Computing small failure probabilities is often of interest in the reliability analysis of engineering systems. However, this task can be computationally demanding since many evaluations of expensive high-fidelity models are often required. To address this, a multi-fidelity approach is proposed in this work within the setting of stratified sampling. The overall idea is to reduce the required number of high-fidelity model runs by integrating the information provided by different levels of model fidelity while maintaining accuracy in estimating the failure probabilities. More specifically, strata-wise multi-fidelity models are established based on Gaussian process models to efficiently predict the high-fidelity response and the system collapse from the low-fidelity response. Due to the reduced computational cost of the low-fidelity models, the multi-fidelity approach can achieve a significant speedup in estimating small failure probabilities associated with high-fidelity models. The effectiveness and efficiency of the proposed multi-fidelity stochastic simulation scheme are validated through an application to a two-story two-bay steel building under extreme winds.

计算小故障概率通常是工程系统可靠性分析中的重点。然而，这项任务的计算要求很高，因为通常需要对昂贵的高保真模型进行许多评估。为了解决这个问题，本工作在分层抽样的背景下提出了一种多保真度方法。总体思路是通过集成不同级别的模型保真度提供的信息来减少所需的高保真模型运行次数，同时保持估计故障概率的准确性。更具体地说，基于高斯过程模型建立分层多保真度模型，以有效地预测高保真响应和低保真响应的系统崩溃。由于低保真模型的计算成本降低，多保真方法可以在估计与高保真模型相关的小故障概率时实现显着的加速。通过在极端风力下的两层两开间钢结构建筑的应用，验证了所提出的多保真度随机模拟方案的有效性和效率。