An Efficient Variance-Based Uncertainty Decomposition Methodology for Nuclear Data in LWR Depletion Calculations

Uncertainty quantification and sensitivity analysis are crucial tools for the improvement of nuclear data libraries. Especially when validating calculations for general applications outside the well characterized benchmark systems, e.g. depletion calculations of commercial power reactors, it is essential to investigate the influence of nuclear data on the uncertainty. However, general variance-based stochastic sampling techniques that apply Sobol’ indices require tens of thousands of depletion calculations, making them extremely computationally expensive. Consequently, the uncertainty decompositions of depletion calculation results currently presented in the literature do not go into a high level of detail, whereas more detailed decompositions could reveal points of improvement. The current paper therefore presents a methodology derived from the Sobol’ first order effect index, which is able to calculate a more detailed uncertainty decomposition for a one to three orders of magnitude smaller sample size. The statistical measure used in this adaption reduces the sampled input variable space, whereas the Sobol’ first order effect index samples all input variables. Both are equivalent for all models without non-bilinear interaction terms between the input variables of interest and all other input variables. The reduced sampled input space fraction of variance is applied to decompose the uncertainty on the multiplication factor in a depletion calculation of a PWR pincell model into the contributions of the fission yields of ²³⁵U, as an example to demonstrate the computational feasibility.