Stochastic resonance in a high-order time-delayed feedback tristable dynamic system and its application

Abstract

Abstract A stochastic resonance (SR) tristable system based on a high-order time-delayed feedback is investigated and the feasibility of the system for weak fault signature extraction is discussed. The potential function, the mean first-passage time (MFPT) and the signal-to-noise ratio (SNR) are used to evaluate the model. Firstly, the potential function and stationary probability function (PDF) of the system are derived, and then the influence of the time delay parameters on the MFPT of the particles is analyzed. Secondly, the influences of time-delyed strength e and delyed length τ on the SR system from the perspective of the transition of the particles in the potential wells are discussed, and then the SNR and the effect of the parameters on the SNR are derived. In addition, the high-order time-delayed feedback tristable stochastic resonance (HTFTSR) system is used to deal with faulty bearing data and is compared with traditional tristable stochastic resonance (TSR). The result shows that the nonlinear system model can accurately identify the fault frequency and improve the energy of the characteristic signal under the appropriate system parameters.