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The dynamical analysis for two-dimensional magnetic bearing system under α-stable Lévy noise excitation based on PINNs

Author

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  • Ma, Shaojuan
  • Li, Baolan
  • Li, Hufei

Abstract

This paper mainly investigates the impact of α-stable Lévy white noise on magnetic bearing systems. By using the Physics-informed neural networks (PINNs) algorithm to solve the time-dependent Fokker–Planck-Kolmogorov (FPK) equation, the transient probability density function (PDF) is ultimately obtained. Firstly, the model of magnetic bearing system excited by α-stable Lévy white noise is established. Secondly, the fractional FPK equation for this model under the excitation of α-stable Lévy white noise is derived. Thirdly, a deep learning method based on PINNs is proposed to solve the corresponding fractional FPK equation. Finally, the effectiveness and feasibility of this method are verified through detailed examples. The results show that the PINNs solution is very consistent with the Monte Carlo (MC) results, which shows that PINNs method is suitable for solving the two-dimension space fractional FPK equation, and proves that PINNs algorithm is not only efficient in calculation, but also effective and interpretable.

Suggested Citation

  • Ma, Shaojuan & Li, Baolan & Li, Hufei, 2025. "The dynamical analysis for two-dimensional magnetic bearing system under α-stable Lévy noise excitation based on PINNs," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925011191
    DOI: 10.1016/j.chaos.2025.117106
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    References listed on IDEAS

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    1. Jing Wang & Shaojuan Ma & Peng Hao & Hehui Yuan, 2019. "Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter," Complexity, Hindawi, vol. 2019, pages 1-12, December.
    2. Ma, Zhiying & Hou, Jie & Zhu, Wenhao & Peng, Yaxin & Li, Ying, 2023. "PMNN: Physical model-driven neural network for solving time-fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Franziska Matthäus & Mario S Mommer & Tine Curk & Jure Dobnikar, 2011. "On the Origin and Characteristics of Noise-Induced Lévy Walks of E. Coli," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-8, April.
    4. A. Dubkov & B. Spagnolo, 2008. "Verhulst model with Lévy white noise excitation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 361-367, October.
    5. Gao, Ting & Duan, Jinqiao & Li, Xiaofan, 2016. "Fokker–Planck equations for stochastic dynamical systems with symmetric Lévy motions," Applied Mathematics and Computation, Elsevier, vol. 278(C), pages 1-20.
    6. Ren, Zhicong & Xu, Wei, 2020. "An improved path integration method for nonlinear systems under Poisson white noise excitation," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    7. Liang, Yanming & Guo, Yongfeng & Lin, Zifei, 2024. "Using reservoir computing to solve FPK equations for stochastic dynamical systems under Gaussian or Non-Gaussian excitation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 645-662.
    8. Ge, Gen & Li, ZePeng, 2016. "A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 469-477.
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