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.

多变量信号比单变量信号具有更多丰富，准确的故障特征，因此同时处理多变量信号对故障诊断很有帮助。辛奇异模分解（SSMD）是一种基于辛几何的自适应相空间重构方法，旨在处理单变量信号。四元数奇异频谱分析（QSSA）是传统欧几里得几何学中的一种多元信号处理方法，因此原始多元信号的基本特征可能会被破坏。因此，提出了辛四元数奇异模分解（SQSMD），将多元信号分解为一系列独立的有意义分量，同时使原始多元时间序列的基本特征保持不变。SQSMD通过在没有用户定义参数的情况下自动选择嵌入维数来对构造的四元数汉密尔顿矩阵进行辛相似变换，然后通过四元数奇异模分解分解变换后的轨迹矩阵以获得四元数本征向量和奇异值，最后得到辛四元数奇异谱分量（ SQSSC是通过从整体上从多变量信号中获取故障信息来增强故障特性而获得的。仿真和实验的多元信号结果表明了该方法的有效性和优越性。然后通过四元数奇异模分解对变换后的轨迹矩阵进行分解，得到四元数本征向量和奇异值，最后通过从多元信号中整体获取故障信息来得到辛四元数奇异谱分量（SQSSC），以增强故障特性。仿真和实验的多元信号结果表明了该方法的有效性和优越性。然后通过四元数奇异模分解对变换后的轨迹矩阵进行分解，得到四元数本征向量和奇异值，最后通过从多元信号中整体获取故障信息来得到辛四元数奇异谱分量（SQSSC），以增强故障特性。仿真和实验的多元信号结果表明了该方法的有效性和优越性。