Automated resonance evaluation; Non-convex decomposition method for resonance regression and uncertainty quantification

Abstract

This work serves as a proof of concept for an automated tool to assist in the evaluation of experimental neutron cross section data in the resolved resonance range. The resonance characterization problem is posed as a mixed integer nonlinear program (MINLP). Since the number of resonances present is unknown, the model must be able to be determine the number of parameters to properly characterize the cross section curve as well as calculate the appropriate values for those parameters. Due to the size of the problem and the nonconvex nature of the parameterization, the optimization formulation is too difficult to solve as whole. A novel method is developed to decompose the problem into smaller, solvable windows and then stitch them back together via parameter-cardinality and parameter-value agreement routines in order to achieve a global solution. A version of quantile regression is used to provide an uncertainty estimate on the suggested cross section that is appropriate with respect to the experimental data. The results demonstrate the model's ability to find the proper number of resonances, appropriate average values for the parameters, and an uncertainty estimation that is directly reflective of the experimental conditions. The use of synthetic data allows access to the solution, this is leveraged to build-up performance statistics and map the uncertainty driven by the experimental data to an uncertainty on the true cross section.