Improvement Of Kalman Filter And Kalman Estimator In The Application Of Structural Damage Detection

Structural health monitoring technique plays an important role in structural safety and reliability assessment. In the frame of structural health monitoring, structural damage detection theory has been greatly developed at the moment, among them, the vibration-based structural parameters identification method has become a significant research aspect. In the time domain analysis, the least square estimation (LES) and the extended Kalman filter (EKF) have derived dramatic attention. There are two limitations for the application of EKF in structural damage detection:1) EKF can only be used when the external forces are set to be known;2) the state vector in EKF contains structural parameters, which leads to the nonlinear coupling of the response state vector and parameters. Thus, the solution of the EKF approach may easily become unstable. On the other hand, the relatively large extended state vector will result in low computational efficiency when dealing with complex structure.The main work of this thesis concentrates on the improvement of EKF, by introducing the technique of cross-correlation function, the theory of Kalman estimator and the concept of separating structural state and parameters, the thesis overcomes some drawbacks of EKF and enlarge its application.The first part of this thesis combines the structural responses based cross-correlation function technique and EKF to make it capable to be used in the structural damage detection on the condition of unknown ambient excitation. When the excitations which act on the structure are independent stationary white noise process, then using the proposed method can identify the structural parameters accurately. On the other hand, because of the characteristics of cross-correlation function, the effect of noise which contaminate the original signal can be eliminated during the process, so the identified structural parameters perform great anti-noise property. Numerical and experimental validations all show the feasibility of the proposed method in structural damage detection.In the second part of this thesis, in order to remove the drawbacks of the EKF approach, a new approach which makes it possible to identify structural state X and unknown parameters9in two steps, referred to as the Two-step Kalman filter approach, is proposed in this paper. In this approach, the structural response state vector X is considered as an implicit function of the unknown parameters θ. Then, through Tayler expansion, the responses observation function can be linearized, and the parametric vector θ and the response state vector X are estimated in two steps by using the Kalman filter separately. Thus, the problem of calculation instability and solution divergence in EKF can be avoided, and the computational storage can also be saved due to the degradation of the dimension of the state vector. Numerical and experimental examples are conducted to test its feasibility and accuracy in structural damage detection.Extended Kalman Estimator, referred to as EKE, was proposed by our research group to make it possible in structural damage detection when limited input and output are used. Moreover, considering the limitation of requirement for input information in EKF approach and inspired by the concept of two-step Kalman filter method, a two-stage two-step Kalman estimator approach is proposed. In the first stage, by using Kalman estimator sequentially in two steps, the structural state X and unknown parameters θ in k+1time point are identified separately on the condition that only the k time point observation information is required; in the second stage, since the updated structural state X and unknown parameters θ are derived, the external excitation can be derived by using least square estimation. Numerical and experimental examples validate the proposed method.The three parts of this thesis aim at making some improvement of the EKF, considering the drawbacks of EKF. Numerical and experimental results validate the proposed methods. Computation results and comparison figures present the accuracy and efficiency of the methods.