发表机构
The University of Texas at Tyler; The Pennsylvania State University（泰勒德州大学; 宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出二次点估计法（QPEM）用于相关非高斯输入的不确定性量化，通过copula集成建模联合分布，在无需数值优化下高效精确估计输出矩，并在多种场景中验证其优于其他采样方法。
AI 中文摘要
作为点估计法（PEM）在一般$n$维空间中评估感兴趣量（QoI）概率矩的扩展，二次点估计法（QPEM）近期已被开发。该方法被定义为在Gaussian空间中完全表示高达五阶的输入矩，为样本位置和权重提供一般解析表达式，无需任何数值优化。与基于PEM的方法（其sigma点数量随问题维度线性增长）相比，QPEM能显著提高输出QoI矩的估计精度，同时在大幅维度范围内具有可负担且具有竞争力的计算成本。本工作进一步增强了QPEM，通过将copula集成到框架中，从而能够通过估计边际分布和所涉及随机变量的依赖结构来有效建模联合输入概率密度函数。基于copula的QPEM的有效性和高效性能在众多其他采样方法中，通过考虑两种实际场景的各种示例得到展示：（i）当联合依赖结构可从数据推断时，以及（ii）当仅知道边际分布和相关性矩阵时。
英文摘要
As an extension of the Point Estimate Method (PEM) to evaluate probabilistic moments of quantities of interest (QoI) in general $n$-dimensional spaces, the Quadratic Point Estimate Method (QPEM) has been recently developed. This new method is defined to fully represent up to fifth-order input moments in the Gaussian space, providing general analytical expressions for sample locations and weights, without requiring any numerical optimization. The QPEM can significantly improve the estimation accuracy of the output QoI moments, in relation to PEM-based methods whose numbers of sigma points grow linearly with the problem dimension, while at the same time having an affordable and competitive computational cost up to a considerable number of dimensions. The QPEM is further enhanced in this work by enabling copula integration into the framework, which enables effective modeling of the joint input probability density function by estimating marginals and the dependence structure of the involved random variables. The validity and efficient performance of the copula-based QPEM are showcased against numerous other sampling methods in various examples considering two practical scenarios: (i) when the joint dependence structure can be inferred from data, and (ii) when only marginal distributions and correlation matrices are known.
