Flux estimation from Vanadium and Cobalt Self Powered Neutron Detectors (SPNDs): Nonlinear exact inversion and Kalman filter approaches

Abstract

Self Powered Neutron Detectors (SPNDs), which are widely used in a nuclear reactor for flux measurement, typically have different types of dynamics based on their emitter material: one delayed, second prompt and possibly nonlinear response characteristics. The measurement from the SPNDs hence need compensation to obtain the actual input flux. In this paper, we discuss the modeling of and input estimation design for Vanadium and Cobalt SPNDs. We obtain the structure and parameters of the Vanadium SPND model from its radioactive decay mechanism. We then obtain the other parameters of the model applying system identification tools on the available data corresponding to reactor trip. For Cobalt SPND, we design two model based input/state estimators; the nonlinearity being the key feature: the ‘Exact Model Inversion’ and the Extended Kalman filter. In the exact model inversion, we demonstrate that input flux can be calculated by solving a third degree polynomial. In the extended Kalman filter estimator, we propose a novel approach to improve the step response of Kalman filter algorithms by ‘resetting’ the state error covariance matrix. We use Matlab® simulation and reactor data to compare the advantages of the two filters. We show that in both Vanadium and Cobalt SPND cases, Kalman filter based algorithms provide a reasonable balance between speed and noise suppression. While the exact inversion provides an almost prompt, but noisy response to step changes, the modified Kalman filter has a noise-free response with a few minutes of settling time. We also demonstrate the ability of the proposed covariance reset Kalman filter to track step/sudden changes in the input.