An extended stratified sampling approach for probabilistic performance assessment of structures under wind and seismic hazards

Abstract

Risk-based decision-making for the assessment and design of the built environment against natural hazards is fast gaining recognition not just for critical structures but also for engineered structures in general. Performance-based engineering has enabled the development of robust approaches, often realized through a sequence of high-fidelity numerical models, addressing hazard analysis, structural/non-structural analysis, and damage/loss analysis. These approaches are formalized within a probabilistic setting to account for the inevitable uncertainties affecting the problem. The adequacy of the structure is evaluated through the estimation of multiple failure probabilities and subsequently ensuring that they meet target values. The associated computational demand can become exacerbated when the propagation of uncertainty is combined with computationally expensive models. In this paper, an efficient two-stage sampling approach is proposed based on the generalization of stratified sampling, for the stochastic simulation of responses and the simultaneous evaluation of multiple small failure probabilities. Unlike traditional stratified sampling, any stratification variable can be selected, not necessarily belonging to the input set, while the first stage of sampling efficiently generates samples in each stratum using subset simulation when Monte Carlo simulation is considered infeasible. Based on a set of user-defined target coefficients of variation (COV) for the failure probabilities, the optimal sample allocation is obtained as a solution to a constrained-optimization problem. This leads to minimal model evaluations in the second sampling stage for estimating failure probabilities without compromising the required accuracy. For the calculation of the COV, theoretical expressions are derived by taking into account the sample correlations induced by Markov chains and the uncertainty in the estimated strata probabilities. The potential benefits of the scheme are illustrated on an archetype 45-story reinforced concrete building subject to extreme hurricane-induced winds. The example is representative of high-dimensional risk assessment problems in performance-based wind engineering. The case study demonstrates the advantage of working with a generalized stratification variable, the resulting reduction in computational burden while achieving desired accuracies, as well as providing a numerical validation of the derived COV expressions. Moreover, when a hazard intensity measure is chosen as the stratification variable, the simulation scheme facilitates the integration of prior information to update fragility functions using a Bayesian approach which is also illustrated in this paper.