Improved Shift-Invariant Sparse Parsing of Mechanical Fault Based on Feature Atom

In complex operating conditions, the monitoring signals of mechanical equipment are susceptible to interference from multiple vibration sources and environmental noise, resulting in weak fault features. The difficulty of extracting weak features brings challenges to equipment fault diagnosis. Therefore, an improved shift-invariant sparse parsing (ISISP) model based on feature atom (FA) is proposed to parse fault features for fault diagnosis. First, the FA construction method based on the time-frequency analysis of the signal is proposed to match the time-domain impulse information. The signal is decomposed, and the component details are reconstructed based on the tunable Q-factor wavelet transform (TQWT). FA is constructed by extracting the optimal wavelet function of the reconstructed components according to the maximum kurtosis criterion. Second, the ISISP algorithm for minimizing residuals is proposed to parse the fault features. Through the correlation analysis between the FA and the original signal, the amplitude features of the impulse components are better preserved by the improved matching pursuit (IMP) algorithm based on minimizing the residuals at the offsets. The sparsity parameterization method of the model based on a priori parameters is proposed. Then, the fault information is identified by the envelope spectrum analysis of the sparsely reconstructed signal obtained from the ISISP model. Finally, analysis of the simulated signal, consisting of periodic impulse signals and multiple redundant components, is used to verify the validity of the ISISP model and the applicability of parameter selection. The harmonic energy ratio (HER) parameter of the reconstructed signal is proposed to quantify the effect of analyzing the envelope spectral features of the reconstructed signal. The feature extraction validity of the ISISP model is verified by experimenting with multiple bearings and gears fault signals. The advantages of the ISISP model are verified by comparison with TQWT_GMC, fast spectrum kurtosis (fast SK), shift-invariant KSVD, and shift-invariant sparse coding (SISC).