Piecewise time-delay tri-stable stochastic resonance system and its application in bearing fault diagnosis

Current studies of time-delay based systems are compared to classical tri-stable stochastic resonance (CTSR) system and do not reflect the effect of adding a delay term on unsaturated systems. In this paper, a piecewise delayed tri-stable stochastic resonance (PTTSR) system is proposed. Firstly, the equivalent Langevin for PTTSR system is derived and compared with the output of CTSR and piecewise tri-stable stochastic resonance (PTSR) systems, where the addition of the time-delay term can further improve the output amplitude. Secondly, mean first pass time (MFPT) and output signal-to-noise ratio ( SNR ) are derived, and the effects of different parameters on MFPT and SNR are investigated. increasing the feedback intensity and time-delay length improved the output SNR . Then, the input period signal is then numerically simulated using the signal-to-noise ratio gain ( SNRG ) as a measurement, which increases by 2.75 dB for PTTSR system compared to PTSR system. Finally, the three systems are used for bearing fault detection and the system parameters are optimized by genetic algorithm. The results showed that the output amplitude of PTTSR system is more than 12 times that of PTSR system and the SNRG increased by more than 2 dB. This demonstrates the superior performance of PTTSR system in detecting weak signals and provides good feasibility in engineering applications.