Bayesian calibration and fitting of nuclear thermal–hydraulic models by Markov chain Monte Carlo methods using the Gibbs sampler

Abstract

This paper applies Bayesian methods to obtain the joint probability distribution function (PDF) of the unknown parameters of some of the correlation types used in thermal hydraulics, which are conditioned to a set of results of separate effect experiments. The problem is solved by Markov chain Monte Carlo methods using the Gibbs sampler. In this paper it is shown how to obtain the conditional PDFs for each one of the parameters, which define two typical correlations that appear in thermal–hydraulic problems, i) the heat transfer in the walls of a pipe and ii) the penetration length of steam discharged in a subcooled pool. The equations for the conditional probabilities of each one of the parameters are deduced and then used to build the Gibbs sampler which is then programmed in R. The PDFs are obtained for each one of the parameters and from these the maximum a posteriori of each one of the parameters is obtained. The new correlations obtained in this way are compared with the experimental data and show satisfactory performance for the case of the penetration of steam in a subcooled pool. Also, we study two cases one with a small number of experimental data and another one with a large number, it is observed that if the number of parameters is small the Markov chain converges fast to the region of high probability of the parameters for both cases with a small number of data and with large number of data, but if the number of parameters increases then the convergence for the case with small number of data becomes poor, however the convergence continuous being very fast for the case with large number of experimental data.