An adaptive method based on fractional empirical wavelet transform and its application in rotating machinery fault diagnosis

Compared with the stable running condition, the vibration signals of rotating machinery during the startup or run-down stage have more abundant information, and these are more sensitive to weak changes in the machine operating state. Therefore, it is of great importance to accurately and efficiently extract state feature information of rotor startup vibration signals. However, non-stationary cases such as amplitude modulation, frequency modulation and a strong background noise do exist in a rotor system with variable speeds, which makes the extraction of feature information more difficult. As a novel analysis method, empirical wavelet transform (EWT) can automatically extract empirical modes of non-stationary signals. Nevertheless, rotor startup vibration signals can be seen as multi-component linear frequency modulation (LFM) signals whose components overlap with each other in the Fourier spectrum, which makes the EWT analysis method no longer valid. Therefore, a new analysis method named 'fractional empirical wavelet transform (FrEWT)' is proposed in this paper, which effectively combines the advantages of fractional Fourier transform (FrFT) and EWT. On the one hand, FrFT is very suitable for analyzing LFM signals, which provides each LFM component of the rotor startup vibration signal with compact support and enables the components to be separated from each other in an appropriate fractional Fourier domain. On the other hand, based on the analysis of the EWT, a wavelet filter bank in the fractional Fourier domain is constructed adaptively to extract the fault feature components of rotor startup vibration signals. Finally, the effectiveness of the proposed method is verified by both simulated and experimental data. The analysis results prove that the proposed method demonstrates excellent performance.