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Research and application of stochastic resonance in quad-stable potential system

To solve the problem of low weak signal enhancement performance in the quad-stable system, a new quad-stable potential stochastic resonance (QSR) is proposed. Firstly, under the condition of adiabatic approximation theory, the stationary probability distribution (SPD), the mean first passage time (MFPT), the work (W), and the power spectrum amplification factor (SAF) are derived, and the impacts of system parameters on them are also extensively analyzed. Secondly, numerical simulations are performed to compare QSR with the classical Tri-stable stochastic resonance (CTSR) by using the genetic algorithm (GA) and the fourth-order Runge–Kutta algorithm. It shows that the signal-to-noise ratio (SNR) and mean signal-to-noise increase (MSNRI) of QSR are higher than CTSR, which indicates that QSR has superior noise immunity than CTSR. Finally, the two systems are applied in the detection of real bearing faults. The experimental results show that QSR is superior to CTSR, which provides a better theoretical significance and reference value for practical engineering application.