Piecewise asymmetric exponential potential under-damped bi-stable stochastic resonance and its application in bearing fault diagnosis

It is difficult to extract weak signals in strong noise background, therefore a piecewise asymmetric exponential potential under-damped bi-stable stochastic resonance (PAEUBSR) system is proposed. First, the theoretical analysis of the steady-state probability density (SPD), mean first passage time (MFPT) and output signal-to-noise ratio (SNR) are derived under the adiabatic approximation theory. At the same time, the influence of different system parameters on system performance is explored. Then the PAEUBSR system is applied to the fault signal diagnosis of different types of bearings, and the parameters are optimized through the adaptive genetic algorithm (AGA). The test results are compared with the exponential potential over-damped symmetric bi-stable stochastic resonance (EOSBSR) system and the exponential potential under-damped symmetric bi-stable stochastic resonance (EUSBSR) system. Finally, the detection results on two sets of bearing fault data show that the PAEUBSR system has better effects on the enhancement and detection of bearing fault signals. This provides good theoretical support and application value for this system in subsequent theoretical analysis and practical engineering applications.