Sparse Envelope Spectra for Feature Extraction of Bearing Faults Based on NMF

Periodic impulses and the oscillation response signal are the vital feature indicators of rolling bearing faults. However, finding the suitable feature frequency band is usually difficult due to the interferences of other components and multiple resonance regions. According to the characteristics of non-negative matrix factorization (NMF) on a spectrogram, the feature extraction method from a sparse envelope spectrum for rolling bearing faults is proposed in this paper. On the basis of the time-frequency distribution (TFD) of the periodic transient oscillations, the basic matrix can be interpreted as the spectral bases, and the time weight matrix corresponding to spectral bases can be extracted by NMF. Because the bases and the weights have a one-to-one correspondence, the frequency band filtering with the basic component and the time domain envelope of the weight vector are calculated respectively. Then, the sparse envelope spectrum can be derived by the inner product of the above results. The effectiveness of the proposed method is verified by simulations and experiments. Compared with band-pass filtering and spectral kurtosis methods, and considering the time weights and corresponding the spectral bases for the periodic transient oscillations, the weak fault-rated feature can be enhanced in the sparse spectrum, while other components and noise are weakened. Therefore, the proposed method can reduce the requirement of selecting frequency band filtering.