Simultaneous Identification of Structural Parameter and External Excitation with an Improved Unscented Kalman Filter

The structural parameters identification without the prior known time history of external force is still a challenging problem for nonlinear structures. In this study, a new nonlinear system identification method is proposed to evaluate the structural parameters without the prior information of excitation time history. Excitation decomposition algorithm is utilized to the system identification. The structural excitation time history is decomposed by orthogonal approximation. With this approximation, the inverse problem of the external excitation identification is transformed into the inverse problem of parameter identification. An improved Unscented Kalman filter (UKF) is proposed to identify the structural parameters and coefficients of the orthogonal decomposition only based on the acceleration measurements. The computation of the square roots of matrix may be ill-posed. The singular value decomposition (SVD) method instead of Cholesky decomposition is applied to calculate the square roots of the covariance matrix in the updating step of UKF identification to improve the robustness. The calculation of the covariance matrix is also modified to ensure its symmetric property so that error propagation can be mitigated. For the complicate excitation identification, the proposed method can be improved for practical application. The structural response would be divided into several windows. In each window the proposed method is performed iteratively for accuracy identification result. A single degree of freedom structure and a three-story hysteretic nonlinear shear frame are investigated numerically with the proposed identification method. Results from the simulation studies demonstrate that the structural parameters and excitation can be accurately identified. The proposed improved UKF can also simultaneously identify the structural parameters and dynamic excitation fairly accurately with measurement noise.