Automation 2023: Key Challenges in Automation, Robotics and Measurement Techniques 3031258436, 9783031258435

Table of contents :
Foreword
Contents
About the Editors
Control and Automation
Output Zeroing of the Descriptor Continuous-Time Linear Systems
1 Introduction
2 Descriptor Continuous-Time Linear Systems
2.1 Weierstrass-Kronecker Decomposition of the Descriptor Systems
2.2 Controllability and Observability of the Descriptor Systems
2.3 Transfer Matrices of the Descriptor Systems
3 Output Zeroing Problem
4 Numerical Example
5 Concluding Remarks
References
Numerical Estimation of the Internal Positivity of the Fractional Order Model of a Two-Dimensional Heat Transfer Process
1 Introduction
2 Preliminaries
2.1 Elementary Ideas
2.2 Positivity
3 The Considered Heat System and Its State-Space Model
4 The Algorithms of the Numerical Testing of the Internal Positivity
5 Simulations
6 Conclusions
References
FOPID and PID - Comparison of Control Quality and Execution Time on the Example of Two Rotor Aerodynamical System
1 Introduction
2 FOPID Controller
3 Grey Wolf Optimizer
4 Mathematical Model of the Two Rotor Aerodynamical System
5 Implementation of Simulation
6 Results of Simulation
7 Conclusion
References
Analysis of Sounding Rocket Dispersion Using Monte-Carlo Simulation
1 Introduction
2 Methods
2.1 Test Platform
2.2 Rocket Model and Control System
3 Results
3.1 Minimum Number of Simulations
3.2 Rocket Dispersion Analysis
3.3 Rocket Dispersion Analysis - Malfunction
4 Discussion
5 Conclusions
References
Proactive-Reactive Approach to Disruption-Driven UAV Routing Problem
1 Introduction
2 Related Work
3 Disruption Management Vehicle Routing Problem
4 Proactive-Reactive Mission Planning for UAV Fleet
5 Computational Example
6 Conclusions
References
Network Aspects of Remote 3D Printing in the Context of Industry as a Service IDaaS
1 Introduction
2 Related Works
3 Proposed System Architecture Model
4 Network Stability and Operation Tests
5 Conclusions
References
The Concept of Use of Process Data and Enterprise Architecture to Optimize the Production Process
1 Introduction
2 Methods of Data Acquisition
3 Illustrative Example
4 Problem Description
5 Formalization of the Mathematical Model for the Illustrative Example
6 Proposal for a Future VSM Map
7 Conclusion
Appendix A. Data and Results for Experiment Number 10
References
Autonomous Mobile Flock Traffic Simulation in Digital Twin Mode
1 Introduction
2 Methodology for Urban Traffic Generation
3 Results and Discussion
4 Conclusions
References
Neural Network Model for Predicting Technological Losses of a Sugar Factory
1 Introduction
2 Review of the Literature References
3 Methods
4 Result and Discussion
5 Conclusion
References
Robotics
Parametric Identification of the Mathematical Model of a Mobile Robot with Mecanum Wheels
1 Introduction
2 Kinematics and Dynamics
3 Problem Statement
4 Experimental Verification
5 Conclusion
References
Localization of Agricultural Robots: Challenges, Solutions, and a New Approach
1 Introduction
2 Satellite-based Localization and Its Limitations
3 Exploiting the Environment Structure for Localization
4 Localization with Artificial Landmarks
5 SLAM in Agricultural Robotics
6 Achieving Accurate Localization with GNSS and SLAM
6.1 Factor Graph Representation of the Localization Problem
6.2 Graph Constraints Related to GNSS
6.3 Graph Constraints Related to SLAM
7 Results
8 Final Remarks
References
The Concept of a Gripper with Pose Estimation for Automotive Components
1 Introduction
2 Methodology
3 Results and Discussion
4 Summary
References
SpacePatrol - Development of Prospecting Technologies for ESA-ESRIC Challenge
1 Introduction
2 Overview of ESA-ESRIC Space Resources Challenge
2.1 Idea
3 Field Tests
3.1 1st Stage
3.2 2nd Stage
4 SpacePatrol System
4.1 Concept of Operation
4.2 Assets
4.3 Sensors
4.4 Communication
4.5 Localisation
4.6 Navigation
5 Lessons Learned
5.1 Achievements
5.2 Future Changes
5.3 Summary
References
Scanning Electrochemical Microscope Based on Visual Recognition and Machine Learning
1 Introduction
2 Concept of SECM
3 Results
4 Conclusions
References
Measuring Techniques and Systems
Simulation of Ultrasonic Vibration Propagation Through Resonators for Acoustic Coagulation Intensification
1 Introduction
2 Analysis of the State of the Problem
3 Materials and Methods
4 Results and Discussion
5 Conclusions
References
Mathematical Model of the Approximate Function as the Result of Identification of the Object of Automatic Control
1 Introduction
2 Materials and Methods
3 Result and Discussion
4 Conclusion
References
Regression Analysis on the Values of the Specific Activity of 137Cs in Radioactive Soil Contamination
1 Introduction
2 Research Materials and Methods
3 Results and Discussion
4 Conclusions
References
Quasi-Digital Measuring System for Mechanical Quantities
1 Introduction
2 Materials and Methods
3 Result and Discussion
4 Conclusion
References
Hyperspectral Imaging System for Food Safety Inspection
1 Introduction
2 Laboratory Experimental Setup and Results
3 Development of On-line Inspection System
4 Conclusions
References
Principal Components Method in Control Charts Analysis
1 Introduction
2 Theory of Principal Component Method
3 Numerical Example
4 Conclusions
References
Polynomial Maximization Method for Estimation Parameters of Asymmetric Non-Gaussian Moving Average Models
1 Introduction
2 Mathematical Formulation of the Problem
3 Theoretical Results
4 Statistical Modeling
5 Conclusions
References
Nanocomposites for Improved Non-enzymatic Glucose Biosensing
1 Introduction
2 Nanocomposites Used in Non-enzymatic Glucose Sensors
3 Conclusions
References
Author Index

Citation preview

Lecture Notes in Networks and Systems 630

Roman Szewczyk Cezary Zieliński Małgorzata Kaliczyńska Vytautas Bučinskas   Editors

Automation 2023: Key Challenges in Automation, Robotics and Measurement Techniques

Lecture Notes in Networks and Systems Volume 630

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

Roman Szewczyk Cezary Zieliński Małgorzata Kaliczyńska Vytautas Bučinskas •

•

•

Editors

Automation 2023: Key Challenges in Automation, Robotics and Measurement Techniques

123

Editors Roman Szewczyk Industrial Research Institute for Automation and Measurements (PIAP) Warsaw, Poland Małgorzata Kaliczyńska Industrial Research Institute for Automation and Measurements (PIAP) Warsaw, Poland

Cezary Zieliński Industrial Research Institute for Automation and Measurements (PIAP) Warsaw, Poland Vytautas Bučinskas Faculty of Mechanics, Department of Mechatronics, Robotics and Digital Manufacturing Vilnius Gediminas Technical University Vilnius, Lithuania

ISSN 2367-3370 ISSN 2367-3389 (electronic) Lecture Notes in Networks and Systems ISBN 978-3-031-25843-5 ISBN 978-3-031-25844-2 (eBook) https://doi.org/10.1007/978-3-031-25844-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Foreword

Recently Europe faces one of the most severe energy crises and raw materials shortage in its modern history. This crisis, caused by the Russian aggression on Ukraine, creates a challenge for the industry in Europe. It should be noted that this crisis negatively influences not only European economic development, but also the foundations of its democratic societies. One of the paths to alleviate this acute problem is to save resources, especially in the industry. The most efficient way for long-term saving of resources and thus mitigation of the associated economic and social risks is to speed up the Industry 4.0 transformation. The key idea “produce more with less resources” which stands behind Industry 4.0 transformation gives a realistic promise of overcoming recent problems. This volume presents the results of recent research, which supports the postulated transformation. It contains papers written by both scientists and engineers dealing with diverse aspects of: measuring techniques, robotics, mechatronics systems, control, industrial automation, numerical modelling and simulation as well as application of artificial intelligence techniques required by the transformation of the industry towards the Industry 4.0. We strongly believe that the solutions and guidelines presented in this volume will be useful for both researchers and engineers solving problems that have emerged during the recent crisis. December 2022

Roman Szewczyk Cezary Zieliński Małgorzata Kaliczyńska Vytautas Bučinskas

v

Contents

Control and Automation Output Zeroing of the Descriptor Continuous-Time Linear Systems . . . Tadeusz Kaczorek and Kamil Borawski

3

Numerical Estimation of the Internal Positivity of the Fractional Order Model of a Two-Dimensional Heat Transfer Process . . . . . . . . . . Krzysztof Oprzędkiewicz

13

FOPID and PID - Comparison of Control Quality and Execution Time on the Example of Two Rotor Aerodynamical System . . . . . . . . . Jakub Żegleń-Włodarczyk

29

Analysis of Sounding Rocket Dispersion Using Monte-Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dariusz Miedziński, Robert Głȩbocki, and Mariusz Jacewicz

39

Proactive-Reactive Approach to Disruption-Driven UAV Routing Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grzegorz Radzki, Grzegorz Bocewicz, and Zbigniew Banaszak

51

Network Aspects of Remote 3D Printing in the Context of Industry as a Service IDaaS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mateusz Salach, Andrzej Paszkiewicz, Marek Bolanowski, Andrzej Kraska, and Jakub Więcek The Concept of Use of Process Data and Enterprise Architecture to Optimize the Production Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zbigniew Juzoń, Jarosław Wikarek, and Paweł Sitek Autonomous Mobile Flock Traffic Simulation in Digital Twin Mode . . . Mantas Makulavičius, Rokas Bagdonas, Karolina Lapkauskaite, Justinas Gargasas, and Andrius Dzedzickis

62

73 85

vii

viii

Contents

Neural Network Model for Predicting Technological Losses of a Sugar Factory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nataliia Zaiets, Lidiia Vlasenko, and Nataliia Lutska

93

Robotics Parametric Identification of the Mathematical Model of a Mobile Robot with Mecanum Wheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Zenon Hendzel and Maciej Kołodziej Localization of Agricultural Robots: Challenges, Solutions, and a New Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Piotr Skrzypczyński and Krzysztof Ćwian The Concept of a Gripper with Pose Estimation for Automotive Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Adam Rydzewski and Piotr Falkowski SpacePatrol - Development of Prospecting Technologies for ESAESRIC Challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Grzegorz Gawdzik, Filip Jędrzejczyk, Michał Bryła, Marcin Słomiany, Miron Kołodziejczyk, Jakub Główka, and Matuesz Maciaś Scanning Electrochemical Microscope Based on Visual Recognition and Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Jurga Subačiūtė-Žemaitienė, Andrius Dzedzickis, Antanas Zinovičius, Vadimas Ivinskij, Justė Rožėnė, Rokas Bagdonas, Vytautas Bučinskas, and Inga Morkvėnaitė-Vilkončienė Measuring Techniques and Systems Simulation of Ultrasonic Vibration Propagation Through Resonators for Acoustic Coagulation Intensification . . . . . . . . . . . . . . . . . . . . . . . . . 165 Igor Korobiichuk, Vladyslav Shybetskyi, Myroslava Kalinina, and Katarzyna Rzeplinska-Rykala Mathematical Model of the Approximate Function as the Result of Identification of the Object of Automatic Control . . . . . . . . . . . . . . . . . 173 Igor Korobiichuk, Viktorij Mel’nick, Vera Kosova, Zhanna Ostapenko, Nonna Gnateiko, and Katarzyna Rzeplinska-Rykala Regression Analysis on the Values of the Specific Activity of 137Cs in Radioactive Soil Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Igor Korobiichuk, Viktoriia Melnyk-Shamrai, Volodymyr Shamrai, and Valentyn Korobiichuk Quasi-Digital Measuring System for Mechanical Quantities . . . . . . . . . . 195 Igor Korobiichuk, Dmytro Ornatskyi, Mariia Kataieva, and Dmytro Shcherbyna

Contents

ix

Hyperspectral Imaging System for Food Safety Inspection . . . . . . . . . . 204 Berenika Linowska and Piotr Garbacz Principal Components Method in Control Charts Analysis . . . . . . . . . . 212 Yevhen Volodarskyi, Oleh Kozyr, and Zygmunt Lech Warsza Polynomial Maximization Method for Estimation Parameters of Asymmetric Non-Gaussian Moving Average Models . . . . . . . . . . . . . . . 223 Serhii Zabolotnii, Oleksandr Tkachenko, and Zygmunt Lech Warsza Nanocomposites for Improved Non-enzymatic Glucose Biosensing . . . . . 232 Antanas Zinovičius, Vadimas Ivinskij, Timas Merkelis, Jūratė Jolanta Petronienė, and Inga Morkvėnaitė-Vilkončienė Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

About the Editors

Prof. Roman Szewczyk received both his PhD and DSc in the field of mechatronics. He specializes in modelling of properties of magnetic materials as well as in sensors and sensor interfacing, in particular magnetic sensors for security applications. He leads the development of: a sensing unit for a mobile robot developed for the Polish Police Central Forensic Laboratory and methods of non-destructive testing based on magnetoelastic effect. Professor Szewczyk has been involved in over 10 European Union-funded research projects within the FP6 and FP7 as well as projects financed by the European Defence Organization. Moreover, he has lead two regional- and national-scale technological foresight projects and was active in the organization and implementation of technological transfer between companies and research institutes. Roman Szewczyk is Secretary for Scientific Affairs in the Industrial Research Institute for Automation and Measurements PIAP. He is also Associate Professor at the Faculty of Mechatronics, Warsaw University of Technology, and Vice Chairman of the Academy of Young Researchers of the Polish Academy of Sciences. Prof. Cezary Zieliński received his MSc/Eng., PhD and habilitation degrees in control and robotics from the Faculty of Electronics and Information Technology, Warsaw University of Technology (WUT), Warsaw, Poland. He is: a full professor of WUT, the head of the Robotics Research Group, the director of the Institute of Control and Computation Engineering and the professor of Industrial Research Institute for Automation and Measurement PIAP. His research concentrates on robot control and programming methods. His research interests focus on robotics, in general, and in particular include: robot programming methods, formal approach to the specification of architectures of multi-effector and multi-receptor systems, robot kinematics, robot position-force control, visual servo control and design of digital circuits. He is the author/co-author of over 200 conference and journal papers as well as books concerned with the above-mentioned research subjects.

xi

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About the Editors

Dr. Małgorzata Kaliczyńska received her MSc/Eng. degree in cybernetics from the Faculty of Electronics, Wrocław University of Technology, and her PhD degree in the field of fluid mechanics from the Faculty of Mechanical and Power Engineering in the same university. Now she is Assistant Professor at the Industrial Research Institute for Automation and Measurement PIAP and Editor of the scientific and technological magazine “Measurements Automation Robotics”. Her areas of research interest include distributed control systems, Internet of Things, Industry 4.0, information retrieval and webometrics. Prof. Vytautas Bučinskas received engineering degree in automotive engineering from the Vilnius Civil Engineering Institute in 1985. The same year he started as an engineer of work safety in VISI, Lithuania. In 1987 he became involved in research at the same institute. In 2000 he was employed as a researcher in the Faculty of Mechanics, Department of Machine Engineering. In 2002 he obtained a doctoral degree in the field of Theory of Machines and became an associate professor at the Department of Machine Engineering, Vilnius Technical University. In 2012 he became a full professor at the same department. In 2013 the Department of Mechatronics and Robotics was established where he became the chairman. After the merging of two departments, he heads Department of Mechatronics, Robotics and Digital Manufacturing. His current research interests include design of mechatronic systems, dynamical properties of mechatronic systems, energy harvesting from vibrations. He is a fellow of the Lithuanian Association of Engineering Industry (LINPRA), Lithuanian Association of Robotics. He is an author of Lithuanian, European, US and Japanese patents. Currently he is an investigator in four H2020 ECSEL JU projects 3Ccar, Autodrive, A4DI and AI4CSM, where research focuses on autonomous vehicles and electric mobility.

Control and Automation

Output Zeroing of the Descriptor Continuous-Time Linear Systems Tadeusz Kaczorek(B) and Kamil Borawski(B) Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D Street, 15-351 Bialystok, Poland {t.kaczorek,k.borawski}@pb.edu.pl

Abstract. In the article the output zeroing problem of the descriptor continuous-time linear systems is studied. Necessary and sufficient conditions are given under which the transfer matrix of the considered class of dynamical systems is zero. It is shown that the output zeroing problem is connected to the controllability and observability of the descriptor systems. The study is based on the Weierstrass-Kronecker decomposition method. The considerations are illustrated by a numerical example.

Keywords: Continuous-time zeroing · Transfer matrix

1

· Descriptor system · Linear · Output

Introduction

A dynamical system is called descriptor (singular) if its mathematical model is represented by a combined set of differential and algebraic equations. Descriptor linear systems have been investigated in [1–15]. The computation of Kronecker’s canonical form of a singular pencil has been analyzed in [16]. The notion of controllability and observability and the decomposition of linear systems have been introduced by Kalman [17,18]. These notions are the basic concepts of the modern control theory [6,15,19–22]. They have been also extended to descriptor linear systems [5,6,23–25]. It is well-known that the controllability and observability of linear systems are generic properties of the systems [21]. Zeroing of state variables in descriptor electrical circuits by state-feedbacks has been examined in [7,8]. Invariant decoupling and blocking zeros of fractional linear systems [26] and positive linear electrical circuits with zero transfer matrices [27] has also been studied. In this paper output zeroing of the descriptor continuous-time linear systems will be investigated. The paper is organized as follows. In Sect. 2 the basic definitions and theorems concerning descriptor continuous-time linear systems are recalled. In Sect. 3 necessary and sufficient conditions are established under which T. Kaczorek and K. Borawski—These authors contributed equally to this work. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 3–12, 2023. https://doi.org/10.1007/978-3-031-25844-2_1

4

T. Kaczorek and K. Borawski

the transfer matrix of the considered class of dynamical systems is zero. Numerical example is presented in Sect. 4. Concluding remarks are given in Sect. 5. The following notation will be used: R - the set of real numbers, Rn×m - the set of n × m real matrices and Rn = Rn×1 , C - the field of complex numbers.

2 2.1

Descriptor Continuous-Time Linear Systems Weierstrass-Kronecker Decomposition of the Descriptor Systems

Consider the descriptor continuous-time linear system described by the equations E x˙ = Ax + Bu,

(1a)

y = Cx, n

(1b)

m

p

where x = x(t) ∈ R , u = u(t) ∈ R , y = y(t) ∈ R are the state, input and output vectors and E, A ∈ Rn×n , B ∈ Rn×m , C ∈ Rp×n . It is assumed that det E = 0 and the pencil is regular, i.e. det[Es − A] = 0 for some s ∈ C.

(2)

It is well-known [6,28] that if the condition (2) holds, then there exists a pair of nonsingular matrices P, Q ∈ Rn×n such that   0 In1 s − A1 (3) , A1 ∈ Rn1 ×n1 , N ∈ Rn2 ×n2 , P [Es − A]Q = 0 N s − In2 where n1 = deg{det[Es − A]}, n2 = n − n1 and N is a nilpotent matrix with the nilpotency index µ, i.e. N µ−1 = 0 and N µ = 0. The matrices P and Q can be computed using one of procedures given in [6,28]. Premultiplying (1a) by the matrix P and introducing the new state vector   x ¯1 ¯1 ∈ Rn1 , x ¯2 ∈ Rn2 , (4) = Q−1 x, x x ¯= x ¯2 we obtain

P EQQ−1 x˙ = P AQQ−1 x + P Bu, −1

y(t) = CQQ

x

(5a) (5b)

and using (3) we get x ¯˙ 1 = A1 x ¯1 + B1 u,

(6a)

Nx ¯˙ 2 = x ¯2 + B2 u,

(6b)

y1 (t) = C1 x ¯1 ,

(6c)

y2 (t) = C2 x ¯2 ,

(6d)

Output Zeroing of the Descriptor Continuous-Time Linear Systems

where

5



 B1 , B1 ∈ Rn1 ×m , B2 ∈ Rn2 ×m , B2   CQ = C1 C2 , C1 ∈ Rp×n1 , C2 ∈ Rp×n2

(7b)

y(t) = y1 (t) + y2 (t).

(7c)

PB =

(7a)

and

2.2

Controllability and Observability of the Descriptor Systems

Definition 1. The subsystem (6a), (6c) of the descriptor system (1) is called ¯1 (0) ∈ Rn1 and every finite state controllable if for every initial state x ¯10 = x ¯1 (tf ) = x ¯1,f ∈ Rn1 there exist a time tf > 0 and input u(t) in [0, tf ] such that x x ¯1,f . Definition 2. The subsystem (6b), (6d) of the descriptor system (1) is called controllable if for every initial state x ¯20 = x ¯2 (0) ∈ Rn2 and every finite state n2 x ¯2,f ∈ R there exist a time tf > 0 and input u(t) ∈ C q (the set of q times ¯2 (tf ) = x ¯2,f . piecewise continuously differentiable functions) in [0, tf ] such that x Theorem 1 [6]. The subsystem (6a), (6c) of the descriptor system (1a) is controllable if and only if   rank R1 = rank B1 A1 B1 . . . An1 1 −1 B1 = n1 . (8) Theorem 2 [6]. The subsystem (6b), (6d) of the descriptor system (1a) is controllable if and only if   rank R2 = rank B2 N B2 . . . N µ−1 B2 = n2 . (9) Definition 3. The subsystem (6a), (6c) of the descriptor system (1) is called observable if there exists a finite time tf > 0 such that for given u(t) and y1 (t) ¯10 = x ¯1 (0). in [0, tf ] it is possible to find its unique initial condition x Definition 4. The subsystem (6b), (6d) of the descriptor system (1) is called observable if there exists a finite time tf > 0 such that for given u(t) and y2 (t) ¯20 = x ¯2 (0). in [0, tf ] it is possible to find its unique initial condition x Theorem 3 [6]. The subsystem (6a), (6c) of the descriptor system (1) is observable if and only if ⎡ ⎤ C1 ⎢ C1 A1 ⎥ ⎢ ⎥ rank O1 = rank ⎢ (10) ⎥ = n1 . .. ⎣ ⎦ . C1 An1 1 −1

6

T. Kaczorek and K. Borawski

Theorem 4 [6]. The subsystem (6b), (6d) of the descriptor system (1) is observable if and only if ⎡ ⎤ C2 ⎢ C2 N ⎥ ⎢ ⎥ (11) rank O2 = rank ⎢ ⎥ = n2 . .. ⎣ ⎦ . C2 N µ−1

2.3

Transfer Matrices of the Descriptor Systems

It is well-known [28] that the transfer matrix of a descriptor system (1) consists of two parts, i.e. T (s) = C[Es − A]−1 B = Tsp (s) + Tp (s),

(12)

where Tsp (s) is a strictly proper part and Tp (s) is a polynomial part. Using the Weierstrass-Kronecker decomposition from (12) we obtain T (s) = C1 [In1 s − A1 ]

−1

−1

B1 + C2 [N s − In2 ]

where Tsp (s) = C1 [In1 s − A1 ]

−1

B2 ,

B1

is the transfer matrix of the subsystem (6a), (6c) and   −1 Tp (s) = C2 [N s − In2 ] B2 = −C2 In2 + N s + . . . + N µ−1 sµ−1 B2 .

(13a) (13b)

(13c)

is the transfer matrix of the subsystem (6b), (6d).

3

Output Zeroing Problem

In this section a class of descriptor continuous-time linear systems with zero transfer matrices will be analyzed. Theorem 5. The transfer matrix of the subsystem (6a), (6c) satisfies Tsp (s) = C1 [In1 s − A1 ]

−1

B1 = 0

(14)

if and only if all of the following conditions are met: 1) the subsystem (6a), (6c) is uncontrollable, i.e. rank R1 < n1 , where R1 is defined by (8); 2) the subsystem (6a), (6c) is unobservable, i.e. rank O1 < n1 , where O1 is defined by (10); 3) C1 B1 = 0.

Output Zeroing of the Descriptor Continuous-Time Linear Systems

7

Proof. Using the inverse Laplace transform and the Cayley-Hamilton theorem it can be shown that

n−1  −1 L−1 [Tsp (s)] = L−1 C1 [In1 s − A1 ] B1 = ck (t)C1 Ak1 B1 ,

(15)

k=0

where ck (t), k = 0, 1, . . . , n − 1 are nonzero linearly independent functions of time t. Using the similarity transformation [6,15,17,20] we obtain ⎤ ⎡ ⎡ ⎤ A11 A12 A13 A14 B11 ⎢ 0 A22 0 A24 ⎥ ⎢ B12 ⎥ −1 ⎥ ⎢ ⎥ P1−1 A1 P1 = ⎢ ⎣ 0 0 A33 A34 ⎦ , P1 B1 = ⎣ 0 ⎦ (16) 0 0 0 A44 0   C1 P1 = 0 C12 0 C14 , where (A11 , B11 , 0) represents the controllable and unobservable part; (A22 , B12 , C12 ) represents the controllable and observable part; (A33 , 0, 0) represents the uncontrollable and unobservable part; (A44 , 0, C14 ) represents the uncontrollable and observable part. It is well-known [4,17,27] that the transfer matrix (14) represents only the controllable and observable part of the subsystem (6a), (6c) and so −1

Tsp (s) = C1 [In1 s − A1 ]

B1 = C12 [Ir1 s − A22 ]

−1

B12 , r1 < n1 .

(17)

If the subsystem (6a), (6c) is uncontrollable and unobservable, then A22 = 0 and   Tsp (s) = 0 if and only if C12 B12 = C1 B1 = 0. Theorem 6. The transfer matrix of the subsystem (6b), (6d) satisfies   Tp (s) = −C2 In2 + N s + . . . + N µ−1 sµ−1 B2 = 0

(18)

if and only if all of the following conditions are met: 1) the subsystem (6b), (6d) is uncontrollable, i.e. rank R2 < n2 , where R2 is defined by (9); 2) the subsystem (6b), (6d) is unobservable, i.e. rank O2 < n2 , where O2 is defined by (11); 3) C2 B2 = 0. Proof. If the pencil (2) is regular, then by the similarity transformation we obtain ⎡ ⎡ ⎤ ⎤ N11 N12 N13 N14 B21 ⎢ 0 N22 0 N24 ⎥ −1 ⎢ ⎥ ⎥ , P B2 = ⎢ B22 ⎥ P2−1 N P2 = ⎢ 2 ⎣ 0 0 N33 N34 ⎦ ⎣ 0 ⎦ (19) 0 0 0 N44 0   C2 P2 = 0 C22 0 C24 ,

8

T. Kaczorek and K. Borawski

where (N11 , B21 , 0) represents the controllable and unobservable part; (N22 , B22 , C22 ) represents the controllable and observable part; (N33 , 0, 0) represents the uncontrollable and unobservable part; (N44 , 0, C24 ) represents the uncontrollable and observable part. It is well-known [15,19,20] that the transfer matrix (18) represents only the controllable and observable part of the subsystem (6b), (6d) and so −1

−1

Tp (s) = C2 [N s − In2 ] B2 = C22 [N22 s − Ir2 ] B22 =   µ−1 µ−1 B22 , r2 < n2 . = −C22 Ir2 + N22 s + . . . + N22 s

(20)

If the subsystem (6b), (6d) is uncontrollable and unobservable then N22 = 0 and   Tp (s) = 0 if and only if C22 B22 = C2 B2 = 0. From the above considerations we obtain the following theorem. Theorem 7. The transfer matrix (13) of the descriptor system (1) satisfies the condition T (s) = 0 (21) if and only if 1) the subsystem (6a), (6c) is uncontrollable and unobservable; 2) the subsystem (6b), (6d) is uncontrollable and unobservable; 3) C1 B1 = 0 and C2 B2 = 0. Proof. The proof follows immediately from Theorems 5 and 6.

 

Some equivalent conditions can also be formulated. Theorem 8. For the descriptor system (1) the following conditions are equivalent: 1) the system (1) is uncontrollable, unobservable and CB = 0; 2) the transfer matrix of the system (1) is a zero matrix, i.e., T (s) = 0; 3) the matrix   Es − A B C[Es − A] CB is singular for s ∈ C satisfying (2); 4) the matrix   Es − A [Es − A]B C CB is singular for s ∈ C satisfying (2).

Output Zeroing of the Descriptor Continuous-Time Linear Systems

9

Proof. The conditions 1) and 2) follows immediately from Theorem 7. Therefore, we shall show the proof for the conditions 3) and 4). Note that if the conditions 1) and 2) are satisfied, then       Es − A  [Es − A]2 [Es − A]B Es − A B = 0, (22) det = det C[Es − A] CB C where the matrix [Es−A] is nonsingular for s ∈ C (by the condition (2)). Taking into account that      Es − A 0 Es − A B [Es − A]2 [Es − A]B = C[Es − A] CB 0 Ip C[Es − A] CB    (23) Es − A [Es − A]B Es − A 0 = C CB 0 Im 

and det

   Es − A 0 Es − A 0  0, det = = 0 for s ∈ C 0 Ip 0 Im

from (23) we obtain the conditions 3) and 4).

4

(24)  

Numerical Example

Consider the descriptor continuous-time linear system (1) with ⎤ ⎡ ⎤ ⎡ −6 0 0 0 −1.5 0 −2 0 0 0 0 0 ⎢ 1 0 ⎢ 0 0 0 1 0 0⎥ 0 1 0 0 ⎥ ⎥ ⎢ ⎥ ⎢ ⎢ −3 0 ⎢ −1 0 0 0 0 0 ⎥ 0 0 −1 0 ⎥ ⎥, ⎥, A = ⎢ E=⎢ ⎢ 0 0 ⎢ 0 0 −0.5 0 0 0 ⎥ 0 0 0 −0.5 ⎥ ⎥ ⎢ ⎥ ⎢ ⎣ 1.2 0.2 0 0 0.3 ⎣ 0.4 0.2 0 0 0 0 ⎦ 0 ⎦ 2.25 0 0.125 0 0.6875 0 0.75 0 0 0 0.125 0

(25)

 T   B = −4 1 −2 0 0.8 1.625 , C = −1 0 0 2 1 0 . The matrix pencil (E, A) of (25) is regular since

In this case

det[Es − A] = 0.00625 s3 − 0.0125 ss2 − 0.0125 ss = 0.

(26)

⎤ ⎡ ⎤ 010000 0 1 0 0 00 ⎢0 0 1 0 0 0⎥ ⎢ −2 0 3 0 0 0 ⎥ ⎥ ⎢ ⎥ ⎢ ⎢0 0 0 0 1 0⎥ ⎢ 1 0 0 0 5 0⎥ ⎥ ⎢ ⎥ ⎢ P =⎢ ⎥, Q = ⎢1 0 0 0 0 0⎥, ⎥ ⎢ ⎢ 0 0 0 −2 0 0 ⎥ ⎣0 0 0 0 0 1⎦ ⎣ 1 0 4 0 0 8⎦ 000100 2 0 −4 0 0 0

(27)

⎡

10

T. Kaczorek and K. Borawski

n1 = n2 = 3, µ = 3 and ⎡

⎤ ⎤ ⎡ 100000 110000 ⎢0 1 0 0 0 0⎥ ⎢0 3 0 0 0 0⎥ ⎥  ⎥ ⎢ ⎢    ⎥ ⎢ ⎢0 0 1 0 0 0⎥ A1 0 0 0 1 0 0 0⎥ I3 0 ⎥, ⎢ ⎢ = P EQ = ⎢ = P AQ = ⎢ ⎥, ⎥ 0 N 0 I3 ⎢0 0 0 0 1 0⎥ ⎢0 0 0 1 0 0⎥ ⎣0 0 0 0 0 1⎦ ⎣0 0 0 0 1 0⎦ 000000 000001 

(28)

     T  B1 = P B = 1 2 0 0 1 0 , C1 C2 = CQ = 2 −1 0 0 0 1 , B2

From (8)–(11) and (28) we have 

rank R1 = rank B1 A1 B1 A21 B1



⎡

⎤ 13 9 = rank ⎣ 2 6 18 ⎦ = 2 < n1 , 00 0

⎡ ⎤ 2 −1 0  rank O1 = rank C1 C1 A1 C1 A21 = rank ⎣ 2 −1 0 ⎦ = 1 < n1 , 2 −1 0 

⎡

⎤ 010   rank R2 = rank B2 N B2 N 2 B2 = rank ⎣ 1 0 0 ⎦ = 2 < n2 , 000 

rank O2 = rank C2 C2 N C2 N

 2

(29)

⎡

⎤ 001 = rank ⎣ 0 0 0 ⎦ = 1 < n2 . 000

Therefore, by Theorems 1–4 it follows that both subsystems (6a), (6c) and (6b), (6d) with (28) are uncontrollable and unobservable. From (28) we also have ⎡ ⎤ ⎡ ⎤   1   0 (30) C1 B1 = 2 −1 0 ⎣ 2 ⎦ = 0, C2 B2 = 0 0 1 ⎣ 1 ⎦ = 0. 0 0 According to Theorem 7, the transfer matrix of the considered descriptor system is zero. We can check it using (13) and (25). Thus, we obtain ⎡ ⎤−1 ⎡ ⎤ 1 s − 1 −1 0   Tsp (s) = C1 [I3 s − A1 ]−1 B1 = 2 −1 0 ⎣ 0 s − 3 0 ⎦ ⎣ 2 ⎦ 0 0 0 s−1 ⎡ 1 ⎤⎡ ⎤ 1 0 1   s−1 s2 −4s+3 1 ⎦ ⎣ 2 ⎦ = 0, (31) 0 = 2 −1 0 ⎣ 0 s−3 1 0 0 0 s−1 ⎤⎡ ⎤ ⎡ 0 1 s s2     Tp (s) = −C2 I3 + N s + N 2 s2 B2 = − 0 0 1 ⎣ 0 1 s ⎦ ⎣ 1 ⎦ = 0 00 1 0

Output Zeroing of the Descriptor Continuous-Time Linear Systems

11

and T (s) = Tsp (s) + Tp (s) = 0,

(32)

which confirms the previous considerations. It is easy to check that the conditions 3) and 4) of Theorem 8 are also satisfied for the matrices (25).

5

Concluding Remarks

In this paper output zeroing of the descriptor continuous-time linear systems has been formulated and solved. It has been shown that the transfer matrix of such system is zero if and only if both subsystems (6a), (6c) and (6b), (6d) are uncontrollable, unobservable and C1 B1 = 0, C2 B2 = 0 (Theorem 7). Some additional conditions for solving the problem has also been established (Theorem 8). The considerations can be extended to the positive and fractional descriptor linear systems.

References 1. Borawski, K.: Analysis of the positivity of descriptor continuous-time linear systems by the use of Drazin inverse matrix method. In: Szewczyk, R., Zieli´ nski, C., Kaliczy´ nska, M. (eds.) AUTOMATION 2018. AISC, vol. 743, pp. 172–182. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77179-3 16 2. Borawski, K.: Superstabilization of descriptor continuous-time linear systems via state-feedback using Drazin inverse matrix method. Symmetry 12(6), 1–17 (2020) 3. Campbell, S.L., Meyer, C.D., Rose, N.J.: Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients. SIAM J. Appl. Math. 31(3), 411–425 (1976) 4. Dai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences, Springer, Heidelberg (1989). https://doi.org/10.1007/BFb0002475 5. Duan, G.R.: Analysis and Design of Descriptor Linear Systems. Springer, New York (2010). https://doi.org/10.1007/978-1-4419-6397-0 6. Kaczorek, T.: Linear Control Systems, vol. 1. Wiley, New York (1993) 7. Kaczorek, T.: Zeroing of state variables in descriptor electrical circuits by statefeedbacks. Przeglad Elektrotechniczny 89(10), 200–203 (2013) 8. Kaczorek, T.: Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks. Arch. Electr. Eng. 63(3), 321–333 (2014) 9. Kaczorek, T., Borawski, K.: Positivity and cyclicity of descriptor electrical circuits with chain structure. Bull. Pol. Acad. Sci. Tech. Sci. 70(1), 1–7 (2022) 10. Kaczorek, T., Rogowski, K.: Fractional Linear Systems and Electrical Circuits. SSDC, vol. 13. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-113616 11. Kaczorek, T., Ruszewski, A.: Analysis of the fractional descriptor discrete-time linear systems by the use of the shuffle algorithm. J. Comput. Dyn. 8(2), 153–163 (2021) 12. Kaczorek, T., Sajewski, L  : Transfer matrices with positive coefficients of positive descriptor continuous-time linear systems. In: Szewczyk, R., Zieli´ nski, C., Kaliczy´ nska, M. (eds.) Automation 2019, pp. 86–94. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-13273-6 9

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13. Sajewski, L  : Solution of the state equation of descriptor fractional continuoustime linear systems with two different fractional. In: Szewczyk, R., Zieli´ nski, C., Kaliczy´ nska, M. (eds.) Progress in Automation, Robotics and Measuring Techniques. AISC, vol. 350, pp. 233–242. Springer, Cham (2015). https://doi.org/10. 1007/978-3-319-15796-2 24 14. Virnik, E.: Stability analysis of positive descriptor systems. Linear Algebra Appl. 429(10), 2640–2659 (2008) 15. Zak, S.H.: Systems and Control. Oxford University Press, New York (2003) 16. Van Dooren, P.: The computation of Kronecker’s canonical form of a singular pencil. Linear Algebra Appl. 27, 103–140 (1979) 17. Kalman, R.E.: Mathematical descriptions of linear systems. SIAM J. Control 1, 152–192 (1963) 18. Kalman, R.E.: On the general theory of control systems. In: Proceedings of the First International Congress on Automatic Control, Butterworth, London, pp. 481–493 (1960) 19. Antsaklis, P.J., Michel, A.N.: Linear Systems. Birkhauser, Boston (2006) 20. Kailath, T.: Linear Systems. Prentice-Hall, Englewood Cliffs, New York (1980) 21. Klamka, J.: Controllability of Dynamical Systems. Kluwer Academic Publishers, Dordrecht (1991) 22. Rosenbrock, H.H.: State-Space and Multivariable Theory. Wiley, New York (1970) 23. Cobb, D.: Controllability, observability and duality in singular systems. IEEE Trans. Autom. Contr. 29(2), 1076–1082 (1984) 24. Klamka, J.: Complete controllability of singular 2-D system. In: Proceedings of 13th IMACS World Congress, Dublin, Ireland, pp. 1839–1840 (1991) 25. Yip, E., Sincovec, R.: Solvability, controllability and observability of continuous descriptor systems. IEEE Trans. Autom. Contr. 26(3), 702–707 (1981) 26. Kaczorek, T.: Invariant, decoupling and blocking zeros of fractional linear systems. Acta Mechanica et Automatica 12(1), 44–48 (2018) 27. Kaczorek, T.: Invariant decoupling and blocking zeros of positive linear electrical circuits with zero transfer matrices. Circuits Systems Signal Process. 36, 4716–4728 (2017) 28. Kaczorek, T., Borawski, K.: Descriptor Systems of Integer and Fractional Orders. Studies in Systems, Decision and Control, Springer, Cham (2021). https://doi.org/ 10.1007/978-3-030-72480-1

Numerical Estimation of the Internal Positivity of the Fractional Order Model of a Two-Dimensional Heat Transfer Process (B) Krzysztof Oprzedkiewicz 

Department of Automatic Control and Robotics, Faculty of Electrical Engineering, Automatic Control, Informatics and Biomedical Engineering, AGH University of Science and Technology, al. A Mickiewicza 30, 30-059 Krakow, Poland [email protected]

Abstract. In the paper the numerical estimation of the internal positivity of the model of a two dimensional heat transfer process is addressed. The considered thermal process is described by the fractional order state equation, derived from parabolic heat equation with homogenous Neumann boundary conditions and distributed control and observation. Two numerical algorithms of the positivity testing are proposed and compared. The first one consists in the full examination of the whole area. The next one uses Monte Carlo method. From tests it can be concluded that the considered model can be internally positive only for its lower orders and heating and measurements located closely to the corner of the tested area. The use of the Monte Carlo method allows to significantly shorten the duration of computations. The presented results can be useful in measurements using a thermal camera.

Keywords: Fractional order system method · Thermal camera

1

· Positivity · Monte Carlo

Introduction

There are many different processes in economy, biology, medicine, chemistry and engineering, which are described by models with all positive signals: control, state and output. Such systems can be described with the use of special models, so called positive models. It is characteristic that analysis of some properties for positive systems is simplier than in non positive case as well as a number of problems is easier to solve for non positive systems. Positive systems have been investigated by many Researchers for years. Theoretical fundamentals are presented e.g. in books: [8,10,14,16,17]. An interesting “academic” example of a positive system presents the paper [28]. The fractional order calculus is a convenient tool to describe many complex physical phenomena. Non-integer models have been presented by many c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 13–28, 2023. https://doi.org/10.1007/978-3-031-25844-2_2

14

K. Oprzedkiewicz 

Authors, e.g. by [4,5,7,9,23,26]. Analysis of anomalous diffusion problem using fractional order approach and semigroup theory was presented for example by [24]. An observability problem for fractional order systems has been discussed e.g. by [13]. The use of the Kelvin scale allows to describe thermal processes by positive models. Different classes of heat processes have been considered by researchers and engineers for years. Thermal processes can also be described using Fractional Order (FO) approach. This issue is presented e.g. in papers [1,2,6,15,18,25]. It is important to note that fundamental, known results do not associate the positivity to the construction of a real system. Practical guidelines about construction of a positive system or testing the positivity of a real experimental thermal plant have been proposed only in the paper [20], but this approach is a little bit bounded by assumptions about the form of a state equation. The simpliest way to testing of the positivity is an examination of a positivity of control and output matrices for particular construction of a tested system. This approach can be used for systems with relatively small amount of places for testing. If a number of possible locations of measurement is big, a computational complexity of such a job is growing rapidly. Such a situation occurs when using a thermal imaging camera. This is the motivation to propose of the Monte-Carlo based method of looking for “positive” and “non positive” parts of an image from thermal camera. The proposed method allows to estimate an area of internal positivity for thermal image. The use of the Monte Carlo method allows to obtain a good estimate of positivity areas with a relatively low effort of calculations. The paper is organized as follows. Preliminaries give some elementary ideas from fractional calculus as well as from theory of positive systems. Next the considered, two dimensional heat system and its state-space fractional order model are recalled. Furthermore two testing algorithms are proposed. The first one consists in full examination of the whole considered area, the next one uses Monte Carlo approach. Finally both algorithms are numerically validated.

2 2.1

Preliminaries Elementary Ideas

Elementary ideas from fractional calculus can be found in many books, for example: [5,12,22] or [23]. Here only some definitions necessary to explain of main results will be given. Firstly the fractional-order, integro-differential operator is given (see for example [5,14,23]):

Numerical Estimation of the Internal Positivity

15

Definition 1 (The elementary fractional order operator). The fractional-order integro-differential operator is defined as follows: ⎧ α d f (t) ⎪ α>0 α ⎪ ⎪ ⎨ dt f (t) α = 0 α . (1) a Dt f (t) = ⎪ t ⎪ α ⎪ ⎩ f (τ )(dτ ) α < 0 a

where a and t denote time limits for operator calculation, α ∈ R denotes the non integer order of the operation. Next remember an idea of Gamma Euler function [14]: Definition 2. The Gamma function ∞ Γ (x) =

tx−1 e−t dt.

(2)

0

Furthermore recall an idea of Mittag-Leffler functions. The two parameter Mittag-Leffler function is defined as follows: Definition 3 (The two parameter Mittag-Leffler function). Eα,β (x) =

∞  k=0

xk . Γ (kα + β)

(3)

For β = 1 we obtain the one parameter Mittag-Leffler function: Definition 4. The one parameter Mittag-Leffler function Eα (x) =

∞  k=0

xk . Γ (kα + 1)

(4)

The fractional-order, integro-differential operator (1) can be described by different definitions, given by Gr¨ unwald and Letnikov (GL Definition), Riemann and Liouville (RL Definition) and Caputo (C Definition). Only C definition will be employed in this paper. It is as follows [14]: Definition 5. The Caputo Definition of the FO operator.

16

K. Oprzedkiewicz 

Definition 6 (The Caputo definition of the FO operator). C α 0 Dt f (t)

1 = Γ (V − α)

∞ 0

f (V ) (τ ) dτ. (t − τ )α+1−V

(5)

In (5) V is an integer limiter of the non integer order: V − 1 ≤ α < V ∈ N. If V = 1 then consequently 0 ≤ α < 1 is considered and the definition (5) takes the form: ∞ ˙ f (τ ) 1 C α dτ. (6) 0 Dt f (t) = Γ (1 − α) (t − τ )α 0

For the Caputo operator the Laplace transform can be defined [12]: Definition 7. The Laplace transform for Caputo operator α α L(C 0 Dt f (t)) = s F (s), α < 0 α α L(C 0 Dt f (t)) = s F (s) −

v−1 

sα−k−1 0 Dtk f (0),

(7)

k=0

α > 0, v − 1 < α ≤ v ∈ N. A fractional-order linear Multi-Input, Multi-Output (MIMO) state space system, employing C definition is described as follows: C α 0 Dt x(t)

= Ax(t) + Bu(t) . y(t) = Cx(t)

(8)

where α ∈ (0, 1) denotes the fractional order of the state equation, x(t) ∈ RN , u(t) ∈ RL , y(t) ∈ RP are the state, control and output vectors respectively, A, B, C are the state, control and output matrices respectively. 2.2

Positivity

Next recall ideas and conditions of internal and external positivity of the FO system (see e.g. [11,14]). Definition 1 (The internal positivity). P The FO system (8) is called internally positive if x(t) ∈ RN + , y(t) ∈ R+ , t ≥ 0 N M for any initial conditions x0 ∈ R+ and all inputs u(t) ∈ R+ . Theorem 1. The FO system (8) is internally positive if and only if: P A ∈ MN , B ∈ RU + , C ∈ R+ .

where MN denotes the set of Metzler matrices.

(9)

Numerical Estimation of the Internal Positivity

17

Definition 2 (The external positivity). The FO system (8) is called externally positive if and only if y(t) ∈ RP +, t ≥ 0 . for homogenous initial condition x0 = 0 and all inputs u(t) ∈ RM + Theorem 2. The FO system system (8) is externally positive if and only if its impulse response matrix g(t) is nonnegative for t ≥ 0, i.e.: xM g(t) = L−1 {C(sα I − A)−1 B} ∈ RP . +

(10)

The crucial remark here is, that the internal positivity always implies the external positivity, but the reverse implication is not a true. The prooving the external positivity without internal positivity is not a trivial issue. The solution of this problem for one dimensional heat transfer equation has been presented in the paper [20].

3

The Considered Heat System and Its State-Space Model

The Fig. 1 shows the simplified scheme of the considered heat system. This is the PCB plate of size X × Y pixels. The values of X and Y are determined by the resolution of a sensor of a camera. The plate is heated by flat heater. Coordinates of the hetaer are denoted by xh1 , xh2 , yh1 and yh2 respectively. Then the heated area H is defined as follows: H = {0 < x < X, 0 < y < Y : xh1 ≤ x ≤ xh2 , yh1 ≤ y ≤ yh2 }.

(11)

The surface area SH of the heater is equal: SH = dxh dyh . where:

dxh = xh2 − xh1 , dyh = yh2 − yh1 .

(12)

(13)

The temperature is measured using thermal camera, the area of measurement is configurable and denoted by S. Its coordinates are equal xs1 , xs2 , ys1 and ys2 . S = {0 < x < X, 0 < y < Y : xs1 ≤ x ≤ xs2 , ys1 ≤ y ≤ ys2 }.

(14)

The surface area SS of the measurement area is equal:

where:

SS = dxs dys .

(15)

dxs = xs2 − xs1 , dyh = ys2 − ys1 .

(16)

18

K. Oprzedkiewicz 

Fig. 1. The simplified scheme of the experimental system. Origin of the coordinate system is located in the left upper corner.

More details about the construction of this laboratory system are given in the section “Experimental Results”. The heat transfer in the surface is described by the Partial Differential Equation (PDE) of the parabolic type. All the side surfaces of plate are much smaller than its frontal surface. This allows to assume the homogeneous Neumann boundary conditions at all edges of the plate as well as the heat exchange on the surface needs to be also considered. It is expressed by coefficient Ra . The control and observation are distributed due to the size of heater and size of temperature field read by camera. The heat conduction coefficient aw along both directions x and y is the same. The two dimensional, Integer Order (IO) heat transfer equation has been considered in many papers (e.g. [3,19,27]). The fractional version with fractional derivative along the time and 2’nd order integer derivative along the length is presented with details in the paper [21]. This paper presents the model employing the fractional derivatives along both coordinates. This allows to obtain better accuracy with its smaller size. The proposed model is as follows:

Numerical Estimation of the Internal Positivity

⎧ β

∂ Q(x, y, t) ∂ β Q(x, y, t) ⎪ C α ⎪ ⎪0 Dt Q(x, y, t) = aw + − ⎪ ⎪ ∂xβ ∂y β ⎪ ⎪ ⎪ ⎪ ⎪ ⎪−Ra Q(x, y, t) + b(x, y)u(t), ⎪ ∂Q(0,y,t) ⎪ ⎪ = 0, t ≥ 0 ⎪ ∂x ⎪ ⎪ ⎨ ∂Q(X,y,t) = 0, t ≥ 0 ∂x ∂Q(x,0,t) = 0, t ≥ 0 ⎪ ⎪ ∂y ⎪ ⎪ ∂Q(x,Y,t) ⎪ = 0, t ≥ 0 ⎪ ⎪ ∂y ⎪ ⎪ ⎪ Q(x, y, 0) = Q0 , 0 ≤ x ≤ X, 0 ≤ y ≤ Y ⎪ ⎪ ⎪ ⎪ X Y ⎪ ⎪ ⎪ Q(x, y, t)c(x, y)dxdy. ⎩y(t) = k0

19

(17)

0 0

β

β

In (17) α and β are non integer orders of the system, ∂ Q(x,y,t) , ∂ Q(x,y,t) ∂xβ ∂y β denote the fractional derivative along the x and y respectively, aw > 0, Ra ∈ R are coefficients of heat conduction and heat exchange, k0 is a steady-state gain of the model, b(x, y) and c(x, y) are heater and sensor functions described as follows:  1, x, y ∈ H, b(x, y) = (18) 0, x, y ∈ H.  1, x, y ∈ S, c(x, y) = (19) 0, x, y ∈ S. The construction of the experimental system requires to assume the homogenous Neumann boundary conditions. This yields the following form of eigenfunctions and eigenvalues:

wm,n (x, y) =

⎧ 1, m, n = 0, ⎪ ⎪ ⎪ nπy ⎪ ⎨ 2Y πn cos Y , m = 0, n = 1, 2, ...

2X mπx ⎪ πm cos X , n = 0, m = 1, 2, ... ⎪ ⎪ nπy 1 ⎪ ⎩ π2  cos mπx X cos Y , m, n = 1, 2, ... β mβ nβ Xβ

λm,n = −aw

+

(20)

Yβ

mβ nβ + π β − Ra , m, n = 0, 1, 2, .. Xβ Yβ

(21)

Consequently the considered two dimensional heat equation (17) can be expressed as an infinite dimensional state equation:  C α 0 Dt Q(t) = AQ(t) + Bu(t), (22) y(t) =< CQ(t) > .

20

K. Oprzedkiewicz 

where: AQ(t) = aw

∂ β Q(x, y) ∂ β Q(x, y) + ∂xβ ∂y β

− Ra Q(x, y),

D(A) = {Q ∈ H 2 (0, 1) : Q (0) = 0, Q (X) = 0, Q (Y ) = 0},

(23)

aw , Ra > 0, CQ(t) =< c, Q(t) >, Bu(t) = bu(t). The notation in (23) follows directly from the method of solution of a parabolic equation with the use of variables separation method, H 2 (0, 1) is the Hilbert space The state vector Q(t) is defined as beneath: T

Q(t) = [q0,0 , q0,1 , q0,2 ..., q1,1 , q1,2 , ...] .

(24)

The main difference to the model presented in the paper [21] is that the non integer order β must be taken into account in the state, control and observation operators. This is presented below. The state operator A takes the following form: A = diag{λ0,0 , λ0,1 , λ0,2 , ..., λ1,1 , λ1,2 , ..., λ2,1 , λ2,2 ..., λm,n , ...}.

(25)

The control operator takes the following form: B = [b0,0 , b0,1 , ..., b1,0 , b1,1 , ...]T . where:

(26)

X Y bm,n =< b(x, y), wm,n >=

b(x, y)wm,n (x, y)dxdy. 0

(27)

0

Taking into account (20) we obtain: ⎧ ⎪ ⎪SH2 m, n = 0, ⎪ ⎪ ⎨ 2Y2 dxh anhy , m = 0, n = 1, 2, 3, ..., hyn bm,n = 2X 2 ⎪ ⎪ h2xm dyh amhx , n = 0, m = 1, 2, 3, ..., ⎪ ⎪ ⎩ kmn a hxm hyn mhx anhy , m, n = 1, 2, 3, ...

(28)

where SH , dxh and dyh are described by (12), (13) and: mπ , X nπ . = Y

hxm = hyn km,n =

1 2  π β mβ + Xβ

(29)

nβ Yβ

.

(30)

Numerical Estimation of the Internal Positivity

amhx = sin(hxm xh2 ) − sin(hxm xh1 ), anhy = sin(hyn yh2 ) − sin(hyn yh1 ).

21

(31)

The output operator is as beneath: C = [c0,0 , c0,1 , ...., c1,0 , c1,1 , ...]. where:

(32)

X Y cm,n =< c(x, y), wm,n >=

c(x, y)wm,n (x, y)dxdy. 0

(33)

0

In (33) each element cm,n is expressed analogically, as (28): ⎧ ⎪ Ss m, n = 0, ⎪ ⎪ ⎪ 2Y 2 ⎨ h2yn dxs ansy , m = 0, n = 1, 2, 3, ..., cm,n = 2X 2 ⎪ ⎪ h2xm dys amsx , n = 0, m = 1, 2, 3, ..., ⎪ ⎪ ⎩ kmn a hxm hyn msx ansy , m, n = 1, 2, 3, ...

(34)

In (34) hxm,yn and kmn are expressed by (29), (30), SH , dxh and dyh are described by (15), (16) and: amsx = sin(hxm xs2 ) − sin(hxm xs1 ), ansy = sin(hyn ys2 ) − sin(hyn ys1 ).

(35)

Assume the homogenous initial condition in the equation (17):Q(x, y0) = 0 Then the step response is as follows: y∞ (t) =

∞ ∞  

ym,n (t).

(36)

m=1 n=1

where m, n-th mode of response is as follows: ym,n (t) =

Eα (λm,n tα ) − 1(t) bm,n cm,n . λm,n

(37)

In (37) Eα (..) is the one parameter Mittag-Leffler function (4), λm,n , bm,n and cm,n are expressed by (21), (27) and (33) respectively. Analogically the impulse response takes the following form: g∞ (t) =

∞ ∞  

gm,n (t).

(38)

m=1 n=1

where m, n-th mode of response is as follows: gm,n (t) = Eα,α (λm,n tα ) bm,n cm,n . In (39) Eα,α (..) is the two parameter Mittag-Leffler function (3).

(39)

22

K. Oprzedkiewicz 

During simulations it is possible to use of the finite - dimensional sums only. Consequently (36) and (38) take the following form: yM N (t) =

M  N 

ym,n (t).

(40)

gm,n (t).

(41)

m=0 n=0

gM N (t) =

M  N  m=0 n=0

The values of M and N assuring the assumed accuracy and convergence of the model can be estimated numerically or analytically.

4

The Algorithms of the Numerical Testing of the Internal Positivity

The numerical tests of the internal positivity use the necessary and sufficient condition (9). Its use requires to compute the control and output matrices B and C for each tested point using relations (27) and (33). If we need to test the whole sensor of a thermal camera, the numerical complexity of such a job is hard. For the camera considered in this paper the size of the sensor is: X × Y where: X = 380 and Y = 290 pixels. The examination of the whole sensor requires to compute and testing the B and C matrices 110200 times. On the other side, the examination of the whole area is most accurate and results can be used as a reference to testing with the use of another methods. In simplification the full testing of the whole area takes the following form: B_pos=0; C_pos=0; % Arrays to mark positive locations Kph=0;Kps=0; % Numbers of positive locations of heater and sensor TIC; FOR mx=1 TO X FOR ny=1 TO Y compute B,C, IF B positive THEN B_pos(mx,ny)=1;Kph=Kph+1; END; IF C positive THEN C_pos(mx,ny)=1;Kps=Kps+1; END; END; END; DURATION=TOC; %Duration of calculations MESH(1:X,1:Y,B_pos); HOLD ON; MESH(1:X,1:Y,C_pos); VIEW(2);

Numerical Estimation of the Internal Positivity

23

In a real situation we need to fastly find “positive” points to make accurate measurements. This can be done using Monte Carlo method, where all tested points are drawn inside permitted area limited by values of X and Y . The variable N t denotes the amount of tests. The proposed algorithm is as follows: B_pos=0; C_pos=0;Kph=0;Kps=0; % Variables as above TIC; r=rand(Nt,4); %Drawing of locations of heater and sensor, Nt - number of tests. xh=r(:,1)*X; yh=r(:,2)*Y; xs=r(:,3)*X; ys=r(:,4)*Y; FOR mx=1 TO Nt FOR ny=1 TO Nt compute B,C for coordinates xh,yh,xs,ys, IF B positive THEN B_pos(mx,ny)=1;Kph=Kph+1; END; IF C positive THEN C_pos(mx,ny)=1;Kps=Kps+1; END; END; END; DURATION=TOC; MESH(x_h,y_h,B_pos); HOLD ON; MESH(x_s,y_s,C_pos); VIEW(2);

5

Simulations

Simulations were done with the use of the algorithms presented in the previous section. Constant parameters of the model are given in the Table 1. Firstly the full examination of the whole area was done. During tests the “positive” locations of the heater and measurements as well as duration of calculations were estimated. Results are collected in the Table 2 and illustrated by Figs. 2, 3, 4 and 5. Table 1. Parameters of the model X

Y

α

β

aw

Ra

dxh dys dxs dys

380 290 0.9356 1.6167 0.0538 0.0089 120 20

2

2

24

K. Oprzedkiewicz  Table 2. Results of full tests. Orders M , N Kph

Kps

Duration [s]

2

13000 20601 1.6063

3

1575

5076

2.6459

4

78

2170

3.8758

5

0

1196

5.4510

Fig. 2. The “positive” locations of heater and measurement for M=N=2 and full test.

Fig. 3. The “positive” locations of heater and measurement for M=N=3 and full test.

Fig. 4. The “positive” locations of heater and measurement for M=N=4 and full test.

Numerical Estimation of the Internal Positivity

25

Fig. 5. The “positive” locations of heater and measurement for M=N=5 and full test.

Next the estimations were done using Monte Carlo method. The locations of heater and sensor were generated using uniform distribution obtained via MATLAB function rand. During each experiment 1000 places were tested. Exemplary results for different orders M , N of the model are collected in the Table 3 and illustrated by Figs. 6, 7, 8 and 9. Table 3. Results of simulations for Monte Carlo based tests. Orders M , N Number of tests Nt Kph Kps Duration [s] 2

1000

111

180 0.0240

3

1000

14

55

0.0342

4

1000

1

24

0.0389

5

1000

0

8

0.0523

All tested locations

"Positive" locations of heater and sensor

250

200

200

Y in pixels

Y in pixels

Heater Sensor

250

150

150

100

100

50

50

0

0 0

50

100

150

200

X in pixels

250

300

350

0

100

200

300

X in pixels

Fig. 6. The “positive” locations of heater and measurement for M=N=2 and 1000 tests.

26

K. Oprzedkiewicz  "Positive" locations of heater and sensor

All tested locations

250

200

200

Y in pixels

Y in pixels

Heater Sensor

250

150

150

100

100

50

50

0

0 0

50

100

150

200

250

300

350

0

100

X in pixels

200

300

X in pixels

Fig. 7. The “positive” locations of heater and measurement for M=N=3 and 1000 tests. "Positive" locations of heater and sensor

All tested locations

250

200

200

Y in pixels

Y in pixels

Heater Sensor

250

150

150

100

100

50

50

0

0 0

50

100

150

200

250

300

350

0

100

X in pixels

200

300

X in pixels

Fig. 8. The “positive” locations of heater and measurement for M=N=4 and 1000 tests. "Positive" locations of heater and sensor

All tested locations

250

200

200

Y in pixels

Y in pixels

Heater Sensor

250

150

150

100

100

50

50

0

0 0

50

100

150

200

X in pixels

250

300

350

0

100

200

300

X in pixels

Fig. 9. The “positive” locations of heater and measurement for M=N=5 and 1000 tests.

From Tables 2, 3 and Figs. 2, 3, 4, 5, 6, 7, 8 and 9 it can be observed that the increasing of the size of the model M , N descreases the area of the internal positivity. Next, the results obtained using Monte Carlo method are compliant to exact tests of the whole area and the duration of calculations is significantly shorter.

Numerical Estimation of the Internal Positivity

27

Furthermore, the positivity is easier to keep for observation tahn for control of the considered plant. In each situation the amount of positive locations of measurement, expressed by Kps is greater than the amount of positive locations of heater, described by Kph . This property will be very useful in further investigations because it can be employed to testing the positivity of heat systems without explicitly defined control, e.g. it allows to analyse responses to inital conditions.

6

Conclusions

The main final conclusion from this paper is that the proposed statistical approach allows to obtain good estimation of internally positive location of heating and measurements for the considered, two dimensional heat plant. The numerical complexity of the Monte Carlo method is much smaller than a full examination of the whole area and results are comparable. The spectrum of further investigations of the presented issue covers first of all the analytical justification of the presented numerical results. Next, the external positivity of the considered system should be investigated. This problem is important because it can be expected that an area of the external positivity will be broader than the internal one, considered in this paper. Acknowledgments. This paper was sponsored by AGH UST project no 16.16. 120.773.

References 1. Almeida, R., Torres, D.F.M.: Necessary and sufficient conditions for the fractional calculus of variations with caputo derivatives. Commun. Nonlinear Sci. Numer. Simul. 16(3), 1490–1500 (2011) 2. Baeumer, B., Kurita, S., Meerschaert, M.: Inhomogeneous fractional diffusion equations. Fract. Calc. Appl. Anal. 8(4), 371–386 (2005) 3. Berger, J., Gasparin, S., Mazuroski, W., Mendes, N.: An efficient two-dimensional heat transfer model for building envelopes. Numer. Heat Transf. Part A Appl. 79(3), 163–194 (2021) 4. Caponetto, R., Dongola, G., Fortuna, L., Petras, I.: Fractional order systems: modeling and control applications. In: Chua, L.O. (ed.) World Scientific Series on Nonlinear Science, pp. 1–178. University of California, Berkeley (2010) 5. Das, S.: Functional Fractional Calculus for System Identification and Control. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-540-72703-3 6. Dlugosz, M., Skruch, P.: The application of fractional-order models for thermal process modelling inside buildings. J. Building Phys. 1(1), 1–13 (2015) 7. Dzieli´ nski, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bull. Pol. Acad. Sci. Tech. Sci. 58(4), 583–592 (2010) 8. Farina, L., Rinaldi, S.: Positive Linear Systems: Theory and Applications. Wiley, New York, Chichester, Weinheim, Brisbane, Singapore, Toronto (2011) 9. Gal, C.G., Warma, M.: Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evol. Equ. Control. Theory 5(1), 61–103 (2016)

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10. Kaczorek, T.: Positive 1D and 2D Systems. Springer, New York (2002). https:// doi.org/10.1007/978-1-4471-0221-2 11. Kaczorek, T.: Positive stable realizations of fractional continuous-time linear systems. Int. J. Appl. Math. Comput. Sci. 21(4), 697–702 (2011) 12. Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011). https://doi.org/10.1007/978-3-642-20502-6 13. Kaczorek, T.: Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems. Int. J. Appl. Math. Comput. Sci. 26(2), 277–283 (2016) 14. Kaczorek, T., Rogowski, K.: Fractional Linear Systems and Electrical Circuits. Bialystok University of Technology, Bialystok (2014) 15. Kochubei, A.: Fractional-parabolic systems, preprint, arxiv:1009.4996 [math.ap] (2011) 16. Krause, U.: Positive Dynamical Systems in Discrete Time. Theory, Models, and Applications. De Gruyter, Berlin (2015) 17. Luenberger, D.G.: Introduction to Dynamic Systems. Theory, Models and Applications. Wiley, Hoboken (1979) 18. Mitkowski, W.: Approximation of fractional diffusion-wave equation. Acta Mechanica et Automatica 5(2), 65–68 (2011) 19. Moitsheki, R.J., Rowjee, A.: Steady heat transfer through a two-dimensional rectangular straight fin. Math. Probl. Eng. 2011(3), 1–13 (2011) K.: Positivity problem for the class of fractional order, distributed 20. Oprzedkiewicz,  parameter systems. ISA Trans. 112(1), 281–291 (2021) K., Mitkowski, W., Rosol, M.: Fractional order model of the two 21. Oprzedkiewicz,  dimensional heat transfer process. Energies 14(19), 1–17 (2021) 22. Ostalczyk, P.: Discrete Fractional Calculus. Applications in Control and Image Processing. World Scientific, New Jersey, London, Singapore (2016) 23. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999) 24. Popescu, E.: On the fractional cauchy problem associated with a feller semigroup. Math. Rep. 12(2), 181–188 (2010) 25. Rauh, A., Senkel, L., Aschemann, H., Saurin, V.V., Kostin, G.V.: An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems. Int. J. Appl. Math. Comput. Sci. 26(1), 15–30 (2016) 26. Sierociuk, D., et al.: Diffusion process modeling by using fractional-order models. Appl. Math. Comput. 257(1), 2–11 (2015) 27. Yang, L., Sun, B., Sun, X.: Inversion of thermal conductivity in two-dimensional unsteady-state heat transfer system based on finite difference method and artificial bee colony. Appl. Sci. 9(4824), 1–13 (2019) 28. Zheng, M., Ohta, Y.: Positive fir system identification using maximum entropy prior. IFAC PapersOnLine 51(15), 7–12 (2018)

FOPID and PID - Comparison of Control Quality and Execution Time on the Example of Two Rotor Aerodynamical System ˙ Jakub Zegle´ n-Wlodarczyk(B) Department of Automatics and Robotics, AGH University, Krak´ ow, Poland [email protected]

Abstract. The article presents two types of control for the Two Rotor Aerodynamical System (TRAS). The first one contains four PID controllers, the second two FOPID controllers and two PID controllers. Their coefficients were optimized by the Grey Wolf Optimizer (GWO) algorithm. The implementation of such control sets made it possible to compare the control quality and execution time of both versions of controllers. The simulations were performed in the Matlab/Simulink environment. Keywords: Two rotor aerodynamical system · Twin rotor aerodynamical system · TRAS · PID · FOPID · Optimization ORA · Control quality · Execution time

1

· GWO ·

Introduction

Air traffic has become a popular topic in recent times. In addition to airplanes, there are also helicopters that allow people to reach more inaccessible places. It is related to the possibility of vertical take-off and the use of small landing spaces. The Two Rotor Aerodynamical System (TRAS) is a scaled down laboratory version of the helicopter. However, both systems have a few differences. Most of all, TRAS works in a tether and the attack angle of the rotor blades is constant [1]. It is a system that can be classified as a non-linear. In addition, it is characterized by the presence of cross-coupling [2,2]. Therefore, it is a good system for testing controllers. One of the most popular and proven controllers is PID. Many articles have been written on this topic. Therefore, PID is very well suited for making comparisons. There have been many studies comparing many different controllers to PID. Examples include Model Predictive Controller (MPC) [3], Linear-Quadratic Regulator (LQR) [4] and Fuzzy Logic Controller [5]. There are four controllers in the TRAS system. Therefore, all coefficients should be optimized. One of the popular algorithms is Grey Wolf Optimizer c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 29–38, 2023. https://doi.org/10.1007/978-3-031-25844-2_3

30

˙ J. Zegle´ n-Wlodarczyk

(GWO), which is based on the behavior of a pack of wolves - their hierarchy and hunting strategy. Many works have shown that it fulfills its task in the optimization of PID controllers [6]. The fractional calculus was born from the question of what would happen if the n-th derivative would not be an integer number. This resulted in the development of new controllers, including the Fractional Order PID (FOPID). However, the fractional calculus requires more computing power. More theoretical information and calculation examples can be found in the book [7]. All of the above defines the problem indicated in this article - comparison of FOPID and PID controllers on the example of the TRAS system. It was decided to take into account two factors: control quality (using value of the cost function) and execution time. The next part of this article provides information about the FOPID controller. Later chapter presents the GWO algorithm. The next section deals with the mathematical model of the TRAS system. Then the implementation of the simulation is described. The final part presents the results and conclusions.

2

FOPID Controller

The FOPID controller is generalisation of the classic PID version, which emerges as a result of the assumption that the integral and the derivative parts may be of a non-integer order. This brings up two additional parameters - λ and μ. The transfer function of the FOPID controller is shown below in Eq. 1: Gc (s) = KP +

KI + KD sμ sλ

(1)

where: KP - coefficient of proportional action KI - coefficient of integral action KD - coefficient of derivative action λ - order of integral μ - order of differentiation The non-integer order of s should be utilized in order to use the FOPID controller. One example is the Oustaloup Recursive Approximation which was used in this paper [8]. This method is done in the frequency range of ω: sλ ≈ Co Π

s + ωk s + ωk

(2)

where each coefficient is described by: ωk = ωb

ωh ωb

k+N +0.5(1−r) 2N +1

, ωk = ω b

ωh ωb

k+N +0.5(1−r) 2N +1

, Co =

ωh −r ωk 2 Π . ωb s + ωk

(3)

where (ωb , ωh ) is the fixed pulsation interval and N is the fixed degree of the approximation.

FOPID and PID - Comparison of Control Quality and Execution Time

3

31

Grey Wolf Optimizer

Grey Wolf Optimizer is a meta-heuristic optimization method, which is modeled on the behavior of a pack of grey wolves - their hierarchy and hunting method [9,10]. The pack is divided into four subgroups: • • • •

alpha group - contains only a leader who commands the entire pack, beta group - alpha helpers, delta group - their task is to scout, hunt, help other groups, etc., omega group - contains the weakest individuals. When hunting, wolves use a strategy in which there are 3 stages:

1. Tracking and approaching a victim 2. Circling and harassing 3. Attacking the victim The algorithm can be described using the 4–8 formulas:

D = |C ∗ Xv (t) − X(t)|

(4)

X(t + 1) = Xv (t) − A ∗ D

(5)

A = 2a ∗ r1 − a

(6)

C = 2 ∗ r2

(7)

X(t + 1) =

Xα + X β + X δ 3

(8)

where X is the position of wolf, Xv is the location of prey, t is the current iteration, r1 , r2 ∈ [0,1] are random numbers, Xα , Xβ and Xδ specify the location vector of the alpha, beta and delta, a decrease in each iteration from 2 to 0. The algorithm ends when the maximum number of iterations is reached.

4

Mathematical Model of the Two Rotor Aerodynamical System

Two Rotor Aerodynamical System can be classified as high order nonlinear MIMO (Multiple Input Multiple Output) [11]. Example of laboratory case of such a setup is prepared by INTECO - shown in Fig. 1. The system includes a beam, at both ends of which there are two Fig. 1. Aerodynamical model of TRAS [11] rotors (main and tail) controlled by DC motors. The beam is prepared in such a way that allows the system to rotate in the X and Y planes. The system can be described by four variables: horizontal angle, vertical angle, horizontal angular velocity, vertical angular velocity. The

32

˙ J. Zegle´ n-Wlodarczyk

aerodynamic forces are controlled only by changing the speed of the rotors (the angle of attack of the rotors is constant in relation to the beam). This is possible by changing the supply voltages of the DC motors. There are cross-couplings in the system as each rotor affects both measured angles - horizontal and vertical. The mathematical model assumes that: • dynamics of the propeller subsystem can be described by the first order differential equations, • friction in the system is of the viscous type, • propeller-air subsystem could be described in accord with postulates of the flow theory. Variables needed to describe the system: Mv - total moment of forces in the vertical plane Mh - sum of moments of forces acting in the horizontal plane Jv - sum of moments of inertia relative to the horizontal axis Jh - sum of moments of inertia relative to the vertical axis αv - pitch angle of the beam αh - azimuth angle of the beam Ωh - angular velocity of the beam around the vertical axis Ωv - angular velocity around the horizontal axis ωv - angular velocity of the main rotor ωh - angular velocity of the tail rotor lm - length of the main part of the beam lt - the length of the tail part of the beam Fv (ωm ) - dependence of the propulsive force on the angular velocity of the rotor Fh (ωt ) - dependence of the propulsive force on the angular velocity of the tail rotor fv - friction coefficient in the horizontal axis fh - friction coefficient in the vertical axis Uh - horizontal DC-motor PWM control input

Uv - vertical DC-motor PWM voltage control input Hh - differential equation ωh = Hh (Uh , t) Hv - differential equation ωv = Hv (Uv , t) Kh - horizontal angular momentum Kv - vertical angular momentum mt - mass of the tail part of the beam mtr - mass of the tail motor with tail rotor mts - mass of the tail shield mm - mass of the main part of the beam mmr - mass of the main DC-motor with main rotor mms - mass of the main shield mb - mass of the counter-weight beam mcb - mass of the counter-weight lt - length of the tail part of the beam lm - length of the main part of the beam lb - length of the counter-weight beam lcb - distance between the counter-weight and the joint rms - radius of the main shield rts - radius of the tail shield khv - constant kvh - constant a1 - constant a2 - constant

For the vertical plane around horizontal axis one can obtain Eq. 9 using Newton’s second law of motion: Mv = Jv

d2 αv dt2

(9)

Additional Eqs. 10 and 11 are useful for determining the motion of the system: Ωh =

dαh dt

(10)

Ωv =

dαv dt

(11)

FOPID and PID - Comparison of Control Quality and Execution Time

33

In the case of the vertical axis, it should be remembered that the driving torques are generated by the rotors and the moment of inertia depends on the angle of the beam inclination. With that in mind, the movement around vertical axis can be described as rotative motion of a solid (Eq. 12): d2 αh (12) dt2 Using Eqs. 9–12, the TRAS system can be described as follows (13, 14, 15, 16): Mh = Jh

lm Fv (ωm ) − Ωv kv + g((A − B) cos αv − C sin αv ) − dωv = dt Jv

2 1 2 Ωh (A

+ B + C) sin 2αv Uh khv

...

+Uh khv − a1 Ωv abs(ωv ) Jv

(13)

dαv = Ωv dt Mh dKh lt Fh (ωt ) cos αv − Ωh kh + Uv kvh − a2 Ωh abs(ωh ) = = dt Jh D sin2 αv + E cos2 αv + F dαh Kh = Ωh = dt Jh αv

(14) (15) (16)

where: A = ( m2t + mtr + mts )lt B = ( m2m + mmr + mms )lm C = ( m2b lb + mcb lcb ) 2 D = m3b lb2 + mcb lcb

2 E = ( m3m + mmr + mms )lm + ( m3t + 2 mtr + mts )lt 2 F = mms rms +

mts 2 2 rts

Additionally, the following Eqs. 17 and 18 describe the motion of the rotors: Ih

dωh = Uh − Hh−1 (ωh ) dt

(17)

where: Ih - moment of inertia of the tail rotor Iv - moment of inertia of the main rotor

Iv

dωv = Uv − Hv−1 (ωv ) dt

(18)

34

5

˙ J. Zegle´ n-Wlodarczyk

Implementation of Simulation

This article focuses on the comparison of FOPID and PID controllers in terms of control quality and operation time. For this purpose a simulation (shown in the Fig. 2) was prepared in the Matlab/Simulink environment. In the central place there is a simulation model of the TRAS system (marked in gray). The outputs are azimuth angle, pitch angle, azimuth RPM, pitch RPM. The last two outputs are for reference only. Azimuth and pitch angles are used for control. With the usage of negative feedback loop both are sent to the PID/FOPID controllers. Due to the fact that the cross-coupling can be observed in the system, four controllers were used for the control. Both of the TRAS system inputs have prepared control that separately takes into account both angles.

Fig. 2. Simulation model of the TRAS system with FOPID and PID controllers

The initial range of the PID and FOPID coefficients that the GWO algorithm is trying to find are given below: KP = [0 : 50], KI = [0 : 50], KD = [0 : 50], λ = [0 : 1],

(19)

μ = [0 : 1] Furthermore, Table 1 defines additional parameters that had to be specified at the beginning of the GWO algorithm. In order to estimate the quality of the system operation, the following cost function was used: ∞ J = (|ea (t)| + |ep (t)|) dt. (20) 0

FOPID and PID - Comparison of Control Quality and Execution Time

35

Table 1. Initial parameters for GWO algorithm Parameters

Values

Number of wolves in herd

5

Maximum number of iterations 200

where: ea (t) - difference between the set point and the actual value of the azimuth angle ep (t) - difference between the set point and the actual value of the pitch angle

6

Results of Simulation

It was decided to prepare two types of control variants: • Variant 1 - all controllers in PID version, • Variant 2 - controllers processing the azimuth angle values in the FOPID version, controllers processing the values of the pitch angle in the PID version. In order to select the best controller coefficients, many simulations with the GWO algorithm were carried out. The final values are shown in Table 2. Table 2. Example of coefficients for all variants Variant 1

P

I

λ

D

μ

Azimuth PID

363.59 2.80

–

284.79 –

Azimuth-Pitch PID

2.93

10.29

–

61.14

–

Pitch-Azimuth PID

1.88

1.15

–

7.31

–

Pitch PID

55.11

27.75

–

62.50

–

λ

D

μ

Variant 2

P

I

Azimuth FOPID

2.49

139.55 −0.0064 12.41

0.99

Azimuth-Pitch FOPID 3.47

11.93

−0.94

8.87

0.062

Pitch-Azimuth PID

2.07

0.042

–

4.72

–

Pitch PID

33.65

1.089

–

67.45

–

Figure 3 shows the azimuth angle behavior. When the lower position is first reached for the first variant, a slight stop occurs, but the loss is quickly made up for. At the set point, both variants behave similarly, only towards the end version 1 is slightly further away. The upper setpoint is reached in the same way. However, it can be seen that the first option has slight problems with getting closer to the set value completely - the oscillations are not exactly around 0.8 value. When the second lower position is reached, the differences are only visible towards the end.

36

˙ J. Zegle´ n-Wlodarczyk

In variant 1 with PID controllers the first oscillation appears before the set point is approached. Variant 2 with FOPID controllers achieves the setpoint more smoothly. The behavior around the value -0.8 is quite similar with the difference that variant 1 oscillates slightly below the set point and variant 2 slightly above. In the case of pitch angle (Fig. 4) one can see the differences right from the start. Variant 1 is above the set point for the first few seconds. HowFig. 3. TRAS response for azimuth angle ever, around the maximum of the set value, it starts to fall below. Variant 2, after initial oscillations, very quickly reaches the set value and maintains it all the time. Further differences can be seen after the 20th second (then the set value of the azimuth angle changes). In this case option 2 performs much better - the oscillations are definitely smaller. A similar problem occurs at the 40th second - the azimuth angle setpoint changes again. Variant 2 responds faster, but ultimately the initial deviation is very Fig. 4. TRAS response for pitch angle similar between the two control versions. The difference appears later variant 1 remains under the set value for a long time (approx. 5 s). Table 3 shows the values of the cost function for both variants. The data shows that the version with two FOPID controllers had a better result. The main differences of the two control systems are outlined above. Table 3. Value of cost function for both variants Cost function Variant 1 307.75 Variant 2 296.60

Figures 5 and 6 show a comparison of the execution times of individual controllers. Each graph contains information about controllers for which the input signal was the same (ea (t) or ep (t)). Furthermore, Table 4 shows the average value of the calculations. FOPID controllers were about an order of magnitude

FOPID and PID - Comparison of Control Quality and Execution Time

37

slower than their classic counterparts, but were still fast enough to meet real-time control requirements. The simulations were achieved with fixed step 0.02, which shows that there is still a significant margin of time left. Measurements have been performed on computer with Intel(R) Core(TM) i5-4460 CPU @ 3.20GHz processor.

Fig. 5. Comparison of execution time between Azimuth FOPID and PitchAzimuth PID

Fig. 6. Comparison of execution time between Azimuth-Pitch FOPID and Pitch PID

Table 4. Average execution time for FOPID and PID controllers Controller version

Average execution time

Azimuth FOPID

1.5488e-07

Azimuth-Pitch FOPID 1.2072e-07

7

Pitch-Azimuth PID

1.3610e-08

Pitch PID

2.7482e-08

Conclusion

The results in this article allow the following conclusions to be drawn: • two types of control have been prepared for the TRAS system: the first with four PID controllers, the second with two FOPID controllers and two PID controllers, • the GWO algorithm found the appropriate coefficients for all controllers, • cost function values indicate that the system with FOPID controllers provided better control for the system, • FOPID controllers that use the ORA approximation are slower than their classic counterparts by an order of magnitude, but still meet the requirements of real-time systems. It is planned to compare the simulation with the real TRAS system from INTECO.

38

˙ J. Zegle´ n-Wlodarczyk

References 1. Ahmad, M., Ali, A., Choudhry, M.A.: Fixed-structure H∞ controller design for two-rotor aerodynamical system (TRAS). Arab. J. Sci. Eng. 41, 3619–3630 (2016) 2. Almtireen, N., Elmoaqet, H., Ryalat, M.: Linearized modelling and control for a twin rotor system. Autom. Control. Comput. Sci. 52, 539–551 (2018) 3. Abinaya, P., Muniraj, R., Amritha, S., Sivapalanirajan, M.: Performance comparison of MPC and PID controller for single input single output process. In: 2019 International Conference on Recent Advances in Energy-efficient Computing and Communication (ICRAECC), pp. 1–6 (2019) 4. Argentim, L.M., Rezende, W.C., Santos, P.E., Aguiar, R.A.: PID, LQR and LQRPID on a quadcopter platform. In: 2013 International Conference on Informatics, Electronics and Vision (ICIEV), pp. 1–6 (2013) 5. Bharali, J., Buragohain, M.: A comparative analysis of PID, LQR and Fuzzy logic controller for active suspension system using 3 Degree of Freedom quarter car model. In: 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), pp. 1–5 (2016) 6. Anbumani, K., Ranihemamalini, R., Pechinathan, G.: GWO based tuning of PID controller for a heat exchanger process. In: Third International Conference on Sensing, Signal Processing and Security (ICSSS), pp. 417–421 (2017) 7. Ostalczyk, P.: Discrete Fractional Calculus: Applications in Control and Image Processing World Scientific, Singapore (2015) 8. Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(1), 25–39 (2000) 9. Mirjalili, S., Mirjalili, S.M., Lewis, A.: Grey wolf optimizer. In: Advances in Engineering Software, vol. 69, pp. 46–61 (2014) ˙ 10. Zegle´ n-Wlodarczyk, J., Dziedzic, K.: Optimization of the FOPID parameters of the 3D crane control system by using GWO. In: 2021 25th International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 13–18 (2021) 11. INTECO. Two Rotor Aerodynamical System User’s Manual

Analysis of Sounding Rocket Dispersion Using Monte-Carlo Simulation Dariusz Miedzi´ nski, Robert Gle¸bocki, and Mariusz Jacewicz(B) Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Nowowiejska 24 Street, 100190 Warsaw, Poland {dariusz.miedzinski,robert.glebocki,mariusz.jacewicz}@pw.edu.pl

Abstract. In this paper the Monte-Carlo method was used to investigate the sounding rocket dispersion. It was assumed that the rocket is equipped with a control unit composed of 32 solid propellant lateral thrusters. The 6 degree-of-freedom model was developed and implemented in the MATLAB/Simulink environment. Several factors affecting the projectile dispersion were taken into account, including uncertainties in rocket’s inertial and aerodynamic parameters, magnitude and direction of wind velocity as well as uncertainties in initial conditions. In addition, the influence of the malfunction of the rocket fins and the time of flight of its occurrence on the mean impact point was investigated.

Keywords: Sounding rocket Malfunction analysis

1

· Monte-Carlo · Impact point dispersion ·

Introduction

Vertically launched sounding rockets have been used for years. The typical mission profile is composed of vertical launch, ascending flight and descending phase. These rockets after reaching the apogee are going back to the earth. One of the most important problems is to predict the safety area during the real flight. Several factors might influence the impact point location, for example uncertainties in mass parameters, launch conditions, main motor characteristics, wind and aerodynamic parameters. The launcher structure might deflect and oscillate during the launch phase. On the other hand, the environmental conditions are difficult to predict before the real flight. Some technical inaccuracies (for example fins misalignment) might also influence the projectile aerodynamic characteristics and cause some unintended behavior of the rocket. Moreover, typically these rockets does not have the control system that can be used to point the projectile to the intended location. Adding the controlled flight functionality could increase the unit cost of the sounding rocket. In that way after projectile launch often there is no possibility to influence intentionally D. Miedzi´ nski, R. Gl¸ebocki and M. Jacewicz—These authors contributed equally to this work. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 39–50, 2023. https://doi.org/10.1007/978-3-031-25844-2_4

40

D. Miedzi´ nski et al.

the rocket trajectory. The reasonable control system intended for use with these rockets should be as simple as possible and low cost. Sometimes, these sounding rockets are equipped with some rescue systems (for example parachute) or even pyrotechnical auto-destruction systems. However, if these subsystems fail during flight the rocket might hit the ground at relatively large speed. The projectile might fly outside the border of the test range. In the worst-case scenario the rocket disintegration might appear during the flight. Such possibilities should be considered before each rocket firing. To ensure a high safety level the safety area must be precisely estimated. To predict the rocket dispersion Monte-Carlo simulation might be used. This method is often used in external ballistics. Up to this time several authors addressed the problem of sounding rocket dispersion. Noga et al. [1] shown how Monte-Carlo might be used for sounding rocket mission planning and suggested that this approach might be replaced by the much simpler root sum square method. Soares et al. [2] developed open source flight simulator that allows to predict the landing points. Wilde [3] analysed the risk areas for spin stabilized sounding rocket. He concluded that spin stabilisation could reduce the impact point dispersion. Le et al. [4] discussed the influence of fin cant angle on the dispersion and also concluded that the spin motion about the longitudinal axis of symmetry might reduce the dispersion. Eerland et al. [5] developed an open-source code that might be used for impact point prediction purposes. Saghafi and Khalilidelshad [6] presented how the Monte-Carlo simulation might be used to identify some potential design weakness. They investigated the influence of a large number of model parameters on the projectile dispersion. In the above-mentioned works only unguided rockets were considered. However, only a few researchers also addressed the problem of controlling the sounding rockets. Scheurpflug et al. [7] presented the results of Monte-Carlo simulations for two simulation scenarios (unguided and guided flight). The topic of projectiles dispersion reduction have been well studied in the context of military applications. A parametric analysis of dispersion for the guided military projectile was presented by Jacewicz et al. in [8,9]. Jitpraphai and Costello [10] reported that the reduction might be effectively reduced using lateral thrusters. First, the main motivation behind the presented study was to evaluate a parametric analysis for various system uncertainties. In that way the influence of several factors on the projectile dispersion might be understood in detail. This knowledge could be used for the purpose of flight trials planning. Second, the important contribution of this paper is the use of control system based on the lateral thrusters to decrease the sounding projectile dispersion. The lateral motors are used in several anti-aircraft guided missiles and anti-tank short range projectiles. On the other hand, their usage for sounding rockets have not been considered up widely to this time. In this paper the Monte-Carlo method was used to investigate the influence of several parameter uncertainties on the resulting dispersion for both: uncontrolled and controlled projectiles. This research partially fills the gap in the literature on the subject of guided sounding rockets.

Analysis of Sounding Rocket Dispersion Using Monte-Carlo Simulation

41

The rest of the manuscript is organized as follows. In Sect. 2 the test platform and the research methodology have been described. In Sect. 3 the results of numerical simulations have been shown. The paper ends with the summary of main findings. Some further research directions are also suggested.

2 2.1

Methods Test Platform

A single-stage rocket was used as a test platform. The rocket is equipped with a solid propellant motor and is aerodynamically stabilized with four trapezoidal fins (Fig. 1). lateral thrusters

nose cone

main motor

control unit

Fig. 1. Projectile used as a test platform.

During the flight, the rocket spins around the longitudinal axis of symmetry due to fin cant angle. The length of the projectile is around 1.7 m and the diameter equals 0.122 m. The initial mass of the projectile is 35.7 kg and after main motor burnout it decreases to 29.7 kg. The main motor burns for around 4 s and gives a maximum thrust of 7300 N. It was assumed that the rocket is equipped with a control system that is composed of a set of 32 small, solid propellant lateral thrusters. These motors could generate forces that are perpendicular to the longitudinal axis of symmetry of the projectile. Each thruster might be used only once. The single lateral motor operates by 0.05 s and could generate force 800 N. The main advantage of this kind of actuator (when compared to deflected aerodynamic control surfaces and main motor thrust vectoring) is simple design and the absence of movable parts. 2.2

Rocket Model and Control System

Six degree of freedom mathematical model of the rocket was developed. It was assumed that the simulation starts at the moment when the projectile leaves the launcher. The details about this model could be found in [9,11,12]. The uncertainties in mass, moments of inertia, initial conditions, aerodynamic coefficients and main motor thrust misalignment have been considered. It was assumed that the wind azimuth and velocity do not change with altitude. The control system is used in the descending phase of flight to decrease the impact point dispersion. At first, the coordinates of the preferred impact point

42

D. Miedzi´ nski et al.

location must be known and implemented in the onboard processing unit. In the last portion of trajectory, if the projectile is not pointed to the desired location the lateral motors are activated to change the missile flight path. To realize effectively the guidance process the projectile must rotate about the longitudinal axis with some angular rate (typically between 2000◦ /s and 6000◦ /s). The lateral thrusters are fired when several conditions are fulfilled simultaneously. These conditions are as follows: • The i-th lateral motor has not been already fired (where i = 1...32). • The time between two firings must be larger than τ : t − tlast > τ.

(1)

where t is actual time of flight (measured from launch) and tlast is time of previous motor firing. The minimum allowed time between two motor firings was set to τ = 0.5 s. • The side thruster should be fired at the right projectile roll angle: |γ − Φi − π − P τsk | < ε.

(2)

where γ is the commanded flight direction (for example γ = 0◦ means ascending flight, γ = 90◦ flight in left, etc.), Φi is the angular location of the i-th thruster with respect to projectile body, P is projectile roll angular velocity, τsk is one half of time of the thruster operation (in this case τsk = 0.025 s). • The actual pitch angle is smaller than some predefined value Θg and the time from launch is larger than the threshold tg : Θ < Θg ∧ t > tg .

(3)

The guidance process should starts in the last, descending phase of flight so Θg = −5◦ and tg = 40 s. In that way it is ensured, that the controlled flight will not start too early. The detailed description of the firing logic algorithm might be found in [8,9]. Modified proportional navigation algorithm [13,14] was applied to calculate the value of γ in Eq. 2. It was assumed that the projectile is equipped with a strapdown inertial navigation system integrated with GPS receiver. The flight parameters (linear accelerations and angular rates) are measured using onboard inertial measurement unit (IMU). The IMU is equipped with low cost sensors (three accelerometer and three gyroscopes) created using microelectromechanical system technology. Projectile linear velocity and position might be estimated from abovementioned data.

3

Results

The developed model was implemented in MATLAB/Simulink 2020b. Fixed step, Runge-Kutta 4th order solver was used to numerically integrate the equations of motion. The step size was set to 0.0002 s. The model was optimized to

Analysis of Sounding Rocket Dispersion Using Monte-Carlo Simulation

43

make the calculations efficient. To increase the simulation speed the Simulink “Accelerator Mode” has been used. Parallel Computing Toolbox was used to further speed up the calculations. For each simulation run the trajectory has been saved for postprocessing purposes. The calculations took place on the workstation equipped with Intel(R) Xeon(R) W-2295 [email protected] (18 cores/36 threads) and 64 GB RAM. The projectile was fired at elevation angle 75◦ from location (0,0,0). It was assumed that the parachute is not used in the descending phase. To generate the pseudorandom input data the Marsenne-Twister algorithm was used [15]. The parameters has been calculated as a sum of nominal value and the Gauss distribution with zero mean and standard deviation σ. Only wind azimuth was generated using a uniform distribution. The parameters of the numerical simulation are presented in Table 1. Table 1. Simulation parameters Parameter [unit]

Symbol Mean value Standard deviation

Initial mass [kg] Propellant mass [kg] Initial CoG location [mm] Initial CoG location [mm] Initial CoG location [m] Final CoG location [mm] Final CoG location [mm] Final CoG location [mm] Initial moment of inertia [10−6 · kgm2 ] Initial moment of inertia [10−6 · kgm2 ] Initial moment of inertia [10−6 · kgm2 ] Initial product of inertia [10−6 · kgm2 ] Initial product of inertia [10−6 · kgm2 ] Initial product of inertia [10−6 · kgm2 ] Final moment of inertia [10−6 · kgm2 ] Final moment of inertia [10−6 · kgm2 ] Final moment of inertia [10−6 · kgm2 ] Initial product of inertia [10−6 · kgm2 ] Initial product of inertia [10−6 · kgm2 ] Initial product of inertia [10−6 · kgm2 ] Initial axial velocity [m/s] Initial side velocity [m/s] Initial normal velocity [m/s] Initial roll rate [◦ /s]

m0 mp xcg0 ycg0 zcg0 xcgk ycgk zcgk Ixx0 Iyy0 Izz0 Ixy0 Iyz0 Ixz0 Ixxk Iyyk Izzk Ixyk Iyzk Ixzk U0 V0 W0 P0

29.7 6 714.1 −0.7 −0.17 799.8 −0.87 −0.22 69029 6473585 6473434 −5408 220 −183 59389 5464885 5464730 −3638 219 266 40 0 0 0

2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 [%] 2 1 1 σP1 (continued)

44

D. Miedzi´ nski et al. Table 1. (continued)

Parameter [unit]

Symbol Mean value Standard deviation ◦

Initial pitch rate [ /s] Q0 0 Initial yaw rate [◦ /s] R0 0 ◦ Initial roll angle [ ] Φ0 0 Initial pitch angle [◦ ] Θ0 90 Initial yaw angle [◦ ] Ψ0 0 ◦ Thrust pitch misalignment [ ] ΘT 0 Thrust yaw misalignment [◦ ] ΨT 0 1 V¯W Wind speed [m/s] VW ΨW 0 Wind azimuth [◦ ] Aerodynamic coeff. [-] Ci NA3 a Dependent on the run, values provided in Sect. 3.2 b A uniform distribution in the range from 0 [◦ ] up to 360 [◦ ] c According to the tabulated values

3.1

1 σQ 1 σR 1 σΦ 1 σΘ 1 σΨ 1 σΘ T 1 σΨ T 2.5 2 σΨ W 5 [%]

was used

Minimum Number of Simulations

At first it was required to estimate the minimum possible number of simulations. Too small number of simulation runs will result in unreliable results. On the other hand, the large number of simulation evaluations effects in a large computational cost and long calculation time. To obtain the minimum required number of simulation runs the single scenario was evaluated 10000 times. The projectile position was calculated in On xn yn zn (North-East-Down) coordinate frame. In this convention, xn axis is pointed to the geographic north, yn is pointed in east direction and zn axis is pointed toward the surface of the Earth. The obtained three dimensional trajectories and resulting dispersion pattern are presented in Fig. 2. The vertical coordinate zn is negative because zn = −h where h is flight altitude.

Fig. 2. Results of 10000 runs for trajectory (left) and dispersion pattern (right).

Analysis of Sounding Rocket Dispersion Using Monte-Carlo Simulation

45

Using the obtained results, the mean point of impact (MPI) was calculated as: n

xM P I =

1 xi . n i=1

yM P I =

1 yi . n i=1

(4)

n

(5)

where n is number of firings, xi and yi are coordinates of the i-th impact point. Next, it was assumed that the ground truth location of the impact point might be calculated for n=1000. Later, the mean impact point was calculated as a function of number of simulation runs. The resulting plot is presented in Fig. 3.

Fig. 3. Mean point of impact location as a function of number of runs.

From Fig. 3 it might be concluded that the minimum number of runs is approximately 1000. 3.2

Rocket Dispersion Analysis

3.2.1 Influence of Initial Angular Rates on the Dispersion The simulations were evaluated for five combinations of standard deviations of initial angular rates (0.25◦ /s, 2.50◦ /s, 4.00◦ /s, 5.50◦ /s, 7.00◦ /s) and mean values of wind speed (2.5 m/s, 5.0 m/s, 7.5 m/s, 10.0 m/s, 12.5 m/s). For each scenario 1000 runs was evaluated. Next, the same process took place for the controlled rockets. Totally 1000 × 5 × 5 × 2 simulations have been evaluated. Statistical analysis was performed to investigate the projectile dispersion. Circular Error Probable (CEP) was used as a measure of dispersion. CEP is a radius of circle centered on the MPI inside which lands 50% of launched rockets. Median estimator was applied to obtain the value of CEP. The values of CEP for the uncontrolled firings are presented in Table 2.

46

D. Miedzi´ nski et al.

Table 2. Dispersion for initial angular rates uncertainties (uncontrolled launches). σP , σQ , σR Vw = 2.5 m/s Vw = 5.0 m/s Vw 7.5 = m/s Vw = 10.0 m/s Vw = 12.5 m/s 0.25◦ /s

786.95

895.43

1062.60

1161.40

1268.80

2.50◦ /s

815.91

888.17

1054.60

1141.90

1279.30

4.00◦ /s

835.34

882.66

1034.30

1158.30

1286.80

5.50◦ /s

864.57

912.38

1011.50

1180.20

1307.30

7.00◦ /s

849.60

943.69

1018.50

1168.80

1343.80

The same experiments have been evaluated for the controlled rockets. The values of CEP are shown in Table 3. Table 3. Dispersion for initial angular rates uncertainties (controlled launches). σP , σQ , σR Vw = 2.5 m/s Vw = 5 m/s Vw 7.5 = m/s Vw = 10 m/s Vw = 12.5 m/s 0.25◦ /s

382.99

464.75

531.95

664.65

843.00

2.50◦ /s

384.33

449.73

528.14

653.60

809.26

4.00◦ /s

406.46

456.69

553.45

677.95

806.73

5.50◦ /s

425.87

453.87

582.44

681.66

819.89

7.00◦ /s

445.08

496.93

602.63

690.31

840.41

The dispersion strongly depends on the mean wind speed. The influence of the initial angular rates uncertainties on the CEP is less important. The using of control system could decrease the rocket dispersion significantly. 3.2.2 Influence of the Initial Euler Angles on the Dispersion The same methodology was then used to investigate the influence of uncertainties in the initial attitude angles of the rocket (0.25◦ , 1.00◦ , 2.00◦ , 3.00◦ , 4.00◦ ) on the resulting dispersion, using the mean values of wind speed from Sect. 3.2.1. The results for uncontrolled flights are presented in Table 4 and for controlled ones in Table 5. Table 4. Dispersion for initial Euler angles uncertainties (uncontrolled launches). σΦ , σΘ , σΨ Vw = 2.5 m/s Vw = 5.0 m/s Vw 7.5 = m/s Vw = 10.0 m/s Vw = 12.5 m/s 0.25◦

786.95

895.43

1062.60

1161.40

1268.80

1.00◦

786.16

924.56

1003.70

1119.60

1315.50

2.00◦

820.81

944.84

1050.00

1217.50

1348.30

3.00◦

890.94

977.50

1101.70

1259.80

1432.00

4.00◦

1061.20

1152.70

1220.90

1341.60

1437.30

Analysis of Sounding Rocket Dispersion Using Monte-Carlo Simulation

47

Table 5. Dispersion for initial Euler angles uncertainties (controlled launches). σΦ , σΘ , σΨ Vw = 2.5 m/s Vw = 5.0 m/s Vw 7.5 = m/s Vw = 10.0 m/s Vw = 12.5 m/s 0.25◦

382.99

464.75

531.95

664.65

843.00

1.00◦

386.50

452.61

534.15

677.42

839.71

2.00◦

450.70

540.22

599.05

742.44

896.83

3.00◦

491.77

616.72

690.62

823.38

898.21

4.00◦

612.67

727.48

793.08

865.27

1033.30

Dispersion increases with increasing the standard deviation of initial Euler angles and the mean wind speed. The CEP for uncontrolled firings is larger when compared with the guided projectiles. The maximum value of CEP for uncontrolled simulations was 1437.30 m (angular rates standard deviation 4◦ /s and mean wind speed 12.5 m/s). On the other hand, maximum CEP for guided flight is only 1033.30 m (for the same conditions). 3.2.3 Influence of the Main Motor Thrust Misalignment on the Dispersion The last set of simulations took into account the effect of main motor thrust misalignment angles. A set of various misalignment angles was defined (0.2◦ , 0.4◦ , 0.6◦ , 0.8◦ , 1.0◦ ). Obtained dispersion values for unguided rockets, using the same number of mean wind speeds from Sect. 3.2.1, are shown in Table 6 and for controlled in Table 7. The CEP increases rapidly with increasing the main motor thrust misalignment. Table 6. Dispersion for main motor thrust misalignment uncertainties (uncontrolled launches) σΘT , σΨT

Vw = 2.5 m/s Vw = 5.0 m/s Vw = 7.5 m/s Vw = 10.0 m/s Vw = 12.5 m/s

0.2◦

786.95

895.43

1062.60

1161.40

1268.80

0.4◦

1355.20

1387.40

1529.90

1594.70

1711.90

0.6◦

1963.90

2044.20

2121.90

2211.00

2279.70

0.8◦

2494.70

2634.40

2743.10

2820.50

2885.80

1.0◦

3043.40

3165.40

3295.60

3416.40

3432.90

Table 7. Dispersion for main motor thrust misalignment uncertainties (controlled launches) σΘT , σΨT

Vw = 2.5 m/s Vw = 5.0 m/s Vw 7.5 = m/s Vw = 10.0 m/s Vw = 12.5 m/s

0.2◦

382.99

464.75

531.95

664.65

843.00

0.4◦

867.04

904.36

1021.50

1170.20

1320.90

0.6◦

1530.90

1562.40

1661.60

1772.10

1793.30

0.8◦

2095.30

2219.50

2316.70

2370.80

2405.40

1.0◦

2824.60

2887.30

3091.30

3170.30

3182.30

48

3.3

D. Miedzi´ nski et al.

Rocket Dispersion Analysis - Malfunction

Next, the influence of rocket malfunction on the dispersion was investigated. It was assumed that after certain time the emergency state could appear (for example the single fin might be desintegrated). This failure could create an asymmetry in the aerodynamic loads and might influence the projectile trajectory. A set of simulations was performed for the case of spinning and not spinning projectile. Time of malfunction was iterated between 0 and 75 s and for each time 1000 of Monte Carlo simulations were performed with nominal values of standard deviations in all parameters from Table 1. The plot of the mean impact point as a function of malfunction time for both cases of spinning motion is presented in Fig. 4.

4

Discussion

From the set of Tables 2, 3, 4, 5, 6 and 7 it might be concluded that the uncertainties in initial angular rates have smaller influence on the dispersion size compared to effect of the mean wind speed. For the unguided flight the CEP values resulting from different wind speeds are in range from 786.95 m to 3432.90 m. When the control system was used the CEP was reduced to the range from 382.99 m to 3182.30 m. The analysis of the rocket malfunction, in terms of losing one of the lifting surfaces, showed that this event has the biggest impact on the distance from the launch position during the initial phase of flight. It might also be

Fig. 4. Mean point of impact location as a function of time of malfunction.

Analysis of Sounding Rocket Dispersion Using Monte-Carlo Simulation

49

concluded that the spinning motion of the projectile has a stabilizing effect, counteracting the disturbances resulting from additional aerodynamic effects caused by the flow asymmetry after losing one of the fins. The spinning motion reduced the mean impact point distance from the launch position by about 20 m, whereas the overall malfunction increased it by more than 200 m. The mean distance is further increased if the malfunction takes place until the 20th second of flight by up to 30 m for spinning motion and up to 100 m for non-spinning flight.

5

Conclusions

In this paper the Monte-Carlo simulation was used to investigate the influence of various uncertainties on the dispersion of sounding rocket. The simulations were performed for five different values of either initial angular rates, initial attitude angles or initial thrust misalignment angles and mean wind speed values. The using of control system composed of lateral thrusters could decrease significantly the rocket dispersion. Additionally the influence of losing one of the lifting surfaces on the mean impact point distance from the launch position was investigated. It was found that the most important factor that affects the projectile behaviour is the mean wind speed and the biggest influence of the fin malfunction occured during initial phase of the flight. Further research might concentrate on evaluating the flight trials in order to validate the obtained results. The influence of other parameters (for example the lateral motor thrust, fin cant angle, etc.) on the dispersion might be also investigated. Acknowledgment. This work was supported by The National Centre for Research and Development Grant number DOB-SZAFIR/03/B/002/01/2021.

References 1. Noga, T., Michal´ ow, M., Ptasi´ nski, G.: Comparison of dispersion calculation methods for sounding rockets. J. Space Saf. Eng. 8, 288–296 (2021). https://doi.org/ 10.1016/j.jsse.2021.08.006 2. Soares, J.L.G., et al.: RocketPy: Combining Open-Source and Scientific Libraries to Make the Space Sector More Modern and Accessible (2022) 3. Wilde, P.: Range safety requirements and methods for sounding rocket launches. J. Space Saf. Eng. 5, 14–21 (2018). https://doi.org/10.1016/j.jsse.2018.01.002 4. Le, V.D.T., Nguyen, A.T., Nguyen, L.H., Dang, N.T., Tran, N.D., Han, J.-H.: Effectiveness analysis of spin motion in reducing dispersion of sounding rocket flight due to thrust misalignment. Int. J. Aeronaut. Space Sci. 22(5), 1194–1208 (2021). https://doi.org/10.1007/s42405-021-00383-x 5. Eerland, W.J., Box, S., S´ obester, A.: Cambridge rocketry simulator - a stochastic six-degrees-of-freedom rocket flight simulator. J. Open Res. Softw. 5, 1–5 (2017). https://doi.org/10.5334/jors.137

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6. Saghafi, F., Khalilidelshad, M.: A Monte Carlo dispersion analysis of a rocket flight simulation software. In: Al-Dabass, D. (ed.) Proceedings 17th European Simulation Multiconference, pp. 222–228. Society for Modelling and Simulation International, Nottingham (2003) 7. Scheurpflug, F., Kallenbach, A., Cremaschi, F.: Sounding rocket dispersion reduction by second stage pointing control. J. Spacecr. Rocket. 49, 1159–1162 (2012). https://doi.org/10.2514/1.A32193 8. Jacewicz, M., Gbocki, R.: Parametric study of guidance of a 160-mm projectile steered with lateral thrusters. Aerospace 7, 61 (2020). https://doi.org/10.3390/ aerospace7050061 9. Jacewicz, M., Glebocki, R., Ozog, R.: Monte-Carlo based lateral thruster parameters optimization for 122 mm rocket. In: Szewczyk, R., Zieli´ nski, C., Kaliczy´ nska, M. (eds.) AUTOMATION 2020. AISC, vol. 1140, pp. 125–134. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-40971-5 12 10. Jitpraphai, T., Costello, M.: Dispersion reduction of a direct fire rocket using lateral pulse jets. J. Spacecr. Rocket. 38, 929–936 (2001). https://doi.org/10.2514/2.3765 11. Gl¸ebocki, R., Jacewicz, M.: Sensitivity analysis and flight tests results for a vertical cold launch missile system. Aerospace 7(22), 168 (2020). https://doi.org/10.3390/ aerospace7120168 12. Jacewicz, M., Lichota, P., Miedzi´ nski, D., Gl¸ebocki, R.: Study of model uncertainties influence on the impact point dispersion for a gasodynamicaly controlled projectile. Sensors 22(9), 1–20 (2022). https://doi.org/10.3390/s22093257 13. Moran, I., Altilar, T.: Three Plane Approach for 3D True Proportional Navigation. https://doi.org/10.2514/6.2005-6457. https://arc.aiaa.org/doi/abs/10.2514/ 6.2005-6457 14. Jitpraphai, T., Burchett, B., Costello, M.: A comparison of different guidance schemes for a direct fire rocket with a pulse jet control mechanism, p. 38 (2002). https://doi.org/10.2514/6.2001-4326 15. Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998). https://doi.org/10.1145/272991.272995

Proactive-Reactive Approach to Disruption-Driven UAV Routing Problem Grzegorz Radzki , Grzegorz Bocewicz(B)

, and Zbigniew Banaszak

Faculty of Electronics and Computer Science, Koszalin University of Technology, Koszalin, Poland {grzegorz.bocewicz,zbigniew.banaszak}@tu.koszalin.pl

Abstract. The dynamics of the environment in which UAV missions are carried out forces the need to predict situations threatening their planned implementation. A study of the literature on the subject shows a gap related to the work dedicated to modelling and planning the mission of the UAV fleet, taking into account the impact of the environment on its course. The dynamics of environmental changes caused by variable weather conditions (change in wind direction and its intensity, the temperature and humidity, turbulence occurrence etc.), as well as order changes, emphasizes the growing importance of proactive planning methods, and in particular, due to the ad hoc occurrence of unforeseen sudden events, including the possibility of moving obstacles (e.g., bird migrations), and also reactive planning. In order to fill this gap, a new extension of the well-known VRP class, with a new so-called DMVRP, has been proposed. On the basis of a model that takes into account the impact of some of the previously mentioned disruptions, a method of proactive-reactive planning of UAVs missions was developed. Computer experiments indicate the possibilities of its use online for situations occurring in practice, including those caused by ecological disasters. Keywords: Disruptions · Disruptions management · UAV · VRP

1 Introduction This article considers the Disruption Management Vehicle Routing Problem (DMVRP), which is an extension of the classic formulation of the VRP problem to include the occurrence of adverse events (disruptions). The VRP problem formulated by Dantzig and Ramsey in 1959 [1] was a generalization of the TSP problem [2]. In its original form, VRP is defined as follows. The directed graph G = (V, E), representing the transportation is given,   network,   where: V = {v1 , . . . , vn } is the set of vertices, and E ⊆ (v i , vj  vi , vj ∈ V 2 , i = j is a set of arcs. Each arc is assigned a value (weight) from the domain of non-negative real numbers specified by the function C: E → R+ 0 . In this network, the vertex of the v1 represents the base, and the ∈ V\{v vertices v i 1 } represent delivery points and related orders. The weights of the   arcs vi , vj ∈ E connecting the vertices represent the cost of transportation between them (time, distance, etc.). The transport of goods to individual customers is carried © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 51–61, 2023. https://doi.org/10.1007/978-3-031-25844-2_5

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out via a fleet of homogeneous vehicles U = {u1 , . . . , uk , . . . , um } (where: uk represents the k-th vehicle of the fleet, and m determines the number of vehicles). The routes along which vehicles move  are represented by routes defined as closed paths  (cycles): πi = vi1 , vi2 , . . . , vil(i) , where: l(i)-is the length of the i-th route; i1 = 0;     i2 , . . . , il(i) ∈ {1, .., n}; vil , vil+1 ∈ E for l = 1, . . . , (l(i) − 1) and vil(i) , vi1 ∈ E. Each πi route is assigned a cost cπ i determined as the sum of the weights of the arcs l(i)−1 that make up this route: cπ i = l=1 C(vil , vil+1 ) + C(vil(i) , vi1 ). The transport costs of the entire vehicle fleet are determined by: CK = m i=1 cπ i . With these assumptions, the problem of vehicle routing boils down to the answer to the question: What set of routes Π = {π1 , . . . , πi , . . . , π m } guarantees the minimum value of the CK cost? [3]. In the presented approach to the VRP problem, however, there are no variables and limitations specifying the various cases encountered in practice. The needs associated with this implied new formulation of the VRP class extends this problem with elements that could take into account, among others: vehicle load capacity (Capacitated Vehicle Routing Problem, CVRP [1]), division of missions into several submissions (Split Delivery Vehicle Routing Problem, SDVRP [4]), time windows (Vehicle Routing Problem with Time Windows, VRPTW [5]) as well as the occurrence of many bases in the transportation network (Multi Depot Vehicle Routing Problem, MDVRP [6]). The general assumptions about the vehicle used in the VRP problem allow easy adaptation of the problem for various types of vehicles used, e.g., land (trucks) [7], surface (ships) [8], underwater (submarines) [9] or air (UAVs) [10]. The dynamics of the environment and the related specificity of the missions carried out in them are characterized by numerous randomly variable parameters [10], implying situations in which proactively planned missions (before implementation) become nonactual. Changes in parameters leading to interferences of planned missions will hereinafter be referred to as disruptions [11–13]. The most common types of disruptions found in the literature are: damage to vehicle [7, 14, 15], rescheduling of orders [16, 17], change in the value of the order [17], and others such as change in wind direction and intensity, and change in the weight of UAV caused by the unloading of deliveries. These disruptions occur sporadically [18]. In this context, this article is a continuation of our previous research on the problem of routing the UAV fleet in a dynamic environment. The main contributions of this study are three-fold and include: • A literature review attempting to systematize the types of disruptions involved in UAV mission planning. • Proposal of a generic model of proactive-reactive mission planning of the UAV fleet, taking into account the occurrence of selected disruptions. • Development of sufficient conditions for which it reduces the space of solutions acceptable, to an extent that allows for planning missions of the scale occurring in practice. The paper is organized as follows. Section 2 reviews the relevant literature discussing the taxonomy of disruptions addressed in the problems of disruption Management VRP (DMVRP). Section 3 introduces the reference problem representing the DMVRP class.

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Section 4 presents a method of proactive-reactive mission planning for a UAV fleet. Section 5 includes an example of the use of the developed method. Finally, Sect. 6 provides the conclusions followed by the description of future research.

2 Related Work Most of the studies dealing with the problems of vehicle routing focus mainly on its two variants, i.e., CVRP and VRPTW, covering cases of transport carried out by mobile vehicles (trucks). Studies focusing on ground vehicles prevail over other surface/underwater or air vehicles. In all these categories, relatively little attention is paid to unmanned solutions. Even less attention is paid to route planning and navigation in dynamic environments. Among the solutions belonging to the last of these groups, one should distinguish a dynamically growing interest in UAVs’ applications. The specificity determining the use of vehicles of this type is distinguished by both design limitations (in particular electric drive limiting flight time and length) and the impact of interference caused by changing weather conditions. Both of these factors strongly determine the lifting capacity and range of UAVs. Among the disruptions having a decisive impact on the success of the planned mission, one should distinguish disruptions caused by the specificity of: • Environments: precipitation (snow, hail, rain), wind (direction, speed), temperature, humidity, obstacles (moving, stationary). • Vehicle design: damage to modules (drive, power, control, etc.), battery discharge, lost-no/damaged charge, loss of connectivity, software errors. • Distribution network: change of delivery date, change of order size/type, change in the number of recipients, change of planning horizon time [19].

Disruption Management Vehicle Routing Problem Traditional vehicles (e.g., trucks) indoor (AGV)/outdoor (military, fireservice, life-saving)

UAV

Moving obstacles Vehicle breakdowns Road traffic (traffic jams, Change of delivery time glaze etc.) and road Change of customer demand conditions (potholes, sinkholes, etc.) Loss of connectivity

Changing weather conditions

Hardware and software malfunctions Fig. 1. Disruptions determining the dynamics of air and ground vehicle environments

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Figure 1 highlights the main causes of disruptions that affect the success of unmanned vehicle missions carried out on land and in the air. Some of them, such as vehicle breakdowns or loss of connectivity, apply to both types of vehicles, while others, such as traffic jams or changing weather conditions, are taken into account when planning land vehicle or UAV missions, respectively. It should be noted that many of them, including loss/damage to cargo, change of the type of order, change of the horizon time of placing, are not considered at all in the literature. The most common case of disruptions considered in the literature is damage to the vehicle. The response to this type of disruption (by sending a reserve vehicle from the base) is aimed at reducing the costs of the mission delays, non-delivery/cancellation of delivery to a given point, or maximization of profit [21, 22]. Another type of disruption often found in the literature is road accidents (traffic jams, accidents). The re-scheduling of missions as a result of this type of event is aimed at minimizing the length of the route covered and/or maximizing deliveries [23, 24]. A separate group of disruptions concerns changes in the transportation network (change in the volume of orders, delivery times). In this case, the authors are looking for new missions that will allow minimizing the cost of the entire operation, or minimizing the differences between the baseline [24]. The NP-hard nature of VRP, as well as its extensions, means that individual types of interference are most often considered, such as those related to vehicle breakdowns. Studies that take into account the simultaneous impact of several different disruptions are rare [18]. From the perspective of mission planning of the UAVs fleet, an important type of disruption is those associated with an unforeseen change in the environment of the mission - in particular, a change in weather conditions. A sudden change in wind speed and/or direction can increase flight time (increase energy consumption resulting in early battery discharge) and consequently non-execution of the plan/loss of the vehicle [11, 20].

3 Disruption Management Vehicle Routing Problem Disruption management boils down to an ad-hoc correction of an already implemented plan. It plays a particularly important role in situations where a disruption detected during the implementation of a proactively planned mission prevents its continuation. In that context this study considers the Problem of the Disruption Management Class Vehicle Routing Problem, DMVRP, which assumes the occurrence of disruptions during the implementation of the mission as well as an appropriate response to them. The considered disruptions include: a change in forecast weather conditions, a change in the location and/or number of delivery points/bases as well as a change in the value of orders (demand for delivered goods). For future considerations, let’s introduce the concept of the state of the IS(t) mission at the moment of time t:   (1) IS(t) = M(t), W ∗ (θ, t), G ∗ (t), Z∗ (t) where:   • M(t) - UAV allocation at moment t : M (t) = va1 , . . . , vak , . . . , vam , where: ak ∈ {1, . . . , n}, vak vertex operated by the uk vehicle. At moment t, the uk vehicle may

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serve the recipient or move towards him, W ∗ (θ, t) - forecast weather conditions at the time of t • G ∗ (t) - transport network, i.e., the number and location of delivery points/bases at the time t, Z ∗ (t) - sequence of demands for goods at the time of t. Mission state (1) for which at moment t ∗ the condition (2) is met is called IS(t ∗ ) disruption:      ∗ ∗ (2) W θ, t = W(θ ) ∨ ∗ G t ∗ = G ∨ Z ∗ (t ∗ ) = Z where: W(θ ), G, and Z mean respectively: weather conditions, distribution network, quantity of ordered goods known at the time of setting the proactive plan. In order to clarify the concepts introduced, let us consider the following example. A transport network with an area of 100 km2 consisting of one base VB = {v1 } and 10 delivery points VD = {v2 . . . v11 } is given, see Fig. 2a). For each of the delivery points, the quantity of the expected goods zi as well as delivery times VDTW i are specified.

Fig. 2. Example of a) distribution network, and b) delivery times and customers’ demand.

The transport of goods is carried out by a fleet of four homogeneous UAVs U = {u1 , u2 , u3 , u4 }, of which the vehicle u4 is a reserve vehicle. The technical parameters of the UAV are presented in the Fig. 2b) table. It is assumed that during the implementation of the mission, the weather conditions presented in Fig. 3a) take place. Figure 3a) represents, in polar coordinates, the forecast values of the wind speed vw in the direction of θ ∈ 0◦ ; 360◦ ) that do not exceed 9 m/s (function W(θ )). With these assumptions, mission S of the UAV fleet is sought, guaranteeing timely deliveries (in the assumed time horizon H = 2 h) of the required quantities of goods. Meeting the requirements imposed on timely delivery forces the development of plans for the implementation of missions resistant to forecasted changes in weather conditions. The projected changes are given in the form of a set of pairs (θ, vw) (see Fig. 3a) W = {(θ, vw)|θ ∈ 0◦ ; 360◦ ), vw ∈ 0, W(θ ) }, where: W(θ ) is a function whose values determine the maximum forecast wind speed vw for direction θ . To assess

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the resilience of mission plans S, the function ϒk (θ ) is introduced. The ϒk (θ ) function determines the wind speed limits (for a given direction θ ) that guarantee the feasibility of mission plan S in the G network: ϒk (θ ) = max k (θ ), where: k (θ ) – a set of vw wind speed values at which the uk vehicle’s battery is not exhausted.

Fig. 3. a) Forecasted weather conditions, and b) example of robustness function.

In order to assess the robustness of mission plans S, the ϒk (θ ) resilience function is introduced. The ϒk (θ ) function determines the wind speed limits (for a given direction θ) that guarantee the feasibility of mission plan S in the G network: ϒk (θ ) = max k (θ ) where: k (θ ) – a set of vw wind speed values (for direction θ ) at which the uk vehicle’s battery is not exhausted. It is assumed that the mission plan S is resistant to W weather conditions when the values of the function ϒk (θ ) for each UAV (uk ∈ U ) and each wind direction θ is greater than the value of the function W(θ ): ∀uk ∈U ∀θ∈0◦ ; 360◦ ) Υ k (θ ) ≥ W(θ ). An example of the robustness function ϒk (θ ) is illustrated in Fig. 3b). Condition ϒk (θ ) ≥ W(θ ), guaranteeing the robustness of mission S to the forecast weather conditions, holds. In this context, a disruption IS(t ∗ ) should be understood as a change in weather in which the wind speed exceeds the permissible value (defined by ϒk (θ )). To sum up, the search for mission plans S, resistant to the given changes in weather conditions W, is the main goal of proactive planning, which boils down to the question: Is there a mission plan S that guarantees timely delivery of the required amount of goods in the event of a disruption of IS(t ∗ )? When looking for an appropriate answer, it is necessary to identify the disruption, assess its impact on the course of the mission, and choose the appropriate response. These steps make up the method of proactive-reactive planning of UAV flight missions described in Sect. 4.

4 Proactive-Reactive Mission Planning for UAV Fleet The diagram of the mission planning procedure S, guaranteeing the timely execution of orders for forecasted weather conditions (proactive planning), and its correction in situations of disruption (reactive planning), is presented in Fig. 4. The course of the planned

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mission S is monitored on an ongoing basis for the occurrence of selected types of disruption IS(t ∗ ) forcing correction (re-routing) of the adopted plan. This means that the reactive planning process can be initiated multiple times during a UAV mission carried out according to a predetermined proactive plan. The proposed method assumes that at the stage of the mission preparation, the parameters of the UAVs and distribution network G used, as well as the forecasted conditions of weather changes (determining the directions of θ and maximum wind speeds), are known. At the proactive planning stage, it is assumed that: disruption of IS(t ∗ ) may include both changes in the structure of the distribution network and weather conditions. The adopted assumptions limit the search space, which increases the chances of finding an acceptable solution. However, they do not guarantee its existence. The lack of acceptable solutions may occur, for example, in situations related to the occurrence of overlapping time windows VDTW (e.g., a UAV must deliver goods to two delivery points on the same date), too short planning horizon H , as well as too small a UAV fleet, or limitations imposed by the technical parameters of the fleet (too low UAV capacity).

Fig. 4. The algorithm of proactive-reactive mission planning for UAV fleet

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The proposed method takes into account the forecasted changes in weather conditions and disruptions occurring ad hoc and related to the nature of the environment (e.g., exceeding the forecasted wind speeds, temperature jumps, etc.) and the specificity of the orders carried out (e.g., changes in the size of orders, their collection dates, etc.).

5 Computational Example The application of the developed method is illustrated by the following example. A distribution network from Fig. 2 is given. The weather forecast assumes that the wind speed will not exceed 9 ms (see Fig. 3a). It is required that the delivery of goods is completed within the period H = 1 h. In other words, the answer to the question is sought: Is there a mission plan S that guarantees timely delivery of the required quantity of goods in the given weather conditions? The answer to such a question is determined at the stage of proactive planning (Fig. 4) using the representation of the declarative model of the problem [10], implemented in the IBM ILOG CPLEX declarative programming environment. The first acceptable solution was obtained in 17s (Intel Core i7-M4800MQ 2.7 GHz, 32 GB RAM). The implementation of the received proactive mission plan S (see Fig. 5) is monitored on an ongoing basis. At the moment t = 500 s there is a change in weather conditions, from the assumed. vw = 9 ms to vw = 11 ms (in the direction of θ = 110◦ −130◦ ) - see Fig. 3b). The change in weather conditions means that the flight mission of the u1 vehicle is no longer executable because, during the flight from the point of delivery of the v4 to the point of v5 , the vehicle’s battery u1 is prematurely depleted - see Fig. 5. Due to the change (disruption of IS(500)) in weather conditions, a new plan should be set to enable the mission to be carried out in the new conditions. This means searching for an answer to the question: Is there a mission plan S that guarantees timely delivery of the required quantity of goods in the event of a disruption of IS(500)? In an attempt (see Fig. 5) to re-schedule a proactive plan, its first acceptable solution was obtained after t = 8 s. The received plan assumes that the UAV u1 is returned to the base. Due to the fact that the remaining vehicles u2 and u3 cannot take over its tasks (the demand for goods exceeds their load capacity), the task of delivering the goods to the nodes v5 and v8 will be taken over by a reserve drone v4 . The designated reactive mission plan of the UAV fleet allows deliveries to continue with the set changes in weather conditions. This is possible thanks to the use of a reserve UAV (u4 ). In general, there may be many more alternative response scenarios to disruption. They may concern both decisions regarding changes in UAV behavior (both in the air and staying in the base) as well as decisions regarding delays in the execution of orders.

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Fig. 5. Computational results

6 Conclusions DMVRP class problems extend the classic VRP problem to include the possibility of disruptions occurring, and responding appropriately to them. Taking into account this type of events makes it possible to improve the quality of services provided, as well as to minimize the costs associated with not completing the order or re-planning the mission. The proposed method of planning the mission of the UAV fleet takes into account anticipated disruptions (forecasted weather conditions) and ad hoc ones, both related to the nature of the environment and the specificity of the orders carried out, which complements the state of the literature in this area. The obtained interference response times do not exceed 30 s for a fleet of 4 UAVs. This is sufficient for outdoor applications (urban areas > 3 km2 ). The presented approach also assumes the use of communication between UAVs via a central unit, also used in making decisions related to and occurrences of interference. Future work assumes the extension of the scope of the considered disruptions by: changes in the weight of the transported cargo, the impact of turbulences and moving obstacles (e.g., bird migrations), as well as the inclusion of imprecise data.

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Network Aspects of Remote 3D Printing in the Context of Industry as a Service IDaaS Mateusz Salach1(B) , Andrzej Paszkiewicz1(B) , Marek Bolanowski1(B) , Andrzej Kraska2 , and Jakub Wi˛ecek2 1 Department of Complex Systems, Rzeszow University of Technology, al. Powsta´nców

Warszawy 12, 35-959 Rzeszów, Poland {m.salach,andrzejp,marekb}@prz.edu.pl 2 Enf Sp. z o.o, ul. Mieszka I 73C, 35-303 Rzeszów, Poland

Abstract. The idea of Industry as a Service (IDaaS) is the concept of sharing devices among companies, as well as for individual users. In IDaaS model user has access to industries endpoint devices (manufacturing equipment) with specialized software and dedicated tools. Examples of devices that can be leased/shared in this way are e.g. 3D printers, CNC machines, bending machines etc. In this paper a model of architecture of web application is presented for scheduling and reserving access to endpoint devices, in particular, the focus was on 3D printers. Studies have been conducted on analyzing the stability of system operation under connection and packet loss for various network load scenarios. The results have been analyzed and presented. Keywords: Industry 4.0 · IDaaS · Computer networks · Distributed systems

1 Introduction One of the key paradigms of Industry 4.0 systems is the strong interconnection of manufacturing systems located in different business entities. Of course, this approach can be implemented relatively simply for newly designed generating units, where the individual components of the manufacturing systems have network interfaces managed by a consistent supervisory environment that makes data and equipment access available to others. However, manufacturing systems may be in operation for a long time, and thus there is a large group of equipment on the market that lacks advanced network interfaces and applications that enable remote operation. On the other hand, even new machines dedicated to SMEs do not have advanced industrial collaboration systems built in. Of course, there are devices and dedicated systems on the market (even open source) that allow sharing selected resources by adding hardware components or access gateways in the form of separate devices. These solutions dedicated to 3D printing solutions will be discussed in the related work section. The common feature of these systems is the adoption of an end-to-end approach in which the system is dedicated to providing resources to end users with full automation, component selection and estimation, tariffing, booking, etc. In essence, the added printer can fully automatically fulfill the orders of end customers, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 62–72, 2023. https://doi.org/10.1007/978-3-031-25844-2_6

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who do not need to be experts in the 3D printing area. While this approach works well in some 3D printing systems its widespread application to SME manufacturing machines may be problematic. Research interviews conducted showed that the main motivation of SME entrepreneurs in terms of sharing resources is, on the one hand, the desire to make better use of the specialized machines they own, and on the other hand, the possibility of acquiring missing machines to complete the manufacturing process (owned machine park) for a given group of artifacts. In such an approach, it is crucial to provide remote access to the manufacturing machine and software that will be operated remotely by an expert or the customer will work with locally available personnel operating the machine. In such a case, it is also necessary to be able to visually inspect the manufacturing process for ongoing monitoring and quality control of the produced artifacts. The creation of a universal system that responds to these needs and makes the full range of manufacturing equipment available is very time-consuming, expensive and uneconomical due to the wide variety of available equipment. Therefore, in the paper, the authors proposed and implemented a simplified, rapidly implementable system model that allows the sharing of manufacturing entities with particular emphasis on the remote system for supervising the work and quality of manufactured artifacts, along with the determination of the limiting operating parameters of the network link integrating the various elements of the systems. An exemplary implementation of this system was realized in the production environment of the company (Enf Sp. z o.o. in Rzeszów, Poland) providing a manufacturing entity consisting of a computer with software, industrial camera system, industrial 3D printer. It should be noted that it was deliberately not chosen a printer that is compatible with existing solutions on the market for automating access to manufacturing equipment. The work is divided into the following parts: Sect. 2 analyzes the currently available solutions that enable remote access to devices, with particular emphasis on systems dedicated to 3D printing devices. Section 3 presents the assumptions of the proposed model and its practical implementation in a real environment. Section 4 presents the results of the study, which includes the optimization of the operation criteria in the context of determining the impact of the limit saturation of the access link on the process of supervising the manufacturing process. The paper concludes with a summary, which also refers to plans for further research work and implementations.

2 Related Works Many solutions have been developed to maintain access to specialized devices such as CNC machines or 3D printers. In case of CNC machines, it is usually a dedicated, manufacturer software which allows a user to access device remotely [1–3]. An example of such system is SINUMERIK Operate, remote monitoring system created for CNC machine based on Siemens controllers. SINUMERIK Operate is a function which allow user to remotely monitor CNC machine over VNC Viewer, however with a small modification enabled by producer it is possible to remotely control a CNC machine. A TCU.ini file has to be reconfigured based on Siemens guidelines to allow user to have additional remote control over device, not only remote monitoring [4]. Another worth mention solution is Welotec VPN Security Suite designed by Welotec GmbH. This system allows users to remotely access any device connected via PLC over OpenVPN in a

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secure way. However, such solution requires a dedicated PLC which must be connected with endpoint device. All communication goes through dedicated PLC so the endpoint device must be connected and programmed to use a PLC [5]. This limits the field of endpoint devices. With 3D printers such remote access solutions are more popular mainly through a large community of 3D printer enjoyers and industries. There some dedicated solutions in a field of power industry [6–8], a cloud-based systems [9, 10], mobile [11, 12], robotics [13–15] or dedicated solutions for 3D printed part analysis [16–18]. One of the most popular solution is OctoPrint, a system based on Python which allows users to see printing status with parameters such as printing time left, percentage of printing. For 3D printers the OctoPrint can display status like hotend and bed temperature, start a 3D print and give user a live view from camera if it is attached to computer. OctoPrint is also available as a distribution for Raspberry Pi as OctoPi modification which allows a user for similar functions as OctoPrint application. OctoPi is commonly used with Raspberry Pi 3B and higher and also with Raspberry Pi Zero 2 W mostly due to power savings. The Raspberry Pi Zero 2 W requires less power than standard Raspberry Pi. Unfortunately, OctoPi is not recommended for Raspberry Pi Zero W due to low performance microcontroller and RAM. OctoPrint has over 300 plugins written by hobbyists for many 3D printers which extends its compatibility. Unfortunately, OctoPrint is still not compatible with some 3D printers such as some MakerBots. Much more advanced system is 3DPrinterOS. It is a cloud-based operating system in which it is possible to manage your 3D printers and 3D prints. 3DPrinterOS allows users to upload, slice and print a 3D print created by user. It is possible to upload a project into cloud service and perform operations on a 3D model similar to typical slicer program. From web interface a user can rotate, scale and move object. Beside such features a user can fix a 3D model and slice it for 3D printing. A cloud service allows user to integrate all his 3D printers into one system. It is possible to add a 3D printer by MAC address and while it is connected to specific device such as computer or for example Raspberry Pi it is possible to schedule and start 3D print job. Service has also a live view model from cameras integrated to the system. A user can see its printer and watch while it is printing a 3D model. A 3DPrinterOS is a software created by 3D Control System in 2015. It is meant for industry and education for specific price. While all products have similar functionality, they are focused strictly on one aspect of the job – 3D printing. For more all systems require a basic knowledge of usage of 3D printer to determine the parameters of 3D print. The idea is to develop and test a system for industry where a client can schedule a job remotely, choose appropriate machine – no matter if it is a 3D printer or CNC and use the guidance from specialist dedicated for each system. The user needs ability to choose at which time period he or she will use the endpoint device and have possibility to analyze and watch a performed job remotely by using very specific devices such as long-range camera. All solutions mentioned above are also dedicated for a narrow group of devices. Such solutions cannot be universal systems for small and medium-sized companies. These systems give a large amount of functions and configurations which are good for standard users, sometimes without knowledge. Our proposed solution is prepared strictly for advanced users, has no unnecessary tools and gives users an easy-to-operate system with additional help if required by user.

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3 Proposed System Architecture Model Figure 1 presents an architecture model of proposed system. Finally, it has to be easy for implementation. Control Module Device (PC) Internet

Manufacturing enty3

User database VPN acces (AAA)

Manufacturing device IP Camera

Network edge

Manufacturing enty1

Users

Manufacturing enty2

Fig. 1. Proposed system architecture model.

The basic element used in the system is a manufacturing entity. It is a set of devices associated with a single production station, e.g., a CNC machine with a microcomputer operating it, on which the machine control software and auxiliary software (e.g., CAD for model preparation) are located. Control Module is a central AAA system responsible for authentication, authorization and logging of users’ work. Using the website, users can offer their resources and also can reserve access to various resources. The system is also responsible for storing and sharing VPN channel configurations prepared by authorized users. At a certain time, the client receives login credentials and, through the VPN channel, logs in with a remote session to the microcomputer handling the remote session. From that point on, he can use the shared resources. It should be noted that this approach allows sharing machines that are connected directly to the microcomputer. In the following section, an implementation of the proposed model will be presented on the example of sharing a manufacturing entity consisting of a microcomputer, a 3D printer and a high-resolution industrial camera. Proposed system must calculate cost of usage instantly no matter what kind of job a user has specified. Sometimes a user may need help as part of support as for example a user might be specialist in the area of 3D modeling but have no knowledge of how to use slicer or 3D printer. The need of operator should be taken into account. For that purposes a web application has been developed to achieve such requirements. Figure 2 presents a concept model architecture of the sharing system. A user can be connected to device (e.g., PC) through remote desktop protocol (RDP) and have restricted access to device system i.e., a user has full privileges for using dedicated software and all endpoint devices (manufacturing equipment) connected to it however a user cannot modify operating system parameters and configuration. A web application and its database are stored on a company server. A user has access to website from the Internet to login and schedule access to dedicated devices. All information required for contact with user and data related to devices and their endpoint devices are also stored in the same database which contains records related to device reservations.

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Fig. 2. A device sharing system architecture model - 3D printer example.

A user can choose a device with endpoint devices attached to it such as 3D printers, CNC machines etc. and schedule a time period for full access to the device. User can also ask for operator help if needed. Once an order is complete a user by accepting it sends a notification to operator for acceptance. The operator verifies order and sends a user a login information to access the device, such as credentials and VPN connection strings. Each device has its own credentials stored inside the internal database for access. VPN connection strings are created and sent by the operator to the user. It allows a user to access device through RDP and an IP camera through HTTPS only for defined time periods as connection is shut down after end time defined by a user in web application form. For each connection or order, a new VPN connection strings are generated for security of access. Records related to users and devices are stored in the MySQL database. The web application database stores data related to users, devices and orders. Each device has possibility to have many endpoint devices attached to it. Each device can also have a specialized software installed on. It can be for example specialized 3D modeling software such as Fusion360, Solidworks, Blender or software dedicated for attached endpoint device such as Ultimaker Cura, SuperSlicer, PrusaSlicer etc. While device is reserved for a user, another user cannot access it during defined time period. While user logs in into device a software for live viewing can be accessed such as long-range camera with very high digital zoom. It can be operated by user during job (3D printing) to check a 3D model during and after processing. A view from the camera is shown on Fig. 3. For reliable access and stability a few tests have been performed. Several parameters have been taken into account to analyze stability of connection and ability to operate a machine during established connection. These parameters and range of conducted research has been described in the next chapter.

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Fig. 3. A view from the IP camera.

4 Network Stability and Operation Tests The primary tests have shown that a key parameter influencing system stability is a quality of network connection. Its low-quality affects both a quality of surveillance process over dedicated machine and in some cases possibility of interactive control. In order to take into account, the variability of the quality of the link, both different values of its load were used, as well as a change in the value of the delay by introducing an additional (virtual) delay to actual delay of network infrastructure. An IP industry level camera with high resolution has been chosen to determine a boundary condition of quality of the network connection. To analyze connection stability a few scenarios have been developed and processed. Two hardware models were established and configured for testing. Test were divided into two sections: a live video from camera and connection stability with device, both through VPN access from external network. The primary parameters taken into account for live view were: • Stability of connection • Image quality while in case of connection to device thorough remote desktop protocol (RDP) the primary parameters were: • Stability of connection • Possibility of usage of system (delays) For test purposes a desktop computer with Windows 10 Pro was used with configuration Intel Core i5-8500 CPU, 3 GHz, 16 GB RAM memory and Intel Ethernet 1 Gb network card. The camera used for testing was IPC6252SL-X33UP. The network was configured by using a VPN server as a virtual machine. In order to introduce an additional (virtual) delay was used Linux qdisc. Both pieces of software was installed

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on a Dell PowerEdge R940 server with Debian OS. The 4 switches were Extreme x690. A PC with 3D printer Makerbot Replicator z18 as endpoint device and separately IP camera were connected to switch 1 through 10 gigabit ethernet ports (Fig. 4). Network was loaded by Ixia Novus One network generator in two scenarios: 10 Gb/s and 1 Gb/s transfer by changing network load by 10% on each test starting from 100% - full network load for each scenario.

Fig. 4. The network infrastructure established for tests.

Several tests have been performed to analyze stability of connection and accessibility to live video from IP camera. First test assumed loading network infrastructure with 100% load (10 Gb/s uplink and download). In each step a virtual delay has been increased starting from 1 ms up to 20 ms in 10 Gb/s load scenario. In each configuration (10 Gb/s and 1 Gb/s) there was a delay caused by configuration and network access (actual delay). In 100% load a primary ping was 35 ms, in 90% load it was 7 ms and in case of 80% load it was 1 ms. These values of delay must be added to overall results. In case of camera image quality (video) a 5-point scale has been considered: • • • • •

4 – no lag on the live view 3 – slightly visible lag on the live view 2 – visible lag on the live view 1 – disconnection after more than 40 s 0 – disconnection after less than 5 s

The tests have been performed with 100%, 90% and 80% load on a network. Results of measurements are presented in Fig. 5a. In 100% load scenario quality of connection with camera is very good with up to 3 ms – virtual delay (38 ms – sum of virtual and actual delay). Starting from 4 ms (39 ms) a pixelization can be noticed during the live view from camera. A critical point of connection was reached during measurements with 12 ms (47 ms) and 13 ms (48 ms) delay. A connection has been lost after approximately 40 s. With 14 ms (49 ms) delay in three attempts a connection has been lost in few seconds. After analyzing a 5 s max delay has been taken into account 0 for scale. For 90% load on the network (both uplink and download) measurements were better than for 100% load. A connection was very good up to 5 ms virtual delay as it started

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to worsen from 10 ms delay. The critical point of virtual delay in 90% load case was 16 ms. Connection to camera started to crash but still it was possible to see video in 16–17 ms virtual delay. From a threshold value of 18 ms onward, every attempt at a video connection ended in less than 10 s. In many attempts it was less than 5 s and due to such results a 0 point has been added to 18 ms virtual delay. The last analysis on network stability has been taken with 80% network load. Results of 80% were similar to 90% network load however connection lasted longer than in case of 90%. A critical point of virtual delay was 18–19 ms with connection loss at 20 ms.

Fig. 5. Results of connection stability through change of delay time: a) link load 10 Gb/s, b) link load 1 Gb/s.

Another test was performed with the same network topology and infrastructure however with 1 Gb/s uplink and download and only 100% and 90% network load scenarios have been taken into account due to results of 90% load. Tests were performed from external network through VPN connection. In terms of virtual delay values from 1 ms to 10 ms there has been no changes on 5-point scale. Therefore, the virtual delay time values had to be significantly increased. First test was performed with 1 Gb/s network

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load on both uplink and download by network generator. It can be noticed that there is no difference in connection starting from 1 ms up to 100 ms in case of virtual delay (Fig. 5b). A small pixelization has been detected at 150 ms virtual delay. A connection has been stable for up to 700 ms virtual delay. In connection attempts involving the range of 700–1000 ms virtual delay a several connection loss has been noticed. In case of 2000 ms virtual delay, connection has crashed in less than 5 s’ period. Second test has been performed with 90% load on the network infrastructure. As mentioned above results of 90% load have been close to 80% load test. It can be noticed that connection is stable staring from 10 ms up to 2000 ms virtual delay. Several tests have been performed in delays beyond the presented scale. A connection has been lost with 0-point scale (after less than 10 s) at 60 000 ms delay. Unfortunately, a usage of an operating system was impossible due to high delay so only connection with camera has been taken into account in this test scenario. The third test has been performed with additional parameter such as packet loss. Test has been conducted by using the same network infrastructure and configuration with identical system point scale from 4 to 0. The base delay (35 ms) caused by the network infrastructure was the same as in test performed before. As it can be noticed in Fig. 6, packet loss combined with delay is important factor in system stability. With network load on a level of 100% each higher delay time has influenced connection stability making the system interface hard to use. By 10% packet loss results can be similar to the ones presented in Fig. 6 with 100% network load. It happens due to low packet loss so connection is stable. The main factor in that scenario is delay. In the second scenario (15% packet loss), some instability of the connection can be observed, although the level of packet loss effect is still small. Fourth test shows much influence of packet loss on connection since from the beginning it can be noticed that quality of connection is lower than usual. With high delay value (600 ms + 35 ms) a connection collapses. In first few samples a connection became highly unstable (point 1) however several analyses indicated that the factor of connection loss in less than 10 s (point 0) was higher than connection loss in less than 40 s (point 1).

Fig. 6. Results of packet loss parameter based on delay in link load 100% scenario.

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5 Conclusions The processes of globalization and, at the same time, limited resources and difficulties in accessing them make it necessary to look for new methods and means of efficient use of available equipment, production lines and even entire factories in the development of Industry 4.0. The Industry as a Service (IDaaS) concept addresses this issue. Of course, it encompasses many solutions, however, this article focuses only on the specific aspect of making specific manufacturing entities available via the Internet in the form of 3D printers and the necessary environment. This environment can consist of an access unit, specialized software, control equipment, as well as qualified personnel. The presented approach opens up wide possibilities for flexible and scalable creation of distributed manufacturing environments. In the course of the work carried out, special attention was paid to the quality of the vision inspection service of the incremental manufacturing process. Accordingly, a study of the impact of the load on communication links, as well as the change in the value of delays on the quality of this service was carried out. As a result of the research, threshold values of link saturation and delay values determining the usability and availability of this service were identified. Note that phenomena related to the increase in the number of users, the increase in actively used manufacturing entities can affect the values of the above-mentioned communication parameters. In the future, further research is planned involving maintenance and network control of scalable and flexibly changing distributed design and manufacturing environments. Declarations. Funding: This research paper was developed under the project financed by the Minister of Education and Science of the Republic of Poland within the “Regional Initiative of Excellence” program for years 2019–2023. Project number 027/RID/2018/19, amount granted 11 999 900 PLN. The research work presented in the article was also carried out as part of ENF sp. z o.o.’s implementation of the research agenda included in project POIR.02.01.00-00-0025/17.

References 1. Wen-zheng, Z., Hu, Y.: Design and implementation of CNC machine remote monitoring and controlling system based on embedded internet. In: 2010 International Conference on Intelligent System Design and Engineering Application, Changsha, Hunan, China, pp. 506– 509. IEEE (2010) 2. Torrisi, N.M., de Oliveira, J.F.G.: Remote monitoring for high-speed CNC processes over public IP networks using CyberOPC. Int. J. Adv. Manuf. Technol. 60(1–4), 191–200 (2012). https://doi.org/10.1007/s00170-011-3580-3 3. Mori, M., Fujishima, M.: Remote monitoring and maintenance system for CNC machine tools. Procedia CIRP 12, 7–12 (2013). https://doi.org/10.1016/j.procir.2013.09.003 4. https://www.welotec.com/solution/security-and-connectivity-for-ot-networks-and-remotemaintenance/. Accessed 20 Oct 2022 5. https://support.industry.siemens.com/cs/document/109765064/sinumerik-operate-enableremote-control-for-external-vnc-viewer. Accessed 20 Oct 2022 6. Vozisova, O., Eroshenko, S., Koksharova, E., Khalyasmaa, A., Dmitriev, S.: Application of 3D scanning and printing technologies in Electric power industry. In: 2016 IEEE International Conference on Industrial Technology (ICIT), Taipei, Taiwan, pp. 892–897. IEEE (2016)

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7. Egorov, A., Larionova, A., Kovalenko, P.: 3D printing of 35, 100, 220, 330 and 500 kV gas-insulated current transformers (UETM TRG series). In: 2019 IEEE 60th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), Riga, Latvia, pp. 1–5. IEEE (2019) 8. Vozisova, O., Bliznyuk, D., Egorov, A., Snegirev, D., Koksharova, E.: Electric power system kit. Modular integrated transformer substation. In: 2016 57th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), Riga, Latvia, pp. 1–4. IEEE (2016) 9. Jo, C.H., et al.: Development of a cloud-based automated 3D printing system. KSME-C 7(3), 171–176 (2019). https://doi.org/10.3795/KSME-C.2019.7.3.171 10. Liu, C., Jiang, P., Jiang, W.: Embedded-web-based remote control for RepRap-based opensource 3D printers. In: IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society, Beijing, pp. 3384–3389. IEEE (2017) 11. Cho, B.-H.: Analysis/design and implementation of 3D print remote control and printing mobile software. J. Inst. Internet Broadcast. Commun. 15(5), 177–182 (2015) 12. Bailey, C., et al.: Augmenting computer-aided design software with multi-functional capabilities to automate multi-process additive manufacturing. IEEE Access 6, 1985–1994 (2018). https://doi.org/10.1109/ACCESS.2017.2781249 13. Gao, J., Rong, W., Zhang, Y., Wang, L., Sun, L.: Semi-automated 3D printing system for magnetic-driven microrobots. In: 2020 IEEE Eurasia Conference on IOT, Communication and Engineering (ECICE), Yunlin, Taiwan, pp. 407–409. IEEE (2020) 14. Zhang, X., et al.: Large-scale 3D printing by a team of mobile robots. Autom. Constr. 95, 98–106 (2018). https://doi.org/10.1016/j.autcon.2018.08.004 15. Nguyen, H., Adrian, N., Yan, J.L.X., Salfity, J.M., Allen, W., Pham, Q.-C.: Development of a robotic system for automated decaking of 3D-printed parts. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France, pp. 8202–8208. IEEE (2020) 16. Paraskevoudis, K., Karayannis, P., Koumoulos, E.P.: Real-time 3D printing remote defect detection (stringing) with computer vision and artificial intelligence. Processes 8(11), 1464 (2020). https://doi.org/10.3390/pr8111464 17. Straub, J.: Automated testing and quality assurance of 3D printing/3D printed hardware: assessment for quality assurance and cybersecurity purposes. In: 2016 IEEE AUTOTESTCON, Anaheim, CA, USA, pp. 1–5. IEEE (2016) 18. Petsiuk, A.L., Pearce, J.M.: Open source computer vision-based layer-wise 3D printing analysis. Addit. Manuf. 36, 101473 (2020). https://doi.org/10.1016/j.addma.2020.101473

The Concept of Use of Process Data and Enterprise Architecture to Optimize the Production Process Zbigniew Juzo´n , Jarosław Wikarek , and Paweł Sitek(B) Kielce University of Technology, Al. Tysi˛aclecia P.P. 7, 25-314 Kielce, Poland {zjuzon,j.wikarek,sitek}@tu.kielce.pl

Abstract. The paper presents a concept that allows to identify and locate elements of the production process, the optimization of which affects the quality of the entire process. The developed concept is based on an efficient information exchange mechanism between the business layer and the technological layer through the use of enterprise architecture and process data. The practical application of the proposed concept facilitates the construction of detailed optimization/decision models for selected parts of the production process. The paper also presents the practical application of the presented concept for a sample production process for which an optimization model in the form of mathematical programming was developed. The implementation of the model taking into account all the constraints identified at the analysis stage made it possible to propose an optimal production plan and reduce interoperation stocks. Keywords: Production optimization · Data acquisition · Enterprise architecture · Mathematical programming · TOGAF · RFID

1 Introduction Enterprises that want to be competitive in the market are forced to constantly improve their work organization. Company management should have an accurate picture of the company’s operations on an ongoing basis. It is necessary to ensure an efficient information exchange mechanism between the business layer and the technological layer. It should be emphasized that at the level of the enterprises, data is stored at various levels (business/technology), which may be of significant importance in the process of optimizing the production system. In order to see the data collected on the level of business or technology in the enterprises, the right perspective must be used. Using the assumptions of the enterprise architecture based on the Open Group Architecture Framework (TOGAF) standard [1], one can consider the organization as a complex ecosystem, and using programming methods such as mathematical programming, constraint programming, dynamic programming etc., one can also plan production processes. Another issue when conducting a production system analysis is the selection of the level at which the system will be analyzed. For this purpose, it is convenient to use the enterprise architecture due to its universal character and the possibility of its adaptation to various © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 73–84, 2023. https://doi.org/10.1007/978-3-031-25844-2_7

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decompositions (Fig. 1). When applying the assumptions of the enterprise architecture to develop a mathematical model to optimize the production system, it should be borne in mind that the preparation of production consists of constructional, technological and organization preparation (Fig. 2). customers technologies people

the main elements of the production process

logistics

finances material resources

methods of work organization

information system

Fig. 1. Main elements and their components describing the production system constructional and technological development

research and development works

technological preparation of production

production

sale

Fig. 2. Main stages of the production process

Enterprise architecture it is a description of the structure and functions of the organization’s components (such as: business processes, resources or infrastructure) and their mutual connections (relations). Enterprise architecture describes the current state of the organization (as it is), the target state (what it will be) and the process of transition between these two states. The enterprise architecture consists of 4 domains: • business architecture – describes the business strategy and methods of managing the organization, organizational structure and main business processes, as well as the relationships between these elements. • data architecture – describes the main types and sources of data necessary for the functioning of the organization. • application architecture – describes individual applications, their deployment, mutual interaction and relations between these applications and the organization’s business processes. • technical architecture (technical infrastructure) – describes the ICT infrastructure that is the basis for the functioning of the application.

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The main research motivation was to propose such an approach to optimizing the production process, which, based on data from both the technological and business layer of the process, enables: (a) identification of process optimization/improvement areas, (b) facilitating the construction of detailed optimization/decision models, and (c) ensuring the flow of information between the layers of the process. The most important achievements of the presented research include: • presentation of the concept of optimization of the production process with the use of enterprise architecture and process data; • development of a detailed model for the optimization of selected elements of an exemplary production process; • implementation of the model in a mathematical programming environment; • modification of an exemplary production process based on the obtained optimization results. The rest of the paper is organized as follows. The method of obtaining data is presented in Sect. 2. The area related to materials and methods is presented in Sects. 3–5, where an illustrative example is provided with a description of the research problem and the definition of the mathematical model for the illustrative example. The results are discussed in Sect. 6 based on the experiments performed. The discussion area is included in Sect. 7, which contains conclusions and information on future research.

2 Methods of Data Acquisition Obtaining data from the production system using a survey method or providing verbal data from the production line by workers themselves is not the best solution, as the data appears with a significant delay and may be affected by errors. It is necessary to introduce sensors that can measure, for example, temperature, pressure, etc. on an ongoing basis at the level of the manufacturing process [2]. The key issue is therefore to ensure an efficient (automatic) data flow from the production system with the use of various technologies for identifying the state of the process to the planning level of the production process. Structural preparation of production includes, among others, the determination of functional and construction assumptions, selection of materials, development of designs and prototypes of products together with construction documentation, verification and simulation of the structure in terms of strength and behavior in various conditions [3]. The scope of technological preparation of production includes planning and designing technological processes, the purpose of which is to prepare documentation of production processes. Documentation of processes includes, among others selection of the type and sequence of implementation of technological operations, selection of machine tools and workstations, parameterization of machining processes and description of the machining plan or operation [4]. The analysis of real data obtained from the production system is an important step in the process of optimizing the production system. We proposed the concept (Fig. 3) which makes it possible to locate the elements of the production process that can improve/optimize the operation of the entire process.

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analysis of data and processes in order to locate elements at the level of the production process that can improve / optimize the operation of the entire production system

selected data and processes for the development of a mathematical model

Fig. 3. The course of the process of analyzing actual data for optimization purposes

In the data analysis process, by the concept proposed in Fig. 3, it is possible to develop a mathematical model of the technological process under consideration, and then propose optimization at the level of the production process [5]. It should be emphasized that the actual data collected from the sensors using Radio Frequency Identification (RFID) technology [6] should then be analyzed and interpreted. Using the assumptions of enterprise architecture, it is possible to consider and analyze data obtained directly from the production system, taking into account business, technological requirements, among other things. As a consequence, the above will allow the development of a detailed model for the considered technological process to automate it [7]. The implementation of automation in the production system requires the introduction of process status identification.

3 Illustrative Example The illustrative example shown was inspired by [7]. At a manufacturing plant, signal lamps are manufactured for use in household appliances. The lamps are produced in three colors and their daily production is 1705 pieces. To develop a detailed model to optimize the current production system, it is necessary to visualize the functioning of the current production system along with the identification of its problems. For this purpose, sensors were placed in the production plant at each production stage, the purpose of which was to obtain real data from the production system on individual production stages. The current state Value Stream Mapping (VSM) map was built by downloading real data from the production system. The VSM map is a graphical diagram of the process showing the relationship between the material flow and the information flow. “Value stream mapping method (…) is used to map material and information flows in the production system of a manufacturing enterprise” [8]. When the number of goods flowing through the process increases and the processes become more complex, asset identification with the help of RFID technology not only increases efficiency, but it becomes the backbone of the whole production line. RFID tags enable increased automation in goods tracking at several phases in today’s manufacturing and/or logistic chains. RFID brings visibility and efficiency starting from managing the prototype parts until the outbound distribution of the finished goods. To analyze the data

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obtained directly from the production system using RFID, it will be necessary to develop a model of the production process using Business Process Model and Notation (BPMN) (Fig. 4).

Fig. 4. VSM map of the current production process of the signal lamp

Fig. 5. Production model of the signal lamp in BPMN

The production model of the signal lamp (Fig. 5) was developed with the use Business Process Model and Notation (BPMN), onto which the data obtained from the production system was applied. It shows that a change of the quality control model can be considered and it will be necessary to introduce changes also to the level of the assembly process due to the excessively long duration of this process.

4 Problem Description The VSM map of the current state (Fig. 4 and Fig. 5) of the discussed process marks the data obtained from the production system along with a presentation of the process control method, material flow, technological operations with their basic parameters, transport operations, inventory locations and their size. The processing time is shown at the bottom of the map (Fig. 5). It is long due to the large amount of stock in progress. For the example considered, the process models were developed using BPMN. The result of modelling is process models, which are a simplified, non-material reflection of real processes. Then, using the approach resulting from the assumptions of the enterprise architecture, in particular, the assumptions that are used to develop an architecture meta-model (1)

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using information contained in the process models BPMN (Fig. 5), the data obtained from the production system using sensors using RFID technology was analyzed. M = (Rs , P, R)

(1)

where: Rs − resources (all tangible and intangible elements of the production process that are necessary to produce products, e.g., machines, raw materials, workers, tools, etc.); P − processes (all phenomena and consciously undertaken actions that result in a gradual occurrence of the desired changes in the subject of work under their influence); R − relationships (all connections and interdependencies that affect the production or maintenance of products or services). The analysis of actual data obtained from the production system and BPMN process models allowed to identify a number of key issues: • Production control that is executed through the production schedule. Individual positions are working without taking into account the needs of the next position. This causes an accumulation of work-in-progress inventories and problems with the timely execution of orders. • Waste related to overproduction. The volume of production stocks in progress is as high as weekly production. This is due to a significant diversification of the assortment of small elements that are produced in stock because they are a component of other finished products. • Manufacturing based on manual assembly, which is the longest and most laborintensive operation. The technological complexity of the products is low, therefore the costs that the company would incur to modernize the assembly stations would be small • Numerous machine downtime caused mainly by waiting for component deliveries. Based on the above observations and identified problems, two basic research questions Q1 and Q2 were formulated for the case under consideration. These are the following questions: How to modify the processes to develop an optimal production plan (Q1)? and How to minimize inventories in the manufacturing process (Q2)?

5 Formalization of the Mathematical Model for the Illustrative Example To solve the identified problems (Sect. 4), it was decided to develop a mathematical model (Table 1) for illustrative example and using the possibilities of mathematical programming, it is possible to propose a change at the level of the production process. As a result of the analysis of the architecture meta-model (1) and the assumptions resulting from the assumptions of the enterprise architecture, it was found that the regulator should be “assembly operations” in the example under consideration, as no actions following assembly are continuous.

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Table 1. Defining elements of the mathematical model Architecture meta-model

Symbol

Components of the model

Description

Rs

P

Sets

Set of products

R

P

p, g

Set of all positions (production centers, machines) Indexes

Product index (p, g ∈ P)

r

Position index (r ∈ R)

t

Planning period t ∈ [1..T]

wp

Parameters

Time needed for its implementation/delivery from the outside/delivery to the recipient

bp

For production party/delivery/shipping

cp

Product initial supply

dp

The maximum allowable stock of the product

dr,t

Has a certain production capacity in period t

zp,t

For external demand zp,t determines the size of the order for the product p during the period t

ap,g

Products have a specific structure ap,g determines how much product g needs to make the product p, ap,g = 0 means that the product g is not directly included in the product p

nr

Each position in the period t can only produce product type number (e.g. preparation of the material for processing material, i.e. performing further products/operations., etc (continued)

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Z. Juzo´n et al. Table 1. (continued)

Architecture meta-model

Symbol

Components of the model

Description

R

X p,r,t

Decision variables

How many batches of the product p should be produced in period t on the site r

V p,t

Product supply p at the end of the period t

Y p,t

Product demand p (number of parties) at the end of the period t resulting from orders and the implementation of the products in which it enters

U p,r,t

If the product p is produced, produce in the period t in the station r is U p,r,t = 1 otherwise U p,r,t = 0

f r,p

Parameters

er,p

(2)

Product p can be produced at the r center and the related coefficient er,p determines how long it takes to produce product p at the r center How much time does it take to create a product p in the center of r

Constraints

The amount of demand for each product in each period

(3, 4)

Inventory balance for each product in each period

(5)

Not exceeding the production capacity of the position

(6)

Connection of the variables X p,r,t and U p,r,t (st - large constant)

(7)

Integer nature of decision variables

(8)

The number of products in the station (continued)

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Table 1. (continued) Architecture meta-model

Symbol

Components of the model

(9)

Model objective function minimizing inventory



Yg,t = zg,t +

ap.g · bp · (

p∈P∧t+w(p)≤T

Vp,t−1 + bp ·



Description



Xp,r,t+w(p) ) ∀g ∈ P, t ∈ [1..T]

(2)

r∈R

(fr,p · Xp,r,t ) = Yp,t + Vp,t ∀p ∈ P, t ∈ [2..T]

(3)

r∈R

cp + bp · 



(fr,p · Xp,r,1 ) = Yp,1 + Vp,1 ∀p ∈ P

(4)

r∈R

(bp · er,p · Xp,r,t ) ≤ dr,t ∀r ∈ R, t = [1..T]

(5)

p∈P

Up,r,t ≤ Xp,r,t ∀p ∈ P, r ∈ R, t ∈ [1..T] st · Up,r,t ≥ Xp,r,t ∀p ∈ P, r ∈ R, t ∈ [1..T] Xp,r,t ∈ N∀p ∈ P, r ∈ R, t ∈ [1..T] Up,r,t ∈ {0, 1}∀p ∈ P, r ∈ R, t ∈ [1..T]  Up,r,t ≤ nr ∀r ∈ R, t ∈ [1..T] p∈P

min

 

Vp,t

(6) (7) (8) (9)

p∈P t∈[1..T]

6 Proposal for a Future VSM Map The application of the assumptions of the enterprise architecture in the field of analysis of real data obtained from the production system using sensors using RFID technology in conjunction with the analysis of production processes enabled the development of a mathematical model (Table 1). Based on the mathematical model (2).. (9) and the data obtained in accordance with the concept (Fig. 3), an implementation model was built. The experiments were carried out for various data instances (Table 2). For the experiment number 10 in (Appendix A) answers to questions Q1 and Q2 are presented. All experiments were performed on a computer with the following specifications: Processor: Intel (R) Core (TM) i5-7300U CPU @ 2.60 GHz 2.70 GHz, RAM: 8 GB, operating system: Windows 10 Pro. By solving the model using a mathematical programming solver LINGO, we obtain results that are the basis for modifying the original production process in such a way

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Z. Juzo´n et al. Table 2. Different data instances for the mathematical model (Appendix A)

Experiment number Planning horizon [T] Number of products [P] Number of centers/cells [C] 1

3

5

2

2

3

10

4

3

3

15

8

4

3

20

10

5

6

5

2

6

6

10

4

7

6

15

8

8

6

20

10

9

10

5

2

10

10

6

4

11

10

15

8

12

10

20

10

as to obtain optimization/improvement at the level of the current production system [8]. In results of that, it is possible to propose a combination of the assembly process with quality control to shorten the production time (Fig. 6). The proposed change can be put on the VSM map of the future, which is a schematic picture of the functioning of the reorganized production system. An example of a proposal for a future VSM map change, which, after approval at the management level, can be implemented into the actual production system is shown in Fig. 6. Client

Supplier

RFID

order and sales department

RFID monitoring nodes

warehouse manufacturing process

assembly process + quality control

RFID

RFID

RFID

shipping 1x week (according to the contract)

Producon Model

process duration (unchanged)

manufacturing process

process duration (unchanged)

assembly process + quality control

Storage to warehouse

the new quality control model and reducing the duration of the assembly process (change proposal)

Fig. 6. VSM map of the status of the signal lamp’s future production process

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7 Conclusion The conducted experiment confirmed that the analysis of real data obtained directly from the production system using sensors, including the analysis of processes operating at the production line level, is an important step in planning the production process. Using the assumptions of the architecture, we review the data influencing the functioning of the manufacturing process and classify the actual data obtained from the production system. Such action will consequently provide key information for the development of a mathematical model to optimize the production system. Solving the mathematical model using the mathematical programming solver (LINGO) for different data instances (Table 2), we can propose a change to the existing production process and solve problems that appeared at the stage of process analysis using the assumptions of enterprise architecture, in particular the TOGAF standard. As a result of optimization/improvement, we can propose a change at the level of the production process, which, after approval at the level of the Management Board, can be implemented into the actual production system. It is recommended to place VSM on the map of the future and use BPMN notation to present a diagram of the reorganized production system (Fig. 6). In further works, it is planned to apply the proposed concept to urban logistics problems, including the use of UAV in last mile deliveries considering the problem of energy consumption [9, 10, 11]. It is also planned to use artificial neural networks to determine the validity of applying the proposed concept to specific cases and data instances.

Appendix A. Data and Results for Experiment Number 10 Sample Data for the Model ! T - Planning horizon; 10~ ! P - Number of products; 6~ ! C - Number of centers/cells; 4~ !Time needed to deliver the product - in (p); 4 1 1 1 1 2~ !Product batch - b (p); 2 2 2 2 2 2~ !Initial stock of the product - c (p); 0 0 0 0 0 0~ !How much product g is needed to make product p - a (p, g) (end row, component column); 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0~ !External demand for a product from (p, t) (product line, period column - there have been no orders recently); 000000000300000000000000000000000000000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0~ !How many position in the period can produce types of products n (r); 2 2 1 2~ !Production capacity of the station in the period d (y, t) (state row, period column); 480 480 480 480 480 480 480 0 480 480 480 480 480 480 480 480 480 0 480 480 480 480 480 480 480 480 480 0 480 480 480 480 480 480 480 480 480 0 480 480~ !Can the product be created on the position f (r, p) (staple row, product column); 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1~

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!How much time does it take to make a batch of the product at the stand e (r, p) (state row, product column); 9 9 0 0 0 0 9 9 0 0 0 0 0 0 9 9 0 0 0 0 0 0 9 9 Result: Answer to Question Q1 and Q2: Production Plan product = 1 station = 2 period = 10 number of lots = 2 production volume = 4 product = 3 position = 3 period = 6 number of lots = 2 production volume = 4 product = 4 position = 3 period = 5 number of batches = 2 production volume = 4 product = 6 position = 4 period = 5 number of lots = 2 production volume = 4 product = 1 period = 10 stock = 1 product = 4 period = 5 stock = 4

References 1. The Open Group Architecture Framework - TOGAF Standard. https://pubs.opengroup.org/ architecture/togaf9-doc/arch/index.html. Accessed 21 Nov 2022 2. Burduk, A.: Stability analysis of the production system using simulation models. In: Pawlewski, P., Greenwood, A. (eds.) Process Simulation and Optimization in Sustainable Logistics and Manufacturing. E, pp. 69–83. Springer, Cham (2014). https://doi.org/10.1007/ 978-3-319-07347-7_5 3. Bartodziej, C.J.: The Concept Industry 4.0: An Empirical Analysis of Technologies and Applications in Production Logistics. Springer, Wiesbaden (2016). https://doi.org/10.1007/ 978-3-658-16502-4 ´ 4. Cwikła, G.: Methods of manufacturing data acquisition for production management - a review. Adv. Mater. Res 837, 618–623 (2013) https://doi.org/10.4028/www.scientific.net/ AMR.837.618 5. Weng, D., Yang, L.: Design and implementation of barcode management information system. In: Zhu, R., Ma, Y. (eds.) Information Engineering and Applications. LNEE, vol. 154, pp. 1200–1207. Springer, London (2012). https://doi.org/10.1007/978-1-4471-2386-6_158 6. Design and implementation of barcode management information system, Pozna´n, ScanPoland (1990) 7. Sitek, P., Wikarek, J.: A multi-level approach to ubiquitous modeling and solving constraints in combinatorial optimization problems in production and distribution. Appl. Intell. 48, 1344– 1367 (2017). https://doi.org/10.1007/s10489-017-1107-9 8. Holms, D.: AMPL at the University of Michigan. https://ampl.com. Accessed 21 Nov 2022 9. Wikarek, J., Sitek, P.: A data-driven approach to constraint optimization. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) AUTOMATION 2019. AISC, vol. 920, pp. 135–144. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-13273-6_14 10. Thibbotuwawa, A., Nielsen, P., Zbigniew, B., Bocewicz, G.: Factors affecting energy consumption of unmanned aerial vehicles: an analysis of how energy consumption changes in ´ atek, J., Borzemski, L., Wilimowska, Z. (eds.) ISAT 2018. relation to UAV routing. In: Swi˛ AISC, vol. 853, pp. 228–238. Springer, Cham (2019). https://doi.org/10.1007/978-3-31999996-8_21 11. Aiello, G., Inguanta, R., D’Angelo, G., Venticinque, M.: Energy consumption model of aerial urban logistic infrastructures. Energies 14, 5998 (2021). https://doi.org/10.3390/en14185998

Autonomous Mobile Flock Traffic Simulation in Digital Twin Mode Mantas Makulaviˇcius(B) , Rokas Bagdonas , Karolina Lapkauskaite , Justinas Gargasas , and Andrius Dzedzickis Vilnius Gediminas Technical University, Saul˙etekio al. 11, 10223 Vilnius, Lithuania [email protected]

Abstract. Traffic congestion in urban areas is the main reason for the long traveling time from one place to another. This happens due to the decisions and reaction times of each driver. Reducing the influence of the driver solution on the control of the vehicle, i.e., increasing the autonomy of the vehicle, can minimize waiting times at traffic light-controlled and uncontrolled intersections. By minimizing the waiting time at the crossroad, the overall traffic intensity can be reduced as well. This research focuses on obtaining information from simulations at specific crossroads for further observations and traffic optimizations, e.g., by implementing machine learning methods. In order to represent the impact of different levels of autonomous vehicles on the autonomous mobile flock traffic, the open-source SUMO (Simulation of Urban MObility) software is used to simulate the traffic in a digital twin mode. The obtained simulation results provide information about the average speed of surrounding vehicles and the number of vehicles over a period of time, with different scenarios reflecting the density ratio of various levels of vehicle autonomy. Keywords: Traffic simulation · Urban traffic · Traffic monitoring · SUMO

1 Introduction Traffic congestion in urban areas is the main reason for the long traveling time from one place to another. This happens due to the decisions and reaction times of each driver [1, 2]. One of the possibilities to prevent the influence of the driver is to make a vehicle more autonomous. These vehicles with the use of sensors, communication equipments and computational tools can replace the drivers imperfections [2]. Autonomous vehicles are defined by six levels of automation, where zero level means no automation and level five means full automation [3]. These levels with corresponding values of predefined parameters can be implemented into traffic simulations [4]. There are o lot of software tools decicated for traffic simulations to represent digital twin mode. Simulation of Urban MObility (SUMO) is one of the most convienent simulation platforms [5]. It allows to implement and simulate the dynamic behavior of vehicles, such as acceleration or deceleration, road line change, and vehicle-to-vehicle connectivity [6, 7]. Besides, there are additional tools to extract data of traffic maps using © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 85–92, 2023. https://doi.org/10.1007/978-3-031-25844-2_8

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OpenStreetMap (OSM) [8] and edit those maps using NETEDIT [9] or eNetEditor [10]. Moreover, vehicle-to-infrastructure communication, which includes traffic light regulations or parking places, bus stops, and others, can be implemented to simulate the smart infrastructure’s influence on the surrounding traffic [5, 10]. Another example of using SUMO simulations is the localization of pedestrians imitating vehicle-to-pedestrian situations with Radio frequency identification (RFID) [11], or is the overall pedestrian influence on the traffic [12]. SUMO simulations can be also implemented with other programming tools, e.g., MATLAB, Python or Unity 3D, and network connectivity simulators, e.g., NS3, OMNET++, to perform online and offline simulations [8, 13, 14]. These additional tools are used to simulate the connectivity with vehicles and perform the signal strength monitoring. In this study, we implement the SUMO simulation tool together with Python and Traffic Control Interface (TraCI) to imitate autonomous mobile flock traffic in digital twin mode to extract and represent traffic data. These data correspond to a number of vehicles and their average speed over a specific period of time. Such data can be useful for observing traffic congestions at traffic light-controlled and uncontrolled crossroads and generating paths for autonomous vehicles.

2 Methodology for Urban Traffic Generation In order to represent a digital twin model of live action traffic environment, the methodology of model generation and required data acquisition has been created (Fig. 1). The main simulation environment is chosen to be SUMO because of its improved and expanded features on traffic simulation [5].

Fig. 1. Methodology for the simulation of urban traffic.

The first stage of traffic simulation is the development of the map. The map of the real or imaginary place where the traffic will be simulated must be made or generated from available online sources. For this purpose, a supplementary software tool – OSM is chosen for traffic map extraction and generation where all the road lines, traffic lines, and pedestrian crossings are represented. After the generation of the map, an additional tool NETEDIT is used to remove unwanted road regions or reduce the overall map that is irrelevant to the research. Furthermore, it was used to add missing road lines or traffic

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lights that are present in real situations. Additional environmental elements such as bus stops, parking zones or road connections can be added on demand. For the simulation, the urban part of Vilnius city in Lithuania has been used (Fig. 2a). After the extraction and preprocessing of the map, it has been uploaded into the SUMO simulation (Fig. 2b). The thicker the line, the more road lanes there are.

Fig. 2. Map of interest: a) part of the real map from OpenStreetMap; b) SUMO map, preprocessed in NETEDIT for further simulations.

To generate random traffic, it is necessary to define main traffic routes, like the vehicle route’s beginning, mid-route, and ending. Further, according to [4], different automation vehicle levels can be defined with Krauss Model by defining several parameters shown in Table 1. Table 1. Different Krauss Model parameters for various vehicle automation levels [4]. Automation level

Mingap (m)

Acceleration (m/s2 )

Deceleration (m/s2 )

Emergency deceleration (m/s2 )

Sigma

Tau (s)

Level 0

2.5

2.6

4.5

8.0

0.5

1.0

Level 1

2.0

3.05

4.5

8.0

0.4

0.95

Level 2

1.5

3.5

4.5

8.0

0.3

0.9

Level 3

1.25

3.6

4.5

8.0

0.2

0.8

Level 4

0.75

3.7

4.5

8.0

0.0

0.7

Level 5

0.5

3.8

4.5

8.0

0.0

0.6

From the table, the mingap is the minimum allowed gap between the corresponding vehicle and the vehicle in front, Sigma is the human imperfection (from 0 to 1) and Tau is the minimum reaction time of the driver. These parameters are contained in.xml file, which is readable by SUMO. These and other parameters can be coded as an example:

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In this code line, id is the corresponding name for described parameters of the autonomous level. Length is describing the average length of all vehicles in simulation, which according to [15] is equal to 4.5 m. maxSpeed is the maximum speed of the corresponding vehicle in m/s. In our simulation it was set equal to 14 m/s (50 km/h) that corresponds to the speed limit in Lithuania. As well as the vehicle identification and its automation level, depart time in seconds, and route points can be coded:

According to these.xml command lines, a Python code is written to randomly generate vehicles with different autonomous level, departure, mid-route, ending routes for N number of vehicles and for specific simulation time. The departing time of each randomly generated vehicle is distributed evenly. The depart beginning, mid-route and ending places of each vehicle are generated randomly as well (Fig. 3). Two points of interest are defined as RSU1 and RSU2 which are representations of data-gathering infrastructure units from their surrounding vehicles within a specific range and over a specific period of time.

Fig. 3. Route map in SUMO simulation, here: B – places of the route beginning, M – places of the mid-route, E – places of the route ending, RSU – roadside units.

For the values retrieval, the Python programming language and TraCI are implemented together. RSUs are used to gather information regarding the number of vehicles and their average speed at the corresponding crossroads. The 1st crossroad (RSU1) is regulated by traffic lights, and the 2nd (RSU2) is not. Several cases of different probability ratios (%) of different levels of automation have been generated to evaluate the car automation influence on traffic (Table 2). Automation levels 4 and 5 are excluded in these simulations because there are no vehicles with these levels in the real-life traffic under study. Nonetheless, without these two levels, these simulations are important to show the influence of vehicle autonomy on the traffic.

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Table 2. Different simulation cases. Level 0

Level 1

Level 2

Level 3

Case 1

100%

–

–

–

Case 2

50%

50%

–

–

Case 3

40%

30%

30%

–

Case 4

30%

20%

20%

20%

3 Results and Discussion During the simulation for each second one random vehicle with a different level of autonomy shows up from the random beginning of the route, and it does not matter when that vehicle ends its trip. The simulation is defined to run for 500 s and to use a total of 200 vehicles for each case. Values are retrieved from RSU1 and RSU2, which detect vehicles in the range of 50 m. Retrieved values are the number of vehicles and the average speed of those vehicles from the RSU1, where the intersection is controlled with a traffic light, are presented in Fig. 4 and Fig. 5, respectively.

Fig. 4. Number of vehicles during the simulation at the RSU1 in the range of 50 m.

From graph in Fig. 4. it can be concluded, that for the case 4, all 200 vehicles were able to finish their trips before the end of simulation because there are no vehicles detected at the RSU1. However, the lower ratio of automotive vehicles (cases 3, 2, and 1) resulted more vehicles to be still present at this crossroad. From the speeds graph in Fig. 5. it can be noted, that in the case 4, for most of the simulation time, the average vehicle speed is the highest, therefore, all the vehicles were able to finish the simulation within desired time range. In the same manner, values are retrieved from the RSU2, where the intersection is not controlled by any traffic lights, are presented in Fig. 6 and Fig. 7, respectively.

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Fig. 5. Average speed of the vehicles during the simulation at the RSU1 in the range of 50 m.

Fig. 6. Number of vehicles during the simulation at the RSU2 in the range of 50 m.

The diagram in Fig. 6 shows that there are fewer vehicles at RSU2 due to the smaller size of the intersection with fewer road lanes connecting to it. In all cases where there was at least one level of automation, the vehicles were able to complete the simulation. At both RSU1 and RSU2 when the vehicles were congested at the end of the simulation (Fig. 4 and Fig. 6, respectively), their movement speeds are not noticeable (Fig. 5 and Fig. 7, respectively). It is apparent from all the cases and the retrieved graphs of both RSUs that minimum allowed gap between vehicles, acceleration, inaccuracy of drivers, and minimum reaction time have a noticeable impact on the traffic in the urban area. The advantage of these simulations is that it can show us how important is vehicle autonomy for traffic. Furthermore, the obtained results will be used for the implementation of machine learning for the traffic congestion predictions and vehicle rerouting or traffic light optimization. Despite the fact, the main disadvantage is that to achieve high level of vehicle autonomy is still difficult in current times and especially achieving that

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Fig. 7. Average speed of the vehicles during the simulation at the RSU2 in the range of 50 m.

on a higher scale, such as in cities. Additionally, running these simulations the unpredictability of pedestrian behavior, leading to more assumptions that are not applicable to the real world.

4 Conclusions Our simulation of autonomous mobile flock traffic in digital twin mode has been implemented. Firstly, the actual traffic map can be reflected in the simulation and random routes with specific beginning, middle and ending points can be defined. Secondly, vehicles with different autonomous levels can be specified with random departure time and route. From the obtained results, it can be concluded shortly, that with bigger ratio of autonomous vehicles in traffic, traffic congestions are reduced. In cases with the higher vehicle autonomy level, 200 vehicles were able to finish the simulation in less than 500 s. Our obtained results from simulations allow us to estimate if there is a traffic congestion at the traffic light-controlled and uncontrolled intersections. In further work this methodology and more obtained data will be used together with machine learning methods to optimize traffic. Acknowledgement. This work is part of the AI4SCM project, receiving funding from the European H2020 research and innovation programme, ECSEL Joint Undertaking, under grant agreement No. 101007326.

References 1. Parrado, N., Donoso, Y.: Congestion based mechanism for route discovery in a V2I–V2V system applying smart devices and IoT. Sensor 15(4), 7768–7806 (2015). https://doi.org/10. 3390/s150407768

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2. Flanagan, S.K., Tang, Z., He, J., Yusoff, I.: Investigating and modeling of cooperative vehicleto-vehicle safety stopping distance. Future Internet 13, 1–24 (2021). https://doi.org/10.3390/ fi13030068 3. Higatani, A., Saleh, W.: An investigation into the appropriateness of car-following models in assessing autonomous vehicles. Sensors 21, 1–15 (2021). https://doi.org/10.3390/s21217131 4. Lu, Q., Tettamanti, T.: Impacts of autonomous vehicles on the urban fundamental diagram. In: Road and Rail Infrastructure V, vol. 5, pp. 1265–1271 (2018). https://doi.org/10.5592/co/ cetra.2018.714 5. Lopez, P.A., Behrisch, M., Bieker-Walz, L., et al.: Microscopic traffic simulation using SUMO. In: IEEE Conference on Intelligent Transportation Systems, Proceedings, ITSC 2018, pp. 2575–2582, November 2018. https://doi.org/10.1109/ITSC.2018.8569938 6. Klischat, M., Dragoi, O., Eissa, M., Althoff, M.: Coupling SUMO with a motion planning framework for automated vehicles, vol. 62, pp. 1–9 (2019). https://doi.org/10.29007/1p2d 7. Liu, W., Wang, X., Zhang, W., et al.: Coordinative simulation with SUMO and NS3 for vehicular ad hoc networks. In: Proceedings - Asia-Pacific Conference on Communications, APCC 2016, pp. 337–341 (2016). https://doi.org/10.1109/APCC.2016.7581471 8. Mallissery, S., Pai, M.M.M., Mehbadi, M., et al.: Online and offline communication architecture for vehicular ad-hoc networks using NS3 and SUMO simulators. J. High Speed Netw. 25, 253–271 (2019). https://doi.org/10.3233/JHS-190615 9. Jat, S., Tomar, R.S., Sharma, M.S.P.: Traffic congestion and accident prevention analysis for connectivity in vehicular ad-hoc network. In: Proceedings of IEEE International Conference on Signal Processing,Computing and Control, pp. 185–190, October 2019. https://doi.org/10. 1109/ISPCC48220.2019.8988463 10. Kurczveil, T., López, P.Á.: eNetEditor: rapid prototyping urban traffic scenarios for SUMO and evaluating their energy consumption. In: Proceedings of the SUMO User Conference - Intermodal Simulation for Intermodal Transport, pp. 146–169 (2015). https://doi.org/10. 13140/RG.2.1.2874.2563 11. Griggs, W.M., Verago, R., Naoum-Sawaya, J., et al.: Localizing missing entities using parked vehicles: an RFID-based system. IEEE Internet Things J. 5, 4018–4030 (2018). https://doi. org/10.1109/JIOT.2018.2864590 12. Jing, P., Huang, W., Chen, L.: Car-to-pedestrian communication safety system based on the vehicular ad-hoc network environment: a systematic review (2017). https://doi.org/10.3390/ info8040127 13. Olaverri-Monreal, C., Errea-Moreno, J., Díaz-álvarez, A., et al.: Connection of the SUMO microscopic traffic simulator and the unity 3D game engine to evaluate V2X communicationbased systems. Sensors 18 (2018). https://doi.org/10.3390/s18124399 14. Almeida, J., Rufino, J., Alam, M., Ferreira, J.: A survey on fault tolerance techniques for wireless vehicular networks. Electronics 8, 1–21 (2019). https://doi.org/10.3390/electronics8 111358 15. Average Car Length Guide (Car Lengths in Meters and Inches) - Car Roar (2022). https://car roar.com/car-length/. Accessed 2 Nov 2022

Neural Network Model for Predicting Technological Losses of a Sugar Factory Nataliia Zaiets1

, Lidiia Vlasenko2

, and Nataliia Lutska3(B)

1 National University of Life and Environmental Sciences of Ukraine, Kiev 03041, Ukraine

[email protected]

2 Kyiv National University of Trade and Economics, Kyiv 02156, Ukraine 3 National University of Food Technologies, Kyiv 01033, Ukraine

[email protected]

Abstract. To ensure the implementation of the concepts of Industry 4.0 and Lean 4.0 in order to improve the efficiency of the functioning of a manufacturing enterprise, it is necessary not only to keep records of technological losses, but also to predict them. Loss of sugar in molasses is a defining characteristic of the resource efficiency of a sugar refinery that processes sugar beets. The article proposes a neural network model of sugar loss in molasses and sugar yield with an error of less than 3%. The input variables of the forecast model are automatically measured technological variables of the main beet processing processes. The proposed model can be used for real-time forecasting. This makes it possible to identify the stages of production where the loss of sugar in molasses is the greatest, as well as to simulate various situations by changing the input data. That is, the developed model is an integral part of the management decision support system, and its use increases the yield of sugar by reducing losses. Keywords: Losses · Molasses · Neural network · Forecast · Sugar · Beet · Learn-production

1 Introduction The trends of a modern manufacturing enterprise are its digitalization at different management levels. This is facilitated by the development of Industry 4.0 and related processes, in particular the development of the intellectual component of modern factories. Also, as part of the development of the latest approaches to the organization and conduct of production processes, actively developing and implemented robotics plays. The use of the latest technologies is aimed at improving the efficiency of the processes of a manufacturing enterprise at all levels, increasing resource and energy efficiency, and increasing competitiveness. It should also be noted that illiterate enterprise reengineering, abrupt and unbalanced digitalization of an enterprise can have a negative financial effect, lead to unrecoverable significant costs. Therefore, when reorganizing production, it is necessary to carefully consider the strategy. In the context of global economic and energy crises that are occurring today due to the aggression of the Russian Federation © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 93–104, 2023. https://doi.org/10.1007/978-3-031-25844-2_9

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against Ukraine, the issue of reducing production costs has become extremely relevant. This can be achieved by integrating various enhancements at different levels. In today’s realities, an evolutionary approach to continuous improvement of an enterprise using various methods and tools is relevant in order to increase profits by reducing added value. It is possible to reduce the final cost of products by reducing waste, all types of losses, downtime, and simplifying individual operations. This significantly increases the competitiveness of the enterprise and its products. The principles described above are typical for the concept of Lean Manufacturing, which, under the influence of Industry 4.0, has turned into Lean 4.0 [1, 2]. The wellknown successful experience of enterprises that simultaneously implement the Lean 4.0 methodology and Industry 4.0 tools indicates the high promise of this option, in contrast to the production of only one initiative separately. After all, the principles of loss reduction combined with IoT, IIoT, cloud technologies, machine learning, work from big data and intelligent methods can create a truly economic workshop. Food sector enterprises are those that use a lot of energy and raw materials. The quantity and quality of the final product directly depends on the strict observance of the technological regulations, the quality and storage conditions of raw materials, reduction of downtime, and various types of losses. As a result of the processing of sugar beet in the last stage of crystallization, a byproduct is obtained - molasses. This effluent contains sucrose, water and insoluble nonsugars left in the diffuse juice after it has been purified with lime. In Ukraine, molasses is used in other industrial enterprises, in particular, in the manufacture of alcohol, citric or lactic acid, as well as in the cultivation of baker’s yeast. However, for the sugar industry, molasses is a waste, the amount of sugar in which they try to minimize. In this case, various technological methods are used, such as reducing the water consumption when dissolving the last massecuite, maintaining the optimum temperature of the massecuite in the crystallization unit during centrifugation, etc. That is, the loss of sugar in molasses is an immeasurable loss at all technological stages of sugar production. And building a model of sugar loss in molasses will identify places where more sugar is lost and will make it possible to predict these losses for the future. Object of the study is processes for predicting sugar losses in molasses, which are non-measurable indicators of the resource efficiency of sugar production. Subject of the study is the neural network model of sugar loss in molasses, the input variables of which are variables from factory automation systems and an industrial laboratory, which will allow its prediction. The purpose of the work is to develop a neural network model of the main loss characteristic of a sugar mill, which allows it to be used for real-time forecasting, thereby increasing sugar yield by reducing losses.

2 Review of the Literature References Enough authors have been involved in the use of machine learning models in the management of sugar production [3, 4]. In works [5–8], using the methods of fuzzy sets, heuristic dynamic programming and neural networks, optimal pH values for sugar production are

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provided. Reference [9] highlights the successful implementation of a digital twin for condition monitoring of a four-stage evaporation line for sugar cane processing. In [10], the results of the analysis of the influence of the measured variables of the evaporator plant on the calculation of steam flows and their variability, as well as their influence on the global heat transfer coefficient under various operating conditions, are presented. But these works are devoted to the processing of sugar cane, not beets. The most popular machine learning models today are neural networks. They are able to effectively approximate a large state space, which is characterized by non-linearity and uncertainty. Neural network models are superior to expert models in that they do not need to evaluate all possible states, resulting in higher accuracy [11–13]. However, they require many additional settings to be defined, and deep learning models require a lot of computing power. Therefore, a significant proportion of applied research based on the neural network model uses simple network architectures, such as the MLP multilayer perceptron [14]. Due to data preprocessing and simple neural network architecture, it is possible to obtain a model that has high accuracy and reliability. To ensure the release of products of a given quantity and quality, it is important to reduce various losses. In particular, the condition of the initial product or raw material plays an important role. The use of machine learning methods can provide monitoring of the state of raw materials (sugar beets, fruits, etc.) based on a deep convolutional neural network (has applied a deep convolutional neural network) [15], which will allow creating a queue for sending raw materials to production. This will reduce the loss of raw materials due to the prevention of its deterioration and timely use. The use of machine learning methods is part of the intellectualization of production as part of the implementation of the industry 4.0 concept. Machine learning methods work on the basis of data obtained in real time in the form characteristic of cyberphysical systems: human to machine, machine to machine and data acquisition and processing [16]. This approach allows you to get an idea of all the processes taking place in production, identify bottlenecks and where the main losses occur; provides employees with timely operational corrective actions; improve energy and resource efficiency. The simultaneous combination of Lean 4.0 and Industry 4.0 concepts provides an increase in the operational efficiency of production [17]. Cloud technologies contribute to the rapid adjustment of technological regulations and the technological process in the event of deviations, as well as instant reactions to the appearance of downtime due to equipment malfunctions [18]. The advantages of such modernization of the enterprise should also include a reduction in the time required for diagnosing and initiating corrective actions, and coordinating the work of related departments. This leads to a reduction in equipment downtime through an optimal schedule for the use and fullness of the devices [1, 2, 8]. For sugar production, the introduction of the Lean concept [19] significantly improved the process of coordinating the work of neighboring departments, reduced downtime of equipment, reduced the processing of semi-finished products, improved the consistency of equipment operation, which led to a decrease in intermediate losses. But not enough attention was paid to reducing the intermediate losses of the technological component of the production process.

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3 Methods Industry 4.0 includes tools: Internet of Things (IoT); Industrial Internet of Things (IIoT); Big data and analytics; cloud computing; machine learning and artificial intelligence; Additive manufacturing or 3D printing; advanced robotics; simulation; Augmented and virtual reality; Horizontal and vertical system integration (including Information technology and Operational technology integration) (Fig. 1) [20], which, in combination with the principles of continuous improvement of production Lean 4.0, make it possible to improve technological processes, predict possible failures before their occurrence, monitor and predict possible losses in order to further correct them.

Fig. 1. Vertical and horizontal integration in a smart factory

For the production of the final product - sugar, the process of its creation must take place using a certain set of input data. The production process is changeable and the conditions for its passage are always different. This is due to the high variability of its components. The sources of variability include: Employees, Equipment, Processes, Materials, Measurement (Fig. 2). On Fig. 2 is a cause-and-effect diagram showing the influence of various components of the production process on total losses. Losses are affected by incorrectly made decisions at different levels by decision makers (industrial and production personnel are workers directly involved in the production process and its maintenance and non-production personnel are non-production workers), unskilled actions to maintain equipment, low qualification of personnel and etc. Also, the source of losses can be failures in the organization of economic processes, errors in organizational processes, non-compliance with the technological regulations in production, associated with problems in the operation of technological, control or electrical equipment, the appearance of various kinds of breakdowns, downtime through repairs or irregular work of the production component. The quality of input raw materials can also significantly increase losses, in particular, the quality of sugar beet has a high impact on the amount of sugar produced: flabbiness, frostbite, early or late harvest. When collecting Human to Machine data, there

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are losses associated with the peculiarities of conducting chemical analyzes, the subjective view or experience of the specialist’s experience. Such data should include data from the production laboratory, visual and organoleptic. Data collection of the Machine to Machine type, corresponding to obtaining the values of technological variables based on an automation system, is characterized by the possibility of losses associated with the stability of its operation. When collecting and working with data from other Data Acquisition & Processing software products, such as ERP, MES, intelligent add-ons, one should take into account the errors that occur in mathematical calculations and methods used to solve the tasks. Equipment

Employees

Processes

Control Equipment

Industrial and production personnel

Non-production personnel

Technological Equipment

Technological Processes

Economic Processes

Electrical Equipment

Organizational Processes Losses

Raw Human to Machine Data Acquisition & Processing Measurement

Machine to Machine

Semi-finished product

Materials

Fig. 2. Causal diagram of the influence of sources of variation on losses

The main types of sugar losses during processing are: sugar losses during storage and transportation of beets (0.5–1% by weight of beets); loss of sugar in production (1.1– 1.3% by weight of beets); loss of sugar in molasses (2–2.5% by weight of beets). At the same time, the amount of sugar losses during storage and intra-factory transportation depends on storage conditions, the length of the season and the handling equipment used, etc. Loss of sugar in production or processing is defined as the difference between the amount of sucrose entering the raw material plant and the amount of sucrose in the produced sugar and molasses. This number consists of accounted and unaccounted losses. The accounted ones, namely those determined in the industrial laboratory, include losses in pulp and filtration sediment, which were studied in the models of each department [11, 12]. Other losses are unaccounted for, for example, those caused by thermal decomposition of sucrose, its decomposition under the action of microorganisms, mechanical entrainment of drops, mechanical spills, as well as possible errors in laboratory studies. It is impossible to determine unaccounted losses directly on the basis of analyzes (hence their name - indefinite, unaccounted for). They are determined based on the sugar balance during production reports. Thus, during the implementation of the technological process, losses amount to approximately 25% of the total (total) losses, and the rest (about 75%) are losses in molasses. In this case, 0.67% of sucrose is lost in accordance with the departments:

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0.17% – in diffuse installations; 0.11% – in the juice cleaning department; 0.11% – in the evaporation plant; 0.17% – in the food department; 0.01% – in condensates; 0.1% – undeciphered). Consider a model for predicting losses in molasses. Since this variable directly affects the sugar yield, we will add one more output variable to the model in the Table 1. Input and output variables of the synthesized model are given. Table 1. The main variables of the model №

Branch

Designation

Variable interpretation

Inputs 1

2

3

4

5

6

7

8

Tank 1 after DS

DSS

Tank 2 after DSS

ES

Tank 3 after ES

VA I product

VA II product

VA III product

Var1

pH

Var2

Juice temperature

Var3

Time of stay

Var4

pH I saturation

Var5

pH II saturation

Var6

Juice temperature

Var7

Juice temperature

Var8

Time of stay

Var9

pH

Var10

Juice temperature

Var11

Time of stay

Var12

Dry matter

Var13

Temperature in Tank I

Var14

Temperature in Tank II

Var15

Temperature in Tank III

Var16

Temperature in Tank IV

Var17

Temperature in Tank V

Var18

Time of stay

Var19

pH

Var20

Syrup temperature

Var21

Time of stay

Var22

Temperature

Var23

pH

Var24

Time of stay

Var25

Temperature

Var26

pH

Var27

Time of stay

Var28

Temperature

Var29

pH

Var30

Time of stay

Var31

The sugar content of molasses

Outputs Product

(continued)

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Table 1. (continued) №

Branch

Designation

Variable interpretation

Var32

Sugar yield

Thus, we obtain a model, which is described by the dependence: ⎡ ⎤ Var1  ⎢ Var2 ⎥ Var31 ⎥ y = fNN (x); y = ;x=⎢ ⎣ . . . ⎦, Var32 Var30 

(2)

where Var1–Var32 are NN inputs and outputs (see Table 1). Thus, the main estimates of resource efficiency at the last stage of processing of the plant are the loss of sugar in molasses and the yield of sugar. The first score should be the lowest, the second the highest. In the course of work, the methods of correlation analysis determined the variables that affect the results. The values of the correlation coefficients between the input and predicted variables (Table 2) indicate a close relationship between the selected inputs and outputs, which confirms the use of the neural network model. Table 2. Values of correlation coefficients between input and predicted variables Correlation coefficient Train Var31

Validation Var31

Test Var31

Train Var32

Validation Var32

Test Var32

MLP 30-22-2

0.8922

0.8665

0.8718

0.8619

0.8505

0.8588

MLP 30-13-2

0.9364

0.9311

0.9359

0.9173

0.8880

0.9243

MLP 30-20-2

0.9428

0.9278

0.9294

0.9408

0.9244

0.9425

MLP 30-9-2

0.9370

0.9301

0.9413

0.9598

0.9511

0.9582

MLP 30-11-2

0.9548

0.9543

0.9800

0.9607

0.9525

0.9634

Experimental data was collected from the Kashperovsky sugar factory for a 3-month season of its operation in 2020. In the experiment, all data samples were divided into training, validation and test sets in accordance with the ratio of 70-15-15%. The following hyperparameters of neural networks were chosen: from 5 to 32 hidden neurons, learning for 30 epochs and using cross entropy, learning rate η = 10.0 and regularization parameter λ = 1000.0.

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20 neural networks of various architectures were built, but the MLP-type network showed the most accurate prediction. This neural network structure is versatile for approximating non-linear complex functions with many variables and is easy to implement. The results of training on the back-propagation method in Statistica Neural Networks for the best of them are shown in Table 3. As shown in the test sample, the forecast error is 5%. Table 3. The results of solving the optimization problem of the synthesis of the model in the form of neural networks Training perfect

Validation perfect

Test perfect

Training error

Validation error

Test error

Training algorithm

MLP 30-22-2

0.9543

0.9551

0.9511

0.0006

0.0006

0.0006

BFGS 298

MLP 30-13-2

0.9580

0.9574

0.9523

0.0007

0.0006

0.0007

BFGS 360

MLP 30-20-2

0.9607

0.9625

0.9609

0.0007

0.0006

0.0006

BFGS 381

MLP 30-9-2

0.9683

0.9680

0.9647

0.0006

0.0005

0.0006

BFGS 292

MLP 30-11-2

0.9735

0.9724

0.9709

0.0004

0.0004

0.0005

BFGS 290

Table 4. The results of the selected NN Samples (for target Var31)

MLP 30-11-2

Samples (for target Var31)

MLP 30-11-2

Minimum prediction (Train)

42.13

Minimum residual (Validation)

−4.77

Maximum prediction (Train)

49.20

Maximum residual (Validation)

Minimum prediction (Validation)

42.83

Minimum residual (Test)

−5.03

Maximum prediction (Validation)

48.41

Maximum residual (Test)

3.70

Minimum prediction (Test)

43.49

Minimum standard residual (Train)

Maximum prediction (Test)

49.04

Maximum standard residual (Train)

4.34

−2.79

2.69

Minimum prediction (Missing)

Minimum standard residual (Validation)

−2.98

Maximum prediction (Missing)

Maximum standard residual (Validation)

2.72

Minimum residual (Train)

−4.32

Minimum standard residual (Test)

−3.11

Maximum residual (Train)

4.18

Maximum standard residual (Test)

2.29

The selected model MLP 30-11-2 in all cases provides better generalization capabilities than other models. According to the results of survey statistics given in Table 3, it

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can be seen that the chosen model has a high degree of adequacy. In particular, it demonstrates the smallest errors in all variants. The results of the statistics of sugar losses in molasses (Var31) are given in Table 4. These estimates confirm its effectiveness in predicting the initial data.

4 Result and Discussion Based on the results of the synthesized neural network (2), we obtained the dependences shown in Figs. 3 and 4 with an error of less than 3%. Studies of the obtained surfaces show that the dependencies are purely nonlinear. The use of analytical mathematical models that take into account a large number of input data would lead to a multidimensional nonlinear model through differential equations, the use of which is problematic in practice. In contrast, we got a simple model in the form of neural networks, which can be easily used, and if the performance of the network is insufficient, it can be trained with new data. Based on the results of the forecast, you can better understand the instability and trend in the data.

Fig. 3. Dependence of sugar losses in molasses on: a – pH I and II saturation; b – temperature and pH in the VA I product.

Using the developed neural network model, it is possible to identify the stages of production, where the loss of sugar in molasses is the greatest. It is also possible to simulate different situations by changing the input data and predict losses due to subsequent changes. For example, Fig. 5 shows the Pareto chart calculated using the loss model. Analyzing the losses, it can be concluded that in this time period the largest losses of sugar in molasses occurred in the food section, as well as before the diffusion juice entered the purification station.

5 Conclusion More than half of digital transformation projects and the implementation of Industry 4.0 concepts are accompanied by certain problems: the high cost of implementing technical and software solutions; Significant periods of development and proof-of-concepts

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Fig. 4. Dependence of sugar yield on: a – diffuse juice temperatures after I and II saturation; b – temperatures in II and V in Tanks ES

Fig. 5. Pareto chart of losses in molasses

that attempt to cover many functions and tasks of the enterprise; uncertainty about predevelopment performance data, including improvement targets. But with the intellectualization of the technological component using machine learning methods that satisfy a clearly defined business goal, the risk of project failure is reduced and its payback period is reduced. This paper proposes a model for predicting sugar losses in molasses and sugar yield. The developed forecast model is based on a neural network - a multilayer perceptron with three layers, each of which contains thirty, eleven and two neurons, respectively. The neural network provided high performance in all training samples over 97%. Such accuracy indicates the possibility of effective practical use of such a structure model. Thus, the sugar loss model in molasses is the main component of the monitoring system for technological departments of production and an integral part of the management decision support system, and further research is aimed at developing such a system.

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Robotics

Parametric Identification of the Mathematical Model of a Mobile Robot with Mecanum Wheels Zenon Hendzel1 and Maciej Kołodziej2(B) 1 Faculty of Mechanical Engineering and Aeronautics, Department of Applied,

Mechanics and Robotics, Rzeszow University of Technology, Rzeszow, Poland [email protected] 2 Doctoral School of Engineering and Technical Sciences at the Rzeszow, University of Technology, Rzeszow, Poland [email protected]

Abstract. In this work, on the basis of the parametric identification process, a new mathematical model of an industrial robot with mecanum wheels was developed. Based on the prediction error, a synthesis of the parameters identification of the mathematical model of the robot was performed. The gradient method was used to determine the values of the mathematical model parameters. The aim of the parametric identification process was to formulate a mathematical model for the synthesis of control algorithms. We use a continuous-time formulation and the parametric identification task is understood as the selection of the best mathematical model in a given class of models. Numerous experimental studies have been carried out on typical motion trajectories used in mobile robotics. Experimental and validation studies in numerous experiments have shown obtaining correct values of the identified parameters of the mathematical model of the robot. Keywords: Parametric identification · Mobile robot · Mecanum wheels

1 Introduction In recent years, a lot of effective theoretical and experimental parameter estimation methods have been reported in literature. Due to importance to model-based control, parameter identification has attracted much attention. Estimating the value of the dynamic parameters of the system can be calculated through different estimators [2, 10]. Due to the non-linearity and complexity of the mathematical model of industrial robots, gradient methods are often used in parametric identification procedures [11, 13, 15]. Recently, in [3, 14], an analysis and comparison of many methods of parametric identification used in robotics was carried out. The main contribution in the work [3] is the parametric identification of a two-degree-freedom robotic arm. An identification algorithm based on a convolutional neural network and the dynamic model of the robot identifies the parameters of the dynamic model. However, in the work [14] for parametric identification of a SCARA robot with 3-Degrees of Freedom the following methods was presented: least squares, Hopfield Neural Networks, Extended Kalman filter, and Unscented Kalman © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 107–117, 2023. https://doi.org/10.1007/978-3-031-25844-2_10

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filter. In this article, we formulate a new mathematical model of an industrial robot with mecanum wheels, using the parametric identification process. The object of research is a four-wheeled mobile robot Husarion Panther [12] equipped with mecanum wheels. It was assumed that the parameter estimation process would be conducted on the basis of signals recorded during the robot’s movement. The aim of the parametric identification process was to formulate a mathematical model for the synthesis of control algorithms. The paper is organized as follows. In Sect. 2, kinematics and dynamics equations for mecanum wheel mobile robot are formulated. Section 3 contains description of gradient descent estimator and transforming the robot’s mathematical model into an identification procedure. Experimental and validation results are presented in Sect. 4. Finally, resumes results of the research are given in Sect. 5.

2 Kinematics and Dynamics Figure 1 shows the kinematic structure and the actual construction of the analyzed mobile robot. a) y1

1

b)

A1

A2 H=l SH=l 1 A 4B=l SB=l 1

A3

3

-VH

f(xS , yS )=0

-

y

VS B

o

x1

H

s

x A2

5 4

A4

2

Fig. 1. a) Robot diagram, b) real robot

The basic components of this model are frame 5 and the driving units. Wheels 1–4 are the elements of the driving unit. These wheels rotate along their own axes, with angular velocities ωi , which do not change their position relative to the frame. Rollers are located on the wheel perimeter, set at an angle of a α = π/4 [rad] to the driving wheel axis. Knowing the geometry of the system and applying the classical methods used in mechanics, we obtain a description of the kinematics of a mobile wheeled robot in the form [7, 8]: ˙ + l1 sinα) = ω1 (R + r)cosα x˙ s cos(β − α) + y˙ s sin(β − α) − β(lcosα

(1)

˙ + l1 sinα) = ω2 (R + r)cosα x˙ s cos(β + α) + y˙ s sin(β + α) + β(lcosα

(2)

˙ x˙ s cos(β + α) + y˙ s sin(β + α) − β(lcosα + l1 sinα) = ω3 (R + r)cosα

(3)

Parametric Identification of the Mathematical Model

˙ x˙ s cos(β − α) + y˙ s sin(β − α) + β(lcosα + l1 sinα) = ω4 (R + r)cosα

109

(4)

Equations (1–4) were used to determine the desired motion trajectory for the control system by solving the inverse kinematics problem. On the other hand, by solving a simple kinematics task, linear parameters of the characteristic point s were determined. The dynamic equations of robot motion were adopted in the form [7, 9] M(q)¨q + C(q, q˙ )˙q + F(ω) = u

(5)

matrices M(q), C(q, q˙ ), and vector F(ω), take form ⎤ ⎡ a2 sin(β − α) − a1 cosβ −a3 a1 sinβ + a2 cos(β − α) M(q) = ⎣ a2 cos(β + α) − a8 sin(β − α) a2 sin(β + α) − a8 cos(β − α) −a4 ⎦ a1 cosβ + a2 cos(β − α) a2 sin(β − α) + a1 sin(β − α) a3 ⎤ ⎡ −a2 sin(β − α)β˙ a2 cos(β − α)β˙ 0 C(q, q˙ ) = ⎣ −a2 sin(β + α)β˙ a2 cos(β + α)β˙ 0 ⎦ −a2 sin(β − α)β˙ a2 sin(β − α)β˙ 0 ⎡ ⎤ ⎡ ⎤ ⎤ ⎡ a5 sgnω1 xs M1 F(ω) = ⎣ a6 sgnω3 ⎦q = ⎣ ys ⎦u = ⎣ M3 ⎦ a7 sgnω4

β

M4

where u – is the control vector containing the driving torques of the robot’s road wheels and F(ω) is the vector of resistance to motion. The vector of parameters a = [a1 , . . . , a8 ]T contains parameters resulting from the geometry, mass distribution and resistance to the robot’s motion, the physical sense of the parameters  is as  follows Ik [kgm], a3 = IS + 4Iz + mk l2 + l12 k/4c + [9]: a1 = (mr +4m2k )kcosα [kgm], a2 = 2k Ik c Ik c  2k [kgm], a4 = 2k kgm , a5 = N1 f1 [Nm], a6 = N3 f3 [Nm], a7 = N4 f4 [Nm], a8 = (mr + 4mk )k/2[kgm]. Where k = (R + r)cosα, c = lcosα + l1 sinα, Iz -mass moment of inertia of the wheel calculated with respect to the axis zAj passing through the centre of the wheel mass and perpendicular to the plane of movement, Ik - mass moment of inertia of the j-th wheel calculated with respect to the axis passing through the centre of the wheel mass and perpendicular to the plane of the wheel, mr – weight of the robot frame, mk - weight of the robot wheel.

3 Problem Statement The problem of identification consists in setting up a suitably parameterized identification model and adjusting the parameters of the model to optimize a performance function based on the error between the output of the robot and identification model outputs. An important issue in the process of estimating the parameters of a mathematical model is to obtain as much information as possible about the properties of the real system. In terms of identification, the linearity of the mathematical model in relation to the estimated parameters is of great importance.

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Let us write the dynamic equations of motion of the robot (5) in a linear form with respect to the parameter vector a Y(q, q˙ , q¨ )a = u(t)

(6)

where the n-dimensional vector u(t) contains the input of the model, the m-dimensional vector a contains unknown parameters to be estimated, and the n × m matrix Y(q, q˙ , q¨ ) is a signal matrix. Equation (5) transformed into the form (6), cannot be directly used to estimate the parameters, because there are hardly measurable acceleration signals¨q(t), and determining these quantities by numerical differentiation introduces large errors. To eliminate q¨ (t) in the Eq. (6), let us filter, multiply, both sides of the equation by λf /D+λf [13], where λf – positive selected filter coefficient„ D = d/dt – derivative operator. Then the matrix in Eq. (6) will be of the form Yf (q, q˙ )a =

λf Y(q, q˙ , q¨ ) D + λf

(7)

Similarly, we can write the control signal u(t) as uf (t) =

λf u(t) D + λf

(8)



Marking the vector of parameters in Eq. (6) as a, then the response of the mathematical model uf (t) is determined from the relationship (the function arguments are omitted in the following text)





uf = Yf a

(9)

and the prediction error is [13]

e = uf − uf

(10)

where uf is the measured signal. It should be noted that the output uf is actually the filtered version of the physical input to the robot. Then we write the prediction error as

∼

e = Yf a − Yf a = Yf a ∼

(11)



where a= a − a is a parameter estimation error. The estimation criterion was defined as J(e) = eT e

(12)

The basic idea in gradient estimation is that the parameters should be updated so that the prediction error is reduced. By updating the parameters in converse direction of the gradient of the squared prediction error (12) with respect to parameters, we get a˙ = −2YfT e

(13)

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where:  - diagonal matrix constant, positively defined. Taking the Eq. (5) into account, the elements of the matrix Yf (q, q˙ , q¨ ) have the form ⎤ ⎡ y˙ f11 . . . y˙ f18 Yf (q, q˙ ) = ⎣ y˙ f21 . . . y˙ f28 ⎦ (14) y˙ f31 . . . y˙ f38 and matrix elements have the following form y˙ f11 = (¨xsinβ − y¨ cosβ − yf11 )λf , y˙ f13 = (−β¨ − yf13 )λf , y˙ f14 = −yf14 λf ˙ ˙ y˙ f12 = (¨xcos(β − α) + y¨ sin(β − α) − x˙ βsin(β − α) + y˙ βcos(β − α) − yf12 )λf , y˙ f15 = (sgnω1 − yf15 )λf , y˙ f16 = −yf16 λf , y˙ f17 = −yf17 λf , y˙ f18 = y−f18 λf , ¨ f24 )λf , y˙ f25 = −yf25 λf , y˙ f21 = −yf21 λf , y˙ f23 = −yf23 λf ,˙yf24 = (−β−y ˙ ˙ + α) + y˙ βcos(β + α) − yf22 )λf , y˙ f22 = (¨xcos(β + α) + y¨ sin(β + α) − x˙ βsin(β y˙ f26 = (sgnω3 −yf26 )λf ,˙yf27 = −yf27 λf , y˙ f31 = (¨xcosβ + y¨ sinβ−yf31 )λf , ¨ f33 )λf y˙ f28 = (−¨x(sin(β − α)) + y¨ cos(β − α)−yf28 )λf , y˙ f33 = (β−y ˙ ˙ y˙ f32 = (¨xcos(β − α) + y¨ sin(β − α) − x˙ βsin(β − α) + y˙ βcos(β − α)−yf32 )λf , y˙ f34 = −yf34 λf , y˙ f35 = −yf35 λf , y˙ f36 = −yf36 λf , y˙ f37 = (sgnω4 −yf37 )λf , y˙ f38 = −yf38 λf and the signal uf was written as ⎡ ⎤ ˙ f1 M ˙ f3 = (M3 − Mf3 )λf , M ˙ f4 = (M4 − Mf4 )λf ˙ f1 = (M1 − Mf1 )λf , M ˙ f3 ⎦, M uf = ⎣ M ˙ f4 M (15) It should be mentioned that the correct estimation of the model parameters is conditioned by a good excitation of the real system through an appropriate selection of the set trajectory.

4 Experimental Verification In order to assess the unknown parameters of the a1 of the mathematical model of the robot, numerous experimental studies were conducted. Experiments was carried out with following two types of desired trajectory shown in Fig. 2. Tests to acquire the experimental data necessary for parametric identification were carried out in four variants in order to replicate as accurately as possible the typical operating environment of a mobile robot. PD control was applied, the robot moved at the set speed v0 = 0.3 [m/s], moving along a loop-shaped path of motion with a radius of 0.7 [m], shown in Fig. 2a, and a sine-shaped path of motion with an amplitude of 0.7 [m], Fig. 2b. The following remarks stem from the conducted considerations. The analyzed system has 3 degrees of freedom, and the 4 driving wheels. In the literature, these types of systems are referred to as over-actuated [1]. To determine additional steering signal M2 [Nm], one most often apply the complex method of optimal separation of steering (control allocation) [1]. In this paper, for the solution of the over-actuated type of system, it has been assumed that the powers of the driving modules are different. This is due to numerous experimental studies conducted.

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Fig. 2. Path of motion, a) loop-shaped, b) sine-shaped.

Taking into consideration the energy losses in the transfer of this power, one has obtained additional equations, on the basis of which the missing wheel 2 driving moment M2 has been determined. M2 = M4 + 0.0322M3 − 0.0322M1

(16)

In order to carry out the identification process, a measurement experiment was conducted using a fast prototyping laboratory stand. The stand includes a PC with dSpace digital signal processing (DSP) board, a power supply module, and a control object, shown in Fig. 3. Matlab/Simulink R2012a, with dSpace RTI1103 Board Library 3.3.1 [4] toolbox environment were used to program the algorithms The card generates a signal which is scaled by constant 1/16.66 experimentally determined, incremental encoders measure the angular velocity of the wheels, the angle of rotation is determined by numerical integration. Using Eqs. (1–4) a simple kinematic problem was solved by determining the linear parameters of the characteristic point s. Diagram illustrating the control system used during tests is shown on the scheme in Fig. 3b. The first variant of the measurement experiment was a loop-shaped trajectory with the assumption that the rotation angle of the robot frame β(t) does not change. The second variant was an experiment along a loop-shaped trajectory, it was assumed that the angle of rotation of the robot frame varies with time. The third variant was a sinus-shaped trajectory, it was assumed that the rotation angle of the robot frame does not change in time. The fourth variant is a sinus-shaped trajectory, assuming that the angle of rotation of the robot frame changes over time. Measured control signals M1 , M2 , M3 , M4 of each variant is shown in Fig. 4 and 5. The masses and basic dimensions of the robot are shown in Table 1. Table 1. Husarion Panther parameters l[m]

l1 [m]

mr [kg]

mk [kg]

R[m]

r[m]

0.34

0.22

45

2.4

0.09

0.01

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Fig. 3. a) Fast prototyping station, b) diagram of the control system used during the tests

Fig. 4. Experimental data of the driving torques of the wheels for loop-shaped path, a) β(t) = const, b) β(t)  = const

Fig. 5. Experimental data of the driving torques of the wheels for a sine wave path, a) β(t) = const, b) β(t)  = const

Using the identification procedure described in point 3, the parameters of the a i model were estimated, where the non-linear function of resistance to motion was approximated by the relation  Fi (ωi ) = ωi 0.1429 (1 + exp(−5 · (kh − 5))−1 − (1 + exp(−5(kh − 27)))−1 (17)

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where i = 1, 3, 4, kh is discrete form of time. The identification procedure was carried out for 8 parameters. Due to the use of the gradient procedure in parameter estimation, the initial conditions were selected after a numerous search of the parameter space in order to avoid the local extreme of the objective function (12). The initial conditions of the procedure are given in Table 2. Table 2. Initial conditions a1 [kgm]

a2 [kgm]

a3 [kgm]

a4 [kgm]

a5 [Nm]

a6 [Nm]

a7 [Nm]

a8 [kgm]

0.02

1.81

0.90

0.90

0.90

0.90

0.90

0.03

Table 3 presents the values of the estimated parameters for various signals of the robot’s motion excitation. Table 3. Values of estimated parameters Loop-shaped path

a1 [kgm]

a2 [kgm]

a3 [kgm]

a4 [kgm]

a5 [Nm]

a6 [Nm]

a7 [Nm]

a8 [kgm]

β(t) = const

1.43

0.55

0.1

0.12

10.52

10.54

10.51

1.53

β(t)  = const

0.20

0.55

0.21

0.26

10.43

10.15

10.48

0.04

β(t) = const

0.46

0.08

0.04

0.05

10.75

10.66

10.65

0.01

β(t)  = const

1.33

0.01

0.04

0.05

10.77

10.29

10.36

0.01

Sine wave path

As can be seen from the parameter estimates presented in Table 3 it was found that depending on whether the angle of rotation of the robot frame changes over time, the parameters take on different values. It was also observed that the parameters a5 , a6 , a7 , corresponding to the resistance to motion of the mobile robot, for each set of experimental data take values close to 10.5 [Nm], however, the remaining parameters for different experiments have different values. Based on the numerical optimization analysis, it can be concluded that the assumed motion trajectory partially meets the criterion of uniform excitation of the tested system. In order to validate the obtained solutions, the average values of the parameter estimates are presented in Table 4. Table 4. Average values of parameter estimates a1 [kgm]

a2 [kgm]

a3 [kgm]

a4 [kgm]

a5 [Nm]

a6 [Nm]

a7 [Nm]

a8 [kgm]

0.85

0.29

0.09

0.12

10.61

10.41

10.50

0.39

Another simulation was carried out to verify the adopted parameter values. It consisted of searching the parameter space, carried out for the coefficients a6 , a7 , assuming

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115

that the other coefficients of the model are constant, and their values correspond to the average values. The analysis shows that in the 10.3[Nm] ≤ a6 ≤ 10.48[Nm] and 10.43[Nm] ≤ a7 ≤ 10.62 [Nm] area, there is a minimum estimation criterion, which is shown in Fig. 6. The identification shows that the coefficients determining the solution of the dynamic equations of motion, i.e. the motion resistances, are correctly estimated.

Fig. 6. Diagram of the optimal objective function, a) estimation criterion hypersurface for parameters a6 , a7 , b) projection onto the subspace

First validation variant was carried out on a loop-shaped trajectory shown in Fig. 2a, it was assumed that the angle of rotation of the robot frame β(t) varies with time.

Fig. 7. Validation results, angular velocity difference, wheel 1, a) loop-shaped path, b) sine wave path

Another validation was carried out on a sine wave trajectory shown in Fig. 2b. With the assumption that the rotation angle of the frame does not change in time. The

robot 1 n root-mean-squared error (RMSE), ε1 = n i=1 δi was used as a quality indicator, where the difference between the angular velocities of wheel 1 obtained from the experiment and obtained from the simulation was defined as the error δi , shown in Fig. 7, n = 3001 is the number of measurements for first variant, n = 2501 for second variant. The angular velocity errors for the remaining wheels have similar values. Table 5 shows the quality index values for each signal.

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δϕ˙i = ϕ˙ i − ϕ˙i Loop-shaped ε1

0.25

Sine wave ε1

0.46

The errors listed in Table 5 show that larger mapping errors occur in the implementation of the given path of the robot S point in the form of a sine wave. This result can be justified by a more complex motion path realized in the control system with a PD controller.

5 Conclusion This paper proposes a gradient method for estimating the parameters of an industrial robot with mecanum wheels. Numerous experimental studies have been carried out on typical motion trajectories used in mobile robotics. The simulation results compared with the results of experimental tests confirm a good estimation of unknown parameters of the mathematical model of the robot. Future research directions include verification of control algorithms for a mobile robot with mecanum wheels.

References 1. Bodson, M.: Evaluation of optimization methods for control allocation. J. Guid. Control Dyn. 25(4), 703–711 (2002) 2. Bubnicki, Z.: Identification of Control Objects (in Polish). PWN, Warsaw (1974) 3. Carreon-Diaz de Leon, C.L., et al.: Parameter Identification of a Robot Arm Manipulator Based on a Convolutional Neural Network, Digital Object Identifier (2022) 4. dSpace: DS1103 PPC Controller Board. Hardware Installation and Configuration. Padeborn: dSpace GmbH (2010) 5. Eykhoff, P.: System Identification: Parameter and State Estimation. Wiley-Interscience, London (1974) ˙ 6. Giergiel, M., Hendzel, Z., Zylski, W.: Modelling and Control of Wheeled Mobile Robots. WNT, Warsaw (2002). (in Polish) 7. Hendzel, Z.: robust neural networks control of omni-mecanum wheeled robot with HamiltonJacobi inequality. J. Theoret. Appl. Mech. 56(4), 1193–1204 (2018) 8. Hendzel, Z.: A description of the motion of a mobile robot with Mecanum wheels – kinematics. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Automation 2019. AUTOMATION 2019. Advances in Intelligent Systems and Computing, vol. 920. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-13273-6_33 9. Hendzel, Z.: A Description of the motion of a mobile robot with Mecanum wheels – dynamics. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Automation 2019. AUTOMATION 2019. Advances in Intelligent Systems and Computing, vol. 920. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-13273-6_32 10. Huang, W., Min, H., Guo, Y. Liu, M.: A review of dynamic parameters identification for manipulator control. Cobot. Mingxin (2022)

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11. Leboutet, Q., Roux, J., Janot, A., et al.: Inertial parameter identification in robotics: a survey. Appl. Sci. 11 (2021) 12. Panther - outdoor AMR: Husarion|Autonomous Mobile Robots Made Simple, https://hus arion.com/manuals/panther(n.d.) 13. Slotine, J.J.W., Li, W.: Applied Non-Linear Control, Prentice Hall, New Jersey (1991) 14. Urrea, C.; Agramonte, R.: Evaluation of parameter identification of a real manipulator Robot. 14, 1446, Symmetry (2022) ˙ 15. Zylski, W.: Kinematics and dynamics of mobile wheeled robots. Publishing House Rzeszow Univ. of Technology (1996). (in Polish)

Localization of Agricultural Robots: Challenges, Solutions, and a New Approach ´ Piotr Skrzypczy´ nski(B) and Krzysztof Cwian Institute of Robotics and Machine Intelligence, Pozna´ n University of Technology, ul. Piotrowo 3A, 60-965 Pozna´ n, Poland {piotr.skrzypczynski,krzysztof.cwian}@put.poznan.pl

Abstract. An important factor in precision agriculture is the accurate localization of the field machinery, which is necessary to apply the agrotechnical treatment precisely to the target location. As robots start to replace manned machines, appropriate localization techniques have to be deployed to allow these robots to localize accurately on large areas that often contain very few salient features. This paper provides a brief survey of the approaches to localization in agricultural robotics illustrated by example solutions from the literature. Then, a new approach to robot localization on large areas with sparse features is presented, leveraging the ubiquitous GNSS solution in its low-cost form combined with classic SLAM methods. We present preliminary results obtained on an electric work cart that demonstrate improved localization accuracy.

1

Introduction

Implementation of the precision agriculture concept requires robots that navigate the fields autonomously and target selected areas or even individual plants with proper treatment. Localization is not only an algorithmic problem but also a technological challenge [24]. As demonstrated by the vast amount of work devoted to different methods and aspects of robot localization in the last three decades, the way we should solve the localization problem depends to a large extent on the characteristics of the environment, the defined task, and the robot itself – what sensors it has on-board, and what computing power is available to the localization procedures. This observation defines localization as a highly domain-specific problem. Precision agriculture applications constitute a specific domain that calls for specific robot localization solutions and adaptation of the general-purpose methods. First of all, agriculture robots operate in most cases on large-scale fields, where the path length and the area covered by the working robot are much bigger than for other scenarios, such as applications of service or delivery mobile robots. At the same time, an agricultural robot needs to know its position with a centimeter-level precision in order to precisely remove weeds using mechanical methods or to deliver the chemicals selectively [2]. An example of a multipurpose agricultural robot is the Agrorob developed at Lukasiewicz-PIMR [30] c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 118–128, 2023. https://doi.org/10.1007/978-3-031-25844-2_11

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(Fig. 1A). Another problem for localization are the characteristics of the environment. Localization in a natural environment is usually much harder than in a man-made environment. Fields and orchards are semi-structured, with dominating natural elements (vegetation), but also man-made structures, such as fences, ditches, and human-planted crops or trees structured in rows. Moreover, this environment is changing along with the natural seasons and the growth of vegetation. Different plant species may look very differently at different growth stages, which introduces additional difficulties for localization methods based on passive vision. Characteristics of a typical field environment are shown by the multi-sensor Rosario dataset [21], one of the very few datasets intended for testing robot navigation under agricultural environments (Fig. 1B,C). Also the agriculture equipment and the nature of tasks performed by the robotized machines add specific requirements. The used components should be rugged, reliable, easy to maintain, and come at a reasonable cost to make practical sense of a robotized tractor or a combine harvester. The approaches to localization in agriculture robots can be roughly divided into four groups, depending on the type of information from the environment that is used to compute the robot’s position. – – – –

positioning systems with an external reference, localization with artificial landmarks, localization exploiting the semi-structured nature of the field environment, localization with natural features extracted from an unstructured environment.

Fig. 1. Examples of agricultural robots and environments: a larger Agrorob vehicle from Lukasiewicz-PIMR (adopted from [30]), a small weed-removing robot used to collect the Rosario dataset (adopted from [21]), and an example camera frame from this dataset showing an environment typical to agricultural scenarios

2

Satellite-based Localization and Its Limitations

Whenever the precision agriculture concept is applied to large fields, localization is accomplished using Global Navigation Satellite Systems (GNSS): NAVSTAR, GLONASS, Galileo, or Beidou, commonly known as GPS (Global Positioning System) [1]. It is a standard practice to guide large, usually manned agricultural machines employing GPS when performing broad-acre cropping and similar tasks. Achieving high-precision localization requires differential GPS (DGPS),

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which involves the transmission of correction signals from a ground station. Agricultural DGPS solutions routinely achieve sub-meter accuracy [29], but the correction signal is degraded in some environments due to the presence of such obstacles as forests neighboring fields of crop or tree canopies in orchards. They obscure the view of the satellites degrading the localization accuracy even if the DGPS signal is present. Some tasks, like mechanical weed removal, require even more accurate localization. Although positioning accuracy of several centimeters is achievable with Real-Time Kinematic GPS (RTK-GPS), this approach involves high costs of installation and maintenance. Reliable RTK-GPS solutions use dual frequency and multi-constellation GPS receivers, and require a correction signal from a nearby ground station [19]. Unfortunately, these receivers are still rather expensive. More affordable systems with single frequency receivers are less reliable, as they are prone to accuracy degradation when they do not see an appropriate number of satellites, or the ground station signal is lost temporarily. Moreover, the correction signal gets degraded at longer distances from the base station, while transmitting the correction data over the GSM network implies higher costs and dependency on the GSM network coverage. All these problems make the GPS-based localization with an external referencing feasible only for large and expensive farming vehicles, while smaller mobile robots that fit better into the concept of ecology-friendly precision farming need solutions that are less expensive and easier to maintain.

3

Exploiting the Environment Structure for Localization

Crop rows can be distinguished from the soil using vision sensors (cameras) and algorithms that recognize the visual appearance of the crop and such features as color and texture. For this task low-cost monocular vision systems can be employed [25]. Typically, segmentation and classification methods are employed to extract from the images information needed to compute the position and orientation of the robot relative to the crop rows [10]. For some applications extracting the edges along the harvested crops is necessary. However, the visual appearance of plants is subject to significant changes due to the different vegetation stages and external factors such as sunny or cloudy skies, rain, dust, or clusters of weeds that mix with the main plant species. Therefore, some localization systems employ laser ranging to detect crop rows by measuring the difference in height between the crop and the soil [28]. Tree rows in orchards require different data processing methods to detect components of the tree rows, such as trunks, stems, or tree canopies. As detecting these structures from visual data is difficult, laser scanners are used more often than for the field applications. Range data make it possible to detect either tree trunks [12] or dense canopies [13].

4

Localization with Artificial Landmarks

Passive artificial landmarks that are commonly employed in the navigation of industrial mobile robots found much less acceptance in agricultural applications.

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The reason seems to be the extended areas over which the farming robots have to localize. Broad-acre fields make the deployment of artificial landmarks a laborious and time-consuming task. However, smaller-scale applications of agricultural robots, such as those in greenhouses or orchards may benefit from augmenting the environment with markers introduced purposefully for navigation. An example is the system from [17] that used reflective tape attached to tree trunks in order to improve detection by a laser scanner. Li et al. [16] proposed a localization system based on artificial landmarks and omnidirectional vision for agricultural robots in small-area indoor or outdoor environments. Localization solutions based on specific augmentation of the working area are also justified from the practical and economic point of view if the considered environment prohibits effective use of the localization approaches that exploit natural features. An example of such a challenging application is the monitoring of steep slope vineyards, with harsh terrain conditions and reduced availability of the GPS signal. Duarte et al. [5] developed a robot localization system that works under these conditions using wireless sensors as artificial landmarks. This system employs Bluetooth-based sensors and the RSSI (Received Signal Strength Indication) data to support the GPS-based localization procedure whenever the GPS accuracy gets degraded.

5

SLAM in Agricultural Robotics

While many approaches to robot localization in the agricultural context try to exploit the specific structures commonly encountered in the considered application sites, some researchers attempt to adopt a more general approach with the Simultaneous Localization and Mapping (SLAM) or Visual Odometry (VO) algorithms. The concept of SLAM assumes that the robot builds a map of the environment while estimating its own position within this map. VO is simpler, as it estimates the trajectory of a robot computing the egomotion between the consecutive observations, but without establishing a global map [22]. Although non-linear optimization techniques have been adopted to solve the SLAM problem, leading to a broad family of graph-based approaches [11], there are still few applications of SLAM to agriculture robots. Low affordability and high maintenance costs discourage the use of such sensors as 3-D LiDAR (Light Detection and Ranging). On the other hand, the lack of easily identifiable salient features, and the changing nature of vegetation-covered areas with low repeatability of feature detection decreases the efficiency of visual odometry and visual-SLAM methods, which in other application areas are considered the most cost-effective localization systems [24]. Overcoming these difficulties requires the application of specific methods and sensor configurations, such as stereo vision cameras facing downward to the ground in the robot described in [8] that ensures reliable visual odometry measuring the ground movement and compensating for differences in the ground elevation. Recent advances in machine learning opened new possibilities to detect natural features useful for localization even among irregularly shaped and constantly changing vegetation. The approach to time-invariant plant localization proposed in [14] employs deep neural network architecture to localize the stems of plants from multi-spectral images (RGB and near infra-red) in a way invariant to their vegetation stage.

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Some recent results, like those reported in [23] suggest that general-purpose visual-SLAM algorithms can be adopted for localization in agricultural robotics. Also [9] tested two SLAM algorithms based on graph optimization: a version of the feature-based ORB-SLAM [20], and the direct LSD-SLAM [6]. The results demonstrated that both approaches are feasible in this application context, but in both cases, the stereo-based variants of these algorithms outperformed the monocular versions.

6

Achieving Accurate Localization with GNSS and SLAM

Our brief survey of the literature suggests that while local precise positioning is achievable referring to the semi-structured field environment, accurate localization on large field areas is mainly relying on the GNSS. This approach raises a number of issues depending on the nature of the environment and the possibility of employing advanced GPS modes. However, whenever GNSS measurements are unavailable or corrupted, SLAM or visual odometry can make it possible to localize the agricultural robot. On the other hand, integration of GNSS absolute pose measurements into a SLAM framework may limit the drift of the estimated robot trajectories. These observations gave rise to our research on integrating GNSS and SLAM into a unified localization system for outdoor localization. In our recent paper [4] we introduced a framework for the integration of LiDAR-based odometry or SLAM with raw GNSS measurements, demonstrating improved trajectory accuracy and robustness to GPS outages in urban environments. This framework exploits constraints imposed on the receiver by GNSS measurements: pseudoranges and Doppler shift, and implements tight integration by a factor graph, similarly to the more popular visual-inertial SLAM [18]. This idea can be adopted for the localization of agricultural robots, but to make such an approach feasible in field scenarios we need to ensure a good cost-toeffect ratio and use only affordable hardware components. As advanced LiDARs, like those used in [4], are still too expensive for farming equipment, we present in this paper preliminary results of adopting our integration framework to monocular visual SLAM, which is the most affordable localization modality in unknown environments. 6.1

Factor Graph Representation of the Localization Problem

We use the factor graph formulation that builds a graph of constraints imposed by observations on the robot poses. This graph is then optimized using the g2 o library [15] in order to obtain a trajectory that minimizes the residual errors. The approach is universal with regard to the SLAM system implementation, although we integrate for experiments the recent feature-based ORB-SLAM3 [3]. In SLAM, the local associations between the observations constrain the poses of the robot along the trajectory. In the factor graph, the poses are nodes, while relative transformations between the poses are considered edges with factors

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representing the observations. Each optimizable node represents i-th pose of the robot Xi . Non-optimizable nodes of the graph represent the poses of the GNSS satellites known at the time of the measurement. The factor graph representation of these nodes and constraints can be expressed as:  E(X) = e(Xk , rsn , epk ) Ωp e(Xk , rsn , epk ) k∈G n∈N

+



T D e(Xk , Xk+1 , (eD k,k+1 ) ) ΩD e(Xk , Xj , ek,k+1 )

k∈G

+



e(Xi , Xi+1 , (esi,i+1 )T ) Ωs e(Xi , Xi+1 , esi,i+1 )

(1)

i∈S

where e(.) represents the (scalar or vector) error function parameterized differently for each component, while G, N and S are the set of all nodes having GNSS measurements, the set of all observed satellites from all constellations, and the set of all nodes having SLAM odometry measurements, respectively. 6.2

Graph Constraints Related to GNSS

The pose of a satellite is calculated using the broadcasted data with the opensource RTKLIB library [27]. RTKLIB procedures are applied to extract n-th and trosatellite coordinates rsn , satellite clock bias δns , ionospheric delay dion n . We use the GNSS pseudorange measurement error as the pospheric delay dtrop n factor graph constraint: trop p s r − δi,n ) · c + dion epi = pi,n − [ρi,n − (δi,n i,n + di,n + i,n ],

(2)

where i is graph node index, n is a satellite index (all constellations), and ρi,n is a range from n-th satellite to the receiver, computed using the known pose of this satellite, as detailed in [4]. The remaining parameters, pn that represents multipath range error, and biases δns and δnr are computed from the GNSS messages data, but to calculate the receiver clock bias δnr at least four pseudorange values to satellites of the same constellation are necessary [4]. The information matrix Ωp in (1) is a scalar value, as the pseudorange constraints are scalars as well. It is calculated using RTKLIB procedures. In contrast to pseudoranges, the Doppler shift constraints are 3-DOF translations calculated based on the receiver velocity vir and the time between the successive GNSS observations. The i-th node velocity vir is computed from the broadcasted Doppler shift using RTKLIB. Then, the error function for factor graph constraints stemming from the Doppler shift is the following: rD r r eD i,i+1 = ri+1 − ri − vi,i+1 · ti,i+1 ,

(3)

rD and ti,i+1 are where rri is the receiver position (translation part), while vi,i+1 average velocity and time between the i-th and i + 1-th poses. The 3×3 information matrix ΩD associated with the Doppler shift constraints is again calculated by the RTKLIB procedures.

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Graph Constraints Related to SLAM

Constraints produced by visual SLAM are full 6-DOF transformations produced by the visual odometry part of the algorithm, that relate the consecutive robot poses. The error function is given as: esi,i+1 = [(TSi )−1 · TSi+1 ]−1 · (Ti )−1 · Ti+1 ,

(4)

where TSi ,TSi+1 are two consecutive 6-DOF poses along the trajectory estimated by SLAM. The 6×6 information matrix Ωs of the visual odometry constraints is obtained as an inversion of the covariance matrix Cs that models the uncertainty of the vehicle pose in ORB-SLAM3 odometry. Although it is possible to recover the pose uncertainty in this type of SLAM from the Hessian matrices in the optimization back-end (also based on the g2 o library), we prefer to set the values at the diagonal of Cs upon experimental results, obtaining a covariance matrix that matches observed errors with respect to the ground truth. The estimated covariance is scaled by the distance covered by the vehicle since the previous node and then used to compute Ωs . This simple approach can be used with any SLAM or visual/LiDAR odometry component [4].

7

Results

The proposed localization method was verified in a preliminary experiment implemented using an electric work cart (Melex, Fig. 2A,B) on a 700 m long trajectory that was elapsed three times in order to simulate the repetitive motion of an agricultural vehicle while completing agrotechnical treatment on a large field. As the electric cart cannot be used on public roads, the experiment was performed within the campus area of Pozna´ n University of Technology, choosing an environment dominated by lawn areas, trees, and bushes. This allowed us to simulate an environment with a lot of vegetation and relatively few landmark objects (Fig. 2C), which is typical to agricultural scenarios.

Fig. 2. Electric vehicle (work cart) used in the experiment (A,B), and example point features detected by ORB-SLAM3 during this experiment (C)

The ground-truth trajectory was obtained using a Ublox C099-F9P sensor with a ZED-F9P module for RTK-GPS mounted on the roof of the vehicle

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(Fig. 2A), ensuring localization accuracy of 2cm with a position frame rate 10 Hz when operating in L1/L2 modes. Commercial RTK corrections transmitted via the Internet were obtained via an LTE modem. The same physical receiver was used to obtain raw GNSS measurements, then used to estimate the trajectory. The raw measurements were not altered by any information obtained over the LTE channel, thus emulating a basic, low-cost GPS device. The sensor used for SLAM-based localization was a standard global-shutter grayscale camera connected via USB to a computer running Linux, ROS (Robot Operating System), and our localization software. Table 1. Absolute pose errors of the trajectories estimated using RTKLIB (GNSS), ORB-SLAM3 (visual SLAM) and our method (GNSS/visual) Localization method

ATEmax

GNSS RTKLIB

20.75 [m] 0.09 [m] 3.96 [m]

ORB-SLAM3

11.91 [m] 0.50 [m] 4.33 [m]

GNSS/ORB-SLAM3 (ours) 6.85 [m]

ATEmin ATEmean ATERMS

0.40 [m] 2.37 [m]

4.86 [m] 4.99 [m] 2.72 [m]

In order to assess the accuracy of the trajectories estimated by the investigated localization methods we applied the Absolute Trajectory Error (ATE) metric introduced in [26]. Results obtained in the preliminary experiment are gathered in Table 1. Values of the mean and Root Mean Squared (RMS) errors shown in this table were computed over the entire trajectory of the experiment. The trajectories estimated by all three methods are plotted in Fig. 3, with color error bars that visually indicate the ATE values along the trajectory.

Fig. 3. Plots of the ground truth and estimated trajectories for GNSS-based localization with RTKLIB (A), ORB-SLAM3 (B), and our new approach (C). Note that the color error bars are scaled differently for each plot

The quantitative results in Table 1 and visual inspection of the qualitative results in Fig. 3 make it evident, that the combination of GNSS and visual SLAM constraints allowed us to estimate a more accurate trajectory of the electric work

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cart, than each of the component methods alone. Although the absolute pose errors are considerably larger than the declared accuracy of the latest commercial RTK-GPS solutions, they are comparable to the results in [23]. This reveals the potential of using tight integration within the factor graph framework to provide agricultural robots with reliable pose estimates from affordable sensors.

8

Final Remarks

The purpose of this paper is twofold: (i) to show the challenges we encounter localizing robots in agricultural scenarios and review typical solutions described in the literature; (ii) to demonstrate that combining two state-of-the-art localization methods using the factor graph approach improves the localization accuracy, still keeping the entire system low-cost and simple on the hardware side. We plan to test the proposed GNSS/SLAM solution in real crop field conditions in near future, exploring also paths with tight U-turns that are typical in agriculture but can be problematic for SLAM [23]. Due to the flexibility of the factor graph formulation, the proposed method can be potentially augmented also by other constraints, for example stemming from the observations of some characteristic structures within the field area.

References 1. Bakker, T., van Asselt, K., Bontsema, J., M¨ uller, J., van Straten, G.: Autonomous navigation using a robot platform in a sugar beet field. Biosys. Eng. 109(4), 357– 368 (2011) 2. Ball D., et al.: Farm workers of the future: Vision-based robotics for broad-acre agriculture. IEEE Robot. Autom. Mag. 24(3), 97–107 2017 3. Campos, C., Elvira, R., Rodr´ıguez, J.J.G., Montiel, J.M.M., Tard´ os, J.D.: ORBSLAM3: an accurate open-source library for visual, visual-inertial, and multimap SLAM. IEEE Trans. Rob. 37(6), 1874–1890 (2021) ´ 4. Cwian K., Nowicki M. R., Skrzypczy´ nski, P.: GNSS-augmented lidar slam for accurate vehicle localization in large scale urban environments. In: 17th International Conference on Control, Automation, Robotics and Vision (ICARCV), Singapore (2022) 5. Duarte M., dos Santos F.N., Sousa A., Morais R.: Agricultural wireless sensor mapping for robot localization. In: Reis L., et al.(eds.) Robot 2015: Second Iberian Robotics Conference, Advances in Intelligent Systems and Computing, vol. 417, pp. 359–370. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-27146-0 28 6. Engel, J., Sch¨ ops, T., Cremers, D.: LSD-SLAM: large-scale direct monocular SLAM. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8690, pp. 834–849. Springer, Cham (2014). https://doi.org/10.1007/ 978-3-319-10605-2 54 7. English A., Ball D., Ross P., Upcroft B., Wyeth G., Corke, P.: Low cost localisation for agricultural robotics. In: Proceedings of the Australasian Conference on Robotics and Automation, Australia, pp. 1–8 (2013) 8. Ericson S., Astrand B.: A vision-guided mobile robot for precision agriculture. In: Proceedings of 7th European Conference on Precision Agriculture, Wageningen, Netherland, pp. 623–630 (2009)

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9. Ericson, S.: Vision-based perception for localization of autonomous agricultural robots, Ph. D. Dissertation, University of Sk¨ ovde, Sweden (2017) 10. Gottschalk, R., Burgos-Artizzu, X.P., Ribeiro, A., Pajares, G.: Real-time image processing for the guidance of a small agricultural field inspection vehicle. Int. J. Intell. Syst. Technol. Appl. 8, 434–443 (2010) 11. Grisetti, G., K¨ ummerle, R., Stachniss, C., Burgard, W.: A tutorial on graph-based SLAM. IEEE Intell. Transp. Syst. Mag. 2(4), 31–43 (2010) 12. Guivant, J., Masson, F., Nebot, E.: Simultaneous localization and map building using natural features and absolute information. Robot. Auton. Syst. 40, 79–90 (2002) 13. Hansen, S., Bayramoglu, E., Andersen, J.C., Ravn, O., Andersen, N., Poulsen, N.K.: Orchard navigation using derivative free Kalman filtering. In: Proceedings of the American Control Conference, pp. 4679–4684 (2011) 14. Kraemer F., Schaefer A., Eitel A., Vertens J., Burgard W.: From plants to landmarks: time-invariant plant localization that uses deep pose regression in agricultural fields. In: International Conference on Intelligent Robots and Systems (IROS) Workshop, Agri-Food Robotics (2017) 15. K¨ ummerle R., Grisetti G., Strasdat H., Konolige K., Burgard W.: g2o: a general framework for graph optimization. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 3607–3613 (2011) 16. Li, M., Imou, K., Wakabayashi, K., Yokoyama, S.: Review of research on agricultural vehicle autonomous guidance. Int. J. Agri. Biol. Eng. 2, 1–16 (2009) 17. Libby, J., Kantor, G.: Deployment of a point and line feature localization system for an outdoor agriculture vehicle. In: IEEE International Conference on Robotics and Automation, Shanghai, China, pp. 1565–1570 (2011) 18. Liu J., Gao W., Hu Z.: Optimization-based visual-inertial SLAM tightly coupled with raw GNSS measurements. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 11612–11618 (2021) 19. Marucci A., Colantoni A., Zambon I. Egidi G.: Precision farming in hilly areas: the use of network RTK in GNSS technology. Agriculture 7, 60 (2017) 20. Mur-Artal, R., Tard´ os, J.D.: ORB-SLAM2: an open-source SLAM system for monocular, stereo, and RGB-D cameras. IEEE Trans. Rob. 33(5), 1255–1262 (2017) 21. Pir´e T., Mujica M., Civera J., Kofman E.: The Rosario dataset: multisensor data for localization and mapping in agricultural environments. Int. J. Rob. Res. 38, 1–9 (2019) 22. Scaramuzza, D., Fraundorfer, F.: Visual odometry: Part I the first 30 years and fundamentals. IEEE Rob. Autom. Mag. 18(4), 80–92 (2011) 23. Shu F., Lesur P., Xie Y., Pagani A., Stricker D.: SLAM in the field: an evaluation of monocular mapping and localization on challenging dynamic agricultural environment. In: IEEE Winter Conference on Applications of Computer Vision (WACV), Waikoloa, pp. 1760–1770 (2021) 24. Skrzypczy´ nski, P.: Mobile robot localization: where we are and what are the challenges? In: Szewczyk, R., Zieli´ nski, C., Kaliczy´ nska, M. (eds.) ICA 2017. AISC, vol. 550, pp. 249–267. Springer, Cham (2017). https://doi.org/10.1007/978-3-31954042-9 23 25. Søgaard, H.T., Olsen, H.J.: Determination of crop rows by image analysis without segmentation. Comput. Electr. Agri. 38, 141–158 (2003) 26. Sturm, J., Engelhard, M., Endres, F., Burgard, W., Cremers, D.: A benchmark for the evaluation of RGB-D SLAM systems. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 573–580 (2012)

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The Concept of a Gripper with Pose Estimation for Automotive Components Adam Rydzewski1

and Piotr Falkowski2,1(B)

1 Institute of Aeronautics and Applied Mechanics, Faculty of Power and Aeronautical

Engineering, Warsaw University of Technology, Warsaw, Poland 2 Łukasiewicz Research Network, Industrial Research Institute of Automation and

Measurements PIAP, Warsaw, Poland [email protected]

Abstract. Robotic grasping is a critical and challenging process for manufacturing. The variety of grippers allows adjusting the setup to many applications but does not enable its universality, which is particularly important for the automotive industry. While manipulating a wide range of elements with different sizes, it is crucial to develop the methodology for detecting their pose and gripping. This paper presents a concept of using a pin array gripper to universally grasp the object of an approximately known position and then estimate its accurate pose. The estimation is based on the signals from extendable pins related to their positions. Within the experimental trials gripping of three models available online and one 3D-scanned object were simulated. Based on their pose, the expected pins’ positions were calculated. The results exposed the potential of improving the gripping process model by adding resultant force impact on the object orientation. The presented outcomes prove that the approach can be used for pose estimation. The simulation approach is helpful in generating the databases for learning algorithms without using expensive real-life setups and a wide range of physical objects. Keywords: Automotive · Industry 4.0 · Pose detection · Robotics · Universal gripper

1 Introduction State of the Art Robotic grasping is critical within production lines and other industrial setups. Realising such tasks often requires flexibility and universality. For these applications, various soft devices are available [1, 2]. Despite their significant advantages, they easily suffer from wear and tear due to continuous contact with dirty metal parts. Moreover, their exact behaviour is difficult to predict. On the contrary, vacuum grippers are much more predictable, but they may malfunction due to surface contamination [1]. Classic mechanical grippers can address a wide range of applications when the grasp is well-planned and repeatable. According to Du et al. [3], grasp detection consists of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 129–139, 2023. https://doi.org/10.1007/978-3-031-25844-2_12

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three tasks: object localisation, object pose estimation, and grasp estimation. In some cases, the object’s location and pose are known from the previous stage of the robotised process. Otherwise, those two have to be detected. The most common automatic techniques involve machine vision or laser scanning [4]. The described needs to create space for the application of pin array grippers. They were introduced by the Omnigripper in 1985 [5]. Later on, numerous different variations of the concept were developed [6–10]. Their mechanical structure even contributed to other industrial devices, e.g. Hubert Meintrup’s vices [11]. Thanks to their working principle, an object’s exact pose may remain unknown during grasping if its final orientation does not have to be considered. Also, its initial position must be known only approximately. On the other hand, the disadvantage of pin array grippers is their mechanical complexity. However, this drawback can be used to detect the object’s orientation. For this, every pin would provide feedback and, thus, tactile information about the gripped element. Such data can be useful in the following phases of the robotised process. This way, less vulnerable to dirt, pin array grippers could replace machine vision and laser scanning techniques. In this paper, we propose a different approach to grasping action than the ones presented by Du et al. [3] and Kumra and Kanan [12]. Grasp detection is simplified to only roughly identifying the object’s position. Trajectory planning and execution are to be done conventionally, but as soon as a stable grasp is provided, the object’s pose is estimated based on the feedback from the gripper. Design and Research Intent As a result of this and future studies, a universal gripper will be designed. Preliminary requirements are based on the available automotive elements as the benchmark of potentially challenging to localise and grip (see Fig. 1). These include: – An ability to provide a stable grasp of objects with different sizes (5–50 cm), a wide variety of masses (0.5 - 50 kg) and irregular shapes. – Resistance to dirt and lubricants. – A capability of reducing the number and impact of collisions between carried objects with a priori unknown pose. – Resilience to those collisions which were unable to be avoided. The third requirement is to be met by acquiring information on the pins’ position. Assuming that the shape of the grasped objects is known, it would allow estimating their pose. The presented concept of the device is based on the design visualised in Fig. 2. It consists of two similar jaws (1), each with multiple cylindrical pins positioned horizontally in parallel and freed to reciprocating motion (2). The object to be grasped (3) should be located between the jaws, which are oriented pin-side to this object. Then either jaws or single pins have to be moved toward others. Thanks to this, some pins will lean against the object and adapt to its shape.

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Fig. 1. Exemplary parts to be carried by the gripper

In contrast to many other designs [5–10], the pins are arranged horizontally. It enables the grasp of irregular objects (e.g. broader at their top) thanks to geometrical locking. In particular cases, they eliminate the need to exert a horizontal force on a gripped object (Fig. 3).

Fig. 2. Pin array gripper scheme; (1) jaws, (2), pins, (3) gripped object

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Fig. 3. Geometrical locking (A) in comparison to friction-based grasping (B)

The paper is a proof of concept for the gripper and the algorithm for shape and pose estimation. It is based on simulation trials involving real-life designs. Moreover, the results are going to be used for further research on the gripper’s mechanical design and learning algorithms.

2 Methodology To find the optimal gripper’s structure, its performance was initially simulated. For an actual application, it is necessary to prepare software capable of estimating an object’s pose best fitting to signals from pins. To validate the performance of the algorithms, it is worth writing an additional module to simulate the expected gripper’s response. It calculates feedback comprising pins’ positions for a given object’s 3D model pose. Within the paper, this module is presented to illustrate the operation of the device. At the later stages of research, it will be used to generate sets of signals gathered from pins based on the simulated object’s pose. These will be used to feed the learning algorithms to estimate the actual position of the element and potentially its geometry if not provided. Simulation Algorithm A sample object’s bounding sphere diameter (BSD) is defined as the minimum diameter of a virtual sphere enclosing the whole object. All the other randomisation values relate to this characteristic dimension. The centre of this sphere is placed at the coordinate system origin, and every rotation is relative to its axes. After such an operation, the object remains inside this sphere. The algorithm uniformly randomises the orientation of the input part’s’ model (every rotation have to be equally probable) and then aligns the position of the two grippers’ jaws – so that the part is located between them. The 3D uniform random component (varying from -0.15BSD to 0.15BSD) added to the object’s position makes it not centred.

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Later, the pins’ arrangement is generated. Its attributes (e.g. pins’ diameters, the shape of the pin array’s outline or spacing between pins) are easily adaptable. Next, two depth maps are rendered and projected to the jaws’ planes. Based on these, inside the cross-section of every pin, the pixel laying closest to the jaw is found. The depth assigned to this pixel after being disrupted with a random, normally-distributed (σ = 1/30 of the pins’ diameter) component (representing measurement uncertainties and noises) is a simulated value of the pins’ positions. The algorithm was written in Python using Trimesh [13] and Pyrender [14] libraries. Models Acquisition The key benchmark model in the stl format for simulations was obtained from 3D scanning the cleaned real-life automotive elements (see Fig. 4). This was realised with the GOM ATOS II scanner and GOM Professional software. The generated mesh was based on eight scans and polygonised with the creation tolerance of 0.0072 mm. The trials were also conducted with the use of automotive parts geometries available online [15–17].

Fig. 4. 3D-scanned automotive part (single scan on the left; final model on the right)

3 Results and Discussion The designed algorithm was tested based on four different geometries of various sizes. The results for the same object were compared to analytically validate whether they distinguish clearly between different poses. The renders and simulated pins’ positions were presented for the left jaw only for comparison purposes. However, they are also available for the right jaw. Therefore, the position of the detail can be estimated based on the two depth maps.

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Figures 5, 6, 7 and 8 include depth maps of the gripped object projected on the left jaw with overlaid generated pins’ arrangement (on the left) and the map of the simulated position of the pins while gripping the object (on the right). Circles representing unaffected pins remained unfilled and marked as “inf”.

Fig. 5. Algorithm outputs for the model of a water pump cover (the part in two different random positions and orientation on the left; corresponding computed positions of pins on the right)

The first two test objects (see Fig. 5 and Fig. 6) are small automotive parts [15, 16]. For each of them, two results of the algorithm output are presented. It can be observed that due to that randomisation, for some poses, the objects exceed the operational space of the jaws. On the other hand, because the outlines spread by the outermost pins are not matched to the objects’ shapes, numerous pins do not interact with the surface. Signals from those pins still carry valuable information for the pose estimation; there is no object ahead of them. In real life, unmoved pins will appear maximally ejected, and such signals will be mapped to the “inf” state.

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On the contrary, some pins that, according to simulation, have leaned against the object may exceed their maximal extension, so in real-life operation, they would not do so. A clipping function may be added to the algorithm, but it requires more detailed assumptions on the gripper’s mechanism. While designing and simulating such a construction, this aspect has to be considered.

Fig. 6. Algorithm outputs for the model of a connecting rod (the part in two different random positions and orientation on the left; corresponding computed positions of pins on the right)

The simulation exposed the potential problem. As described in the Methodology section, the algorithm finds the closest pixel inside the pin cross-section and sets its distance as the pin’s extension. This happens even if there is only one such pixel for a pin. The physical structure would probably move the object or deviate due to its finite stiffness and limited friction. The adverse effects of such behaviour in the estimation phase can be partially neglected. This can be realised by assigning weights to pins’ indications according to the defined level of trust or implementation. Moreover, the model can include force impact on the gripping pose and project the pin positions after the potential displacement of the grasped object.

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Fig. 7. Algorithm outputs for the model of a crankshaft (the part in two different random positions and orientation on the left; corresponding computed positions of pins on the right)

When designing a pin array gripper for grasping larger objects, its size can be scaled proportionally to the desired application. For such cases, either pin dimeters or their number has to be increased. However, if the gripper is designed for both big and small parts, it will grip objects much larger than its jaws. This is presented in Figs. 7 and 8. The pins’ diameter and layout were maintained as in the previous simulations. Figure 7 shows the algorithm’s output fed with the model of a crankshaft [17]. Its length of 676 mm exceeds the maximal size defined as the design intent but still verifies well the gripper’s behaviour. It is worth noticing that the simulation does not include gravity effects and assumes total immobility of the gripped object relative to the gripper. For reliable outcomes, the algorithms can be enhanced by the prior assumption of the object displacement based on the gravity forces. It is expected that pose estimation for larger elements will be more challenging because it is more likely to find second piece of the similarly shaped surface. It is particularly problematic for regular elements with repetitive geometrical sections, such as crankshafts (see Fig. 7). One potential solution is adding a few additional single pins separated from the main grasping area. They can provide extensive tactile feedback.

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Fig. 8. Algorithm outputs for the model of a 3D-scanned part (the part in two different random positions and orientation on the left; corresponding computed positions of pins on the right) Summary

Finally, the case proved that when dealing with objects of very different sizes, the maximal random drift cannot be defined as the set share of the BSD. In extreme situations, this may lead to missing the part by all the pins. This issue does not cause problems if all the gripped elements are comparable in scale. Otherwise, the random drift has to be constrained by a constant value. The real-life 3D-scanned large element was tested to verify whether non-smooth surfaces would affect the results (see Fig. 8). However, due to the algorithm’s robustness, this did not cause any significant differences. The major challenges remain as for the previous details.

4 Summary The concept of the pin array gripper with the pose estimation function corresponds to the need of the industry, particularly the automotive sector. It enables operation with multiple, irregular, dirty elements of various sizes. As mentioned in the introduction, to make the solution beneficial, it must be simpler, more reliable and cheaper than

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machine vision or laser scanners. Therefore the following studies should be focused on the following questions: – In which way do different parameters of the gripper influence the precision of pose determination of a gripped object and the strength of the grip? – How to comprise the gripper’s limitations with meeting the design intent and obtaining competitive accuracy of prediction? These two form the base for the follow-up research. It will be continued with the use of machine learning and more accurate simulation models. The algorithm presented in this paper will be applied to generate learning databases and perform tests without the need for a physical setup. This can contribute to reducing the costs of the grippers’ development and easily extend the base of detectable elements. The major challenge for the scripts is to reflect the object’s actual position while the jaws are closed. The model should be improved with the potential force effects of the pins leaning on smaller objects and displacement caused by gravity while the centre of mass is out of the operation area.

References 1. Mykhailyshyn, R., et al.: A systematic review on pneumatic gripping devices for industrial robots. Transport 37(3), 201–231 (August 2022). https://doi.org/10.3846/transport.2022. 17110 2. Zhang, B., et al.: State-of-the-art robotic grippers, grasping and control strategies, as well as their applications in agricultural robots: a review. Comput. Electr. Agric. 177 (2020). https:// doi.org/10.1016/j.compag.2020.105694 3. Du, G., Wang, K., Lian, S., Zhao, K.: Vision-based robotic grasping from object localization, object pose estimation to grasp estimation for parallel grippers: a review. Artif. Intell. Rev. 54(3), 1677–1734 (2020). https://doi.org/10.1007/s10462-020-09888-5 4. Cheng, F., et al.: Object recognition and user interface design for vision-based autonomous robotic grasping point determination. In: PROJECTIONS - Proceedings of the 26th CAADRIA Conference, vol. 1, pp. 633–642, December 2021. https://doi.org/10.52842/conf. caadria.2021.1.633 5. Scott, P.B.: The ‘omnigripper’: a form of robot universal gripper. Robotica 3, 153–158 (September 1985). https://doi.org/10.1017/S0263574700009073 6. Fu, H., Yang, H., Song, W., Zhang, W.: A novel cluster-tube self-adaptive robot hand. Robot. Biomimet. 4(1), 1–9 (2017). https://doi.org/10.1186/s40638-017-0082-2 7. Fu, H., Zhang, W.: The development of a soft robot hand with pin-array structure. Appl. Sci. 9(5)(1011) (2019). https://doi.org/10.3390/APP9051011 8. Mo, A., et al.: Concentric rotation pin array gripper for universal grasp. In: 2018 3rd International Conference on Advanced Robotics and Mechatronics (ICARM), pp. 112–117 January 2019. https://doi.org/10.1109/ICARM.2018.8610678 9. Mo, A., Fu, H., Zhang, W.: A universal gripper base on pivoted pin array with chasing tip. In: Chen, Z., Mendes, A., Yan, Y., Chen, S. (eds.) ICIRA 2018. LNCS (LNAI), vol. 10985, pp. 100–111. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-97589-4_9 10. Mo, A., Zhang, W.: A novel universal gripper based on meshed pin array. Int. J. Adv. Robot. Syst. 16 (2019). https://doi.org/10.1177/1729881419834781 11. Meintrup, H.: Workpiece holder with retaining pins. patent number: DE19702848C1 (1998)

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12. Kumra, S., Kanan, C.: Robotic grasp detection using deep convolutional neural networks. In: IEEE International Conference on Intelligent Robots and Systems, pp. 769–776, December 2017. https://doi.org/10.1109/IROS.2017.8202237 13. Trimesh [Computer software], version 3.12.5. https://github.com/mikedh/trimesh 14. Pyrender [Computer software], version 0.1.45. https://github.com/mmatl/pyrender 15. Otto – Desing: Engineering, Manufacturing, model of the Yamaha water pump cover. https:// grabcad.com/library/yamaha-tz250-4dp-waterpump-cover-1. Accessed 4 Nov 2022 16. Shaba Alam, A.: Model of a piston and a connecting rod assembly. https://grabcad.com/lib rary/bajaj-glamour-125cc-piston-connecting-rod-assembly-1. Accessed 4 Nov 2022 17. Positko, V.: Model of a crankshaft. https://grabcad.com/library/crankshaft-343. Accessed 4 Nov 2022

SpacePatrol - Development of Prospecting Technologies for ESA-ESRIC Challenge Grzegorz Gawdzik , Filip Jędrzejczyk(B) , Michał Bryła , Marcin Słomiany , Miron Kołodziejczyk, Jakub Główka , and Matuesz Maciaś Łukasiewicz Research Network - Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland {grzegorz.gawdzik,filip.jedrzejczyk,michal.bryla,marcin.slomiany, miron.kolodziejczyk,jakub.glowka,mateusz.macias}@piap.lukasiewicz.gov.pl

Abstract. This article describes a SpacePatrol project which goal was to prepare a robotic solution for the ESA-ESRIC Space Resources Challenge - Development of Prospecting Technologies - the first competition of this type. The aim of the challenge was to present a system that would allow to search and identify natural resources in a moon analogue terrain with conditions similar to real ones. The article presents our approach to each phase of the challenge with description of introduced solutions. The idea is to present the SpacePatrol system in its final stage with detailed information about concept of operation, used sensors and technologies, followed by lessons learned and future plans. Keywords: Challenge · Moon · Mobile robot · Manipulation · SLAM · GNSS-denied localisation · Lunar geology · Regolith · ESA Space resources prospecting

1

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Introduction

SpacePatrol is a space-related project that was realised by Łukasiewicz - PIAP (Łukasiewicz Research Network - Industrial Research Institute for Automation and Measurements PIAP) in 2021 and 2022 and partially financed by European Space Agency (ESA). The goal was to prepare a robotic solution that would meet requirements of the ESA-ESRIC Space Resources Challenge - Development of Prospecting Technologies and take part in the competition. The aim of the challenge is to present, in a moon analogue terrain and simulated lunar conditions, a system, that would allow to search and identify natural resources in the shortest possible time and ensure scientific geological analysis. A preparation of such solution is not an easy task, as it requires utilization of multiple technologies, development of hardware and software features and preparation of effective and holistic concept of operation which would assure successful realisation of the mission. The challenge consisted of three main stages with limited number of participants qualified for each stage [3]. The first stage, in which 13 teams took part, was concluded c The Author(s), under exclusive license to Springer Nature Switzerland AG 2023  R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 140–154, 2023. https://doi.org/10.1007/978-3-031-25844-2_13

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with first field test, which took place in Noordwijk (Netherlands) in 2021. The second stage, in which 5 teams took part, was also concluded with field test, which took part in Esch (Luxembourg) in 2022. The sole participant that will conduct further system development within the 3rd stage is about to be selected at the beginning of 2023. Next sections of this article will present detailed description of our solution, which, although initially was based purely on our experience from other projects, became more mature, and basing on the results from each stage, proved to be a well-planned and developed solution.

2 2.1

Overview of ESA-ESRIC Space Resources Challenge Idea

The challenge was organised to look for innovative technical methods for prospecting resources on the Moon, that is considered as the next step in human exploration. The primary goal is to locate and characterise resources like metals with some ground truth measurements and produce an accurate map of the area. To achieve it ESA and ESRIC asked European industries and research institutions to participate in the challenge that is focused on development and effective use of terrestrial prospecting technologies adapted to operate in the environment with lunar mimic conditions. Conditions. The proposed solution had to take into account several limitations imposed by the challenge. As for the first field test, they were as follows: – communication link between the operators and the robot had a simulated moon-to-earth latency, about 3 s (in one direction) – no sensors and devices that use Earth-specific features (like GPS, magnetometers) could be used – time to perform the task was limited to 2.5 h with several loss-of-signal periods, during which communication with the robot was impossible – all of the equipment used in a test site had to weigh less than 100 kg – test site was illuminated in a moon-like way – strong light from a low angle Conditions were modified for the second field test: – time to perform the task was extended to 4 h – weight limit was extended: all the assets could weigh 300 kg in total, with limit of 100 kg per single asset – additional stationary asset could be used, connected to the wired network and power – weight of the stationary asset was limited to 20 kg, however it was not included in the assets total weight limit – in the last 15 min of operation, randomly selected asset was lost and could not be used for the rest of the operation

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All of the required outputs had to be delivered in one hour after the end of time limit (including report with conducted analysis), what highly limited the possible data post-processing. Several types of outputs were expected: – Map of the test site with marked locations of the boulders – Report explaining chemical composition of the boulders and regolith – Additional boulder data – size, photos from multiple angles, shape, etc. The teams were not allowed to inspect the tests locations prior to the test. Moreover the only information about the tests area was limited to the points mentioned above, therefore solutions had to be prepared without precise knowledge about terrain characteristics, on-site structures or dustiness of the field tests. Test Site – 1st Stage. Test site during the first field test was split into two, distinctly different parts. The first part was a traverse zone (Fig. 1a), with a flat concrete surface and two types of obstacles – paper-mâche boulders which had to be avoided and three ramps of varying height and slope which had to be driven through. The robot had to navigate through it to reach the second zone, region of interest (Fig. 1b). Its surface was covered with layer of regolith simulant. On the top six boulders were placed, which mineral composition had to be analysed by the robot.

Fig. 1. Test site during the 1st field test – images from the robot cameras, ESTEC, Noordwijk (Netherlands), 2021.

Test Site – 2nd Stage. The second phase was more oriented towards scientific analysis and deposits prospecting. Test site was a more challenging single zone lunar space of size 40m x 60m, fully covered with lunar regolith simulant, boulders and craters. This time, the aim was to explore and map the entire available space, in the meantime identifying, characterizing and mapping geological features including boulders and deposits of resources (rutile/titanium dioxide and Fe ilmenite).

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Fig. 2. Test site during the 2nd field test, Esch-sur-Alzette (Luxembourg), 2022.

3 3.1

Field Tests 1st Stage

Solution. Our solution and concept of operation was built upon use of a single robot, based on a PIAP PATROL [13], equipped with additional sensors and devices allowing the high-level control, based on setting the goals for the mobile base and the manipulator. Platform was equipped with XRF (X-ray fluorescence) spectrometer Skyray Genius XRF, mounted on the manipulator, which was used for determining the chemical contents of the boulders. The complete platform can be seen in Fig. 3. Due to the fact, that there was no funding provided for the preparation to first stage of the challenge, most of the sub-components of the solution were developed previously in scopes of the other projects realized by Łukasiewicz - PIAP: two RaCER projects funded by ESA [10,15], APRIL, ASSISTANCE, CAMELOT, Robot Union (all funded by European Union within Horizon 2020) and in self-funded development activities. Conclusions. During the first field test the proposed solution demonstrated its capability to fulfill all of the required tasks - we have managed to reach the region of interest after the successful, collision-less traverse through the first zone, take the multiple images of the boulders and measure the chemical composition of one of the rocks. As a result, our team was selected to the second stage of the competition. Our internal assessment was that system performance can be significantly improved by optimization of processes, control scheme and automated reporting features. The primary goal of the next attempt was to do the same, but “more, faster and better”.

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Fig. 3. PIAP PATROL in configuration used during the first field test, ESTEC, 2021

3.2

2nd Stage

Solution Improvement. With respect to our conclusions and due to the changes in requirements, mentioned in the Sect. 2.1 that occurred between stages of the competition, a new operation concept was developed. It is described in details in the Sect. 4.

4 4.1

SpacePatrol System Concept of Operation

The system is composed of two physically separated parts. The first one is a Control Room side, where all the team members are present, and that provides means to remotely communicate (receive data and command) with the second side - lunar one. In its final shape the lunar part of the system is composed of three types of assets: main mobile asset which plays role of a researcher, supportive mobile assets acting as scouts, and a stationary asset with PTZ camera - mounted on the lander. The scouts quickly traverse the area and explore it, searching for craters, boulders and simultaneously mapping the area. They indicate geologically interesting regions that are marked on the map. The regions are then analysed and characterized (in a time consuming operation) by the researcher, that has dedicated sensors on-board. The stationary PTZ is used for gathering visual data about the environment and mission progress, taking photos and indicating supportive goals for the mobile robots. It significantly increases

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situational awareness of the mission manager in the area close to the lander. This approach relays on assets collaboration and therefore decreases time required for area analysis and mapping, as researcher is able to focus on data collection for only previously identified and selected potential deposits of resources. Moreover, in this collaborative approach all mobile assets participate in the environment mapping task, increasing this way its quality. Our solution used PIAP Patrol based robot as a researcher, PIAP Gryf based robot as a scout and custom stationary PTZ as a stationary asset. Roles and Teamwork. The system, that was used in the 2nd field test assigns roles of a 5-person team in the Control Room as follows: – Mission manager (high-level operation planning and reporting, control of the stationary PTZ) – Geologist (analysis of the geological data, support in high-level operation planning) – Main mobile asset (researcher) base operator – Main mobile asset (researcher) payload operator – Supportive mobile asset (scout) operator The roles of team members were chosen for optimal conditions in which all assets are functional, however if conditions of the operation change (e.g., failure of one of the assets, indisposition of one of the operators) the roles could be divided at any time in another required way. It is possible due to the fact that the whole system was designed and developed in a way that guarantee modularity and ability to share roles, e.g., it is possible to run the GUI of any robot on each computer in the Control Room. This collaborative approach is supported by the following tools: – Subsystem of markers, that automatically creates timestamped event with attached position, orientation, semantic information and image, on any key action executed by robotics assets automatically (e.g., on performing geological measurements, taking photo, etc.) or on direct operator request (e.g., to mark discovered objects). The markers are visible by all operators, and can be used also to point goals or interesting objects by any team member to the rest (e.g., by mission manager to set navigation goal to operator of mobile asset). – Automatic synchronization of data, between PCs of the team members. Robots Cooperation. Each asset on the lunar side is connected to the Control Room in a way that they could be used independently, however they are all cooperating with each other in a number of ways: – Point clouds generated from mobile assets are used to create a single map of operating environment, which allows to cover greater area and improve its resolution in areas that were traversed more than once.

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– Data is synchronized between the assets (automatically during the LOS or on demand), which increases the system resilience to the loss of one of the assets - data stored on the lost asset is also stored on the other assets. – All the PTZ cameras could be set to quickly look at or track mobile assets additional view from another perspective improved the situational awareness of the operator and was used to speed up several operations, especially the ones related to the geological analysis of environment objects. – All the PTZ cameras could be set to quickly look at or track a marker set by other operator - it allows to immediately get photos of the key objects of interest (boulders, craters) from multiple perspectives or identify intention of the geologist and mission manager (navigation goal set with use of a marker) – Additional cameras of the scout could be used to improve the situational awareness of the operator of the researcher, especially in a complex operation, such as investigating objects of interest. 4.2

Assets

Fig. 4. Assets used during challenge. PIAP PATROL with payloads (Researcher) on the right, PIAP GRYF with payloads (Scout) on the left, Stationary PTZ in the middle.

Researcher Robot. During the challenge the modified PIAP PATROL mobile robot (shown in the Fig. 4) was used as a researcher. The modification consisted of adding additional high-level controller and sensors which are described in the following sections. During modification additional on-board computer was added and used for capturing and processing raw data from most of the sensors and to control the robot. Researcher robot is composed of two subsets (Mobile Base, Manipulator) and is operated by two dedicated operators, one for

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each subset: Researcher Base Operator and Researcher Payload Operator. The robot has two autonomy control modes which are: Click&Go (selecting target robot position and orientation by clicking on the interactive map) and Leapfrogging (defining goal as a sum of simple movements, such as: move forward 1m, turn 30◦ C, etc., provided by operator via dedicated user interface. Final goal is visualized as a translucent model of robot and expected path, which can be analyzed by the operator before confirming the goal and sending the command to the robot.). It is also equipped with remote safety stop. Scout Robot. Modified PIAP GRYF [12] mobile robot (shown in the fig. 4) is a mobile asset used as a scout to explore the environment and enhance mapping. The modification consisted of adding additional high-level controller and sensors which will be described in the following section. It was equipped with PTZ camera, LiDAR 3D, Front and Rear Cameras and is operated by a dedicated operator. The robot has two autonomy control modes, same as Researcher robot: Click&Go and Leapfrogging. It is also equipped with remote safety stop. Modification of PIAP GRYF included the same on-board computer as the one used for the PIAP PATROL. Stationary PTZ. It is a multi-functional stationary asset (shown in the fig. 4). Its main role is to provide enhanced awareness to the mission manager and the geologist. It enables photo taking with up to x30 zoom, provides full HD video stream and allows to track the mobile assets or focus on other selected objects. Stationary PTZ is also a base for two radio beacons (secondary localisation system) which acts as an anchor for this localisation system. On-board computer for Stationary PTZ was the same as for the PIAP PATROL. 4.3

Sensors

PIAP PATROL mobile robot is equipped with multiple additional sensors: – PTZ, Gripper, Front and Rear Cameras for basic situational awareness. – Velodyne VLP-16 LIDAR 3D for mapping and enhanced situational awareness. – Olympus Vanta M portable X-Ray Fluorescence (XRF) spectroscope used for identification and analysis of elements contained in test samples. It allows to gain, simultaneously, information on both the occurrence and quantity of both economically important (Ti, V, and possibly Sc), light (Mg, Al, Si, P, S, K, Ca, Sc, Ti, V, Cr), and heavy elements (Fe, Cu, Rb, Sr, Zr, Ba, rare earth elements, and U) and was used as a main sensor for geological identification and characterisation of object of interest. – Intel RealSense D435i (for contextual 3D images) and Intel RealSense D405 (for detailed 3D images) – stereoscopic and depth cameras that enhance the situational awareness during investigation of object of interest and allow to build 3D models of them and their surroundings as a supporting geological information.

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– Time-of-flight infrared proximity sensor VL53L4CD as a supportive instrument providing high precision distance readings between XRF sensor and the measured surface. – VectorNav VN-100 Inertial Measurement Unit (IMU) with a disabled compass (due to the challenge conditions), as an additional source for robot localization. – Set of Ultra Wide Bandwidth (UWB) Pozyx tags used as a supporting localization and heading estimation system. Two are mounted on the mobile base and rest are deployable beacons. PIAP GRYF mobile robot is equipped with multiple additional sensors: – – – –

PTZ, Front and Rear Cameras for basic situational awareness. LIDAR 3D for mapping and enhanced situational awareness. VectorNav VN-100 IMU as an additional source for robot localization. One UWB Pozyx tag mounted to the asset and used as a supporting localization and heading estimation system.

Stationary PTZ is equipped with the following sensors: – PTZ camera for basic situational awareness. – Two of UWB Pozyx tags mounted to the asset and used as a supporting localization and heading estimation system. 4.4

Communication

As the entire system is built on top of Robot Operating System (ROS) Noetic, also data exchange between the system components is based on ROS. In our case the lunar and the Control Room sides were linked by 5s delayed, bandwidth limited network, which was introduced by ESA to reflect Moon-Earth communication conditions. ROS uses TCP/IP [9], which seamlessly works for interfacing components over non-delayed network, but leads to timeouts over delayed one. To overcome this issue a UDP based communication channel had to be established. Our approach assumed creation of two independent instances of ROS-based network (lunar one and control room one) linked through a custom UDP-based bridge, and transmitting only necessary data to save the bandwidth. Each asset is equipped with the MikroTik Omnitik 5ac access point that is connected to on-board components (computer, sensor etc.) of that asset. Additionally during the whole challenge the Loss Of Signal (LOS) events between the Control Room and the lunar assets were monitored. When LOS event occurred both sides were aware of that and could perform autonomous actions like taking panorama photos of the environment, data synchronization, etc. 4.5

Localisation

The localization subsystem provides the system with information about robotic assets position and orientation. It plays the key role in the system as it is used:

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– in local robot navigation stack solution to support heading and localization information – in that case it is used by the robot controller to perform driving tasks. – for 3D mapping component. – for modification of mission progress and monitoring in order to create 2D map of the area in the reporting phase. The main source of localization is Lidar Odometry And Mapping (LOAM), based on LIO-SAM [11] package, which in addition to localization is using gathered point clouds to build 3D map of environment which example was shown in the Fig. 5

Fig. 5. Resulting 3D map of test site during the challenge with marked paths of both mobile assets.

Radio Beacons. It was supposed that dusty lunar environment, with unknown number of features that LOAM can use as a reference, can be challenging and may lead to fault of our main localization system, so we decided to develop a secondary one using completely different basis – UWB radio beacons. The system consists of two types of the beacons - fixed, which are placed on the platform, and deployable, which are placed by the manipulator in the spots selected by an operator. The measurement of the distances between each of the beacons allows to estimate the position and orientation of the robot in the coordinate system defined by the deployed beacons. Since the beginning the system was treated as a backup, and despite it proved during the tests to be correct and useful, during the mission it was used partially, just to confirm reliability, as the main localization system worked flawlessly.

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Navigation

Planning and Executing Maneuvers. Mobile assets are equipped with nonholonomic drive systems which can execute one maneuver type: driving an arch defined by its radius. We also explicitly expose two special cases of this maneuver: driving forward and rotate in-place. Full maneuver setup includes selecting maneuver type, goal distance and maximal forward velocity. After maneuver is selected, control commands are calculated by high level constrained iLQR closedloop controller ( [5,8]) that is planning a fixed number of commands ahead and chooses the first one for execution. Kinematic model is used to predict mobile asset dynamics. Optimal path is found by reduction of weighted average of cost functions, such as following the radius, handling constraints on velocity and acceleration and moving forward to goal. High-level desired velocity commands are passed to low-level mobile asset controller inside mobile asset dedicated hardware. At each execution cycle controller server is checking if the goal is reached or if the allowed time for execution did not reach timeout. Avoiding Collisions. To avoid collision e.g. while traversing narrow spaces, local 2.5D gridmap around the vehicle is built and potential collision cells are selected. Before newly computed trajectory is sent as controls to the mobile base, controller keeps moving towards previously known and safe pose on the path. Elevation Mapping and Traversability Estimation. For creation of local 2.5D map and traversability estimation we use an open source approach ( [4,14]). Front mounted LIDAR is a source of point cloud data.

5 5.1

Lessons Learned Achievements

In the second phase, we have demonstrated multiple features related to the following areas: Situational Awareness and Team Cooperation. Our solution provides all users of the system a common situational awareness due to constantly updated data, gathered by the sensors and shared among the system, to ensure most upto-date information. All data generated by each sensor is delivered to the users, who can select which of them shall be displayed and how. All team members had access to the map, which shown current position and orientation of the assets, elevation of the terrain that was generated by LOAM, actual point clouds from on-board LiDARs, background image with cells and markers indicating interesting objects and supporting navigation. As far as video streams are concerned all team members had access to them, but the stationary PTZ had crucial role, which provided overview about mission progress, confirmed localisation of the assets and their relation to each other and terrain objects, provided additional source of visual information during scientific measurements.

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Control, Navigation and Localisation. The system has two methods of control which are called Click&Go and leapfrogging. First one is very easy to use and straightforward, whereas leapfrogging gives more control over robots movement with quick feedback in the loop. Therefore Click&Go approach is more useful in traversing across areas with low density of obstacles, while the second one is better in complex terrain or short distances. Two separate localization systems were implemented – the main and supportive one. The first uses LOAM and provides odometry and mapping from LiDAR. The second is based on radio beacons mounted on the assets and additionally set up with a use of manipulator on the ground. The position of the assets is estimated by triangulation and relation between all beacons. Deployment of beacons is automatized, therefore with a use of one command the system is able to grasp the beacon and place it on the ground on the pre-selected spot. Reduction of human control in manipulation also enabled automatization of measurement taking of the deposits and boulders, what increased effectiveness and accelerated the whole process. LOS Policy, Synchronisation, Automatic Panorama and Logging. In case of loss of signal (LOS) we decided not to command the robot traversing due to risks coming from the unknown environment (we had limited access to the data about the test site before experiment, as there was not even any picture or map). Therefore, we utilized the time another way. All logic and control was on lunar assets, so they were capable of triggering and executing tasks (taking panoramic images and performing data synchronisation between the robots). Panoramic images helped to analyse the environment and better plan the future steps. All actions performed by the assets were logged. Each taken photo had a reference to the 3D position and orientation of the camera, each taken measurement and each screenshot were also saved to ease the later process of data and performance analysis. Collection of Geological Data. The solution proved its ability to provide extensive quantitative and qualitative data that are sufficient for correct identification and characterization of the objects of interest present on the lunar surface. Report Generation. The process of report generation was automatized. It involved use of the markers subsystem, which allowed to create a detailed mission logbook. Based on this logbook and the 2D/3D maps that were also generated automatically, the report could be complemented by comments of team members and data analysis performed by the geologist. 5.2

Future Changes

Manipulation and Detection. It is recommended to decrease time of geological analysis. Provision of additional sensor to detect changes in the chemical

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characteristics of the terrain in a continuous way, e.g. multispectral camera to enable visual detection and classification of the chemical composition based on the pre-trained image classifiers, that take place before time consuming measurement made with XRF sensor. Data Usage. Sharing of raw data from the sensors among the robots, combined with increase of data processing on-site with a use of on-board computers. Reduction of data transfer between robots and Control Room to speed up the processing time and enable usage of all raw data on-site. Sending only final effect of data processing. Collaborative SLAM. Extend single-robot SLAM (Simultaneous localization and mapping) to collaborative SLAM (C-SLAM) (see [7] for a survey), which aims to use data gathered on all robots to improve each robot state estimate as well as maintain globally consistent map. UWB beacons can be used for direct inter-robot loop closures. As for indirect inter-robot loop closures, [6] and [16] suggest low bandwith approach to exchange compact descriptors and only in case of candidate detection, send full feature set. Robot Control and Cooperation. Increase of autonomy level by efficient exploration with exploration planners (e.g. [1,2]). Usage of behaviour trees for making decisions and supervising high-level actions, like searching selected area or measuring object of interest. In that case the robot would traverse to the area, omit obstacles, make measurements and provide feedback about the results. Further development of markers and radio beacons to increase reliability and robustness of both systems and therefore increase their technology readiness level. 5.3

Summary

In this article we presented upgraded SpacePatrol system that was prepared for the second stage of the ESA-ESRIC Space Resources Challenge. Based on experiences gained during the first field trial we have upgraded our solution to obtain better performance and be in-line with updated challenge conditions. The system successfully proved its ability to realize the mission, and provide all required outputs, including 2D/3D maps (Fig. 5) with metadata, scientific characterization of geological objects including finding and characterizing resources deposit, and a report describing mission course and the findings. All of the subsystems worked correctly with no major issues impacting overall mission course or result. Based on the preliminary feedback from ESA we identified areas for further improvement. Our development plans aim at addressing issues as: 1) the Control Room side is overloaded by the number of performed tasks, so keeping the high efficiency of work by the team, that was presented in the field test is impossible in

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a long missions, 2) scaling solution up to greater areas might be problematic, as it would require engaging additional assets and team members, increasing workload of the geologist and the mission manager, that even for the current number of assets is too high. To mitigate those shortcomings we plan to better integrate science operations and robot control as well as introduce more autonomous functionalities. Acknowledgements. The project was partially financed by European Space Agency according to ESA Contract ITT No. AO/2-1811/21/NL/AT, 83/NS/2021 “Space Resources Challenge – Development of Prospecting Technologies”. We gratefully acknowledge the technical assistance as well as important comments and suggestions provided by the rest of our colleagues engaged in realisation of SpacePatrol project from Łukasiewicz - PIAP.

References 1. Cao, C., Zhu, H., Choset, H., Zhang, J.: Tare: a hierarchical framework for efficiently exploring complex 3d environments (2021) 2. Dang, T., Tranzatto, M., Khattak, S., Mascarich, F., Alexis, K., Hutter, M.: Graphbased subterranean exploration path planning using aerial and legged robots. J. Field Rob. 37(8), 1363–1388 (2020). Wiley Online Library 3. ESRIC, E.: ESA and ESRIC space resources challenge (2022) 4. Fankhauser, P., Bloesch, M., Hutter, M.: Probabilistic terrain mapping for mobile robots with uncertain localization. IEEE Rob. Autom. Lett. (RA-L) 3(4), 3019– 3026 (2018) 5. Howell, T.A., Jackson, B.E., Manchester, Z.: Altro: a fast solver for constrained trajectory optimization. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 7674–7679 (2019) 6. Huang, Y., Shan, T., Chen, F., Englot, B.: Disco-slam: Distributed scan contextenabled multi-robot lidar slam with two-stage global-local graph optimization. IEEE Rob. Autom. Lett. 7(2), 1150–1157 (2022) 7. Lajoie, P., Ramtoula, B., Wu, F., Beltrame, G.: Towards collaborative simultaneous localization and mapping: a survey of the current research landscape. CoRR abs/2108.08325 (2021) 8. Ma, J., Cheng, Z., Zhang, X., Tomizuka, M., Lee, T.H.: Alternating direction method of multipliers for constrained iterative LQR in autonomous driving. CoRR abs/2011.00462 (2020) 9. OpenRobotics.org: Ros/tcpros. http://wiki.ros.org/ros/tcpros (2013) 10. Pustułka, P., et al.: Racer as reliable training ground for the human enabled robotic architecture and capability for lunar exploration and science (heracles) missions 11. Shan, T., Englot, B., Meyers, D., Wang, W., Ratti, C., Daniela, R.: LIO-SAM: tightly-coupled lidar inertial odometry via smoothing and mapping. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5135– 5142. IEEE (2020) R https://www.antiterrorism.eu/portfolio-posts/ 12. Łukasiewicz PIAP: Piap gryf. piap-gryf/ (2022) R https://www.antiterrorism.eu/portfolio-posts/ 13. Łukasiewicz PIAP: Piap patrol. robot_eod_piap_patrol/ (2022)

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14. Wermelinger, M., Fankhauser, P., Diethelm, R., Krüsi, P., Siegwart, R., Hutter, M.: Navigation planning for legged robots in challenging terrain. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1184–1189 (2016) 15. Wittels, P., et al.: Racer: determination of the maximum speed of fast teleoperated rover for lunar exploration (2018) 16. Zhong, S., Qi, Y., Chen, Z., Wu, J., Chen, H., Liu, M.: DCL-SLAM: a distributed collaborative lidar slam framework for a robotic swarm (2022)

Scanning Electrochemical Microscope Based on Visual Recognition and Machine Learning Jurga Subaˇci¯ut˙e-Žemaitien˙e , Andrius Dzedzickis , Antanas Zinoviˇcius , Vadimas Ivinskij, Just˙e Rož˙en˙e , Rokas Bagdonas, Vytautas Buˇcinskas , and Inga Morkv˙enait˙e-Vilkonˇcien˙e(B) Vilnius Gediminas Technical University, 10223 Vilnius, Lithuania [email protected]

Abstract. Scanning electrochemical microscopy is an advanced tool for studying electrochemically active surfaces, including biological ones. Experiments with biological systems must be performed fast since their reactions and states change very fast. SECM can be easily equipped with a top-mounted light microscope with a known distance between the probe and the camera. This hardware solution, in combination with machine learning algorithms, would allow for the automatic finding of target locations, selecting exact positions for measurements, and compensating for positioning inaccuracies. This article demonstrates a newly constructed SECM setup. In addition, it allows faster user adaptation to unknown topography and shortened scanning times. Keywords: Scanning electrochemical microscopy · Machine learning · Visual recognition

1 Introduction Scanning electrochemical microscopy (SECM) is a part of the scanning probe microscopy family. A micro or nanoscale electrode is used as a probe in typical systems. The commonly used ultramicroelectrode (UME) has a lower than 25 µm diameter [1]. To spatially resolve the local electrochemical activity of the sample immersed in the solution, UME is placed near the surface and then moved in 3D space [2]. Even though SECM is a pretty new method, first introduced by the Bards group in the late 1980s, it is a well-established method for characterizing local electrochemical behavior between liquid/solid, liquid/liquid, and liquid/gas interfaces [3]. Over the years, it has rapidly developed new operation modes and probe types. Positioning SECM modes can be divided: a) constant distance, b) constant height c) hoping; Electrochemical detection SECM modes are: a) feedback (FB), b) generation/collection, c) redox competition, d) potentiometric and e) alternating current mode. In recent years SECM has found a wide range of applications in biological systems such as enzymes, antibodies, biofilms, living cells, and DNA [4–8]. SECM has numerous advantages compared to other methods. SECMs’ non-destructive nature allows repeated measurements of the same sample [9]. The sample does not have to be biased, allowing it © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 155–162, 2023. https://doi.org/10.1007/978-3-031-25844-2_14

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to be immobilized on the non-conductive substrate [3]. Reaction kinetics can be evaluated without touching the sample [5]. The sample preparation can be simplified as it only needs to be exposed to external redox mediators. Besides the advantages, measurements can be taken in the desired medium in vivo to examine the biological response to specific stimuli [10]. However, the classic SECM setup has limitations. The signal depends on the distance between UME, and the sample surface, UME crash into the sample at some modes can cause damage. Furthermore, it is hard to achieve sub-µm spatial resolution [11, 12] when SECM is adapted to measure biological samples, inverted microscope limits available space to monitor the experiment. Additionally, compared to other SPM methods, SECM scanning time takes longer and requires a great deal of attention and patience to find and target the area of interest [13]. Limitations give rise to the development of a wide range of advanced SECM techniques where a feedback control system is implemented to maintain a constant distance between the probe and the sample. One of the most popular solutions is shear-force distance control, as it can be easily implemented by introducing a piezo pusher, which would vibrate the electrode at the resonance frequency with an amplitude of a few nanometers. The laser beam would simultaneously be focused on the very tip of UME, and the Fresnel diffraction pattern is projected onto the split-photodiode where the software would continually keep a predefined vibration amplitude to maintain a constant distance [14]. Another method would be to attach a set of two piezoelectric plates to UME mechanically. One would excite the UME causing it to resonate, and the other would act as a detector for tip oscillation amplitude [15]. Other ways include ion conductance positioning, alternating current SECM, and atomic force microscopy (AFM) positioning [16–18]. Among them, AFM combination with SECM is superior as it relieves more than one limitation at the same time: a) improves spatial resolution (sub-µm resolution can be achieved); b) maintain a constant distance between the sample and probe; c) prevents UME crashes into the sample; d) gathers topographical data at the same time [19]. However, progress is very limited when it comes to improving user experience and speeding up target detection. Many commercially available SECM apparatus has inverted light microscopes or side cameras to find target area and monitor experimental progress. When probing biological samples, catalytically active regions can be far away from each other. The location of reactive regions on the sample’s surface can take a long time and some luck. SECM can be easily equipped with a top-mounted light microscope with a known distance between the probe and the camera. This hardware solution, combined with AC-SECM and machine learning algorithms, would automatically find target locations, select exact positions for measurements, and compensate for positioning inaccuracies [17, 20, 21]. To combine the equipment and incorporate automation, LabView software was used. Machine learning was chosen for automating sample detection as biological samples from the same batch can be slightly different. For object detection modified YOLOv5 model was used to detect immobilized samples and send coordinates to SECM, and a separate algorithm compensates for inaccuracies appearing from stepper motors. This article demonstrates a newly constructed SECM setup and its functionality via example. Automating the detection of immobilized glucose oxidase enzyme on a dielectric surface, mapping electrochemical activity, evaluating reaction kinetics in

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different sample locations, and repeating experiments automatically. In addition, it allows faster user adaptation to unknown topography and shortened scanning times.

2 Concept of SECM Home-made scanning electrochemical microscopy was used for the experiments (Fig. 1). It consists of the following core modules: mechanical system, optical system, motion controller, potentiostat, and main control unit. The main controller (PC) controls the whole system, runs the user interface, performs vision recognitions, generates motion and measurement commands for the motion controller and potentiostat, and processes obtained scanning results. Lower-level controllers and devices perform the more specific tasks assigned to them.

Fig. 1. The concept of automated SECM: 1-PC; 2-Potentiostat; 3-Control unit; 4-Antivibration table; 5-Frame; 6-Electrode drive; 7-Camera drive; 8-Camera; 9-Objective; 10-Electrode holder; 11-electrode; 12-stage with X and Y drives; 13-counter electrode; 14-reference electrode.

The mechanical system of the developed microscope has four degrees of freedom. It is based on the kinematic scheme of the typical orthogonal manipulator like 3D printing or a similar CNC machine. The first z-axis is used to control the focal distance of the optical microscope. The second one moves SECM ultramicroelectrode up and down. The optical microscope and the measuring electrode are mounted on separate axes due to the need for asynchronous motion. The x and y-axis have a resolution of about 1 µm and control the movements of the table on which the test specimen is placed. Z-axes have a resolution of about 0.75 µm. The high accuracy and resolution of the drives are ensured by using micrometric pitch ball-screw drives controlled by stepper motors operating at 1/256 micro-step mode and advanced control methods.

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The motion controller is equipped with a fully capable Orange Pi microcomputer running Machinekit software on the Armbian operating system. Machinekit – a special version of LinuxCNC adapted for microcomputers. In our case, it receives the motion command from the main computer through the Ethernet protocol and executes the corresponding action. Implementing the LinuxCNC in scanning microscopy is not a typical solution; more often, it is used to control custom-made devices such as 3D printers, CNC machines, or various robots. Nevertheless, it has few advantages compared to custom-developed control algorithms: (I) well-tested drives calibration and synchronization algorithm; (II) compatibility with all types of stepper motor drivers; (III) a simple configuration process for a new device; (IV) possibility to compensate backlashes and other inaccuracies in the drives; (V) possibility to implement position feedback sensors. Thus, using the LinuxCNC allows for solving main motion control problems and assures sufficient accuracy. The high-level control is realized by running a custom-made control module in LabVIEW software. It performs analysis of the vision data from the optical microscope; ensures user interface; communicates with the motion controller, which converts motion commands into the corresponding signals and transmits them to the motor drivers. Simultaneously the same model controls the electrochemical measurements by sending the corresponding command to the potentiostat and receiving obtained results. Therefore, using commercially available modules, relatively low-cost components, design, and software solutions proven in other fields, and an original control and data fusion algorithm, an automated scanning electrochemical microscope with image recognition has been developed.

3 Results The SECM, based on machine learning, works by the algorithm, provided in Fig. 2. A camera scans the sample, and the objects of interest are defined by visual recognition methods after initial pre-processing of low-contrast images. When a research object (living cell or microstructure) is detected and identified, the center points of defined objects are calculated. After that, the sample is moved by a constant calibrated distance in order to position the center of the object of interest directly under the measurement probe. After precise positioning in the x and y-axes, the object height on the z-axis is defined by approaching the measurement probe and observing the intensity of the electrochemical signal response. After object localization and approximation of its height detection, further, it is scanned by SECM, applying initially predefined motion trajectory patterns and registering an electrochemical signal to build the data set containing information about the discrete positions and electrochemical activity at that point. The reliable functionality of the designed SECM hardly depends on the accuracy characteristics of the implemented drives, especially taking into account that it is impossible to track the object and probe position with the same camera. Therefore the precise calibration of offset between the measurement probe and the camera’s objective center is essential, as well as the positioning accuracy of the z-axis since conversion between object position in the figure and its real coordinates depends on the microscope scale level that is defined from the drive position.

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Fig. 2. Control algorithm

To evaluate the accuracy characteristics of the developed mechanical systems were performed positioning accuracy measurements that defined dependencies between drives stroke and positioning error on the X and Y axis (Fig. 3). Measurements were performed using laser distance sensor LAT 61 K308 IUP (Urbach, Germany) wich measurement range 30 mm, and resolution 0.5µm. For each set of measurements, the sensor was placed parallelly to the axis of interest and adjusted to measure its position. Position data were recorded after making forward and backward motions with predefined strokes. Strokes of 1mm, 10 mm, and 50 mm were selected, taking into account real application cases: object detection and localization require bigger strokes, and object scanning requires small strokes. Performed measurements were repeated 30 times. The average results and their confidence intervals are presented in Fig. 3.

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Fig. 3. Positioning error dependencies on stroke

The higher positioning errors were observed at the X-axis, except when the stroke was only one millimeter. The positioning error difference of more than 2 µm between the x and y-axes is quite predictable and can be explained by load variation on those axes. The load on the x-axis is smaller. Also, from Fig. 3, it is seen that error dependency from the stroke is quite stable and has a clear trend, and could be compensated using typical techniques or machine learning together with visual recognition [20, 21].

4 Conclusions The visual recognition of objects nowadays has a broad range of applications. A developed mechanical system together with machine learning can be a great tool for the improvement of routine operations. Measurements results show that the accuracy of the device in x and y-axes (error less than 5 µm) is sufficient for the electrochemical characterization of various objects. The new design of SECM allowed us to measure the whole sample automatically, allowing us to search for the active areas, recognize them, register electrochemical signals, and compare the data from visual recognition with them. In this way, the whole measurement process becomes less time-consuming, and more accurate, and provides information about many objects at a time. The technologies, which are used in different areas of microscopy, could be applied to SECM and lead to a breakthrough in this field. Acknowledgments. This project has received funding from the European Regional Development Fund (project No 01.2.2-LMT-K-718-03-0063) under a grant agreement with the Research Council of Lithuania (LMTLT).

References 1. Bard, A.J., Faulkner, L.R., White, H.S.: Electrochemical Methods: Fundamentals and Applications, 3rd edn. (2022)

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2. Morkvenaite-Vilkonciene, I., Ramanaviciene, A., Kisieliute, A., Bucinskas, V., Ramanavicius, A.: Scanning electrochemical microscopy in the development of enzymatic sensors and immunosensors. Biosens Bioelectron 141, 111411 (2019) 3. Kubota, L.T., da Silva, J.A.F., Sena, M.M., Alves, W.A. (eds.): Tools and Trends in Bioanalytical Chemistry. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-82381-8 4. Petroniene, J., et al.: Evaluation of redox activity of human myocardium-derived mesenchymal stem cells by scanning electrochemical microscopy. Electroanalysis 32, 1337–1345 (2020) 5. Ramanavicius, A., et al.: Scanning electrochemical microscopy and electrochemical impedance spectroscopy-based characterization of perforated polycarbonate membrane modified by carbon-nanomaterials and glucose oxidase. Colloids Surf A Physicochem. Eng. Asp 624, 126822 (2021) 6. Zinovicius, A., et al.: Scanning electrochemical impedance microscopy in redox-competition mode for the investiga-tion of antibodies labelled with horseradish peroxidase. Materials 14(14), 4301 (2021) 7. Caniglia, G., Kranz, C.: Scanning electrochemical microscopy and its potential for studying biofilms and antimicrobial coatings. Anal. Bioanal. Chem. 412(24), 6133–6148 (2020). https://doi.org/10.1007/s00216-020-02782-7 8. Alawad, A., et al.: SECM for studying the immobilization and repartition of a redox antitetracycline aptamer on screen-printed carbon electrodes. Electroanalysis 33, 292–295 (2021) 9. Gwon, H.J., Lim, D., Ahn, H.S.: Bioanalytical chemistry with scanning electrochemical microscopy. Bull. Korean. Chem. Soc. 42, 1400–1410 (2021) 10. Shi, M., Wang, L., Xie, Z., Zhao, L., Zhang, X., Zhang, M.: High-content label-free singlecell analysis with a microfluidic device using programmable scanning electrochemical microscopy. Anal. Chem. 93, 12417–12425 (2021) 11. Horrocks, B.R., Wittstock, G.: Biotechnological application of scanning electrochemical microscopy. Scann. Electrochem. Microsc. 243–296 (2022) 12. Patel, A.N., Kranz, C.: (Multi)functional Atomic Force Microscopy Imaging. Ann. Rev. Anal. Chem. 11, 329–350 (2018) 13. Preet, A., Lin, T.E.: A review: scanning electrochemical microscopy (SECM) for visualizing the real-time local catalytic activity. Activity Catalyst 11, 594 (2021) 14. Hengstenberg, A., Kranz, C., Schuhmann, W.: Facilitated tip-positioning and applications of non-electrode tips in scanning electrochemical microscopy using a shear force based constantdistance mode. Chem. Eur. J. 6, 1547–1554 (2000) 15. Ballesteros Katemann, B., Schulte, A, Schuhmann, W.: Constant-distance mode scanning electrochemical microscopy (SECM)—Part I: adaptation of a non-optical shear-force-based positioning mode for SECM tips. Chem. Eur. J. 9, 2025–2033 (2003) 16. Morris, C.A., Chen, C.C., Baker, L.A.: Transport of redox probes through single pores measured by scanning electrochemical-scanning ion conductance microscopy (SECM-SICM). Analyst 137, 2933–2938 (2012) 17. Mandler, D.: Micro and nanopatterning. In: Bard, A.J., Mirkin, M.V. (eds.) Scanning Electrochemical Microscopy, pp. 379–418. CRC Press, Boca Raton (2022). https://doi.org/10.1201/ 9781003004592-14 18. Shi, X., Ma, Q., Marhaba, T., Zhang, W.: Probing surface electrochemical activity of nanomaterials using a hybrid atomic force microscope-scanning electrochemical microscope (AFM-SECM). J. Vis. Exp. 2021, 1–23 (2021) 19. Shi, X., Qing, W., Marhaba, T., Zhang, W.: Atomic force microscopy - Scanning electrochemical microscopy (AFM-SECM) for nanoscale topographical and electrochemical characterization: principles, applications, and perspectives. Electrochem Acta 332, 135472 (2020)

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20. Sumanas, M., Petronis, A., Bucinskas, V., Dzedzickis, A., Virzonis, D., MorkvenaiteVilkonciene, I.: Deep Q-learning in robotics: improvement of accuracy and repeatability. Sensors 22(10), 3911 (2022). https://doi.org/10.3390/s22103911 21. Bucinskas, V., et al.: Improving industrial robot positioning accuracy to the microscale using machine learning method. Machines 10(10), 940 (2022). https://doi.org/10.3390/machines1 0100940

Measuring Techniques and Systems

Simulation of Ultrasonic Vibration Propagation Through Resonators for Acoustic Coagulation Intensification Igor Korobiichuk1(B) , Vladyslav Shybetskyi2 , Myroslava Kalinina2 and Katarzyna Rzeplinska-Rykala3

,

1 Institute of Automatic Control and Robotics, Warsaw University of Technology, Warsaw,

Poland [email protected] 2 National Technical University of Ukraine, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine 3 Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland [email protected]

Abstract. A comprehensive computer model of ultrasonic vibrations through resonators in the air was constructed in the universal software system of analysis by finite elements method ANSYS. Analysis system “Modal” has been applied for identifying the natural frequency of the system in the frequency range of 20 000 – 25 000 Hz. The impact of the ultrasonic emitter on the deformation of the resonators was determined by using “Harmonic Response” system. Obtained acoustic pressure levels in the air created by the oscillation of resonators under the action of ultrasound. This study can be used in the design of automatic systems of air purification systems based on acoustic coagulation. Keywords: Acoustic coagulation · Ultrasound · Resonator · ANSYS

1 Introduction The annual expenses for medicines per capita are steadily increasing both in Europe and in the world [1]. So in Germany they increased in last year from 880.2 to 947.8 US dollars, in France from 697.9 to 726.2 US dollars, and in Italy from 651.3 to 670.5 US Dollars. Basically, the increase is due to the price of the cost of production of medicines. The production of each particular medicinal product includes a complex sequence of basic and auxiliary technological operations. But none of them can do without the stage of air preparation. It can be ventilation air that provides appropriate working conditions for employees, or technological, which provides conditions for the course of basic technological operations. Air for technological operations is removed from the environment and may contain [2]: • Large coarse particles greater than 10 µm in xdiameter. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 165–172, 2023. https://doi.org/10.1007/978-3-031-25844-2_15

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• Coarse particles (also known as PM10–2.5): particles with diameters generally larger than 2.5 µm and smaller than, or equal to, 10 µm in diameter • Fine particles (also known as PM2.5): particles generally 2.5 µm in diameter or smaller. • Ultrafine and nanoparticles which are generally classified as having diameters less than 0.1 µm. The total number of suspended particles in the air can reach 109 per 1 m3 . Two or three stepped filtration is used to capture them in pharmaceutical plants. The filters are placed in series: from filters with the largest diameter of the pores and the lowest efficiency (pre-cleaning filters) to filters with small pores and high efficiency (HEPA and ULPA filters) [3]. The latter are expensive, have a sufficiently high hydraulic resistance, and therefore loss of energy and after some time they cannot be regenerated and must be replaced. To reduce the load on fine filters, pre -treatment methods that reduce the amount of fine particles that will reach these filters due to their coagulation with larger parts can be used. Such coagulation can be carried out by using additional conditions, such as electrical, acoustic or magnetic field or chemical treatment for coagulation of fine particles [4, 5]. The work considers acoustic coagulation as one of the most promising ways of preliminary air preparation.

2 Analysis of the State of the Problem For the first time, this phenomenon was interested in 1931 by Patterson and Cawod, which used it to condensed smoke. Subsequently, acoustic coagulation technology was used for condensation of fogs on runways, partly in chemical production and metallurgy. In this direction, many studies were conducted and the value of the optimal process parameters was obtained, which are very different from others. Volk and William studies for the precipitation of the dispersed soot of aerosols set the optimal frequency of 3 kHz, and the level of acoustic pressure 120 dB [6]. Tiwary 0set 2 kHz as optimal [7]. Gallego notes in its experiments that for flue gases the optimal value of 20 kHz [8]. Instead, Yao scientific group that used a standing wave with acoustic pressure 140–160 dB determines the frequency of about 9 kHz as the best [9]. Such a big difference indicates that not all factors that affect coagulation have been taken into account. Considering that the optimal meanings of all researchers have the maximum possible values of acoustic pressure for the system under study, it can be suggested that the best process was done with the coincidence of the ultrasonic radiation frequency with the natural frequency of the system. Therefore, the use of resonators will not only spread ultrasonic vibrations more evenly in volume, but also enhance them by selecting the correct design. However, the search for such a design can be extremely complex and expensive, so the first stage of research should be determining the natural frequencies of the system and its impact on the acoustic environment. Therefore, the purpose of this study is to build a computer model of the radiation propagation process through a simple resonator for further examination of the resonators influence on the particles weighted in the air flow.

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3 Materials and Methods The final elements method implemented in the universal software system ANSYS is used to model physical processes [10]. To determine the natural frequencies analysis system “Modal” was selected. Obtained results were transmitted into “Harmonic Response” system to further model to find the impact of the ultrasonic emitter on the resonator. The data was then transmitted to “Harmonic Acoustic” to simulate the oscillation propagation process in the acoustic environment [11, 12]. The modeling is carried out for the resonator, which is contains a plate 1 of 2 mm thick and round section of 2 mm in diameter (Fig. 1). The total number of resonating elements is 13. The lower part of the resonator is connected to the ultrasonic emitter 3. The frequency range of the emitter is 20,000 - 25,000 Hz; the pressure - 20 Pa. The resonator is located in the intersection of a duct of 125 per 100 mm. To simplify and reduce the cost of production, the resonator is proposed to print on 3-D printer with ABS Plastic, which properties were used for modeling.

Fig. 1. Model of resonators in acoustic environment: modeling areas: I - volume of air; II – volume of resonator; 1 – plate; 2 – resonating element; 3 – ultrasonic emitter; FS – boundary “Fixed Support”; RB – boundary “Radiation Boundary”; RW – boundary “Rigid Wall”

Under constructing of a computer model, three modules were connected as follows: geometry, mesh and modeling results from “Modal” were completely used for modeling in “Harmonic Response”, from which geometry and modeling results were sent to “Harmonic Acoustic”. Geometry was loaded in “Modal”, where area I was excluded (Fig. 1). Mesh type – mechanical, number of elements 8 375, number of nodes 19 305. The boundary condition

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“Fixed Support” was set on the both side faces of the plate marked as FS. The modeling was performed for frequencies in the range of 20 000 – 25 000 Hz. The simulation results were transferred to the next system. In the “Harmonic Response” the ultrasonic emitter was replaced with boundary condition, which transduces the pressure that creates by emitter. The modeling was performed for the same frequency range. In the “Harmonic Acoustic” modeling areas was inverted and area II was suppressed. The type of grid is mechanical, the number of elements 103 182, the number of nodes 442 940. The boundary condition of “Radiation Boundary” was set at the front and rear ends of the region, which made it possible not to take into account their impact on the spread of oscillations. The boundary type “Rigid Wall” was set on the upper and side walls, for modeling the walls of the duct. The velocity of the elements of the resonator has been imported from the “Harmonic Response”.

4 Results and Discussion The analysis was performed for the frequency range of 20 000 – 25 000 Hz. This frequency range is chosen in view of the frequency required to capture particles with a diameter of 2.5 µm and less [13]. Of greatest interest are natural frequencies, in which all resonators come into motion, so frequency range can be shortened for further calculations. For example, at 20611 Hz frequency, only one element of the resonator comes into motion (Fig. 2).

Fig. 2. Contour of total deformations of resonators at natural frequency 20 611 Hz

To build a complex picture of the spread of acoustic radiation through the resonator, the natural frequency of 20 200 Hz is much more appropriate (Fig. 3). Although the amplitude of oscillations is smaller, the complex movement of each of the resonators will allow to turbulize the flow of air which past the resonators more effectively, which will lead to more number of collision of suspended particles.

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Fig. 3. Contour of total deformations of resonators at natural frequency 20 200 Hz

When the ultrasonic emitter was added to the system, the frequencies of the resonance of the entire system were changed. At frequencies up to 20 405 Hz only those elements of the resonator that are directly above it come into motion (Fig. 4).

Fig. 4. Contour of total deformations of resonators at natural frequency 20 405 Hz with ultrasonic oscillations

Further growth leads to the distribution of load on all elements of the resonator and at a frequency of 20 682 Hz is distributed evenly to all elements (Fig. 5). Further increase in frequency does not significantly change the contour of deformations, but the maximum values are slightly reduced.

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Fig. 5. Contour of total deformations of resonators at natural frequency 20 682 Hz with ultrasonic oscillations

The value of the maximum deformations of the resonators at 20 405 Hz is higher, but it is on the plate. The average deformation values are higher at a frequency value of 20 682 Hz. When modeling the influence of emitters on the air for most frequencies, complex pressure distribution is formed, with constant alternation of maximums and minimums. The most intensive resonators affect the part that is located directly above the emitter. The maximum pressure value is fixed at a frequency of 23 791 Hz, which corresponds to 58 mode of natural frequencies, and is 0.0148 Pa (Fig. 6).

Fig. 6. Contour of pressure distribution in air at frequency of 23 791 Hz

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The amplitude value can be increased by the use of more powerful emitters and more numbers of emitters. At this frequency the pressure zone alternate with zones where the pressure remains unchanged. But since these zones are placed between maxims and minimums, the movement of air in these places will also occur. In addition to the maximum pressure values at this frequency, the maximum amplitude has kinetic energy. Although its value is quite low, its increase due to the design of resonators will have a positive effect on the effectiveness of coagulation of particles.

5 Conclusions A comprehensive computer model was built for the process of ultrasonic vibrations through resonators. Next conclusions could be made: 1. For resonators consisting of a large number of elements, a large number of natural frequencies are possible. With certain frequency values, only single elements come into motion, which makes it possible to exclude them from further calculations. 2. The injection of the pressure created by an ultrasonic emitter into the system redistributes deformation of the surface of the resonator elements. 3. The influence of resonators on the acoustic environment surrounding them creates changes in pressures that can drive the particles weighted in the air. The maximum pressure value is fixed at a frequency of 23 791 Hz, and is 0.0148 Pa. This study is the first step in constructing a computer model of ultrasonic radiation influence on fine particles weighted in the air. In the future, it is planned to combine it with a model of fluid flow with the sus-pended particles for automatic control systems.

References 1. OECD data: Pharmaceutical spending (2022). https://data.oecd.org/healthres/pharmaceu tical-spending.htm 2. U.S. Environmental Protection Agency: Particle Pollution and Your Patients’ Health (2022). https://www.epa.gov/pmcourse/what-particle-pollution 3. William, J.R., Volk, M.: Sonic agglomeration of aerosol particles (1975) 4. Osborne, M.W., Gail, L., Ruiter, P., Hemel, H.: Applied membrane air filtration technology for best energy savings and enhanced performance of critical processes. Eur. J. Parent. Pharmaceut. Sci. 18(3), pp. 76–82 (2013) 5. Qu, Z., Cao, J., Chang, S., Zhang, Z., Cheng, G., Ding, J.: Triboelectric based high-efficiency filter device for engineering polluted hydraulic oil. Nano Energy 100, 107497 (2022). https:// doi.org/10.1016/j.nanoen.2022.107497 6. Al-Othman, A.A., et al.: Modified bio-electrocoagulation system to treat the municipal wastewater for irrigation purposes. Chemosphere 307, 135746 (2022). https://doi.org/10. 1016/j.chemosphere.2022.135746 7. Tiwary, R., ReethofOliver, G., McDaniel, H.: Acoustically generated turbulence and its effect on acoustic agglomeration. J. Acoust. Soc. Am. 76, 841–849 (1984) 8. Gallego-Juárez, J.A., et al.: Application of acoustic agglomeration to reduce fine particle emissions from coal combustion plants. Environ. Sci. Technol 33, 3843–3849 (1999)

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9. Yao, G., Zhao, B., Shen, X.L.: experimental study and numerical analysis of the acoustic agglomeration of coal-fired inhalable particles. J. Eng. Thermal Energy Power 21, 175–178 (2006) 10. KShakhovska, N.: Advances in Intelligent Systems and Computing. AISC, vol. 512. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-45991-2 11. Korobiichuk, I., Semeniuk, S., Shybetskyi, V., Kostyk, S., Povodzinsky, V.: Development of a bioreactor design for cultivation of cell cultures. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Automation 2022: New Solutions and Technologies for Automation, Robotics and Measurement Techniques. AISC, vol. 1427, pp. 317–328. Springer, Cham (2022). https://doi. org/10.1007/978-3-031-03502-9_32 12. Korobiichuk, I., Shybetskyi, V., Mel’nick, S., Kosstyk, S., Kalinina, M.: Optimization of heat exchange plate geometry by modeling physical processes using CAD. Energies 15(4), 1430 (2022). https://doi.org/10.3390/en15041430 13. Korobiichuk, I., Shybetskyi, V., Kostyk, S., Kalinina, M., Tsytsiura, A.: Ways to reduce the creation of vortex during homogenization of liquid products. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Automation 2022: New Solutions and Technologies for Automation, Robotics and Measurement Techniques. AISC, vol. 1427, pp. 329–343. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-03502-9_33

Mathematical Model of the Approximate Function as the Result of Identification of the Object of Automatic Control Igor Korobiichuk1(B) , Viktorij Mel’nick2 , Vera Kosova2 , Zhanna Ostapenko2 , Nonna Gnateiko2 , and Katarzyna Rzeplinska-Rykala3 1 Institute of Automatic Control and Robotics, Warsaw University of Technology, Warsaw,

Poland [email protected] 2 National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine [email protected] 3 Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland [email protected]

Abstract. The authors have developed and improved a mathematical model that de-scribes the impact of errors in determining the structure of the approximating function on the results of the identification of automatic control objects. The influence of high-frequency “noise” on signal characteristics and identification quality has been studied. The methods of determining the parameters of the selected approximating structure based on the system’s response to a known input signal have been analyzed. Attention is paid to objects that, at first approximation, can be reduced to elementary dynamic links. Algorithms and their software implementation have been given to determine the parameters of approximating structures based on the transient and frequency characteristics of the object. An unconventional method of determining the transfer function using the least squares method has been proposed. Keywords: Approximating functions · Transfer function · Automatic control · Least squares method · Mathematical model

1 Introduction In the study of dynamic systems, the choice of the structure and determination of the model parameters of the research object plays a significant role. If the adequacy of the model is not guaranteed, then the results lose any meaning [1, 2]. The matter is complicated by the fact that the degree of the model’s adequacy depends on many factors, for example, the frequency range, the purity of the input signal, and the conditions in which the system will work [3, 4]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 173–182, 2023. https://doi.org/10.1007/978-3-031-25844-2_16

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The universality of the mathematical description expands the possibilities of taking into account many factors that affect its properties and also establishes the degree of validity of assumptions and simplifications in the process of analyzing the dynamics as a whole [5, 6]. The least squares method with its ability to mitigate possible errors in the initial data used to identify a dynamic object, as well as with its “tolerance” to the incomplete correspondence of the approximating structure to the depth properties of the object under study [7], can be applied for identification by series points of the amplitude-phase characteristic of the corresponding channel [8]. The model takes into account all the features of the process. To evaluate the dynamic characteristics of an object or any other element of an automatic system (which will be referred to simply as an object in the future), it is convenient to use the recorded reaction y(t) of a given object to a known (predetermined or recorded synchronously with the reaction) input signal x(t) [9].

2 Materials and Methods The approximate transfer function of the channel under study is usually sought in the form W (p) =

bn pn +... b1 p + b0 . an pn +... + a1 p + 1

(1)

The differential equation corresponds to it an y(n) + ... + a1 y + y = bn x(n) + ... + b1 x + b0 x.

(2)

Numerous methods of determining the order n and the coefficients of the transfer function (1) have been proposed, including the one by processing signals x(t) and y(t), for example, the Simoyu Method, the sequential integration method of Eq. (2) over time, and others. A characteristic feature of the problem is the possible presence of errors in the values of x(t) and y(t). To reduce the influence of these errors on the identification results, the functions x(t) and y(t) are smoothed, which leads to the occurrence of additional smoothing errors, i.e. the circle of problems is closed. The second feature of the problem is the possible inconsistency of the structure (1) with the deep features of the dynamic behavior of the studied object. For example, the order of n is below the “true” one. The latter circumstance always occurs when the transfer higher-order functions approximate the transfer function of type (1) (the problem of reducing the order of systems). And for objects with distributed parameters, the “true” order is generally infinite.

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Attempts to “forcefully” bring such objects to the structure (1) may be the result of a problem with determining the coefficients of this structure (starting from the illconditioning of the corresponding system of algebraic equations, which has to be solved, and ending with “unacceptable” values of the coefficients, for example, when the clearly stable object can receive the denominator of its transfer function with roots in the right half-plane of the complex plane, etc.). When approximating curves by analytical dependencies, in particular, when smoothing them, the least squares method (LSM), which includes an element of smoothing, is widely used. We will use this feature of LSM to compensate for the impact of errors (including due to structure inconsistency) when solving the identification problem. Let us assume that the functions x(y) and y(t) are given by the arrays X,Y:CoefR of their ordinate of this structure -1 X Y

0

1

2

3

...

m

m

x0

x1

x2

x3

...

xm

-1

0

1

2

3

...

m

h

y0

y1

y2

y3

...

ym

Here type CoefR = array[-1.. Mmax] of real; h – time step, h = D/m; D - signal observation time x(t) and y(t); m – number of time steps. Let us take the following function as an identification quality index E0 =

m  2  (n) (n) an yi + . . . + a1 yi + yi − bn xi − . . . − b1 xi − b0 xi .

(3)

i=0

Here, the index i means that the corresponding function is defined at the point t = ih. Equating the derivatives of E 0 relative to the coefficients a1 , a2 ,…, an , b0 ,b1 ,…, bn , to zero, we obtain a system of equations, the solution of which will be the coefficients of structure (1). However, as it was noted above, x(t) and y(t) signals may have errors, including high-frequency errors. And this can dramatically worsen the accuracy of the derivatives determination present in formula (3), especially derivatives of high orders. The result will be a deterioration in the quality of identification [9]. The influence of high-frequency “noise” can be possibly weakened by k successive integrations (0 ≤ k ≤ n) of Eq. (2) over time t in the range from 0 to t. Then Eqs. (2) appear in the form n  z=1

az ez (t) +

n  z=0

bz fz (t) + g(t) = 0,

(4)

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where

⎧ ⎧ z−1 t t

z−1 t (k=z+s) ⎪ ⎪ ⎪ ⎪ ⎪ ... ydt k=z − y0 (k−z+s)! , 1 ≤ z ≤ k − 1, ⎪ ⎨ ⎪ ⎪ ⎪ s=0 0 0 ⎪ e = z (t) ⎪ k−1 ⎪

z−k+s t s ⎪ ⎪ ⎪ ⎪ y(z−k) − ⎪ y0 ⎪ ⎩ ⎪ s! , k ≤ z ≤ n, ⎪ ⎪ s=0 ⎧ ⎪ ⎨ z−1 t t

(s) t (k−z+s) ⎪ ⎪ ⎪ x0 (k−z+s) − ... xdt k−z , 0 ≤ z ≤ k − 1, ⎨ ⎪ ⎪ 0 0 ⎪ fz (t) = s=0 k−1 ⎪ ⎪

⎪ s ⎪ (z−k+s) ⎪ t (z−k) , k ≤ z ≤ n, ⎪ ⎪ x0 ⎪ ⎩ ⎪ s! − x ⎪ ⎪ s=0 ⎪ ⎪ ⎪ t t ⎪ ⎪ g(t) = ... ydt k . ⎩ 0

⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

0

Here, the notation is used y0(0) (0)

x0

 d s y  = = s dt t=0,  d s x  (s) = x|t=0 ; x0 = s  dt t=0. (s) y|t=0 ; y0

Let us take it as an identification quality index. E=

m  n n   [ az ez (ih) + bz fz (ih) + g(ih)]2 . i=0 z=1

The minimization conditions of E are as follows:  ∂E ∂as = 0, 1 ≤ s ≤ n, ∂E ∂bs = 0, 0 ≤ s ≤ n. Substituting the value of E from (5) into (6) and dividing by 2, we obtain:   ⎧ m  n n



⎪ ⎪ az ez (ih) + bz fz (ih) + g(ih) es (ih) = 0, 1 ≤ s ≤ n, ⎨ z=0 i=0 z=1   m n n



⎪ ⎪ az ez (ih) + bz fz (ih) − g(ih) fs (ih) = 0, 0 ≤ s ≤ n. ⎩ i=0

z=1

(5)

z=0

(6)

(7)

z=0

If the sought coefficients are placed in the following sequence a1 , a2 ,…, an , b0 , b b 2 ,…, b n , then the elements of the extended matrix C of the system (7) of linear algebraic equations can be calculated using the following formulas ⎧ m

⎪ ⎪ ez (ih)es (ih), 1 ≤ s ≤ n, ⎪ ⎪ ⎪ i=0 ⎪ ⎨

m Cz,s ez (ih) fs−n−1 (ih), n + 1 ≤ s ≤ 2n + 1, = (8) 1≤z≤n ⎪ i=0 ⎪ ⎪ m ⎪

⎪ ⎪ ez (ih)G(ih), s = 2n + 2. ⎩

1,

i=0

Mathematical Model of the Approximate Function

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

m

m

177

fz−n−1 (ih)es (ih), 1 ≤ s ≤ n,

i=0

Cz,s fz−n−1 (ih) fs−n−1 (ih), n + 1 ≤ s ≤ 2n + 1, = n + 1 ≤ z ≤ 2n + 1 ⎪ i=0 ⎪ ⎪ m ⎪

⎪ ⎪ fz−n−1 (ih)g(ih), s = 2n + 2. ⎩

(9)

i=0

After the C:Matr array is formed (type Matr = array[1..2*Nmax + 1, 1..2*Nmax + 2] of real), we call the SystUr [2] procedure as follows. SystUr(2*n + 1,C,A). Array A returns as. -1

0

1

2

..

n

n+1

n+2

..

2n+1

2n+1

~

a1

a2

..

an

b0

b1

..

bn

This array is split into two.

A

B

-1

0

1

2

...

n

n

1

a1

a2

...

an

-1

0

1

2

...

n

n

b0

b1

b2

...

bn

If necessary, the arrays A and B (especially B) can be edited, i.e., the contents of the cell with number -1 can be adjusted (downward) when higher coefficients by the modulus turn out to be lower than some predetermined small quantity ε [10, 11]. Let us arrange the described algorithm in the form of a WpXY procedure. At the same time, we will assume that the time step h is sufficiently small that the integration operation in the formulas for e(t), f(t), g(t) of Eq. (4) could be implemented using the trapezoidal formula, and differentiation in the same formulas - through left, right and central differences.

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3 Result and Discussion Mathematical modeling is performed to find out the influence of high-frequency “noise” errors by means of k successive integrations (0 ≤ k ≤ n) of Eq. (2) over time t within the range from 0 to t compensation. The Turbo Pascal program was used to obtain approximating functions. We denote the input signal as X(t) (Fig. 1), and the output signal as Y(t) (Fig. 2), t = 28 s, step h = 2 (Table 1). Table 1. Approximating functions X

Y

1,29

2,776

0

2,716

3,126

2

1,362

2,581

4

2,548

3,938

6

3,008

3,694

8

0,792

3,396

10

1,614

2,146

12

2,442

1,258

14

0,88

1,917

16

0,663

1,836

18

3,527

0,141

20

1,344

0,989

22

1,883

1,319

24

2,816

2,687

26

2,337

2,508

28

Fig. 1. Input signal

t

Mathematical Model of the Approximate Function

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Fig. 2. Output signal

The result of approximating linear function was presented on Fig. 3.

Fig. 3. Approximating linear function

The result of approximating cubic function was presented on Fig. 4.

Fig. 4. Approximating cubic function

In Fig. 3 shows the approximation using a linear function - a straight line. In Fig. 4 presents the approximation using a power function of the 3rd order.

4 Conclusion As a result was developed of feature of LSM to compensate for the impact of errors (including due to structure inconsistency) when solving the identification problem. The obtained results of mathematical modeling make it possible to state that with an increase in the degree of the function, the approximation of points is more accurate and takes on a form close to the input signal. Thus, it is possible to ensure a reduction (weakening), and in some cases, even leveling of the impact on the high-frequency error.

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References 1. Tan, C., Zhao, H., Ding, H.: Non-redundant inertial parameters determination for dynamic identification of branched articulated robots. Indus. Robot: Int. J. Robot. Res. App. 49(6), 1229–1241 (2022). https://doi.org/10.1108/IR-12-2021-0296 2. Hirono, K., A. Udugama, I., Hayashi, Y., Kino-Oka, M., Sugiyama, H.: A dynamic and probabilistic design space determination method for mesenchymal stem cell cultivation processes. Indust. Eng. Chem. Res. 61(20), 7009–7019 (2022). https://doi.org/10.1021/acs.iecr.2c00374 3. Korobiichuk, I., Bezvesilna, O., Tkachuk, A., Nowicki, M., Szewczyk, R.: Piezoelectric gravimeter of the aviation gravimetric system. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Challenges in Automation, Robotics and Measurement Techniques. AISC, vol. 440, pp. 753–761. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29357-8_65 4. Yefymenko, N.V., Lutsenko, N.V.: Angular motion control of spacecraft by vector measurements. J. Autom. Inf. Sci. 51(3), 36–47 (2019). https://doi.org/10.1615/JAutomatInfScien. v51.i3.40 5. Korobiichuk, I., Ladanyuk, A., Boiko, R., Hrybkov, S.: Features of control processes in organizational-technical (technological) systems of continuous type. J. Autom. Mob. Robot. Intell. Syst. 14(4), 11–17 (2020). https://doi.org/10.14313/JAMRIS/4-2020/39 6. Korobiichuk, I., Mel’nick, V., Kosova, V., Maksymenko, K.: Equations of disturbed motion of the moving part of the gyroscope suspension. Sensors 22(19), 7442 (2022). https://doi.org/ 10.3390/s22197442 7. Azimi, V., Farzan, S., Hutchinson, S.: A robust time-varying Riccati-based control for uncertain nonlinear dynamical systems. J. Dyn. Syst. Measur. Control 144(10), 101001 (2022). https://doi.org/10.1115/1.4054884 8. Yetisir, F., Poser, B.A., Grant, P.E., Adalsteinsson, E., Wald, L.L., Guerin, B.: Parallel transmission 2D RARE imaging at 7T with transmit field inhomogeneity mitigation and local SAR control. Magn. Reson. Imaging 93, 87–96 (2022). https://doi.org/10.1016/j.mri.2022.08.006 9. Pisarenko G.S., Boginich O.E.: Oscillations of kinematically excited mechanical systems considering energy dissipation. Institute for Problems of Strength of the National Academy of Sciences of Ukraine. Nauk. Kyiv, Dumka, 220 p. (1982) 10. Smith, M.K.B.: The Use of Solubility Parameters to Select Membrane Materials for pervaporation of Organic Mixtures. A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy, The University of Waikato: Hamilton, New Zealand (2006) 11. Kladun, O.A.: Nonlinear amplitude of the suspension under natural conditions. Bull. ZHTU. Techn. Sci. 3(42), 74–79 (2007)

Regression Analysis on the Values of the Specific Activity of 137 Cs in Radioactive Soil Contamination Igor Korobiichuk1(B) , Viktoriia Melnyk-Shamrai2 , Volodymyr Shamrai2 , and Valentyn Korobiichuk2 1 Łukasiewicz Research Network – Industrial Research Institute for Automation and

Measurements PIAP, Warsaw, Poland [email protected] 2 Zhytomyr Polytechnic State University, Zhytomyr, Ukraine [email protected]

Abstract. The publication analyzes the content of 137 Cs in the above-ground phytomass of representatives of the lingonberry family growing in wet subors in a radioactively contaminated area. It was established that the highest average values of the specific activity of 137 Cs were characteristic of Vaccinium myrtillus L., and the lowest values were characteristic of Vaccinium uliginosum L. A regression analysis was performed between the values of the specific activity of 137 Cs in representatives of the lingonberry family and the values of the density of radioactive soil contamination. The results indicate the existence of a close, directly proportional linear relationship between these indicators for all studied species - the values of the correlation coefficients (r) were 0.72–0.86, and the significance coefficients p = 0.00001, which indicates the high reliability of the connection at the 95% confidence level. The values of 137Cs concentration in the studied species have a close linear relationship with the density of radioactive soil contamination. Keywords: Radioactive contamination · Regression analysis · Specific activity ·

137 Cs · Accumulation coefficient · Transition coefficient

1 Introduction As a result of the accident at the Chernobyl nuclear power plant, the forests of Ukraine were exposed to intense radioactive contamination. According to the results of research conducted in 1991–1992, out of 3.2 million hectares of surveyed forest land in the State Forest Fund of Ukraine, 1.23 million hectares (39%) had a density of radioactive soil contamination of 137 Cs over 37 kBq/m2 . The territory of Polissia of Ukraine, where almost 40% of all forests of the state are concentrated, was the most affected by radioactive pollution [1, 2]. Before the Chernobyl accident, the forestry industry of Ukraine was characterized by the multi-purpose use of forest resources. The forests of Ukraine are rich in a large number of berry plants: blueberry (Vaccinium myrtillus L.), lingonberry © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 183–194, 2023. https://doi.org/10.1007/978-3-031-25844-2_17

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(Vaccinium vitis-idaea L.), bog blueberry (Vaccinium uliginosum L.), marsh cranberry (Oxycoccus palustris Pers), raspberry (Rúbus idáeus L.), blackberry (Rubus caesius L.), dogwood (Rubus saxatilis L.) and wild strawberry (Fragaria vesca L.). Blackberry, lingonberry, bog blueberry, bog cranberry and raspberry spread over large areas and create highly productive thickets. These species account for more than 90% of the harvest of all wild berries in Ukraine. The main areas of these berry species are concentrated in the northwestern part of Polissia of Ukraine: Zhytomyr region – 74.1 thousand ha, Rivne region – 89.2 thousand ha, and Volyn region – 54.7 thousand ha. Since the density of radioactive soil contamination in the northern part of Polissia was the maximum, harvesting of wild berries was prohibited on a significant part of the forest areas, and harvesting of wild berries was regulated on the other part. More than 30 years have passed since the accident at the Chernobyl nuclear power plant, the radiation situation has changed, but the main reservoir of radionuclides currently remains the forest soil, which continues to influence the pace and direction of their migration to other components of ecosystems and food chains to humans [3, 4]. Plants that form a grass-shrub cover are characterized by a relatively shallow location of the root system, so studying the features of 137 Cs entering the phytomass 30 years after surface precipitation is of great interest for understanding the behavior of radionuclides in forest ecosystems. Forest ecosystems are more complex than agricultural ecosystems, as they include a diverse number of plant communities that grow on different types of soil and in different environmental conditions. All this leads to a high degree of variability in the distribution of radioactive elements in various components of forest vegetation. It has been established [5, 6] that grass-shrub plants play an important role in the accumulation and redistribution of radionuclides in forest ecosystems. In addition, a wide range of 137 Cs and 90 Sr radioactive contamination of different plant species within the same ecotope was found [1]. The works [7] analyzed radioactive 137 Cs contamination of the ground phytomass of plants of pine plantations under different types of forest vegetation conditions. Publications [2, 8, 9] note that fluctuations in the specific activity of radionuclides in different types of vegetation depend on: systematic position, life form, location of the root system, composition and physical and chemical properties of radioactive fallout, form and route of arrival of radioactive elements to the ecosystem, soil characteristics (type, richness, moisture and acidity of the soil, granulometric and mineralogical composition of the soil). The study of specific characteristics of the intensity of 137 Cs accumulation from the soil to representatives of the grass-shrub cover is the basis for evaluating the possibility of targeted economic use of their various species in conditions of radioactive contamination. For each phytocenosis, the interspecies differences in the average values of the 137 Cs transition coefficient vary widely and are specific. For example, in green-moss pine forests [10], the plants of the grass-shrub cover can be arranged in the following order according to the decreasing coefficient of transition: ferns (Pteridophyta) – Rannikovi family (Scrophulariaceae) Meadow sedge (Melampyrum pratense L.) – Buckwheat (Polygonaceae) Sorrel (Rumex) – Cowberry (Vacciniaceae) Blueberry, Cowberry (Vaccinium myrtillus L., V. vitis-idaea L.) – St. John’s wort (Hypericaceae) – Asteraceae – Liliaceae – Stinging nettle (Lamiaceae) – Roses (Rosaceae)) Wild strawberries (Fragaria vesca L.) – Poaceae – Pears (Pyrolaceae), and in blueberry

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pine forests: ferns (Pteridophyta) – Ericaceae – Lingonberry (Vacciniaceae) – Morning glory (Scrophulariaceae) – Primulaceae – Lilies (Liliaceae) - Roses (Rosaceae). Analyzing the intensity of 137 Cs accumulation by the berry species of the grassshrub cover, the scientists came to the general conclusion that among the berry species, the shrubs of the lingonberry family (Vacciniaceae) are characterized by the maximum intensity of radionuclide accumulation [10, 11]. The researchers reported the average values of the transition coefficient of 137 Cs in the leaves of the species of the given families in the conditions of blueberry pine: Blueberry (Vaccinium myrtillus L.) (66) > Cranberry (V. vitis-idaea L.) (52) > Bog blueberry (V. Uliginosum L.) (39), and in the swamp pine: Bog blueberry (Vaccinium uliginosum L.) (207) > Blueberry (V. Myrtillus L.) (157). It was found out [12] that blueberry shoots have significantly higher values of specific radionuclide activity than berries, this is explained by the gradual accumulation of 137 Cs in the shoots over several years, as well as the biological features of the plant. Many representatives of the grass-shrub cover belong to medicinal plants, therefore, harvesting of wild medicinal raw materials is carried out in almost all types of forest vegetation conditions. The first publications on the radioactive contamination of medicinal plants contained information only on the values of the specific activity of 137 Cs in the studied samples [13]. The most widely presented studies on the study of the features and intensity of 137 Cs accumulation by medicinal plants (raw materials) by Ukrainian researchers [12, 14–16]. According to scientists, the content of 137 Cs depends on the type of plant, trophicity and moisture of the soil, the density of radioactive contamination of the soil, weather conditions and growing seasons. According to the intensity of 137 Cs accumulation, different types of medicinal plants growing in close to optimal types of forest vegetation conditions were divided into five groups. The first group is very strong accumulators, the value of the coefficient exceeds 100, the second group is strong accumulators, the coefficient varies from 50 to 100, medium - 10–50, weak 1–10 and very weak - less than 1. The scientists made the following conclusions regarding the radioactive contamination of representatives of the grass-shrub cover: the highest content of 137 Cs was noted in fern-like plants, and the lowest in higher flowering plants; in one type of forest vegetation conditions, representatives of one family accumulate 137 Cs in different ways; the transition coefficient of 137 Cs depends on the type of forest soil, the location of the root system in the soil profile; a 5–6-fold difference in the minimum and maximum values of the transition coefficient of 137 Cs into the above-ground phytomass of plants was noted for the same edatope; in hygromorphic landscapes, the accumulation of 137 Cs is 1–2 orders of magnitude higher compared to automorphic ones [2, 10, 17–19]. In recent years, the occurrence of fires in forest massifs in radioactively contaminated territories is an increasingly frequent phenomenon, so researchers are conducting various assessments of the impact of fires on vegetation [20] and assessing the risks of possible redischarge of radionuclides from forest fires beyond the boundaries of forest massifs [21]. In addition, the publication [22] considers the possibility of using certain types of vascular plants as test objects for bioindicative analysis of radioactive contamination. A review of the literature shows that the study of radioactive contamination of the grass-shrub layer of forest ecosystems is different, some issues have been ignored by researchers, others have been studied fragmentarily, and some require more in-depth research. In addition, a

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significant part of the publications was written based on the results of research conducted in the first years after the accident. Therefore, the study of radioactive contamination of above-ground phytomass of representatives of the lingonberry family in the pine forests of Ukrainian Polissia is relevant for assessing the possible use of non-wood forest products and for the introduction of radionuclides to humans through food chains.

2 Research Materials and Methods The research was carried out on permanent sampling areas (PSA No. 1–3) laid out in the Narodychy forestry of the State Enterprise “ Narodytske Specialized Forestry”. To determine the level of radioactive contamination of berry species of the lingonberry family, the following plant species were studied: blueberry (Vaccinium myrtillus L.), lingonberry (Vaccinium vitis-idaea L.) and bog blueberry (Vaccinium uliginosum L.). Permanent test areas (100 × 100 m in size) were laid according to the standard method (Table 1). According to the results of the conducted phytoindicative analysis, which is based on the composition of the grass-shrub cover, soil conditions, and species of indicator plants, it was established that the studied plant species grow in wet forests. The research is based on the classical method of comparative forest ecology with its detailing by individual radioecological directions. Table 1. Characteristics of permanent sampling areas Indicators

PSA No. 1

PSA No. 2

PSA No. 3

Quarter/division

10/6

10/7

10/27

Type of forest vegetation conditions

Wet subors (B3)

Age, years

90

70

105

Composition of plantations

10 Ps

10 Ps

10 Ps

Average height, m

27

24

26

Average diameter, cm

36

28

38

Forest quality class

1

1

1

Growth

Lonely

Undergrowth

Clearly expressed

Projective coverage of the grass-shrub layer, %

85–90

80–85

80–85

Projective cover of the moss layer, %

80–85

85–90

75–85

Soil

Sod-medium podzolic sandy

Association

Pine forest with buckthorn-bilberry-green moss

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To characterize the permanent sampling areas, a complete species description was carried out according to the grass-shrub and moss cover with the determination of the dominant plant species [23]. The assessment of the projective cover of above-ground vegetation on each sampling area was carried out using a Ramensky grid (1 m x 1 m), in 25 repetitions in a checkerboard pattern. Samples were selected according to generally accepted methods in radioecology. To assess the content of radionuclides in the components of the grass-shrub cover (by species), the aerial phytomass of plants was selected in 3–5 repetitions [14, 24]. According to the phytomass of the selected topsoil samples, soil samples were taken using a cylindrical drill with a diameter of 57 mm at 5 points (envelope method) to a depth of 15 cm. Preparation of samples for spectrometric analyzes included the following phases: drying to an air-dry state, grinding and homogenization, filling vessels and weighing them. The specific activity of 137 Cs in soil and plant samples was measured in the radiological laboratory of the Zhytomyr Polytechnic State University using the GDM-20 scintillation spectrometry system. Data processing was carried out using system software (WinDAS, M). All samples were measured under identical conditions, the relative error of the specific activity of 137 Cs in the samples did not exceed 10%. Statistical processing of the obtained results was carried out according to generally accepted statistical methods in Microsoft Excel and Statistica 10.0 application programs. One-factor variance analysis was used to assess the significance of the difference in mean values. Correlation-regression analysis was used to establish the relationship between the studied parameters.

3 Results and Discussion A certain variation in the density of radioactive soil contamination was established on each test area. Thus, at PSA No. 1, the average value of this indicator was 263 ± 57 kBq/m2 , which is 1.7 times more than the minimum (148 kBq/m2 ) and 1.5 times less than the maximum value (389 kBq/m2 ). A similar situation was observed at other test areas: at PSA No. 2, the density of radioactive soil contamination ranged from 150 to 410 kBq/m2 (the average value was 284 ± 69 kBq/m2 ); at PSA No. 3, the average density of radioactive soil contamination was 273 ± 63 kBq/m2 , and the fluctuations ranged from 155 to 440 kBq/m2 . When analyzing the obtained values of the density of radioactive soil contamination, special attention was paid to the coefficient of variation (V), which characterizes the fluctuation (variability) of the levels of 137 Cs contamination of the soil, and the coefficient of significance (p), which determines the assessment of the degree of confidence in the truth of the results. Thus, the coefficient of variation on all test plots ranged from 21.5 to 24.4%, which indicates the average variability of the obtained results. The coefficient of significance (p) did not exceed 2.5%, and was 2.0% for PSA No. 1, 2.4% for PSA No. 2, and 1.7% for PSA No. 3. The absence of a reliable difference between the average values of the density of radioactive soil contamination on permanent test plots (PSA No. 1, 2, 3) is confirmed by the results of one-factor variance analysis - Ffact. = 2.8 < F(2;409;0.95) = 3.0.

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The regularities of radioactive contamination of the above-ground phytomass of plants of the grass-shrub cover were studied in the wet subors of the Ukrainian Polissia using the example of the following species of the lingonberry family: blueberries, lingonberries, and bog blueberries. These species are the most typical representatives of the grass-shrub cover of humid subors, and occupy large areas and are highly productive. A comparative analysis of the distribution of the specific activity of 137 Cs in the bushes of the lingonberry family was carried out, on the basis of which the following patterns can be noted: the lowest content of 137 Cs was noted in bog blueberries on all test plots, and blueberries are characterized by significantly higher values of the studied indicator than lingonberries (Fig. 1). Thus, at PSA No. 1, the content of 137 Cs in blueberries is 19362 ± 599 Bq/kg, which is 1.5 and 1.8 times more than in the above-ground phytomass of lingonberries and bog blueberries, the reliability of the results is confirmed by one-factor variance analysis Ffact. = 33.9 > F(1;54;0.95) = 4.0 and Ffact. = 25.0 > F(1;45;0.95) = 4.1, respectively, and bog blueberries accumulate 1.2 times less compared to lingonberries (Ffact. = 5.2 > F(1;18;0.95) = 4.4). During the analysis of the average values of the specific activity of 137 Cs at PSA No. 2, it was established that it accumulates almost equally in the aboveground phytomass of blueberry and lingonberry (Ffact. = 0.4 < F(1;41;0.95) = 4.1), and the excess of the studied indicator over the phytomass of the bog blueberries in blueberries is 1.7 times (Ffact. = 47.7 > F(1;44;0.95) = 4.1), and in lingonberries – 1.8 times (Ffact. = 259.0 > F(1;20;0.95) = 4.1). At PSA No. 3, the content of 137 Cs in lingonberries and bog blueberries was almost the same, this is confirmed by Fisher’s test at the 95% confidence level - Ffact. = 3.5 < F(1;32;0.95) = 4.1. The specific activity of 137 Cs in blueberries was 1.2 times higher compared to lingonberries, and 1.4 times higher than in bog blueberries (Ffact. = 6.8 > F(1;83;0.95) = 3.9 and Ffact. = 7.5 > F(1;96;0.95) = 3.9). In all test areas, with sufficient uniformity of the density of radioactive soil contamination, the accumulation coefficients of 137 Cs in the above-ground phytomass of representatives of the lingonberry family varied widely - from 0.8 to 22.9, the maximum values of the accumulation coefficient were characteristic of blueberries, and the minimum values were characteristic of bog blueberries (Fig. 2). For example, at PSA No. 1, PSA No. 2, and PSA No. 3, the coefficient of accumulation of radionuclide in the phytomass of bog blueberries is 2.2, 2.0, and 1.3 times lower compared to the above-ground phytomass of blueberries, respectively, according to the test areas. As for the lingonberry phytomass, the intensity of radionuclides input is 1.5 and 2.4 times higher than for the phytomass of bog blueberries on the PSA No. 1 and PSA No. 2, and on the PSA No. 3 there is no difference between the studied indicator. On PSA No. 1 and PSA No. 2, the above-ground phytomass of lingonberry is characterized by 1.5- and 1.3-times lower values of the accumulation coefficient compared to blueberries, and on PSA No. 2 the opposite dependence was established, here the phytomass of blueberries absorbs 1.2 times less. When comparing the coefficient of accumulation of 137 Cs in the above-ground phytomass of plants of the lingonberry family, according to the results of one-factor variance analysis, it was established that there is or is not a reliable difference in the average values of the intensity of accumulation between all species, where Ftheor. > Fpractice and Ftheor. < Fpractice . We also constructed a ranked series of the studied species according to the 137 Cs accumulation coefficient (in order of its decrease): blueberries > lingonberries > bog blueberries.

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Fig. 1. The average values of the specific activity of 137 Cs in representatives of the lingonberry family, that grow in wet subors forests of the Ukrainian Polissia, Bk/kg

Fig. 2. Average values of the accumulation coefficient of 137 Cs in representatives of the lingonberry family in wet subors

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The transition coefficient of 137 Cs in the “soil - above-ground phytomass” system for the studied species was calculated on all test plots (Fig. 3). The distribution of lingonberry plants by the coefficient of transition of 137 Cs into above-ground phytomass corresponds to the distribution by the accumulation coefficient. The coefficient of transition of 137 Cs into the above-ground phytomass of bog blueberries at PSA No. 1 is 2.0 and 1.5 times lower compared to the studied indicator for blueberries and lingonberries, respectively (Ffact. = 15.02 > F(1;55;0.95) = 4.02 and Ffact. = 104.8 > F(1;28;0.95) = 4.2). At PSA No. 2, similar regularities were observed regarding the values of the transition coefficient as at PSA No. 1. Thus, lingonberry and blueberry are characterized by a 2.0and 1.8-times excess of the transition coefficient compared to bog blueberries (Ffact. = 40.67 > F(1;20;0.95) = 4.38 and Ffact. = 39.70 > F(1;44;0.95) = 4.06). No difference in the average values of the transition coefficient was found between lingonberry and blueberry at the PSA No. 1 and PSA No. 2 - Ffact. = 3.79 < F(1;54;0.95) = 4.02 and Ffact. = 1.69 < F(1;41;0.95) = 4.08, respectively. On the basis of the dispersion analysis, it can be stated that there is no significant difference between the analyzed types for the values of the transition coefficient on PSA No. 3 - Ffact. = 1.48 < F(1;106;0.95) = 3.08. However, here the blueberry is characterized by the highest indicator of the transition coefficient and is 62.6 m2 •kg−1 •103 , while for lingonberry and bog blueberries the analyzed indicator is 1.2 and 1.4 times less, respectively. The analysis of radioactive contamination of above-ground phytomass of representatives of the lingonberry family in wet forests makes it possible to construct a number of species according to the intensity of the 137 Cs transition: blueberry > lingonberry > bog blueberries.

Fig. 3. Average values of the transition coefficient of 137 Cs in representatives of the lingonberry family in wet subors

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Within the entire data set, a regression analysis was performed between the values of the specific activity of 137 Cs in representatives of the lingonberry family and the values of the density of radioactive soil contamination. The results indicate the existence of a close, directly proportional linear relationship between these indicators for all studied species - the values of the correlation coefficients (r) were 0.72–0.86, and the significance coefficients p = 0.00001, which indicates the high reliability of the connection at the 95% confidence level (Figs. 4, 5, and 6).

Fig. 4. Dependence of the specific activity of 137 Cs in lingonberry phytomass on the density of radioactive soil contamination

Using the results of the regression analysis, it is possible to calculate the expected content of 137 Cs at certain values of the density of radioactive soil contamination. On the basis of the obtained regression equations, it is possible to make a decision regarding the procurement of one or another raw material from representatives of the lingonberry family, taking into account the maximum permissible levels (DGN-2008). Thus, the harvesting of bog blueberry as a medicinal raw material is possible when the density of radioactive contamination of the soil is less than 80 kBq/m2 , and the harvesting of lingonberries and blueberries in wet subors should be prohibited.

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Fig. 5. Dependence of the specific activity of 137 Cs in blueberry phytomass on the density of radioactive soil contamination

Fig. 6. Dependence of the specific activity of 137 Cs in the phytomass of bog blueberry on the density of radioactive soil contamination

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4 Conclusions It was established that the maximum content of 137 Cs in wet subors is observed in the above-ground phytomass of blueberries (19362 Bq/kg), and the minimum - in the bog blueberries (6166 Bq/kg). In the forests of the Ukrainian Polissia under conditions of wet subors, the indicators of the intensity of 137 Cs influx into the above-ground phytomass of representatives of the lingonberry family varied widely: the accumulation coefficient – from 0.8 to 22.9, the transition coefficient – 19–180 m2 ·kg−1 ·10–3 . It was established that the specific activity of 137 Cs in representatives of the lingonberry family of the wet subors has a reliable (p = 0.00001), close (r = 0.72–0.86) directly proportional linear relationship with the density of radioactive soil contamination. It is advisable to prohibit the harvesting of representatives of the lingonberry family as medicinal raw materials. It is only possible to harvest bog blueberries in territories where the density of radioactive soil contamination will not exceed 80 kBq/m2 .

References 1. Krasnov, V.P.: Radioecology of the forests of Polissia of Ukraine. Zhytomyr, Volyn (1998) 2. Krasnov, V.P., Orlov, A.A., Buzun, V.A., Landin, V.P., Shelest, Z.M.: Applied Radioecology of Forest. Zhytomyr, “Polissya” Publishers (2007) 3. Korobiichuk, I., et al.: Synthesis of optimal robust regulator for food processing facilities. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Automation 2017. AISC, vol. 550, pp. 58–66. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54042-9_5 4. Korobiichuk, I., Lysenko, V., Opryshko, O., Komarchyk, D., Pasichnyk, N., Ju´s, A.: Crop monitoring for nitrogen nutrition level by digital camera. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Automation 2018. AISC, vol. 743, pp. 595–603. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77179-3_56 5. Korobiichuk, I., Davydova, I., Korobiichuk, V., Shlapak, V., Panasiuk, A.: Measurement of qualitative characteristics of different types of wood waste in the forestries Zhytomyr Polissya. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Automation 2021: Recent Achievements in Automation, Robotics and Measurement Techniques. AISC, vol. 1390, pp. 297–308. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-74893-7_28 6. Tsvetnova, O.B., Shcheglov, A.I.: The role of vegetation cover in regulation of fluxes of the technogenic radionuclides at the different stages after radioactive fallout. Radiats. Biol. Radioecol. 49(2), 158–165 (2009) 7. Melnyk, V.V.: 137Cs distribution peculiarities in forest bio-geocenosis components of Ukrainian Polissia fresh woods. Bull. Poltava State Agrarian Acad. 2, 88–98 (2020). https:// doi.org/10.31210/visnyk2020.02.11 8. Nadtochii, P.P., Malinovskyi, A.S., Mozhar, A.O., et al.: Experience of overcoming the consequences of the Chernobyl disaster, Kyiv, The world (2003) 9. Tsvetnova, O.B., Shcheglov, A.I.: Radionuclides in the grass-shrub layer of forest biogeocenoses. Radiat. biology, Radioecol. 39(4), 462–467 (1999) 10. Ermakova, O.O.: Radioecological monitoring of 137Cs accumulation in living ground cover plants in forest cenoses. Radioactivity in Nuclear Explosions and Accidents 2000: International Conference 24–26 April 2000, Moscow, Proceedings. T. 2., St. Petersburg, Gidrometeoizdat, pp. 13–18 (2000)

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11. Kuzmich, O.T.: The content of 90Sr and 137Cs in the above-ground organs of plants of the lingonberry family. IV congress on radiation research November 20–24, 2001, abstract report vol II (sections VI-IX B), Russian University of Friendship of Peoples, p 653 (2001) 12. Boyko, O.L.: Dynamics of 137Cs content in berry and medicinal plants of forests of Ukrainian Polissya according with year. Sci. Bull. NLTU Ukraine,. 22(06), 16–20 (2012). http://nbuv. gov.ua/UJRN/nvnltu_2012_22.6_5 13. Dmitriev, S.V., Fetisov, A.A., Pertsev, V.A., et al.: Contamination of wild medicinal plants with cesium-137. Hygiene Sanit. 12, 51–53 (1991) 14. Kaletnyk, M.M., Krasnov, V.P., Savuschyk, M.P.: Recommendations for forest management in conditions of radioactive contamination, Kyiv, Derzhkomlishosp (1998) 15. Krasnov, V.P., Orlov, O.O., Irklienko, S.P. et al.: Peculiarities of cesium-137 accumulation by medicinal plants Vacciniaceae S.F. Gray and Ericaceae Juss. on Ukrainian Polissia, Ukrainian Botan. J. 52(4), pp 472–478 (1995) 16. Oplov, O.O., Kpasnovl, V.P., Ipklienkol, S.P., et al.: The study of radioactive pollution of the Likapskiy forests of the Ukrainian Polissia, Problems of forest ecology and forestry in Ukraine. Sci. Members Polish ALNDS, Zhytomyr 3, 48–54 (1996) 17. Fesenko, S.V., Soukhova, N.V., Sanzarova, N.I., et al.: 137Cs availability for soil to understory transfer in different types of forest ecosystems. Sci. Total Environ. 269, 87–103 (2001) 18. Krasnov, V.P., Kurbet, T.V., Korbut, M.B., Boyko, O.L.: 137Cs allocation in forest ecosystems of Ukrainian Polissya. Agroecological Journal 1, 82–87 (2016) 19. Orlov, O.O.: Forest ecosystems: analytical review. Problems of forest ecology and forest use in Ukraine, Zhytomyr, Volyn, Ruta. 5(11), 18–32 (2005) 20. Landin, V., Tishchenko, O., Gurelia, V., Kuchma, T., Feshchenko, V.: Impact of forest fire on the vegetable cover of radioactively contaminated areas. Agroecol. J. 1, 68–80 (2021). https:// doi.org/10.33730/2077-4893.1.2021.227241 21. Ager, A.A., et al.: The wildfire problem in areas contaminated by the Chernobyl disaster. Sci. Total Environ. 696, 133954 (2019). https://doi.org/10.1016/j.scitotenv.2019.133954 22. Pavlenko, A.P.: Bioindication of 137Cs forest ecosystem pollution by using test objects. Agroecol. J. 0(1), 19–27 (2020). https://doi.org/10.33730/2077-4893.1.2020.201265 23. Krasnov, V.P., Orlov, O.O., Vedmid, M.M.: Atlas of indicator plants and types of forest vegetation conditions of the Ukrainian Polissia, Monograph, Novohrad-Volynskyi (2009) 24. SOU 74.14-37-425:2006. Method of soil sampling for radiation control. Soil quality. Ministry of Agrarian Policy of Ukraine, Kyiv (2006)

Quasi-Digital Measuring System for Mechanical Quantities Igor Korobiichuk1(B) , Dmytro Ornatskyi2 , Mariia Kataieva2 , and Dmytro Shcherbyna2 1 Łukasiewicz Research Network – Industrial Research Institute for Automation and

Measurements PIAP, Warsaw, Poland [email protected] 2 National Aviation University, Kyiv, Ukraine {dmytro.ornatskyi,mariia.kataieva, shcherbyna.dmytro}@npp.nau.edu.ua

Abstract. The article proposes a quasi-digital measuring system for mechanical quantities and gives the results of modeling measuring transducers for working with piezoresistive strain gauges and differential capacitive sensors based on quadratic voltage-to-frequency converters (VFC) whose informative parameter is the frequency of the output quasi-harmonic signal. A comparison with the characteristics of frequency converters based on integrating sweep converters is given. To reduce the random component error caused by internal and external noises, a precision wideband system of phase auto-adjustment of frequency (PAAF) was developed, the peculiarity of which is that an iterative integrating converter is used as a smoothing element of the pulsation at the output of the two-semiperiod synchronous detector (TSD), the output voltage of the integrator is fed to the input of the controlled generator. A VFC with pulse feedback is used as a controlled generator. All this ensures a significant reduction of phase noise caused not only by synchronous, but also by asynchronous broadband interference, characteristic of cable communication lines (20 µV/m). Keywords: Quasi-digital measuring system · Measurement of mechanical quantities · System of phase auto-adjustment of frequency · Error reduction

1 Introduction Typically, measurement systems use 2 types of signal processing systems: digital, where signal processing takes place using transformations such as Fourier, Hilbert, etc. But these methods impose rather strict requirements on the speed of analog converters and the performance of microprocessor systems. Therefore, there is another method of building measurement systems in which pre-processing of analog signals is performed before their quantization, including nonlinear filtering, these are so-called quasi-digital systems [1–5].

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 195–203, 2023. https://doi.org/10.1007/978-3-031-25844-2_18

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The main part of the trends in the development of measuring transducers (MT) is related to the improvement of their sensitive elements (primary transducers) [6]. At the same time, the main tasks requiring solutions include: increasing the stability of sensitive elements by reducing their random and systematic errors [7]; expansion of measurement boundaries; cost reduction due to simplification of the general installation and, in particular, of electrical connections [8–12]. Capacitive, piezoresistive, and resistor VPs remain among the promising types of VPs. In the presence of highly stable sensitive VP elements, the following problems must be solved [12–14]: 1. To standardize VP by characteristics when using accurate normalization of their errors using Table Electronic Data Sheet (TEDS); 2. Increasing the reliability of MT and their resistance to external destabilizing factors with the establishment of specific requirements for resistance to these factors, for example, to the effects of electromagnetic radiation; 3. Development of the electronic part of the VP to ensure more accurate and comprehensive processing of signals of sensitive elements thanks to the latest electronic means. At the same time, single-crystal microcomputers with self-monitoring and internal diagnostics systems based on artificial intelligence and neural networks can be used. Connecting devices of such VPs should ensure their connection to Feldbus-type digital networks; 4. Improvement of interactive systems of interaction of the operator with electronic units of the MT, providing wider possibilities of operation and convenience of maintenance; 5. Implementation of electronic circuits of VP on special custom integrated circuits or in the form of integrated structures together with sensitive elements on the same silicon chips containing both digital and analog signal processing devices. One of the promising ways to solve these problems is the use of frequency integrating scaling converters (FSC). For example, [15] considers an example of the implementation of a universal CHIRP module for working with tensor-resistive bridge sensors and differential capacitive sensors. The disadvantages of such a solution include low sensitivity, especially when working with capacitive differential sensors, as well as the influence of dynamic errors of the integrator, which deteriorates metrological characteristics in the high-frequency range [16]. To eliminate the above-mentioned shortcomings, measuring converters were developed for working with differential-capacitive sensors and with bridge strain gauges based on quadratic voltage-frequency converters (QVFC).

2 Materials and Methods Figure 1 shows the functional diagram of the measuring converter of the unbalance of the tension bridge to the frequency.

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The main ratios for this scheme are: UA UA , i2 = , Rs (1 + δ) Rs (1 − δ) UA UA i  = i2 − i1 = − Rs (1 − δ) Rs (1 + δ) Rs (1 + δ) − Rs (1 − δ) UA   = UA · 2δ = 2 2 Rs Rs 1 − δ

i1 =

(1)

where δ – is the relative change in the resistance of the strain gauge under the influence of the measured value; is the nominal resistance of the strain gauge; Rs – nominal resistance of the load cell; UA – is a voltage at the adder input.

Fig. 1. Functional scheme of the measuring converter of the tension bridge imbalance to frequency based on the QVFC

At the same time, the UB voltage at the output of the adder will be equal to UB = −i · R5 = −UA

R5 · 2δ. Rs

(2)

That is, with a positive change in the upper tension resistor, the voltage UB will have the opposite phase to the voltage, UA which will lead to a decrease in the output frequency of the converter. That is, with the opposite sign of δ the voltages UA and UB will be in phase, which will lead to an increase in the output frequency fout . When R1 = R3 an increase in sensitivity can be achieved by reducing the resistor R4 and increasing the resistor R5 . The results of modeling the transformation function for the strain-resistive sensor are shown in Fig. 2. During simulation, the following values were obtained: at δ = −1%, the output frequency of the converter was 3.881 kHz, at δ = +1%, the output frequency of the

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Fig. 2. Results of simulation of the transformation function for the strain-resistive sensor

converter was 1.511 kHz, the center frequency at δ = 0 is 2.727 kHz, which corresponds to the maximum relative frequency change about 50%. Polynomials of the transformation function from the first to the third order for the strain-resistive sensor are shown in Table 1. Table 1. Polynomials of the transformation function for a strain-resistive sensor 1

First-order polynomial transformation functions y = a0 + a1 · x The value of the coefficients

a0 = 2.7099091 a1 = −1.1874545

Sum of Squares of Deviation 2

0.0013044

Transform functions of the second-order polynomial y = a0 + a1 · x + a2 · x2 The value of the coefficients

a0 = 2.17202587 a1 = −1.1874545 a2 = −0.0258741

Sum of squares of deviation 3

0.0003854

Third-order polynomial transformation functions y = a0 + a1 · x + a2 · x2 + a3 · x3 The value of the coefficients

a0 = 2.7202587 a1 = −1.1993143 a2 = −0.258741 a3 = 0.16657

Sum of squares of deviation

0.0037225

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Errors for the tensor-resistive sensor are given in Table 2. Table 2. Value of errors for strain gauge The additive error is shown

0.7%

The multiplicative is given

0.2%

The root-mean-square value of the random reduced error

≈0.5%

The functional measurement diagram of the converter for working with differential capacitive sensors is shown in Fig. 3.

Fig. 3. Functional measurement diagram of the converter for working with differential capacitive sensors

i1 =

dUA dUA · cs (1 − δ), i2 = · cs (1 + δ), dt dt

A at R5 = R6 => UB = −R7 (i2 − i1 ) = −R7 · dU dt · cs · 2δ, if ωc1 3  R7 , then UB – triangular voltage anti-phase UA . At the same time, when R1 = R3  R4 , the output frequency of UA will be directly proportional to δ.

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3 Result and Discussion As a result of the simulation, the following results were obtained, presented in Fig. 4.

Fig. 4. Results of simulation of the transformation function for a differential-capacitive sensor

The polynomial transformation functions from the first to the third order for the capacitive sensor are shown in Table 3. Table 3. Polynomial transformation functions for a capacitive sensor 1

First-order polynomial transformation functions y = a0 + a1 · x

The value of the coefficients

a0 = 24.1155455 a1 = 5.5669545

Sum of squares of deviation 2

0.0063099

Transform functions of the second-order polynomial y = a0 + a1 · x + a2 · x2

The value of the coefficients

a0 = 24.1323403 a1 = 5.5669545 a2 = −0.0419872

Sum of squares of deviation 3

0.0038898

Third-order polynomial transformation functions y = a0 + a1 · x + a2 · x2 + a3 · x3

The value of the coefficients

a0 = 24.1323403 a1 = 5.5815977 a2 = −0.0419872 a3 = −0.0205662

Sum of squares of deviation

0.0037225

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Errors for the capacitive sensor are listed in Table 4. Table 4. Value of errors for a capacitive sensor The additive error is shown

0.1%

The multiplicative is given

0.17%

The root mean square value of the random reduced error

≈0.2%

In order to reduce the random error component, a biased broadband PAAF system was developed, the functional scheme of which is presented in Fig. 5. The circuit contains a two-half-period synchronous (TSD) detector, at the input of which a triangular-shaped input signal from measuring transducers is received. A feature of the circuit is that an iterative integrating converter is used as a ripple smoothing element at the output of the TSD, the output voltage of the integrator is fed to the input of the controlled generator.

Fig. 5. Functional scheme of the pre-emptive broadband PLL system

A VFC with pulse feedback is used as a controlled generator. All this ensures a significant reduction of phase noise caused not only by synchronous, but also by asynchronous broadband interference, characteristic of cable communication lines (20 µV/m).

4 Conclusion Due to the combination of primary and secondary measuring transducers on one chip and the use of new measuring transducers for working with piezoresistive strain gauges and differential-capacitive sensors, based on quadratic voltage-to-frequency converters (VFC) whose informative parameter is the frequency of the output quasi-harmonic signal and the protected frequency demodulator based on the original PLL system and the

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latest methods of error correction with TEDS managed to improve the metrological characteristics of existing frequency converters, by the very front, sensitivity - more than an order of magnitude, immunity, which makes it possible to increase the accuracy of nano- and micro-positioning.

References 1. Hedayatipour, A., Haque, M., McFarlane, N.: Quasi-digital output low Pawer CMOS Temperature Sensor. In: International Midwest Symposium on Circuits and Systems, p. 995 (2014) 2. Sanga, R., et al.: Deployment of quasi-digital sensor for high temperature molten salt level measurement in pyroprocessing plants. Rev. Sci. Instrum. 89(4), 045007 (2018). https://doi. org/10.1063/1.5012803 3. Shen, K., Shakhtarin, B.I., Neusypin, K.A., Samokhvalov, A.A.: Synthesis of quasi-optimal digital phase-locking systems under the action of additive noises. J. Commun. Technol. Electron. 62(8), 868–873 (2017). https://doi.org/10.1134/S1064226917080113 4. Li, D., et al.: A Quasi-digital QPSK modulator design for biomedical devices. ACM J. Emerg. Technol. Comput. Syst. 18(2), 1–16 (2022). https://doi.org/10.1145/3465379 5. Aiassa, S., et al.: Quasi-digital biosensor-interface for a portable pen to monitor anaesthetics delivery. In: 2019 15th Conference on Ph.D. Research in Microelectronics and Electronics (PRIME), Lausanne, Switzerland, 15–18 July 2019, [S. l.] (2019). https://doi.org/10.1109/ prime.2019.8787764 6. Korobiichuk, I. Analysis of errors of piezoelectric sensors used in weapon stabilizers. Metrol. Meas. Syst. 24(1), 91–100 (2017). https://doi.org/10.1515/mms-2017-0001 7. Korobiichuk, I., Bezvesilna, O., Tkachuk, A., Chilchenko, T., Nowicki, M., Szewczyk, R.: Design of piezoelectric gravimeter for automated aviation gravimetric system. J. Automat. Mob. Robot. Intell. Syst. 10(1), 43–47 (2016). https://doi.org/10.14313/JAMRIS_1-2016/6 8. Yang, X., Chen, M., Jia, Z.: Analysis and design of a self-oscillating quasi-digital fluxgate current sensor for DC current measurement. Rev. Sci. Instrum. 92(2), 025001 (2021). https:// doi.org/10.1063/5.0030868 9. Korobiichuk, I.: Mathematical model of precision sensor for an automatic weapons stabilizer system. Measurement 89, 151–158 (2016). https://doi.org/10.1016/j.measurement.2016. 04.017 10. Sanga, R., et al.: Deployment of an inductance-based quasi-digital sensor to detect metallic wear debris in lubricant oil of rotating machinery. Measure. Sci. Technol. 29(7) (2018) 11. Korobiichuk, I., Bezvesilna, O., Kachniarz, M., Koshovyj, M., Kvasnikov, V.: Methods and ways of piezoelectric accelerometers fastening on the objects of research. Acta Phys. Pol. A 133(4), 1112–1115 (2018). https://doi.org/10.12693/APhysPolA.133.1112 12. Sanga, R., Sivaramakrishna, M., Prabhakara, G.: Deployment of the inductance-based quasi digital sensor and instrument to monitor the metallic liquid level. Int. J. Instrum. Technol. 3, 19–29 (2022) 13. Korobiichuk, I., Bezvesilna, O., Tkachuk, A., Nowicki, M., Szewczyk, R.: Piezoelectric gravimeter of the aviation gravimetric system. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) Challenges in Automation, Robotics and Measurement Techniques. AISC, vol. 440, pp. 753–761. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29357-8_65 14. Cao, D., Liu, S., Jiang, C.: Maximum energy transfer conditions in parametric amplification of current-output fluxgate sensors. Sens. Actuators A 173(1), 136–140 (2012). https://doi. org/10.1016/j.sna.2011.11.010

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15. Bardin V.A., et al.: Module and its integration with nano-and microelectromechanical systems of sensors and actuators. Nano- i Mikrosistemnaya Tehnika 19(2), 93–104 (2017). https:// doi.org/10.17587/nmst.19.93-104 16. Ornats’kiy, D.P.: Pulse repetition frequency multiplier, Patent 470920 USSR: H 03k 13/20, No. 1969153/2621; D10/26/1973; publ. May 15, 1975, Bull. No. 18, 3 p.

Hyperspectral Imaging System for Food Safety Inspection Berenika Linowska(B) and Piotr Garbacz Łukasiewicz Research Network – Institute for Sustainable Technologies, Radom, Poland {berenika.linowska,piotr.garbacz}@lukasiewicz.gov.pl

Abstract. The paper presents the analysis of the capability of developing a hyperspectral imaging system for on-line detection of foreign bodies in food products. In the first part of the article, based on literature review authors briefly introduce unique features of hyperspectral technology and its potential use in industrial inspection systems. For the purposes of material identification tests the experimental station was developed. In the final part of the article, on the basis of conducted research a concept of on-line inspection system is proposed. Keywords: Hyperspectral imaging · Food inspection · Food safety

1 Introduction Hyperspectral imaging (HSI), thanks to its unique features, is increasingly used in various areas of science and industry, such as: geology, ecology, agriculture, medicine, cartography, forensics, art history, food and pharmaceutical manufacturing [1]. HSI systems enable the registration of several hundred images in various bands of the electromagnetic spectrum. Spectral signatures are recorded for each pixel in the image of the observed surface, showing the relationship between the light reflectance and the wavelength. As a result, a three-dimensional data structures (hyperspectral cubes) are obtained, which can be analyzed both in the spatial (x, y) and spectral (λ) domains [2]. Examples of recorded hyperspectral images and the spectral signature for a selected point in space are shown in Fig. 1. Hyperspectral technology has so far been used mainly in laboratories and off-line analysis systems. However, due to the development in hyperspectral sensing technologies, it is increasingly used in on-line quality inspection on production lines. One of the most demanding areas is the food industry. The food industry manufacturers are obligated to address number of standards to be met during the production process. Food safety is a set of necessary conditions and actions that must be taken during all stages of the food production process in order to ensure the health and life of future consumers. In order to meet all these requirements, entrepreneurs are looking for the best and most effective technological solutions.

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Fig. 1. Green leaf a) hyperspectral images, b) spectral signature for a selected point in space [3]

Hyperspectral imaging, due to its unique capabilities enables reliable quality inspection of demanding production processes. Among others it can be applied to inspect the freshness of food products, detect foreign bodies as well as to inspect the packaging process (Fig. 2).

Fig. 2. HSI examples in food safety a) meat inspection [4], b) packaging inspection [4]

Based on the literature review, it can be stated that hyperspectral imaging technology is used more and more often when conducting material identification. Nevertheless, it still requires the development of advanced solutions in the field of lighting as well as image processing and analysis algorithms.

2 Laboratory Experimental Setup and Results The main objective of the conducted research was to check the applicability of the HSI method for the selected application. An experimental setup was developed in order to validate the capabilities of identifying different types of material. Figure 3 shows the test stand that has been equipped with hyperspectral camera, halogen illuminator, LED illuminator, linear drive and a touch panel. The system enables movement of the test sample with precise control of the range and speed. The Hyperspec® MV.X VNIR linear hyperspectral camera from Headwall was used for the tests (Fig. 4a). The sensor records one pixel line at a time, while the second spatial dimension is obtained by moving the camera’s field of view in a specific direction (Fig. 4b). Cameras of this type are the most common systems in industrial sectors due to their high spectral resolution and reduced data capture time.

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Fig. 3. Hyperspectral imaging stand: 1 - hyperspectral camera, 2 - LED illuminator, 3 - linear drive, 4 - halogen illuminator, 5 - touch panel

Fig. 4. a) Hyperspec® MV.X VNIR hyperspectral camera [5], b) The principle of operation of a linear hyperspectral camera [6].

The research was conducted with use of the Metaphase LED illuminator (Fig. 5a) which covers the range of visible light and near-infrared light (Fig. 5b). This device uses the Mix-LED technology, which is characterized by increased efficiency, extended life of the light source and the ability to adapt to specific requirements [7].

Fig. 5. a) Metaphase LED illuminator [8], b) spectral characteristics [8]

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To evaluate the proposed system in a typical application tests have been carried out to detect foreign bodies (plastic) in meat (Fig. 6). The sample material was selected in such a way as to be of the closest color to other parts of the tested object, i.e., bones or membranes of meat. Various types of meat were used for the tests, such as: chicken, beef and pork.

Fig. 6. Test meat sample a) beef sample photo, b) classified image after analysis, c) spectral characteristics of materials: background (blue), package (pink), bone (yellow), plastic (navy blue), membranes (green), meat (red)

The analysis of the recorded data was performed with the use of the perClass Mira software [8], which enables, among others, pixel classification, objects segmentation and classification. A machine learning pipeline used in Mira requires manual labeling of the classes. Based on training data a statistical model is created automatically and each pixel is assigned to the predefined classes. In the proposed solution raw spectral frame from a line-scan camera is processed with used of created model. Then per-pixel decisions are read out and a 2D classified image is created by accumulating consecutively incoming data. Next the classified image is processed with use of morphological filters and segmented based on grayscale values corresponding to the predefined classes. On the basis of the obtained data, it can be concluded that with the use of the presented system it is possible to detect foreign bodies. Significant differences can be seen in the spectral characteristics of the analyzed materials (Fig. 6c). Thus, it is possible

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to identify objects of the similar color (Fig. 6b), which in many cases can’t be achieved with classical monochrome or RGB imaging systems [10]. The main limitations of the developed test stand are low power of the illuminator used and lack of trigger input in the used camera. The illuminator used in the test doesn’t allow setting short exposure time during the acquisition process, which is required in typical industrial applications. Another issue is that Headwall MV.X camera only allows for free-run acquisition mode so tracking position of detected foreign objects is not straightforward.

3 Development of On-line Inspection System Based on the results of the experiment it was decided to develop custom made halogen illuminator for the prototype version of the system. In order to determine the uniformity of light simulations were performed in the Dialux software [9]. Due to the fact that the selected camera is linear, the light uniformity was analyzed on a narrow surface with dimensions of 0.05 × 0.50 m (Fig. 7). The working distance between the illuminator and the tested surface was 0.5 m. Based on the simulation performed, the suitable distance between the bulbs was selected.

Fig. 7. Light intensity distribution on the analyzed surface (isolines)

The designed halogen illuminator is a modular solution (Fig. 8 a). One unit can connect to the appropriate number of consecutive units depending on the needs regarding the width of analyzed area (Fig. 8 b). A single module consists of four halogen bulbs with a narrow beam angle of 10˚ and the power of 50 W.

Fig. 8. Designed halogen illuminator a) model b) prototype units

Due to the need to accurately track the analyzed objects in the prototype version of the system, it was desirable to use an imaging system with synchronization input. The selected camera was a Specim FX10 [4] with spectral range from 400 to 1000 nm.

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The proposed inspection system (Fig. 9) consists of hyperspectral cameras with lens and halogen illuminator. Image processing and analysis is done with use of industrial computer equipped with Intel Octa-Core 3.00 GHz CPU. The status of inspection of every scanned line is sent to the PLC with unique ID which allows tracking of anomalies and controlling the ejector.

Fig. 9. Prototype of inspection system during the tests.

During the experiment an industrial transporter was used that allows movement of the samples. Based on the recorded scans a per-pixel classifier model was built for detecting foreign objects in meat articles. Next, the model was uploaded into run-time application implemented in Adaptive Vision Studio [10]. Based on the tests, it was found that the time required for processing single hypercube is less than 3 ms and required exposure time of camera to avoid blurring effect [11] and ensure high signal to noise ratio is 2 ms. Thus, assuming a frequency of camera trigger 300 Hz and scanning resolution of 2 mm/pulse, the maximum allowed speed of sample movement for proposed system configuration is up to 0.6 m/s. The effectiveness of the developed system was checked on the basis of tests in working conditions similar to those on the production line. The conducted tests were done with use of beef and chicken meat and four plastic samples of foreign objects differing in color and size (Table 1). During the test plastic objects of different color and size were placed at various locations on meat surface. Every plastic sample was placed on two types of meat (Fig. 10a, b) and passed through inspection system 25 times, which made a total of 200 tries.

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Parameter

Sample 1

Sample 2

Sample 3

Sample 4

Object color

Red

White

Red

White

Object size [mm2 ]

300

300

50

50

Fig. 10. Detection test of plastic objects: a) sample 1 (beef) photo b) sample 2 (chicken) photo c) classified image of sample 1 d) classified image of sample 2

Every sample that consists foreign object has been detected on the classified images (Fig. 10c, d) and there were no false-positive results. The detection efficiency of the system shows that it can be used in the food industry to increase the level of security.

4 Conclusions Ensuring compliance with food safety and quality standards is crucial to maintaining the high level of trust that consumers have in food manufacturers presently. Hyperspectral technology can be of benefit to the manufacturing sector through capability of identifying materials based on their spectral signature. The purpose of this research was to develop an efficient hyperspectral vision system for detection of foreign objects in food directly on production line. In order to test the proposed method under simulating working condition a prototype inspection system was developed. Mass production of food requires inspection systems characterized by the appropriate speed. Although the hyperspectral camera sensors and new generation processing units are capable to meet the requirements of high-speed inspection, there is an issue with lack of suitable lighting devices. The halogen illumination technology is characterized with broad spectrum and high intensity. However due to different types of inspection application requiring diverse width of imaging area there is a need for custom design to guarantee illumination uniformity. The proposed inspection system consists of modular lightning unit that can be extended to meet the production line requirements. The main drawbacks of halogen technology are low life expectancy

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and emitted heat which may prevent their use in the inspection of sensitive products. For this reason, it is planned to use other solutions, such as high-power mix-LED illuminators in future tests. The presented method is characterized by the high detection efficiency of foreign objects. As it has been shown it can be applied in most demanding application like meat articles inspection. Future work will be focused on adapting the developed solution to the requirements for devices used in the food industry [13] and machine learning model performance optimization. Tests carried out under real conditions will allow the verification of the proposed method over a long period of time.

References 1. Nalepa, J.: Recent advances in multi- and hyperspectral image analysis. Sensors 21(18), 6002 (2021). https://doi.org/10.3390/s21186002 2. Chang, C.I.: Hyperspectral Imaging: Techniques for Spectral Detection and Classification. Springer, New York (2003) 3. Mishra P.: Close range hyperspectral imaging of plants: a review. Biosyst. Eng. 164, 49–67 (2017) 4. Specim. https://www.specim.fi 5. Headwall - Hyperspec® MV.X. https://www.headwallphotonics.com/ 6. Winston, W.Y.: Multiplexed optical imaging of tumor-directed nanoparticles: a review of imaging systems and approaches. Nanotheranostics 1(4), 369–388 (2017) 7. Prophotonix: Illumination in Multispectral & Hyperspectral Imaging. https://www.propho tonix.com 8. Metaphase: Manufacturer of LED hyperspectral illuminators. https://www.metaphase-tech. com 9. PerClass Mira Software. https://www.perclass.com 10. Taghizadeh, M.: Comparison of hyperspectral imaging with conventional RGB imaging for quality evaluation of Agaricus bisporus mushrooms. Biosys. Eng. 108(2), 191–194 (2011) 11. Dialux: lighting design software. https://www.dialux.com 12. Adaptive Vision Studio. https://adaptive-vision.com 13. Cyberoptics Semiconductor: High Speed, Real-Time Machine Vision (2019). http://www.ima genation.com/pdf/highspeed.pdf 14. Meghwal, M.: Good manufacturing practices for food processing industries: purposes, principles and practical applications, Chapter 1002 P22 (15) (2016)

Principal Components Method in Control Charts Analysis Yevhen Volodarskyi1 , Oleh Kozyr1 , and Zygmunt Lech Warsza2(B) 1 Department of Information and Measuring Technologies, Igor Sikorsky Kyiv Polytechnic

Institute, Kyiv, Ukraine [email protected], [email protected] 2 Łukasiewicz Research Network - Industrial Research Institute of Automation and Measurements, Warszawa, Poland [email protected]

Abstract. Shewhart control charts are successfully used to control a multiparameter technological process, provided there is no correlation between controlled parameters. In this case, the space of dispersion of allowable values of the resulting vector x components is a hyper-parallelepiped with pairs of opposite sides corresponding to the upper and lower allowable deviations of measured process parameters. If there is a correlation between these parameters, the real area of acceptable scattering is a hyper-ellipsoid, axes of which are inclined with respect to the axes of the hyper-parallelepiped. In this case, the use of Shewhart charts leads to methodological erroneous decisions. Another control tool in the presence of correlation is the Hotelling chart, which can be successfully used to assess the quality of a multidimensional process. However, it should be noted that the Hotelling criterion itself allows assessing the state of the process as a whole, without highlighting the cause of its disorder. The Hotelling chart does not show which indicator directly (or the combined influence of indicators) is associated with a process violation. It is possible to radically solve the problem of controlling a multidimensional process by the use of principal components method. This method is based on applying a linear transformation of the resulting vector, which makes it possible to proceed to an independent analysis for each component without distorting the original relation of correlated data. In addition, the principal component method projects a multidimensional resulting vector into the space of components of a lower dimension. Most often, as practice has shown, the variation of the resulting vector can be explained by only two or three components. This allows to build control charts. The article describes in detail the method of constructing control charts based on principal components. Evaluation of the effectiveness of the application of the method is carried out on simulated data, which are close to the measurement results obtained during the control of a real technological process. The results show that the proposed method is effective for controlling a multi-parameter technological process in the presence of a correlated parameters. Keywords: Control of a multi-parametric technological process · Shewhart control charts · The principal components method

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 212–222, 2023. https://doi.org/10.1007/978-3-031-25844-2_20

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1 Introduction The concept of quality assurance was based initially on the identification of nonconformities and their elimination by correcting them, or, in extreme cases, by disposing of the product. For many years it was the only, although quite expensive way to ensure the quality of production of various types of products. The disadvantage of this approach is that its tasks did not include studying the features of the production process and preventing online situations leading to inconsistencies. The objective of this approach is to fix the discrepancy of the product, and if it occurs, to separate it from the good product, and to prevent nonconforming products from entering the further stages of the production process [1]. Such an approach can be called quality management for each individual unit of production, since in order to improve quality assurance, it is necessary to check each unit of production, i.e., make total control. The need to improve the economic performance of the production process and reduce production costs led to the emergence of new ideas. In 1924, the American engineer and mathematician Walter Shewhart, later a well-known consultant and specialist in the field of quality management, proposed the idea of process control in order to prevent inconsistencies [2]. To do this, he developed a fairly simple tool based on the methods of probability theory and mathematical statistics, which made it possible to maintain the process in a statistically stable state and thereby prevent the appearance of inconsistencies. Such a tool, called Shewhart control charts, gave birth to a new concept of quality assurance. This concept assumes that the quality of products is created during the course of the production process, and not as a result of control their results, when it is always too late to correct them. In this sense, it is always too late to control, since the identified discrepancy is an event that has already occurred and cannot be prevented. But it is possible to prevent the onset of nonconformity if the preventive control of the characteristics of the process is carried out. Statistical methods for analyzing the accuracy and stability of characteristics that are used to control technological processes, are regulated by special documents. In the case, when process control can be provided by one indicator of product quality only, the use of Shewhart control charts [1] is very promising and effective. However, in many cases, product quality is characterized by several indicators, which, in most cases, are correlated. Then, independent control on individual indicators can lead to erroneous decisions about the disorder (or vice versa) of the technological process. If several parameters of the process have to be controlled simultaneously, the Shewhart control charts can be successfully used only in the case, if these parameters are not correlated. For the set of Shewhart control charts of the mean value (x- charts) the based on the over- significance level α i in the calculation for each indicator is determined  all significance level α 0 for the characteristic resulting vector X x1 , x2 , . . . , xi , . . . , xp [1]. If there is no information about the significance of each of the components of X, then all coefficients α i are equal and are defined as α = α0 /n. The upper and lower control limits for the i-th parameter of the technological process are determined from the relationships: – for the upper border: UCLi = μ0i + z|1− α | σi 2

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– for the lower border: LCLi = μ0i − z|1− α | σi 2

where: μ0i and σ i - are the average value and the standard deviation respectively, which are determined based on the results of preliminary studies or specified in regulatory documents. In this case, the scattering region of acceptable values of the resulting vector xi will be limited by a hyper-parallelepiped with opposite sides corresponding to difference of limits UCL i - LCL i . To test the hypothesis H0 : μ = μ0 in the one-dimensional case for a data sample of size n with a known variance of the general population, the following statistics are used z=

x − μ0 √ σ/ n

When considering a multidimensional random variable, if we raise the left and right parts of the expression to the second degree, we get the expression: z2 = n(x − μ0 )2 (σ )−1 Which can be represented in matrix form as: T 2H = n(X − μ0 )T  −1 (X − μ0 ) The resulting expression is a generalized Hotelling characteristic (T 2 Hotelling statistics). It is used in assessing the quality of a multi-parameter technological process in the presence of a correlation of its indicators [2]. With a known covariance matrix Σ, the Hotelling statistic has a chi-square distribution. In this case, during statistical control of a multi-parameter object, the position of the controlled boundary at a given significance level α is determined directly from the table of chi-square distribution quantiles, i.e.: 2 = χ2(1−α)p Tkp

It should be noted that the Hotelling criterion itself allows assessing the state of the process as a whole, without highlighting the cause of its disorder. The Hotelling map does not show which indicator directly (or the combined influence of indicators) is associated with a process violation. To test the hypothesis that the i-th indicator is the reason for the disorder of the process, its individual Hotelling criterion is used [3, 4]. However, when an influencing indicator is identified, it may turn out that neither the first nor the second of them are the cause of the process disruption. The reason is the combined effect of these indicators. This may be the reason for the restrictions on the use of Hotelling control charts. The problem of controlling a multidimensional process in the presence of a correlation of parameters can be solved by using the method of principal components in the construction of control charts [5]. This method is based on applying a linear transformation of the resulting vector, which makes it possible to proceed to an independent analysis for each component without distorting the original correlation data field [6].

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2 Theory of Principal Component Method The principal component (PC) method is the multivariate linear transformation of a set of correlated factors into a set of orthogonal components. The purpose of this operation is to extract the basic (main) components that contribute to the greatest extent to the initial dispersion of the controlled data, that is to create the area of their dispersion with the highest possible accuracy. The components-parameters that make the greatest contribution to this dispersion space of process parameters are sequentially distinguished. As a rule, the number of such components is two or three, which makes it possible to use the PC method in the construction of control charts, as the simplest and most illustrative tool in the study of process variability.   Suppose there is a multidimensional system of p factors X x1 , x2 , . . . , xi , . . . , xp in the form of a matrix ⎛ ⎞ x1,1 x1,2 . . . x1,i . . . x1,p ⎜x ⎟ ⎜ 2,1 x2,2 . . . x2,i . . . x2,p ⎟ ⎜ . .. . . ⎟ ⎜ . ⎟ . . . . .. . . . .. ⎟ ⎜ . (1) X=⎜ ⎟ ⎜ xj,1 xj,2 . . . xj,i . . . xj,p ⎟ ⎜ ⎟ .. . . ⎟ ⎜ .. ⎝ . . . . . .. . . . .. ⎠ xm,1 xm,2 . . . xm,i . . . xm,p  T where: each factor is a sample of m average elements xi xi1 , xi2 , . . . , xij , . . . , xim from n observations drawn from a normal population with means a0 a1 , a2 , . . . , ai , . . . , ap and covariance matrix: ⎛ ⎞ σ12 ρ12 σ 1 σ2 . . . ρ1i σ1 σi . . . ρ1p σ1 σp ⎜ρ σ σ 2 . . . ρ2i σi . . . ρ2p σ2 σp ⎟ ⎜ 12 2 1 σ2 ⎟ ⎜ ⎟ .. .. .. .. ⎜ ⎟ . . ... . ... . ⎜ ⎟ (2) =⎜ ⎟ 2 ⎜ ρ1i σi σ1 ρ2i σi σ2 . . . σi . . . ρip σi σp ⎟ ⎜ ⎟ .. .. .. .. ⎜ ⎟ ⎝ ⎠ . . ... . ... . ρ1p σp σ1 ρ2p σp σ2 . . . ρip σp σi . . . σp2 where: σi2 is the variance of the factor xi ; ρ ip - correlation coefficient between factors xi , xp . If there is a correlation between the initial values, to ensure the possibility of independent monitoring of each of them, it is necessary to transform the matrix (1) of the input values so that the new variables (column vectors) included in the transformed matrix are pairwise orthogonal. At the same time, information about the dispersion of input values should be as close as possible to the original dispersion. With this formulation, the task is to find the matrix of principal components F by multiplying the matrix X of input parameters by the matrix of transformation coefficients V, i.e., by performing its linear transformation: F =X·V The matrix V is orthonormal.

(3)

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The essence of the linear transformation of the original system of features, which leads to the PC, we will consider in its geometric interpretation on two factors. Sup T pose we have a two-dimensional observing system x1 x11 , x12 , . . . , x1j , . . . , x1m and  T x2 x21 , x22 , . . . , x2j , . . . , x2m extracted from a normal population with mean values a0 (a1 , a2 ) and a covariance matrix:

 σ12 ρσ1 σ2 = , ρ| < 1, σ 1 > 0, σ 2 > 0| ρσ1 σ2 σ22 Geometrically, this means that the points x 1i and x 2i (i = [1 … n]) will be located approximately in the outline of an ellipse like on Fig. 1.

Fig. 1. Geometric interpretation of the PC

Therefore, to study the influence of the characteristics of the parameters x1 and x2 , it is convenient to pass to new coordinates f 1 and f 2 using transformations: f 1 = (x1 − a1 )cosα + (x2 − a2 )sinα f 2 = −(x1 − a1 )sinα + (x2 − a2 )cosα where: tgα =

2ρσ1 σ2 , σ12 −σ22

(it is assumed that σ 1 2 > σ 2 2 ).

To determine the transformation matrix, we will proceed from the need to provide independent control/monitoring of the parameters xi . This can be achieved when the covariance matrix (2) is diagonal - all elements of the matrix, except those on the main diagonal, are equal to zero. To diagonalize the matrix  and the matrix of transformation coefficients V is determined. Using the method of spectral decomposition of real, positive, symmetric matrices [7], we represent the diagonalizable covariance matrix (2) as a product of three matrices:  = V ·  · VT

(4)

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where: Λ is a diagonal matrix with an eigenvalue of the matrix on its main diagonal. Any non-zero vector v is called an eigenvector of the covariance matrix (2) if a number λ is found such that the equality holds: v = λv

(5)

This number λ is called an eigenvalue (the eigenvalue of the matrix), based on which the eigenvector is found. Based on above, the diagonal matrix Λ can be written as: ⎛ ⎞ λ1 0 . . . 0 . . . 0 ⎜ 0 λ ... 0 ... 0 ⎟ ⎜ ⎟ 2 ⎜ . . .. .. ⎟ ⎜ . . ⎟ ⎜ . . ... . ... . ⎟ =⎜ ⎟ ⎜ 0 0 . . . λi . . . 0 ⎟ ⎜ . . . . ⎟ ⎜ . . ⎟ ⎝ . . . . . .. . . . .. ⎠ 0 0 . . . 0 . . . λp We multiply the matrix Eq. (4) by V on the right and obtain:  · V = V · V T · V

(6)

Since for an orthonormal matrix the transformed matrix V T and the inverse matrix V are equivalent expressions, we have that V T ·V = I. Here I is the identity matrix, in which the elements on the main diagonal are equal to one, and all the rest are zeros. Then expression (6) will be written as: –1

V = V ··I

(7)

Based on (7) to get PC matrix (3) the eigenvalues and eigenvectors have to be found. If during a linear transformation (deformation) of a matrix there exists a vector that does not change direction, then it is an eigenvector of the transformation. Any vector parallel to an eigenvector will also be an eigenvector. There will be an infinite number of such vectors. The task is to find a vector such that the dispersion in this direction is maximum. Since the variables x1 , x2 , . . . , xi , . . . , xp can have different physical nature and vary in different ranges, to formalize further analysis, it is necessary to consider a normalized centered value: yi =

xi − ai σi

Then, Eq. (3) can be rewritten as: F =Y ·V

(8)

To find the matrix of transformation coefficients V, we will proceed, considering the relation (5), from expression (7). Let’s transform it to the form: ( − λI)v = 0

(9)

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To find the eigenvalues of matrix (2), we use expression (9). Since the eigenvector v is not equal to zero, we will further consider the equation: | −λI| = 0

(10)

The solution of Eq. (10) will make it possible to set the weights for the indicator components in determining f 1 the first principal component. The eigenvalues of matrix (2) can be found from the equation of the determinant of expression (10). Considering that the identity matrix I is diagonal, we find the determinant from which we obtain the characteristic equation: ⎡ ⎤ σ12 − λ ρ12 σ1 σ2 . . . ρ1i σ1 σi . . . ρ1p σ1 σp ⎢ρ σ σ σ2 − λ ... ρ σ σ ... ρ σ σ ⎥ 2i 2 i 2p 2 p ⎥ ⎢ 12 2 1 2 ⎢ ⎥ .. .. .. .. ⎢ ⎥ . . ... . ... . ⎢ ⎥ ⎢ ⎥= λp + bp−1 λp−1 + · · · + b1 λ + b0 ⎢ ρ1i σi σ1 ρ2i σi σ2 . . . σi2 − λ . . . ρip σi σp ⎥ ⎢ ⎥ .. .. .. .. ⎢ ⎥ ⎣ ⎦ . . ... . ... . 2 ρ1p σp σ1 ρ2p σp σ2 . . . ρip σp σi . . . σp − λ (11) Matrix Eq. (11) describes a system of linear homogeneous equations. Which has an infinite number of solutions. In this regard, we first find an intermediate vector ui . Let us take the values of the element of this vector with the same indices equal to uii = 1. Then the matrix Eq. (10) for the eigenvalue λi can be represented as ⎛ ⎞⎛ ⎞ ⎛ ⎞ σ12 − λi ρ12 σ1 σ2 . . . ρ1i σ1 σi . . . ρ1p σ1 σp ui1 0 ⎜ ρ σ σ σ 2 − λ . . . ρ σ σ . . . ρ σ σ ⎟⎜ u ⎟ ⎜ 0 ⎟ i 2i 2 i 2p 2 p ⎟⎜ i2 ⎟ ⎜ ⎟ ⎜ 12 2 1 2 ⎜ ⎟⎜ . ⎟ ⎜ . ⎟ .. .. .. .. ⎜ ⎟⎜ . ⎟ ⎜ . ⎟ . . ... . ... . ⎜ ⎟⎜ . ⎟ ⎜ . ⎟ (11a) ⎜ ⎟⎜ ⎟ = ⎜ ⎟ ⎜ ρ1i σi σ1 ρ2i σi σ2 . . . σi2 − λi . . . ρip σi σp ⎟⎜ 1 ⎟ ⎜ 0 ⎟ ⎟ ⎜ ⎜ ⎜ ⎟ ⎟ .. .. .. .. ⎜ ⎟⎜ .. ⎟ ⎜ .. ⎟ ⎝ ⎠⎝ . ⎠ ⎝ . ⎠ . . ... . ... . 2 ρ1p σp σ1 ρ2p σp σ 2 . . . ρip σp σ i . . . σp − λi 0 uip The obtained matrix equation corresponds to a system of equations with p − 1 number of unknown ui .  2  σ1 − λi ui1 + ρ12 σ1 σ2ui2 + · · · + ρ1p σ1 σp uip = −ρ1i σ1 σi ρ12 σ2 σ1 ui1 + σ22 − λi ui2 + · · · + ρ2p σ2 σp uip = −ρ2i σ2 σi .. . . = ..   (12) = − σ2 − λ ρ σ σ u + ρ σ σ u + ··· + ρ σ σ u .. .

i1 i 1 i1

i2 i 2 i2

ip i p ip

. = ..

i

i

  ρ1p σp σ1 ui1 + ρ2p σp σ2 ui2 + · · · + σp2 − λi uip = −ρip σp σi

We use p − 1 first equations of system (11) to find the unknown elements of the vector ui . To learn the i-th eigenvector vi , the vector ui must be normalized. The orthonormality

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of the matrix V means that each column vector of the matrix V has unit length, i.e., vTi vi = 1. From a geometric point of view, the diagonalization of the covariance matrix (2) is a non-uniform scaling - in each direction, the stretching, in general, occurs with a different scaling. Therefore, it is necessary to normalize the resulting vector ui using the equation: vi = 

ui

(13)

uTi ui

Using expressions (11–13) we find eigenvectors for all eigenvalues λ1 > λ2 > … > λp . As a result, we obtain the matrix V, which will allow to calculate the PC matrix (8).

3 Numerical Example Assessing the positive effect of using control charts on principal components, we consider a numerical example. Suppose two defining indicators x1 i x2 , are set, on which the quality of the implementation of the technological process depends. When studying the course of the technological process under normal conditions, all of them (external and internal) were reproduced within the specified/established norms. For these indicators were found: the average values a1 = 5 and a2 = 44, the root-mean-square deviations were σ 1 = 0,39 and σ 2 = 0,88, and the correlation coefficient ρ = 0.7. Then a sample of twenty control points for each indicator will be generate using the normal distribution N(a, σ ) with the addition of values modeled the discord of the process. At each i-th control point (i = [1, …, 20]) five measurements were carried out. The found average values of indicators characterizing the quality of the tested process are presented in Fig. 2.

Fig. 2. Average values of process quality indicators

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Based on the available data (Fig. 2), we construct Shewhart carts for which central lines CL 1 = 5 and CL 2 = 44 are chosen. The overall level of significance in this construction is α = 0.005. At the same time, the significance level for calculating the control lines for each of carts was α 1 = α 2 = 0.0025. For the indicator x1 , the upper control line UCL 1 = 6.52 and the lower control line LCL 1 = 5.48 were determined, and for the second indicator x2 these values are UCL 2 = 45.18 and LCL 2 = 42.82. The results of obtained for control charts are shown in Fig. 3.

Fig. 3. Shewhart control charts on initial data

Based on the same data, we construct control charts for the principal components f 1 and f 2 . After substitute values: σ 12 = 0.1521, σ 22 = 0.7744, ρσ 1 σ 2 = 0.2402 into expression (2) the covariance matrix is obtain:

 0.1521 0.2402 = . (14) 0.2402 0.7744 To find the eigenvalues, we use expression (10). Considering that the identity matrix I is diagonal, we obtain the determinant of the matrix Σ and characteristic equation. From this equation equal to zero, we obtain the eigenvalues of the matrix (14), ie., λ1 = 0.8563 and λ2 = 0.0701, each of which corresponds to an eigenvector. Let us determine the eigenvectors of matrix (14) for the found eigenvalues λ1 and λ2 . Matrix Eq. (11) for this example will take the following form:   

ui1 0 0.1521 − λi 0.2402 = (15) ui2 0.2402 0.7744 − λi 0

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Substituting into (15) the eigenvalues λ1 and λ2 , we obtain the corresponding system of equations, as in (12). Solving which we find intermediate vectors u1 and u2 . Using the normalizing Eq. (13), we obtain the eigenvectors v1 i v2 , which form the matrix of transformation coefficients V:

 0.3229 −0.9464 V= 0.9464 0.3229 Using the matrix of normalized-centered input values, based on Eq. (8), we determine the coordinates of the initial data in the plane of the principal components. Figure 4 shows the points characterizing the change in the process on control charts using principal components.

Fig. 4. Control charts using principal components

As can be seen from Fig. 4, the second main component at the 6th , 13th and 16th points crosses the lower control limit, the excess of which is evidence of the disorder of the process. It follows from the analysis carried out that there were three disruptions in the technological process. If these deviations do not lead to a critical situation, then their consistent identification can serve as a tool for correcting the technological process, since they are repetitive. If any output is critical, then the results of the sixth checkpoint can be used to stop the process. The use of Shewhart control charts states that the tested technological process proceeds within the normal range.

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4 Conclusions Shewhart charts are widely used in the control of single-parameter technological processes. However, when controlling two or more parametric processes, due to the presence of a correlation between quality indicators, their use in most cases gives a false result (both detection and non-detection of process disorder). A reliable result in such case can be obtain by the use of multi-parameter criteria, one example of which is the use of Hotelling control charts. In most cases, they allow at the first stage to identify the presence of a process disorder, and if there is such, at the second stage, by applying a particular criterion, to identify the "behavior" of each of the components. However, Hotelling maps may not always show which indicator directly (or the combined influence of indicators) is associated with a process violation. The problem of estimating the separate independent influence of the components can be solved by using the method of principal components in the control charts. In addition, with a large number of parameters affecting the course of the technological process, the method of principal components allows you to evaluate the course of the process by two or three parameters. This makes it easy to build control charts. All this testifies to the prospects of using the main components in the construction of control charts.

References 1. Joint Committee for Guides in Metrology: Evaluation of Measurement Data—the Role of Measurement Uncertainty in Conformity Assessment, JCGM 106:2012:2012 BIPM, Sèvres. https://www.bipm.org/documents/20126/2071204/JCGM_106_2012_E.pdf/ fe9537d2-e7d7-e146-5abb-2649c3450b25 2. Shewhart, W A: The application of statistics as an aid in maintaining quality of a manufactured product., J. Am. Stat. Assoc. 20(152), 546–548 (1925). 110.1080/01621459.1925.10502930 3. Volodarsky, E., Warsza, Z.L., Kosheva, l., Dobrolyubova, M.: Zastosowanie kart kontrolnych Hotellinga w kontroli jako´sci wieloparametrowego procesu technologicznego. (Application of Hotelling control charts for the quality control of multiparameter technological process) Przemysł Chemiczny 4. 579–583 (2018). https://doi.org/10.15199/62.2018.4.1312 4. Bersimis, S., Psarakis, S., Panaretos, J.: Multivariate statistical process control charts: an overview. Qual. Reliab. Engng. Int. 23(5), 517–543 (2007). https://doi.org/10.1002/qre.829 5. Montgomery, D.C.: Introduction to Statistical Quality Control, 3rd edn. John Wiley & Sons, New York (1996) 6. Jackson, J.E., Mudholkar, G.S.: Control procedures for residuals associated with principal component analysis. Technometrics 21(3), 341–349 (1979). https://doi.org/10.1080/00401706. 1979.10489779 7. Strang, G.: Eigenvalues and eigenvectors. In: Introduction to Linear Algebra, 5th edn, Wellesley-Cambridge Press, ch 6, pp. 283–297 (2016), ISBN:978-09802327-7-6. https://math. mit.edu/~gs/linearalgebra/ila0601.pdf 8. Volodarsky, E., Warsza, Z., Kosheva, L.A., Id´zkowski, A.: Precautionary statistical criteria in the monitoring quality of technological process. In: Szewczyk, R., Kaliczy´nska, M. (eds.) SCIT 2016. AISC, vol. 543, pp. 740–750. Springer, Cham (2017). https://doi.org/10.1007/9783-319-48923-0_80 9. Volodarsky, Y., Pototskiy, I., Warsza, Z.L.: The Use of CUSUM-Charts for Identification the Technological Process Disorder at the Initial Stage. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) AUTOMATION 2020. AISC, vol. 1140, pp. 147–156. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-40971-5_14

Polynomial Maximization Method for Estimation Parameters of Asymmetric Non-Gaussian Moving Average Models Serhii Zabolotnii1 , Oleksandr Tkachenko2 , and Zygmunt Lech Warsza3(B) 1 Cherkasy State Business College, Cherkasy, Ukraine 2 Ivan Franko National University of Lviv, Lviv, Ukraine 3 Łukasiewicz Research Network – Industrial Research Institute of Automation and

Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warszawa, Poland [email protected]

Abstract. This paper considers the application of the Polynomial Maximization Method to find estimates of the parameters Non-Gaussian Moving Average model. This approach is adaptive and is based on the analysis of higher-order statistics. Case of asymmetry of the distribution of Moving Average processes is considered. It is shown that the asymptotic variance of estimates of the Polynomial Maximization Method (2nd order) analytical expressions that allow finding estimates and analyzing their uncertainty are obtained. This approach can be significantly less than the variance of the classic estimates based on minimize Conditional Sum of Squares or Maximum Likelihood (in Gaussian case). The increase in accuracy depends on the values of the coefficient’s asymmetry and kurtosis of residuals. The results of statistical modeling by the Monte Carlo Method confirm the effectiveness of the proposed approach. Keywords: Estimation parameters · Moving average · Polynomial maximization · High-order statistics · Non-Gaussian processes

1 Introduction It is known that MA (Moving Average) processes are a particular case of a broader class of ARMA (Auto-Regressive Moving Average) time series models. Initially they were developed to solve the problems of predicting the behavior of dynamic objects, they have subsequently found the widest spread for predicting geophysical, financial, biomedical, and other processes. For quite a long time, the theory of synthesis and analysis of time series models has been developing within the framework of linear filtration theory, theoretical foundations of which were laid in works of Wiener [1] and Kalman [2]. From the mathematical point of view, the linear predictor (independent variable) is optimal only when the processes have normal law of probability distribution. However, many researchers note the idealization of such an assumption, which, although simplifies the final solution, often does not correspond to realities of many practical problems [3–8]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 223–231, 2023. https://doi.org/10.1007/978-3-031-25844-2_21

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From the statistical point of view, a significant difference between the prediction errors (residuals) of the fitted model and the Gaussian idealization leads to an increase in the uncertainty of the resulting estimates of the parameters of such models. There are several ways to increase the estimation accuracy. One of them is the parametric approach based on the use of M-estimates obtained on the basis of the Maximum Likelihood Method (MML) or its various modifications. There are many distribution types used to describe the random component of ARMA models. For example, in [3] processes with gamma and lognormal innovations are studied, in [4] - Student’s distribution, in [5] - mixtures of normal and Poisson distribution, in [6] - family of Exponential Power distributions, in [7] - poly-mixtures based on Laplace distributions, in [8] - Cauchy distribution, etc. One of the key elements of the parametric approach is the need to solve the problem of identifying the type and finding estimates of the probability distribution parameters of the random component of time series models. A number of methods for joint [3] or iterative and adaptive estimation have been developed [9, 10]. An alternative approach to accounting for Non-Gaussian processes is to use the apparatus of higher-order statistics (moments, cumulants or their functions). This approach is characterized by a substantial reduction in the level of necessary a priori information, as well as by algorithmic simplification in practical implementation. The price for this is sub-efficiency of obtained solutions, which is caused by partiality of such description (in comparison with probability density function). Examples of the use of this approach for solving the problems of identification of various predictive models and estimation of their informative parameters can be found in [11–15]. In this article we propose to use the Polynomial Maximization Method (PMM) [16] to find estimates of parameters of MA-models. This method, similarly, to MML, uses the principle of maximizing the functional from the sampled data in the vicinity of the true value of the estimated parameters. However, to form such a functional, not the density of distribution, but a description in the form of higher-order statistics is used. This study is a continuation of the works [17–19] in which the application of PMM to the problem of parameter estimation of linear and polynomial regression and autoregressive model at asymmetrically distributed Non-Gaussian statistical data is considered.

2 Mathematical Formulation of the Problem Consider a vector X = {x1 , x2 , ..., xN } containing the values of the time series described by the moving average model. xv =

Q q=1

−−→ bq ξv−q + ξv , v = 1, N ,

(1)

where the samples ξv are a sequence of equally distributed independent random variables with zero mathematical expectation. Their distribution differs from the Gaussian (normal) law and has substantial asymmetry. An additional limitation is that the random variable ξ has finite moments  μr upto order 4th. The general task is to find estimates of the vector parameter θ = b1 , ...bQ based on statistical analysis of the set of samples X. In this case, the probability distribution law of a random variable ξ is a priori unknown.

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3 Theoretical Results The idea of using PMM to estimate the parameters of MA models is based on the mathematical analogy between model (1) and linear (by parameters) regression. Since the samples of a random variable ξ are statistically independent, the set of ξv−q , values can be formally treated as predictors of a multivariate linear regression of the current value of series xv . In this way, to solve this problem we can use the results of [17], which deals with the application of PMM to find estimates of the vector parameter of a linear regression. Note that this estimation method is based on the property of maximization of the functional in the form of the stochastic polynomial LSN =

N

S

v=1

i=1

φi (xv ) ∫b ki,v (a)dz −

S i=1

N v=1

∫b i,v ki,v (a)dz,

(2)

where −→ −−→ i,v = E{φi (xv )}, i = 1, S, v = 1, N

(3)

in the proximity of the true value of the estimated parameter b. If we use the power transformations φi (xv ) = (xv )i as basic functions, then the sequence of mathematical expectations (3) is a set of initial moments αi,v of appropriate order. By analogy with the maximum likelihood method, the estimation of the parameter b can be found from the solution of the equation of the form    S N  d i  = ki,v (xv ) − αi,v  = 0, (4) LSN  i=1 v=0 db b=bˆ b=bˆ where the optimal coefficients ki,v , which maximize the functional (2), are found from the solution of the system of linear algebraic equations S

d −→ −−→ αi,v , i = 1, S, v = 1, N , (5) db −→ where F(i,j)v = α(i+j),v − αi,v αj,v , i, j = 1, S. This approach  can beeasily extended to the case of finding estimates of the vector parameter θ = b1 , ...bQ or this purpose, it is necessary to form Q polynomials of the general form (2) for each component of the vector parameter. Thus, the desired estimates can be found as a solution to a system of equations of the form   S N −−→ (q) i ki,v (xv ) − αi,v  = 0, q = 1, Q. (6) j=1

i=1

kj,v F(i,j)v =

v=1

bq =bˆ q

Analysis of (6) shows that the required estimates of the parameter vector are found from the condition of equality to zero of the sums of weighted by optimal coefficients (minimizing the variance of estimates at the used degree of the stochastic polynomial) differences of theoretical and empirical values of moments of the observed statistical data. The main difficulty is the lack of a priori information about the theoretical values of the first 2S initial moments of αi,v , which depend both on the estimated parameters θ = b1 , ...bQ and on the moments μr of the random variable ξ .

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As in [17], an adaptive approach can be applied to solve this problem. It consists in replacing the a priori μr values by a posteriori μˆ r estimates. They can be calculated based on the analysis of the residuals ε obtained after estimating the MA model parameters by the maximum likelihood method (under the assumption of distribution normality) or an iterative modification of the least squares method (minimization of conditional sums of squares). If the type of MA model and its order are identified correctly, then the sequence of residuals ε will be a random process of “white noise” type, the probabilistic properties of which are close to the distribution of random variable ξ . The values of uncorrelated εv−q samples are used as repressors in the original model (1). In [17] it is shown that for the linear version of PMM (when using a stochastic polynomial of degree S = 1) the resulting system of Eq. (6) for estimating parameters of regression models is equivalent to the system of Least Squares Method (LSM) equations. However, it is known that the efficiency of such LSM estimations significantly decreases when the distribution of the random component of the regression model differs from the Gaussian law. Therefore, let us consider below a new approach to nonlinear estimation of MA model parameters based on the use of quadratic power stochastic polynomials. When stochastic polynomials of order S = 2 are used, PMM estimates of MA model (1) can be found from solution of the system of equations N v=1



Q (q) k1,v xv −

q=1



 Q (q) bq εv−q + k2,v (xv )2 −

q=1

bq εv−q

2

 − μ2

−−→ = 0, q = 1, Q.

(7)

−→ (q) where: optimal coefficients ki,v , i = 1, 2 provide minimization of dispersion of estimates of components of required parameter using degree of polynomial S = 2. These coefficients are found as a solution of the corresponding system of the form (5) and can be represented as (q) k1,v

Q μ4 − μ22 + 2μ3 q=1 bq εv−q μ23 (q)    = εv−q , k2,v = −  εv−q , 2 2 μ2 μ4 − μ2 − μ3 μ2 μ4 − μ22 − μ23

(8)

By substituting the coefficients (8) into (7), after certain transformations the system of equations for finding the estimates can be written   

2 N Q Q −−→ bq εv−q + Bv bq εv−q + Cv εv−p A = 0, q = 1, Q, (9) v=1

where

q=1

q=1

  A = μ3 , Bv = μ4 − μ22 − xv μ3 , Cv = xv2 μ3 − xv μ4 − μ22 − μ2 μ3

(10)

depend on the sample values xv and moments μ2 − μ4 of the random component ξ of the model (1). Obviously, at the degree of the polynomial S = 2 PMM-estimates can be found only numerically. It has been proved [16] that nonlinear PMM parameter estimates are consistent and asymptotically unbiased. Expressions describing the variance of PMM-estimates for the

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asymptotic case (at N → ∞) can be obtained as elements of the main diagonal of the variation matrix, which is the inverse of the matrix composed of elements (q,p)

JSN

=

N

S

v=1

(q)

i=1

ki,v

∂ −−→ αi,v , q, p = 1, Q. ∂bp

(11)

In a statistical sense, the amount of information extracted is conceptually close to the amount of information according to Fisher and tends to its limit value at the degree of polynomial S → ∞ [16]. As shown in [17], the asymptotic values of variance of PMM-estimates of vector parameter, obtained by using the degree of polynomial S = 1, coincide with LSM-estimates, as well as MML-estimates (at normally distributed data). Therefore, a dimensionless coefficient ( bq )

gS

σ 2b S ( q) = 2 . σb 1 ( q)

(12)

can be used as a criterion of efficiency of PMM-estimates obtained by using polynomials of some degree S. This coefficient is the same for all components of the estimated vector parameter θ and with S = 2 can be represented as (b ) g2 q = 1 −

μ2 γ32  3 2 = 1 − . 2 + γ4 μ2 μ4 − μ2

(13)

The transition in expression (13) from the moment description to the cumulant description is due to the well-known fact the deviation of the values of the cumulant  that r/2 coefficients of higher orders γr = κr κ2 from zero shows the degree of difference from the Gaussian distribution. Given the inequality γ4 + 2 ≥ γ32 , we can conclude that the variance reduction coefficient g 2 is a dimensionless value which belongs to the range (0; 1]. Thus, as the asymmetry of the ξ distribution increases, the relative reduction of the variance can be quite significant.

4 Statistical Modeling To verify the theoretical results, we modified a set of functions written in R, which implemented the procedure of multiple Monte Carlo tests of finding polynomial estimates of regression and autoregressive models [13–15]. Now it additionally allows to carry out the comparative analysis of accuracy of different methods of estimation of parameters of moving average models, the random component of which has Non-Gaussian distribution. When implementing this statistical modeling, two models were used as an object of research: MA(1) with parameter b1 = 0.4 and MA(2) with parameters b1 = 0.4; b2 = −0.2. The value of informative parameters was estimated by means of built-in function R arima ( ), using two classical methods: “CSS” (minimization of Conditional Sum of Squares) and “ML” Maximum Likelihood (optimized for Gaussian model), as well as custom quadratic modification of Polynomial Maximization Method. Sequences

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of independent and equally distributed random variables with gamma distribution with different values of shape parameter were used as asymmetric random component of MA model, which were determined for the degree of asymmetry. The parameters (moments up to the 4th order) of the random component, which are necessary for finding adaptive PMM-estimates, were considered to be unknown a priori and instead of them a posteriori estimates were used 1 N (14) μˆ r = (εv )i . v=1 N calculated from the residuals from the application of classical methods. The sum of the experimental values of the efficiency coefficients obtained for the series M = 104 of multiple experiments are presented in Tables 1, 2, 3 and 4. Table 1. Relative efficiency of the PMM estimates (S = 2) of parameters MA(1) model compared to CSS estimates Gamma distribution parameter shape

Theoretical values

Monte Carlo statistical simulation results

γ3

N = 50

1

2

6

2

1.4

4

1

γ4

g2

N = 100

N = 200

γˆ3

γˆ4

(b ) gˆ 2 1

0.5

1.6

3.1

0.95

1.8

4.1

0.59

1.9

4.9

0.57

3

0.6

1.2

1.6

0.79

1.3

2.2

0.7

1.3

2.5

0.69

1.5

0.71

0.8

0.8

0.81

0.9

1.1

0.82

1

1.3

0.83

γˆ3

γˆ4

(b ) gˆ 2 1

γˆ3

γˆ4

gˆ 2

(b1 )

Table 2. Relative efficiency of PMM-estimates (S = 2) of parameters MA(1) model compared to MML-estimates (Gaussian model). Gamma distribution parameter shape

Theoretical Values

1

2

6

2

1.4

4

1

γ3

γ4

Monte Carlo statistical simulation results g2

N = 50

N = 100

N = 200

γˆ3

γˆ4

(b ) gˆ 2 1

0.5

1.6

3.1

0.7

3

0.6

1.1

1.6

0.74

1.3

2.1

0.69

1.3

2.5

0.68

1.5

0.71

0.8

0.8

0.78

0.9

1.1

0.79

0.9

1.3

0.83

γˆ3 1.8

γˆ4

(b ) gˆ 2 1

γˆ3

γˆ4

gˆ 2

(b1 )

4.1

0.57

1.9

4.8

0.56

The analysis of the empirical values of the efficiency coefficients presented in Tables 1, 2, 3 and 4 shows that polynomial estimates of the informative parameters studied by MA models are more accurate compared to classical estimates. The range of variance reduction is quite wide: from units of percent to twice the value. At the same time, the trends of accuracy changes depending on the degree of Non-Gaussianity (numerically expressed by the value of skewness and kurtosis coefficients) in general

Polynomial Maximization Method for Estimation Parameters

229

Table 3. Relative efficiency of the PMM estimates (S = 2) of parameters MA(2) model compared to CSS estimates Gamma distribution parameter shape

1

Theoretical values

Monte Carlo statistical simulation results

γ3

N = 50

γ4

g2

γˆ3

2

6

0.5

1.5

γˆ4

2.8

N = 100 (b ) gˆ 2 1 (b ) gˆ 2 2

γˆ3

0.98

1.7

γˆ4

4.1

0.66 2

1.4

3

0.6

1.1

1.5

0.57

4

1

1.5

0.71

0.8

0.8

0.69

N = 200 (b ) gˆ 2 1 (b ) gˆ 2 2

γˆ3

0.55

1.9

γˆ4

(b2 )

gˆ 2 4.9

0.68 1.2

2.1

0.59

0.9

1

0.74

0.75

0.49 0.67

1.3

2.5

0.61

0.9

1.2

0.73

0.75

0.81

(b1 )

gˆ 2

0.79

0.87

0.91

Table 4. Relative efficiency of the PMM estimates (S = 2) of parameters MA(2) model compared to MML-estimates (Gaussian model) Gamma distribution parameter Shape

1

Theoretical values

Monte Carlo statistical simulation results

γ3

N = 50

γ4

g2

γˆ3

2

6

0.5

1.5

γˆ4

2.9

N = 100 (b ) gˆ 2 1 (b ) gˆ 2 2

γˆ3

0.9

1.7

γˆ4

4

0.69 2

1.4

3

0.6

1.1

1.5

0.62

1

1.5

0.71

0.7

0.8

0.7 0.82

γˆ3

0.48

1.9

γˆ4

1.2

2.1

0.63

(b2 )

4.9

1.1

0.71 0.88

0.51 0.67

1.3

2.5

0.78 0.9

(b1 )

gˆ 2 gˆ 2

0.64

0.76 4

N = 200 (b ) gˆ 2 1 (b ) gˆ 2 2

0.61 0.8

0.9

1.3

0.73 0.92

correlate with the theoretical dependence (13). Significant differences are observed only for small values of the sample size of statistical data N . This can be explained by the factor that with a small amount of statistical data, the posterior estimates of the parameters γˆ3 and γˆ4 have a fairly high variance, as well as a significant bias (as evidenced by the tabular data). However, with N growth, this problem is leveled, and the experimental values asymptotically approach the theoretical ones.

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5 Conclusions The set of obtained results confirms the possibility of effective application of the Polynomial Maximization Method for solving problems of finding estimates of informative parameters of Moving Average models for those situations when the nature of the random component has a Non-Gaussian asymmetric distribution. In general, the proposed approach to finding parameter estimates can be interpreted as adaptive and compromise in terms of practical implementation. The algorithm for obtaining polynomial estimates does not require a priori knowledge of the probability distribution law. To implement it, it is sufficient to obtain information about the values of a limited set of higher-order statistics. Consequently, it has significantly less implementation complexity compared to the approach based on the Maximum Likelihood Method. At the same time, polynomial estimates are characterized by higher accuracy (according to the variance ratio criterion) compared to the estimates of classical methods optimized for Gaussian probability model. The next research tasks in this direction may be: • consideration of the option of estimating parameters of MA models with symmetry of Non-Gaussian statistical data distribution • comparison of the efficiency of adaptive estimates of the Polynomial Maximization Method and Maximum Likelihood Method optimized for the corresponding NonGaussian distributions • polynomial estimation of parameters of more complex types of Non-Gaussian time series models (ARMA, GARH, etc.).

References 1. Wiener, N.: Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications. A Classified Report by MIT Radiation Lab., Cambridge, MA, February 1942. Later Published (1949). Wiley, New York (1942) 2. Kalman, R.E.: A new approach to linear filtering and prediction probabilities. Trans. ASME J. Basic Eng. D82, 35–45 (1960) 3. Li, W.K., McLeod, A.I.: ARMA modelling with Non-Gaussian innovations. J. Time Ser. Anal. 9(2), 155–168 (1988). https://doi.org/10.1111/j.1467-9892.1988.tb00461.x 4. Tiku, M.L., Wong, W.-K., Vaughan, D.C., Bian, G.: Time series models in non-normal situations: symmetric innovations. J. Time Ser. Anal. 21, 571–596 (2000). https://doi.org/10.1111/ 1467-9892.00199 5. Ozaki, T., Iino, M.: An innovation approach to Non-Gaussian time series analysis. J. Appl. Probab. 38(A), 78–92 (2001) 6. Barnard, R.W., Trindade, A.A., Indika, R., Wickramasinghe, P.: Autoregressive moving average models under exponential power distributions. ProbStat Forum 07, 65–77 (2014). www. probstat.org.in 7. Nguyen, H.D., McLachlan, G.J., Ullmann, J.F., Janke, A.L.: Laplace mixture autoregressive models. Statist. Probab. Lett. 110, 18–24 (2016) 8. Rojas, I., et al.: Expectation-maximization algorithm for autoregressive models with Cauchy innovations. Eng. Proc. 18(1), 21 (2022). https://doi.org/10.3390/ENGPROC2022018021

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9. Beran, R.: Adaptive estimates for autoregressive processes. Ann. Inst. Stat. Math. 28(1), 77–89 (1976) 10. Phillips, R.F.: Partially adaptive estimation via a normal mixture. J. Econometrics 64(1–2), 123–144 (1994) 11. Swami, A., Mendel, J.M.: ARMA parameter estimation using only output cumulants. IEEE Trans. Acoust. Speech Signal Process. 38(7), 1257–1265 (1990). https://doi.org/10.1109/29. 57554 12. Giannakis, G.B.: On estimating noncausal nonminimum phase ARMA models of NonGaussian processes. IEEE Trans. Acoust. Speech Signal Process. 38(3), 478–495 (1990). https://doi.org/10.1109/78.127981 13. Al-Smadi, A., Alshamali, A.: Fitting ARMA models to linear Non-Gaussian processes using higher order statistics. Signal Process. 82(11), 1789–1793 (2002). https://doi.org/10.1016/ S0165-1684(02)00340-7 14. Al-Smadi, A.: Cumulant-based approach to FIR system identification. Int. J. Circuit Theory Appl. 31(6), 625–636 (2003). https://doi.org/10.1002/cta.254 15. Rosadi, D., Filzmoser, P.: Robust second order least-squares estimation for regression models with autoregressive errors. Stat. Pap. 60(1), 105–122 (2019) 16. Kunchenko, Y.: Polynomial Parameter Estimations of Close to Gaussian Random variables. Shaker Verlag, Aachen (2002) 17. Zabolotnii, S., Warsza, Z.L., Tkachenko, O.: Polynomial estimation of linear regression parameters for the asymmetric PDF of errors. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) AUTOMATION 2018. AISC, vol. 743, pp. 758–772. Springer, Cham (2018). https:// doi.org/10.1007/978-3-319-77179-3_75 18. Zabolotnii, S., Tkachenko, O., Warsza, Z.L.: Application of the polynomial maximization method for estimation parameters in the polynomial regression with Non-Gaussian residuals. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) AUTOMATION 2021. AISC, vol. 1390, pp. 402–415. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-74893-7_36 19. Zabolotnii, S., Tkachenko, O., Warsza, Z.L.: Application of the polynomial maximization method for estimation parameters of autoregressive models with asymmetric innovations. In: Szewczyk, R., Zieli´nski, C., Kaliczy´nska, M. (eds.) AUTOMATION 2022. AISC, vol. 1427, pp. 380–390. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-03502-9_37

Nanocomposites for Improved Non-enzymatic Glucose Biosensing Antanas Zinoviˇcius1 , Vadimas Ivinskij1 , Timas Merkelis1 , J¯urat˙e Jolanta Petronien˙e1,2 , and Inga Morkv˙enait˙e-Vilkonˇcien˙e1,2(B) 1 Vilnius Gediminas Technical University, 10223 Vilnius, Lithuania

[email protected] 2 State Research Institute Center for Physical Sciences and Technology, Vilnius, Lithuania

Abstract. Most research in the field of biosensors during the last decade was focused on biocompatible and more sensitive solutions for glucose measurement. A comparison between state-of-the-art technologies and those that have long been established might give some clues as to which new directions to turn to create more efficient glucose sensors. Within the scope of this review, we cover the use of conducting polymers, conducting polymer nanowires, polymers with embedded metal nanoparticles, polymeric ionic liquid-based structures, carbon nanostructures as well as nanoparticles of other materials. Keywords: Nanocomposite · Carbon nanomaterials · Conductive polymers

1 Introduction Sweat provides information about a person’s metabolic state. It is a biofluid with a broad range of biomarkers, which can be collected in a non-invasive way. The standard biofluid is blood, which is standardized and shows physiologic feedback. The need for laboratory equipment prevented the clinical implementation of sweat as a diagnostic biofluid. The incidence of diabetes is increasing exponentially, and regular glucose monitoring is critical to managing diabetes. The glucose level is still measured in blood by an invasive method. The devices available in the market for blood glucose detection measure the amount of sugar in a small sample of blood from the fingertip placed on a test paper. Non-invasive glucose monitoring could be possible using a sweat sensor-based approach. Wearable and digital technologies bring innovations that enable individuals to regularly and non-invasively monitor their fitness and health. While these techniques can measure a wide range of physiological parameters, including heart rate and physical activity, they lack the ability to quantify the biochemical parameters needed to treat a wide range of pathological health conditions. For example, hypoglycemia with blood glucose below the normal range is a risk for diabetics, especially after strenuous exercise [1]. Similarly, as a chronic disease, diabetes is characterized by abnormally elevated blood sugar levels, ultimately leading to serious damage to the heart, blood vessels, eyes, and kidneys. According to the World Health Organization (WHO) [2], about 422 million people worldwide suffer from diabetes. Regular blood glucose monitoring is essential for the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 232–239, 2023. https://doi.org/10.1007/978-3-031-25844-2_22

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treatment of type 1 or type 2 diabetes. Subjects will find it helpful to see how the number increases or decreases as they eat a variety of foods, take medications and are physically active. Awareness and the ability to monitor blood glucose have made significant improvements in the management of diabetes. Combining treatments with appropriate protocols will gradually stop the increase in people’s diabetes and hypoglycemia problems. Sweat is considered as one of the critical bio-beverages beneficial for noninvasive, non-stop tracking programs due to its precise nature. Sampling sweat provides a consistent supply of glucose, physiologically significant electrolytes, and metabolites. Such a device can be freely placed around the body as a sapling is conducted using non-invasive methods and easily monitored. In human subjects, sweat glucose has been efficaciously measured and suggested in early 1947–1954 [3, 4]. Since sweat response happens quickly and the sweat gland is tremendously vascularized, glucose stages within the frame may be expected from sweat samples [5]. The content of glucose in human sweat is from 0.06–0.2 mM and corresponds to 3.3–17.3 mM in blood glucose [5, 6]. However, substantial demanding situations stay in acquiring correct sweat glucose data, along with modifications in environmental parameters along with temperature, infection from the skin, sporadic sampling without iontophoretic incitement, low production rate, and the integration of old samples with brand-new samples. Despite the best interaction, the glucose level analysis in sweat is extraordinarily hard in view of its low concentration (~one hundred times lower than blood glucose), which consequently needs highly sensitive devices. In the past few decades, several detection devices have been established for glucose sensing such as acoustic, magnetic, thermal, optical, and electrical transducers. Among these devices, electrochemically induced diabetic sensors have been considered the most promising for monitoring glucose levels due to their superior performance, easy fabrication, and miniaturization [7–9].

2 Nanocomposites Used in Non-enzymatic Glucose Sensors Electrochemical glucose sensors are mainly classified into enzymatic and non-enzymatic sensors. In the former, glucose-sensitive enzymes such as glucose oxidase (GOx) and glucose dehydrogenase (GDH) are important components for the modification of electrode surfaces. The GOx enzyme-based commercially available electrochemical glucose sensors suffer from poor environmental stability and involve complex GOx immobilization processes on the sensor surface [10]. Additionally, GOx loses its catalytic activity at higher (>8.0) and lower (10 wt.%) and increase the cross-linking [25, 26]. However, this would inevitably hinder the mass transport of ions in the gel and thus limit the conductivity. This challenge calls for fine optimizations of the balanced performance that fit the sensor application. To enhance the mechanical strength of the gelatin, another hydrophilic biopolymer, can be used [27, 28]. Glycerol, which is widely used in cosmetics and hand-cleaning gels, will be added to improve the stability of the gel by inhibiting the evaporation of water [29] (Table 1).

Nanocomposites for Improved Non-enzymatic Glucose

235

Table 1. Nanocomposites in non-enzymatic glucose biosensing. Nanocomposite

Biosensor parameters

Ref.

FTO-modified rGO

LOD 0.011 μM, SV 1402 μA cm−2

[30]

Nanostructured Au-Ni alloy

LOD of 5.84 μM, LR between 10 μM and 20 mM, SV 0.96 μA mM−1

[31]

Ag nanoparticles decorated PmAPNFs

LOD 0.062 μM, LR 0.1–8 mM, SV 17.45 μA M−1 cm−2

[32]

Fe2O3-ZNRs

LOD 12 μM, LR up to 18 mM

[33]

CNTs on patterned Au nanosheets coated with CoWO4/CNT nanocomposites

SV 10.89 μA mM−1 cm−2

[34]

PEDOT: PSS with laser-induced graphene LOD 3 μM, and Pt and Pd nanoparticles LR between 10 μM – 9.2 mM, SV 247.3 μA mM−1 cm−2

[35]

Graphite modified with PEDOT: PSS and CuO nanoparticles

SV 663.2 μA mM−1 cm−2

[36]

Au nanoparticles on PANI-modified GCE

LOD 0.1 mM, LR between 0.3 mM and 10 mM

[37]

Borophene (β12) nanosheets with PANI on Au

LOD 0.5 mM, LR between 1 mM and 12 mM, SV of 96.93 μA mM−1 cm−2

[38]

CoNi2S4 nanoflake-modified Ni wire

LOD 0.3 μM, [39] LR between 0.001 mM and 3 mM or between 3 mM and 8 mM depending on the variation, SV of 2473 μA mM−1 cm−2 or 1794 μA mM−1 cm−2 depending on the variation

PB, rGO, and Au nanoparticles

LR between 1 μM and 222 μM, [40] SV of 40.6 μA mM−1 cm−2 or LR between 0.222 mM and 25 mM with SV of 1.9 μA mM−1 cm−2

Mesoporous Ni2P-Cu3P

LOD 0.1 μM, LR between 4 μM and 5 mM, SV of 4700 μA mM−1 cm−2

[41]

Methyl L-DOPA nanoparticles and dopamine

LOD 23 μM, LR up to 70 mM, SV of 752.5 μA mM−1 cm−2

[42]

(continued)

236

A. Zinoviˇcius et al. Table 1. (continued)

Nanocomposite

Biosensor parameters

Ref.

NiCo nanoparticles f-MWCNTs

LOD 0.26 μM, SV of 10.15 μA/mM−1 cm−2

[43]

NiFe layered double hydroxide (LDH) LOD 0.10 μM, nanosheets (NSs) on Cu nanowires (NWs) LR between 1 μM and 0.9 mM, SV of 7.88 mA mM−1 cm−2 N and S co-doped chitosan polymer matrix-derived composite

LOD 2.72 μM, LR between 160 μM and 11.76 mM, SV of 13.62 mA mM−1 cm−2

[44]

[45]

LOD - limit of detection, LR - linear range, SV - sensitivity, FTO - fluorine-doped tin oxide, rGO - reduced graphene oxide, PmAPNFs - poly(m-aminophenol) nanofibers, Fe2O3-ZNRs zinc oxide nanorods modified with iron oxide, CNTs - carbon nanotubes, PEDOT: PSS - Poly (3, 4-ethylene dioxythiophene)-poly (styrene sulfonate), PANI - conductive polyaniline, GCE glassy carbon electrode, PB - Prussian blue, f-MWCNTs - functionalized multi-walled carbon nano-tubes, Methyl L-DOPA - l-3,4-dihydroxyphenylalanine.

3 Conclusions The composite materials can be used to develop a sweat non-enzymatic glucose sensor. The common (blood sensor) glucose sensors cause environmental problems, energy consumption issues, and recycling. Also, common glucose sensors made in factories are relatively expensive and impossible to renew. Glucose sensors, using some composite materials, can be made from biocompatible and biodegradable materials. To ensure efficient use of material, the sensor can be made by 3D printing technologies. The future developments of such sensors are the improvement of the sensing part, which will be recyclable, biodegradable, biocompatible, and produced “in place” using additive manufacturing technologies. Acknowledgments. This project has received funding from the Research Council of Lithuania (LMTLT), agreement No S-MIP-22-87.

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Author Index

B Bagdonas, Rokas, 85, 155 Banaszak, Zbigniew, 51 Bocewicz, Grzegorz, 51 Bolanowski, Marek, 62 Borawski, Kamil, 3 Bryła, Michał, 140 Buˇcinskas, Vytautas, 155 C ´ Cwian, Krzysztof, 118 D Dzedzickis, Andrius, 85, 155 F Falkowski, Piotr, 129 G Garbacz, Piotr, 204 Gargasas, Justinas, 85 Gawdzik, Grzegorz, 140 Gł¸ebocki, Robert, 39 Główka, Jakub, 140 Gnateiko, Nonna, 173 H Hendzel, Zenon, 107 I Ivinskij, Vadimas, 155, 232

J Jacewicz, Mariusz, 39 J˛edrzejczyk, Filip, 140 Juzo´n, Zbigniew, 73 K Kaczorek, Tadeusz, 3 Kalinina, Myroslava, 165 Kataieva, Mariia, 195 Kołodziej, Maciej, 107 Kołodziejczyk, Miron, 140 Korobiichuk, Igor, 165, 173, 183, 195 Korobiichuk, Valentyn, 183 Kosova, Vera, 173 Kozyr, Oleh, 212 Kraska, Andrzej, 62 L Lapkauskaite, Karolina, 85 Linowska, Berenika, 204 Lutska, Nataliia, 93 M Macia´s, Matuesz, 140 Makulaviˇcius, Mantas, 85 Mel’nick, Viktorij, 173 Melnyk-Shamrai, Viktoriia, 183 Merkelis, Timas, 232 Miedzi´nski, Dariusz, 39 Morkv˙enait˙e-Vilkonˇcien˙e, Inga, 155, 232

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. Szewczyk et al. (Eds.): AUTOMATION 2023, LNNS 630, pp. 241–242, 2023. https://doi.org/10.1007/978-3-031-25844-2

242 O Oprz˛edkiewicz, Krzysztof, 13 Ornatskyi, Dmytro, 195 Ostapenko, Zhanna, 173 P Paszkiewicz, Andrzej, 62 Petronien˙e, J¯urat˙e Jolanta, 232 R Radzki, Grzegorz, 51 Rož˙en˙e, Just˙e, 155 Rydzewski, Adam, 129 Rzeplinska-Rykala, Katarzyna, 165, 173 S Salach, Mateusz, 62 Shamrai, Volodymyr, 183 Shcherbyna, Dmytro, 195 Shybetskyi, Vladyslav, 165 Sitek, Paweł, 73

Author Index Skrzypczy´nski, Piotr, 118 Słomiany, Marcin, 140 Subaˇci¯ut˙e-Žemaitien˙e, Jurga, 155 T Tkachenko, Oleksandr, 223 V Vlasenko, Lidiia, 93 Volodarskyi, Yevhen, 212 W Warsza, Zygmunt Lech, 212, 223 Wi˛ecek, Jakub, 62 Wikarek, Jarosław, 73 Z Zabolotnii, Serhii, 223 Zaiets, Nataliia, 93 ˙ Zegle´ n-Włodarczyk, Jakub, 29 Zinoviˇcius, Antanas, 155, 232