Integrated framework for model assessment and advanced uncertainty quantification of nuclear computer codes under Bayesian statistics

Abstract

A framework for model evaluation and uncertainty quantification (UQ) is presented with applications oriented to nuclear engineering simulation codes. Our framework is inspired by the previous research on Bayesian statistics and model averaging. The methodology is demonstrated by performing UQ of three thermal-hydraulic computer codes used for two-phase flow simulation inside nuclear reactors, and conclusions regarding their performance are drawn. The complexity of the framework implementation depends upon the information to be drawn about the models as well as the nature of the models and the data. Uncertainties inherent in the input parameters and experimental data, along with predictive and model-form uncertainty can be quantified in this methodology. A composite (average) model based on the competent models can be created for improved response prediction. Two benchmarks featuring steady-state void fraction data in full-scale light water reactor (LWR) channels are used to demonstrate the methodology. The results show that the three models/codes demonstrate variable competitiveness in reproducing the data (i.e. goodness of fit with the data). There is no consistent trend at which each code excels. The predictive uncertainty (representing individual model deficiency or discrepancy) dominates the model-form uncertainty for many cases in this study due to two reasons: (1) presence of a single competent model for a specific response and (2) poor agreement with experimental data for certain responses at which nuclear codes struggle, such as low pressure and subcooled boiling conditions. In general, improvements in composite predictions (based on posterior model weights) are observed for BFBT data, while slight improvement is found for PSBT. For PSBT, the predictive uncertainty of RELAP5 and TRACE dominates the response uncertainty causing weak improvement. Additional efforts are needed to improve the closure models of these codes in future to reduce the model discrepancy contribution. This framework can be utilized for this purpose at which various closure models for the same code can be assessed in terms of their effect on the final response uncertainty. The proposed framework is flexible and extendable to other types of physics, models, and data. Developing the underlying methodology of calculating the model weights is the main focus in the subsequent studies.