Investigating dimensionally-reduced highly-damped systems with multivariate variational mode decomposition: an experimental approach

Structural health monitoring (SHM) is an essential engineering field aimed at ensuring the safety and reliability of civil infrastructures. This study proposes a methodology using multivariate variational mode decomposition (MVMD) for damage detection and modal identification. MVMD decomposes multi-sensor vibration responses into intrinsic modal components, facilitating the extraction of natural frequencies and damping ratios by analyzing amplitude decay in the identified modes. Mode shapes are determined through peak-normalization of Fourier spectra corresponding to each mode. The methodology is further applied to detect damage by identifying changes in the extracted modal parameters and spatial features of the structure. The proposed approach enables damage detection by tracking variations in modal parameters and spatial structural characteristics. To validate its efficacy, the methodology is applied to a benchmark eight-degree-of-freedom (8-DOF) system from Los Alamos National Laboratory (LANL), demonstrating its robustness in identifying structural damage under non-stationary excitation and narrowband frequency content. The results confirm that MVMD provides a reliable and adaptable framework for modal analysis and damage assessment in complex infrastructure systems, addressing key challenges such as environmental variability and practical scenarios.