Advanced methodology for uncertainty propagation in computer experiments with large number of inputs

Bertrand Iooss (1, 2, 3) , Amandine Marrel (4)

1 EDF R&D PRISME - Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
4 CEA - Commissariat à l'énergie atomique et aux énergies alternatives

In the framework of the estimation of safety margins in nuclear accident analysis, a quantitative assessment of the uncertainties tainting the results of computer simulations is essential. Accurate uncertainty propagation (estimation of high probabilities or quantiles) and quantitative sensitivity analysis may call for several thousand of code simulations. Complex computer codes, as the ones used in thermal-hydraulic accident scenario simulations, are often too cpu-time expensive to be directly used to perform these studies. A solution consists in replacing the computer model by a cpu inexpensive mathematical function, called a metamodel, built from a reduced number of code simulations. However, in case of high dimensional experiments (with typically several tens of inputs), the metamodel building process remains difficult. To face this limitation, we propose a methodology which combines several advanced statistical tools: initial space-filling design, screening to identify the non-influential inputs, Gaussian process (Gp) metamodel building with the group of influential inputs as explanatory variables. The residual effect of the group of non-influential inputs is captured by another Gp metamodel. Then, the resulting joint Gp metamodel is used to accurately estimate Sobol' sensitivity indices and high quantiles (here $95\%$-quantile). The efficiency of the methodology to deal with a large number of inputs and reduce the calculation budget is illustrated on a thermal-hydraulic calculation case simulating with the CATHARE2 code a Loss Of Coolant Accident scenario in a Pressurized Water Reactor. A predictive Gp metamodel is built with only a few hundred of code simulations and allows the calculation of the Sobol' sensitivity indices. This Gp also provides a more accurate estimation of the 95%-quantile and associated confidence interval than the empirical approach, at equal calculation budget. Moreover, on this test case, the joint Gp approach outperforms the simple Gp.

Mots clés: Quantile; Gaussian process; Sobol' indices; Metamodel; Screening

Domaines: Statistiques [math.ST]; Sciences de l'ingénieur [physics]; Applications [stat.AP]

Bertrand Iooss, Amandine Marrel. Advanced methodology for uncertainty propagation in computer experiments with large number of inputs. Nuclear Technology, 2019, 205, pp.1588-1606. ⟨hal-01907198v2⟩