A Two-Stage Kalman Estimation Approach to Identify Parameters of a Nonlinear Elastic Structure

Abstract

When structural damage occurs, nonlinearity usually exists in damaged structures. So far, some progresses in the identification of nonlinearity in structures have been made. The extended Kalman filter (EKF) has been applied for the identification of nonlinear 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 estimator approach, which is not available in the previous literature, is proposed for the identification of nonlinear structural parameters. In the first stage, state vector of a nonlinear structure is considered as an implicit function of the nonlinear structural parameters, and the parametric vector is estimated directly based on the Kalman estimator. In the second stage, state vector of the nonlinear 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 nonlinear parameters and state vector are respectively derived and presented, by using the Kalman estimator method respectively. The proposed approach is straightforward. To demonstrate the accuracy and effectiveness of the proposed approach, numerical example of identifying the parameters of a 4-story nonlinear elastic Duffing-type shear-beam building is conducted. Simulation results show that the proposed approach is able to identify nonlinear structural systems.