Optimization of segmentation fragments in empirical wavelet transform and its applications to extracting industrial bearing fault features

Empirical wavelet transform is a wavelet filter bank to decompose a bearing fault signal into several sub-signals for extracting bearing fault features and it attracts lots of attention recently because it looks like a hybrid of wavelet transform and empirical mode decomposition. However, an assumption for use of empirical wavelet transform is that segmentation fragments in empirical wavelet transform must be established in advance. To satisfy this assumption, an artificial rule based on local maxima of the frequency spectrum of a signal was previously proposed to establish segmentation fragments in empirical wavelet transform. Obviously, because the artificial rule completely relies on local maxima, it is not always reliable and not optimal to establish segmentation fragments in empirical wavelet transform for bearing fault feature extraction. In this paper, empirical wavelet transform for extracting bearing fault features is formulated as a constrained optimization problem. Segmentation fragments in empirical wavelet transform are optimized to jointly maximize bearing fault signatures in squared envelope spectra obtained by empirical wavelet transform. Industrial bearing fault signals are used to illustrate how the constrained optimization problem can find the optimal segmentation fragments in empirical wavelet transform. Comparisons with empirical wavelet transform guided by the artificial rule as well as two advanced fault diagnosis algorithms including spectral kurtosis and spectral correlation are made to experimentally demonstrate that the optimal segmentation fragments in empirical wavelet transform can result in higher detection performance.