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Second-order coupled tristable stochastic resonance and its application in bearing fault detection under different noises

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Abstract

Bearing fault is the most likely to occur in mechanical fault, and stochastic resonance (SR), as a noise enhanced signal processing tool, can find mechanical faults as early as possible, so as to avoid larger problems. However, most of the existing research methods are based on the first-order Langevin equation. According to the previous studies of many scholars, the weak signal detection ability of the second-order system is better than that of the first-order system, and the coupled system also has better performance due to the addition of the control system. So, in order to detect the fault signal more easily, a second-order coupled tristable stochastic resonance system (SCTSR) based on the adaptive genetic algorithm (AGA) is proposed, it is an improvement on improving the first-order coupled tristable stochastic resonance system (FCTSR). First, based on the fourth-order Runge–Kutta algorithm (F-RK), the performances of monostable, bistable and tristable control systems to SCTSR are compared, it is verified that the monostable system has the best performance as SCTSR’s control system. Secondly, the equivalent potential function of SCTSR is derived, and the influences of each system parameters on it are researched. The output signal-to-noise ratio gain (SNRG) is chosen as a measure to verify that SCTSR’s performance is better than that of FCTSR, and the influences of parameters on SNRG are discussed. SCTSR and FCTSR are used to detect low-, high- and multi-frequency cosine signals combined with AGA. The simulation results are compared with the wavelet transform method, which proves the performance superiority of SR, and also prove that SCTSR is easier to detect weak signals and has a stronger de-noising ability. Finally, SCTSR and FCTSR are applied in bearing fault detection under Gaussian white noise and trichotomous noise. The results also prove that SCTSR can get larger peaks and SNRG, and it is easier to detect fault signals. This proves that SCTSR’s performance is superior that of other methods in bearing fault detection, and has better engineering application value.

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 61771085), Research Project of Chongqing Educational Commission (KJ1600407, KJQN201900601) and Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0836). The authors also would like to thank the anonymous reviewers for their valuable comments and suggestions. They help us to improve the work comparatively and fundamentally.

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  1. School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications (CQUPT), Chongqing, 400065, China

    Gang Zhang, Yujie Zeng & Tianqi Zhang

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  1. Gang Zhang
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Correspondence to Yujie Zeng.

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Zhang, G., Zeng, Y. & Zhang, T. Second-order coupled tristable stochastic resonance and its application in bearing fault detection under different noises. Nonlinear Dyn 111, 8987–9009 (2023). https://doi.org/10.1007/s11071-023-08303-2

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