Modal decomposition and identification for a population of structures using physics-informed graph neural networks and transformers

Modal identification is key to structural health monitoring and control, offering vital insights into dynamic behavior. This study proposes a novel deep learning framework that combines graph neural networks (GNNs), transformers, and a physics-informed loss to perform modal decomposition and identification among a population of structures. The transformer extracts single-degree-of-freedom (SDOF)-equivalent modal response estimates from multi-degree-of-freedom (MDOF) measurements, enabling the identification of natural frequencies and damping ratios. The GNN encodes structural topology to infer the corresponding mode shapes. Trained in a fully unsupervised, physics-informed manner, the model leverages modal decomposition theory and mode independence, requiring no labeled data. Validation through simulations and lab experiments demonstrates accurate recovery of modal properties from sparse measurements under varying loading and structural conditions. Comparisons with conventional modal identification methods highlight the framework’s effectiveness, robustness, and superior performance, establishing it as a powerful tool for population-level structural monitoring.