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作者： Chistyakov, Viktor F. Chistyakova, Elena V. Laboratory for Differential Equations and Control Systems Institute for System Dynamics and Control Theory SB RAS Irkutsk Russia

In this paper, we study systems of Fredholm integral equations with a singular matrix multiplying the leading part. We address the solvability issues of such systems with separable kernels and, similarly to differenti... 详细信息

关键词： Fredholm integral equations

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Volterra Series Models for Nonlinear Automatic control systems

Volterra Series Models for Nonlinear Automatic Control Syste...

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2024 International Russian Automation Conference, RusAutoCon 2024

作者： Solodusha, Svetlana Markova, Evgeniia Kokonova, Yuliya Melentiev Energy Systems Institute Sb Ras Irkutsk Russia Matrosov Institute for System Dynamics and Control Theory Sb Ras Irkutsk Russia Irkutsk National Research Technical University Irkutsk Russia

The paper presents algorithms for constructing nonlinear integral models based on the Volterra series tool. Modeling of dynamic processes means assessing the response to possible external changes in real time. The vector of input signals may include measured influences and control actions to be identified based on an analysis of the current state. We use identification algorithms based on the theory of Volterra polynomial equations of the first kind. An approach to the approximate solution to selected types of nonlinear systems of Volterra integral equations using the Newton-Kantorovich method is presented. We use the numerical solution to the corresponding linear system of equations as a trial solution. Calculation schemes obtained with help the standard quadrature methods are given. © 2024 IEEE.

关键词： Integral equations

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Simulation of Nonlinear Dynamic Processes with Volterra Polynomials and Continued Fractions

Simulation of Nonlinear Dynamic Processes with Volterra Poly...

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2023 International Conference on Industrial Engineering, Applications and Manufacturing, ICIEAM 2023

作者： Solodusha, Svetlana Kokonova, Yuliya Melentiev Energy Systems Institute of Sb Ras Matrosov Institute for System Dynamics and Control Theory Irkutsk Russia Irkutsk National Research Technical University Irkutsk Russia

ISBN: (纸本)9781665475952

In this paper, we propose a technique for increasing the accuracy of modeling nonlinear dynamics of input-output systems using finite segments (polynomials) of Volterra integral power series. We highlight a case when the Volterra kernel identification problem is solved. The linear part of the Volterra polynomials of power N is formed as an equivalent continued fraction. Assuming that the corresponding Volterra kernel is known with some error, such an approach allows us to obtain a model with a new linear part that depends on the error. At the same time, prognostic properties of the integral model can be improved by the using the connection coefficient. The problem of indentifying such a parameter was solved using a special extremal problem. We analyzed the performance of the approach for some dynamic systems. Tests examples were used to compare our approach with the known modeling method that employs a series of Volterra polynomials whose transient responses are tuned to different test signal heights. © 2023 IEEE.

关键词： Transient analysis

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An artificial neural network for surrogate modeling of stress fields in viscoplastic polycrystalline materials

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npj Computational Materials 2023年第1期9卷 1981-1990页

作者： Mohammad S.Khorrami Jaber R.Mianroodi Nima H.Siboni Pawan Goyal Bob Svendsen Peter Benner Dierk Raabe Microstructure Physics and Alloy Design Max-Planck-Institut für EisenforschungDüsseldorfGermany Ergodic Labs Lohmühlenstraße 6512435 BerlinGermany Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany Material Mechanics RWTH Aachen UniversityAachenGermany

The purpose of this work is the development of a trained artificial neural network for surrogate modeling of the mechanical response of elasto-viscoplastic grain *** this end,a U-Net-based convolutional neural network(CNN)is trained using results for the von Mises stress field from the numerical solution of initial-boundary-value problems(IBVPs)for mechanical equilibrium in such microstructures subject to quasi-static uniaxial *** resulting trained CNN(tCNN)accurately reproduces the von Mises stress field about 500 times faster than numerical solutions of the corresponding IBVP based on spectral *** of the tCNN to test cases based on microstructure morphologies and boundary conditions not contained in the training dataset is also investigated and discussed.

关键词： methods boundary faster

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On Active-Set Methods for Quadratic Problems with Positive Semidefinite Matrices 23rd

On Active-Set Methods for Quadratic Problems with Positive...

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23rd International Conference on Mathematical Optimization theory and Operations Research, MOTOR 2024

作者： Vasiliev, Igor Gruzdeva, Tatiana Barkova, Mariia Boyarkin, Denis Iakubovskii, Dmitrii Matrosov Institute for System Dynamics and Control Theory of SB RAS 134 Lermontov str. Irkutsk664033 Russia Melentiev Energy Systems Research Institute of SB RAS 130 Lermontov str. Irkutsk664033 Russia

ISBN: (纸本)9783031733642

Quadratic programming problems (QP) arise in a vast variety of real-world applications in finance, engineering, operational research, and many other fields. A huge number of methods and their various modifications have been developed for solving convex QPs. One of the first algorithms popularized as the solution method for QPs was the active-set method. The main idea of the method is selection of a set of binding constraints (an active set) and then iteratively adaptation it by adding and dropping constraints from the index set. The dual active-set (DAS) method of Goldfarb and Idnani is still well-known to be efficient and numerically stable. Taking advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point of the method, its implementation utilizes the Cholesky and QR factorizations and procedures for updating them. At the same time, it suffers from the restriction that it cannot be applied to problems with positive semidefinite objective matrices, whereas in practice optimization problems may often be of such structure. We propose an add-in to the method of Goldfarb and Idnani that allows solving problems with positive semidefinite matrices directly by the DAS algorithm with a warm-start where a good estimate of the optimal active set is used to start the algorithm. The proposed technique is based on the well-known possibility of representing any matrix, as a difference of two, positive definite ones and solving then a sequence of so-called partially linearized problems. It can be viewed as a particular case of the special local search method for DC minimization problems. A computational experiment to testing the proposed approach was carried out on QPs with positive semidefinite objective matrices from the Maros and Meszaros test set. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Iterative methods

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Fast and reliable reduced-order models for cardiac electrophysiology

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GAMM Mitteilungen 2023年第3-4期46卷 e202370014-e202370014页

作者： Chellappa, Sridhar Cansız, Barış Feng, Lihong Benner, Peter Kaliske, Michael Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Institute for Structural Analysis Technische Universität Dresden Dresden Germany

Mathematical models of the human heart increasingly play a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The ultimate aim is to aid medical practitioners diagnose and treat the many ailments affecting the heart. Towards this, modeling cardiac electrophysiology is crucial as the heart's electrical activity underlies the contraction mechanism and the resulting pumping action. Apart from modeling attempts, the pursuit of efficient, reliable, and fast solution algorithms has been of great importance in this context. The governing equations and the constitutive laws describing the electrical activity in the heart are coupled, nonlinear, and involve a fast moving wave front, which is generally solved by the finite element method. The numerical treatment of this complex system as part of a virtual heart model is challenging due to the necessity of fine spatial and temporal resolution of the domain. Therefore, efficient surrogate models are needed to predict the electrical activity in the heart under varying parameters and inputs much faster than the finely resolved models. In this work, we develop an adaptive, projection-based reduced-order surrogate model for cardiac electrophysiology. We introduce an a posteriori error estimator that can accurately and efficiently quantify the accuracy of the surrogate model. Using the error estimator, we systematically update our surrogate model through a greedy search of the parameter space. Furthermore, using the error estimator, the parameter search space is dynamically updated such that the most relevant samples get chosen at every iteration. The proposed adaptive surrogate model is tested on three benchmark models to illustrate its efficiency, accuracy, and ability of generalization. © 2024 The Authors. GAMM - Mitteilungen published by Wiley-VCH GmbH.

关键词： Heart

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Soft sensor for monitoring dynamic changes in cell composition 9

Soft sensor for monitoring dynamic changes in cell compositi...

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9th IFAC Conference on Foundations of systems Biology in Engineering, FOSBE 2022

作者： Espinel-Ríos, Sebastián Morabito, Bruno Bettenbrock, Katja Klamt, Steffen Findeisen, Rolf Laboratory for System Theory and Automatic Control Otto von Guericke University Magdeburg Germany Analysis and Redesign of Biological Networks Max Planck Institute for Dynamics of Complex Technical Systems Germany Control and Cyber-Physical Systems Laboratory TU Darmstadt Germany

ISBN: (纸本)9781713867890

Precise and accurate online monitoring methods are needed to enable smart biomanufacturing and automation. Most of the sensors available focus on process parameters such as metabolite and dissolved gas concentrations, cell density or viability, among other variables like pH, temperature, etc. In this work, we develop a soft sensor algorithm to estimate the cell composition online, a very important aspect often overlooked in the bioprocess monitoring literature. Our strategy is based on full information estimation, an optimization-based estimator that takes into account the dynamics of the cell metabolism and considers all the available measurements from the beginning of the process, thus it has a memory effect. Being able to track dynamic changes in cell composition can open the door to promising applications, e.g., predictive control and automation of biosystems. As a case study, we consider the Escherichia coli's metabolism growing on glycerol under different levels of oxygen supply. We compare the performance of our soft sensor method against resource balance analysis, a previously proposed estimator based on steady-state assumptions. Overall, the presented full information estimator was able to track the dynamic changes in cell composition significantly more accurately. We also discuss how our estimation strategy can be transformed into a moving horizon estimation, where only the available measurements in a fixed and moving window are considered, thereby reducing possible computational burdens. Copyright © 2022 The Authors.

关键词： Metabolism

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Active learning enhanced deep-learning surrogate model for fast MEMS design with high-dimensional design parameter spaces

Active learning enhanced deep-learning surrogate model for f...

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IEEE International Conference on Nano/Micro Engineered and Molecular systems (NEMS)

作者： Chenzi Wang Lihong Feng Wenshuai Lu Wei Bian Zheng You Peter Benner Department of Precision Instrument Tsinghua University Beijing China Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

ISBN: (数字)9798350359831

ISBN: (纸本)9798350359848

MEMS devices suffer from errors in manufacturing processes such as lithography, etching, thinning, etc. These errors cause non-negligible deviations between the actual device performance and the ideal performance obtained from finite element method (FEM) simulation in the design stage. Often, parametric sweeps via FEM simulations at heuristically selected geometrical and material parameter samples are implemented, in order to analyze the corresponding device performance deviations. This analysis is empirical and often fails due to large number of possible design parameter variations caused by manufacturing. Performing parametric sweeps for all possible parameter instances would result in an exponential increase in FEM simulations. In this paper, we propose a novel active learning enhanced deep-learning surrogate model, which replaces the FEM simulation and faithfully predicts the device performance deviations under numerous parameter variances. This provides a powerful tool for predicting device yield at the design stage. Furthermore, the proposed active learning technique could be applied to efficient training of deep learning models for other MEMS design problems.

关键词： Micromechanical devices Performance evaluation Training Nanoelectromechanical systems Training data Predictive models Data models

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Volterra Series Models for Nonlinear Automatic control systems

Volterra Series Models for Nonlinear Automatic Control Syste...

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International Russian Automation Conference (RusAutoCon)

作者： Svetlana Solodusha Evgeniia Markova Yuliya Kokonova Melentiev Energy Systems Institute SB RAS Matrosov Institute for System Dynamics and Control Theory SB RAS Irkutsk Russia Irkutsk National Research Technical University

ISBN: (数字)9798350349818

ISBN: (纸本)9798350349825

关键词： Heuristic algorithms Integral equations Mathematical models Polynomials Vectors Real-time systems Power systems Numerical models Standards Resistance heating

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Model order reduction via substructuring for a nonlinear, differential-algebraic machine tool model with moving loads

Model order reduction via substructuring for a nonlinear, di...

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92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)

作者： Aumann, Quirin Benner, Peter Saak, Jens Vettermann, Julia Mathematics in Industry and Technology Faculty of Mathematics Technische Universitat Chemnitz Reichenhainer Str. 41 Chemnitz09126 Germany Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

Machine tools are permanently exposed to complex static, dynamic and thermic loads. This often results in an undesired dis¬placement of the tool center point (TCP), causing errors in the production process and thus limiting the achievable workpiece quality. Recent research efforts try to counter these effects by process-parallel solutions utilizing machine internal data. Therefore, fast simulation models are a fundamental requirement. Here, model order reduction (MOR) becomes crucial. The resulting low-dimensional models are required for various applications, e.g., in digital twins, the correction of thermally in¬duced errors at the TCP during the production process as well as for lifetime calculations in predictive maintenance. In this contribution, we present a strategy of MOR for a coupled thermo-mechanical model with a nonlinear subsystem and moving loads, using the example of a feed axis with nonlinear machine components. Applying tailored substructuring tech¬niques, we are able to separate the linear and nonlinear system components. This allows to apply classic linear MOR methods to the much larger linear part, whereas the small nonlinear part is kept, and thus enables drastically reduced computing times. The relative movement is considered by a switched system approach. Transient thermo-mechanical interactions of the feed axis are calculated in a final investigation, comparing the performance of the resulting reduced-order model and the original one. © 2023 The Authors.

关键词： Machine tools

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