Addressing statistical uncertainty in a surrogate model framework for Performance-Based Risk Optimization of structures subjected to seismic actions

Integrating risk-based optimization into Performance-Based Earthquake Engineering (PBEE) is challenging due to the high computational cost of evaluating consequences and the uncertainties inherent in seismic performance assessments.Statistical variability, for instance, arises from the inherent uncertainty in estimating Engineering Demand Parameters (EDPs) using statistical estimators based on a limited number of Nonlinear Time History Analyses.In a Performance-Based Risk Optimization framework, such variability becomes a critical factor that must be carefully addressed.This study proposes a metamodeling framework that incorporates statistical variability as regression noise and uses Kriging to estimate the median and standard deviation of EDPs, assuming a lognormal distribution.This integration allows the surrogate models to accurately represent and propagate statistical uncertainty within the optimization process.A practical application is presented in which expected repair and construction costs of a steel structural frame are minimized through multi-objective optimization, adopting the FEMA P-58 methodology within the PBEE framework.The results demonstrate that the proposed approach significantly reduces computational costs while preserving accuracy.The main contribution of this work is the development of a Gaussian Process-based surrogate modeling framework that efficiently estimates joint lognormal EDP parameters, directly addressing statistical variability and enabling robust, performance-based design optimization.