Resonance Parameter Covariance Research Articles

Investigation of Uncertainty Propagation in the Resolved Resonance Range

This paper presents a comparative study using the first-order formula (also called “sandwich”) and the multivariate sampling methodologies for propagating uncertainty in the resolved resonance region. A distinctive aspect of this work is the generation of random cross sections by sampling Resonance Parameters (RPs) taking in consideration their correlations provided in nuclear data libraries via the Resonance Parameter Covariance Matrix (RPCM). SCOOBY (Sampling COvariance OBservatorY), a newly developed sampling tool, is presented in this paper. This tool relies on the GAIA-2 nuclear data processing code to read and correct the RPCM and generate random cross sections. The study compares the sandwich method that relies on sensitivity coefficients and covariance matrices, with the sampling method, which involves numerous Monte Carlo simulations with random cross sections. The comparison is tested on an ICSBEP benchmark, PU-MET-MIXED-002, chosen for its sensitivity to 239Pu cross sections. The results indicate that both methods quantify similar uncertainties, confirming the reliability of both the SCOOBY module and the GAIA-2 code. By using the PU-MET-MIXED-002 benchmark and sampling 239Pu resonance parameters, this work demonstrates the effectiveness of these methodologies in estimating uncertainty in criticality safety calculations. The findings highlight the robustness of these approaches in uncertainty propagation, suggesting the need for further research on additional benchmarks and expanded uncertainty propagation studies.

Resonance parameter covariance representation: file32 versus file33

Sensitivity and uncertainty analysis in error propagation studies are carried out based on nuclear data uncertainty information available in the basic nuclear data libraries such as ENDF, JEFF, JENDL and others. The uncertainty files (covariance matrices) are generally obtained from analysis of experimental data. In the resonance region, the computer code SAMMY is used for analyses of experimental data and generation of resonance parameters. In addition to resonance parameters evaluation, SAMMY also generates resonance parameter covariance matrices (RPCM). The intent of this paper is to discuss the use of the RPCM in contrast to the use of a cross section covariance matrix (CSCM) representation. For so, the resonance evaluation for 48Ti in the resonance range from 10−5 eV to 400 keV is used. The RPCM is translated into two distinct CSCM by using a coarser and a finer group structures. The results are presented and discussions of the feasibility of using these covariance representations are depicted.

On the Use of Zero Variance Penalty Conditions for the Generation of Covariance Matrix between Model Parameters

This paper presents models developed to generate covariances between observable, latent and nuisance variables. The methodology consists in using “variance penalty” terms as a measure of the contribution of the uncertainty of the latent and nuisance variables to the variance of a given calculated quantity z. The Resonance Parameter Covariance Matrix for 241Am obtained with the Zero Variance Penalty model (ZVP) is compared with the corresponding one provided by Monte-Carlo.

ORNL Resolved Resonance Covariance Generation for ENDF/B-VII.1

Resonance-parameter covariance matrix (RPCM) evaluations in the resolved resonance regionwere done at the Oak Ridge National Laboratory (ORNL) for the chromium isotopes, titanium isotopes, 19F, 58Ni, 60Ni, 35Cl, 37Cl, 39K, 41K, 55Mn, 233U, 235U, 238U, and 239Pu using the computer code SAMMY. The retroactive approach of the code SAMMY was used to generate the RPCMs for 233U. For 235U, the approach used for covariance generation was similar to the retroactive approach with the distinction that real experimental data were used as opposed to data generated from the resonance parameters. RPCMs for 238U and 239Pu were generated together with the resonance parameter evaluations. The RPCMs were then converted in the ENDF format using the FILE32 representation. Alternatively, for computer storage reasons, the FILE32 was converted in the FILE33 cross section covariance matrix (CSCM). Both representations were processed using the computer code PUFF-IV. This paper describes the procedures used to generate the RPCM and CSCM in the resonance region for ENDF/B-VII.1. The impact of data uncertainty in nuclear reactor benchmark calculations is also presented.

Evaluation of the Chromium Resonance Parameters Including Resonance Parameter Covariance

The intent of this work is to report the results and describe the procedures utilized to evaluate the chromium isotopes' cross sections, i.e., (50)Cr, (52)Cr, (53)Cr, and (54)Cr, for criticality safety applications. The evaluations were done in the resolved resonance region using the reduced Reich-Moore R-matrix formalism. The novel aspect of this evaluation is the inclusion of new transmission and capture cross-section measurements performed at the Oak Ridge Electron Linear Accelerator (ORELA) for energies below 100 keV and the extension of the (53)Cr energy region. The resonance analysis was performed with the multilevel R-matrix code, SAMMY, which utilizes the generalized least-squares technique based on the Bayes' theory. Complete sets of resonance parameters and resonance parameter covariance matrices (RPCMs) were obtained for each of the chromium isotopes from the SAMMY analysis of the experimental database.

Recent Advances with the AMPX Covariance Processing Capabilities in PUFF-IV

was modified to take advandage of Basic Linear Algebra Subprograms (BLAS) routines for the most time-consuming matrix multiplications. This led to a substantial decrease in execution time. This faster processing capability allowed us to investigate the conversion of File 32 data into File 33 data using a larger number of user-defined groups. While conversion substantially reduces the ENDF/B file size requirements for evaluations with a large number of resonances, a trade-off is made between the number of groups used to represent the resonance parameter covariance as a point-wise covariance matrix and the file size. We are also investigating a hybrid version of the conversion, in which the low-energy part of the File 32 resonance parameter covariances matrix is retained and the correlations with higher energies as well as the high energy part are given in File 33.

Simulation of robust resonance parameters using information theory

Due to complex nature of resonance region interactions, significant effort has been devoted to quantify the resonance parameter uncertainty information through covariance matrices. Statistical uncertainties arising from measurements contribute only to the diagonal elements of the covariance matrix, but the off-diagonal contributions arise from multiple sources like systematic errors in cross-section measurement, correlation due to nuclear reaction formalism, etc. All the efforts have so far been devoted to minimize the statistical uncertainty by repeated measurements but systematic uncertainty cannot be reduced by mere repetition. The computer codes like SAMMY and KALMAN so far developed to generate resonance parameter covariance have no provision to improve upon the highly correlated experimental data and hence reduce the systematic uncertainty. We propose a new approach called entropy based information theory to reduce the systematic uncertainty in the covariance matrix element wise so that resonance parameters with minimum systematic uncertainty can be simulated. Our simulation approach will aid both the experimentalists and the evaluators to design the experimental facility with minimum systematic uncertainty and thus improve the quality of measurement and the associated instrumentation. We demonstrate, the utility of our approach in simulating the resonance parameters of Uranium-235 and Plutonium-239 with reduced systematic uncertainty.

Covariance Analyses of Self-Shielding Factor and Its Temperature Gradient for Uranium-238 Neutron Capture Reaction

Covariances of the self-shielding factor and its temperature gradient for the uranium-238 neutron capture reaction have been evaluated from the resonance parameter covariance matrix and the sensitivity of the self-shielding factor and its temperature gradient to the resonance parameters. The resonance parameters and their covariance matrix for uranium-238 were taken from JENDL-3.3, while the sensitivity coefficients were calculated by varying resonance parameters and temperature. A set of computer code modules has been developed for the calculation of the sensitivity coefficients at numerous resonance levels. The present result shows that the correlation among resonance parameters yields a substantial contribution to the standard deviations of the self-shielding factor and its temperature gradient. In addition to the standard deviations of these quantities, their correlation matrices in the JFS-3 70 group structure are also obtained.

Covariance Matrix Evaluation and Processing in the Resolved/Unresolved Resonance Regions

This document serves as a summary of the work of Subgroup 20 (SG20) on covariance matrix evaluation and processing in the resolved/unresolved resonance regions, organised under the auspices of the Nuclear Energy Agency’s Nuclear Science Committee Working Party on International Evaluation Co-operation (WPEC). The work described in this report focuses on:- summarising the issues related to covariance evaluation in the resonance region;- discussing the retroactive method used in the SAMMY code [1];- describing the compact format for storing huge covariance matrices in ENDF-6 files;- recent developments and upgrades of processing codes to generate a multi-group covariance matrix from resonance parameter covariance data.

Covariance and sensitivity data generation at ORNL

Covariance data are required to assess uncertainties in design parameters in several nuclear applications. The error estimation of calculated quantities relies on the nuclear data uncertainty information available in the basic nuclear data libraries, such as the US Evaluated Nuclear Data Library, ENDF/B. The uncertainty files in the ENDF/B library are obtained from the analysis of experimental data and are stored as variance and covariance data. In this paper we address the generation of covariance data in the resonance region done with the computer code SAMMY. SAMMY is used in the evaluation of the experimental data in the resolved and unresolved resonance energy regions. The data fitting of cross sections is based on the generalised least-squares formalism (Bayesian theory) together with the resonance formalism described by R-matrix theory. Two approaches are used in SAMMY for the generation of resonance parameter covariance data. In the evaluation process SAMMY generates a set of resonance parameters that fit the data, and, it provides the resonance parameter covariances. For resonance parameter evaluations where there are no resonance parameter covariance data available, the alternative is to use an approach called the 'retroactive' resonance parameter covariance generation. In this paper, we describe the application of the retroactive covariance generation approach for the gadolinium isotopes.