Quaternion singular spectrum analysis using convex optimization and its application to fault diagnosis of rolling bearing

Abstract With the rapid development of multi-source information fusion and multi-dimensional sensor technologies, the signal processing technology based on multi-channel signal has obvious advantages in noise elimination and signal reconstruction. In this paper, the correlation of four-channel signals is described by the quaternion domain, and a quaternion singular spectrum analysis method based on the convex optimization is proposed. Singular spectrum analysis (SSA) is used to analyze a single channel vibration signal in the phase space, which is performed by different singular spectrum characteristics of the trajectory matrix. For the signal processing in the quaternion domain, the trajectory matrixes developed by embedding procedure of four channels are employed to generate the augmented trajectory matrix. Then, the useful signal and unwanted signal such as noise can be distinguished by quaternion singular value decomposition (QSVD) to augmented trajectory matrix. It should also be noted that the convex optimization with non-convex penalty functions for QSVD is utilized to accurately estimate non-zero singular value, which can be set as regularization item in the matrix low-rank approximation. The proposed method is validated through numerical simulation signal and experimental signal. By comparing the results obtained from the proposed method, signal channel Fast Fourier Transform (FFT), SSA and multivariate empirical mode decomposition (MEMD), it is found that the application of the proposed model leads to a better solution to extract the feature frequency in mechanical fault diagnosis.