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

TL;DR

This paper introduces a new efficient methodology for second-level global sensitivity analysis (GSA2) using weighted HSIC measures, applied to a nuclear reactor accident simulation, reducing computational costs while assessing input uncertainty impacts.

Contribution

It develops a single-loop Monte Carlo approach for GSA2 with weighted HSIC estimators, enabling uncertainty quantification of input distributions without extensive model evaluations.

Findings

Method reduces computational cost for GSA2

Effective in assessing input distribution uncertainties

Successfully applied to nuclear reactor accident scenario

Abstract

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.