Physics-informed machine learning for the structural health monitoring and early warning of a long highway viaduct with displacement transducers

• Static monitoring of a long, curved highway viaduct in a complex urban setting. • Grey-box model integrates physics-based laws with Gaussian Process Regression. • The proposed approach predicts bearing displacements using only temperature and time. • Grey-box outperforms white- and black-box models in both accuracy and robustness. • Early Warning System with Kernel Density Estimation (KDE) detects sub-millimetric displacement anomalies reliably. In Bridge Structural Health Monitoring (SHM), damage detection is often hindered by environmental and operational variability. Confounding influences such as traffic, wind, and especially temperature can significantly affect measurements, making it difficult to distinguish true damage-related anomalies. This challenge is critical in static monitoring of long steel viaducts, where thermal effects dominate displacements, making small damage-induced perturbations difficult to detect. To address this, the study introduces a Physics-Informed Machine Learning (PIML) model that establishes a reliable baseline for the ‘normal conditions’ of the infrastructure. This baseline isolates anomalies attributable to structural damage while accounting for temperature effects. The proposed grey-box approach combines data-driven modelling with physical knowledge of thermal behaviour, enhancing both accuracy and interpretability. A real-world application is presented on a long-span highway viaduct, where longitudinal displacements are monitored using temperature and displacement sensors. By using only temperature and time as inputs, the model captures nonlinear daily and seasonal thermal cycles without additional instrumentation. To assess reliability, an Early Warning System (EWS) is developed based on displacement anomaly thresholds and Kernel Density Estimation (KDE). The PIML model is evaluated against black-box (purely data-driven) and white-box (purely physics-based) alternatives. Damage scenarios are simulated by introducing anomalies into experimental data to test each model’s capability to detect abnormal behaviour while filtering out environmental effects. Results show that the grey-box PIML consistently outperforms black- and white-box models in accuracy, robustness, and anomaly discrimination. These findings demonstrate the potential of PIML to advance SHM practices and enable reliable automated EWSs for bridge monitoring.