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 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 failure probability estimators. The practicality of the scheme is demonstrated using two examples involving the estimation of failure probabilities associated with highly nonlinear responses induced by wind and seismic excitations.

翻译：基于性能的自然灾害工程通过严格评估结构在潜在极端随机荷载下的不确定性行为，以失效概率形式针对既定准则进行结构设计与评估。因此，高效随机模拟方案是计算框架的核心，旨在利用有限样本集估计与多个极限状态相关的失效概率。本文提出一种广义分层抽样方案，包含两个抽样阶段：第一阶段致力于生成分层样本并估计各层概率，第二阶段则针对分层失效概率进行估计。第一阶段抽样支持选择广义分层变量（即未必属于输入随机变量集合），其概率分布无需先验已知。为提高效率，当蒙特卡洛模拟不可行时，提出基于马尔可夫链蒙特卡洛的第一阶段抽样，并根据用户设定的目标极限状态变异系数实现最优第二阶段抽样。推导了这些系数的表达式，充分考虑马尔可夫链引起的样本相关性和各层概率估计的不确定性。该随机模拟方案在高维可靠度问题中发挥近最优分层抽样的优势，支持更广泛的分层变量选择，并通过机制近似控制失效概率估计器的精度。通过两个案例验证该方案实用性，分别涉及风致与地震激励下高度非线性响应的失效概率估计。