A novel piecewise tri-stable stochastic resonance system with time-delayed feedback and its application

It is of great significance to judge whether mechanical equipment has faults, so it is necessary to study the extraction of mechanical fault characteristic signals. Stochastic resonance (SR) has been applied diffusely in feature extraction because of its excellent output performance, but there are few studies on SR with time-delay feedback (TF) terms. In some cases, the output of the system will be improved when the TF term is added to the SR system, so it is meaningful to study the SR with TF term. Because piecewise tri-stable system has good characteristics of overcoming output saturation, on the basis of piecewise tri-stable SR (PTSR), the time-delay feedback PTSR (TFPTSR) is proposed, and for purpose of further studying the internal mechanism of this system, its generalized potential function and the law that the parameter causes its change are derived and studied. Then the probability density function (PDF) of the proposed model and its mean first-passage time (MFPT) are calculated and compared with the variation of the generalized potential function together with the Signal to noise ratio (SNR), through such research, the difficulty of the system to produce stochastic resonance and the degree of the output performance are directly related to the system parameters. Finally, the proposed TFPTSR method processes the same signal as the PTSR method, and it is found that the TFPTSR method can get better output SNR.