An effective PGML method combining FEM and LSTM for recovering missing sensor data in real-world building monitoring

Sensor data loss poses a major challenge in structural health monitoring (SHM), as it undermines the accuracy of structural response evaluation. While conventional neural networks (NNs) and the Finite Element Method (FEM) are widely used, they face challenges in standalone response reconstruction at sensor-missing locations, particularly under sparse monitoring conditions. NNs, such as Long Short-Term Memory (LSTM) models, excel at learning mappings but require training data which is unavailable at sensor-missing locations. FEM simulations can provide full-field data, but their predictions often deviate from actual measurements due to idealized assumptions and parameter uncertainties. To address these limitations, this study introduces a physics-guided machine learning (PGML) method that first utilizes a calibrated FEM model to establish the spatial relationships between sensor-equipped and sensor-missing locations. An LSTM network is then trained to map FEM predictions to measured sensor responses at sensor-equipped locations. By combining the physical insights from FEM with the data-driven mapping of LSTM, the proposed method enables reliable reconstruction of responses at sensor-missing locations, thereby augmenting the LSTM’s ability to infer unobserved structural responses. The method is validated using shaking table data from a 12-story reinforced concrete frame subjected to various seismic excitations. Validation results confirm that the PGML achieves more accurate response reconstruction than standalone FEM, demonstrating its practical advantage for SHM applications with incomplete sensor data.