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Reliability analysis of a class of stochastically excited nonlinear Markovian jump systems

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  • Hu, Rongchun
  • Zhang, Dongxu
  • Gu, Xudong

Abstract

It is inevitable for the nonlinear systems to suffer from external stochastic disturbance. Meanwhile, the components failure will bring abrupt changes in its substructures, which can be considered as the internal stochastic disturbance. It is demonstrated that the components failure performs random jumpy factors switching between a finite number of modes. This salient feature allows us to identify this type of dynamic behaviors as response of nonlinear hybrid systems undergoing Markovian jumps. In this paper a novel method is presented to analyze the dynamical reliability of multi-degree-of-freedom (DOF) nonlinear stochastic systems undergoing Markovian jumps. Firstly, the Markovian jump process is introduced to formulate the aforementioned systems as continuous-discrete hybrid systems. Secondly, a two-step approximate method is applied to convert the hybrid systems to one governed by a set of averaged Itô stochastic differential equations (SDEs) of mechanical energies. Then the associated averaged backward Kolmogorov equation and the Pontryagin equation are constructed and solved to yield the conditional reliability function and the mean first-passage time of the original system respectively. Finally, an example of two coupled Duffing oscillators is illustrated to compare the analytical results and those from Monte Carlo simulation to verify the effectiveness of the proposed method.

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  • Hu, Rongchun & Zhang, Dongxu & Gu, Xudong, 2022. "Reliability analysis of a class of stochastically excited nonlinear Markovian jump systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
  • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010912
    DOI: 10.1016/j.chaos.2021.111737
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    References listed on IDEAS

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    1. Li, Wei & Xu, Wei & Zhao, Junfeng & Jin, Yanfei, 2006. "First-passage problem for strong nonlinear stochastic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 414-421.
    2. Altan, Aytaç & Karasu, Seçkin, 2020. "Recognition of COVID-19 disease from X-ray images by hybrid model consisting of 2D curvelet transform, chaotic salp swarm algorithm and deep learning technique," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. La Barbera, A & Spagnolo, B, 2002. "Spatio-temporal patterns in population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 120-124.
    4. Dehghanpour, Kaveh & Afsharnia, Saeed, 2015. "Electrical demand side contribution to frequency control in power systems: a review on technical aspects," Renewable and Sustainable Energy Reviews, Elsevier, vol. 41(C), pages 1267-1276.
    5. Karasu, Seçkin & Altan, Aytaç & Bekiros, Stelios & Ahmad, Wasim, 2020. "A new forecasting model with wrapper-based feature selection approach using multi-objective optimization technique for chaotic crude oil time series," Energy, Elsevier, vol. 212(C).
    6. Warner J. Venstra & Hidde J. R. Westra & Herre S. J. van der Zant, 2013. "Stochastic switching of cantilever motion," Nature Communications, Nature, vol. 4(1), pages 1-6, December.
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    Cited by:

    1. Aravindh Dharmarajan & Parivallal Arumugam & Sakthivel Ramalingam & Kavikumar Ramasamy, 2023. "Equivalent-Input-Disturbance Based Robust Control Design for Fuzzy Semi-Markovian Jump Systems via the Proportional-Integral Observer Approach," Mathematics, MDPI, vol. 11(11), pages 1-16, June.
    2. Yang, Te & Wang, Zhen & Huang, Xia & Xia, Jianwei, 2022. "Sampled-data exponential synchronization of Markovian jump chaotic Lur'e systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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