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Two-Dimensional Tri-stable Stochastic Resonance system and its application in bearing fault detection

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  • Zhang, Gang
  • Liu, Xiaoman
  • Zhang, Tianqi

Abstract

A Two-Dimensional Tri-stable Stochastic Resonance (TDTSR) system with adjustable parameters is proposed to address the problem of difficult parameter tuning in one-dimensional stochastic resonance systems. Firstly, under the limitation of adiabatic approximation theory, the Steady-state Probability Density (SPD) and output Signal-to-Noise Ratio (SNR) of the system are derived, and the effects of system parameters (a, b, c, r, k) on them are analyzed. The results prove that particles are more capable of transiting between potential wells to obtain better resonance effect when the system is coupled. Then, TDTSR system and the One-Dimensional Tri-stable Stochastic Resonance (ODTSR) system are analyzed and simulated numerically respectively, which show that the Mean Signal-to-Noise Ratio Gain (MSNRG) of TDTSR system is greater than that of ODTSR system. Finally, the two systems are applied in bearing faults detection, and the system parameters are optimized by genetic algorithm. The experimental results indicate that TDTSR system is excellent than ODTSR system, which provides a great theoretical significance and practical value for engineering applications.

Suggested Citation

  • Zhang, Gang & Liu, Xiaoman & Zhang, Tianqi, 2022. "Two-Dimensional Tri-stable Stochastic Resonance system and its application in bearing fault detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    • Handle: RePEc:eee:phsmap:v:592:y:2022:i:c:s0378437122000012
    DOI: 10.1016/j.physa.2022.126855
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    References listed on IDEAS

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    1. Vishwamittar, & Batra, Priyanka & Chopra, Ribhu, 2021. "Stochastic resonance in two coupled fractional oscillators with potential and coupling parameters subjected to quadratic asymmetric dichotomous noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Qiao, Zijian & Shu, Xuedao, 2021. "Coupled neurons with multi-objective optimization benefit incipient fault identification of machinery," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Xu, Pengfei & Jin, Yanfei, 2018. "Stochastic resonance in multi-stable coupled systems driven by two driving signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1281-1289.
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    1. Zhang, Gang & Zeng, Yujie & Jiang, Zhongjun, 2022. "A novel two-dimensional exponential potential bi-stable stochastic resonance system and its application in bearing fault diagnosis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).

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