A unified approach for time-domain and frequency-domain finite element model updating

Abstract

Reliable finite element (FE) models play a vital role in accurately predicting structural behaviors under various loading conditions in structural engineering applications. This paper presents a unified approach for solving time-domain and frequency-domain FE model updating problems. In this approach, both types of problems are formulated as stochastic dynamic systems with embedded parameter-to-data maps, enabling the estimation of unknown model parameters. The unscented Kalman filter (UKF) is employed as an effective tool to solve these dynamic systems and update the parameters in a derivative-free manner. Additionally, this study addresses specific aspects of FE model updating, including constraint implementation, covariance inflation, and sparse regularization. The analytical solutions for the Kalman gain and updated parameters under bound constraints are derived, guaranteeing that the model parameters adhere to predefined bounds. A method for inflating the estimated error covariance is used to mitigate issues caused by abrupt fluctuations in the measured structure. Covariance inflation techniques are applied to account for uncertainties not accurately captured by assumed covariance matrices. Furthermore, a variable transformation strategy is adopted to convert the sparse regularization problem into a Tikhonov regularization problem, which can be solved by the UKF with measurement augmentation. Sparse regularization facilitates more accurate and interpretable results in applications such as damage identification. The proposed unified approach is verified through extensive validation examples. The results demonstrate the effectiveness and reliability of the approach in accurately estimating the unknown parameters of FE models for structural engineering applications.