Research on fault detection of asymmetric piecewise well-posed stochastic resonance system

Stochastic resonance of an asymmetric piecewise well-posed system driven by a periodic forcing and Gaussian white noise is investigated. Aiming at the problem that the output saturation of the classical stochastic resonance (CSR) system needs to be further improved, the dimensionality of the quartic function is reduced to a quadratic function, and the well position of the function becomes asymmetric. First, the potential function and mean first passage time are analyzed, and then the signal to noise ratio formula of the system is derived through adiabatic approximation theory. Second, the system is simulated and tested. Theoretical analysis and numerical simulation show that the system in a well-posed symmetric case has better performance than the CSR system, but is better in a well-posed asymmetric case. Finally, the bearing fault detection is processed by using the proposed system. The results show that the fault frequency can be more accurately identified by the well-posed asymmetry, and the energy of the characteristic signal can be improved further. The theoretical basis and reference value of the system are provided for further application in practical engineering testing.