Optimal Uncertainty Quantification of a Risk Measurement From a Thermal-Hydraulic Code Using Canonical Moments

Abstract

In uncertainty quantification studies, 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 bounded distributions satisfying 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 maximal quantile based on the theory of canonical moments. It allows an effective, free of constraints, optimization. This methodology is applied on an industrial computer code related to nuclear safety.

Optimization of Quasi-convex Function over Product Measure Sets

“…This powerful Theorem provides numerous industrial applications. We develop for example the optimization of the quantile of the output of a computer code whose input distributions belong to measure spaces [26]. We also highlight through several illustrated applications how our framework generalizes both the Optimal Uncertainty Quantification [21] and the robust Bayesian analysis [15,3].…”

“…Thought, we have an explicit representation of the extreme points, the optimization is non trivial because of the high number of generalized moment constraints enforced. In [26], the authors present an original parameterization of the problem in the presence of classical moment constraints, allowing fast computation of the quantities of interest presented in Section 4.…”

“…Lower Quantile Function. A classical measure of risk, widely used in industrial application [28,26], is the quantile of the output. It is a critical criteria for evaluating safety margins [17].…”

“…The computation of the maximum quantile is equivalent to the computation of the lowest failure probability inf µ∈A F µ over the same class of measures. Indeed, we have the following duality transformation [26]:…”

An Information Geometry Approach to Robustness Analysis for the Uncertainty Quantification of Computer Codes

“…Meynaoui et al (2019) and Chabridon et al (2018) propose approaches that deal with "second-level" uncertainty, i.e., uncertainty in the parameters of the input distributions. An alternative approach known as "optimal uncertainty quantification" avoids specifying the input probability distributions, transforming the problem into the definition of constraints on moments (Owhadi et al, 2013;Stenger et al, 2019). The latter is out of the scope of the present work; here we consider that the initial probability distributions input by the user remain important.…”