Addressing Ambiguities in Constrained Sensitivity Analysis for Reactor Physics Problems

This paper presents an algorithm for completing sensitivity analysis that respects linear constraints placed on the associated model’s input parameters. Any sensitivity analysis (linear or nonlinear, local or global) focuses on measuring the impact of input parameter variations on model responses of interest, which may require the analyst to execute the model numerous times with different model parameter perturbations. With the constraints present, the degrees of freedom available for input parameter variations are reduced, and hence any analysis that changes model parameters must respect these constraints. Focusing here on linear constraints, earlier work has shown that constraints may be respected in many ways, causing ambiguities, i.e., nonuniqueness, in the results of a sensitivity analysis, forcing the analyst to introduce dependencies with downstream analyses, e.g., uncertainty quantification, that employ the sensitivity analysis results. This paper develops the theoretical details for a new algorithm to select model parameter variations that automatically satisfy linear constraints resulting in unique results for the sensitivity analysis, thereby removing any custom dependencies with downstream analyses. To demonstrate the performance of the algorithm, it is applied to solve the multigroup eigenvalue problem for the multiplication factor in a representative CANDU core-wide model. The model parameters analyzed are the group prompt neutron fractions, whose summation must be equal to one over all energy groups. The results indicate that the new algorithm identifies the gradient direction uniquely which represents the direction of maximum change while satisfying the constraints, thus removing any ambiguities resulting from the constraints as identified by earlier work.