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Abstract
The advantages of stochastic resonance (SR) have received extensive attention and research in the field of weak signal extraction. It can be used to extract fault signals from rotating machinery. To deeply improve the output signal-to-noise ratio (SNR), a second-order underdamped tristable stochastic resonance (SUTSR) is proposed in the present study. The potential function, the steady-state probability density of particles and the SNR are used to evaluate the model. Firstly, the relationship between the noise intensity and the SNR of SUTSR is studied. Then, using the steady-state solution curve, the output response of the SUTSR system is discussed from the perspective of steady-state input, and the output response of the system is further studied when inputting low-frequency harmonic signals. Finally, SUTSR model is used to process bearing signal data with inner ring fault and rolling element fault, and the processing result is compared with tristable system and second-order underdamped bistable system. The results show that, in the background of strong noise, the SUTSR system can accurately identify the characteristic frequency of the fault signal and then greatly improve the energy of the weak fault signal under appropriate system parameters.
Highlights
Stochastic resonance is a nonlinear system containing characteristic signals and noise
Under the small parameters and combined with progressive elimination theory’s condition, the output signal-to-noise ratio (SNR) of the second order stochastic resonance model based on multi-steady state is deduced
The proposed second-order underdamped tristable stochastic resonance (SUTSR) system can extract the weak fault signal under strong noise background more effectively comparing with the traditional multi-stationary stochastic resonance system and the underdamped secondorder bistable stochastic resonance system
Summary
Stochastic resonance is a nonlinear system containing characteristic signals and noise. In terms of signal processing, the output of the underdamped system equation is equivalent to the secondary filtering, so the second-order stochastic resonance model has a better filtering effect on signal processing. Under the small parameters and combined with progressive elimination theory’s condition, the output SNR of the second order stochastic resonance model based on multi-steady state is deduced. It can be seen from Fig., Fig. and Fig. that non-monotonic change in SNR indicates the presence of stochastic resonance phenomenon of FIGURE 9. From the perspective of Brownian particle motion, the steadystate response of Eq (12) means that the velocity and acceleration of Brownian motion are both zero
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