Multi-Frequency Signal Detection Based on Frequency Exchange and Re-Scaling Stochastic Resonance and Its Application to Weak Fault Diagnosis

Mechanical fault diagnosis usually requires not only identification of the fault characteristic frequency, but also detection of its second and/or higher harmonics. However, it is difficult to detect a multi-frequency fault signal through the existing Stochastic Resonance (SR) methods, because the characteristic frequency of the fault signal as well as its second and higher harmonics frequencies tend to be large parameters. To solve the problem, this paper proposes a multi-frequency signal detection method based on Frequency Exchange and Re-scaling Stochastic Resonance (FERSR). In the method, frequency exchange is implemented using filtering technique and Single SideBand (SSB) modulation. This new method can overcome the limitation of "sampling ratio" which is the ratio of the sampling frequency to the frequency of target signal. It also ensures that the multi-frequency target signals can be processed to meet the small-parameter conditions. Simulation results demonstrate that the method shows good performance for detecting a multi-frequency signal with low sampling ratio. Two practical cases are employed to further validate the effectiveness and applicability of this method.