Time–frequency manifold sparse reconstruction: A novel method for bearing fault feature extraction

• TFM sparse reconstruction method is proposed for bearing fault feature extraction.
• Image sparse reconstruction improves the merit of TFM analysis in denoising.
• The amplitude and phase of transients are well kept in the sparse reconstruction.
• It is realized to express nonlinear signal processing results explicitly in theory.
• Experimental results verify the effectiveness of the proposed method in denoising.

In this paper, a novel transient signal reconstruction method, called time–frequency manifold (TFM) sparse reconstruction, is proposed for bearing fault feature extraction. This method introduces image sparse reconstruction into the TFM analysis framework. According to the excellent denoising performance of TFM, a more effective time–frequency (TF) dictionary can be learned from the TFM signature by image sparse decomposition based on orthogonal matching pursuit (OMP). Then, the TF distribution (TFD) of the raw signal in a reconstructed phase space would be re-expressed with the sum of learned TF atoms multiplied by corresponding coefficients. Finally, one-dimensional signal can be achieved again by the inverse process of TF analysis (TFA). Meanwhile, the amplitude information of the raw signal would be well reconstructed. The proposed technique combines the merits of the TFM in denoising and the atomic decomposition in image sparse reconstruction. Moreover, the combination makes it possible to express the nonlinear signal processing results explicitly in theory. The effectiveness of the proposed TFM sparse reconstruction method is verified by experimental analysis for bearing fault feature extraction.