Weak fault feature extraction in non-Gaussian noise interference based on adaptive recombination empirical wavelet transform incorporated by sparse coding shrinkage

Abstract The fast kurtogram is a very useful tool in the field of fault diagnosis, but it also contains two drawbacks. On the one hand, its kurtosis indicator is susceptible to random impulse interference, leading to frequency band mis-selection. On the other hand, the frequency band division method determined by the tree filter bank may cause under or over decomposition problems. Therefore, in this paper, a novel fault diagnosis theory is constructed combining the adaptive recombination empirical wavelet transform (AREWT) with the envelope spectral energy ratio (ESER). Adaptive decomposition of frequency bands is first performed using AREWT. Afterwards, the ESER is proposed as a statistical indicator to choose the optimal demodulation frequency band which overcomes the effects of non-Gaussian noise interference and improves diagnostic accuracy. To further highlight the fault elements of the selected components, an adaptive sparse coding shrinkage algorithm is introduced for sparsely denoising sensitive components. Correspondingly, clear fault feature frequency components can be extracted from the envelope spectrum. Finally, the practicability and superiority of the proposed AREWT-ESER approach are fully validated through numerical simulation signals and case studies.