Program - Brookhaven National Laboratory

Laboratory, Oak Ridge, Tenn., November 2011. [7] M. L. Williams, et al, “Development Of A Statistical
Sampling Method For Uncertainty Analysis With Scale,” PHYSOR 2012 - Advances in Reactor Physics ,
Knoxville, Tennessee, USA, April 15-20, 2012. [8] G. Ilas, I. C. Gauld, “Analysis of Uncertainty in Spent
Nuclear Fuel Source Terms Due to Nuclear Data Uncertainties,” Letter Report to Nuclear Regulatory
Commission, ORNL/LTR-2012/34, Oak Ridge National Laboratory, (January 2012).
RC 2 11:00 AM
Pseudo-measure Simulations and Shrinkage for the Experimental Cross-Section Covariances
Optimisation
S. Varet, P. Dossantos-Uzarralde, E. Bauge
CEA
N. Vayatis
ENS Cachan
It is well known that the experimental cross-section covariances play an important role in the evaluated
cross-sections uncertainty determination (in particular in the generalized χ2 minimisation). One can determine
the experimental covariance matrix Σ from a classical uncertainty propagation formula and a detailed
experimental process description. In particular, the determination of Σ requires the experimental parameters
variances and covariances. However these data are rarely available. Another classical method is the
Σ empirical estimator. However, most of the time, we only dispose on one measure per energy. Therefore
the experiment repetitions aren’t enough of them to use the classical empirical estimator. That’s why
we need to find alternatives for the Σ determination. Some of them, like kriging, consist in exploiting
an a priori structure for the covariance matrix Σ. Nevertheless the imposed structure and the needed
assumptions are not always realistic for cross-section measurements. In this general context our interest
is focused on the construction of an efficient experimental covariance matrix estimator. Our approach
is based on pseudo-measures simulations. To take into account the smoothness of the cross-section as a
function of the energy, we simulate pseudo-measures as a gaussian noise centered on a SVM regression
model. With the true measures and the pseudo-measures we can compute a Σ empirical estimator. We
then quantify the obtained estimator quality with the help of a bootstrap approach. The problem is still
that the estimation is not optimal. Thus, in order to optimize the resulting matrix, we have chosen to
use the shrinkage approach. Indeed, the shrinkage approach consists in finding the optimal matrix (in the
sense that it minimizes the error between the true matrix and its estimation) between the initial estimator
and a target matrix that satisfies some properties we want to reach (invertibility, conditionning,...). All the
results are illustrated with a toy model (where all quantities are known) and also with Mn55 25 cross-section
measurements.
RC 3 11:20 AM
Inverse Sensitivity/Uncertainty Methods Development for Nuclear Fuel Cycle Applications
G. Arbanas, M. E. Dunn, and M. L. Williams
Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 USA
The Standardized Computer Analyses for Licensing Evaluation (SCALE) [1] software package includes
codes that propagate uncertainties available in the nuclear data libraries to compute uncertainties in nuclear
application performance parameters (”responses”). We extend this capability to include an inverse
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