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.

因为经典的三稳态随机共振（CTSR）系统在信号放大方面有很大的输出饱和。本文提出了一种分段不饱和欠阻尼三稳态随机共振（PUUTSR）系统。首先，通过改变输入信号的幅度比较CTSR和PUUTSR系统输出信号的幅度，结果证明PUUTSR系统克服了CTSR系统的输出饱和。然后，从理论上分析了PUUTSR系统的稳态概率密度（SPD）和信噪比（SNR）。此外，在相同条件下对PUUTSR、CTSR和分段不饱和过阻尼三稳态随机共振(PUOTSR)系统进行了数值模拟，发现PUUTSR系统具有最大的信噪比和最强的信号放大能力。最后，将这三个系统应用于故障信号的检测。在轴承外圈故障诊断中，PUUTSR可以将故障频率处的频谱峰值提高到8638，而CTSR只能提高到20.7。在内环故障诊断中，PUUTSR可以将故障频率处的频谱峰值提高到7837，而CTSR只能提高到4.665。最终的实验结果证明了其在实际应用中的优越性。PUUTSR可以将故障频率处的频谱峰值提高到7837，而CTSR只能提高到4.665。最终的实验结果证明了其在实际应用中的优越性。PUUTSR可以将故障频率处的频谱峰值提高到7837，而CTSR只能提高到4.665。最终的实验结果证明了其在实际应用中的优越性。