Weak Fault Diagnosis Based on a Flexibly Tunable Potential-Well–Barrier Bistable Stochastic Resonance Method

The traditional stochastic resonance (SR) system is constrained by the structure of its potential function, which affects the matching between the signal and parameters, making it challenging for the system to achieve the optimal SR output. Based on the Logistic function, a bistable stochastic resonance model (LMBSR) is presented in this paper, featuring flexible regulation of the potential well and barrier. This model enables precise control of the potential function structure through the introduction of system parameters a and b. Building upon the bistable SR model, the Kramers escape rate and the theoretical SNR are derived. By studying the influence of parameters a and b on the particle transition rate and the theoretical SNR output, the SR theory of LMBSR system is analyzed. The study shows that the optimal theoretical response of SR can be achieved when the system parameters are selected in a reasonable interval. To verify the effectiveness of the LMBSR system in signal detection, this paper introduces the general variable scale method into the LMBSR system to realize the effective matching between the system and the large parameter signal. Simulation and experimental comparisons are then conducted between the LMBSR system and the classical bistable system. The results demonstrate that the proposed method exhibits superior fault feature extraction capability in bearing fault signal processing.