A Unified Approach for Time 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 both time 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 method is employed as an effective tool to solve these dynamic systems and update the parameters. Additionally, this study addresses specific settings within FE model updating, including constraints implementation, covariance inflation, and sparsity regularization. Constraints on estimated parameters are effectively incorporated, ensuring adherence to predefined bounds. Covariance inflation techniques are applied to account for uncertainties not accurately captured by assumed covariance matrices. Moreover, sparsity regularization techniques are introduced to promote sparsity in estimated parameters, facilitating more accurate and interpretable results for special applications such as damage identification. The proposed unified approach is numerically verified through extensive simulations. The results demonstrate the effectiveness and reliability of the approach in accurately estimating the unknown parameters of FE models for structural engineering applications.