Counterfactuals are widely used to explain ML model predictions by providing alternative scenarios for obtaining the more desired predictions. They can be generated by a variety of methods that optimize different, sometimes conflicting, quality measures and produce quite different solutions. However, choosing the most appropriate explanation method and one of the generated counterfactuals is not an easy task. Instead of forcing the user to test many different explanation methods and analysing conflicting solutions, in this paper, we propose to use a multi-stage ensemble approach that will select single counterfactual based on the multiple-criteria analysis. It offers a compromise solution that scores well on several popular quality measures. This approach exploits the dominance relation and the ideal point decision aid method, which selects one counterfactual from the Pareto front. The conducted experiments demonstrated that the proposed approach generates fully actionable counterfactuals with attractive compromise values of the considered quality measures.
反事实被广泛用于解释 ML 模型的预测结果，为获得更理想的预测结果提供替代方案。反事实可以通过多种方法生成，这些方法可以优化不同的质量度量，有时甚至是相互冲突的质量度量，并产生截然不同的解决方案。然而，选择最合适的解释方法和生成的反事实之一并非易事。本文建议使用一种多阶段组合方法，在多重标准分析的基础上选择单一的反事实，而不是强迫用户测试多种不同的解释方法并分析相互冲突的解决方案。它提供了一种折中的解决方案，在几种流行的质量衡量标准上得分都很高。该方法利用支配关系和理想点辅助决策方法，从帕累托前沿选择一个反事实。所进行的实验表明，所提出的方法能生成完全可操作的反事实，并在所考虑的质量衡量标准方面具有有吸引力的折衷值。
{"title":"A multi-criteria approach for selecting an explanation from the set of counterfactuals produced by an ensemble of explainers","authors":"Ignacy Stkepka, Mateusz Lango, Jerzy Stefanowski","doi":"10.61822/amcs-2024-0009","DOIUrl":"https://doi.org/10.61822/amcs-2024-0009","url":null,"abstract":"Counterfactuals are widely used to explain ML model predictions by providing alternative scenarios for obtaining the more desired predictions. They can be generated by a variety of methods that optimize different, sometimes conflicting, quality measures and produce quite different solutions. However, choosing the most appropriate explanation method and one of the generated counterfactuals is not an easy task. Instead of forcing the user to test many different explanation methods and analysing conflicting solutions, in this paper, we propose to use a multi-stage ensemble approach that will select single counterfactual based on the multiple-criteria analysis. It offers a compromise solution that scores well on several popular quality measures. This approach exploits the dominance relation and the ideal point decision aid method, which selects one counterfactual from the Pareto front. The conducted experiments demonstrated that the proposed approach generates fully actionable counterfactuals with attractive compromise values of the considered quality measures.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140388925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this study is to apply and evaluate the usefulness of the hybrid classifier to predict the presence of serious coronary artery disease based on clinical data and 24-hour Holter ECG monitoring. Our approach relies on an ensemble classifier applying the distributivity equation aggregating base classifiers accordingly. Such a method may be helpful for physicians in the management of patients with coronary artery disease, in particular in the face of limited access to invasive diagnostic tests, i.e., coronary angiography, or in the case of contraindications to its performance. The paper includes results of experiments performed on medical data obtained from the Department of Internal Medicine, Jagiellonian University Medical College, Kraków, Poland. The data set contains clinical data, data from Holter ECG (24-hour ECG monitoring), and coronary angiography. A leave-one-out cross-validation technique is used for the performance evaluation of the classifiers on a data set using the WEKA (Waikato Environment for Knowledge Analysis) tool. We present the results of comparing our hybrid algorithm created from aggregation with the distributive equation of selected classification algorithms (multilayer perceptron network, support vector machine, k-nearest neighbors, naïve Bayes, and random forests) with themselves on raw data.
{"title":"Assessment Measures of an Ensemble Classifier Based on the Distributivity Equation to Predict the Presence of Severe Coronary Artery Disease","authors":"Ewa Rak, A. Szczur, Jan G. Bazan, S. Bazan-Socha","doi":"10.34768/amcs-2023-0026","DOIUrl":"https://doi.org/10.34768/amcs-2023-0026","url":null,"abstract":"Abstract The aim of this study is to apply and evaluate the usefulness of the hybrid classifier to predict the presence of serious coronary artery disease based on clinical data and 24-hour Holter ECG monitoring. Our approach relies on an ensemble classifier applying the distributivity equation aggregating base classifiers accordingly. Such a method may be helpful for physicians in the management of patients with coronary artery disease, in particular in the face of limited access to invasive diagnostic tests, i.e., coronary angiography, or in the case of contraindications to its performance. The paper includes results of experiments performed on medical data obtained from the Department of Internal Medicine, Jagiellonian University Medical College, Kraków, Poland. The data set contains clinical data, data from Holter ECG (24-hour ECG monitoring), and coronary angiography. A leave-one-out cross-validation technique is used for the performance evaluation of the classifiers on a data set using the WEKA (Waikato Environment for Knowledge Analysis) tool. We present the results of comparing our hybrid algorithm created from aggregation with the distributive equation of selected classification algorithms (multilayer perceptron network, support vector machine, k-nearest neighbors, naïve Bayes, and random forests) with themselves on raw data.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"23 1","pages":"361 - 377"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139345513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Usha Rani Kandukuri, A. J. Prakash, Kiran Kumar Patro, B. Neelapu, R. Tadeusiewicz, Paweł Pławiak
Abstract Obstructive sleep apnea (OSA) is a long-term sleep disorder that causes temporary disruption in breathing while sleeping. Polysomnography (PSG) is the technique for monitoring different signals during the patient’s sleep cycle, including electroencephalogram (EEG), electromyography (EMG), electrocardiogram (ECG), and oxygen saturation (SpO2). Due to the high cost and inconvenience of polysomnography, the usefulness of ECG signals in detecting OSA is explored in this work, which proposes a two-dimensional convolutional neural network (2D-CNN) model for detecting OSA using ECG signals. A publicly available apnea ECG database from PhysioNet is used for experimentation. Further, a constant Q-transform (CQT) is applied for segmentation, filtering, and conversion of ECG beats into images. The proposed CNN model demonstrates an average accuracy, sensitivity and specificity of 91.34%, 90.68% and 90.70%, respectively. The findings obtained using the proposed approach are comparable to those of many other existing methods for automatic detection of OSA.
摘要 阻塞性睡眠呼吸暂停（OSA）是一种长期睡眠障碍，会导致睡眠时呼吸暂时中断。多导睡眠图（PSG）是一种监测患者睡眠周期中不同信号的技术，包括脑电图（EEG）、肌电图（EMG）、心电图（ECG）和血氧饱和度（SpO2）。由于多导睡眠图的高成本和不便性，本研究探讨了心电图信号在检测 OSA 中的实用性，并提出了一种利用心电图信号检测 OSA 的二维卷积神经网络（2D-CNN）模型。实验使用了 PhysioNet 上公开的呼吸暂停心电图数据库。此外，还采用恒定 Q 变换 (CQT) 进行分割、过滤，并将心电图搏动转换为图像。所提出的 CNN 模型的平均准确率、灵敏度和特异性分别为 91.34%、90.68% 和 90.70%。使用所提议的方法得出的结果可与其他许多现有的 OSA 自动检测方法相媲美。
{"title":"Constant Q–Transform–Based Deep Learning Architecture for Detection of Obstructive Sleep Apnea","authors":"Usha Rani Kandukuri, A. J. Prakash, Kiran Kumar Patro, B. Neelapu, R. Tadeusiewicz, Paweł Pławiak","doi":"10.34768/amcs-2023-0036","DOIUrl":"https://doi.org/10.34768/amcs-2023-0036","url":null,"abstract":"Abstract Obstructive sleep apnea (OSA) is a long-term sleep disorder that causes temporary disruption in breathing while sleeping. Polysomnography (PSG) is the technique for monitoring different signals during the patient’s sleep cycle, including electroencephalogram (EEG), electromyography (EMG), electrocardiogram (ECG), and oxygen saturation (SpO2). Due to the high cost and inconvenience of polysomnography, the usefulness of ECG signals in detecting OSA is explored in this work, which proposes a two-dimensional convolutional neural network (2D-CNN) model for detecting OSA using ECG signals. A publicly available apnea ECG database from PhysioNet is used for experimentation. Further, a constant Q-transform (CQT) is applied for segmentation, filtering, and conversion of ECG beats into images. The proposed CNN model demonstrates an average accuracy, sensitivity and specificity of 91.34%, 90.68% and 90.70%, respectively. The findings obtained using the proposed approach are comparable to those of many other existing methods for automatic detection of OSA.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"46 1","pages":"493 - 506"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139343702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework. We set forth a formal method that maintains the incomplete knowledge of both the Bayesian model and the Markov system’s states. We suggest a methodology that uses Tikhonov’s regularization technique to compute a Bayesian Nash equilibrium and the accompanying game mechanism. Our framework centers on a penalty function approach, which guarantees strong convexity of the regularized reward function and the existence of a singular solution involving equality and inequality constraints in the game. We demonstrate that the approach leads to a resolution with the smallest weighted norm. The resulting individually rational and ex post periodic incentive compatible system satisfies this requirement. We arrive at the analytical equations needed to compute the game’s mechanism and equilibrium. Finally, using a supply chain network for a profit maximization problem, we demonstrate the viability of the proposed mechanism design.
{"title":"Computing a Mechanism for a Bayesian and Partially Observable Markov Approach","authors":"J. Clempner, A. Poznyak","doi":"10.34768/amcs-2023-0034","DOIUrl":"https://doi.org/10.34768/amcs-2023-0034","url":null,"abstract":"Abstract The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework. We set forth a formal method that maintains the incomplete knowledge of both the Bayesian model and the Markov system’s states. We suggest a methodology that uses Tikhonov’s regularization technique to compute a Bayesian Nash equilibrium and the accompanying game mechanism. Our framework centers on a penalty function approach, which guarantees strong convexity of the regularized reward function and the existence of a singular solution involving equality and inequality constraints in the game. We demonstrate that the approach leads to a resolution with the smallest weighted norm. The resulting individually rational and ex post periodic incentive compatible system satisfies this requirement. We arrive at the analytical equations needed to compute the game’s mechanism and equilibrium. Finally, using a supply chain network for a profit maximization problem, we demonstrate the viability of the proposed mechanism design.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"6 1","pages":"463 - 478"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139345520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.
{"title":"Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation","authors":"A. Malinowska, T. Odzijewicz, A. Poskrobko","doi":"10.34768/amcs-2023-0025","DOIUrl":"https://doi.org/10.34768/amcs-2023-0025","url":null,"abstract":"Abstract This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"38 1","pages":"349 - 359"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139346766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Piotr Bartłomiejczyk, Frank Llovera Trujillo, Justyna Signerska-Rynkowska
Abstract The work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour. In particular, using recent theorems of rotation theory for Lorenz-like maps, we provide a classification of periodic spiking patterns in this model.
{"title":"Spike Patterns and Chaos in a Map–Based Neuron Model","authors":"Piotr Bartłomiejczyk, Frank Llovera Trujillo, Justyna Signerska-Rynkowska","doi":"10.34768/amcs-2023-0028","DOIUrl":"https://doi.org/10.34768/amcs-2023-0028","url":null,"abstract":"Abstract The work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour. In particular, using recent theorems of rotation theory for Lorenz-like maps, we provide a classification of periodic spiking patterns in this model.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"43 1","pages":"395 - 408"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139345325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Bodnar, U. Foryś, M. Piotrowska, Mariusz Bodzioch, J. A. Romero-Rosales, J. Belmonte-Beitia
Abstract Chimeric antigen receptor T (CAR-T) cell therapy has been proven to be successful against different leukaemias and lymphomas. Its success has led, in recent years, to its use being tested for different solid tumours, including glioblastoma, a type of primary brain tumour, characterised by aggressiveness and recurrence. This paper presents an analytical study of a mathematical model describing the competition of CAR-T and glioblastoma tumour cells, taking into account their immunosuppressive capacity. The model is formulated in a general way, and its basic properties are investigated. However, most of the analysis considers the model with exponential tumour growth, assuming this growth type for simplicity. The existence and stability of steady states are studied, and the subsequent focus is on two different types of treatment: constant and periodic. Finally, protocols for CAR-T cell therapy of glioblastoma are numerically derived; these are aimed at preventing the tumour from reaching a critical size and at prolonging the patients’ survival time as much as possible. The analytical and numerical results provide theoretical support for the treatment of glioblastoma using CAR-T cells.
{"title":"On the Analysis of a Mathematical Model of CAR–T Cell Therapy for Glioblastoma: Insights from a Mathematical Model","authors":"M. Bodnar, U. Foryś, M. Piotrowska, Mariusz Bodzioch, J. A. Romero-Rosales, J. Belmonte-Beitia","doi":"10.34768/amcs-2023-0027","DOIUrl":"https://doi.org/10.34768/amcs-2023-0027","url":null,"abstract":"Abstract Chimeric antigen receptor T (CAR-T) cell therapy has been proven to be successful against different leukaemias and lymphomas. Its success has led, in recent years, to its use being tested for different solid tumours, including glioblastoma, a type of primary brain tumour, characterised by aggressiveness and recurrence. This paper presents an analytical study of a mathematical model describing the competition of CAR-T and glioblastoma tumour cells, taking into account their immunosuppressive capacity. The model is formulated in a general way, and its basic properties are investigated. However, most of the analysis considers the model with exponential tumour growth, assuming this growth type for simplicity. The existence and stability of steady states are studied, and the subsequent focus is on two different types of treatment: constant and periodic. Finally, protocols for CAR-T cell therapy of glioblastoma are numerically derived; these are aimed at preventing the tumour from reaching a critical size and at prolonging the patients’ survival time as much as possible. The analytical and numerical results provide theoretical support for the treatment of glioblastoma using CAR-T cells.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"4 1","pages":"379 - 394"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139344841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. Korvel, P. Treigys, Krzysztof Kakol, Bożena Kostek
Abstract The Lombard effect is an involuntary increase in the speaker’s pitch, intensity, and duration in the presence of noise. It makes it possible to communicate in noisy environments more effectively. This study aims to investigate an efficient method for detecting the Lombard effect in uttered speech. The influence of interfering noise, room type, and the gender of the person on the detection process is examined. First, acoustic parameters related to speech changes produced by the Lombard effect are extracted. Mid-term statistics are built upon the parameters and used for the self-similarity matrix construction. They constitute input data for a convolutional neural network (CNN). The self-similarity-based approach is then compared with two other methods, i.e., spectrograms used as input to the CNN and speech acoustic parameters combined with the k-nearest neighbors algorithm. The experimental investigations show the superiority of the self-similarity approach applied to Lombard effect detection over the other two methods utilized. Moreover, small standard deviation values for the self-similarity approach prove the resulting high accuracies.
摘要 伦巴第效应是指在有噪音的情况下，说话者的音调、强度和持续时间会不由自主地增加。它使在嘈杂环境中更有效地交流成为可能。本研究旨在探讨一种检测语音朗伯德效应的有效方法。研究了干扰噪音、房间类型和人的性别对检测过程的影响。首先，提取与伦巴第效应产生的语音变化有关的声学参数。中期统计建立在这些参数之上，并用于自相似矩阵的构建。它们构成了卷积神经网络 (CNN) 的输入数据。然后，将基于自相似性的方法与其他两种方法进行比较，即作为 CNN 输入的频谱图和结合 k 近邻算法的语音声学参数。实验研究表明，应用于伦巴第效应检测的自相似性方法优于其他两种方法。此外，自相似性方法的标准偏差值较小，证明了该方法的高准确度。
{"title":"Investigation of the Lombard Effect Based on a Machine Learning Approach","authors":"G. Korvel, P. Treigys, Krzysztof Kakol, Bożena Kostek","doi":"10.34768/amcs-2023-0035","DOIUrl":"https://doi.org/10.34768/amcs-2023-0035","url":null,"abstract":"Abstract The Lombard effect is an involuntary increase in the speaker’s pitch, intensity, and duration in the presence of noise. It makes it possible to communicate in noisy environments more effectively. This study aims to investigate an efficient method for detecting the Lombard effect in uttered speech. The influence of interfering noise, room type, and the gender of the person on the detection process is examined. First, acoustic parameters related to speech changes produced by the Lombard effect are extracted. Mid-term statistics are built upon the parameters and used for the self-similarity matrix construction. They constitute input data for a convolutional neural network (CNN). The self-similarity-based approach is then compared with two other methods, i.e., spectrograms used as input to the CNN and speech acoustic parameters combined with the k-nearest neighbors algorithm. The experimental investigations show the superiority of the self-similarity approach applied to Lombard effect detection over the other two methods utilized. Moreover, small standard deviation values for the self-similarity approach prove the resulting high accuracies.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"113 1","pages":"479 - 492"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139344077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka–Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.
{"title":"A Method of Lower and Upper Solutions for Control Problems and Application to a Model of Bone Marrow Transplantation","authors":"L. Parajdi, Radu Precup, Ioan Ştefan Haplea","doi":"10.34768/amcs-2023-0029","DOIUrl":"https://doi.org/10.34768/amcs-2023-0029","url":null,"abstract":"Abstract A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka–Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"60 1","pages":"409 - 418"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139345103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A nonsmooth optimization control (NOC) based on a sandwich model with hysteresis is proposed to control a micropositioning system (MPS) with a piezoelectric actuator (PEA). In this control scheme, the hysteresis phenomenon inherent in the PEA is described by a Duhem submodel embedded between two linear dynamic submodels that describe the behavior of the drive amplifier and the flexible hinge with load, respectively, thus constituting a sandwich model with hysteresis. Based on this model, a nonsmooth predictor for sandwich systems with hysteresis is constructed. To avoid the complicated online search for the optimal value of the generalized gradient at a nonsmooth point, the method of the so-called weighted estimation of generalized gradient is proposed. In order to compensate for the model error caused by model uncertainty, a model error compensator (MEC) is integrated into the online optimization control strategy. Afterwards, the stability of the control system is analyzed based on Lyapunov’s theory. Finally, the proposed NOC-MEC method is verified on an MPS with a PEA, and the corresponding experimental results are presented.
{"title":"Nonsmooth Optimization Control Based on a Sandwich Model with Hysteresis for Piezo–Positioning Systems","authors":"Sen Yang, Yonghong Tan, Ruili Dong, Qingyuan Tan","doi":"10.34768/amcs-2023-0033","DOIUrl":"https://doi.org/10.34768/amcs-2023-0033","url":null,"abstract":"Abstract A nonsmooth optimization control (NOC) based on a sandwich model with hysteresis is proposed to control a micropositioning system (MPS) with a piezoelectric actuator (PEA). In this control scheme, the hysteresis phenomenon inherent in the PEA is described by a Duhem submodel embedded between two linear dynamic submodels that describe the behavior of the drive amplifier and the flexible hinge with load, respectively, thus constituting a sandwich model with hysteresis. Based on this model, a nonsmooth predictor for sandwich systems with hysteresis is constructed. To avoid the complicated online search for the optimal value of the generalized gradient at a nonsmooth point, the method of the so-called weighted estimation of generalized gradient is proposed. In order to compensate for the model error caused by model uncertainty, a model error compensator (MEC) is integrated into the online optimization control strategy. Afterwards, the stability of the control system is analyzed based on Lyapunov’s theory. Finally, the proposed NOC-MEC method is verified on an MPS with a PEA, and the corresponding experimental results are presented.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"22 1","pages":"449 - 461"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139345067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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