Bayesian inference and non-linear extensions of the CIRCE method for quantifying the uncertainty of closure relationships integrated into thermal-hydraulic system codes
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Uncertainty Quantification of closure relationships integrated into thermal-hydraulic system codes is a critical prerequisite so that the Best-Estimate Plus Uncertainty (BEPU) methodology for nuclear safety and licensing processes can be implemented. The goal of the CIRCE method is to estimate the (log)-Gaussian probability distribution of a multiplicative factor applied to a reference closure relationship in order to assess its uncertainty. Although this method has been applied with success in numerous physical scenarios, its implementation can still suffer from substantial limitations such as the linearity assumption and the failure to take into account the inherent statistical uncertainty. In the paper, we propose to extend the CIRCE method in two aspects. On the one hand, we adopt the Bayesian setting which puts prior probability distributions on the parameters of the (log)-Gaussian distribution. The posterior distribution of these parameters is then computed with respect to an experimental database by means of Monte Carlo Markov Chain (MCMC) algorithms. On the other hand, we tackle the more general setting where the simulations do not move linearly against the values taken by the multiplicative factor(s). However, MCMC algorithms become time-prohibitive once thermal-hydraulic simulations exceed a few minutes. The method that we have implemented to overcome this handicap relies on the use of a Gaussian process (GP) emulator which can yield both reliable and fast predictions of the simulations. In the second part of the paper, the MCMC algorithms will be applied to quantify the uncertainty of two condensation models at the safety injections with respect to a database of experimental tests. The thermal-hydraulic simulations will be run with the CATHARE 2 computer code.
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