(The) reconstruction of pointwise neutron flux distribution via minimum cross-entropy method

Abstract

The minimum cross-entropy method to reconstruct neutron flux distribution is applied to a more realistic PWR benchmark problem using the results of nodal calculation. The probability distribution that minimizes the cross-entropy provides the most unbiased objective probability distribution within the partial summary information and the prior probability distribution. The flux distribution on the boundary of a fuel assembly is transformed into the probability distribution. Then, the most objective boundary flux distribution is deduced using the nodal results and the Lagrange multipliers. By using this boundary flux distribution as the boundary condition, the imbedded heterogeneous assembly calculation is performed to reconstruct the pointwise neutron flux distribution. The results of application show that the minimum cross-entropy method is sensitive to the errors in average quantities which are used as equality constraints in the optimization problem. This indicates that accuracy in the nodal results is important for reconstruction of the heterogeneous flux distribution. Compared with the results of form function methods, the reconstruction errors are large when the average quantities of nodal calculation are used, but relatively small when the results of VENTURE are used. This thesis also develops an efficient numerical algorithm for inversion of the system matrix to reduce the computing time. This algorithm is based on the block matrix inversion method. This new algorithm led to large computing time reduction in comparison with the existing algorithms.