Low-Rank Enforced Fault Feature Extraction of Rolling Bearings in a Complex Noisy Environment: A Perspective of Statistical Modeling of Noises

The fault feature extraction of rolling element bearings is of critical interest for fault diagnosis. The fault impulses are always buried in strong and complex background noise, which makes it hard to detect the fault characteristics and further diagnose the bearing. Many feature extraction techniques have been developed, which assumed that the noise obeys a single and straightforward Gaussian distribution. However, the noise is usually non-Gaussian and cannot be characterized by a single distribution in practical industrial scenarios. A fault feature extraction model for rolling bearings within complex noise is proposed in this article, where the complex noise is modeled by the Gaussian mixture model (GMM), thus highlighting the fault characteristics. The 2-D representation of the measurement is obtained by exploiting cyclic spectral analysis. Then, the measurement is further modeled as a low-rank faulty component and a complex noise component, where the noise is characterized by the GMM. Therefore, the model is named the GMM enable low-rank (GMM-LR) model. The variational Bayes inference method is employed to estimate the posterior of the proposed model, which can obtain the optimal solution to characterize the fault characteristics. Finally, the bearing fault features are detected by the enhanced envelope spectrum (EES). Both the synthetic and experimental signals are studied to demonstrate the efficacy of the proposed technique. The superiority is also validated by comparisons with envelope spectrum (ES), cyclic spectral analysis, spectral kurtosis (SK), and robust principal component analysis (RPCA).