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Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation

机译：具有随机扩展和基于优化的区间估计的混合不确定性量化

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摘要

Uncertainty quantification (UQ) is the process of determining the effect of input uncertainties on response metrics of interest. These input uncertainties may be characterized as either aleatory uncertainties, which are irreducible variabilities inherent in nature, or epistemic uncertainties, which are reducible uncertainties resulting from a lack of knowledge. When both aleatory and epistemic uncertainties are mixed, it is desirable to maintain a segregation between aleatory and epistemic sources such that it is easy to separate and identify their contributions to the total uncertainty. Current production analyses for mixed UQ employ the use of nested sampling, where each sample taken from epistemic distributions at the outer loop results in an inner loop sampling over the aleatory probability distributions. This paper demonstrates new algorithmic capabilities for mixed UQin which the analysis procedures are more closely tailored to the requirements of aleatory and epistemic propagation. Through the combination of stochastic expansions for computing statistics and interval optimization for computing bounds, interval-valued probability, second-order probability, and Dempster-Shafer evidence theory approaches to mixed UQ are shown to be more accurate and efficient than previously achievable.
机译：不确定性量化（UQ）是确定输入不确定性对目标响应指标的影响的过程。这些输入不确定性的特征可以是偶然的不确定性，这是自然界中固有的不可减少的变异性；或者认知的不确定性，其是由于缺乏知识而可以减少的不确定性。当偶然不确定性和认知不确定性混合在一起时，理想的是将偶然性和认知不确定性源之间保持隔离，以便容易分离并确定它们对总不确定性的贡献。当前针对混合UQ的生产分析使用嵌套采样，其中从外部环路的认知分布中获取的每个样本都会在偶然概率分布上进行内部环路采样。本文演示了混合UQin的新算法功能，该分析程序更紧密地适合于偶然和认知传播的要求。通过将用于计算统计数据的随机扩展和用于计算边界的区间优化相结合，区间混合概率，二阶概率和Dempster-Shafer证据理论的混合UQ理论方法显示出比以前可实现的更为准确和有效。

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