Cascaded Nonlinear Mass Fluctuation Stochastic Resonance System and Its Application in Bearing Fault Diagnosis

Stochastic resonance (SR) can realize bearing fault signal diagnosis by transferring noisy energy. In order to enhance the output response of the system and realize effective signal extraction, the nonlinear mass fluctuation SR system caused by nonlinear asymmetric dichotomous noise is cascaded to obtain the cascaded nonlinear mass fluctuation SR system. First, the output amplitude gain of the first-stage of the system is derived, and the influence of different parameters on it is explored; then the effects of different parameters of the cascaded system on the output amplitude gain and the output SNR are studied separately, which proves that the cascaded system can effectively double enhance the output response of the system; finally, the adaptive genetic algorithm is used to solve the difficulty of parameter adjustment, and the cascaded nonlinear mass fluctuation SR system is applied to the bearing fault diagnosis. The system proposed in this paper takes into account the effects of nonlinear asymmetric dichotomous noise and cascaded systems and performs waveform smoothing and double enhancement of the output signal. It can better extract fault signals and has effective engineering value.

Non-Maxwellian distribution in linear systems and its applications

Bimodality is a typical behavior of bistable nonlinear stochastic differential equations. In this work, we find an exact result for calculating the dynamical and stationary probability distribution function in a simple linear system driven by an asymmetric Markovian dichotomous noise. The results show that asymmetric dichotomous noise leads to a unimodal-bimodal distribution transition, exhibiting eight different non-Maxwellian stationary probability distribution profiles in the parameter space. The noise-induced transitions depend on the correlation time, which characterizes the asymmetric dichotomous noise. The calculations are performed using a linear configuration; but applications to other systems governed by nonlinear equations such as single species population growth models are discussed. In the proper limits, the symmetric case, including the Gaussian white noise limit, is recovered. Numerical simulations show good agreement with analytical results. Finally, a possible experimental setup is proposed.