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Title: Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide

Abstract

The evaluation of uncertainties is essential for criticality safety. This paper deals with material density and composition uncertainties and provides guidance on how traditional first-order sensitivity methods can be used to predict their effects. Unlike problems that deal with traditional cross-section uncertainty analysis, material density and composition-related problems are often characterized by constraints that do not allow arbitrary and independent variations of the input parameters. Their proper handling requires constrained sensitivities that take into account the interdependence of the inputs. This paper discusses how traditional unconstrained isotopic density sensitivities can be calculated using the adjoint sensitivity capabilities of the popular Monte Carlo codes MCNP6 and SCALE 6.2, and we also present the equations to be used when forward and adjoint flux distributions are available. Subsequently, we show how the constrained sensitivities can be computed using the unconstrained (adjoint-based) sensitivities as well as by applying central differences directly. Three distinct procedures are presented for enforcing the constraint on the input variables, each leading to different constrained sensitivities. As a guide, the sensitivity and uncertainty formulas for several frequently encountered specific cases involving densities and compositions are given. An analytic k∞ example highlights the relationship between constrained sensitivity formulas and central differences,more » and a more realistic numerical problem reveals similarities among the computer codes used and differences among the three methods of enforcing the constraint.« less

Authors:
 [1];  [2];  [3];  [4]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Harvard Medical School, Boston, MA (United States)
  3. Univ. of Michigan, Ann Arbor, MI (United States)
  4. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); North Carolina State Univ., Raleigh, NC (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP); USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)
OSTI Identifier:
1374343
Alternate Identifier(s):
OSTI ID: 1348326; OSTI ID: 1438412
Report Number(s):
LA-UR-16-26659
Journal ID: ISSN 0029-5639; TRN: US1702552
Grant/Contract Number:  
AC52-06NA25396; AC05-00OR22725; NA0002576
Resource Type:
Accepted Manuscript
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 185; Journal Issue: 3; Journal ID: ISSN 0029-5639
Publisher:
American Nuclear Society - Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; 97 MATHEMATICS AND COMPUTING; sensitivity analysis; uncertainty quantification; adjoint; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Favorite, Jeffrey A., Perkó, Zoltán, Kiedrowski, Brian C., and Perfetti, Christopher M.. Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide. United States: N. p., 2017. Web. https://doi.org/10.1080/00295639.2016.1272990.
Favorite, Jeffrey A., Perkó, Zoltán, Kiedrowski, Brian C., & Perfetti, Christopher M.. Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide. United States. https://doi.org/10.1080/00295639.2016.1272990
Favorite, Jeffrey A., Perkó, Zoltán, Kiedrowski, Brian C., and Perfetti, Christopher M.. Wed . "Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide". United States. https://doi.org/10.1080/00295639.2016.1272990. https://www.osti.gov/servlets/purl/1374343.
@article{osti_1374343,
title = {Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide},
author = {Favorite, Jeffrey A. and Perkó, Zoltán and Kiedrowski, Brian C. and Perfetti, Christopher M.},
abstractNote = {The evaluation of uncertainties is essential for criticality safety. This paper deals with material density and composition uncertainties and provides guidance on how traditional first-order sensitivity methods can be used to predict their effects. Unlike problems that deal with traditional cross-section uncertainty analysis, material density and composition-related problems are often characterized by constraints that do not allow arbitrary and independent variations of the input parameters. Their proper handling requires constrained sensitivities that take into account the interdependence of the inputs. This paper discusses how traditional unconstrained isotopic density sensitivities can be calculated using the adjoint sensitivity capabilities of the popular Monte Carlo codes MCNP6 and SCALE 6.2, and we also present the equations to be used when forward and adjoint flux distributions are available. Subsequently, we show how the constrained sensitivities can be computed using the unconstrained (adjoint-based) sensitivities as well as by applying central differences directly. Three distinct procedures are presented for enforcing the constraint on the input variables, each leading to different constrained sensitivities. As a guide, the sensitivity and uncertainty formulas for several frequently encountered specific cases involving densities and compositions are given. An analytic k∞ example highlights the relationship between constrained sensitivity formulas and central differences, and a more realistic numerical problem reveals similarities among the computer codes used and differences among the three methods of enforcing the constraint.},
doi = {10.1080/00295639.2016.1272990},
journal = {Nuclear Science and Engineering},
number = 3,
volume = 185,
place = {United States},
year = {2017},
month = {3}
}

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Works referenced in this record:

Ambiguities in the Sensitivity and Uncertainty Analysis of Reactor Physics Problems Involving Constrained Quantities
journal, July 2015

  • Perkó, Zoltán; Lathouwers, Danny; Kloosterman, Jan Leen
  • Nuclear Science and Engineering, Vol. 180, Issue 3
  • DOI: 10.13182/NSE14-17

Adjoint-Weighted Tallies for k -Eigenvalue Calculations with Continuous-Energy Monte Carlo
journal, July 2011

  • Kiedrowski, Brian C.; Brown, Forrest B.; Wilson, Paul P. H.
  • Nuclear Science and Engineering, Vol. 168, Issue 3
  • DOI: 10.13182/NSE10-22

Adjoint-Based k -Eigenvalue Sensitivity Coefficients to Nuclear Data Using Continuous-Energy Monte Carlo
journal, July 2013

  • Kiedrowski, Brian C.; Brown, Forrest B.
  • Nuclear Science and Engineering, Vol. 174, Issue 3
  • DOI: 10.13182/NSE12-46

SCALE Continuous-Energy Eigenvalue Sensitivity Coefficient Calculations
journal, March 2016

  • Perfetti, Christopher M.; Rearden, Bradley T.; Martin, William R.
  • Nuclear Science and Engineering, Vol. 182, Issue 3
  • DOI: 10.13182/nse15-12

SCALE Continuous-Energy Eigenvalue Sensitivity Coefficient Calculations
journal, March 2016

  • Perfetti, Christopher M.; Rearden, Bradley T.; Martin, William R.
  • Nuclear Science and Engineering, Vol. 182, Issue 3
  • DOI: 10.13182/NSE15-12

    Works referencing / citing this record:

    SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k eff , and α Using PARTISN
    journal, July 2018


    Application of Neutron Multiplicity Counting Experiments to Optimal Cross-Section Adjustments
    journal, February 2020

    • Clark, Alexander R.; Mattingly, John; Favorite, Jeffrey A.
    • Nuclear Science and Engineering, Vol. 194, Issue 4
    • DOI: 10.1080/00295639.2019.1698267