Generalized Stratified Sampling for Efficient Reliability Assessment of Structures against Natural Hazards
Publication: Journal of Engineering Mechanics
Volume 149, Issue 7
Abstract
Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure probabilities against stated criteria. As a result, efficient stochastic simulation schemes are central to computational frameworks that aim to estimate failure probabilities associated with multiple limit states using limited sample sets. In this work, a generalized stratified sampling scheme is proposed in which two phases of sampling are involved: the first is devoted to the generation of strata-wise samples and the estimation of strata probabilities, whereas the second phase aims at the estimation of strata-wise failure probabilities. Phase-I sampling enables the selection of a generalized stratification variable (i.e., not necessarily belonging to the input set of random variables) for which the probability distribution is not known a priori. To improve the efficiency, Markov Chain Monte Carlo Phase-I sampling is proposed when Monte Carlo simulation is deemed infeasible, and optimal Phase-II sampling is implemented based on user-specified target coefficients of variation for the limit states of interest. The expressions for these coefficients are derived with due regard to the sample correlations induced by the Markov chains and the uncertainty in the estimated strata probabilities. The proposed stochastic simulation scheme reaps the benefits of near-optimal stratified sampling for a broader choice of stratification variables in high-dimensional reliability problems with a mechanism to approximately control the accuracy of the estimators of multiple failure probabilities. The practicality and efficiency of the scheme are demonstrated using two examples involving the estimation of failure probabilities associated with highly nonlinear responses induced by wind and seismic excitations.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This research effort was supported in part by the National Science Foundation (NSF) under Grant Nos. CMMI-1750339 and CMMI-2118488. This support is gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 149 • Issue 7 • July 2023
Copyright
© 2023 American Society of Civil Engineers.
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Received: Oct 19, 2022
Accepted: Feb 21, 2023
Published online: May 12, 2023
Published in print: Jul 1, 2023
Discussion open until: Oct 12, 2023
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