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Nonlinear system identification in coherence with nonlinearity measure for dynamic physical systems—case studies

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A Correction to this article was published on 06 March 2024

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Abstract

With the recent success in using time series data, many nonlinear identification tools have emerged to learn the nonlinear dynamics of unknown physical systems. However, if the nonlinearity level is very high or too small, in many cases, the identified model fails to precisely learn the actual dynamics of the system, which in turn makes the closed-loop control more challenging. Finding out a suitable system identification routine for identifying a given nonlinear system based on the nonlinearity level is still cryptic. In this article, we propose an integrated framework ‘System identification in coherence with nonlinearity measure’ that involves three reliable nonlinear system identification methods and a ‘Convergence area-based Nonlinear Metric’ (CANM). The nonlinear identification methods in order are (a) An enhanced key term-based Sparse Identification of Nonlinear Dynamics with control (kSINDYc) (b) Standard Nonlinear Least Square method (NL2SQ) and (c) Neural Network-based Nonlinear Auto Regressive Exogenous input (N3ARX) schemes. This article revolves around the central idea of developing kSINDYc to capture the nonlinear dynamics of high nonlinear systems. Furthermore, the nonlinear metric CANM computes the process nonlinearity in the dynamic physical systems that classify the unknown process under mild, medium or highly nonlinear categories. Simulation studies are carried out on five industrial systems with divergent nonlinear dynamics. The user can make a flawless choice of a specific identification method suitable for a given process from CANM.

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The data analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The first author acknowledges the financial support ‘Anna Centenary Research Fellowship’ (ACRF) funded by Centre for Research, Anna University, Chennai, India to carry-out this study.

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Authors and Affiliations

  1. Dublin, Ohio, 43016, United States

    Joanofarc Xavier

  2. Department of EEE, College of Engineering, Anna University, Chennai, 600025, India

    S. K. Patnaik

  3. Department of Chemical Engineering, Chief Scientist and Faculty, CSIR-Central Leather Research Institute, Adyar, Chennai, 600020, India

    Rames C. Panda

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  1. Joanofarc Xavier
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Xavier, J., Patnaik, S.K. & Panda, R.C. Nonlinear system identification in coherence with nonlinearity measure for dynamic physical systems—case studies. Nonlinear Dyn 112, 6475–6501 (2024). https://doi.org/10.1007/s11071-023-09258-0

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