An underdamped stochastic resonance method with stable-state matching for incipient fault diagnosis of rolling element bearings

Most traditional overdamped monostable, bistable and even tristable stochastic resonance (SR) methods have three shortcomings in weak characteristic extraction: (1) their potential structures characterized by single stable-state type are insufficient to match with the complicated and diverse mechanical vibration signals; (2) they vulnerably suffer the interference from multiscale noise and largely depend on the help of highpass filters whose parameters are selected subjectively, probably resulting in false detection; and (3) their rescaling factors are fixed as constants generally, thereby ignoring the synergistic effect among vibration signals, potential structures and rescaling factors. These three shortcomings have limited the enhancement ability of SR. To explore the SR potential, this paper initially investigates the SR in a multistable system by calculating its output spectral amplification, further analyzes its output frequency response numerically, then examines the effect of both damping and rescaling factors on output responses and finally presents a promising underdamped SR method with stable-state matching for incipient bearing fault diagnosis. This method has three advantages: (1) the diversity of stable-state types in a multistable potential makes it easy to match with various vibration signals; (2) the underdamped multistable SR, equivalent to a moving nonlinear bandpass filter that is dependent on the rescaling factors, is able to suppress the multiscale noise; and (3) the synergistic effect among vibration signals, potential structures and rescaling and damping factors is achieved using quantum genetic algorithms whose fitness functions are new weighted signal-to-noise ratio (WSNR) instead of SNR. Therefore, the proposed method is expected to possess good enhancement ability. Simulated and experimental data of rolling element bearings demonstrate its effectiveness. The comparison results show that the proposed method is able to obtain higher amplitude at target frequency and larger output WSNR, and performs better than traditional SR methods.