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Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty

机译：贝叶斯概率概率对大不疑概率的概率繁殖与大的认知不确定性

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摘要

Efficient propagation of imprecise probability models is one of the most important, yet challenging tasks, for uncertainty quantification in many areas and engineering practices, especially when the involved epistemic uncertainty is substantial due to the extreme lack of information. In this work, a new methodology framework, named as "Non-intrusive Imprecise Probabilistic Integration (NIPI)", is developed for achieving the above target, and specifically, the distributional probability-box model and the estimation of the corresponding probabilistic moments of model responses are of concern. The NIPI owns two attractive characters. First, the spatial correlation information in both aleatory and epistemic uncertainty spaces, revealed by the Gaussian Process Regression (GPR) model, is fully integrated for deriving NIPI estimations of high accuracy by using Bayesian inference. Second, the numerical errors are regarded as a kind of epistemic uncertainty, by analytically propagating them, the posterior variances are derived for indicating the errors of the NIPI estimations. Further, an adaptive experiment design strategy is developed to accelerate the convergence of NIPI by making full use of the information of "contribution to posterior variance" revealed by the GPR model. The performance of the proposed methods is demonstrated by numerical and engineering examples.
机译：不精确的概率模型的高效传播是许多领域和工程实践中不确定性量化的最重要，但最具挑战性的任务之一，特别是当由于极端缺乏信息而涉及的认知不确定性很大。在这项工作中，开发了一种以“非侵入式不精确概率集成（NIPI）”的新方法框架，用于实现上述目标，具体地，分布概率盒模型和模型相应概率矩的估计回复是关注的。 nipi拥有两个有吸引力的角色。首先，由高斯过程回归（GPR）模型揭示的梯级和认知不确定性空间中的空间相关信息完全集成了通过使用贝叶斯推断来导出高精度的NIPI估计。其次，通过在分析传播它们的情况下，数值误差被认为是一种认知不确定性，导出后差异是指示NIPI估计的误差。此外，开发了一种自适应实验设计策略，通过充分利用GPR模型的“对后差”的信息充分利用“贡献”的信息来加速NIPI的收敛性。通过数值和工程实施例证明了所提出的方法的性能。

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  • 来源
    《Mechanical systems and signal processing》 |2021年第2期|107219.1-107219.22|共22页
  • 作者

    Pengfei Wei; Fuchao Liu; Marcos Valdebenito; Michael Beer;

  • 作者单位

    School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi'an 710072 China Institute for Risk and Reliability Leibniz Universitcit Hannover Callinstr 34 Hannover 30167 Germany;

    School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi'an 710072 China;

    Departmento de Obras Civiles Universidad Tecnica Federico Santa Maria Av. Espana 1680 Valparaiso Chile;

    Institute for Risk and Reliability Leibniz Universitcit Hannover Callinstr 34 Hannover 30167 Germany Institute for Risk and Uncertainty University of Liverpool Peach Street L69 7ZF Liverpool UK International Joint Research Center for Engineering Reliability and Stochastic Mechanics Tongji University Shanghai 200092 China;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    Uncertainty quantification; Bayesian inference; Probabilistic integration; Imprecise probabilities; Gaussian process regression; Epistemic uncertainty; Active learning;

    机译：不确定性量化;贝叶斯推理;概率集成;不精确的概率;高斯过程回归;认知不确定性;主动学习;

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