Random sampling and validation of covariance matrices of resonance parameters

Lucijan Plevnik,Gašper Zerovnik

doi:10.1051/epjconf/201714602014

Abstract

Analytically exact methods for random sampling of arbitrary correlated parameters are presented. Emphasis is given on one hand on the possible inconsistencies in the covariance data, concentrating on the positive semi-definiteness and consistent sampling of correlated inherently positive parameters, and on the other hand on optimization of the implementation of the methods itself. The methods have been applied in the program ENDSAM, written in the Fortran language, which from a file from a nuclear data library of a chosen isotope in ENDF-6 format produces an arbitrary number of new files in ENDF-6 format which contain values of random samples of resonance parameters (in accordance with corresponding covariance matrices) in places of original values. The source code for the program ENDSAM is available from the OECD/NEA Data Bank. The program works in the following steps: reads resonance parameters and their covariance data from nuclear data library, checks whether the covariance data is consistent, and produces random samples of resonance parameters. The code has been validated with both realistic and artificial data to show that the produced samples are statistically consistent. Additionally, the code was used to validate covariance data in existing nuclear data libraries. A list of inconsistencies, observed in covariance data of resonance parameters in ENDF-VII.1, JEFF-3.2 and JENDL-4.0 is presented. For now, the work has been limited to resonance parameters, however the methods presented are general and can in principle be extended to sampling and validation of any nuclear data.

Highlights

Introduction applied in the programENDSAM, written in the FortranCompared to deterministic uncertainty propagation [1], random sampling is less time efficient, may be more accurate and less cumbersome.In the covariances of existing nuclear data libraries, 95 language, which receives a number of required samples n, a file from a nuclear data library of a certain isotope in ENDF-6 format [6], different mathematical inconsistencies are a common phenomenon
The source code for the program ENDSAM is available from the OECD/NEA Data Bank
The work has been limited to resonance parameters, the methods presented are general and can in principle be extended to sampling and validation of any nuclear data

Summary

Random sampling method

(4) and (5) are often not taken into account in nuclear data libraries In such cases we assume that the correlation matrix from data library is given for a collection of normal parameters, so it applies to the collection x1, . Some cases appear when even a matrix given in a library has some negative eigenvalues and in some cases this happens to be the case after transformation of correlation coefficients In this case we apply Higham’s method [11] to find the nearest correlation matrix in Frobenius norm and work with the resulting matrix. Among resonance parameters in nuclear data libraries, resonance energy ER is the only parameter which is assumed to be normally distributed by ENDSAM, since its relative uncertainty is always very small

Validation of the sampling code

Validation of nuclear data libraries

Findings

Conclusions