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

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 2nd‐level HSIC‐based 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.

Fatigue reliability and sensitivity analysis of aero‐disk considering correlation

“…Copula‐based substitute method (CSM) method from ref. [35] was adopted for a comparative study with 10,000 samples. The simplified Monte Carlo method proposed by Saltelli 33 was also used as a reference.…”

“…GSA method allows for quantifying the influence of the inputs on the output response considering the entire range of input random variables. 35 Therefore, GSA facilitates a comprehensive assessment of the impact of different input values on the output response. 36 In the literature, GSA methods include failure probability-based GSA, 37,38 moment-independent GSA, 39,40 and variance-based GSA.…”

“…In short, it calculates the partial derivative of the output response with respect to a specific input variable. GSA method allows for quantifying the influence of the inputs on the output response considering the entire range of input random variables 35 . Therefore, GSA facilitates a comprehensive assessment of the impact of different input values on the output response 36 .…”

Advanced Studies and Statistical Treatment for Sodium-Cooled Fast Reactor Pin Failures During Unprotected Transient Overpower Accident

“…Concerning the prior distribution of the inputs of OCARINa which impact the distribution of the predicted outputs, it is more complicated, if we do not want make additional simulations of OCARINa. In the framework of sensitivity analysis, Meynaoui et al [25] have recently proposed a solution to evaluate the impact of uncertainty on input distributions that they referred as "second-level uncertainties". Their method relies on importance sampling technique, and keeps the same number of simulations.…”

The ENBIS‐21 quality and reliability engineering international special issue

“…Testik and Unlu 8 compare traditional and fuzzy failure modes and effect analysis to rank risks in different areas of testing and calibration laboratories. Meynaoui et al 9 . deal with an accidental scenario in a sodium‐cooled fast nuclear reactor by means of a global sensitivity analysis of the input parameter distribution used in numerical simulator outputs to model physical phenomena.…”