Uncertainty Propagation in Complex Codes Calculations

The uncertainty propagation is an important segment of quantitative uncertainty analysis for complex computational codes (e.g., RELAP5 thermal-hydraulics) computations. Different sampling techniques, dependencies between uncertainty sources, and accurate inference on results are among the issues to be considered. The dynamic behavior of the system codes executed in each time step, results in transformation of accumulated errors and uncertainties to next time step. Depending on facility type, availability of data, scenario specification, computing machine and the software used, propagation of uncertainty results in considerably different results. This paper discusses the practical considerations of uncertainty propagation for code computations. The study evaluates the implications of the complexity on propagation of the uncertainties through inputs, sub-models and models. The study weighs different techniques of propagation, their statistics with considering their advantages and limitation at dealing with the problem. The considered methods are response surface, Monte Carlo (including simple, Latin Hypercube, and importance sampling) and boot-strap techniques. As a case study, the paper will discuss uncertainty propagation of the Integrated Methodology on Thermal-Hydraulics Uncertainty Analysis (IMTHUA). The methodology comprehensively covers various aspects of complex code uncertainty assessment for important accident transients. It explicitly examines the TH code structural uncertainties by treating internal sub-model uncertainties and by propagating such model uncertainties along with parameters in the code calculations. The two-step specification of IMTHUA (input phase following with the output updating) makes it special case to make sure that the figure of merit statistical coverage is achieved at the end with target confidence level. Tolerance limit statistics provide confidence a level on the level of coverage depending on the sample size, number of output measures, and one-sided or two-sided type of statistics. This information should be transferred to the second phase in the form of a probability distribution for each of the output measures. The research question is how to use data to develop such distributions from the corresponding tolerance limit statistics. Two approaches of using extreme values method and Bayesian updating are selected to estimate the parametric distribution parameters and compare the coverage in respect to the selected coverage criteria. The analysis is demonstrated on the large break loss of coolant accident for the LOFT test facility.