The theoretical method of stochastic resonance (SR) is helpful for the extraction of mechanical fault signals in the background of strong noise. Therefore, SR has been developed rapidly in the field of mechanical fault diagnosis. In the method of fault diagnosis based on SR, the under-damped tri-stable SR system shows its superiority in performance. However, the disadvantage of this model is that the potential function of the nonlinear system is not standardized enough, which brings inconvenience to the subsequent adjustment of system parameters. In order to solve this problem, this paper proposes a standard three-well underdamped stochastic resonance system. The steady-state probability density and output signal-to-noise ratio of the system are fully studied. Finally, a fault signal detection method based on the standard three-well underdamped stochastic resonance system is proposed, and the feasibility of this method in early fault diagnosis is proved by two different experimental platforms.

随机共振（SR）的理论方法有助于在强噪声背景下提取机械故障信号。因此，SR在机械故障诊断领域得到了迅速的发展。在基于SR的故障诊断方法中，欠阻尼三稳态SR系统在性能上表现出优越性。但该模型的缺点是非线性系统的势函数不够标准化，给后续系统参数的调整带来不便。为了解决这个问题，本文提出了一种标准的三井欠阻尼随机共振系统。充分研究了系统的稳态概率密度和输出信噪比。最后，