Adaptive Kalman filters for nonlinear finite element model updating

Abstract This paper presents two adaptive Kalman filters (KFs) for nonlinear model updating where, in addition to nonlinear model parameters, the covariance matrix of measurement noise is estimated recursively in a near online manner. Two adaptive KF approaches are formulated based on the forgetting factor and the moving window covariance-matching techniques using residuals. Although the proposed adaptive methods are integrated with the unscented KF (UKF) for nonlinear model updating in this paper, they can be alternatively combined with other types of nonlinear KFs such as the extended KF (EKF) or the ensemble KF (EnKF). The performance of the proposed methods is investigated through two numerical applications and compared to that of a non-adaptive UKF and an existing dual adaptive filter. The first application considers a nonlinear steel pier where nonlinear material properties are selected as updating parameters. Significant improvements in parameter estimation results are observed when using adaptive filters compared to the non-adaptive approach. Furthermore, the covariance matrix of simulated measurement noise is estimated from the adaptive approaches with acceptable accuracy. Effects of different types of modeling errors are studied in the second numerical application of a nonlinear 3-story 3-bay steel frame structure. Similarly, more accurate and robust parameter estimations and response predictions are obtained from the adaptive approaches compared to the non-adaptive approach. The results verify the effectiveness and robustness of the proposed adaptive filters. The forgetting factor and moving window methods are shown to have a simpler tuning process compared to the dual adaptive method while providing similar performance.