Physics – Constrained Neural Network for the Spatio-temporal Prediction and Reconstruction of the Tilt and Deflection of Smart Bridges.

Abstract

Smart cities increasingly rely on large-scale Internet of Things (IoT) networks to monitor critical infrastructure (such as bridges) and support data-driven decision making. Monitoring the health of bridges requires accurate information on the structural responses - such as tilt and deflection - at critical locations. This information is usually gathered through distributed sensing systems or discrete point sensors. Distributed sensors provide spatially high-resolution information but also generate large volumes of data, increase communication and maintenance costs, and create scalability challenges for long-term monitoring systems. In contrast, discrete sensors can only provide information at their installation positions.

This thesis presents a framework that uses only one discrete sensor per span to reconstruct the longitudinal tilt and deflection of a continuous prestressed concrete girder at uninstrumented positions. The proposed framework integrates autoregressive forecasting and Physics-Constrained Neural Networks (PCNNs) based on Euler–Bernoulli beam theory to address inverse problems associated with uncertain loads and material properties arising from construction imperfections.

Four interconnected models are developed: (i) an Autoregressive (AR) model for multi-day sensor signal forecasting, (ii) a PCNN model that combines sensor measurements with environmental features to reconstruct full-span tilt and deflection responses, (iii) an integrated AR-PCNN pipeline for predictive full-span reconstruction, and (iv) a Finite Element Method (FEM) model used as a baseline for validating the physics-constrained framework. The models are evaluated using real-world data from the IDA-KI OpenLab research bridge. Results show that the AR-PCNN framework achieved an R2 of up to 0.9 while maintaining PDE residual below 4.9x{10}^{-4}, demonstrating strong accuracy and physical consistency.