Symmetric circulant matrix decomposition-based multivariable group sparse coding for rolling bearing fault diagnosis

Singular value decomposition technique proves its effectiveness in mechanical signal analysis by decomposing the test signal into a series of singular spectral components of different frequency bands. Nevertheless, how to adapt this technology to the needs of cyclo-nonstationary signal and how to set the decomposition number while maintaining detailed features to obtain the optimal component containing the most fault information, remains an important issue that needs to be addressed in the field of mechanical fault diagnosis. To overcome these disadvantages, the symmetric circulant matrix decomposition (SCMD) is presented. Two main ideas structure the present technique. Firstly, symmetric circulant matrix is used to generate eigenvectors, which will better adapt to the cyclo-nonstationary signal associated with the structural symmetry of rotating machinery. Then, an impulse fluctuation measure is established to adaptively search for the decomposition number and extract the optimal component. Moreover, to better improve the impulse extraction effect of SCMD, the multivariate group sparse coding based on the multivariate correlation characteristics and intra group sparsity characteristics of impulse signals is proposed, which can enhance impulse features while preserving fault details as much as possible. The reliability and feasibility of the proposed method are verified by the experimental signals. The comparison with several classic methods shows that this method is more effectiveness in weak feature extraction.