonical, and semicanonical. This division of matrices into types gives us rise to bring about to determine whether the type of Hadamard matrix affects the results of image processing, in particular recovery after encryption. The research aims are to investigate the influence of the structure of Hadamard matrices of canonical, semicanonical and noncanonical type on the quality of restored images. Therefore, it has to be solved the following tasks: 1. Developing the image processing method using Hadamard matrices for the encryption. 2. Implementation an application for image processing with three types of Hadamard matrices: canonical, noncanonical, and semicanonical.

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3. Investigation the influence of the structure of Hadamard matrices of canonical, semicanonical and noncanonical type on the quality of restored images. 4. Evaluation the quality of the restored image compared to the original.

3 Theoretical Foundations of the Study The Hadamard matrix H is a square matrix of size N × N. It is composed of the numbers 1 and − 1, which columns are orthogonal. The Hadamard matrix of dimension 4 × 4 is determined by the Kronecker product [10, 11] ⎡ ⎤ 1 1 1 1   1 ⎢ 1 −1 1 −1 ⎥ 1 H2 H2 ⎥ = ⎢ (1) H4 = √ H −H 2 ⎣ 1 1 −1 −1 ⎦ 2 2 2 1 −1 −1 1 where H 2 – the minimum Hadamard matrix of dimension 2 × 2:   1 1 1 H2 = √ 2 1 −1

(2)

Rule (1) can be used to construct Hadamard matrices of higher dimensions N × N, where N = 2n . For any Hadamard matrix, the product of H N is HN · HN T = HN · HN −1 = I

(3)

where I – is an identity matrix. Therefore, Hadamard matrices H N belong to the class of orthogonal matrices, the transposed of which H N T is also an inverse Hadamard matrix HN –1 . Hadamard matrices H are characterized by a fundamental property: with arbitrary row or column permutations of the matrix, the newly formed Hadamard matrices H new remain orthogonal. The property of orthogonality of Hadamard matrices does not change when all elements hij of the i-th row or j-th column of the matrix (1) are multiplied by −1. For an analytical explanation of the row/column permutations process introduced, an example is provided, the permutation matrix being: ⎤ ⎡ 0 k12 0 0 ⎢ 0 0 0 k24 ⎥ ⎥ (4) P=⎢ ⎣ 0 0 k33 0 ⎦ k41 0

0 0

with four non-zero coefficients k ij , which are at the intersection of the i-th row and j-th column. Each coefficient k ij can be characterized by two values of 1 or −1. Keeping that in mind, the matrix (4) has 16 different options, which depend on the value of the coefficients k ij . In total there are 24 different permutations matrices (4) [10]. There are three distinct groups among the set of Hadamard matrices of dimension 4 × 4. Didukh L. A. [10] in her paper, studied the properties of Hadamard matrices used

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to encode the optical information. In this paper, it was established that among the set of Hadamard matrices of dimension 4 × 4, not three but four types can be distinguished. The first of these includes the canonical Hadamard matrices (type C), in which all elements of one row and one column are equal to 1. The second type includes a “50/50” Hadamard matrix with the same number of elements equal 1 and −1. An example of such a matrix is the S-shaped matrix. There are “light” Hadamard matrices with a minimum number of elements equal to −1. These two types are called noncanonical. ⎡ ⎡ ⎤ ⎤ 1 1 1 1 1 1 1 1 ⎢ 1 −1 1 −1 ⎥ ⎢ 1 −1 1 −1 ⎥ ⎥ ⎥ 1⎢ 1⎢ ; HN = ⎣ 1 1 −1 −1 ⎦ (5) HC = ⎣ 1 1 −1 −1 ⎦ 2 2 1 −1 −1 1 1 −1 −1 1 C − type(Canonical) N − type(Noncanonical) The presence of the fourth type of orthogonal Hadamard matrices was established for the first time in this paper [10]. According to the structure of the columns, these matrices correspond to the canonical type of Hadamard matrices. However, due to the structure of the rows, they do not belong to any of the mentioned above types of matrices. The first column, which contains 4 elements, is characterized by the ratio “3/1”, it has 3 light elements and 1 dark, and the next three columns – the ratio “1/3”. A group of matrices with such a row/column structure is called “semicanonical” Hadamard matrices (type S) in [10]. ⎡ ⎤ −1 −1 1 1 ⎢ ⎥ 1⎢ 1 1 1 1 ⎥ 2 ⎣ (6) HS = −1 1 −1 1 ⎦ −1 1 1−1 S − type(Semicanonical) The developed method of image processing using Hadamard matrices for encryption is orthogonal transformation: T h256 = HC,N ,S × f256 × HC,N ,S , T f256 = HC,N ,S × h256 × HC,N ,S ,

(7)

where f 256 – matrix of brightness values of original image pixels; h256 – encrypted matrix of brightness of image pixel; H C,N,S – one of three types of Hadamard matrices: canonical, noncanonical, and semicanonical; H T C,N,S – transposed matrix to one of three types of Hadamard matrices: canonical, noncanonical, and semicanonical. The novelty of the method is in the way of visual representation the encrypted images.

4 Experimental Studies 4.1 The Image Processing Method Using Three Types of Hadamard Matrices Based on the developed method we have implemented an application for image processing with three types of Hadamard matrices: canonical, noncanonical, and semicanonical.

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The procedure is as follows. The Hadamard matrices for image processing are formed from the Kronecker product of the 4 × 4 Hadamard matrix elements. The resulting matrix is multiplied by a two-dimensional array of values, which represent the image brightness. The next step is to multiply the matrix by the transposed Hadamard matrix. The result of processing an image is a two-dimensional array of negative and positive values. These values corresponded to the green and red pixels on visual representation the encrypted image. The image restoration procedure is performed in the opposite direction: the color of each pixel of the encrypted image was converted into a negative and positive value in the two-dimensional array of such values. The transposed matrix is multiplied by this array and by the Hadamard matrix. Hadamard-Image Encryption application provides one-dimensional and twodimensional image processing method using three types of matrices: canonical, noncanonical, and semicanonical. The program consists of main menu commands: File → Open – open monochrome images with the extension tif; Select – select the area in the image to process 256 × 256 pixels; 2D-Encrypt – 2D process according to one of the three types of Hadamard matrices; 2D-Decrypt – process the image in two ways: taking the encrypted image or the numerical data in the matrix as input. The Encrypt (onedimensional encryption) and Decrypt (one-dimensional decription) commands work similarly. The encrypted image is automatically saved in the directory that contains the original image. As a result of the processing, the image was converted to spatial-frequency. When encryption with the canonical Hadamard matrix (Fig. 1, b), a black background with green and red pixels was obtained. Red pixels indicate negative values, and green pixels indicate positive values. The yellow color on the encrypted image appears due to the additive synthesis of red and green pixels, which are located next to each other.

a)

b)

c)

Fig. 1. An example of image a – before encryption; encrypted images with the Hadamard matrices: b – canonical, c – noncanonical

Image decryption aims to restore the original image without losing any quality. Decryption process with usage the matrix of extended values as input provides better image recovery results. As we see, a noticeable difference between encrypted images gives reason to compare the results of the recovery of encrypted images.

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4.2 The Results of Experimental Evaluation the Quality of the Restored Images For experimental research ten monochrome portrait images were selected. Peak Signal to Noise Ratio (PSNR) values, color differences and histograms of brightness of restored images were taken as quality indicators. The quality of the restored image has been evaluated by the average value of the metric E (CIE 1976); the percentage of pixels in the image, for which the amount of color differences across the original and the restored image, is not greater than the specified allowable number. The calculation of E was performed only with the regards to brightness of the images. The determination of color differences was calculated using color transform: 1) from RGB model to XYZ; 2) from XYZ color model to CIE Lab. Ten different halftone portrait images have been processed in Hadamard-Image Encrytion application using the following types of Hadamard matrices: C-type, N-type, S-type. The obtained differences in pixel brightness between images are on average 0.22 for canonical and semicanonical and 0.05 – for noncanonical matrices. The same decryption results for the canonical and semicanonical Hadamard matrices confirm the visual similarity of the restored images. The average value of color differences for images process by the noncanonical Hadamard matrix differs significantly. The average value of differences in brightness between the original and the restored images do not exceed the allowable value (two units). There is a visual mismatch of some individual pixels of the original and the restored image in brightness (noise) after the using investigated Hadamard matrices. In this regard, it was calculated how many pixels in the restored image have a color difference more than two units E (Fig. 2).

Fig. 2. The number of pixels that have color differences E ≥ 2 on the restored images

Note that the total number of pixels in the image was 65 536. The approaches with canonical and semicanonical matrices resulted in almost identical outcomes. The less differences in pixel brightness were obtained using a noncanonical Hadamard matrix.

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The PSNR metric is used to assess the quality of images after various methods of their transformation and compression [12–15]. PSNR was calculated through standard deviation (MSE):



MAX 2I MAX I (8) PSNR = 10log10 = 20log10 √ MSE MSE where MAX I – is the maximum value that the pixel of the image takes. If the pixels have a bit size of 8 bits, MAX I = 255. Typical PSNR values for image compression are in the range from 30 to 40 dB [16]. The peak signal-to-noise ratio (8) is in the range of 27–59 dB for the restored images, Fig. 3. PSNR values for the images restored with a noncanonical matrix (N-type) are 35– 57 dB. This is a higher image recovery quality compared to C-type and S-type matrices. These results confirm the possibility of using a noncanonical Hadamard matrix for image processing, in particular encryption.

Fig. 3. The peak signal-to-noise ratio for ten images using different Hadamard matrices

The analysis of the pixel brightness level of the restored image was evaluated using histograms obtained in Levels dialog box in Adobe PhotoShop. We identified how the histogram of the image affects the quality of restoration and how the same histogram is changing after the restoration has been held. The original is characterized by a more stepped histogram then in the image restored by the noncanonical Hadamard matrix. The image restoration using the other two types of matrices has histograms different. from the original. Most of the restored images had noise in the form of random black and white pixels. A large number of pixels with RGB values (0, 0, 0) and (255, 255, 255) are present on the originals of the noisy restored images. That is, in the shadows

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and in the highlights of the image one can observe an increase in the number of white and black pixels (Fig. 4). Using the Curves tool in Adobe PhotoShop the mismatched output signals in the shadows and in the highlights of the image were corrected. The output pixels are set to 3 in shadows and 253 in highlights of the image. Therefore, the pixels of maximum and minimum brightness were removed in order to avoid artifacts on the restored images.

Fig. 4. The histogram of the original in window tonal range adjustment Adobe PhotoShop

After the correction, the several images were re-encrypted and restored once again. Since processing with a canonical matrix gave the identical results with the semicanonical one, the second processing was carried out with the canonical and noncanonical Hadamard matrices. When using a noncanonical matrix, the difference between the original and the restored images is not visually noticeable and there are no artifacts in the images (Fig. 5).

a)

b)

Fig. 5. Image number 10: a – with artifacts, b – after correction of the original, encryption and decryption

The number of pixels in the restored image that have a large difference in brightness with the original has decreased (Fig. 6). There is no difference in brightness of more than two units E after correcting.

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Fig. 6. Percentage of pixels-artifacts images after decryption

The quality of image after encryption for different matrices depends on the tone range of the original image. One of the requirements for images to be encrypted is the absence of pixels with a maximum and minimum brightness of 255 and 0, respectively. If this condition is met, the number of artifacts is minimal and for E ≥ 1 is zero. Among three types of Hadamard matrices considered, the less color difference and high value of PSNR provides noncanonical matrix in the developed method for image processing.

5 Conclusion Hadamard matrices and orthogonal Hadamard transform are often used for image encryption and provide minimal information loss during recovery. Division of Hadamard matrices into types gives us the reason to determine whether the type of Hadamard matrix affects the results of image processing, in particular recovery after encryption. The novelty of the method is in the way of visual representation the encrypted images. Based on the developed method we have implemented an application for image processing with three types of Hadamard matrices: canonical, noncanonical, and semicanonical. Experimental evaluation the quality of the restored images has been held. The quality of the decoded image was analyzed using the metrics of color difference, peak signal-to-noise ratio and histograms. The less color difference and high value of PSNR provides noncanonical matrix in the developed method for image processing. The results from the analysis of histograms suggest that artifacts appear when the original contains pixels with maximum and minimum brightness. We determined a condition for preparing originals for encryption which ensured the color difference of less than two units. The proposed method can be used to encrypt images, transmit them by modern channels of connection, create digital watermarks, compress and completely restore graphic information.

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References 1. Agaian, S., et al.: Hadamard Transforms, p. 9. SPIE Press, Bellingham, Washington USA (2011) 2. Yu, X., Yang, F., Gao, B., et al.: Deep compressive single pixel imaging by reordering Hadamard basis: a comparative study. IEEE Access 8, 55773–55784 (2020) 3. Kovalchuk, A., Peleshko, D.: Using Hadamard matrices for encryption – decryption of images. Comput. Sci. Inf. Technol. 719, 236–240 (2011) 4. Wang, L., Zhao, S.: Fast reconstructed and high-quality ghost imaging with fast WalshHadamard transform. Photon, Res. 4(6), 240–244 (2016) 5. Savakar, D.G., Pujar, S.: Digital image watermarking using DWT and FWHT. Int. J. Image Graph. Sig. Process. (IJIGSP) 10(6), 50–67 (2018) 6. Jassbi, S.J., Agha, A.E.A.: A new method for image encryption using chaotic permutation. Int. J. Image, Graph. Signal Process. (IJIGSP) 12(2), 42–49 (2020) 7. Mallikarjuna, K., Prasad, K.S., Subramanyam, M.V.: Image compression and reconstruction using discrete Rajan transform based spectral sparsing. Int. J. Image, Graph. Sig. Process. (IJIGSP) 8(1), 59–67 (2016) 8. Zhang, L., Yuan, X., Wang, K., Zhang, D.: Multiple-image encryption mechanism based on ghost imaging and public key cryptography. IEEE Photonics J. 11(4), 1–14 (2019) 9. Zamrani, W., Ahouzi, E., Azami, N., Ghazi, H.El., Sadiki, T.: Optical double phase encryption and spreading technique applied to color image. In: 2016 15th Workshop on Information Optics (WIO), pp. 1–3 (2016) 10. Didukh, L.A., Shovgenyuk, M.V.: Classes of similar Hadamard matrices. Comput. Printing Technol. 22, 54–64 (2010) 11. Hamood, M.T., Boussakta, S.: Fast Walsh–Hadamard–Fourier transform algorithm. IEEE Trans. Signal Process. 59(11), 5627–5631 (2011) 12. Arun, M.R., Selvakumar, S., Sheeba, M.R., Rishma, Sh.F.: Comparing PSNR of different image transforms (DCT, DFT, DWT, DHT, DTT). In: Proceedings of 4-th International Conference on Energy Efficient Technologies for Sustainability. Tamil Nadu, India: St. Xavier’s Catholic College of Engineering (2018) 13. Patel, D., Jose, A.M., Mascarenhas, N., Monis, S.S.: JPEG image compression using DCT and DHT and comparison of both techniques based on mean square error and peak signal to noise ratio. Int. J. Comput. Appl. 81(15), 23–27 (2013) 14. Singh, D.P., Khare, A.: Restoration of degraded gray images using genetic algorithm. Int. J. Image Graph. Sig. Process. (IJIGSP) 8(3), 28–35 (2016) 15. Peleshko, D., Rak, T., Izonin, I.: Image superresolution via divergence matrix and automatic detection of crossover. Int. J. Intell. Syst. Appl. (IJISA) 8(12), 1–8 (2016) 16. Horé, A., Ziou, D.: Image quality metrics: PSNR vs. SSIM. In: 20th International Conference on Pattern Recognition. Istanbul, Turkey, pp. 2366–2369 (2010)

Investigation of Reading Convenience Factors Based on Graph Theory and Systems Analysis Zoryana Selmenska1 , Bohdana Havrysh2(B) , Tetyana Holubnyk1 , Bohdan Kovalskyi1 , and Orest Khamula1 1 Ukrainian Academy of Printing, 79020, 19, Pidholosko St., Lviv 79020, Ukraine 2 Lviv Polytechnic National University, S. Bandera, 12, Lviv 79013, Ukraine

[email protected]

Abstract. Problems in the field of development and use of fonts are investigated, prospects of fonts development on various bases are analyzed. With the help of a graphical hierarchical model of the text reading ease factors priority influence, an expert selection of factors was made, the essence of which is related to the qualitative perception of the text. The formulation and solution of the problem are carried out using the means of graph theory and methods of systems analysis. Having established a set of factors through some set, a subset was chosen and the possible interaction between them was presented in the form of an indicative graph. The main task to solve this problem was the choice of factors for the ease of reading the text in electronic publications related to the actual relationship between them. The implementation of this method is provided on the basis of the existing acquisitions of systems analysis, modeling theory, research methodology, and problem-solving. To work out a complex system, the factors were divided into parts and organized as a hierarchical structure. If we consider a set of elements with a certain number of relationships between them, it is important to know the hierarchical structure of this set with the placement of elements on levels with greater or lesser dominance of some elements over others. Keywords: Text · Type · Ease of reading · Connection graphs · Hierarchy

1 Introduction To develop the information field, it is needed to develop own fonts. After analyzing this issue, the need for own fonts creation and development becomes clear, which in turn will help address the issue of language ideology. The font is no longer understood as part of the publication design [1, 2]. It has become a common way of transmitting the information. With this in mind, it is necessary to represent and distribute typographic fonts, because the typographic font is the foundation of any publication. One of the main factors of a quality publication is the font design of texts, as the font is primarily intended to convey the information contained in the publication. Font programs are also constantly evolving and improving for about 50 years. One of the first programs for creating digital fonts was developed by the American programmer © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 339–349, 2022. https://doi.org/10.1007/978-3-031-03877-8_30

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D. Knut, who created in the 70’s a system for preparing printed documents TeX. It used raster fonts generated by Metafont, which was also developed by D. Knut. This tool does not have a graphical interface in the form of subroutines in a special declarative language. With the help of an experiment conducted by Jared Scruse, it was possible to establish the importance of antiquity for large volumes of text. The experiment was that the experimental group was asked to read several texts reproduced with different fonts. As a result, the duration of focus, the average number of words between them, the amplitude of the saccades (rapid movements by which the eyes “jump” from point to point when we look for an object in sight) were measured [3–5]. It should be noted that with the advent of personal computers, the process of font developing and designing had to change. In fact, this is because a lot of headsets are computer-generated. However, only the tools have changed. Old design methods have replaced specially designed software [6]. 1.1 The Basic Concepts of Computer Fonts There are many programs for fonts creation, but it is important to understand the basic principles that a computer font is a file that contains a description of a set of alphanumeric, business, and pseudo graphic characters that are used to play characters (including text) by a program or operating system. Today, computers store fonts in the form of outlines and provide them with “hints” for intelligent scaling. This technology is used as a single format for text reproduction on monitors, laser printers, etc. High-resolution output devices define only circuits, and instructions play a major role for low-resolution output devices. The instructions, which contain contour data, allow you to optimally display images in raster format according to the capabilities of the resolutions of screens and laser printers. The letters of digital fonts are mathematically described using curves based on their contours. To describe the contours of the letters, various functions are used, which form the segments that make up a continuous curve. That is, the end point of the segment of the curve determines the starting point of the next segment. 1.1.1 A Review on Quality Perception of Text in Electronic Publications The analysis of factors according to the degree of influence on the ease of reading textual information in printed and electronic publications made it possible to group them and highlight generalized factors related to the problems of quality perception of text in electronic publications. As a result, it will be expedient to develop a graphical hierarchical model of the priority influence of text reading ease factors in printed and electronic publications. Important for this task is the expert choice of factors, the essence of which is related to the quality of text perception in electronic publications. The formulation and the problem solution are carried out using the means of graph theory and methods of systems analysis. Let the set of factors be some set H = {h1 , h2 , …, hn }. Let’s choose the subset of the most significant factors H1 ∈ H from this set. For clarity, the mathematical notation of its mnemonic name is made:

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h1 – font style – FSt; h2 – font size – FS; h3 – row length – RL; h4 – font spacing – FSp; h5 – font saturation – FSat; h6 – font typesetting – FT; h7 – electronic edition text color – EETCl; h8 – speed of the electronic edition text reading – SEETR; h9 – electronic edition text complexity – EETC; h10 – electronic edition background color – EEBC; h11 – electronic edition text block size – EETBS; h12 – types of electronic publications – EEP; h13 – output device parameters – ODP.

The subset of factors H1 and the possible interaction between them is given in the form of an oriented graph (Fig. 1). Place the elements of the subset H1 in the vertices of the graph, and the arcs will connect adjacent vertices (hi, hj), for which a connection is defined, which indicates the dependence of the factor hi on hj. For example, the font type depends significantly on the typographic parameters of the font size and typeface, the type of printed edition and the parameters of the device from which the electronic edition is read are also important [4, 9].

Fig. 1. Graph of connections between the text reading ease factors in electronic publications.

Based on the above graph, a binary matrix of dependence B for the set of vertices H is constructed, therefore:  0, if factor i does not depend on factor j bij = 1, if factor i depends on factor j.

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The main solution to this problem is to choose the factors of text reading ease in publications with the actual relationship between them, which is established by experts. Changing the number and content of factors can cause the model modification. The implementation of this method is provided on the basis of using the existing achievements of systems analysis, modeling theory and research methodology, and problem-solving. The hierarchical model is shown in Fig. 2.

Fig. 2. Model of the hierarchy of text reading convenience factors in electronic editions

To work out a complex system, it is not enough to break it into parts, you need to organize these parts in a certain way, namely - hierarchical structures. If we consider a set of elements with a certain number of relationships between them, it is important to know the hierarchical structure of this set by placing elements on levels with more or less dominance of some elements over others. This way of presenting the hierarchy for reading convenience factors in publications reflects how the priority of factors at the lower levels of the hierarchy affects the priority of factors at the upper levels [10, 11]. This model shows that the most important factor in text readability is the parameters of the output device (format, resolution, etc.), which provides high-quality visualization of text on the screen. Also, properties like typographic font size and font typeface (which are the main indicators of the font typeface) are no less important. A high-quality selection of typographic font parameters for each type of output device will provide ease of reading and perception of text from the screen, monitor, or when printing. The least critical factors for the readability of the text in this hierarchy were the factors of text complexity and reading speed, as well as the

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color design of the text and background. At qualitative maintenance of factors of various levels, it is possible to provide the convenience of reading and perception of the text in the edition. Thus, taking into account the analyzed factors that affect the readability of text material, which made it possible to build a structured model hierarchy based on graph theory, identifying the priority factors influencing the quality of electronic publications and readability. This made it possible to identify the main factors by the degree of influence, if we take them into account to optimize the algorithm of the system.

2 Research Methods For research, we analyzed the most common ways to study the readability and legibility of the text [12, 14]: 1. Tachyscopy This technique allows you to determine the exposure time needed to recognize a character, a whole word, or a group of words. Performing a tachistoscopic examination is that the samples with the texts change very quickly during the exposure so that no one can recognize them. 2. Determination of the threshold distance The essence of this method is to determine the threshold distance. To do this, a sign, word or solid text is placed at a certain distance from the observer so that he could not recognize it. The next step is to gradually reduce the distance from the text to the observer until the moment of correct recognition. The required distance is fixed as a dependent derivative - the threshold distance. This method is used to determine the readability of posters and road signs. 3. Determination of threshold lighting This method is similar to the previous one, but you only need to determine the lighting parameters for high-quality recognition of characters, words and solid text. The scope of this method is similar to the previous method. 4. Determination the object optical visibility This technique is performed using an optical instrument that allows you to measure the legibility of characters from a distance easy to read. By changing the focus of the lenses, you can determine the level of recognition of the test material. The results are similar to the techniques of threshold distance and lighting. 5. Reading speed Reading speed as a criterion for the reading ease was proposed by Webber in 1881. However, there are some disadvantages of this method - how to determine the impact on reading speed of text design of typographic parameters and semantics of text material. 6. Eye movement while reading Typographic parameters of the text material affect the perception of long sentences. The less fixations the reader makes on the text, the easier the text is to read. The number of fixations is the main indicator in determining the ease of reading. However, the method

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was not used, because the technical means do not allow to accurately record the points of fixation and regression (return) of eye movement. 7. Blinking frequency The frequency of blinking is also an indicator of the ease of reading text material. As the blink rate increases, the ease of reading text material decreases. However, the increase in this figure may contribute to reader fatigue. Thus, after analyzing the methods of assessing the readability of the text, we can conclude that the use of the method of determining the speed of reading will provide an opportunity to assess the readability of texts of publications.

3 Modeling and Results The speed of reading typographic text is a criterion for the fonts reading ease of different publications types. The value of readability can be the time or amount of text that is spent reading a certain material aloud or about yourself. From the analysis of the results of research [12–15] by Peterson and Tinker (1929) we can identify the main requirements for reading easiness test: • the number of test participants should be sufficient to obtain objective statistics of reading the text in different typographic design; • all parts of the text must have the same complexity; • reading material should be designed in two equivalent forms, so that texts with different typographic design were of equal complexity; • to compare the speed of reading differently designed texts, you need to compare the cost of time to carefully read the material. This figure should be minimal; • texts of parallel forms must have a sufficient volume. Based on the model of the hierarchy of text reading ease factors in electronic publications (which is based on the method of pairwise comparisons) the main factors. of influence were identified. Each of which was assigned a level of importance from the first to the seventh [16]. At the first level of MTRCHFEE (Model of text reading convenience hierarchy factors in electronic editions), there are parameters of output devices, it should be noted that there is no special need to work out and create a representation of the electronic edition for any concrete display formats (Fig. 3), predict which device the user will choose. You do not need to focus on the device but on the resolution of the device. Today, you can create a single electronic resource with a single layout, which will work on phones and any other output devices [17]. This layout is called “Responsive Web Design”.

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Fig. 3. Picture of the parameters of the output devices

4 Comparison and Discussion The main problem to be solved was the choice of factors for reading convenience in printed and electronic publications related to the actual relationship between them. The implementation of this method is provided on the basis of the existing acquisitions of systems analysis, modeling theory, and research methodology, and problem-solving. To work out a complex system, the factors were divided into parts and organized as a hierarchical structure. If we consider a set of elements with a certain number of relationships between them, it is important to know the hierarchical structure of this set with the placement of elements on levels with greater or lesser dominance of some elements over others. With this method of presentation, for reading convenience factors hierarchy in electronic publications reflects both the priority of factors at the lower levels of the hierarchy and the impact on priority factors at the upper levels. This model showed that the most important factors in the readability of text are factors such as the parameters of the output device, as determined for this parameter should use the so-called “rubber layout”, the next priority parameters are the typographic font, based on research priority for continuous text is 18-point size, typed in a straight light pattern, Open Sans headset. The least critical factors for the ease of reading the text in the built hierarchy can be called the complexity of the text, reading speed, and color design of the text and background. If you follow the quality regulation of higher-level factors, you can ensure the ease of reading and perception of the text in electronic publications.

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The average reading speed of the Merriweather headset is 50.6 s. And for the Open Sans headset, the average reading speed of the Open Sans headset is 41.6 s. Histograms of average values of read speeds of headsets are shown in Fig. 4, Fig. 5, Fig. 6. Among the selected fonts of the 12-point font, it can be seen that as the space between the letters increases, the reading speed increases, which can improve the reading convenience. Particularly noticeable is the sharp increase in the reading speed of the Merriweather headset with the increase of additional space letters.

Fig. 4. Comparative histogram of the reading speed average values of the 12th size fonts

Fig. 5. Comparative histogram of the reading speed average values of the 14th size fonts

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Fig. 6. Comparative histogram of the reading speed average values of the 18th size fonts

5 Summary and Conclusion Thus, the results of read speed studies have shown that there is an advantage of chopped fonts over serif fonts. Also, after research, it can be argued that changing the spaces between the letters increases the readability of the text, for example, for all fonts, decorated with 12 pins. For 14-font typefaces, no improvement was observed for chopped fonts, only a slight improvement was noticeable for the serif font. Fonts that are in 18-point font do not need to change the spaces between the letters. Based on the results of the average values of the headsets reading speed, general tables were compiled by groups of fonts in pins 12, 14 and 18, Table 1 was constructed (Fig. 7). Table 1. Estimation of the fonts reading speed average values Fonts

Average time of reading fonts, s without additional spaces between letters

with additional spaces between letters

with serifs of 12 pins

52

50

without serifs of 12 pins

44

43

with serifs of 14 pins

49

49

without serifs of 14 pins

42

42

with serifs of 18 pins

51

51

without serifs of 18 pins

39

40

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Fig. 7. Comparative histogram of average values of font reading speed

These results once again prove that grotesque fonts are better readable in electronic publications, the Open Sans headset showed excellent performance for reading from the display. The Merriweather headset showed lower read speeds. Acknowledgment. The authors are appreciative to colleagues for their support and appropriate suggestions, which allowed improving the materials of the article.

References 1. Kumar, S., Agarwal, S., Prasad, R.: Efficient read alignment using burrows wheeler transform and wavelet tree. In: 2015 Second International Conference on Advances in Computing and Communication Engineering, pp. 133–138 (2015). https://doi.org/10.1109/ICACCE.2015.80 2. Asra, S., Shubhangi, D.C.: Personality trait identification using unconstrained cursive and mood invariant handwritten text. Int. J. Educ. Manage. Eng. (IJEME) 5(5), 20–31 (2015). https://doi.org/10.5815/ijeme.2015.05.03 3. Roopa, M.J., Mahantesh, K.: An impact of frequency domain filtering technique on text localization method useful for text reading from scene images. In: 2019 4th International Conference on Electrical, Electronics, Communication, Computer Technologies and Optimization Techniques (ICEECCOT), pp. 37–43 (2019). https://doi.org/10.1109/ICEECCOT4 6775.2019.9114860 4. Khamula, O.: Technological features of creating fonts for electronic publications: monograph. In: Vasyuta, S., Kuts, J., Khamula, O. (eds.) Ukrainian Academy of Printing, Lviv (2020). 184 p. 5. Akuma, S., Jayne, C.: Factors affecting users’ measure of interest: a study of the effect of task, document difficulty and document familiarity. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 11(5), 47–57 (2019). https://doi.org/10.5815/ijitcs.2019.05.06 6. Engels, R., Chitra, A.: Graph models for knowledge representation and reasoning for contemporary and emerging needs – a survey. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 8(2), 14–22 (2016). https://doi.org/10.5815/ijitcs.2016.02.02

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7. Tymchenko, O., Tymchenko, O.O., Havrysh, B., Khamula, O., Sosnovska, O., Vasiuta, S.: Efficient calculation methods of subtraction signals convolution. In: 2019 IEEE 15th International Conference on the Experience of Designing and Application of CAD Systems (CADSM), pp. 1–4 (2019). https://doi.org/10.1109/CADSM.2019.8779250 8. Quirós, L., Vidal, E.: Learning to sort handwritten text lines in reading order through estimated binary order relations. In: 2020 25th International Conference on Pattern Recognition (ICPR), pp. 7661–7668 (2021). https://doi.org/10.1109/ICPR48806.2021.9413256 9. Erdo˘gmu¸s, N., Özuysal, M.: Scene text localization using keypoints. In: 2015 23rd Signal Processing and Communications Applications Conference (SIU), pp. 1917–1920 (2015). https://doi.org/10.1109/SIU.2015.7130235 10. Yao, C., Bai, X., Liu, W.: A unified framework for multioriented text detection and recognition. IEEE Trans. Image Process. 23(11), 4737–4749 (2014). https://doi.org/10.1109/TIP.2014.235 3813 11. Ramanathan, S., Ramasundaram, M.: Uncovering brain chaos with hypergraph-based framework. Int. J. Intell. Syst. Appl. (IJISA) 12(4), 37–47 (2020). https://doi.org/10.5815/ijisa. 2020.04.04 12. Tensmeyer, C., Wigington, C.: Training full-page handwritten text recognition models without annotated line breaks. In: 2019 International Conference on Document Analysis and Recognition (ICDAR), pp. 1–8 (2019). https://doi.org/10.1109/ICDAR.2019.00011 13. Nguyen, K., Thanh, N.D.: Scene text detection based on structural features. In: 2016 International Conference on Computer, Control, Informatics and its Applications (IC3INA), pp. 48–53 (2016). https://doi.org/10.1109/IC3INA.2016.7863022 14. Peleshko, D., Rak, T., Izonin, I.: Image superresolution via divergence matrix and automatic detection of crossover. Int. J. Intell. Syst. Appl. (IJISA) 8(12), 1–8 (2016). https://doi.org/10. 5815/ijisa.2016.12.01 15. Yadav, S., Kumar, G., Kumar, S.: A graph construction study for graph-based semi-supervised learning: case study on unstructured text data. In: 2019 IEEE International Conference on Big Data (Big Data), pp. 6254–6256 (2019). https://doi.org/10.1109/BigData47090.2019.900 6465 16. Shekkizhar, S., Ortega, A.: Efficient graph construction for image representation. In: 2020 IEEE International Conference on Image Processing (ICIP), pp. 1956–1960 (2020). https:// doi.org/10.1109/ICIP40778.2020.9191232 17. Kustov, V.N., Yakovlev, V.V., Stankevich, T.L.: The information security system synthesis using the graphs theory. In: 2017 XX IEEE International Conference on Soft Computing and Measurements (SCM), pp. 148–151 (2017). https://doi.org/10.1109/SCM.2017.7970522

The Generalized Chaotic System in the Hyper-complex Form and Its Transformations Roman Voliansky1 , Nina Volianska2 , Vitaliy Kuznetsov3(B) , Mykola Tryputen4 , Alisa Kuznetsova5 , and Maksym Tryputen5 1 Electric Engineering Department, Dniprovsk State Technical University, Kamyanske 51918,

Ukraine 2 Energy Engineering Department, Dniprovsk State Technical University, Kamyanske 51918,

Ukraine 3 Electric Engineering Department, National Metallurgical Academy of Ukraine, Gagarina

Avenue, 4, Dnipro, Ukraine [email protected] 4 Department of Automation and Instrumentation, Dnipro University of Technology, Avenue Dmytra Yavornytskoho, 19, Dnipro, Ukraine 5 Department of Calculating Mathematics and Mathematical Cybernetics, Oles Honchar Dnipro National University, 35, D. Yavornitsky Avenue, 4 Building of DNU, Dnipro, Ukraine

Abstract. The paper deals with the development of the mathematical backgrounds to design the novel chaotic systems by transforming existent ones. These backgrounds are based on using well-known shift, rotation, and scale transformations and we offer using hyper-complex numbers to simplify these transformations and represent the transformed chaotic system by using the one 1st order ordinary differential equation. In such form all well known, newly discovered and unknown chaotic systems have the similar mathematical models that are differs only by used nonlinear function of hyper complex variable in the right hand expression. That is why the consideration chaotic system dynamic in the hyper-complex domain allows us to simplify initial system definition as well without applying any transformations. This fact simplifies mathematical definition of chaotic systems and their modeling and simulation. The right-hand expression of the transformed equation in this case are defined as the combination of transformation hyper-complex numbers and source system nonlinearity which is given in the hyper-complex domain. We offer to use variable transformation factors to improve the performance of the considered chaotic system. Since the above-mentioned variable factors can be produced by other chaotic systems, we suggest designing the novel chaotic system by combining existed ones with the linear transformations. As an example, we consider the transformation of the well-known Lorenz system and show the differences between the source system and target one. Keywords: Chaotic system · Quaternion · Coordinate transformation · Modeling and simulation · Secured communication

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 350–359, 2022. https://doi.org/10.1007/978-3-031-03877-8_31

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1 Introduction Chaotic systems now are one of the most rapidly developing branches of modern science and engineering. These systems are used in various fields of a human beings. One can find their usage in financial, social, engineering, scientific, and other applications [1–4]. A wide range of the chaotic systems using can be explained by the unique properties of these systems, which can generate truly random signals. Since, even if these signals are received by an unauthorized person, they cannot be decoded, generating, transmitting, and receiving these signals becomes an important problem. This problem appears due to many engineering applications based on using secured channels of data transmission. The development and use of distributed systems, which are governed by the Internet of Things paradigm, causes the extremely rising of the above-mentioned problem. New secured data exchange protocols can prevent unauthorized use of some elements of these distributed systems and theirs damages. Because of the possible accidents, which can cause unauthorized access to the systems, this problem becomes more important for systems, which are used in industrial, energy, and transport applications. In this case, the use of the novel chaotic system is preferable, because existing ones are well-known and can be compromised. Thus finding of the generalized mathematical backgrounds to design novel chaotic system is quite important scientific problem. The solution of this problem allows improving the securing features of the data transmissions and avoiding accidents due to unauthorized access to transmitted data. A lot of novel chaotic systems are designed every day [5–9] but the main drawback of these systems that their design is highly subjective and cannot be explained from the scientific viewpoint. Moreover, nobody can predict the properties and features of such systems and it is necessary to perform detailed analysis to predict any information leakages from the designed systems. We offer to avoid this drawback by applying some coordinate transformations to well-known or novel chaotic systems to make their dynamic more complex and prevent its decoding. We simplify these transformations by using hyper-complex numbers [7, 11] and representing system dynamic in the hypercomplex domain. One can find that chaotic motion in this case is defined by the initial system dynamic as well as coordinate transformations that are applied to it. We define both of these components by using hyper-complex algebra. Our paper is organized as follows: at first, we show the transformation of the generalized chaotic systems into hyper-complex form, and then we define generalized linear coordinate transformation in the hyper-complex form and use it to write down the differential equation for the transformed system. At third, we show an example of our approach usage. At last, we make conclusions.

2 Method 2.1 Coordinate Transformation for the Generalized Chaotic System Let us consider the generalized nonlinear system, which dynamic is given by the following matrix ordinary differential equation ˙ = F(Y, U), Y

(1)

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T T   here Y = y1 · · · yn is a n-th sized state variable vector, U = u1 · · · um is a m-th T  sized vector of input signals, and F = f1 (Y, U) · · · fn (Y, U) is a n-th sized nonlinear vector function. It is clear that one can use (1) to define the dynamic of a huge class of both nonlinear and linear dynamical systems, so we call this equation as the generalized one. We make this equation more specific by assuming that the considered system has a chaotic dynamic. This assumption reduces the number of functions in the vector F and allows us to claim that the system dynamics is localized in some state space where its attractor is defined. One can use hyper-complex numbers to define this space and system motion in it y˙ = g(y, u) where y is the generalized state variable in the hyper-complex space  n1 i=1 ei yi if i < n; y= 0 if i > n,

(2)

(3)

here ei is a i-th unit vector, u is a generalized input signal, which is defined similar to (3). We use f i (Y,U) components of function F(Y,U) to define the function of hypercomplex argument as follows  n1 i=1 ei gi (y, u) if i < n; g(y, u) = (4) 0 if i > n. The components gi (y,u) can be found by using functions fi (Y,U), hyper-complex numbers y and u as well as the rules of hyper-complex algebra. The consideration of attractors instead of the transients makes it possible to operate with the system trajectories like sets of points in some coordinate space and transform it into another state space, where the system dynamic differs from the initial one. To perform such a transformation we offer to modify (2) by applying well-known coordinate transformations to a state variable (3). Here we apply shift, rotation, and compression transformations for state-space axes transformations. In the hyper-complex notation these transformations can be given in such a way [12]: 1. Shift transformation x = y + s,

(5)

here x is a new state variable and s is a hyper-complex number that corresponds to the axes shift in the desired position. 2. Compression transformation x = cy,

(6)

here c is a hyper-complex number that compresses each component of the initial hyper-complex number. Contrary to the simplest shift transformation, the compression transformation can be defined in several ways such as element-wise multiplication and matrix-wise one. In the first case, each of the components of the “new”

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state variable x depends only on the same component of the initial state variable y in a linear way. Such transformation makes it possible to scale attractor on every axes. In the second case, each component of the transformed state variable depends on the linear combination of several components of the initial state variable y. Such an approach allows us to produce a new attractor by mixing coordinates of the old one. 3. Rotation transformation x = ryr ∗

(7)

here r is a rotation hyper-complex number and r* means conjugated hyper-complex number. The transformations (5)–(7) can be applied at the same time and in the most common case we can write down the following generalized coordinate transformation x = cryr ∗ + s,

(8)

which applying gives us the possibility to transform any attractor in a wide range. One can make it more complex by changing hyper-complex numbers s, r, and c for each point of the attractor. Such changes can be implemented by using several oscillators, which can produce regular and chaotic oscillations. 2.2 Transformed Generalized Chaotic System Modeling The above-shown approach assumes using both chaotic oscillator and transformation block. However, this fact is not a strict requirement to the structure of the chaotic system. Moreover, the above-considered transformations can be included in a chaotic system. Let us consider such inclusion. At first, we use (8) to define hyper-complex state variable y and its derivative y = c−1 r −1 xr ∗−1 − c−1 r −1 sr ∗−1 y˙ = c˙ −1 r −1 xr ∗−1 + c−1 r˙ −1 xr ∗−1 + c−1 r −1 x˙ r ∗−1 + c−1 r −1 x˙r ∗−1 − c˙ −1 r −1 sr ∗−1 − c−1 r˙ −1 sr ∗−1

(9)

− c−1 r −1 s˙ r ∗−1 − c−1 r −1 s˙r ∗−1 ; Then we substitute (9) into (2) and write it down in such a way x˙ = h(x, u, c, r, s),

(10)

Here h(x, u, c, r, s) = crg(c−1 r −1 (x − s)r ∗−1 , u)r ∗ −˙cc−1 x − rx˙r −1 − r ∗ x˙r ∗−1 + c˙ c−1 s +r˙r

−1

∗

s + s˙ + r s˙r

∗−1

(11)

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Thus, expression (11) defines the dynamic of the considered transformed chaotic system by shifting, scaling, and rotating its attractor. This expression can be simplified in the case when the transformation quaternions with constant elements are used   (12) h(x, u) = crg c−1 r −1 (x − s)r ∗ −1 , u r ∗ Functions (11) and (12) are applications of the linear coordinate transformation for the generalized chaotic system. This transformation can be applied to any known chaotic system to design a novel system by changing the attractor of the source system.

3 Results and Discussion 3.1 The Lorenz System in the Quaternion Form Let us show the use of the proposed approach by performing some transformation for the well-known Lorenz system, which is given by the following equations [7] x˙ = σ (y − x); y˙ = x(r − z) − y; z˙ = xy − bz,

(13)

where x, y, z are state variables and σ = 10, r = 28, b = 8/3. The system (13) is described with three differential equations and we use quaternions to represent it into the compact form. It is necessary to say that the number of components in the selected hyper-complex number has to be greater or equal system order. We use imaginary parts of quaternion to define generalized state variable q = 0 + ix + jy + kz,

(14)

as well as a generalized nonlinear function f (q) = 0 + iσ (y − x) + jx(r − z) − jy + kxy − kbz.

(15)

Expressions (14) and (15) give us the possibility to rewrite known Lorenz equations in a quaternion form   (16) q˙ = 0 + iσ qj − qi + jqi (r − qk ) − jqj + +kqi qj − kbqk or   q˙ = 0 + qj (iσ − j) − kbqk + +qi −iσ + jr − jqk + kqj

(17)

here qi = x, qj = y, qk = z. We call (17) as Lorenz equation in the quaternion form. Given form (17) is the simplest quaternion form of the Eqs. (13) because it has only one nonlinear function in the second row of (17) and only this summand is defined with all of three unit vectors.

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Thus, the use of quaternions to describe the dynamic of the chaotic system allows simplifying its differential equations and replacing systems of equations with only one differential equation. Equation (17) can be implemented by using well-known numerical methods [13, 14]. Here we show the simplest recurrent implementation for (17) q = z −1 q + z −1 qj T (iσ − j) − kbTz −1 qk   + + z −1 qi T −iσ + jr − jz −1 qk + kz −1 qj

(18)

and the derivative operator is approximated by using backward difference approximation   q˙ = q − z −1 q /T , (19) here T is a sample period and z−1 is a shift operator. One can find the results of numerical solution (18) in Fig. 1. The attractor in Fig. 1 is similar to the well-known one. Therefore, we claim that the transformations (14)–(17) do not affect on system dynamic but only makes it possible to represent it by using the first order nonlinear ordinary differential equation which solution is defined by using quaternions. Since lots of modern mathematical software allow operating with the complex and hyper-complex number the proposed approach gives us possibility to simplify modeling of the considered chaotic system. Since we use hyper-complex numbers one can consider a solution of (18) as some vector in the 4D state space. The idea of this vector makes some basis for system representation in rectangular, angular and others coordinate systems and as result allows generating various chaotic oscillations. 3.2 Linear Coordinate Transformation for the Lorenz System To change system dynamic one can apply the above-given transformation (8) to the system (17). Let us consider it in detail.

Fig.1. Lorenz attractor in hyper-complex space.

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The shift operation is trivial and it requires defining some shift quaternion. As an example, we use the following one. s = 0 + 10i + 10j + 10k

(20)

Rotation quaternion can be defined by using well-known Euler angles [15]. As an example, we use the following rotation quaternion and its conjugated one r = 0.519 + i0.765 − j0.35 − k0.151.

(21)

r ∗ = 0.519 − i0.765 + j0.35 + k0.151.

(22)

Analysis of expression (8) shows that both scale and rotation operations are performed by multiplying initial quaternion on some other ones. Thus, the task of quaternion scaling by the desired axis is more complicated than the simple multiplication of two quaternions. We solve this task by considering the sum of products of basis quaternion elements ci qi + cj qj + ck qk = 0; cR qi − cj qk + ck qj = ni qi ; cR qj + ci qk − ck qi = nj qj ; cR qk − ci qj + cj qi = nk qk ,

(23)

where ni , nj , nk are desired scale factors for each axis, c is a real part of a scale quaternion. If one solves (23), he finds elements of the scale quaternion in the following way   cR = ni qi2 + nj qj2 + nk qk2 |q|−2 ;   ci = qj qk nj − nk |q|−2 ; cj = qk qi (nk − ni )|q|−2 ;   ck = qi qj ni − nj |q|−2 |q| =



qi2 + qj2 + qk2 .

(24) (25)

Scale factors (25) make it possible to write down the scale quaternion in such a way c = cR + ici + jcj + kck .

(26)

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Imaginary factors of this quaternion are defined by similar formulas which can be generalized as follows cx = qx+1 qx−1 (nx+1 − nx−1 ), x ∈ [1, 3], ifx + 1 > 3 then qx+1 = qi , nx+1 = ni , ifx − 1 < 1 then qx−1 = qk , nx−1 = nk ,

(27)

Analysis of factors (24) shows that the constant scale factor for each axis is guaranteed by using the variable-elements scale quaternion. Elements of this quaternion depend on state variables of the considered chaotic system and they should be defined for each set of the system state variables in a separate way [16, 17]. As an example, we use the following scale factors ni = 1; nj = 2; nk = 3

(28)

to define scale quaternion factors (25). We use (28), (21), (22), and (20) to build the generalized transformation scheme (8) and we use it to perform the transformation for the Lorenz system [18–20]. Result of this transformation is shown in Fig. 2.

Fig. 2. Transformed Lorenz attractor in hyper-complex space.

The comparison of attractors in Fig. 1 and Fig. 2 shows their significant differences in signals values and forms. This fact allows producing chaotic oscillations which differ from the existent ones with the same parameters and initial conditions.

4 Summary and Conclusion The use of hyper-complex numbers makes it possible to reduce the order of the used differential equations and represent the dynamic of any chaotic and hyper-chaotic system by using only one differential equation. This equation can be solved by using numerical methods which operate with hyper-complex numbers. The system attractor can be

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transformed in an easy way by using hyper-complex transformation expressions. One can use these expressions to design a novel chaotic system from the existing one. The transformed system in the general case can be obtained by using variable transformation factors and can combine chaotic oscillations from several chaotic systems to improve secured features of the chaotic communication system. This system can be represented in the normal view with only real numbers by performing inverted transformation from hyper-complex number domain into real number domain by considering imaginary part of the hyper-complex number as state variables of the novel chaotic system. The proposed approach can be extended and the performance of the novel chaotic system can be improved by using the nonlinear transformations. Designed in such a way chaotic system can be used as the generator in secured data transmission channels.

References 1. Qin, H., et al.: The bifurcation and chaos analysis of Chinese net export under the global financial crisis. In: 2009 International Workshop on Chaos-Fractals Theories and Applications, Shenyang, pp. 336–340 (2009) 2. Aili, F., et al.: Chaos and community evolution in social learning with multiple true states. In: Proceedings of the 31st Chinese Control Conference, Hefei, pp. 6415–6420 (2012) 3. Kiseleva, E.M., Hart, L.L., Dovgay, P.A.: On a problem of numerical simulating the derivative of discrete time series with approximate values. J. Autom. Inf. Sci. 47(12), 1–17 (2015) 4. Alain, K.S.T.: Fostin Hilaire Bertrand a secure communication scheme using generalized modified projective synchronization of coupled Colpitts oscillators. Int. J. Math. Sci. Comput. 4(1), 56–70 (2018) 5. Giakoumis, E., et al.: Chaos generator device based on a 32 bit microcontroller embedded system. In: 2018 7th International Conference on Modern Circuits and Systems Technologies (MOCAST), pp. 1–4 (2018) 6. Karthikeyan, R., et al.: Dynamical analysis and FPGA implementation of a chaotic oscillator with fractional order memristor components. Nonlin. Dyn. 91, 1491–1512 (2018). https://doi. org/10.1007/s11071-017-3960-9 7. Li, L., et al.: Quaternion and multiple chaotic systems based pseudo-random number generator. In: 2019 2nd International Conference on Computer Applications & Information Security (ICCAIS), pp. 1–5 (2019) 8. Voliansky, R., et al.: Chaotic time-variant dynamical system. In: 2020 IEEE 15th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET), pp. 606–609 (2020) 9. Agarwal, S.: Chaotic dynamics of complex logistic map in l-superior orbit. Int. J. Inf. Technol. Comput. Sci.. 12(4), 11–18 (2020) 10. Valluri, M.R., et al.: Quaternion public key cryptosystems. In: 2016 World Congress on Industrial Control Systems Security (WCICSS), pp. 1–4 (2016) 11. Méndez-Ramírez, R., et al.: A new simple chaotic lorenz-type system and its digital realization using a TFT touch-screen display embedded system. Complexity, (2017). 13 pages 12. Bhowmik, A.: An encoding schematic based on coordinate transformations. Int. J. Math. Sci. Comput. 6(6), 9–14 (2020) 13. Hart, L.L.: Projection-iteration realization of a Newton-like method for solving nonlinear operator equations. J. Optim. Diff. Eqn. Appl. 27(1), 56–66 (2019) 14. Hart, L.L., Polyakov, N.V.: Projection-iteration realization on the Newton-Kantorovich method for solving nonlinear integral equations. J. Autom. Inf. Sci. 44(1), 40–49 (2012)

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15. Tamayo, A.J.M.: Multirotor modelling and simulation. In: Screws, S.O.A. (ed.) Euler angles, quaternions, wind, 2017 14th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), pp. 1–6 (2017) 16. Kuzenkov, O., et al.: Mathematical model of dynamics of homomorphic objects. In: CEUR Workshop Proceedings, vol. 2516, pp. 190–205 (2019) 17. Kuzenkov, O., Kuznetsov, V., Tryputen, N.: Analysis of phase trajectories of the third Order dynamic objects. In: 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering, UKRCON 2019 - Proceedings, pp. 1235–1243 (2019). DOI: https://doi.org/10. 1109/UKRCON.2019.8879819 18. Gupta, G., Shukla, A.: Performance analysis of NLM interleaving scheme for CPM OFDM system. Int. J. Wirel. Microwave Technol. (IJWMT) 9(1), 11–22 (2019). https://doi.org/10. 5815/ijwmt.2019.01.02 19. Alain, K.S.T., Bertrand, F.H.: A secure communication scheme using generalized modified projective synchronization of coupled colpitts oscillators. Int. J. Math. Sci. Comput. (IJMSC) 4(1), 56–70 (2018). https://doi.org/10.5815/ijmsc.2018.01.04 20. Ziabari, M.T., Sahab, A.R., Fakhari, S.N.S.: Synchronization new 3D chaotic system using brain emotional learning based intelligent controller. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 7(2), 80–87 (2015). https://doi.org/10.5815/ijitcs.2015.02.10

The Impact of Connecting a Wind Power Plant on Emergency Modes of a Traction Substation of an AC Traction System Yurii Kachan1 , Vitaliy Kuznetsov2(B) , and Oleh Bondar3 1 Zaporizhzhia Polytechnic National University, 64, Zhukovsky Street, Zaporizhzhia 69063,

Ukraine 2 National Metallurgical Academy of Ukraine, Gagarina Avenue, 4, Dnipro, Ukraine

[email protected] 3 Dnipro National University of Railway Transport Named after Academician V. Lazaryan,

Dnipro 49010, Ukraine

Abstract. Among the countries of South-Eastern Europe, Ukraine has the greatest technical potential for the implementation of renewable energy sources, and the main part of it is wind power engineering. The traction power supply system of the railways in Ukraine can become an important transiter and consumer of electricity generated by wind power plants. At the same time, the task of ensuring traffic safety and uninterrupted power supply of traction loads requires a preliminary study of the influence of the connected wind power plant capacity on the growing short-circuit currents in the distributive units of the traction substation to which the specified connection is planned. This paper proposes a way to implement such prediction based on a systematic approach, in which a traction substation and an integrated wind power plant are considered as a single electrical-engineering complex, the sources of which work to power the short-circuit point. In previously published studies, the authors usually consider the processes in renewable energy sources and in the traction power supply system separately, without taking into account the mutual influence. The analysis of processes in the short-circuit mode is proposed to perform according to the equivalent circuits for the specified electricalengineering complex developed by the authors with various possible options for connecting a wind power plant using mathematical modeling with proven methods of theoretical electrical engineering. The peculiarity of the study presented in this paper is also the use of the multiplication factor of the short-circuit current as a criterion for assessing the impact of the power of the connected wind power plant on the short-circuit currents of the traction substation. In our opinion, the coefficient applied by us more clearly characterizes the specified influence in comparison with operating values or complex sizes of short-circuit currents. Keywords: AC traction system · traction substation · Wind power plant · Increase in the short-circuit currents · multiplication factor

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 360–373, 2022. https://doi.org/10.1007/978-3-031-03877-8_32

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1 Introduction Based on the provisions of the Energy Strategy of Ukraine for the period up to 2035, a significant increase in the use of all types of renewable energy is envisaged, which can become one of the tools for ensuring the energy security of the state. In particular, for the period up to 2025, the share of renewable energy should increase to the level of 12% of the total volume of primary energy supply, and by 2035 – at least 25%. Therefore, it can be predicted that with a further reduction in the cost of energy from these sources, its economically feasible potential can grow. In turn, such a tendency should update scientific research on the integration of renewable energy sources into the energy system of Ukraine and its individual components. One of the important components of the Ukrainian energy system is the electric power supply system of the Ukrainian railway. At present, the volume of electricity consumed only for traction of trains is 3892.1 thousand kWh. At the same time, the share of energy from wind power plants is 0.81% of the purchased volume, and for solar power plants – 0.75%. In general, in the energy market of Ukraine, the corresponding shares are 0.68% and 0.5%, respectively. In our opinion, this may indicate that, on the one hand, the prospects for the use of renewable energy sources have not yet been realized in the railway power supply system, and, at the same time, the existing volume of consumption today is still insignificant. Currently, the length of the electrified railways of Ukraine is about 9 900 km, of which most (about 5 100 km) are electrified using a traction system of an alternating singlephase current with a voltage of 27.5 kV at a frequency of 50 Hz. The specified railway lines run through the vast territories of the center, west and southwest of the country. According to the estimates of the International Renewable Energy Agency (IRENA), these territories in the Southeast Europe have the greatest technical potential for the implementation of renewable energy sources. Moreover, most of it is wind energy – 859 GWh per year. Given the current trends in the transition to distributed power supply systems in traction power supply systems using renewable energy sources (the so-called hybrid systems [1]), it seems logical to use the mentioned wind energy potential as an additional independent power source for a 27.5 kV AC traction power supply system. At the same time, it should be taken into account that today there is no practical experience of integrating the wind power plants into the traction power supply system of Ukrainian railways, which means that a number of problems of a purely technical nature arise. From the point of view of ensuring uninterrupted power supply of the electric traction network, an important aspect of such integration, in our opinion, is to predict the influence of the connected wind power plant capacity on short-circuit currents in the distributive units of traction substations. Such a prediction is important not only from the point of view of ensuring the train traffic safety, but can also help to assess the necessary amount of the main equipment modernization at the traction substation to which it is planned to connect the wind power plant. We consider mathematical modeling of electromagnetic processes in the distributive units of a traction substation as the most rational way of such a prediction. It is based on a systematic approach, which consists in the fact that the specified substation and the wind power plant are considered together as a single electrical-engineering complex. Therefore, the purpose of our research is to develop

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equivalent circuits for the electrical-engineering complex “AC traction substation – wind power plant” in short-circuit modes with various options for connecting a wind power plant and determination on their basis of the nature of changing steady-state values of short-circuit currents in the distributive units of the traction substation with an increase in the capacity of the connected wind power plant.

2 Methods 2.1 Modern Approaches to Modeling the Short-Circuit Modes in Electric Power Networks As mentioned above, the work involves the implementation of the set purpose in two stages. The first stage involves the development of a computational equivalent circuit for the studied section of the electric power network. Among the works on this topic, we consider it necessary to mention the studies [2] and [3]. In particular, the work [2] is devoted to the selection of an equivalent circuit for calculating the short-circuit currents at a traction substation of an AC traction system. The main attention in the work [3] is paid to taking into account the parameters of the power-supply circuit when calculating the short-circuit currents. At the same time, the traction substation is powered in both cases from an external power supplying system (from two independent sources), and the issues of using the renewable energy sources remain without the attention of researchers. At the second stage of research, the calculation of the electric circuit obtained at the first stage should be performed in order to determine the short-circuit currents. An analysis of recent publications on this topic shows that researchers, when solving the mentioned problems, usually use the computer modeling. An example of such an approach can be seen in the work [4]. In this case, mathematical modeling is used to study the influence of the nature of the load on the short-circuit currents, but in general-purpose power grids. In another work [5], the authors indicate that the computer simulation of the operating modes of the AC traction power supply system performed by them demonstrates good general and high accuracy, including when analyzing the processes on high-speed lines and sections with heavy freight train traffic. The work [6] is another example of a computer modeling application. However, in this case, the purpose of modeling is to make a comprehensive assessment of the electric power quality at an AC traction substation. The work [7] is focused on the analysis of short-circuit currents in the network with distributed generation. The paper presents a method of vectorized calculations performed in the python environment, taking into account the requirements of the IEC 60909 standard (as is the case of [8]). It can also be added that the peculiarities of the operating modes of the traction power supply system are not covered in the two last mentioned works, in contrast, for example, to [9]. This work is directly devoted to the calculation of short-circuit currents in the design of traction substations, although hybrid systems are not studied here. Separately, it is possible to single out a number of works devoted to the study of shortcircuit currents in a traction network, both direct [10] and alternating current [11], as well as for high-speed lines [12]. The issue of the influence of an additional independent energy source on short-circuit currents is also not studied in these works.

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Closer to the end of the review, let us single out the existing works on the study of short-circuit modes directly in the generators of wind power plants and the improvement of their protection system [13–23]. However, in this case, the peculiarities of the operation of these generators for feeding the emergency modes in the AC traction power supply system are not studied, which indicates a lack of a systematic approach to the studied issue. To a certain extent, the works [24–26] can also be considered close to our chosen subject. In particular, in [24] the results of experimental research on the quality of electricity in a system with a wind power plant which is connected to a traction substation of direct current. The issue of integration of solar photovoltaic batteries into distributed power supply systems is described in [25] and [26]. So, in our opinion, in order to solve the problem, when analyzing the electromagnetic processes in short-circuit modes, firstly, it is necessary to consider the traction substation and the connected wind power plant as two subsystems of a single electrical-engineering complex. Secondly, it is necessary to prefer the classical methods of theoretical electrical engineering over less understandable computer modeling, which, however, does not exclude its use, for example, for the purpose of additional verification of the developed model adequacy. 2.2 General Structure and Peculiarities of Subsystems of the ElectriclEngineering Complex “Wind Power Plant - AC Traction Substation” From the point of view of the power supply reliability, traction substations of electrified railways in Ukraine should have at least two independent electric power sources, that is, when the voltage at one of these sources disappears, the voltage at the other must remain within standardized limits. In particular, in the diagram of Fig. 1, two overhead lines act as such sources, and through any of them the traction substation can receive power from an external power supplying system. A specificity is that, unlike DC traction substations, the three primary winding three-phase step-down transformers of the substation are simultaneously traction ones. To ensure complete redundancy, the capacity of each of them allows to fully power the traction loads at a given speed of movement on the electrified section through a 27.5 kV low-voltage winding. Medium-voltage winding 35 kV is intended for power supply of non-traction loads. The structure shown in Fig. 1 is typical for AC traction substations of Ukrainian railways, but there may be certain differences (for example, the primary voltage is 220 kV, a different number of railway power supply feeders, etc.). Based on the current experience of integrating a wind power plant into a DC traction system (Staryi Sambir wind farm), point 2 (Fig. 1), that is, a 35 kV distributive unit, can be considered as one of the rational options for connecting a wind power plant to an AC traction substation. The connection to the 27.5 kV distributive unit (point 1) can be considered as a comparable alternative in terms of capital costs. It should be noted that at DC traction substations, the connection of wind power plants of significant capacity to a traction distributive unit is practically impossible for a number of reasons, one of which is that

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uncontrolled rectifiers of traction converters can interfere with the transit of electricity to the power system in the absence of electricity consumption by the traction load. The structure of the connected wind power plant (Fig. 2) can be taken as similar to the wind farm Staryi Sambir (Lviv region), which has already been successfully integrated into the DC traction power supply system. This wind power plant consists of four generating units based on Vestas V112 turbines. The mentioned turbine has a rated capacity of 3450 kW and operates at a frequency of 50/60 Hz, the diameter of the plant rotor is 112 m, and the pole height reaches 119 m. This turbine can operate in the temperature range from −20 °C to +45 °C, which corresponds to the Ukrainian climatic conditions. The wind power plant is connected to the traction substation through a cable line with a voltage of 35 kV.

External power supplying system

Distributive unit 110 kV Traction transformers

Distributive unit 27,5 kV

Non-traction loads

1

Distributive unit 35 kV

2

Feeders Catenary Fig. 1. Block diagram of the traction substation of the AC traction system at the electrified railways of Ukraine

2.3 Development of Computational Equivalent Circuits It is obvious that the type of the developed equivalent circuits should reflect the structural peculiarities of subsystems of the studied electrical-engineering complex. It also depends on the selected point of connecting the wind power plant to the traction substation and the short-circuit mode at the computational point of the traction substation.

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Figure 3 shows a circuit developed for the analysis of three-phase short-circuit currents on 27.5 kV buses in the case of connecting a wind power plant to point 1 (27.5 kV buses). When connecting a wind power plant to 35 kV buses (point 2, see Fig. 1), a similar circuit has the structure shown in Fig. 4.

Traction substation

Frequency converter

~

High voltage line

~

Step-up transformer

G

Wind

Generator

Fig. 2. The generalized structure of the wind power plant generating unit

When constructing the circuit in Figs. 3 and 4, the following notations are used. E sys , E w1 , E w2 , E wn – complex electromotive forces of the external power supply system and wind generators of wind power plants. Z sys – complex impedance of the external power supply system, provided the substation is powered through a line with a higher current-carrying capacitance. Z TH – complex impedance of the high-voltage winding of the primary step-down transformer. Z TM – complex impedance of the medium-voltage winding of the primary step-down transformer. Z TL – complex impedance of the low-voltage winding of the primary step-down transformer. Z line – complex impedance of the high-tension line connecting the wind power plant and the traction substation. Z g1 , Z g2 , Z gn – complex impedances of wind generators. Z con1 , Z con2 , Z con n – complex impedances of frequency converters of a wind power plant generating sections. 2.4 Short-Circuit Current Analysis In accordance with the set research purpose, among the short-circuit currents of distributive units, three-phase short-circuit currents are primarily of interest, since in the overwhelming majority of cases their values are maximum. At the same time, from the viewpoint of ensuring the uninterrupted and safe traffic of trains, first of all it is necessary to study the influence of connecting a wind power plant on three-phase short-circuit currents in a 27.5 kV distributive unit, from which the traction network is directly powered. Therefore, the complex value of the three-phase short-circuit current shown in the circuits of Figs. 3 and 4 can be calculated as follows: (3)

I sc27,5 =

E eqv Z eqv

,

(1)

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Esys Zsys 110 kV

ZTH ZTM ZTL 27,5 kV

Zline

Zcon1

Zcon2

Zcon n

Zg1

Zg2

Zgn

Ew 1

Ew2

(27,5)

Іsc3

1

Ewn

Fig. 3. Equivalent circuit for calculating the current in the three-phase short-circuit mode on the 27.5 kV buses of the AC traction substation when connecting the wind power plant to point 1

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Esys Zsys 110 kV

ZTH 2

ZTM ZTL 27,5 kV

Zline (27,5)

Іsc3

Zcon1

Zcon2

Zcon n

Zg1

Zg2

Zgn

Ew1

Ew2

Ewn

Fig. 4. Equivalent circuit for calculating the current in the three-phase short-circuit mode on the 27.5 kV buses of the AC traction substation when connecting the wind power plant to point 2

where E eqv – equivalent complex electromotive force feeding the short-circuit point; Z eqv – equivalent complex impedance of a three-phase short-circuit current circuit. Equivalent complex electromotive force in the circuit of Fig. 3: E eqv =

E wes ·

1 Z wes +Z line 1 Z wes +Z line

+ E sys · +

1 Z ext

1 Z ext

,

(2)

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where E wes – complex electromotive force equivalent to all generating sections of the wind power plant; E wes =

E w1 ·

1 Z con1 +Z g1

+ E w2 ·

1 Z con1 +Z g1

+

1 Z con2 +Z g2

1 Z con2 +Z g2

+ . . . + E wn ·

+ ... +

1 Z con n +Z gn

1 Z con n +Z gn

,

(3)

Z wes – complex impedance equivalent to all generating sections of the wind power plant: Z wes =

1 1 Z con1 +Z g1

+

1 Z con2 +Z g2

+ ... +

(4)

1 Z con n +Z gn

The complex impedance of the external power supply system for the circuit in Fig. 3: Z ext = Z sys + Z TH + Z TL .

(5)

For the circuit in Fig. 4, expression (5) has the following form: Z ext = Z sys + Z TH + Z TM .

(6)

3 Results and Discussion As an example, the calculation results are presented based on the above method using the parameters of the equivalent circuit, which correspond to the main equipment set at traction substation Dubno (Western Ukraine). All parameters are based on the rated voltage of the short-circuit stage. The results are shown in Table 1 for the case when the substation is powered from the external power supply system through the line with the lowest impedance of the system for the various capacities of the connected wind power plant. Table 1. Three-phase short-circuit currents on 27.5 kV buses, A Wind power plant connection point

Wind power plant capacity, MW 0

15

30

60

120

240

480

27.5 kV buses

4562

5345

6127

7692

10820

17080

29600

35 kV buses

4562

5691

6655

8210

10370

12810

15000

In order to interpret the obtained results, we proposed to characterize the growth of the current value of the short-circuit current with increasing power of the connected wind power plant using the so-called multiplication factor of the three-phase short-circuit current. This coefficient can be calculated by expression km =

(3)

Isc (Pw ) (3)

Isc (Pw = 0)

,

(7)

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(3) where Isc (Pw ) - the effective value of the three-phase short circuit current on the busbars of the traction substation at the actual value of the power of the connected wind power plant; (3) Isc (Pw = 0) - the effective value of three-phase short circuit current on traction substation busbars in situation of absence of power of the connected wind power plant. In accordance with the results of the calculations presented in Table 1 and on the basis of expression (7), the dependences of the multiplication factor of the three-phase shortcircuit current on the 27.5 kV busbars of the Dubno traction substation with increasing power of the connected wind power plant were obtained. In particular, from Fig. 5 it can be seen that at the capacities of the connected wind power plant up to 100 MW the nature of the influence of this power on the short-circuit currents on the 27.5 kV traction substation busbars does not differ significantly in the case of connecting the wind power plant to 27.5 kV busbars. 1, Fig. 1) or 35 kV (point 2, Fig. 1). With a further increase in power, a much faster increase in the multiplication factor can be observed in the case of connecting a wind power plant to point 1 compared to connecting the same power to point 2. Therefore, the power of a wind farm will have a greater effect on the short-circuit currents of the substation when connected to point 1 compared to the connection to point 2 only at capacities greater than 100 MW.

km 6 5 1 4 3 2 2 1

0

50

100

150

200

250

300

350

400

450 P , MW

Fig. 5. Dependence of the current multiplication factor in the three-phase short-circuit mode on the 27.5 kV busbars of the AC traction substation: 1 - provided that the wind power plant is connected to point 1; 2 - situation of the wind farm connection to point 2

Based on a similar approach, it is possible to calculate the short-circuit currents in other distributive units of a traction substation under various short-circuit modes (including single-phase and two-phase short circuits), as well as when the wind power plant is connected to 110 kV high-voltage buses. The authors are planning to publish the results of such calculations in subsequent works. At the same time, as evidenced by the

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results given in Table 1, with capacities up to 30 MW inclusive, the connection of a wind power plant to both 27.5 kV buses and 35 kV buses does not entail a critical increase in short-circuit currents in the distributive units of the traction substation. The breaking capacity of even outdated sulfur-hexafluoride (SF6) circuit breakers of the VEO-27.51000-16 type with a rated breaking current of 16 kA is more than enough to protect an electrical plant from short circuits. This is one of the prerequisites for the possibility of implementing in the future the concept of hybrid systems of distributed power [1, 27, 28] on the electrified railways of Ukraine. Given the fact that the most common primary step-down transformers of AC traction substations have a capacity of 40 000 kVA, the integration of wind power plants with a capacity of more than 30 MW through the secondary voltage buses of AC traction substations is possible only with the introduction of a high-speed traffic at the section and a complete modernization of a traction substation with the transition to a distributed power supply system. Otherwise, extra-power wind power plants can be connected to the primary voltage buses. In each case, the influence of such a connection on the short-circuit currents can be tested according to the above method.

4 Summary and Conclusion In the end, the main conclusions are presented in the form a thesis that can be drawn from the results of the research performed in the work. 1) Connecting the wind power plants to the traction power supply system of Ukraine is one of the most promising ways to use the potential of renewable energy sources in Eastern Europe. 2) Predicting the influence of the connected wind power plant capacity on the shortcircuit currents of the traction substation is a key factor when ensuring the uninterrupted power supply of traction loads, as well as automation, telemechanics and communication devices. 3) This prediction can be made using the system approach proposed by the authors, in which a traction substation and an integrated wind power plant are considered as a single electrical-engineering complex, the sources of which operate to power the short-circuit point. In previously published studies, the authors usually consider the processes in renewable energy sources and in the traction power supply system separately, without taking into account the mutual influence. 4) The peculiarity of the study presented in this paper is also the use of the multiplication factor of the short-circuit current as a criterion for assessing the impact of the power of the connected wind power plant on the short-circuit currents of the traction substation. In our opinion, the coefficient applied by us more clearly characterizes the specified influence in comparison with operating values or complex sizes of short-circuit currents.

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5) It should be taken into account that in some cases the single-phase short-circuit currents of electrical plants can exceed the three-phase short-circuit currents. Therefore, the issue of the influence of connecting a wind power plant on single-phase shortcircuit currents in the distributive units of this substation requires further research. It is advisable to perform such calculations based on the method of symmetric components, taking into account the corresponding developed equivalent circuits. Also we will outline various directions of further researches. We think, that the process of transition to hybrid systems of distributed power necessiates the development of new complicated equivalent circuits for electrical-engineering complexes, which can include not only traction substations with connected renewable energy sources, but also electric energy storage devices based on supercondensers or lithium-ion batteries. This makes it possible to more efficiently use not only the energy of solar and wind power plants, but also the energy of regenerative braking of electric rolling stock [29], which should become especially relevant when introducing the high-speed traffic on sections of Ukrainian railways. Further research also requires the search for general relations of change and approximating expressions for the dependences of the multiplication factor on the parameters of the circuit of the considered electrical system and the power of the connected renewable energy source. Such research should expand the theoretical foundation, which is a prerequisite for the broad integration of renewable energy sources into the traction power supply system of the Ukrainian railways. It is also necessary to supplement the theoretical calculations with the materials of experimental and statistical studies. Such opportunities will arise after the implementation of the first projects in this direction.

References 1. Sychenko, V., et al.: The concept of a hybrid traction power supply system. MATEC Web Conf. 294, 05010 (2019). https://doi.org/10.1051/matecconf/201929401014 2. Figurnov, E., Zharkov, Yu., Popova, N.: Choosing the type of equivalent circuit of traction substation when calculating short-circuit currents in 25 kV power supply system. Vestnik Railway Res. Inst. 79, 139–144 (2020). https://doi.org/10.21780/2223-9731-2020-79-3-139-144 3. Zharkov, Yu., Popova, N., Figurnov, E.: Accounting power supply schemes for traction substations in the calculation of short circuits in the AC traction network. Vestnik Railway Res. Inst. 78, 10–18 (2019). https://doi.org/10.21780/2223-9731-2019-78-1-10-18 4. Li, Y., Yu, R., Wang, Y., Xie, J., Li, F.: Research on the influence of load on short circuit current. Dianli Xitong Baohu yu Kongzhi/Power Syst. Prot. Control. 43, 40–45 (2015) 5. Yu, X.: General mathematical model of AC traction power supply system simulation based on mathematical reasoning and its application research. In: 2020 IEEE International Conference on Artificial Intelligence and Information Systems (ICAIIS), pp. 441–446 (2020). https://doi. org/10.1109/ICAIIS49377.2020.9194938 6. Bosiy, D.: Power quality complex estimation at alternating current traction substations. Science and Transport Progress. Bulletin of Dnipropetrovsk National University of Railway Transport (2013). https://doi.org/10.15802/stp2013/16573 7. Thurner, L., Braun, M.: Vectorized Calculation of Short Circuit Currents Considering Distributed Generation - An Open Source Implementation of IEC 60909 (2018)

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8. Sweeting, D.: Applying IEC 60909, fault current calculations. IEEE Trans. Industry Appl. IEEE TRANS IND APPL. 48, 575–580 (2012). https://doi.org/10.1109/TIA.2011.2180011 9. Zhong, D.S.: The calculation of short-circuit current in the electrical design of traction substation (2017). https://doi.org/10.2991/iceat-16.2017.14 10. Pires, C., Nabeta, S.I., Cardoso, J.R.: Second-order model for remote and close-up shortcircuit faults currents on DC traction supply. Power Electron. IET 1, 348–355 (2008). https:// doi.org/10.1049/iet-pel:20070399 11. German, L.A., Karpov, I.P.: Refined Method for Calculating Short-Circuit Currents in AC Traction Network. Intellektyalna lektpotexnika, pp. 15–25 (2021). https://doi. org/10.46960/2658-6754_2021_2_15 12. Lu, N., Zhu, F., Yang, C., Yang, Y., Lu, H., Wang, Z.: The Research on Electromagnetic Emission of Traction Network with Short-circuit Current Pulse. IEEE Trans. Transp. Electrificat. 1 (2021). https://doi.org/10.1109/TTE.2021.3115578 13. Li, J., Zheng, T., Wang, Z.: Short-circuit current calculation and harmonic characteristic analysis for a doubly-fed induction generator wind turbine under converter control. Energies 11, 2471 (2018). https://doi.org/10.3390/en11092471 14. Xiang, L., Lee, S.-J., Choi, M.-S.: Short-circuit current characteristics of wind generators 36, 110–114 (2012). https://doi.org/10.3969/j.issn.1000-1026.2012.08.020 15. Hemanth Kumar, M.B., Saravanan, B.: Power quality improvement for wind energy conversion system using composite observer controller with fuzzy logic. Int. J. Intell. Syst. Appl. (IJISA), 10(10), 72–80 (2018). https://doi.org/10.5815/ijisa.2018.10.08 16. Tiwari, R., Ramesh Babu, N.: Comparative analysis of pitch angle controller strategies for PMSG based wind energy conversion system. Int. J. Intell. Syst. Appl. (IJISA) 9(5), 62–73 (2017). https://doi.org/10.5815/ijisa.2017.05.08 17. Haghjoo, F., Eghtesad, M., Yazdi, E.A.: Dynamic modeling and H∞ control of offshore wind turbines. Int. J. Eng. Manuf. (IJEM) 7(1), 10–25 (2017). https://doi.org/10.5815/ijem.2017. 01.02 18. Khani Maghanaki, P., Tahani, A.: Designing of fuzzy controller to stabilize voltage and frequency amplitude in a wind turbine equipped with induction generator. Int. J. Modern Educ. Comput. Sci. (IJMECS) 7(7), 17–27 (2015). https://doi.org/10.5815/ijmecs.2015.07.03 19. Chakkor, S., Baghouri, M., Hajraoui, A.: High resolution identification of wind turbine faults based on optimized ESPRIT algorithm. Int. J. Image, Graph. Signal Process. (IJIGSP) 7(5), 32–41 (2015). https://doi.org/10.5815/ijigsp.2015.05.04 20. Sefidgar, H., AsgharGholamian, S.: Fuzzy logic control of wind turbine system connection to pm synchronous generator for maximum power point tracking. Int. J. Intell. Syst. Appl. (IJISA) 6(7), 29–35 (2014). https://doi.org/10.5815/ijisa.2014.07.04 21. Nowdeh, S.A., Hajibeigy, M.: Economic designing of PV/FC/Wind hybrid system considering components availability. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 5(7), 69–77 (2013). https://doi.org/10.5815/ijmecs.2013.07.08 22. He, Y., Qian, X.: Contemporary development and trend of jiangsu province wind power generation technology. Int. J. Educ. Manag. Eng. (IJEME) 3(2), 46–51 (2013). https://doi. org/10.5815/ijeme.2013.02.08 23. Qian, X., He, Y.: Wind power turbine and its aerodynamic characteristics. Int. J. Educ. Manage. Eng. (IJEME) 2(7), 80–87 (2012). https://doi.org/10.5815/ijeme.2012.07.11 24. Sychenko, V., Kosariev, Ye., Pulin, M., Kuznetsova, I.: The quality of electric energy on tires of 35 kV in the parallel work of the traction substation with a wind power plant. Electromagnetic Compatibility and Safety on Railway Transport (2017). https://doi.org/10.15802/ecsrt2017/ 137709 25. Goncharov, Y., et al.: Transformation of power generated in railways dispossession belt by solar energy. Bull. Pryazovs’k State Tech. Univ. 30, 98–108 (2015). https://doi.org/10.31498/ 2225-6733.30.2015.52705

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26. Gonczarow, J.P., Syczenko, W., Bosyj, D.A., Pastuszenko, M.S., Kosariew, E.N.: Improvement of traction supply system effectiveness with application of electrical alternative energy sources. Problemy Kolejnictwa – Zeszyt 162, 65–82 (2014). DOI: https://doi.org/10.31498/ 2225-6733.30.2015.52705 27. Ostapchuk, O., Kuznetsov, V., Kruczek, W., Kuznetsov, V., Tsyplenkov, D.: Analysis of the neutral grounding modes influence on the reliability characteristics of local systems with renewable energy sources. Diagnostyka 22(1), 45–56 (2021). https://doi.org/10.29354/DIAG/ 132834 28. Ostapchuk, O., Kuznietsov, M., Kuznetsov, V., Kuznetsov, V.: Problems of the use of renewable energy sources in the structure of railway power supply. In: IOP Conference Series: Materials Science and Engineering, vol. 985, no. 1 (2020). https://doi.org/10.1088/1757899X/985/1/012011 29. Bondar, O., Ustymenko, D., Kurylenko, O., Kedria, M., Karzova, O., et al.: Experimental investigation of actual situation of using and accounting of recovered energy of regenerative braking mode at the DC traction system. MATEC Web Conf. 29401005 (2019). https://doi. org/10.1051/matecconf/201929401005

Air Quality Assessment Based on the Selection of Fitting Anomaly Detection Methods Valerii Bagaveev(B) and Rustam Latypov Department of System Analysis and Information Technologies, Kazan Federal University, Kazan 420008, Russia [email protected]

Abstract. The aim of this paper is to detect anomalous values in weather station data to correct ultrafine particle values. The relevance of the topic is determined by the fact that the air quality in large metropolitan areas is constantly deteriorating, and one needs to process the raw data correctly. We analyze data from seven anomaly detection methods. Two of them are uncontrolled detection techniques. We can assert which data are outliers and refine the original data by comparing the methods obtained and summarizing their results. Our innovation is that we have combined three methods: DBSCAN, One-Class SVM, and Isolation Forest, for the best cleanup of the raw data, which is to a certain extent different from the results of the seven methods. Keywords: Anomaly detection · 3-sigma rule · Interquartile range · Distance-based · Density-based · One-class SVM · Isolation forest

1 Introduction Nowadays, the problem of air quality in large cities is acute [1]. The World Health Organization estimates that air pollution with fine particulate matter in houses and the atmosphere leads to the premature death of about 7 million people per year and causes disability in a significant number of people who suffer from air pollution-related illnesses [2]. Therefore, the world’s scientists actively collect and research data on air quality, especially in countries with the most polluted air, such as India and Pakistan. By collecting data from meteorological stations, researchers try to predict air quality in the future [3]. The air quality index’s main factor is particulate matter less than 2.5 microns (PM 2.5). However, due to the considerable noise and emissions in PM 2.5 data, it is difficult to classify and predict air quality using traditional quality prediction models. The known studies on this topic use various methods to solve the problem. For example, the paper [4] presents an image processing-based analysis using a deep convolutional neural network, and the paper [5] gives a hybrid approach based on classification and clustering for the intrusion detection system. Also, when solving this problem, the technology of the Internet of Things is widely used [6–8]. In paper [9], methods for predicting air quality based on a Gradient Boosting Machine are developed. The paper © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 374–386, 2022. https://doi.org/10.1007/978-3-031-03877-8_33

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[10] suggests using recurrent neural networks based on Long Short-Term Memory for this purpose. Unlike other works, we use anomaly detection methods to solve the problem of air quality analysis. We have applied seven of the best-known methods to combine some of them to get the best results. In our computations, we used anomaly detection methods based on supervised techniques: the three-sigma rule [11], interquartile range [12]; methods based on clustering: distance-based [13], where the percentile value is determined by experts [14], density-based (DBSCAN) [15]. Also, methods based on unsupervised techniques are applied: one-class support vector machine (SVM) [16], isolation forest [17]. If all seven anomaly detection methods identify a value as an outlier, we can declare it an anomaly with a high probability.

2 Problem Statement Anomaly detection is the process of detecting unexpected items or events in datasets that are different from usual [17]. The task of searching for anomalies can be divided into two possible types [18]: 1) Outlier Detection – training data contains outliers, defined as observations located at a certain distance from the rest. Thus, outlier detection researchers highlight the areas where the training data is most concentrated while ignoring remote observation data. 2) Novelty Detection – learning data is not contaminated with outliers, and researchers are interested in determining if a new observation is an outlier. In this context, the outlier is also called “novelty.” A sample of air quality in India in 2013 was taken as baseline data [19]. The data contains 730 records, each with nine parameters: the average temperature (T); the minimum temperature (Tm); the maximum temperature (TM); the atmospheric pressure (SLP); the average relative humidity (H); the average wind speed (V); the average visibility (VV); the maximum constant wind speed (VM); the number of solid particles less than 2.5 microns in size (PM 2.5). In practice, it is infrequent to find data in a markup that determines “outlier/not outlier,” so we use unsupervised learning methods in our work. The problem of building a reliable validation scheme is arise when we do not know which data are anomalous. In the course of work, we determine the percentage of anomalous objects in the initial data by changing the predicted values and comparing the results. In this case, we need data pre-preparation. The data presentation is introduced in Table 1. Then, we plot the distribution histograms for each variable and the correlation matrix, shown in Fig. 1 (left and right panel, respectively). According to the given matrix, it can be concluded that the characteristics ‘T’, ‘TM’, ‘Tm’, ‘SLP’, ‘VV’, ‘V’ are correlated. Let’s divide our sample into two parts, correlated characteristics (‘T’, ‘TM’, ‘Tm’, ‘SLP’, ‘VV’, ‘V’) and uncorrelated (‘H’, ‘VM’, ‘PM 2.5’).

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V. Bagaveev and R. Latypov Table 1. Tabular data presentation

№

T

TM

Tm

SLP

H

VV

V

VM

PM 2.5

0

7.4

9.8

4.8

1017.6

93

0.5

4.3

9.4

219.720833

1

7.8

12.7

4.4

1018.5

87

0.6

4.4

11.1

182.187500

2

6.7

13.4

2.4

1019.4

82

0.6

4.8

11.1

154.037500

3

8.6

15.5

3.3

1018.7

72

0.8

8.1

20.6

223.208333

4

12.4

20.9

4.4

1017.3

61

1.3

8.7

22.2

200.645833

(a)

(b) Fig. 1. Histograms of the distribution of each variable (a) and Correlation matrix (b)

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From this plot (Fig. 2 (a)), we can conclude that the data are highly correlated, and some outliers overestimate the correlation. However, we do not take these characteristics into account when building models.

(a)

(b) Fig. 2. Relationship between all pairs of variables of correlated data (a) and Uncorrelated data plot (b)

Figure 2 (b) shows point clouds and points lying separately, that is, outliers. We are in need to detect these points in the future.

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3 Detection Anomalies in Data In this section, we show the various methods and the results of their anomaly detection. The three-sigma rule method allows detecting an anomalous value if the values of a normally distributed random variable deviate from the mathematical expectation M (x) by more than three sigmas (the probability is 1 − 0.9973 = 0.0027) [4]. Those the xi i| value is a blunder if |M (x)−x > k = 3. This algorithm detected 20 anomalous values σ (2.74%), shown in Table 2 and Fig. 3 (a).

(a)

(b) Fig. 3. The result of three-sigma rule (a) and Interquartile Range (b)

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Table 2. Results of the required metrics for each parameter Parameters

Upper_bound

Lower_bound

T

47.417187

TM Tm SLP H VV V VM PM 2.5

Anomalies_count

Anomalies_percentage

3.696629

0.0

0.000000

52.789517

11.674232

1.0

0.136799

41.636203

−3.089007

0.0

0.000000

1030.890655

985.503052

0.0

0.000000

110.515444

17.752681

0.0

0.000000

3.951268

−0.167411

1.0

0.136799

18.531561

−5.270823

4.0

0.547196

38.658636

−7.265476

9.0

1.231190

355.631082

−140.068074

5.0

0.683995

For this method, we have two opposite statements. On the one hand, this method is “hard,” cutting off a large amount of data, making it unstable for practical use. On the other hand, the mean is very dependent on outliers during the calculation, and the more there are, the more biased our mean will be so that the interquartile deviation can be used instead. Also, here we do not consider the interaction of variables; we consider each variable separately. The next method is the interquartile range, which is the difference between the higher and lower quartiles. Anomaly values are those that do not fall within this range [12]. This algorithm detected ten anomalous values (1.37%), shown in Table 3 and Fig. 3 (b). Table 3. Results of the required metrics for each parameter Parameters

Upper_bound

Lower_bound

Anomalies_count

Anomalies_percentage

T

68.25

−18.200000

0.0

0.000000

TM

64.95

−0.500000

0.0

0.000000

Tm SLP H VV V VM PM 2.5

67.60

−29.700000

0.0

0.000000

1056.10

960.200000

0.0

0.000000

135.0

−5.000000

0.0

0.000000

5.40

−1.600000

1.0

0.136700

25.90

−13.300000

0.0

0.000000

39.90

−10.500000

9.0

1.231190

484.70

−287.327083

0.0

0.000000

We also can give two statements. The first is that the boundaries are smoothed; the method is robust to outliers than the three-sigma method. Another one is that the

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interactions between variables are not taken into account, and detection is performed on each variable independently. Another method is the distance-based method. It is based on clustering. First, we form the centroid (the mean vector under all observations) from our initial data. After that, we calculate the distance from each point to the centroid. Finally, given the distances, we calculate the threshold based on the percentile. Points exceeding this “threshold” will be anomalous [13]. In this method, we need to determine two parameters: the distance metric (Euclidean, Manhattan distance, Chebyshev, and others.) and the percentile, which determines how many parameters will qualify as anomalous. The percentile value is determined expertly [7]. For example, in the case of Euclidean distance, expertly established the value of the percentile equal to 95. As a result, this algorithm identified 37 (5.06%) anomaly values (see Fig. 4 (a)).

(a)

(b) Fig. 4. The result of distance-based method with Euclidean distance (a) and distance-based method with Manhattan distance (b)

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In the case of Manhattan distance, expertly established the value of the percentile equal to 95. Like the previous one, this algorithm identified 37 (5.06%) anomalous values (see Fig. 4 (b)). This method more clearly distinguishes clusters of everyday observations that are surrounded by anomalies. Also, there is a tendency for two-dimensional data presentation. The anomalies are mostly located at the edges of the data set. Nevertheless, the disadvantage of this method is that the expert opinion chooses the percentile value. The following method is the density-based algorithm. First, it estimates how closely the points lie to each other. Then, the neighborhood of a point from the sample is selected expertly to search for other nearby points and the critical value of the number of neighbors [15]. On the plot (Fig. 5 (a)), we can see that as the size of the neighborhood increases, the percentage of anomalies tends to zero. This algorithm identified 25 (3.42%) anomaly values (shown in Fig. 5 (b)). Unlike previous methods, this method uses a density/probabilistic approach, thereby using complex cluster shapes. The method is difficult to set up, very sensitive to the parameter of the neighborhood.

(a)

(b) Fig. 5. The dependence of the size of the neighborhood (ε) on the number of clusters and the percentage of anomalies (a) and The result of density-based algorithm (b)

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Starting from this section, we use the methods for detecting anomalies based on unsupervised methods. The One-Class Support Vector Machine method separates the classes with a hyperplane to maximize the distance between them. This method works with both linearly separable data and linearly inseparable data [16]. Classes that are linearly inseparable in the current space can become separable in higher-dimensional spaces. One can transform the attribute space using the Kernel Trick function. We construct an algorithm that separates our original space by a hyperplane. As a result, we get dense data on one side of the plane; on the other side, there are outliers, that is, anomalies.

(a)

(b) Fig. 6. The result of One-Class SVM method (a) and Isolation Forest algorithm (b)

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Using this algorithm, we set the parameter ν = 0.06, which determines the percentage of anomalies that the algorithm is trying to separate from the main part of the sample. As a result, the algorithm detected 43 anomaly values (5.88%), shown in Fig. 6 (a). The model is capable of drawing nonlinear dividing boundaries. However, if the separation distance is too small, then the model may overfit. Another method is the Isolation Forest algorithm, which isolates each point from the rest in the data sample using dividing boundaries. Those points that were easy to isolate with a small number of dividing boundaries were determined and considered outliers (anomalies) [17]. This method also needs an expert assessment of the percentage of anomalies in the contamination hyperparameter. We set contamination value = 0.08. The algorithm detected 59 anomalous values (8.07%, see Fig. 6 (b)). The model uses nonlinear dividing boundaries. However, the disadvantage of this method is the problematic parameter setting, primarily if the amount of anomalous data is not known initially.

4 Final Comparison We analyzed the raw data (730 records) using seven anomaly detection methods and calculated the overall statistics (Table 4). All seven methods found anomalies in 6 entries. Therefore, we can say with a high degree of probability that these data are anomalous. Also, all models did not find outliers in 638 records. Table 4. Total amount of anomaly data detected by a certain number of models The cumulative number of models

The amount of anomaly data

0

638

1

41

2

17

3

13

5

9

7

6

We build a plot (see Fig. 7 (a)) showing which data less than 40% of the methods were recognized as outliers, color them green, what data were recognized as outliers (more than 80% of the models), color them red. Finally, another data we plot with blue color, which from 40 to 80% of the methods are recognized as outliers. According to the plot, we can ensure that the red dots are far from the main mass to be attributed to outliers.

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(a)

(b) Fig. 7. Output data plot (a) and Anomaly detection plot for selected three methods (b)

Most anomalous values were detected by unsupervised methods - Isolation Forest (59/8.07%) and One-Class SVM (43/5.88%). The least of all outliers were identified by the Interquartile Deviation method (10/1.37%). The DBSCAN method proved to be the best, with 25/3.42% anomaly values. On the plot, we can ensure that it identified all values far from the main bulk. For the final best possible cleanup of our raw data, we combine the unsupervised and DBSCAN results. We analyze three models (DBSCAN, SVM, and Isolation Forest) and give a similar table for these methods (see Table 5).

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Table 5. Total amount of anomaly data detected by the selected models The cumulative number of models

The amount of anomaly data

0

653

1

41

2

25

3

12

Visually, we can see that the initial data has been cleared of outliers, the data form dense clumps, and no far-distant points are observed (see Figs. 7 (b), 8).

Fig. 8. Cleared data plot

5 Summary and Conclusion This paper investigates the effectiveness of methods for detecting anomalies in the analysis of air quality. The baseline data was 700 air quality records containing nine different characteristics. In a pairwise comparison, only three of the nine parameters met the requirements that are presented when constructing a correlation matrix. Based on this data, we analyzed seven methods for detecting anomalies. To identify the most effective combinations of methods, it was first determined which data correlated, and such data were excluded. All methods found outliers in 6 records (0.8%) of the original data. Thus, with a high degree of probability, these data can be considered anomalous. DBSCAN, SVM, and Isolation Forest identified 12 records (1.71%) as anomalous. Having studied all the methods in detail, we can conclude that there is no need to build all seven models

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when analyzing air quality since this is a rather laborious process. It is enough to use 3 of these models. By comparing the results of these models, it is already possible to clear outliers from the original dataset. Acknowledgment. This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program (“PRIORITY-2030”).

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Author Index

A Afanasyev, Ivan, 213

Gordienko, Yuri, 248 Guzeev, Sergey, 237

B Bacherikov, Dmytro, 84 Bagaveev, Valerii, 374 Bazilo, Constantine, 84, 281 Berdnyk, Lada, 160 Bezdrabko, Valentyna, 302 Biesiedina, Svitlana, 227 Bondar, Oleh, 360 Borodai, Valerii, 160 Busher, Victor, 134, 203

H Haidai, Serhii, 14, 28 Hart, Liudmyla, 316 Havrylova, Alvina, 160 Havrysh, Bohdana, 339 Holubnyk, Tetyana, 339 Hryhoriev, Viacheslav, 302 Huliienko, Serhii, 14

C Chornyi, Oleksii, 134, 203 D Dudok, Taras, 38 Duduk, Vitalii, 69 Duriahina, Zoia, 60 E Evgeniy, Ovchinnikov, 290 F Fedorov, Eugene, 69 Filimonov, Sergey, 84, 281 Filimonova, Nadiia, 84, 281 G Garanin, Oleksandr, 302 Glazeva, Oksana, 134 Goldberg, Boris, 237

I Izonin, Ivan, 38, 49, 60 K Kachan, Yurii, 134, 360 Khamula, Orest, 339 Khasyanova, Dinara Usmanovna, 272 Khobta, Yurii, 237 Khort, D. O., 149 Klymova, Kateryna, 302 Kornienko, Yaroslav, 14, 28 Korniyenko, Bogdan, 14, 28 Korovii, Oleksandr, 170 Kostiantyn, Tkachenko, 181 Kovalska, Lesia, 302 Kovalskyi, Bohdan, 329, 339 Kryvenchuk, Yurii, 104 Kudria, Volodymyr, 213 Kulchytska, Khrystyna, 329 Kusmierczyk, Jacek, 38 Kutyrev, A. I., 149 Kuzenkov, Oleksandr, 203

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ISEM 2021, LNNS 463, pp. 387–388, 2022. https://doi.org/10.1007/978-3-031-03877-8

388 Kuznetsov, Vitaliy, 120, 134, 160, 203, 350, 360 Kuznetsova, Alisa, 350 L Lada, Nataliia, 69 Ladonia, Mariia, 248 Latypov, Rustam, 374 Leshchenko, Maryna, 69 Liaskovska, Solomiya, 49 Liubeka, Andrii, 14, 28 Lotoshynska, Nataliia, 38 M Malynovska, Yulia, 104 Martyn, Yevgen, 49 Matviienko, Oksana, 302 Mayik, Lyudmyla, 38 Mayik, Volodymyr, 38 Melnyk, Oleksiy, 95 Miroshnychenko, Oleksandra, 237 Miroshnychenko, Sergii, 237 N Nevgasymyi, Andrii, 237 Nikolenko, Anatoliy, 120 Novytskyi, Yurii, 104 O Oleksandr, Tkachenko, 181 Oleshko, Tetiana, 227 Olha, Tkachenko, 181 Onyshchenko, Svitlana, 95 Orekhov, Sergey, 3 P Pashko, Anatolii, 227 Petrashenko, Andrii, 170 Pysanchyn, Nadiya, 329

Author Index R Rak, Alexander, 134 Roman, Fedotkin, 290 Rudnytskyi, Serhii, 69 Rumiantsev, Vladislav, 203 Rusyn, Volodymyr, 193 S Sakhvadze, Gerontiy Zhorovich, 263, 272 Sambas, Aceng, 193 Selmenska, Zoryana, 329, 339 Semeniv, Mariia, 329 Sencovych, Olha, 104 Sergey, Uyutov, 290 Skiadas, Christos H., 193 Smirnov, I. G., 149 Stirenko, Sergii, 248 Stopkin, Vasyl, 120 Streltsov, Oleg, 213 Stupen, Pavel, 213 Sytnikov, Valery, 213 T Tkachenko, Roman, 60 Topylko, Nataliia, 104 Trostianchyn, Andrii, 60 Tryputen, Maksym, 120, 350 Tryputen, Mykola, 120, 203, 350 Tsyplenkov, Dmyro, 160 V Vitaliy, Kryuchkov, 290 Volianska, Nina, 350 Voliansky, Roman, 350 Y Yashchenko, Sergei, 281 Z Zakharchuk, Maryana, 104