220 R. Astroza et al. 0 0.5 1 1.5 2 ˆEcol s Parameter−only (N) Dual−filtering (D) 0 0.5 1 1.5 2 ˆfcol y 0 0.5 1 1.5 2 ˆRcol 0 0 0.5 1 1.5 2 ˆbcol 0 3 6 9 12 0 0.5 1 1.5 2 Time (s) ˆEbeam s 0 3 6 9 12 0 0.5 1 1.5 2 Time (s) ˆfbeam y 0 3 6 9 12 0 0.5 1 1.5 2 Time (s) ˆRbeam 0 0 3 6 9 12 0 0.5 1 1.5 2 Time (s) ˆbbeam Fig. 24.5 Comparison of the parameter estimation time-histories for Case 11 (low-magnitude multi-parameter modeling uncertainty) obtained using the parameter-only and dual adaptive filtering estimation approaches 2 4 6 8 10121416182022242628 Modeling uncertainty Case # 1 10 100 RRMSE (%) Acc. 2nd level Acc. 3rd level Acc. Roof ytrue vs. yInitial ytrue vs. yfinal par-only ytrue vs. yfinal dual-filter Fig. 24.6 RRMSEs between the true observed absolute acceleration responses and the corresponding initial and final FE-predicted responses for low- (1–11) and large-magnitude (12–28) modeling uncertainty cases for the frame subjected to the Los Gatos earthquake record 24.4 Conclusion A dual filtering approach for updating mechanics-based nonlinear finite element (FE) models accounting for modeling uncertainty was presented. In this approach, the Unscented Kalman filter (UKF) was used to estimate the unknown FE model parameters and a linear Kalman filter (KF) to estimate the diagonal terms of the covariance matrix of the simulation error vector based on a covariance-matching technique. Estimation results, in terms of parameter and measured response, of the common parameter-only and the proposed dual approaches were compared and discussed considering as
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