Pulses caused by rotating mechanical faults are weak and often submerged in strong background noise, which can affect the accuracy of fault detection. To solve this problem, we study the stochastic resonance phenomenon of a tristable potential system based on strong noise background and also investigate the influence of time-delayed feedback on this stochastic resonance model. The effects of time-delayed feedback strength on potential energy, steady-state probability density function, and signal-to-noise ratio (SNR) are discussed. The results show that stochastic resonance can be enhanced or suppressed by adjusting the delay time and feedback strength. Combined with bearing fault diagnosis simulation research and experimental verification evaluation, the proposed time-delayed feedback tristable stochastic resonance fault diagnosis method is more effective than the classical stochastic resonance method.

Signal detection and processing have become an important way to diagnose mechanical faults. The classical bistable stochastic resonance (CBSR) method for signal detection can become saturated, where the amplitude of the output signal gradually stabilizes at a relatively low level instead of increasing with further increases of the input signal amplitude. This leads to difficulty in extracting the weak signals from strong background noise. We studied a new mechanism based on unsaturated piecewise linear stochastic resonance (PLSR). The piecewise linear potential model has a unique structure, which can independently adjust the barrier height and potential wall inclination, so the piecewise linear potential model has a rich potential structure. The rich potential structure makes the potential model unsaturated, thus ensuring that the output signals increase as the input signals increase. In addition, according to the piecewise linear model, the output signal-to-noise ratio (SNR) of the system is deducted. Analysis of the influence of signal strength, potential parameters, and angular frequency on the SNR shows that the optimal SNR can be obtained by adjusting the potential parameters. We propose a weak signal detection method for bearing fault diagnosis. This method can effectively extract the weak fault signals from rolling bearings in a strong noise background. The simulated and experimental bearing fault signals verify that the proposed PLSR method is superior to the CBSR method.

Stochastic resonance is the use of nonlinear systems to synchronize an original signal with noise. This method is commonly used to extract useful signals by reducing noise and has been widely used for mechanical weak fault diagnosis. This paper analyzes the characteristics of a periodic non-sinusoidal potential function, considers the shape of the model, and introduces a time-delay. The steady-state probability density function, effective potential function, and signal-to-noise ratio are then analyzed. As a result, a signal detection method for periodic nonsinusoidal time-delay stochastic resonance (PNTSR) is proposed. Experimental and engineering data are used to explain the PNTSR through the simulation. It is found that the PNTSR method has better fault detection results when compared to the classic bi-stable stochastic resonance method.