Minimum-norm solution of ill-posed neutron detector response using constrained quadratic programming

Least squares problems occur frequently in nuclear science including the parameter identification of linear/nonlinear dynamic models, modeling the responses of the spatially distributed detectors, nuclear data treatment, response surface modeling of the thermal margin estimation, etc. Considering the inevitable measurement noise and transport kernel simplification, the ill-posedness of the least squares method can arise and limit the applicability of the assumed model structures. In this paper, a constructive method is proposed with the constrained quadratic programming approach to get the physically meaningful solution. The method is applied to the determination of the parameter vector used to estimate the axially 3-level average core power with ex-core detectors. The test results show the remarkable improvement in accuracy and robustness for the noisy measurement data.