Extreme response assessment is important in the design and operation of engineering structures, and is a crucial part of structural risk and reliability analyses. Structures should be designed in a way that enables them to withstand the environmental loads they are expected to experience over their lifetime, without designs being unnecessarily conservative and costly. An accurate risk estimate is essential but difficult to obtain because the long-term behaviour of a structure is typically too complex to calculate analytically or with brute force Monte Carlo simulation. Therefore, approximation methods are required to estimate the extreme response using only a limited number of short-term conditional response calculations. Combining surrogate models with Design of Experiments is an approximation approach that has gained popularity due to its ability to account for both long-term environment variability and short-term response variability. In this paper, we propose a method for estimating the extreme response of black-box, stochastic models with heteroscedastic non-Gaussian noise. We present a mathematically founded extreme response estimation process that enables Design of Experiment approaches that are prohibitively expensive with surrogate Monte Carlo. The theory leads us to speculate this method can robustly produce more confident extreme response estimates, and is suitable for a variety of domains. While this needs to be further validated empirically, the method offers a promising tool for reducing the uncertainty decision-makers face, allowing them to make better informed choices and create more optimal structures.

翻译：极端响应评估在工程结构的设计与运行中至关重要，是结构风险与可靠性分析的核心组成部分。结构设计应使其能够承受预期寿命内可能遭遇的环境荷载，同时避免不必要的保守设计和过高成本。精确的风险估计虽必不可少，却难以获得，因为结构的长期行为通常过于复杂，无法通过解析方法或暴力蒙特卡洛模拟直接计算。因此，需要采用近似方法，仅通过有限数量的短期条件响应计算来估计极端响应。将代理模型与实验设计相结合是一种日益流行的近似方法，因其能够同时考虑长期环境变异性和短期响应变异性。本文提出一种针对具有异方差非高斯噪声的黑箱随机模型的极端响应估计方法。我们提出了一种基于数学理论的极端响应估计流程，使得实验设计方法能够应用于原本因代理蒙特卡洛模拟成本过高而无法实施的场景。理论分析表明，该方法能够稳健地生成置信度更高的极端响应估计，并适用于多种领域。尽管仍需通过实证进一步验证，但该方法为降低决策者面临的不确定性提供了前景广阔的工具，有助于其做出更明智的决策并构建更优化的结构。