Adaptive Kalman filters for nonlinear finite element model updating

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. © 2020 Elsevier Lt

Nonlinear Model Updating Using Recursive and Batch Bayesian Methods

This paper studies the performance of recursive and batch Bayesian methods for nonlinear model updating. Unscented Kalman filter (UKF) is selected to represent the recursive Bayesian method, and two UKF approaches are investigated and compared, i.e., non-adaptive UKF and adaptive UKF. The proposed new adaptive filter, forgetting factor adaptive UKF, estimates the model parameters and measurement noise covariance in an online manner. The forgetting factor adaptive UKF is based on the principle of matching the covariance of residuals to its theoretical values by updating the measurement noise covariance. The performance of non-adaptive UKF, adaptive UKF and batch Bayesian method are investigated when applied to a numerical nonlinear 3-story 3-bay steel frame structure for parameter estimation of material properties. Different types of modeling errors are considered in the 21 updating models to study the effects of modeling errors on model updating. It is found that adaptive UKF approach provides the most accurate parameter estimations, while batch Bayesian approach gives the smallest errors on response predictions. © 2020, The Society for Experimental Mechanics, Inc