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A data-driven method for probabilistic response of vibro-impact system with bilateral barriers

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Abstract

In this paper, a data-driven method is proposed to approximate the probability density function (PDF) of the response for the vibro-impact system with bilateral barriers. Non-smooth property is a challenge in random dynamical system, resulting in complex dynamics, such as discontinuous-induced singularity, grazing and chattering. The vibro-impact system is generally described as a hybrid form with discrete mapping and continuous differential equation. A non-smooth variable transformation is employed to rewritten this hybrid form to an equivalent piecewise version. For the obtained equivalent system, the Gaussian mixture model is proposed to approach the PDF governed by the Fokker–Planck–Kolmogorov (FPK) equation. The proposed algorithm can accurately simulate the PDF of the vibro-impact system with varied restitution coefficients within the theoretical difference allowed by the non-smooth variable transformation method. Taking account of the symmetry of the inverse transformation, the stationary PDF and moments of responses for the original system are obtained. Additionally, two examples are provided to demonstrate the efficiency and correctness of the proposed method.

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Acknowledgements

This work was supported by the Postgraduate Innovation Fund Project of Xi’an Polytechnic University (No. chx2022024), and the special research project of Shaanxi Education Statistics Research Center (No. 21jty08).

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  1. School of Science, Xi’an Polytechnic University, Xi’an, 710048, Shaanxi, China

    Wenqing Sun, Jinqian Feng, Jin Su & Qin Guo

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  1. Wenqing Sun
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  2. Jinqian Feng
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Correspondence to Jinqian Feng.

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Sun, W., Feng, J., Su, J. et al. A data-driven method for probabilistic response of vibro-impact system with bilateral barriers. Nonlinear Dyn 111, 4205–4219 (2023). https://doi.org/10.1007/s11071-022-08047-5

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