Symplectic quaternion singular mode decomposition with application in gear fault diagnosis

Abstract

Multivariate signals contain more abundant and accurate fault features than univariate signal, so it is beneficial to fault diagnosis with processing the multivariate signals simultaneously. Symplectic singular mode decomposition (SSMD) is an adaptive phase space reconstruction method based on symplectic geometry aiming at processing univariate signal. Quaternion singular spectrum analysis (QSSA) is a multivariate signal processing method in traditional Euclidean geometry, so basic features of original multivariate signals may be destroyed. Therefore, symplectic quaternion singular mode decomposition (SQSMD) is proposed to decompose multivariate signals to a series of independent meaningful components, meanwhile the method keeps essential features of raw multivariate time series unchanged. SQSMD applies symplectic similarity transformation to the constructed quaternion Hamilton matrix by selecting embedding dimension automatically without user-defined parameter, then the transformed trajectory matrix is decomposed by quaternion singular mode decomposition to obtain quaternion eigenvectors and singular values, and finally symplectic quaternion singular spectrum components (SQSSCs) are obtained by taking fault information from multivariate signals as a whole to enhance fault characteristics. Simulated and experimental multivariate signals results indicate the effectiveness and superiority of the proposed method.