Implementation and testing of unscented transformation and low rank approximation to enhance SCALE code uncertainty calculations

Abstract

Recently, the SCALE6.2 code has implemented the Sampler module for randomly sampling important reactor physics inputs from their parental distributions. The Sampler module uses a stochastic sampling technique based on multivariate (MV) sampling which assumes that the input cross-sections are correlated according to a predefined covariance matrix. Although the methodology used in the Sampler module is relatively straightforward and robust, it can be computationally expensive for applications where a large number of Monte Carlo samples are required. In this paper, the SCALE6.2 capabilities are enhanced by implementing the Unscented Transformation (UT) and Low Rank Approximation (LRA) to decrease computational time. The uncertainties are calculated for k-inf due to perturbations in the multi-group cross-sections for a standard PWR fuel pin but the methodology can be applied to any output parameter of interest (such as few group cross sections). First, the UT is applied to generate a set of sigma points which represent the behavior of the system over the entire space. However, since the input model dimensionality is very high, due to the number of isotopes, reactions, and energy-groups, the generation of the sigma sample points may be computationally burdensome. Therefore, the LRA is applied to reduce the order of sampling space which can significantly reduce the computational cost; this model is called the Truncated Unscented Transformation (TUT). The results show that the input-dimension can be reduced from 896 to 112-subspace and the uncertainties in k-inf calculated by TUT sampling with 225 samples are about 5.62×10-1 which agrees well with the full MV sampling with N = 1000 runs and results from TSUNAMI. The results also indicate that the uncertainties calculated by the TUT methodology are not sensitive to the scaling parameter λ assumed in the LRA as long as the appropriate weights are applied.