Journal of the University of Zielona Góra

International Journal of Applied Mathematics and Computer Science

Int.Jnl Appl.Math.Comp.Sci.ONL

<abstract>
<title style='display:none'>Abstract</title>
A novel fault-tolerant tracking control scheme based on an adaptive robust observer for non-linear systems is proposed. Additionally, it is presumed that the non-linear system may be faulty, i.e., affected by actuator and sensor faults along with the disturbances, simultaneously. Accordingly, the stability of the robust observer as well as the fault-tolerant tracking controller is achieved by using the ℋ∞ approach. Furthermore, unknown actuator and sensor faults and states are bounded by the uncertainty intervals for estimation quality assessment as well as reliable fault diagnosis. This means that narrow intervals accompany better estimation quality. Thus, to cope with the above difficulty, it is assumed that the disturbances are over-bounded by an ellipsoid. Consequently, the performance and correctness of the proposed fault-tolerant tracking control scheme are verified by using a non-linear twin-rotor aerodynamical laboratory system.
</abstract>

Abstract

Keywords

<article-title>Fault–Tolerant Tracking Control for a Non–Linear Twin–Rotor System Under Ellipsoidal Bounding</article-title>

Fault–Tolerant Tracking Control for a Non–Linear Twin–Rotor System Under Ellipsoidal Bounding

<abstract>
<title style='display:none'>Abstract</title>
Reliability and safety of an electro-hydraulic position servo system (EHPSS) can be greatly reduced for potential sensor and actuator faults. This paper proposes a novel reconfiguration control (RC) scheme that combines multi-model and adaptive control to compensate for the adverse effects. Such a design includes several fixed models, one adaptive model, and one reinitialized adaptive model. Each of the models has its own independent controller that is based on a complete parametrization of the corresponding fault. A proper switching mechanism is set up to select the most appropriate controller to control the current plant. The system output can track the reference model asymptotically using the proposed method. Simulation results validate robustness and effectiveness of the proposed scheme. The main contribution is a reconfiguration control method that can handle component faults and maintain the acceptable performance of the EHPSS.
</abstract>

Nanjing University of Aeronautics and Astronautics

Electronic Engineering Department, Aviation Key Laboratory of Science and Technology on Aero Electromechanical System Integration

<article-title>A Multi–Model Based Adaptive Reconfiguration Control Scheme for an Electro–Hydraulic Position Servo System</article-title>

A Multi–Model Based Adaptive Reconfiguration Control Scheme for an Electro–Hydraulic Position Servo System

<abstract>
<title style='display:none'>Abstract</title>
A robust economic model predictive control approach that takes into account the reliability of actuators in a network is presented for the control of a drinking water network in the presence of uncertainties in the forecasted demands required for the predictive control design. The uncertain forecasted demand on the nominal MPC may make the optimization process intractable or, to a lesser extent, degrade the controller performance. Thus, the uncertainty on demand is taken into account and considered unknown but bounded in a zonotopic set. Based on this uncertainty description, a robust MPC is formulated to ensure robust constraint satisfaction, performance, stability as well as recursive feasibility through the formulation of an online tube-based MPC and an accompanying appropriate terminal set. Reliability is then modelled based on Bayesian networks, such that the resulting nonlinear function accommodated in the optimization setup is presented in a pseudo-linear form by means of a linear parameter varying representation, mitigating any additional computational expense thanks to the formulation as a quadratic optimization problem. With the inclusion of a reliability index to the economic dominant cost of the MPC, the network users’ requirements are met whilst ensuring improved reliability, therefore decreasing short and long term operational costs for water utility operators. Capabilities of the designed controller are demonstrated with simulated scenarios on the Barcelona drinking water network.
</abstract>

<article-title>Reliability–Aware Zonotopic Tube–Based Model Predictive Control of a Drinking Water Network</article-title>

Reliability–Aware Zonotopic Tube–Based Model Predictive Control of a Drinking Water Network

<abstract>
<title style='display:none'>Abstract</title>
The paper proposes an original, comprehensive, and methodically consistent graph theory-based approach to the description of the diagnosed process and the diagnosing system. The main baseline of the presented approach is in the dichotomous approach to diagnosing. It involves a separate description of both the process and the diagnostic system. This approach reflects the practice of designing implementable diagnostic systems. Thus, it can be seen as a proposal of a new, alternative, and, at the same time, flexible design procedure with great potential for applications. The primary motivation behind it was an attempt to circumvent the numerous limitations of well-known and well-established diagnosis approaches proposed by the communities working on fault detection and isolation (FDI) and artificial intelligence theories for diagnosis (DX). Accordingly, the paper identifies and provides an extensive discussion and a critical analysis of the existing limitations. Numerous examples and references to practical applications of the approach are indicated.
</abstract>

<article-title>A Graph Theory–Based Approach to the Description of the Process and the Diagnostic System</article-title>

A Graph Theory–Based Approach to the Description of the Process and the Diagnostic System

<abstract>
<title style='display:none'>Abstract</title>
New design conditions on the observer based residual filter design for the linear discrete-time linear systems with zoned system parameter faults are presented. With respect to time evolution of residual signals and with a guarantee of their robustness, the design task is stated in terms of linear matrix inequalities, while the recursive implementation of algorithms is motivated by the platform existence for real-time processing. A major objective is to analyze the configuration required and, in particular, a new characterization of the norm boundaries of the multiplicative zonal parametric faults to be projected onto the structure of the set of linear matrix inequalities.
</abstract>

Department of Cybernetics and Artificial Intelligence

<article-title>On Some Ways to Implement State–Multiplicative Fault Detection in Discrete–Time Linear Systems</article-title>

On Some Ways to Implement State–Multiplicative Fault Detection in Discrete–Time Linear Systems

<abstract>
<title style='display:none'>Abstract</title>
This paper deals with the problem of joint state and unknown input estimation for stochastic discrete-time linear systems subject to intermittent unknown inputs on measurements. A Kalman filter approach is proposed for state prediction and intermittent unknown input reconstruction. The filter design is based on the minimization of the trace of the state estimation error covariance matrix under the constraint that the state prediction error is decoupled from active unknown inputs corrupting measurements at the current time. When the system is not strongly detectable, a sufficient stochastic stability condition on the mathematical expectation of the random state prediction errors covariance matrix is established in the case where the arrival binary sequences of unknown inputs follow independent random Bernoulli processes. When the intermittent unknown inputs on measurements represent intermittent observations, an illustrative example shows that the proposed filter corresponds to a Kalman filter with intermittent observations having the ability to generate a minimum variance unbiased prediction of measurement losses.
</abstract>

Laboratory of Modeling, Analysis and Control, National Engineering School of Gabes

Henri Poincaré University Institute of Technology of Longwy, University of Lorraine

<article-title>A Kalman Filter with Intermittent Observations and Reconstruction of Data Losses</article-title>

A Kalman Filter with Intermittent Observations and Reconstruction of Data Losses

{"article-title":"A Kalman Filter with Intermittent Observations and Reconstruction of Data Losses"}

<abstract>
<title style='display:none'>Abstract</title>
Linear parameter varying (LPV) models are being increasingly used as a bridge between linear and nonlinear models. From a mathematical point of view, a large class of nonlinear models can be rewritten in LPV or quasi-LPV forms easing their analysis. From a practical point of view, that kind of model can be used for introducing varying model parameters representing, for example, nonconstant characteristics of a component or an equipment degradation. This approach is frequently employed in several model-based system maintenance methods. The identifiability of these parameters is then a key issue for estimating their values based on which a decision can be made. However, the problem of identifiability of these models is still at a nascent stage. In this paper, we propose an approach to verify the identifiability of unknown parameters for LPV or quasi-LPV state-space models. It makes use of a parity-space like formulation to eliminate the states of the model. The resulting input-output-parameter equation is analyzed to verify the identifiability of the original model or a subset of unknown parameters. This approach provides a framework for both continuous-time and discrete-time models and is illustrated through various examples.
</abstract>

<article-title>Parameter Identifiability for Nonlinear LPV Models</article-title>

Parameter Identifiability for Nonlinear LPV Models

{"article-title":"Parameter Identifiability for Nonlinear LPV Models"}

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we propose a multi-group SEIR epidemic model with spatial diffusion, where the model parameters are spatially heterogeneous. The positivity and ultimate boundedness of the solution, as well as the existence of a global attractor of the associated solution semiflow, are established. The definition of the basic reproduction number is given by utilizing the next generation operator approach, whereby threshold-type results on the global dynamics in terms of this number are established. That is, when the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, while if it is greater than one, uniform persistence of this model is proved. Finally, the feasibility of the main theoretical results is shown with the aid of numerical examples for a model with two groups.
</abstract>

Tianjin University of Technology and Education

<article-title>Global Behavior of a Multi–Group Seir Epidemic Model with Spatial Diffusion in a Heterogeneous Environment</article-title>

Global Behavior of a Multi–Group Seir Epidemic Model with Spatial Diffusion in a Heterogeneous Environment

<abstract>
<title style='display:none'>Abstract</title>
Fuzzy numbers are often used for modeling imprecise perceptions of the real-valued observations. Such epistemic fuzzy data may cause problems in statistical reasoning and data analysis. We propose a universal nonparametric technique, called the epistemic bootstrap, which could be helpful when the existing methods do not work or do not give satisfactory results. Besides the simple epistemic bootstrap, we develop its several refinements that aim to reduce the variance in statistical inference. We also perform an extended simulation study to examine statistical properties of the approaches considered. The discussion of the results is supplemented by some hints for practical use.
</abstract>

Faculty of Mathematics and Information Science

<article-title>Bootstrap Methods for Epistemic Fuzzy Data</article-title>

Bootstrap Methods for Epistemic Fuzzy Data

{"article-title":"Bootstrap Methods for Epistemic Fuzzy Data"}

<abstract>
<title style='display:none'>Abstract</title>
Positive unlabeled (PU) learning is an important problem motivated by the occurrence of this type of partial observability in many applications. The present paper reconsiders recent advances in parametric modeling of PU data based on empirical likelihood maximization and argues that they can be significantly improved. The proposed approach is based on the fact that the likelihood for the logistic fit and an unknown labeling frequency can be expressed as the sum of a convex and a concave function, which is explicitly given. This allows methods such as the concave-convex procedure (CCCP) or its variant, the disciplined convex-concave procedure (DCCP), to be applied. We show by analyzing real data sets that, by using the DCCP to solve the optimization problem, we obtain significant improvements in the posterior probability and the label frequency estimation over the best available competitors.
</abstract>

Faculty of Mathematics and Information Sciences

<article-title>Revisiting Strategies for Fitting Logistic Regression for Positive and Unlabeled Data</article-title>

Revisiting Strategies for Fitting Logistic Regression for Positive and Unlabeled Data

<abstract>
<title style='display:none'>Abstract</title>
We consider the positive-unlabelled multi-label scenario in which multiple target variables are not observed directly. Instead, we observe surrogate variables indicating whether or not the target variables are labelled. The presence of a label means that the corresponding variable is positive. The absence of the label means that the variable can be either positive or negative. We analyze embedded feature selection methods based on two weighted penalized empirical risk minimization frameworks. In the first approach, we introduce weights of observations. The idea is to assign larger weights to observations for which there is a consistency between the values of the true target variable and the corresponding surrogate variable. In the second approach, we consider a weighted empirical risk function which corresponds to the risk function for the true unobserved target variables. The weights in both the methods depend on the unknown propensity score functions, whose estimation is a challenging problem. We propose to use very simple bounds for the propensity score, which leads to relatively simple forms of weights. In the experiments we analyze the predictive power of the methods considered for different labelling schemes.
</abstract>

<article-title>Joint Feature Selection and Classification for Positive Unlabelled Multi–Label Data Using Weighted Penalized Empirical Risk Minimization</article-title>

Joint Feature Selection and Classification for Positive Unlabelled Multi–Label Data Using Weighted Penalized Empirical Risk Minimization

<abstract>
<title style='display:none'>Abstract</title>
Cyberbullying has become more widespread as a result of the common use of social media, particularly among teenagers and young people. A lack of studies on the types of advice and support available to victims of bullying has a negative impact on individuals and society. This work proposes a hybrid model based on transformer models in conjunction with a support vector machine (SVM) to classify our own data set images. First, seven different convolutional neural network architectures are employed to decide which is best in terms of results. Second, feature extraction is performed using four top models, namely, ResNet50, EfficientNetB0, MobileNet and Xception architectures. In addition, each architecture extracts the same number of features as the number of images in the data set, and these features are concatenated. Finally, the features are optimized and then provided as input to the SVM classifier. The accuracy rate of the proposed merged models with the SVM classifier achieved 96.05%. Furthermore, the classification precision of the proposed merged model is 99% in the bullying class and 93% in the non-bullying class. According to these results, bullying has a negative impact on students’ academic performance. The results help stakeholders to take necessary measures against bullies and increase the community’s awareness of this phenomenon.
</abstract>

<article-title>Hybrid Deep Learning Model–Based Prediction of Images Related to Cyberbullying</article-title>

Hybrid Deep Learning Model–Based Prediction of Images Related to Cyberbullying

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Editor-in-Chief <A href="http://staff.uz.zgora.pl/jkorbicz/">Józef Korbicz</A>, University of Zielona Góra, Poland Deputy Editor <A href="http://staff.uz.zgora.pl/ducinski/viewpage.php?page_id=12">Dariusz Uciński</A>, University of Zielona Góra, Poland Associate Editors Harald ASCHEMANN, University of Rostock, Germany Jérôme CIESLAK, University of Bordeaux, France Martin GUGAT, Friedrich-Alexander University of Erlangen-Nuremberg, Germany Marios M. POLYCARPOU, University of Cyprus, Nicosia, Cyprus Silvio SIMANI, University of Ferrara, Italy Jerzy STEFANOWSKI, Poznań University of Technology, Poland Guisheng ZHAI, Shibaura Institute of Technology, Tokyo, Japan Board Members Cherukuri ASWANI KUMAR, VIT University, Vellore, India Czesław BAJER, Polish Academy of Sciences, Warsaw, Poland Andrzej BARTOSZEWICZ, Technical University of Łódź, Poland Miguel BERNAL, Sonora Institute of Technology (ITSON), Obregón, Mexico Kishore BINGI, Vellore Institute of Technology, India Paolo CASTALDI, University of Bologna, Italy Zhaohui CEN, Qatar Enviroment and Energy Research Institute, Ar Rayyan, Qatar Bogusław CYGANEK, AGH University of Science and Technology, Cracow, Poland Stefan DOMEK, West Pomeranian University of Technology in Szczecin, Poland Andrzej DZIELIŃSKI, Warsaw University of Technology, Poland Anna FABIJAŃSKA, Lodz University of Technology, Poland Marcin GORAWSKI, Silesian University of Technology, Gliwice, Poland Michał GROCHOWSKI, Gdańsk University of Technology, Poland Xiao HE, Tsinghua University, Beijing, China Janusz KACPRZYK, Polish Academy of Sciences, Warsaw, Poland Jerzy KLAMKA, Polish Academy of Sciences, Gliwice, Poland Jacek KLUSKA, Rzeszów University of Technology, Poland Joanna KOŁODZIEJ, Cracow University of Technology, Poland Jan M. KOŚCIELNY, Warsaw University of Technology, Poland Zdzisław KOWALCZUK, Gdańsk University of Technology, Poland Adam KRZYZAK, Concordia University, Montreal, Canada Piotr KULCZYCKI, AGH University of Science and Technology, Cracow, Poland Maciej KUSY, Rzeszów University of Technology, Poland Francisco-Ronay LÓPEZ-ESTRADA, Technological Institute of Tuxtla Gutiérrez, Mexico Maciej ŁAWRYŃCZUK, Warsaw University of Technology, Poland Vyacheslav MAKSIMOV, Russian Academy of Sciences, Ekaterinburg, Russia Krzysztof MALINOWSKI, Warsaw University of Technology, Poland Wojciech MITKOWSKI, AGH University of Science and Technology, Cracow, Poland Gang NIU, Tongji University, Shanghai, China Ronald J. PATTON, University of Hull, UK Jimoh O. PEDRO, University of the Witwatersrand, Johannesburg, South Africa Witold PEDRYCZ, University of Alberta, Edmonton, Canada Piotr PORWIK, University of Silesia in Katowice, Poland Vicenç PUIG, Technical University of Catalonia, Barcelona, Spain Jianbin QIU, Harbin Institute of Technology, China Ewaryst RAFAJŁOWICZ, Wrocław University of Technology, Poland Rotislav RAZUMCHIK, Russian Academy of Sciences, Moscow, Russia Leszek RUTKOWSKI, Technical University of Częstochowa, Poland Andrey V. SAVCHENKO, National Research University HSE, Nizhny Novgorod, Russia Piotr SKRZYPCZYŃSKI, Poznań University of Technology, Poland Roman SŁOWIŃSKI, Poznań University of Technology, Poland Florin STOICAN, University POLITEHNICA of Bucharest, Romania Andrzej ŚWIERNIAK, Silesian University of Technology, Gliwice, Poland Zoltán SZABÓ, Hungarian Academy of Sciences, Budapest, Hungary Ryszard TADEUSIEWICZ, AGH University of Science and Technology, Cracow, Poland Didier THEILLIOL, University of Lorraine, Nancy, France Haoping WANG, Nanjing University of Science and Technology, China Marcin WITCZAK, University of Zielona Góra, Poland Baozhen YAO, Dalian University of Technology, China Shen YIN, Harbin Institute of Technology, China Alexey ZHIRABOK, Far Eastern Federal University, Vladivostok, Russia Teresa ZIELIŃSKA, Warsaw University of Technology, Poland Jacek M. ZURADA, University of Louisville, USA Editorial Office Agnieszka Rożewska, University of Zielona Góra, Poland – Manager Agata Wiśniewska-Kubicka, University of Zielona Góra, Poland – Technical Editor Contact AMCS Editorial Office University of Zielona Góra, Institute of Control and Computation Engineering ul. prof. Z. Szafrana 2 65-516 Zielona Góra phone: +48683282506 e-mail: <A href="mailto:amcs@uz.zgora.pl">amcs@uz.zgora.pl</A> website: <A href="http://www.amcs.uz.zgora.pl/">www.amcs.uz.zgora.pl</A> Publisher De Gruyter Poland Bogumiła Zuga 32A Str. 01-811 Warsaw, Poland Acknowledgement Electronic publication of Volume 26 (2016, Nos. 1-4) has been financed with the funds of the Polish Ministry of Science and Higher Education for science promoting activities within the agreement no. 904/P-DUN/2016 <A href="http://www.nauka.gov.pl/en/"><IMG alt="" src="https://www.degruyter.com/staticfiles/images/mnisw_opt.jpg"></A>

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<DIV align=left> The International Journal of Applied Mathematics and Computer Science is a quarterly published in Poland since 1991 by the University of Zielona Góra in partnership with De Gruyter Poland (Sciendo) and historically with Lubuskie Scientific Society, under the auspices of the Committee on Automatic Control and Robotics of the Polish Academy of Sciences. The journal strives to meet the demand for the presentation of interdisciplinary research in various fields related to control theory, applied mathematics, scientific computing and computer science. In particular, it publishes high quality original research results in the following areas: <UL> <LI>modern control theory and practice, </LI> <LI>artificial intelligence methods and their applications, </LI> <LI>applied mathematics and mathematical optimisation techniques, </LI> <LI>mathematical methods in engineering, computer science, and biology. </LI> </UL> We are primarily interested in presenting theoretical and application-orientated full-length research papers dealing with the following topics: <UL> <LI>control theory, including optimal control, system identification, adaptive and robust control, multivariable control, and non-linear systems, </LI> <LI>dynamical systems, including spatiotemporal processes, control problems, state and parameter estimation, and sensor networks, </LI> <LI>fault detection and diagnosis, including model-based approaches, observers, and classifiers, </LI> <LI>fault-tolerant control, including the control of continuous-variable and quantised systems, </LI> <LI>robotics, including modelling and simulation, mobile robots, and optimal trajectory planning, </LI> <LI>mathematical modelling and simulation, including numerical algorithms, </LI> <LI>optimisation, including mathematical optimisation techniques, global optimisation, and evolutionary algorithms, </LI> <LI>artificial intelligence, including machine and deep learning, neural networks, knowledge engineering, fuzzy systems, and search methods, </LI> <LI>data mining, data and image processing, and big data, </LI> <LI>classification and pattern recognition, </LI> <LI>biomedical engineering and biomathematics, </LI> <LI>applications in engineering and medicine. </LI> </UL> The editors welcome proposals for exchange between similar journals. Also, all persons interested in bringing out special issues or sections of AMCS are encouraged to contact the Editor-in-Chief. Specials may be published on any important and timely subject within the scope of the journal. All papers proposed for special issues or sections will be refereed and have to meet the same criteria for scientific quality as articles presented in regular issues. Also, all journal rules and guidelines refer to papers published in specials without any exceptions. ISSN: 1641-876X (print version), 2083-8492 (online version) Why subscribe and read <UL> <LI>Premier source of high quality research from all over the world, with special emphasis on papers from Central and Eastern Europe, </LI> <LI>over twenty years of experience in publishing original articles dealing with various aspects of applying mathematical methods to computer science and engineering, </LI> <LI>extensive scope covering, among other things, control systems, optimization, robotics, mathematical and numerical modeling, artificial intelligence, knowledge processing, fault detection and diagnostics, </LI> <LI>one of the fastest growing journals published in Central and Eastern Europe. </LI></UL> Why submit <UL> <LI>Fast, fair, competent and comprehensive peer review (two or three referees are designated for the assessment of each manuscript), </LI> <LI>fast and efficient publication process, </LI> <LI>thorough language correction for authors who are not native English speakers, </LI> <LI>polishing the structure and technical format of each submission, </LI> <LI>promotion of published papers in the vast scientific community of researchers working in the field. </LI></UL> Archiving Sciendo archives the contents of this journal in <A href="https://www.portico.org/">Portico</A> - digital long-term preservation service of scholarly books, journals and collections. Plagiarism policy The editorial board is participating in a growing community of <A href="https://www.crossref.org/services/similarity-check/">Similarity Check System's</A> users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. </DIV>

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Volume 32 (2022): Issue 2 (June 2022) Towards Self-Healing Systems through Diagnostics, Fault-Tolerance and Design (Special section, pp. 171-269), Marcin Witczak and Ralf Stetter (Eds.)

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