SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient

Aiming at solving the existing sharp problems by using singular value decomposition (SVD) in the fault diagnosis of rolling bearings, such as the determination of the delay step k for creating the Hankel matrix and selection of effective singular values, the present study proposes a novel adaptive SVD method for fault feature detection based on the correlation coefficient by analyzing the principles of the SVD method. This proposed method achieves not only the optimal determination of the delay step k by means of the absolute value ${{r}_{k}}$ of the autocorrelation function sequence of the collected vibration signal, but also the adaptive selection of effective singular values using the index $\rho $ corresponding to useful component signals including weak fault information to detect weak fault signals for rolling bearings, especially weak impulse signals. The effectiveness of this method has been verified by contrastive results between the proposed method and traditional SVD, even using the wavelet-based method through simulated experiments. Finally, the proposed method has been applied to fault diagnosis for a deep-groove ball bearing in which a single point fault located on either the inner or outer race of rolling bearings is obtained successfully. Therefore, it can be stated that the proposed method is of great practical value in engineering applications.