具有函数输入的计算机模型的全局敏感性分析
Global sensitivity analysis of computer models with functional inputs
摘要：
全局敏感性分析用于量化不确定输入参数对数值模型响应变异性的影响。常用的定量方法适用于输入变量为标量的计算机程序。本文旨在说明不同的基于方差的敏感性分析技术，基于所谓的Sobol指数，当一些输入变量是功能，如随机过程或随机空间场。在这项工作中，我们专注于大CPU时间的计算机代码，需要一个初步的元建模步骤，然后再进行敏感性分析。我们建议使用联合建模方法，即，使用两个互连的广义线性模型（GLM）或广义可加模型（GAM）同时对所述码输出的均值和分散进行建模。"均值“模型允许估计每个标量输入变量的敏感性指数，而"分散”模型允许导出函数输入变量的总敏感性指数。所提出的方法相比，一些经典的SA方法的分析功能。最后，所提出的方法被应用到一个具体的工业计算机代码，模拟核燃料辐照。
英文摘要：
Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This paper aims to illustrate different variance-based sensitivity analysis techniques, based on the so-called Sobol indices, when some input variables are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary meta-modeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The ``mean'' model allows to estimate the sensitivity indices of each scalar input variables, while the ``dispersion'' model allows to derive the total sensitivity index of the functional input variables. The proposed approach is compared to some classical SA methodologies on an analytical function. Lastly, the proposed methodology is applied to a concrete industrial computer code that simulates the nuclear fuel irradiation.
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