Data-driven pathways to modal coordinates for structural damage detection
Modal filtering transforms spatial vibration measurements into modal coordinates, simplifying tasks such as model correlation, force identification, and damage detection. Classical modal filters rely on a full modal model consisting of natural frequencies, damping ratios, and mode shapes, which limits applicability when modal parameters are difficult to obtain or when operational conditions vary. Recent results show that modal filters can instead be synthesized directly from measured frequency response functions using natural optimization, eliminating the need for modal analysis and demonstrating that the transformation to modal space is not tied to a single computational pathway. In this work, we broaden this perspective and propose a framework of alternative data-driven pathways to modal coordinates. First, we summarize the optimization-based approach, where modal filters are obtained by maximizing filtration quality using evolutionary search applied to FRFs. Next, we introduce a physics-informed learning route in which a neural network is trained to map physical system parameters to their corresponding modal filters, showing that the transformation can be learned rather than derived. Building on this, we consider a more practical formulation where neural networks infer modal filters directly from FRFs, serving as fast surrogates for optimization-based synthesis. Finally, we outline an exploratory pathway in which structural representations, such as geometric or mesh-based descriptions, are used to estimate modal filters, implicitly learning dynamic behavior from structural information. Together, these pathways illustrate that modal coordinates can be recovered through multiple computational strategies, enabling adaptive, generalizable, and efficient alternatives to classical modal analysis. We show proof-of-concepts for selected pathways based on simulated family of dynamic systems and discuss implications for SHM, model updating, and vibration-based diagnostics.