Piecewise Unsaturated Under-Damped Tri-stable Stochastic Resonance System and Its Application in Bearing Fault Diagnosis

Because the classic tri-stable stochastic resonance (CTSR) system has great output saturation in signal amplification. This paper proposes a piecewise unsaturated under-damped tri-stable stochastic resonance (PUUTSR) system. First, comparing the amplitude of the output signal of the CTSR and PUUTSR systems by changing the amplitude of the input signal, the result proves that the PUUTSR system overcomes the output saturation of the CTSR system. Then, the steady-state probability density (SPD) and signal-to-noise ratio (SNR) of the PUUTSR system are theoretically analyzed. In addition, the PUUTSR, CTSR, and piecewise unsaturated over-damped tri-stable stochastic resonance (PUOTSR) systems are numerically simulated under the same conditions, and it is found that the PUUTSR system has the largest SNR and the strongest signal amplification capability. Finally, the three systems are applied to the detection of the fault signals. In the fault diagnosis of the outer ring of the bearing, PUUTSR can increase the peak value of the frequency spectrum at the fault frequency to 8638, while CTSR can only increase it to 20.7. In the fault diagnosis of the inner ring, PUUTSR can increase the peak value of the frequency spectrum at the fault frequency to 7837, while CTSR can only increase it to 4.665. The final experimental results proved the superiority of its performance in practical applications.