Chapter 24 Finite Element Model Updating Accounting for Modeling Uncertainty Rodrigo Astroza, Andres Alessandri, and Joel P. Conte Abstract A novel approach to deal with modeling uncertainty when updating mechanics-based finite element (FE) models is presented. In this method, a dual adaptive filtering approach is adopted, where the Unscented Kalman filter (UKF) is used to estimate the unknown parameters of the nonlinear FE model and a linear Kalman filter (KF) is employed to estimate the diagonal terms of the covariance matrix of the simulation error vector based on a covariance-matching technique. Numerically simulated response data of a two-dimensional three-story three-bay steel frame structure with eight unknown material model parameters subjected to seismic base excitation is employed to illustrate and validate the proposed methodology. The results of the validation studies show that the proposed approach significantly outperforms the parameteronly estimation approach widely investigated and used in the literature. Keywords Finite element model · Modeling uncertainty · Parameter estimation · Dual filtering 24.1 Introduction Improving the predictive capabilities of models, providing a tool for damage identification, and verifying modeling techniques are some significant problems that are assisted by model calibration. Significant research has been focused on updating linear finite element (FE) models [1]; however, calibration of nonlinear FE models has attracted the attention in recent years. Although the first studies dealing with the updating of nonlinear models of structures were conducted in the 70’s and 80’s (e.g., [2–4]), mechanics-based nonlinear FE models have been the subject of research only the last years (e.g., [5–10]). When state-of-the-art nonlinear FE models are updated using measured response data, a parameter-only estimation approach is considered, because is not feasible to estimate the response variables defining the state vector (e.g., displacements and velocities at every degree of freedom of the model). This implies that modeling uncertainty is not accounted for, which may have detrimental effects in the prediction capabilities of the updated FE model [11] because any FE model is only an approximate representation of the system to be modeled [12–14]. In this paper, a dual adaptive filtering approach is proposed to deal with modeling uncertainty when updating mechanicsbased nonlinear FE models. The method presented addresses the different sources of uncertainty involved in FE model updating, including parameter, modeling, and noise uncertainties. The unscented Kalman filter (UKF) is employed for parameter estimation and a linear Kalman filter is used to estimate the diagonal entries of the covariance matrix of the simulation error vector (e.g., [15, 16]), which are considered time variant because modeling uncertainty may vary in time. 24.2 Problem Formulation The discrete-time equation of motion of a mechanics-based nonlinear FE model under uniform earthquake base excitation can be written as M(p) ¨qk+1 (p) +C(p) ˙qk+1 (p) +rk+1 (qk+1 (p), p) =−M(p)L(p) ¨uk+1 (24.1) R. Astroza ( ) · A. Alessandri Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Santiago, Chile e-mail: rastroza@miuandes.cl J. P. Conte Department of Structural Engineering, University of California, San Diego, CA, USA © Society for Experimental Mechanics, Inc. 2020 R. Barthorpe (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12075-7_24 211
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