An improved fitting method for subgroup parameters based on the heterogeneous cells

An accurate subgroup parameters fitting method, where background cross sections obtained based on heterogeneous cells are used to fit the subgroup level and subgroup weight, is proposed in this paper. Due to the dependence of background cross section on the subgroup level, the calculation of the subgroup parameters is a nonlinear problem, which causes the iteration between fitting subgroup parameters and updating background cross sections. The cubic spline interpolation method is used to update the background cross sections to avoid frequently solving fixed source equations. In the fitting process, the negative subgroup parameters are often obtained, and the accuracy of the subgroup parameters is very sensitive to the iterative initial values of subgroup levels. To avoid these problems, additional constraints ensuring positive subgroup parameters and guaranteeing numerical stability are added to the optimization function. Penalty function method is used to convert the optimization problem with constraints into the one without constraints, making the problem easy to be solved. The proposed method is tested against the problems of pin cell, pressurized water reactor assemblies and plate-type assembly. The numerical results show that the self-shielded cross sections calculated by the proposed method agree well with those by Monte Carlo code.