Sparse representation based on local time–frequency template matching for bearing transient fault feature extraction

• A local TF template matching method is proposed for transient feature extraction.
• The method provides an effective TF domain sparse representation approach.
• Keeping the phase of raw signal satisfies native waveform structure of transients.
• The local TF templates contribute to the TF matching with less computational cost.
• The IF ridge tube gives an effective template matching path in the TF domain.

The transients caused by the localized fault are important measurement information for bearing fault diagnosis. Thus it is crucial to extract the transients from the bearing vibration or acoustic signals that are always corrupted by a large amount of background noise. In this paper, an iterative transient feature extraction approach is proposed based on time–frequency (TF) domain sparse representation. The approach is realized by presenting a new method, called local TF template matching. In this method, the TF atoms are constructed based on the TF distribution (TFD) of the Morlet wavelet bases and local TF templates are formulated from the TF atoms for the matching process. The instantaneous frequency (IF) ridge calculated from the TFD of an analyzed signal provides the frequency parameter values for the TF atoms as well as an effective template matching path on the TF plane. In each iteration, local TF templates are employed to do correlation with the TFD of the analyzed signal along the IF ridge tube for identifying the optimum parameters of transient wavelet model. With this iterative procedure, transients can be extracted in the TF domain from measured signals one by one. The final signal can be synthesized by combining the extracted TF atoms and the phase of the raw signal. The local TF template matching builds an effective TF matching-based sparse representation approach with the merit of satisfying the native pulse waveform structure of transients. The effectiveness of the proposed method is verified by practical defective bearing signals. Comparison results also show that the proposed method is superior to traditional methods in transient feature extraction.