Prior-Knowledge-Guided Missing Data Imputation for Bridge Cracks: A Temperature-Driven SP-VMD-CNN-GRU Framework

Data loss caused by sensor malfunctions in bridge Structural Health Monitoring (SHM) systems poses a critical risk to structural safety assessment. Although deep learning has advanced data imputation, standard “black-box” models often fail to capture the underlying deterioration mechanisms governed by physical laws. To address this limitation, we propose SP-VMD-CNN-GRU, a prior-knowledge-guided framework that integrates environmental thermal mechanisms with deep representation learning for bridge crack data imputation. Deviating from empirical parameter selection, we utilize the Granger causality test to statistically validate temperature as the primary driver of crack evolution. Leveraging this prior knowledge, we introduce a Shared Periodic Variational Mode Decomposition (SP-VMD) method to isolate temperature-dominated annual and daily periodic components from noise. These physically validated components serve as inputs to a hybrid CNN-GRU network, designed to simultaneously capture spatial correlations across sensor arrays and long-term temporal dependencies. Validated on real-world monitoring data from the Luo’an River Grand Bridge, our framework achieves the highest coefficient of determination (R2) of 0.9916 and the lowest Mean Absolute Percentage Error (MAPE) of 12.95%. Furthermore, statistical validation via Diebold–Mariano and Model Confidence Set tests proves that our physics-guided approach significantly surpasses standard baselines (TCN, LSTM), demonstrating the critical value of integrating prior knowledge into data-driven SHM.