Uncertainty Analysis of Time-Dependent Nonlinear Systems: Theory and Application to Transient Thermal Hydraulics

Abstract

An advanced methodology for performing systematic uncertainty analysis of time-dependent nonlinear systems is presented. This methodology includes a capability for reducing uncertainties in system parameters and responses by using Bayesian inference techniques to consistently combine prior knowledge with additional experimental information. The determination of best estimates for the system parameters, for the responses, and for their respective covariances is treated as a time-dependent constrained minimization problem. Three alternative formalisms for solving this problem are developed. The two “off-line” formalisms, with and without “foresight” characteristics, require the generation of a complete sensitivity data base prior to performing the uncertainty analysis. The “online” formalism, in which uncertainty analysis is performed interactively with the system analysis code, is best suited for treatment of large-scale highly nonlinear time-dependent problems.This methodology is applied to the uncertainty analysis of a transient upflow of a high pressure water heat transfer experiment. For comparison, an uncertainty analysis using sensitivities computed by standard response surface techniques is also performed. The results of the analysis indicate the following. Major reduction of the discrepancies in the calculation/experiment ratios is achieved by using the new methodology.Incorporation of in-bundle measurements in the uncertainty analysis significantly reduces system uncertainties.Accuracy of sensitivities generated by response-surface techniques should be carefully assessed prior to using them as a basis for uncertainty analyses of transient reactor safety problems.Conclusions about the future applicability of the uncertainty analysis methodology presented in this work are also discussed.