A Fractional Exponential Power Bistable Stochastic Resonance Method for Rolling Bearing Weak Features Extraction

Stochastic resonance (SR) has been broadly investigated in feature extraction for vibration signals. However, the output saturation of classical bistable SR (CBSR) limits its capacity to extract weak characteristics. Additionally, the existing unsaturated SR methods are restricted to research the integer exponential power models. Therefore, a fractional exponential power bistable SR (FEPBSR) method is proposed to solve these problems. First, a FEPBSR model is constructed. The model owns an independently adjustable potential structure and superior potential wall shape, thereby alleviating output saturation. The path integral method is employed to derive the analytical formulation of signal-to-noise ratio (SNR). Second, an improved SNR index is constructed to effectively address the deviation between the actual feature frequency and the theoretical characteristic frequency. Third, an adaptive FEPBSR method is proposed, where the constructed SNR index is used as the objective function of the particle swarm optimization (PSO) algorithm. After that, the simulated signal is utilized to assess the performance of the method. Finally, the method is applied to diagnose the faults of rolling bearings based on vibration signals in two cases. Results show that, compared with CBSR and other modified unsaturated SR approaches, the proposed method not only has superior capacity in weak feature extraction but also has a higher output SNR.