Noise-Assisted Multivariate Variational Mode Decomposition

Abstract

The variational mode decomposition (VMD) is a widely applied optimization-based method, which analyzes nonstationary signals concurrently. Correspondingly, its recently proposed multivariate extension, i.e., MVMD, has shown great potentials in analyzing multichannel signals. However, the requirement of presetting the number of extracted components K diminishes the analytic property of both VMD and MVMD methods. This work combines MVMD with the noise injection paradigm to propose an efficient alternative for both VMD and MVMD, i.e., the noise-assisted MVMD (NA-MVMD), that aims at relaxing the requirement of presetting K, as well as improving the quality of the resulting decomposition. The noise is injected by adding noise variables/channels to the initial signal to excite the filter bank property of VMD/MVMD on white Gaussian noise. Moreover, an alternative approach of updating center frequencies is proposed, which uses the centroid of the generalized cross-spectrum instead of a simple average of the individual spectral centroids, showing faster convergence. The NA-MVMD is applied to both univariate and multivariate synthetic signals, showing improved analytical ability, noise intolerance, and less sensitivity in selecting the K parameter.

Dynamic Bandwidth Variational Mode Decomposition

“…Further studies should investigate its dependence on bandwidth rate of change (τ αβ ) and constituent count (K) selection. Additionally, exploring noise injection [13], to address the latter, and multivariate signal analysis [17] could extend its capabilities. Future research might also consider bounding the bandwidth of individual modes, allowing for independent mode's dynamic bandwidth.…”

“…Furthermore, VMD uses constant-bandwidth Wiener filters during the optimization in the spectral domain. Similar to EMD, VMD has motivated numerous researchers to investigate and enrich it with diverse attributes [10,11,12], as well as to address drawbacks like the need of constituent count [13,14] and Wiener filters' constant bandwidth [15].…”

Multivariate Swarm Decomposition

“…Given that the performance of the MSwD is not affected by the number of channels, entails that no negative effects are anticipated. This noise injection approach has been successfully applied in the MEMD and MVMD as noise-assisted MEMD [55] and noise-assisted MVMD [56], respectively. Moreover, from the implementation point of view, the MSwD can be accelerated if the input signal is iteratively modulated, while at each iteration it passes from a swarm filter with constant parameters, i.e., M and δ.…”

“…A comprehensive study of suitable metrics for this kind of evaluation is out of the scope of this work. As a suggestion, a couple of promising metrics that can be incorporated in a future extension of the evaluation methodology could be the reconstruction quality factor [57] and the success rate of decomposition [56].…”

Dynamic Bandwidth Variational Mode Decomposition

“…Furthermore, VMD uses constant-bandwidth Wiener filters during the optimization in the spectral domain. Similar to EMD, VMD has motivated numerous researchers to investigate and enrich it with diverse attributes [10,11,12], as well as to address drawbacks like the need of constituent count [13,14] and Wiener filters' constant bandwidth [15].…”