中国物理B ›› 2022, Vol. 31 ›› Issue (8): 80502-080502.doi: 10.1088/1674-1056/ac588b

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Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises

Gang Zhang(张刚)1, Yu-Jie Zeng(曾玉洁)1,†, and Zhong-Jun Jiang(蒋忠均)2   

  1. 1 School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications(CQUPT), Chongqing 400065, China;
    2 Cyberspace Administration of Guizhou Province, Guiyang 550000, China
  • 收稿日期:2022-01-25 修回日期:2022-02-20 接受日期:2022-02-25 出版日期:2022-07-18 发布日期:2022-08-02
  • 通讯作者: Yu-Jie Zeng E-mail:1156885177@qq.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 61771085), the Research Project of Chongqing Educational Commission, China (Grant Nos. KJ1600407 and KJQN201900601), and the Natural Science Foundation of Chongqing, China (Grant No. cstc2021jcyj-msxmX0836).

Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises

Gang Zhang(张刚)1, Yu-Jie Zeng(曾玉洁)1,†, and Zhong-Jun Jiang(蒋忠均)2   

  1. 1 School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications(CQUPT), Chongqing 400065, China;
    2 Cyberspace Administration of Guizhou Province, Guiyang 550000, China
  • Received:2022-01-25 Revised:2022-02-20 Accepted:2022-02-25 Online:2022-07-18 Published:2022-08-02
  • Contact: Yu-Jie Zeng E-mail:1156885177@qq.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 61771085), the Research Project of Chongqing Educational Commission, China (Grant Nos. KJ1600407 and KJQN201900601), and the Natural Science Foundation of Chongqing, China (Grant No. cstc2021jcyj-msxmX0836).

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摘要： Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system (CTSR), a novel unsaturated piecewise linear symmetric tristable stochastic resonance system (PLSTSR) is proposed. Firstly, by making the analysis and comparison of the output and input relationship between CTSR and PLSTSR, it is verified that the PLSTSR has good unsaturation characteristics. Then, on the basis of adiabatic approximation theory, the Kramers escape rate, the mean first-passage time (MFPT), and output signal-to-noise ratio (SNR) of PLSTSR are deduced, and the influences of different system parameters on them are studied. Combined with the adaptive genetic algorithm to synergistically optimize the system parameters, the PLSTSR and CTSR are used for numerically simulating the verification and detection of low-frequency, high-frequency, and multi-frequency signals. And the results show that the SNR and output amplitude of the PLSTSR are greatly improved compared with those of the CTSR, and the detection effect is better. Finally, the PLSTSR and CTSR are applied to the bearing fault detection under Gaussian white noise and Levy noise. The experimental results also show that the PLSTSR can obtain larger output amplitude and SNR, and can detect fault signals more easily, which proves that the system has better performance than other systems in bearing fault detection, and has good theoretical significance and practical value.

关键词: bearing fault detection, weak signal detection, piecewise linear symmetric tri-stable system, output signal-noise-ratio, adaptive genetic algorithm

Abstract: Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system (CTSR), a novel unsaturated piecewise linear symmetric tristable stochastic resonance system (PLSTSR) is proposed. Firstly, by making the analysis and comparison of the output and input relationship between CTSR and PLSTSR, it is verified that the PLSTSR has good unsaturation characteristics. Then, on the basis of adiabatic approximation theory, the Kramers escape rate, the mean first-passage time (MFPT), and output signal-to-noise ratio (SNR) of PLSTSR are deduced, and the influences of different system parameters on them are studied. Combined with the adaptive genetic algorithm to synergistically optimize the system parameters, the PLSTSR and CTSR are used for numerically simulating the verification and detection of low-frequency, high-frequency, and multi-frequency signals. And the results show that the SNR and output amplitude of the PLSTSR are greatly improved compared with those of the CTSR, and the detection effect is better. Finally, the PLSTSR and CTSR are applied to the bearing fault detection under Gaussian white noise and Levy noise. The experimental results also show that the PLSTSR can obtain larger output amplitude and SNR, and can detect fault signals more easily, which proves that the system has better performance than other systems in bearing fault detection, and has good theoretical significance and practical value.

Key words: bearing fault detection, weak signal detection, piecewise linear symmetric tri-stable system, output signal-noise-ratio, adaptive genetic algorithm

中图分类号:  (Fluctuation phenomena, random processes, noise, and Brownian motion)

  • 05.40.-a
05.45.-a (Nonlinear dynamics and chaos) 05.40.Fb (Random walks and Levy flights) 02.60.Cb (Numerical simulation; solution of equations)