Building neutron cross-section dependencies for few-group reactor calculations using stepwise regression Vyacheslav G. Zimin * , Andrey A. Semenov Division 836 ‘‘Laboratory of Simulator Systems’’, Moscow Engineering Physics Institute, Kashirskoe shosse, 31, Moscow, 115409, Russia Received 20 February 2004; accepted 11 June 2004 Available online 12 August 2004 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 ther- mal-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 approx- imated by a polynomial. Construction of the polynomial is performed by a best-fitting selec- tion 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 polyno- mial 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 0306-4549/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2004.06.009 * Corresponding author. E-mail addresses: slava@ets.mephi.ru (V.G. Zimin), and@ets.mephi.ru (A.A. Semenov). Annals of Nuclear Energy 32 (2005) 119–136 www.elsevier.com/locate/anucene annals of NUCLEAR ENERGY