Efficient uncertainty analyses using fast probability integration

Abstract

Fast probability integration (FPI) algorthms are adapted, extended and used to perform nuclear engineering uncertainty analyses. Methods are presented to improve the efficiency and precision of FPI for frequently encountered input distributions, to permit quick estimates of extreme model output quantiles and to provide appropriate sensitivity and uncertainty importance measures. Advantages and disadvantages of FPI as a stand-alone method are explored in two demonstration applications. FPI is first applied to estimate extreme (0.95, 0.99, 0.999 and 0.9999) quantiles of the frequency of a dominant station blackout accident. Sensitivity measures are quantified to indicate how the relative importance of each model input changes at progressively more extreme output quantiles. FPI is next applied to analyze uncertainties in fire damage times predicted by compbrn iiie. Alternative FPI-based uncertainty importance measures are compared and shown to consistently rank the input contributions to the output uncertainty. FPI results are compared with results obtained from Monte Carlo sampling to demonstrate the computational advantage that clearly favors FPI, especially at the more extreme output quantiles. In a third application, Latin hypercube sampling (LHS) is combined with FPI to determine extreme quantiles of peak cladding temperature during the blowdown phase of a large-break loss of coolant accident as modeled by trac-pfi/mod2. The 0.95 quantile peak cladding temperature is reproducibly determined to within 2 K in one LHS-FPI iteration, which is based on only 21 trac-pfi/mod2 runs. To demonstrate convergence for a more extreme case, LHS-FPI is also applied to estimate the 0.999 quantile peak cladding temperature. In each LHS-FPI iteration a final code run is performed to assure that the code-calculated peak cladding temperature agrees with that predicted by LHS-FPI at the most probable point. Importance measures are quantified at this point to identify dominant input-output relationships. Compared with past code scaling, applicability and uncertainty (CSAU) analyses, LHS-FPI offers a significant reduction in the number of best-estimate code runs required while providing additional checks and insights.