Thermal feature subspace based deep learning framework for bridge girder-end displacement reconstruction

Expansion displacement at the girder-end is a significant indicator of the thermal effects on long-span bridges. To address the issue of missing or anomalous bridge girder-end displacement (GED) data caused by sensor failures or transmission interruptions in structural health monitoring (SHM), a feature subspace-based deep learning framework leveraging temperature-displacement correlation for displacement reconstruction is proposed. The framework integrates Singular Spectrum Analysis (SSA) for extracting thermal components and reducing noise interference, minimum redundancy maximum relevance (mRMR) for key feature selection and a hybrid LSTM-Transformer network for capturing multi-scale spatiotemporal dependencies by combining local recurrence with global attention mechanisms. The hyperparameters and feature selection parameters are collaboratively optimized using the Arithmetic Optimization Algorithm (AOA). And a kernel density estimation (KDE)-based approach is further introduced to quantify prediction uncertainty, providing confidence intervals for engineering decision-making. Applied to long-term monitoring data from a single-tower cable-stayed bridge, the proposed method achieved mean absolute errors (MAE) of 0.0850 mm and 0.0406 mm in reconstructing southeast (channel DT-1) and northwest (channel DT-4) girder-end displacements, respectively, with R 2 values exceeding 0.98. The model also accurately captures hysteresis characteristics in temperature-displacement relationships and maintains high performance on hold-out year data, confirming its generalization capability across seasonal variations. The framework exhibits strong robustness under sparse monitoring conditions and effectively handles both local outliers and continuous data gaps. These results highlight its practical potential as a reliable and economical solution for SHM systems under sensor failure scenarios.