Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Abstract

Early fault diagnosis of rolling bearings is of great significance in the application of mechanical equipment, which makes the extraction of weak fault signals particularly critical by stochastic resonance (SR). Compared with bistable SR, tristable SR has stronger advantages in weak signal extraction, but the classical tristable stochastic resonance (CTSR) system was limited by output saturation, which resulted in insufficient signal amplification ability. To solve the above problems, combined with asymmetric system whose output can be improved to a higher degree, a novel piecewise unsaturated asymmetric tristable SR (NPUATSR) system is proposed. Through numerical simulation, it is concluded that NPUATSR output amplitude varies proportionally with the amplitude of the input, which overcomes the output saturation of CTSR. Secondly, the stationary probability density and mean first passage time of particles are derived by using adiabatic approximation theory, and the variation law caused by parameters is analyzed in combination with potential function, the internal mechanism of the system is further studied. Through the output signal-to-noise ratio (SNR), it is found that the performance advantage of NPUTASR system is the most obvious, and different parameters affect the output SNR. Finally, the adaptive genetic algorithm is used to optimize the parameters, and the proposed system is applied to early fault diagnosis on different types of bearings. After comparison with different systems, the results show that NPUATSR can effectively detect the fault frequency, and has the most outstanding advantages in spectrum amplification and anti-noise performance, which proves that NPUATSR system has significant value in practical engineering application.