Experimental Modal Analysis for engineering structures via time-delay Dynamic Mode Decomposition with Control

Experimental Modal Analysis (EMA) has been widely used to identify structural dynamic properties, including natural frequencies, damping ratios, and mode shapes, for structural integrity assessment. The Poly-reference Least Squares Complex Frequency (pLSCF) method is one of the most widely adopted approaches for EMA because of its strong ability to separate closely spaced modes and its robustness to measurement noise. However, pLSCF-based EMA is generally limited to low-dimensional cases with a small number of measurement points, as its computational cost increases rapidly for high-dimensional or continuous structural measurements, particularly with increasing model order. To overcome this limitation, this paper develops a high-dimensional EMA framework based on Dynamic Mode Decomposition with control (DMDc), a powerful data-driven technique originally developed in fluid dynamics, for modal identification under high-dimensional measurement scenarios. Specifically, the relationship between pLSCF and time-delay DMDc is clarified through the discrete state-space representation of the auto-regressive with exogenous inputs (ARX) model for linear systems. By showing that both methods describe the same physical dynamics of the structure, this study provides a physics-based rationale for applying time-delay DMDc to EMA. The capability and advantages of time-delay DMDc for modal parameter identification in both low- and high-dimensional measurements are validated through numerical simulations of a 6-DOF system and experiments on a cantilever beam using a digital camera. The results demonstrate that time-delay DMDc enables robust and reliable modal parameter identification, effectively addressing high-dimensional EMA problems that are difficult for conventional pLSCF and highlighting its potential for real-world structural dynamics applications.