Using physics-informed graph neural networks for modal identification of a population of structures

Abstract. Modal identification is crucial for almost every downstream task related to structural health monitoring (SHM), in the sense that it contains information that is vital across the levels of the SHM hierarchy, including damage identification and prediction of future performance. This study proposes a deep learning model that is built on the Transformer module and the GraphSAGE module for modal identification across a population of structures. The model processes structural dynamic measurements and topology of structural systems to output the decomposed modal responses and corresponding mode shapes of monitored structures. Based on the model input (structural dynamic measurements) and output (modal responses and mode shapes), we exploit the modal decomposition theory and independence of the structural modes, to train the model in a physics-informed manner. We perform numerical simulation to verify the proposed model. Results show that the proposed model can decompose dynamic response for structural configurations from both the training set and the unseen testing set, demonstrating its accuracy and generalization ability in terms of modal decomposition. The decomposed modal responses can further be used to identify natural frequencies and damping ratios.