A Two-Time-Scale Approach for Discrete-Time Kalman Filter Design and Application to AHWR Flux Mapping

In large nuclear reactors such as the Advanced Heavy Water Reactor (AHWR), the core neutron flux distribution needs to be continuously monitored and displayed to the operator. This task is accomplished by an online Flux Mapping System, which employs a suitable algorithm to estimate the core flux distribution from the readings of a large number of in-core detectors. Most of the algorithms available today employ the Flux Synthesis method, Internal Boundary Condition method, and the method based on simultaneous least squares solutions of neutron diffusion and detector response equations. A common feature of these methods is the assumption that the neutron flux profile in the reactor is independent of time. Application of Kalman filtering-based approaches are also found though to a very limited extent. In this paper, we have formulated the task of flux-mapping problem in AHWR as a problem of optimally estimating the time-dependent neutron flux at a large number of mesh points in the core. The solution is obtained using the well-known Kalman filtering technique which works along with a space-time kinetics model of the reactor. However, the attempt to solve the Kalman filtering problem in a straightforward manner is not successful due to severe numerical ill-conditioning caused by the simultaneous presence of slow and fast phenomena typically present in a nuclear reactor. Hence, a grouping of state variables has been suggested whereby the original high-order model of the reactor is decoupled into a slow subsystem and a fast subsystem. Now according to the order of the slow and fast subsystems, the original time update and Kalman gain equations have also been decoupled into separate sets of equations for the slow and fast subsystems. The decoupled sets of equations could be solved easily. The proposed method has been validated in a number of typical transient situations. Overall accuracy in the estimation using the proposed methodology has been very good for mesh fluxes, channel fluxes, quadrant fluxes, and the core average flux.