Time-convolutional network with joint time-frequency domain loss based on arithmetic optimization algorithm for dynamic response reconstruction

Structural Health Monitoring (SHM) systems provide extensive data on in-service bridges, which is crucial for evaluating structural performance. However, data loss frequently occurs due to environmental factors and technical failures. Although missing data reconstruction problem has been largely studied, the accuracy of response reconstruction in the frequency domain is often overlooked. To address this issue, this study proposes to integrate a time-frequency joint loss function within an Arithmetic Optimization Algorithm-Temporal Convolutional Network (AOA-TCN), which leverages temporal and spatial dependencies among measurement points to reconstruct missing dynamic deflection data. The time-frequency joint loss function is enhanced with linear decay weights to increase sensitivity to low-order modal contributions, with an adaptive weighting mechanism balancing loss contributions from time and frequency domains. These adaptive weight parameters are optimized through AOA to enhance the TCN's generalizability. The feasibility and effectiveness of the proposed method are first demonstrated using simulated dynamic deflection data of a finite element model of a continuous beam bridge, and then experimentally verified on a real-world simply-supported beam bridge. The results indicate that the proposed method achieves higher data reconstruction accuracy and more precise modal analysis results compared to existing methods. The Modal Assurance Criterion (MAC) between mode shapes identified using measured data and reconstructed response reached 96.9 %, proving that the proposed method is capable of reconstructing the missing structural response while retaining its frequency-domain information, which is valuable for structural integrity assessment based on modal parameter identification of operational bridges.