Determination of the minimal number and optimal sensor location in a nuclear system with fixed incore detectors

Abstract

The determination of the minimal number of sensors and the optimal sensor location in a nuclear system with fixed incore detectors, which is represented by a linear stochastic distributed parameter system, was studied in this work. The partial differential equation representing nuclear reactor dynamics was approximated to the finite dimensional ordinary differential equation by the modal expansion. A scalar measure of the covariance matrix error in the optimal filter was minimized with respect to the sensor locations. The necessary conditions for optimal sensor location were derived using the matrix minimum principle, thus making the calculations computationally more attractive. The locations of sensors were guessed initially through sensitivity analysis to reach solutions of the optimal location quickly. A method to determine the minimum number of sensors is suggested based on the observability and admissible error bound. Several numerical simulations are performed to determine the minimal number and optimal sensor location for a one-dimensional slab reactor and a two-dimensional ABB Combustion Engineering type reactor with fixed incore detectors. Through the simulations the possibility of practical implementation and the rapid convergence of the algorithm are verified.