Optimal Uncertainty Quantification of a risk measurement from a thermal-hydraulic code using Canonical Moments

Jerome Stenger (1, 2, 3) , Fabrice Gamboa (3) , Merlin M. Keller (1) , Bertrand Iooss (1, 3, 2)

1 EDF R&D PRISME - Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: uncertainty quantification; optimal uncertainty quantification; robustness; canonical moments; computational statistics; stochastic opti- mization

Domaines: Méthodologie [stat.ME]; Applications [stat.AP]; Statistiques [math.ST]; Probabilités [math.PR]

Jerome Stenger, Fabrice Gamboa, Merlin M. Keller, Bertrand Iooss. Optimal Uncertainty Quantification of a risk measurement from a thermal-hydraulic code using Canonical Moments. International Journal of Uncertainty Quantification, 2020, 10, pp.35-53. ⟨hal-01987449v2⟩