An improved stochastic resonance method with arbitrary stable-state matching in underdamped nonlinear systems with a periodic potential for incipient bearing fault diagnosis

Rolling element bearings are critical mechanical parts that are prone to damage, and the detection of their incipient faults plays an important role in ensuring the safe and reliable operation of rotating machinery. The incipient fault characteristics of rolling bearings suffer attenuation from complicated transmission paths and, moreover, are overwhelmed by background noise, hence it is a challenging task to extract them from a complex environment of vibration signals. In contrast to traditional signal processing methods, stochastic resonance (SR) methods can utilize the noise to highlight incipient fault characteristics. However, most overdamped SR methods can hardly suppress multiscale noise, and the monostable, bistable and even tristable SR methods can hardly achieve arbitrary stable-state matching between various mechanical vibration signals and stable-state types. Combined with genetic algorithms (GAs) and the fourth-order Runge–Kutta algorithm to simultaneously obtain the optimal system parameter, damping factor and damping factor of the new SR model, an improved underdamped periodic SR (UPSR) method with arbitrary stable-state matching in underdamped multistable nonlinear systems with a periodic potential for incipient bearing fault diagnosis is proposed. The periodic potential can achieve the matching between various vibration signals and arbitrary stable-state types and, moreover, underdamped SR can suppress the multiscale noise. To improve the performance in bearing fault detection, the signals in the actual engineering environment are preprocessed by prewhitening processing and a Hilbert transform. Therefore, the improved UPSR method is expected to possess a good ability for extracting incipient fault characteristics. Both simulated and experimental comparison with the underdamped bistable SR (UBSR) and fast-Kurtogram methods are adopted to verify the effectiveness of the proposed method. Compared with the above two methods, the proposed method has better fault characteristic frequency extraction performance. The results show that the proposed method could be more suitable and widely used for incipient bearing fault diagnosis in background noise.