Construction of response surfaces for a reactor-like problem with realistic cross section uncertainties
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Copyright (2015) by the American Nuclear Society. In this paper we construct response surfaces for a simple problem with a high-dimensional input space common to nuclear reactor analysis. Response surfaces are challenging to build for these problems due to the extreme dimensionality of the uncertain input space. Deterministic neutron transport calculations commonly discretize the continuous energy variable into energy groups across which material properties can be averaged. This "multigroup" approximation yields thousands of cross sections each with an associated uncertainty. In this analysis a thirty energy-group discretization is chosen yielding 1,440 uncertain input parameters. The cross sections' variances and covariances are obtained with the cross section preparation tool NJOY. A problem of interest is chosen and an equation derived for a quantity of interest (Qol). An adjoint equation is derived to determine the sensitivity of the Qol to individual cross sections; these sensitivity coefficients, paired with the cross section uncertainties, are used to determine which cross sections contribute significantly to the uncertainty in the Qol. A collection of response surfaces for the reduced space are constructed for the Qol using the solutions of the forward problem and the sensitivity coefficients calculated with the adjoint problem. The mean and variance of the Qol is determined by averaging the mean and variance of the Qol on each of the response surfaces. The unique contribution of this paper is the construction of response surfaces for a problem with a very high dimensional input space. The problem examined in this paper is simple and can be solved in seconds. However, the cross section data required is the same as that required for large-scale deterministic nuclear reactor calculations. We successfully construct a family of response surfaces to quantify the uncertainty in the Qol and to serve as a predictive model for this problem, demonstrating that this method is applicable to nuclear reactor analysis problems with a large and uncertain cross section input space.
