We study an industrial computer code related to nuclear safety. A major topic of interest is to assess the uncertainties tainting the results of a computer simulation. In this work we gain robustness on the quantification of a risk measurement by accounting for all sources of uncertainties tainting the inputs of a computer code. To that extent, we evaluate the maximum quantile over a class of distributions defined only by constraints on their moments. Two options are available when dealing with such complex optimization problems: one can either optimize under constraints; or preferably, one should reformulate the objective function. We identify a well suited parameterization to compute the optimal quantile based on the theory of canonical moments. It allows an effective, free of constraints, optimization.

中文翻译：

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使用规范矩从热工液压代码中进行风险测量的最佳不确定性量化

我们研究与核安全相关的工业计算机代码。一个重要的主题是评估影响计算机模拟结果的不确定性。在这项工作中，我们通过考虑污染计算机代码输入的所有不确定性来源，获得了量化风险度量的稳健性。在这个程度上，我们评估了一类分布的最大分位数，这些分布仅由它们的矩约束定义。处理如此复杂的优化问题时有两种选择：一种可以在约束下优化；或者最好，应该重新制定目标函数。我们确定了一个非常适合的参数化，以基于规范矩理论计算最佳分位数。它允许有效的、无约束的优化。