Structural reliability analysis is concerned with estimation of the probability of a critical event taking place, described by \(P(g(\mathbf{X} ) \le 0)\) for some n-dimensional random variable \(\mathbf{X} \) and some real-valued function g. In many applications the function g is practically unknown, as function evaluation involves time consuming numerical simulation or some other form of experiment that is expensive to perform. The problem we address in this paper is how to optimally design experiments, in a Bayesian decision theoretic fashion, when the goal is to estimate the probability \(P(g(\mathbf{X} ) \le 0)\) using a minimal amount of resources. As opposed to existing methods that have been proposed for this purpose, we consider a general structural reliability model given in hierarchical form. We therefore introduce a general formulation of the experimental design problem, where we distinguish between the uncertainty related to the random variable \(\mathbf{X} \) and any additional epistemic uncertainty that we want to reduce through experimentation. The effectiveness of a design strategy is evaluated through a measure of residual uncertainty, and efficient approximation of this quantity is crucial if we want to apply algorithms that search for an optimal strategy. The method we propose is based on importance sampling combined with the unscented transform for epistemic uncertainty propagation. We implement this for the myopic (one-step look ahead) alternative, and demonstrate the effectiveness through a series of numerical experiments.

结构可靠度分析涉及一种临界事件正在发生的概率，所描述的估计\（P（G（\ mathbf {X}）\文件0）\）对于一些Ñ维随机变量\（\ mathbf {X } \）和一些实值函数g。在许多应用中，函数g实际上是未知的，因为函数评估涉及耗时的数值模拟或执行费用昂贵的其他某种形式的实验。本文要解决的问题是，当目标是估计概率\（P（g（\（mathbf {X}）\ le 0）\）时，如何以贝叶斯决策理论的方式优化设计实验。使用最少的资源。与为此目的提出的现有方法相反，我们考虑以分层形式给出的一般结构可靠性模型。因此，我们介绍了实验设计问题的一般表述，其中我们区分了与随机变量\（\ mathbf {X} \）相关的不确定性以及我们希望通过实验减少的任何其他认知不确定性。设计策略的有效性通过残差不确定性的评估来评估，而如果我们想应用搜索最佳策略的算法，则对该数量的有效逼近至关重要。我们提出的方法是基于重要性采样结合无味变换来进行认知不确定性传播的。我们将其用于近视（单步向前）替代方案，并通过一系列数值实验证明其有效性。