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

Favorite, Jeffrey A.; Perkó, Zoltán; Kiedrowski, Brian C.; Perfetti, Christopher M.

doi:10.1080/00295639.2016.1272990

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 »« less

Authors:

Favorite, Jeffrey A. ^[1]; Perkó, Zoltán ^[2]; Kiedrowski, Brian C. ^[3]; Perfetti, Christopher M. ^[4]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Harvard Medical School, Boston, MA (United States)
Univ. of Michigan, Ann Arbor, MI (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: Wed Mar 01 00:00:00 EST 2017

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 University, 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.  doi:10.1080/00295639.2016.1272990.

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                    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

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                    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.

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@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         = {Wed Mar 01 00:00:00 EST 2017},

  month        = {Wed Mar 01 00:00:00 EST 2017}

}

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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

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

Favorite, Jeffrey A.
Nuclear Science and Engineering, Vol. 192, Issue 1
DOI: 10.1080/00295639.2018.1471296

Calculating the k -Eigenvalue Sensitivity to Typical Geometric Perturbations with the Adjoint-Weighted Method in the Continuous-Energy Reactor Monte Carlo Code RMC
journal, June 2019

Li, Hao; Yu, Ganglin; Huang, Shanfang
Nuclear Science and Engineering, Vol. 193, Issue 11
DOI: 10.1080/00295639.2019.1614800

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

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Similar Records

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

Abstract

Citation Formats

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

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

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

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

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

Calculating the k -Eigenvalue Sensitivity to Typical Geometric Perturbations with the Adjoint-Weighted Method in the Continuous-Energy Reactor Monte Carlo Code RMC journal, June 2019

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

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

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

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

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

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

Calculating the k -Eigenvalue Sensitivity to Typical Geometric Perturbations with the Adjoint-Weighted Method in the Continuous-Energy Reactor Monte Carlo Code RMC
journal, June 2019

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