arXiv 2212.124352022-12stat.MEmath.STstat.TH

数值模拟器的二级全局灵敏度分析及其在钠冷快堆事故场景中的应用

Second-level global sensitivity analysis of numerical simulators with application to an accident scenario in a sodium-cooled fast reactor

Anouar Meynaoui, Amandine Marrel, Béatrice Laurent

备注：: This work was intended as a replacement of arXiv:1902.07030 and any subsequent updates will appear there

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AI总结：

针对输入分布不确定对全局灵敏度分析结果的影响，提出基于加权HSIC估计量的单环蒙特卡洛方法，实现计算预算有限的二级全局灵敏度分析，并应用于核反应堆严重事故场景。

摘要：

数值模拟器广泛用于模拟物理现象，全局灵敏度分析（GSA）旨在研究输入不确定性对模拟器输出的全局影响。为了进行GSA，通常使用基于输入/输出依赖度量的统计工具。我们关注希尔伯特-施密特独立性准则（HSIC）。有时，建模输入不确定性的概率分布本身可能是不确定的，量化其对GSA结果的影响非常重要。我们将其称为二级全局灵敏度分析（GSA2）。然而，当使用蒙特卡洛双环方法进行GSA2时，需要大量的模型评估，这对于CPU时间昂贵的模拟器来说是难以处理的。为了解决这一限制，我们提出了一种基于蒙特卡洛单环且计算预算有限的新统计方法。首先，我们从精心选择的输入概率分布中构建一个唯一的输入和模拟器输出样本。从该样本中，我们通过使用加权HSIC度量估计器，对各种假设的输入概率分布进行GSA。证明了这些加权估计器的统计性质。随后，我们定义了输入分布与GSA结果之间的基于HSIC的二级度量，即GSA2指标。通过一个解析示例说明了我们的GSA2方法的效率，从而比较了几种技术选项。最后，将其应用于模拟核反应堆严重事故场景的测试案例。

英文摘要：

Numerical simulators are widely used to model physical phenomena and global sensitivity analysis (GSA) aims at studying the global impact of the input uncertainties on the simulator output. To perform GSA, statistical tools based on inputs/output dependence measures are commonly used. We focus here on the Hilbert-Schmidt independence criterion (HSIC). Sometimes, the probability distributions modeling the uncertainty of inputs may be themselves uncertain and it is important to quantify their impact on GSA results. We call it here the second-level global sensitivity analysis (GSA2). However, GSA2, when performed with a Monte Carlo double-loop, requires a large number of model evaluations, which is intractable with CPU time expensive simulators. To cope with this limitation, we propose a new statistical methodology based on a Monte Carlo single-loop with a limited calculation budget. First, we build a unique sample of inputs and simulator outputs, from a well-chosen probability distribution of inputs. From this sample, we perform GSA for various assumed probability distributions of inputs by using weighted HSIC measures estimators. Statistical properties of these weighted estimators are demonstrated. Subsequently, we define 2 nd-level HSICbased measures between the distributions of inputs and GSA results, which constitute GSA2 indices. The efficiency of our GSA2 methodology is illustrated on an analytical example, thereby comparing several technical options. Finally, an application to a test case simulating a severe accidental scenario on nuclear reactor is provided.

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