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Integrate-and-Differentiate Approach to Nonlinear System Identification

Author

Listed:
  • Artur I. Karimov

    (Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia)

  • Ekaterina Kopets

    (Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia)

  • Erivelton G. Nepomuceno

    (Department of Electronic Engineering, Maynooth University, W23 X021 Maynooth, Ireland)

  • Denis Butusov

    (Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia)

Abstract

In this paper, we consider a problem of parametric identification of a piece-wise linear mechanical system described by ordinary differential equations. We reconstruct the phase space of the investigated system from accelerometer data and perform parameter identification using iteratively reweighted least squares. Two key features of our study are as follows. First, we use a differentiated governing equation containing acceleration and velocity as the main independent variables instead of the conventional governing equation in velocity and position. Second, we modify the iteratively reweighted least squares method by including an auxiliary reclassification step into it. The application of this method allows us to improve the identification accuracy through the elimination of classification errors needed for parameter estimation of piece-wise linear differential equations. Simulation of the Duffing-like chaotic mechanical system and experimental study of an aluminum beam with asymmetric joint show that the proposed approach is more accurate than state-of-the-art solutions.

Suggested Citation

  • Artur I. Karimov & Ekaterina Kopets & Erivelton G. Nepomuceno & Denis Butusov, 2021. "Integrate-and-Differentiate Approach to Nonlinear System Identification," Mathematics, MDPI, vol. 9(23), pages 1-19, November.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:2999-:d:685675
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    References listed on IDEAS

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    1. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Xia, Bing & Zhao, Xin & de Callafon, Raymond & Garnier, Hugues & Nguyen, Truong & Mi, Chris, 2016. "Accurate Lithium-ion battery parameter estimation with continuous-time system identification methods," Applied Energy, Elsevier, vol. 179(C), pages 426-436.
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    Cited by:

    1. Karimov, Artur & Kopets, Ekaterina & Karimov, Timur & Almjasheva, Oksana & Arlyapov, Viacheslav & Butusov, Denis, 2023. "Empirically developed model of the stirring-controlled Belousov–Zhabotinsky reaction," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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