Matching time-frequency enhancement and its application to bearing fault diagnosis under time-varying speed conditions

Performing time-frequency (TF) analysis (TFA) to nonstationary signal can help to reveal the changing frequency trend of the signal as time varies. However, when the frequency changes rapidly, the TFA methods may only restore the outline of frequency due to the extra TF diffusion caused by limited TF resolution. To improve the readability of the time-frequency representation (TFR), linear chirplet transform (LCT) can enhance the energy concentration when the analyzed signals change with a certain trend. Due to that an individual LCT could only enhance the TFR at the time consistent with a certain chirp rate, general linear chirplet transform (GLCT) is then developed by iteratively involving LCT with variable chirp rates to better match the changing features of the frequency. Though GLCT alleviates the time-frequency (TF) diffusion and increase the energy concentration, the superposing operation also brings in additional cross term interferences generated by inappropriate chirp rates. As such, a new matching TF enhancement method is proposed, which aims to enhance the TFR and avoid the cross terms introduced by GLCT. Instead of superposition, the appropriate chirp rate is picked under the guidance of kurtosis and only the corresponding spectral slices are restored for the final result, so that the cross terms can be avoided. Besides, with the selected chirp rate, a novel transforming kernel is developed, enabling the proposed method could enhance the TFR of multiple frequency components simultaneously without iteration. Moreover, the signal reconstruction of the proposed transform is elaborated. The effectiveness of the proposed method is validated by both simulated and experimental analyses.