Uncertainty quantification methodology for model parameters in sub-channel codes using MCMC sampling

Abstract

BackgroundTraditional safety analysis methods rely on expert advice and user self-evaluation, lacking the ability to quantify output uncertainty. In contrast, the best estimation plus uncertainty (BEPU) methodology can quantify the uncertainty of the output, thereby avoiding unnecessary conservative assumptions and improving the economic viability of nuclear power. It is now widely used in the design and safety analysis of nuclear reactors. However, owing to the cognitive limitations of science and numerical approximation in programs, most thermal-hydraulic programs lack sufficient input uncertainty information related to internal models, often relying on expert advice.PurposeThis study aims to investigate the uncertainty quantification methodology for model parameters in sub-channel codes using Markov Chain Monte Carlo (MCMC) sampling.MethodsFirstly, the PSBT void fraction distribution experiments were employed to evaluate the prediction ability of the subchannel program COBRA-IV, and a Python-based uncertainty analysis methodology was developed to quantitatively analyze the model parameter uncertainties that affect the void fraction. Then, the model parameters were assumed to be independent, with their uncertainties following a normal distribution. Based on the Bayesian principle, the most likely maximum a posteriori probability function (PDF) of the model parameters were obtained by combining the prior and observed information, despite the limited actual uncertainty information. Finally, an MCMC sampling methodology was adopted to solve the Bayesian relation, and the statistical uncertainty information of the model parameters were obtained using a stable a posteriori Markov chain, which requires at least 104 magnitudes to achieve convergence and the corresponding forward program runs. Therefore, to reduce the calculation cost and improve the calculation efficiency, a high-precision adaptive BPNN surrogate model was constructed to replace the complex and time-consuming forward program code. Furthermore, a set of uncertainty quantification methods with Python was developed to simultaneously quantify the uncertainty of the model parameters using a statistical method. During the selection of a slip model we discovered that both the slip ratio and turbulence mixing coefficient significantly affected the void fraction. Therefore, we developed.ResultsThe results indicate that after obtaining the uncertainty of the model parameters, the 95% confidence interval of the results generated by the forward propagation of input uncertainty enveloped the experimental values well. Furthermore, by incorporating the mean value of the model parameter uncertainties, obtained via uncertainty quantification, the modified model output exhibited a closer agreement with the experimental values than with the reference values.ConclusionsThe uncertainty quantification analysis methodology established in this study can be applied to the uncertainty analysis of subchannel program model parameters.

Keywords

• markov chain monte carlo sampling
• surrogate model
• uncertainty quantification
• void fraction
• inverse problem solving