Parametric uncertainty quantification using proper generalized decomposition applied to neutron diffusion
Parametric uncertainty quantification using proper generalized decomposition applied to neutron diffusion
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DOI：
10.1002/nme.6077
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发表时间：
2019-08-31
影响因子：
2.9
通讯作者：
Ragusa, Jean C.
中科院分区：
文献类型：
--
作者：
Prince, Zachary M.;Ragusa, Jean C.
在本文中，适当的广义分解（PGD）的方法是不确定性量化的目的。采用具有外源的中子扩散方程作为参数模型，这是一个扩散-反应问题。不确定性参数包括逐区恒定的物质扩散和反应系数以及源强度，在高度非均匀的几何形状中产生大的不确定性空间。在所有不确定变量中参数化的PGD解决方案然后可以用于计算各种感兴趣的量的均值、方差和更一般的概率分布。除了参数化的属性，参数化的几何变化的三维模型也被认为是本文。为了实现和分析一个参数PGD解决方案，算法被开发来分解模型的参数空间和半解析积分的解决方案，用于评估统计矩。变维问题进行评估，以展示PGD的解决高维问题的能力，并分析其收敛性。
In this paper, a proper generalized decomposition (PGD) approach is employed for uncertainty quantification purposes. The neutron diffusion equation with external sources, a diffusion-reaction problem, is used as the parametric model. The uncertainty parameters include the zone-wise constant material diffusion and reaction coefficients as well as the source strengths, yielding a large uncertain space in highly heterogeneous geometries. The PGD solution, parameterized in all uncertain variables, can then be used to compute mean, variance, and more generally probability distributions of various quantities of interest. In addition to parameterized properties, parameterized geometrical variations of three-dimensional models are also considered in this paper. To achieve and analyze a parametric PGD solution, algorithms are developed to decompose the model's parametric space and semianalytically integrate solutions for evaluating statistical moments. Varying dimensional problems are evaluated to showcase PGD's ability to solve high-dimensional problems and analyze its convergence.