Abstract This paper presents a highly efficient and accurate approach to determine the bounds on the first excursion probability of a linear structure that is subjected to an imprecise stochastic load. Traditionally, determining these bounds involves solving a double loop problem, where the aleatory uncertainty has to be fully propagated for each realization of the epistemic uncertainty or vice versa. When considering realistic structures such as buildings, whose numerical models often contain thousands of degrees of freedom, such approach becomes quickly computationally intractable. In this paper, we introduce an approach to decouple this propagation by applying operator norm theory. In practice, the method determines those epistemic parameter values that yield the bounds on the probability of failure, given the epistemic uncertainty. The probability of failure, conditional on those epistemic parameters, is then computed using the recently introduced framework of Directional Importance Sampling. Two case studies involving a modulated Clough-Penzien spectrum are included to illustrate the efficiency and exactness of the proposed approach.

中文翻译：

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限制受不精确随机加载的线性结构的第一次偏移概率

摘要 本文提出了一种高效且准确的方法来确定受到不精确随机载荷的线性结构的第一次偏移概率的界限。传统上，确定这些界限涉及解决双循环问题，其中必须为认知不确定性的每个实现完全传播偶然不确定性，反之亦然。当考虑现实结构（例如建筑物）时，其数值模型通常包含数千个自由度，这种方法在计算上很快变得难以处理。在本文中，我们介绍了一种通过应用算子范数理论来解耦这种传播的方法。在实践中，给定认知不确定性，该方法确定产生故障概率界限的那些认知参数值。然后使用最近引入的定向重要性采样框架计算失败概率，以这些认知参数为条件。包括两个涉及调制 Clough-Penzien 频谱的案例研究，以说明所提出方法的效率和准确性。