A cascaded piecewise unsaturated asymmetric under-damped tri-stable stochastic resonance system and its application in bearing fault diagnosis

In this paper, a cascaded piecewise unsaturated asymmetric under-damped tri-stable stochastic resonance (CPUAUTSR) system is proposed to improve the detection capability of the classical tri-stable system and addresses the output saturation problem. Firstly, it demonstrates the good unsaturated characteristics of the piecewise unsaturated asymmetric under-damped tri-stable stochastic resonance (PUAUTSR) system. Then, the steady-state probability density (SPD), mean first passage time (MFPT) of PUAUTSR system are derived, respectively. Based on the adiabatic approximation theory, the spectral amplification (SA) coefficient of CPUAUTSR system is derived for the first time. The effects of different system parameters on the performance indexes are also investigated. The parameters are optimized using the adaptive genetic algorithm (AGA) and used to measure the stochastic resonance performance using signal-to-noise ratio (SNR). Finally, the piecewise unsaturated asymmetric over-damped tri-stable stochastic resonance (PUAOTSR) and CPUAUTSR system are applied to diagnose the fault signal of bearing. The results show that CPUAUTSR system provides better enhancement and detection of bearing fault signals. In particular, in the detection of bearing inner and outer ring faults, the SNR of the second stage CPUAUTSR system is higher than that of PUAOTSR and first stage CPUAUTSR systems by 8.107 dB, 2.733 dB, 1.879 dB, and 0.185 dB, respectively. These findings provide valuable theoretical support and application prospects for practical engineering.