Unveiling the principles of stochastic resonance and complex potential functions for bearing fault diagnosis

A novel comprehensive method for weak signal blind detection based on adaptive quasi-periodic potential stochastic resonance and its application in bearing fault detection

“…This suggests that different signal frequencies may require different numbers of effective potential wells to achieve the optimal output. In addition, combining equations (10) and (20) shows that when the amplitude response of a single potential well is optimally fixed, the number of effective potential wells n exists as a function of the system parameters a,b,c,d,e and the noise intensity D. This shows that even though there are countless potential wells in the potential model, the particles will only make inter-well local transitions between a finite number of potential wells. This also theoretically verifies that the stochastic resonance phenomenon can be induced by both the system parameters and the noise, reflecting the importance of the parameter selection.…”

“…Instead, stochastic resonance utilizes the coordinated relationship achieved between the signal, the noise, and the nonlinear system to convert the noise energy to the weak signal, thus realizing the purpose of weakening the noise and enhancing the weak signal. This phenomenon is not only widely observed in the natural world, such as biological systems [5] and atmospheric environments [6], but is also utilized in various engineering applications, including sensor design [7,8] and signal enhancement [9,10]. In recent years, the theoretical and experimental exploration of stochastic resonance has spanned multiple fields, including remote sensing [11], neuroscience [12], and fault diagnosis [13].…”