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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties
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An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties

机译：用于PDF表征的扩展多项式混沌扩展和杀菌和认知不确定性的变化

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This paper presents an extended polynomial chaos formalism for epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions (PDF) to uncertainty in probabilistic models of input variables. An "extended" polynomial chaos expansion (PCE) approach is developed that accounts for both aleatory and epistemic uncertainties, modeled as random variables, thus allowing a unified treatment of both types of uncertainty. We explore in particular epistemic uncertainty associated with the choice of prior probabilistic models for input parameters. A PCE-based Kernel Density (KDE) construction provides a composite map from the PCE coefficients and germ to the PDF of quantities of interest (QoI). The sensitivities of these PDF with respect to the input parameters are then evaluated. Input parameters of the probabilistic models are considered. By sampling over the epistemic random variable, a family of PDFs is generated and the failure probability is itself estimated as a random variable with its own PCE. Integrating epistemic uncertainties within the PCE framework results in a computationally efficient paradigm for propagation and sensitivity evaluation. Two typical illustrative examples are used to demonstrate the proposed approach. (C) 2021 ElsevierB.V. All rights reserved.
机译：本文介绍了对认知不确定性的扩展多项式混沌形式主义和用于评估输出概率密度函数（PDF）对输入变量的概率模型的不确定性的敏感性和变化的新框架。开发了“扩展”多项式混沌扩展（PCE）方法，其占梯级和认知的不确定性，如随机变量建模，从而允许对两种类型的不确定性进行统一处理。我们探讨了与选择用于输入参数的现有概率模型相关的认识的不确定性。基于PCE的核密度（KDE）构造提供了来自PCE系数和胚芽的复合地图，以兴趣数量的PDF（QOI）。然后评估这些PDF关于输入参数的敏感性。考虑了概率模型的输入参数。通过对认知随机变量进行采样，生成一个PDF系列，并且故障概率本身估计为随机变量，其PCE是随机变量。整合在PCE框架内的认知不确定性导致计算上的传播和敏感性评估的计算效率范式。两个典型的说明性例子用于证明所提出的方法。 （c）2021 elsevierb.v。版权所有。

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