Sparsity-guided multi-scale empirical wavelet transform and its application in fault diagnosis of rolling bearings

Empirical wavelet transform (EWT) is a signal decomposition method that distinguishes signals from the frequency domain. When processing non-stationary and strong noise signals, a large number of invalid components may be obtained, or modal aliasing may occur. The biggest contribution of sparsity-guided multi-scale empirical wavelet transform (SMSEWT) is that it can optimize the segmentation method and extract useful frequency band, reduce the number of invalid components, and suppress modal aliasing. In order to divide frequency bands containing similar information into final components, Fourier spectrum will be divided equally and used to calculate kurtosis. Frequency bands with similar kurtosis are considered to contain the same kind of information, which will be combined to achieve adaptive segmentation of the spectrum. Subsequently, empirical wavelet filters will be constructed and the time-domain waveforms of each frequency band can be obtained. Using sparsity to select envelope components containing abundant periodic pulses can diagnose bearing faults.