De-mixing variational mode decomposition and its application on operational modal analysis in the presence of closely spaced modes

Abstract

Variational mode decomposition (VMD), and its derivative methods have been demonstrated to be promising signal decomposition tools and widely utilized in modal analysis. However, they inevitably suffer from mode mixing sometimes, greatly impairing the quality of decomposition. This paper proposes a pair of novel VMD-based methods for univariate signal and multivariate signal respectively, referred to as de-mixing VMD (D-VMD) and de-mixing multivariate VMD (D-MVMD), which can greatly alleviate mode mixing in decomposition. The ensemble correlation coefficient is defined to evaluate the correlatedness between one mode and others and then involved in the variational formulation as an additional Lagrangian multiplier item to enhance the constraint in terms of mode mixing. Additionally, a new scheme is proposed to robustly identify modal parameters from the decomposed modal responses. Numerical simulations and a pedestrian bridge were investigated to validate the effectiveness of the proposed methods in identifying closely spaced modes.