Preliminary study on few group cross section representation method based on model tree algorithm

The tabular representation of few-group cross section is widely used for node wise two-step core simulations. However, it may take too much memory usage for pin-by-pin two-step simulations. A few-group cross section representation method for PWR has been developed to reduce memory usage in this paper. The few-group cross sections are represented as the sum of a base term and a collection of partial terms. Each of these terms is fitted by modified model tree. The case matrix of training data set is similar with that of the conventional methods such as the piece wise interpolation and the tabular representation. Two modifications have been made for the model tree algorithm: 1) burnup is the only variable to split data set, 2) linear regression method on nodes of the tree is replaced with polynomial fitting method according to priori knowledge of the relationship between cross sections and state variables. Through the modifications accuracy and generalization ability are achieved without the pruning procedure. Then the lattice calculations for test data set could be canceled. Tests on the typical PWR lattice are performed. Numerical results show that for the worst case the memory usage of this method is less than 30% of the tabular representation, when the maximum error of reactivity is less than 500 pcm. The memory usage for other cross sections is less than 10% with high accuracy. Optimization of the target tolerance criteria should be tested for fast group cross sections. Large errors in thermal group absorption and fission production cross sections lead to large errors in Kin f and it needs more study on regression model. The method combined with the tabular representation might be more suitable for the pin-by-pin two-step simulations. (author)