Study of frequency-shifted and re-scaling stochastic resonance and its application to fault diagnosis

When detecting a weak and high-frequency signal submerged in strong noise, the existing large parameter stochastic resonance (LPSR) models need either a high sampling frequency or a large number of sample points. To breach the above limits and raise the usability of LPSR, a novel method named frequency-shifted and re-scaling stochastic resonance (FRSR) is proposed in this paper. By shifting and re-scaling the frequency, FRSR provides a way to alleviate the contradiction between sampling frequency and the number of sample points. The proposed method is verified with simulated signals. The results show that this method is useful in weak fault diagnosis of mechanical systems which involve high feature frequencies. Compared with the existing LPSR models, FRSR just requires a lower sampling frequency, a smaller data length and has higher efficiency. Finally, the proposed method is applied to a milling machine tool fault diagnosis and an outer ring fault feature of the spindle bearing is found successfully. Thus, FRSR is a meaningful try for SR coming into practical use of mechanical fault diagnosis.