Time domain identification of nonlinear structural dynamic systems using unscented kalman filter

Abstract

In this thesis, the recently developed unscented Kalman filter (UKF) technique is studied for identification of nonlinear structural dynamic systems as an alternative to the extended Kalman filter (EKF). The EKF, which was originally developed as a state estimator for nonlinear systems, has been frequently employed for parameter identification by introducing the state vector augmented with the unknown parameters to be identified. However, the EKF has several drawbacks such as biased estimations and erroneous estimations especially for highly nonlinear dynamic systems due to its crude linearization scheme. To overcome the weak points of the EKF, the UKF was recently developed. The UKF generates a set of points, which captures the mean and covariance information, and accomplishes prediction process by using mapping those points through the nonlinear dynamic and observation equations under consideration, hence it does not require linearization process. Numerical simulation studies have been carried out on SDOF and MDOF systems. The results on the linear and nonlinear SDOF systems show that the UKF gives more accurate and robust estimates under the existence of the system and measurement errors with rough initial guesses for the states and the error covariance matrices. The results on a five-story building structure subjected to nonlinear behavior on the columns on the first floor show that the UKF has good estimation capability. The results from a series of numerical simulations indicate that the UKF is superior to the EKF in the system identification of nonlinear dynamic systems especially highly nonlinear systems.