Mutation detection and fast identification of switching system based on data-driven method

doi:10.1088/1674-1056/acb9f5

Abstract In the engineering field, switching systems have been extensively studied, where sudden changes of parameter value and structural form have a significant impact on the operational performance of the system. Therefore, it is important to predict the behavior of the switching system, which includes the accurate detection of mutation points and rapid reidentification of the model. However, few efforts have been contributed to accurately locating the mutation points. In this paper, we propose a new measure of mutation detection — the threshold-based switching index by analogy with the Lyapunov exponent. We give the algorithm for selecting the optimal threshold, which greatly reduces the additional data collection and the relative error of mutation detection. In the system identification part, considering the small data amount available and noise in the data, the abrupt sparse Bayesian regression (abrupt-SBR) method is proposed. This method captures the model changes by updating the previously identified model, which requires less data and is more robust to noise than identifying the new model from scratch. With two representative dynamical systems, we illustrate the application and effectiveness of the proposed methods. Our research contributes to the accurate prediction and possible control of switching system behavior.

Keywords: mutation detection switching index system identification sparse Bayesian regression

Received: 24 October 2022
Revised: 05 December 2022
Accepted manuscript online: 08 February 2023

PACS:	02.30.Hq	(Ordinary differential equations)
	05.45.-a	(Nonlinear dynamics and chaos)
	02.50.-r	(Probability theory, stochastic processes, and statistics)
	02.60.Pn	(Numerical optimization)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12072261).

Corresponding Authors: Wei Xu
E-mail: weixunpu@nwpu.edu.cn

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Zhonghua Zhang(张钟化), Wei Xu(徐伟), and Yi Song(宋怡) Mutation detection and fast identification of switching system based on data-driven method 2023 Chin. Phys. B 32 050201

[1] Song Y, Xu W and Niu L Z 2022 Sci. China-Technol. Sci. 65 1700
[2] Zhang Y X, Jin Y F, Xu P F and Xiao S M 2020 Nonlinear Dyn. 99 879
[3] Wei W, Xu W and Liu J K 2021 Physica A 582 126246
[4] Yan B B, Li Y, Dai P and Liu S X 2019 J. Aerosp. Eng. 32 04019058
[5] An J G, Yan M, Zhou W B, Sun X H and Yan Z 1988 J. Aircr. 25 216
[6] Brunton S L and Kutz J N 2019 Data-Driven Science and Engineering: Machine Learning (Cambridge: Cambridge University Press) pp. 253-275
[7] Kossack C F and Kendall M G 1956 Br. J. Stat. Psychol. 9 68
[8] Mann H B 1945 Econometrica 13 245
[9] Yamamoto R, Iwashima T, Kazadi S N and Hoshiai M 1985 J. Meteorol. Soc. Jpn. 63 1157
[10] He W P, Feng G L, Wu Q, Wan S Q and Chou J F 2008 Nonlinear Process Geophys. 15 601
[11] Savit R S and Green M L 1991 Physica D 50 95
[12] Pincus S 1995 Chaos 5 110
[13] Abramson N, Braverman D J and Sebestyen G S 1963 IEEE Trans. Inf. Theory 9 257
[14] Goodfellow I, Bengio Y and Courville A 2016 Deep Learning (Cambridge: The MIT Press) pp. 45-63
[15] Kalman R E 1959 J. Fluids Eng.-Trans. ASME 82 35
[16] Ho B L 1965 AT-Autom. 14 545
[17] Gershenfeld N 1999 Kybernetes 35 597
[18] Juang J N, Pappa R S and Alvin K F 1985 J. Guid. Control Dyn. 8 620
[19] Rowley C W, Mezić I, Bagheri S, Schlatter P and Henningson D S 2009 J. Fluid Mech. 641 115
[20] Schmid P J 2010 J. Fluid Mech. 656 5
[21] Tu J H, Rowley C W, Luchtenburg D M, Brunton S L and Kutz J N 2015 J. Comput. Dyn. 1 391
[22] Kutz J N, Brunton S L, Brunton B W and Proctor J L 2016 Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems (Philadelphia: SIAM) pp. 105-118
[23] Takeishi N, Kawahara Y and Yairi T 2017 Proceedings of the 31st International Conference on Neural Information Processing Systems, December 4-9, 2017, Los Angeles, USA, pp. 1130-1140
[24] Lusch B, Kutz J N and Brunton S L 2018 Nat. Commun. 9 4950
[25] Mardt A, Pasquali L, Wu H and Noé F 2018 Nat. Commun. 9 4443
[26] Wehmeyer C and Noé F 2018 J. Chem. Phys. 148 241703
[27] Yeung E, Kundu S and Hodas N 2019 2019 American Control Conference (ACC), July 10-12, 2019, Philadelphia, USA, pp. 4832-4839
[28] Brunton S L, Proctor J L and Kutz J N 2016 Proc. Natl. Acad. Sci. USA 113 3932
[29] Mangan N M, Brunton S L, Proctor J L and Kutz J N 2016 IEEE Trans. Mol. Biol. Multiscale Commun. 2 52
[30] Dam M, Brons M, Rasmussen J J, Naulin V and Hesthaven J S 2017 Phys. Plasmas 24 1
[31] Mangan N M, Kutz J N, Brunton S L and Proctor J L 2017 Proc. R. Soc. A-Math. Phys. Eng. Sci. 473 20170009
[32] Boninsegna L, Nüske F and Clementi C 2018 J. Chem. Phys. 148 241723
[33] Rudy S H, Brunton S L, Proctor J L and Kutz J N 2017 Sci. Adv. 3 e1602614
[34] Zhang Y X, Duan J Q, Jin Y F and Li Y 2021 Nonlinear Dyn. 106 2829
[35] Zhang Y X, Duan J Q, Jin Y F and Li Y 2020 Chaos 30 113112
[36] Markus Q, Markus A, Nathan K J and Brunton S L 2018 Chaos 28 063116
[37] Hoffmann M, Froehner C and Noe F 2019 J. Chem. Phys. 150 025101
[38] Huang Z L, Tian Y P, Li C J, Lin G, Wu L L, Wang Y and Jiang H Q 2020 J. Mech. Phys. Solids 137 103871
[39] Li C J, Huang Z L, Wang Y and Jiang H Q 2020 Sci. China-Technol. Sci. 64 148
[40] Tipping M E 2001 J. Mach. Learn. Res. 1 211
[41] Bishop C M 2007 Pattern Recognition and Machine Learning (New York: Springer-Verlag) pp. 227-240
[42] Tipping M E and Faul A C 2003 Ninth International Workshop on Artificial Intelligence and Statistics, January 3-6, 2003, Florida, USA
[43] Wolf A, Swift J B, Swinney H L and Vastano J A 1985 Physica D 16 285

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