Stochastic resonance of a multi-stable system and its application in bearing fault diagnosis

This paper investigates the stochastic resonance and mean-first passage time of a quad-stable potential in the presence of Gaussian white noise and periodic forcing. The analytical expressions of mean-first passage time and spectral amplification are obtained, respectively. It is found that even small noise intensity can lead to noise-assisted hopping between two adjacent potential wells for the case of small damping coefficient. For large noise intensity, the escape process of Brownian particles is accelerated in an underdamped nonlinear system. Moreover, the curve of spectral amplification displays a typical resonant peak at an optimal noise intensity, suggesting the onset of stochastic resonance. Meanwhile, with the decrease of periodic signal frequency, the peak value of spectral amplification is enhanced. Especially, an optimal quad-stable potential structure exists to maximize the stochastic resonance effect. The proposed multi-stable stochastic resonance method is applied to the fault diagnosis of inner and outer race bearing, and the quantum particle swarm optimization algorithm is used to optimize the system parameters and damping coefficient. The good agreement between fault frequency and theoretical value validates efficiency of the proposed method. Compared with the overdamped tri-stable stochastic resonance method, the performance of fault diagnosis is enhanced substantially by the proposed method.