Sensitivity and uncertainty analysis of a reduced-order model of nonlinear BWR dynamics. III: Uncertainty analysis results

Abstract

This work presents a paradigm analysis of the standard deviations induced in the state functions of a reduced-order model of Boiling Water Reactor (BWR) dynamics by the standard deviations in this model’s imprecisely known parameters and initial conditions. This analysis is performed in the model’s stable region in phase-space, where the state functions converge asymptotically to finite, time-independent values, as well as in the regions in phase-space where the model’s state functions asymptotically evolve into periodic limit-cycle oscillations. The region in phase-space where the model’s state functions behave chaotically is also analyzed. The standard deviations of the state functions in the various regions in phase-space are computed using the first-order sensitivities of the state functions with respect to the model’s imprecisely known parameters and initial conditions. It is shown that in the stable region, the standard deviations induced by the imprecisely known model parameters and initial conditions in each of the BWR-model’s state functions are very large immediately after perturbing the initially critical reactor, reaching values that are about 10 times larger than the respective state functions themselves. Although these standard deviations decay to small values after about 140 s into the transient, the amplitudes of the oscillations of these standard deviations at the start of the transient are so large as to possibly cause the BWR-system to transit from the stable region into an oscillatory region in phase-space. In the limit-cycle oscillatory regions in phase space, as well as in the chaotic region, the standard deviations of the state functions are very large, so that an accurate prediction of the actual value of the respective state functions has a low probability of success. The results obtained in this work indicate that the methods used herein should be implemented into the models used for the design and routine analysis of BWRs, in order to quantify deterministically the uncertainties induced into the operational characteristics of BWRs by the imprecisely known parameters underlying these models, particularly when BWRs are operated close to the limits of their stability regions/maps.