Self-tuning Multivariate Variational Mode Decomposition

The Multivariate Variational Mode Decomposition (MVMD), being an extension of the Variational Mode Decomposition (VMD), inherits the merits of VMD. However, it encounters an issue wherein its decomposition performance relies heavily on two predefined parameters, the number of modes (K) and the penalty factor (ct). To address this issue, a Self-tuning MVMD (SMVMD) algorithm is proposed. SMVMD employs the notion of matching pursuit to adaptively update K and alpha based on energy occupation and mode orthogonality in the frequency domain, respectively. The experimented results of both simulated signals and real cases demonstrate that the proposed SMVMD not only effectively addresses the parameter rectification problem of the original MVMD, but also exhibits the following advantages: (1) SMVMD displays superior resilience to mode-mixing compared to MVMD, along with enhanced robustness to both noise and variations in ct-value. (2) In comparison to the classical algorithms of multivariate empirical mode decomposition, fast multivariate empirical mode decomposition, and multivariate variational mode decomposition, SMVMD showcases the lowest decomposition error and the best decomposition effect.