A Two-Stage Kalman Estimation Approach for the Identification of Structural Parameters under Unknown Inputs

Abstract

Detection of structural damages is critical to ensure the reliability and safety of structures. So far, some progresses in structural identification have been made. The extended Kalman filter (EKF) has been one of the classic time-domain approaches for the identification of structural parameters. However, since the extended state vector contains both the state vector and the structural parameters, EKF approach can identify limited numbers of nonlinear structural parameters due to computational convergence difficulty. To overcome such problem, a two-stage Kalman estimation approach, which is not available in the previous literature, is proposed for the identification of structural parameters. In the first stage, state vector of structures is considered as an implicit function of the structural parameters, and the parametric vector is estimated directly based on the Kalman estimator. In the second stage, state vector of the structure is updated by applying the Kalman estimator with the structural parameters being estimated in the first stage. Therefore, analytical recursive solutions for the structural parameters and state vector are respectively derived and presented, by using the Kalman estimator method in a two-stage approach. The proposed approach is straightforward. Moreover, it can identify more numbers of nonlinear structural parameters with less time of iteration calculation compared with the conventional EKF. A numerical example of identifying the parameters of an 8-storey shear-frame structure is conducted. Simulation results show that the proposed approach is effective and accurate.