Structural Dynamic Response Reconstruction Based on Recurrent Neural Network–Aided Kalman Filter

In structural health monitoring (SHM), an important issue is the limited availability of measurement data due to the spatial sparsity of sensors installed on the structure. These measurements are insufficient to accurately depict the actual dynamic behavior and response of the structure. Therefore, full-field (i.e., every degree of freedom) structural response reconstruction based on sparse measured data has drawn a lot of attention in recent years. Kalman filter (KF) is an effective technology for response reconstruction (also known as state estimation), providing an optimal solution for systems that can be well-represented by a fully known Gaussian linear state-space model. This implies that both the process noise and measurement noise follow known zero-mean Gaussian distribution, which is impractical in many civil engineering applications considering the unavoidable modeling errors and variations of environmental conditions. To address this challenge, a data-physics hybrid-driven method, i.e., KalmanNet, is proposed in this study for response reconstruction of partially known systems. By integrating a recurrent neural network (RNN) module into the KF framework, KalmanNet can efficiently learn and compute the Kalman gain using available monitoring data, without any Gaussian assumptions or explicit noise covariance specifications (e.g., covariance matrices of process and measurement noise). Both numerical and experimental investigations are conducted to validate this method. The results demonstrate that under the influence of non-Gaussian noise and modeling errors, KalmanNet can effectively and accurately reconstruct the structural response from sparse measurements in real-time and has higher accuracy and robustness compared to traditional KF even with optimal parameter settings.