Stochastic resonance with Woods–Saxon potential for rolling element bearing fault diagnosis

• Propose a weak signal detection strategy based on Woods–Saxon stochastic resonance.
• Realize SR output enhancement just by Woods–Saxon potential parameter tuning.
• Suitable for detecting weak signal in different driving frequency and noise level.
• Validity and superiority are verified by simulated and practical bearing signals.

This paper proposes a weak signal detection strategy for rolling element bearing fault diagnosis by investigating a new mechanism to realize stochastic resonance (SR) based on the Woods–Saxon (WS) potential. The WS potential has the distinct structure with smooth potential bottom and steep potential wall, which guarantees a stable particle motion within the potential and avoids the unexpected noises for the SR system. In the Woods–Saxon SR (WSSR) model, the output signal-to-noise ratio (SNR) can be optimized just by tuning the WS potential's parameters, which delivers the most significant merit that the limitation of small parameter requirement of the classical bistable SR can be overcome, and thus a wide range of driving frequencies can be detected via the SR model. Furthermore, the proposed WSSR model is also insensitive to the noise, and can detect the weak signals with different noise levels. Additionally, the WS potential can be designed accurately due to its parameter independence, which implies that the proposed method can be matched to different input signals adaptively. With these properties, the proposed weak signal detection strategy is indicated to be beneficial to rolling element bearing fault diagnosis. Both the simulated and the practical bearing fault signals verify the effectiveness and efficiency of the proposed WSSR method in comparison with the traditional bistable SR method.