Identification of large-scale systems with noisy data using an iterated cubature unscented Kalman filter

Abstract

Online structural health monitoring of large-scale models of infrastructures under hazardous environmental loadings— like earthquakes—has been a vital research topic during recent years. A linear Kalman filter has been employed in many cases in which the desired parameters are extracted in a propagated state vector during a recursive regime. Also, many other kinds of nonlinear filters have been developed for nonlinear systems identification following the linear Kalman filter concept, such as the unscented Kalman filter and the cubature Kalman filter. The main contribution of these two Kalman filtering techniques relies on the propagation of a covariance matrix instead of nonlinear transition and measurement functions. Our extensive literature review shows that divergence of estimated states for large degree-offreedom (DoF) models is the main drawback of these techniques. To overcome this weakness, these two filters’ predefined points, sigma points, are combined—with some modifications—to have more predetermined points for the propagation of states and output of covariance matrices. The proposed technique was developed to be used for large DoF systems with a high level of noisy measured data, which indicates a robust identification system. To evaluate the proposed method, a numerical model (10 DoF linear system) with high levels of noise in the measured response data are employed to evaluate the robustness of the proposed method. The results show that the proposed method is significantly superior to the traditional UKF for noisy measured data in systems with large degrees of freedom.