Combined Underdamped Bistatic Stochastic Resonance for Weak Signal Detection and Fault Diagnosis under Wavelet Transform

Abstract

A novel combined underdamped bistable stochastic resonance (CUBSR) is proposed in this paper. Under the noise-free condition, the output amplitude is used as a measurement index of classical bistable stochastic resonance (CBSR) and CUBSR, which demonstrate CUBSR does not have output saturation characteristics and has a more prominent signal enhancement capability. Then, the expressions of mean first-pass time (MFPT), steady-state probability density (SPD) and signal-to-noise ratio (SNR) are derived. Combined with the fourth-order Runge–Kutta algorithm and genetic algorithm (GA) for numerical simulations, the comparison of the theoretical derivation and numerical simulation of CUBSR can be verified. Then, the two systems are applied to the engineering application of bearing fault diagnosis. Finally, the multi-scale noise-modulated SR method based on wavelet packet transform is studied to overcome the limitation of traditional parameter modulation and to achieve SR detection at multiple frequencies. Simulation analysis and bearing fault diagnosis show that the method can effectively detect the multi-frequency weak signal submerged in noise, resulting in a significant enhancement in signal amplitude.