A novel Lanczos quaternion singular spectrum analysis method and its application to bevel gear fault diagnosis with multi-channel signals

Multi-channel signals collected by multiple sensors contain more operating information than single-channel signal, so multi-channel signal processing method can improve confidence level and accuracy of fault diagnosis. Multivariate empirical mode decomposition (MEMD) is the most widely used multi-channel signal method, however, it has the problem of mode mixing. Quaternion singular spectrum analysis (QSSA) is an effective multi-channel signal denoising method with three defects. It needs huge calculation time, the contribution of irrelevant com-ponents exists in selected singular values, and the obtained denoising signal derives from certain single-channel signal. Hence, a novel multi-channel signal processing method called Lanczos quaternion singular spectrum analysis (LQSSA) is proposed in this paper. First, LQSSA uses Lanczos method during the decomposition of the proposed method, which reduces the calculation time greatly. Then, filter value factor is obtained by introducing Lagrange multiplier to suppress the contribution of the irrelevant components and improve the purity of required signal. Finally, periodic similarity is used to obtain Lanczos quaternion singular spectrum components (LQSSCs) by taking the signal components as a whole, so it breaks the restriction between different channels. The proposed method is applied to simulated signals and experimental signals of bevel gear, and the analysis results show that the proposed method can extract the fault characteristic frequency from the multi-channel signals effectively.