Successive multivariate variational mode decomposition

This paper presents an extension of variational mode decomposition (VMD) for successively extracting the modes of multi-sensor data sets. First, we achieve the multi-channel extension of the univariate mode by introducing the multivariate modulated oscillation model, which can take the correlation between multiple data channels into account. Then the successive scheme is accomplished by adding some new criteria to VMD: the current extracting mode has no or less spectral overlap with the previously obtained modes and the residual signal. Finally, we employ the alternate direction method of the multiplier algorithm (ADMM) to solve it. Compared with other multivariate extending methods whose performances will be degraded if the number of modes is not precisely known, this extension can recursively extract modes and does not need to know the number of modes. Therefore, it achieves better performance on convergence and computation requirements. Moreover, it is more robust to the initial center frequency and possesses the mode-alignment property. We also investigate the relationships between the regularization parameter α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and the spectrum property of modes. Some suggestions for selecting proper solution parameters are provided. Finally, we show promising practical decomposition results on a series of simulating and real-life multi-channel data.