Dynamic Load Identification and Structural Response Reconstruction Based on the Augmented Kalman Filter

For traditional load identification methods the ill-posedness problem brings about relatively large errors, and due to the insufficiency of monitoring sensors, the structural vibration responses at the damage points can’t be exhaustively monitored. Therefore, an augmented Kalman filter (AKF) algorithm-based dynamic load identification and response reconstruction method was proposed. Based on the structural state space formulation, the load vector and the state vector were combined into the augmented-rank state vector（ASV）, and the Kalman filter algorithm was employed to obtain the minimum-variance unbiased (MVU) estimation of the augmented state vector to realize the simultaneous identification of the state and the load vectors. Furthermore, the dynamic response reconstruction of the structure parts without sensors was realized through combination of the optimal state estimation and the observation matrix. Three finite element cases were studied to verify the feasibility and effectiveness of the proposed method. The results show that, this method can well identify the load and reconstruct the response regardless of moving or fixed loads with high accuracy, and is insensitive to measurement noise. The types, the number and the locations of the sensors have some impact on the accuracy of load identification and response reconstruction.