A Novel Method of Pure Output Modal Identification Based on Multivariate Variational Mode Decomposition

This paper proposes a novel parameterized frequency-domain modal parameter identification method, called direct modal variational mode decomposition (DMVMD), based on the multivariate variational mode decomposition (MVMD) framework and the principle of modal superposition. Under the constraint of normalized mode shapes, this paper theoretically derives the relationship between multivariate variational mode decomposition and the natural frequencies and mode shapes of structural systems. The aim is to extract K response modes and their corresponding mode shapes from the excited C-dimensional vibration signals of the measured component’s response. First, the measured multichannel vibration signals are decomposed into IMFs aligned with K-order natural frequencies using multivariate variational mode decomposition (MVMD). Then, the Hilbert equations and mode shape normalization constraints are used to solve the structural natural frequencies and mode shapes. Furthermore, the proposed multimodal identification algorithm has been validated through numerical simulations and experimental examples, demonstrating its high accuracy and robustness in modal identification. Compared to the existing multimodal algorithms related to variational mode decomposition, the proposed method is more direct and elegant. This method has been successfully applied to the modal parameter identification of subway tunnel structures, enabling accurate determination of the location of tunnel damage through analysis of the identified modal parameters.