Identification and Uncertainty Estimation of Structural Parameters

Abstract

In the application of system identification to a structural system, unknown parameters are determined based on the numerical analysis of input and output measurements. The accuracy of an identified parameter and its uncertainty both depend on the numerical method, measurement noise and modeling error. Most studies, however, identify parameter means without addressing the issue of parameter uncertainties. Presented in this paper is an improved version of the commonly used extended Kalman filter (EKF) by incorporating an adaptive filter procedure. The system noise covariance is updated in time segments in order to ensure statistical consistency between the predicted error covariance and the mean square of actual residuals. Comprising two stages in a cycle, the adaptive EKF method not only identifies the parameter values but also gives a useful estimate of uncertainties. Two numerical examples of simulation with noise are presented. The first example illustrates the superior statistical performance of the proposed method over the conventional EKF method. The second example demonstrates the numerical accuracy and efficiency of this method, with and without modeling error, in comparison with a published least‐squares approach.