Comparison and uncertainty of multivariate modeling techniques to characterize used nuclear fuel

Abstract

The ability to characterize used nuclear fuel (UNF) is important for nuclear nonproliferation safeguards, criticality safety, and fuel storage. Multiple efforts have been made to estimate the burnup (BU), initial enrichment (IE), and cooling time (CT) based on multivariate models of isotopic concentrations and radiation signatures of the fuel. This work provides a comparison of multivariate modeling techniques and extends previous work by quantifying the uncertainty of the best model to predict each characteristic. Model inputs used are simulated gamma and neutron emissions from UNF of varying BU, IE, and CT. Modeling techniques explored include Ordinary Least Squares Regression (OLS), Principal Component Regression (PCR), and Partial Least Squares Regression (PLS). Multiple PCR and PLS models were built based on different variable selection methods, such as cross validation and Akaike Information Criteria. The OLS model predictions have a root mean square percent error (RMSPE) of less than 10%, but the models are very unstable. The PCR models exhibit a trade-off between accurate and stable predictions. The best performing PCR and PLS models have similar predictions errors, but the PLS models are favored due to their stability. The best model for each characteristic is a single output PLS model based on cross validation. The uncertainty of each of these models, based on their prediction variance and biases, is 0.220 GWd/MTU, 0.051% U-235, and 0.694 years for the BU, IE, and CT models, respectively. By building a 95% prediction interval based on the corresponding uncertainty of each characteristic, 1.97% of the BU predictions, 23.03% of the IE predictions, and 100% of the CT predictions lack 95% confidence that they are within the prescribed accuracy requirement for the characteristic.