Optimized HSIC-based tests for sensitivity analysis: application to thermal-hydraulic simulation of accidental scenario on nuclear reactor

Reda El Amri (1, 2) , Amandine Marrel (1, 2)

1 CEA Cadarache
2 DER - Département Etude des Réacteurs

Physical phenomena are commonly modeled by numerical simulators. Such codes can take as input a high number of uncertain parameters and it is important to identify their influences on the outputs via a Global Sensitivity Analysis (GSA). However, these codes can be time consuming which prevents a GSA based on the classical Sobol' indices, requiring too many code simulations. This is all the more true as the number of inputs is important. To address this limitation, we consider recent advances in dependence measures, focusing on the Hilbert-Schmidt independence criterion (HSIC). In this framework, this paper proposes new goal-oriented algorithms to optimize the permuted HSIC-based tests for screening and ranking purposes. HSIC-based tests are built upon a sample of inputs/output of the studied model (simulator) and relies on the estimation of a p-value under independence hypothesis. These p-values can be estimated either by an asymptotic approximation (for large sample size) or by permutation method. However in the latter case, a brute approach with a large number of permutations can be prohibitive in practice, especially when the testing procedure is repeated a large number of times. To overcome this, we propose several strategies to greedy estimate the p-value, according to the final goal of GSA. Three sequential permuted tests are thus proposed: screening-oriented, ranking-oriented and ranking-screeningoriented. These algorithms are tested and compared on analytical examples. The performances in terms of accuracy, efficiency and time saving are clearly demonstrated. Their use is then illustrated on a nuclear engineering use case simulating an intermediate-break loss-of-coolant accident on a pressurized water reactor. A convergence study, made computationally tractable by the optimized algorithms, is carried out to assess the convergence of the results, according to the sample size.

Mots clés: Sensitiviy analysis; Hilbert-Schmidt Independence Criterion (HSIC); Independence tests; Sequential permutations

Domaines: Statistiques [stat]; Probabilités [math.PR]

Reda El Amri, Amandine Marrel. Optimized HSIC-based tests for sensitivity analysis: application to thermal-hydraulic simulation of accidental scenario on nuclear reactor. 2021. ⟨cea-03193912⟩