Reducing direct perturbation uncertainty for high-sensitivity coefficients

The results for all four different methods show the reduction in DP uncertainty that is achievable with various techniques. Based on the amount of time it takes to run KENO calculations, it was more efficient, while producing a larger reduction in percentage uncertainty, to run multiple simultaneous, independent calculations at the respective endpoints of the range of perturbations considered. Clustered endpoints had the advantage over spread points of avoiding large leverage differences that lead to reduced impact for smaller perturbations. Although the main focus has been on larger sensitivity values, note that very small sensitivities (i.e., ~0.01) sometimes result in a nonlinear trendline, as shown in Figure 5. In instances such as these, it would be more appropriate to employ the uniform spacing technique to ensure that the points are sufficiently spaced to produce a suitable estimate of the behavior of keff over the larger perturbation range. The DP sensitivity is always the slope of the fit at the nominal density, so higher-order fits may be used if appropriate. Clustering of points for these cases would result in an incomplete picture of the DP behavior and could result in inaccurate sensitivity estimates. The primary purpose of this paper is to demonstrate various techniques that could be employed to efficiently reduce the uncertainty in DP calculations for large sensitivity values. Although all of the methods investigated herein effectively reduced the uncertainty, the most efficient method was the clustered endpoints technique. However, these techniques are only suggestions for a starting point, as more complicated systems and/or material makeups could have a larger effect on the outcome of the DP results. A small investment of time by the analyst using these techniques can increase accuracy in DP calculations and thus confirmation of the resulting sensitivities. Generating these sensitivities is generally a significant investment of time and effort, so a small additional investment is warranted to ensure accurate results.