Effects of probability model misspecification on the number of ground motions required for seismic performance assessment

The number of ground motions used in nonlinear response history analysis (NRHA) determines the precision of the parameter estimates obtained in seismic performance assessments. While this issue has been extensively studied in the earthquake engineering literature, the relationship of probability model misspecification to parameter estimation uncertainty, and the implication to the required number of ground motions needed for NRHA, has not been examined. Probability model misspecification has the potential to increase estimation uncertainty and hence requires a greater number of ground motions to achieve the same precision compared to when misspecification is disregarded. This study develops a procedure to determine the required number of ground motions in seismic code-prescriptive and risk-based assessments with possible probability model misspecification. Specifically, we employ the quasi-maximum likelihood estimation (QMLE), which is robust to probability model misspecification, to evaluate estimation uncertainty. The QMLE approach is applied to an archetype California bridge under the two seismic assessment scenarios. In the code-prescriptive assessment, misspecification errors are identified for dispersion estimates of the bridge column ductility demand. In the most extreme case of the risk-based evaluation, misspecification increases the estimation uncertainty of the mean annual frequency of exceeding a limit state by as much as three times, which substantially increases the required number of ground motions. Based on the findings from this study, we advocate for the use of QMLE to detect and rectify the implications of model misspecification to estimation uncertainty and the number of ground motions used in probabilistic seismic performance assessments.