Statistical developments for target and conditional sensitivity analysis: application on safety studies for nuclear reactor

Amandine Marrel (1) , Hugo Raguet (2) , Vincent Chabridon (3)

1 CEA Cadarache
2 INSA CVL - Institut National des Sciences Appliquées - Centre Val de Loire
3 EDF R&D PRISME - Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation

Numerical simulators are essential for understanding, modeling and predicting physical phenomena. However, the available information about some of the input variables is often limited or uncertain. Global sensitivity analysis (GSA) then aims at determining (qualitatively or quantitatively) how the variability of the inputs affects the model output. However, from reliability and risk management perspectives, GSA might be insufficient to capture the influence of the inputs on a restricted domain of the output (e.g., a distribution tail). To remedy this, we define and use in this work target (TSA) and conditional sensitivity analysis (CSA), which aim respectively at measuring the influence of the inputs on the occurrence of the critical event, and on the output within the critical domain (ignoring what happens outside). As illustrated in the applications, these two notions can widely differ. From existing GSA measures, we propose new operational tools for TSA and CSA. We first focus on the popular Sobol indices and show their practical limitations for both TSA and CSA. Then, the Hilbert-Schmidt Independence Criterion (HSIC), a dependence measure recently adapted for GSA purposes and well-suited for small datasets, is considered. TSA and CSA adaptations of Sobol and HSIC indices, and associated statistical estimators, are defined. Alternative CSA Sobol indices are thus defined to overcome the dependence of inputs induced by the conditioning. Moreover, to cope with the loss of information (especially when the critical domain is associated to a low probability) and reduce the variability of estimators, transformation of the output using weight functions is also proposed. These new TSA and CSA tools are tested and compared on analytical examples. The efficiency of HSIC-based indices clearly appear, as well as the relevancy of smooth relaxation. Finally, these latter indices are applied and interpreted on a nuclear engineering use case simulating a severe accidental scenario on a pressurized water reactor.

Mots clés: Sensitivity analysis; Reliability analysis; Sobol indices; Hilbert-Schmidt independence criterion

Domaines: Méthodologie [stat.ME]; Calcul [stat.CO]; Applications [stat.AP]

Amandine Marrel, Hugo Raguet, Vincent Chabridon. Statistical developments for target and conditional sensitivity analysis: application on safety studies for nuclear reactor. 2020. ⟨hal-02541142v1⟩