Analysis of weak signal detection based on tri-stable system under Levy noise

Stochastic resonance system is an effective method to extract weak signal. However, system output is directly influenced by system parameters. Aiming at this, the Levy noise is combined with a tri-stable stochastic resonance system. The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon. The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth. First, the method of generating Levy noise, the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail. Then, the effects of tri-stable system parameters w, a, b, and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises. Finally, the tri-stable stochastic resonance system is applied to the bearing fault detection. Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w, a, and b under different distributions of Levy noise, then the weak signal can be detected. The parameter intervals which can induce stochastic resonances are approximately equal. Moreover, by adjusting the intensity amplification factor D of Levy noise, the stochastic resonances can happen similarly. In bearing fault detection, the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.