Building neutron cross-section dependencies for few-group reactor calculations using stepwise regression

Abstract

Approximation of few-group neutron cross-sections by functions of burnup and thermal-hydraulics parameters of a fuel cell is considered. The cross-section is written as a sum of two terms: the base cross-section, which depends only on burnup and is computed under the nominal reactor core conditions, and the deviation, which depends on burnup and thermal-hydraulics variables of the cell. A one-dimensional dependence of the base cross-section is interpolated by a cubic spline. Multi-dimensional dependencies of the deviation are approximated by a polynomial. Construction of the polynomial is performed by a best-fitting selection of the polynomial terms using the stepwise regression algorithm. The number of terms to satisfy a user-given accuracy of approximation is minimized. As an example, approximation of a set of two-group macro and micro cross-sections as functions of burnup, coolant and fuel temperature, coolant density and boron concentration is considered for a fuel pin cell of a VVER reactor. The constructed five-dimensional polynomial approximating cross-sections within 0.05% tolerance has about 20 terms for fast group cross-sections and 50 terms for thermal group cross-sections. The error of approximation is verified on the two data sets: the initial data used for approximation and the test data being computed on randomly selected points. Mean square and maximum errors are comparable for all the cross-sections for both sets of data. These results show that the initial data can be applied to control the approximation error.