Automated method for structural modal identification based on multivariate variational mode decomposition and its applications in damage characteristics of subway tunnels

This paper introduces a fully automated modal identification algorithm based on the Multivariate Variational Mode Decomposition (MVMD) of free vibration responses to determine structural modal parameters. Addressing the challenge of setting MVMD parameters, we introduce a fusion parameter combining power spectral cross-entropy with reconstruction error as an adaptive fitness function in the optimization algorithm, enabling optimal parameter selection. Then, modal frequencies, damping ratios, and shapes of structures can be extracted from autonomously decomposed Intrinsic Mode Functions by employing the principle of modal superposition and least squares fitting without manual parameter adjustments. Validated by a four-degree-of-freedom numerical model, the method demonstrated accurate, automatic modal parameter identification. The method was further applied to a subway tunnel structure model experiment. Comprehensive modal identification was conducted on tunnel structures under varying degrees of damage. The results validate the proposed method's effectiveness and reveal the damaged segment structure's multimodal parameter variation patterns and surrounding soil.