Existing variance reduction techniques used in stochastic simulations for rare event analysis still require a substantial number of model evaluations to estimate small failure probabilities. In the context of complex, nonlinear finite element modeling environments, this can become computationally challenging-particularly for systems subjected to stochastic excitation. To address this challenge, a multi-fidelity stratified sampling scheme with adaptive machine learning metamodels is introduced for efficiently propagating uncertainties and estimating small failure probabilities. In this approach, a high-fidelity dataset generated through stratified sampling is used to train a deep learning-based metamodel, which then serves as a cost-effective and highly correlated low-fidelity model. An adaptive training scheme is proposed to balance the trade-off between approximation quality and computational demand associated with the development of the low-fidelity model. By integrating the low-fidelity outputs with additional high-fidelity results, an unbiased estimate of the strata-wise failure probabilities is obtained using a multi-fidelity Monte Carlo framework. The overall probability of failure is then computed using the total probability theorem. Application to a full-scale high-rise steel building subjected to stochastic wind excitation demonstrates that the proposed scheme can accurately estimate exceedance probability curves for nonlinear responses of interest, while achieving significant computational savings compared to single-fidelity variance reduction approaches.

翻译：现有用于罕见事件分析的随机模拟方差缩减技术仍需要大量模型评估来估计较小的失效概率。在复杂的非线性有限元建模环境中，这可能在计算上具有挑战性——特别是对于承受随机激励的系统。为应对这一挑战，本文引入了一种结合自适应机器学习元模型的多保真度分层抽样方案，以高效传播不确定性并估计小失效概率。在此方法中，通过分层抽样生成的高保真度数据集用于训练基于深度学习的元模型，该模型随后作为成本效益高且高度相关的低保真度模型。本文提出了一种自适应训练方案，以平衡低保真度模型开发过程中近似质量与计算需求之间的权衡。通过将低保真度输出与额外的高保真度结果相结合，利用多保真度蒙特卡洛框架获得了层间失效概率的无偏估计。随后使用全概率定理计算总体失效概率。在一个承受随机风激励的全尺寸高层钢结构建筑上的应用表明，所提方案能够准确估计非线性关注响应的超越概率曲线，同时与单保真度方差缩减方法相比实现了显著的计算节省。