Grey-Box Modeling of Temperature–Frequency Interactions: Controlled Laboratory Investigation Using a Bridge Hanger Model

This study extends previous work on grey-box modeling for Structural Health Monitoring (SHM) by transitioning from real-bridge data analysis to controlled laboratory experimentation. Earlier research demonstrated that combining physics-based principles with machine learning (ML) techniques improves temperature compensation of natural frequencies in bridge hangers; however, large time shifts between temperature and dynamic response limited interpretability. To overcome this issue, a scaled laboratory model of a bridge hanger is developed, enabling controlled thermal loading and reproducible boundary conditions. Acceleration and temperature measurements are collected under systematically varied thermal inputs to replicate and analyze the observed time-lag phenomena. Several data-driven models, including Linear Regression and Gradient Boosting Regressor, are re-evaluated in this controlled environment and subsequently enhanced with prior physics knowledge to form grey-box formulations. The results show that the laboratory setting enables isolation of dominant thermo-mechanical mechanisms and provides clarity on their role in spectral evolution. Furthermore, the grey-box models improve temperature-compensation accuracy and offer deeper insight into the origin and magnitude of the temperature–frequency time shifts. The study highlights the value of controlled experiments for improving the reliability of SHM models and supports the transfer of validated grey-box approaches to full-scale bridge applications.