scholarly journals Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation

2021 ◽  
Vol 36 (2) ◽  
pp. 107-115
Author(s):  
Pavel Bokov ◽  
Danniell Botes ◽  
Suzanne Groenewald
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Automatic Differentiation ◽  
Uncertainty Propagation ◽  
Diffusion Problem ◽  
Iteration Algorithm ◽  
Dual Number ◽  
Analytical Formulas ◽  
Cross Section Uncertainty ◽  
Neutron Cross Sections

This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analysis. As an illustration, we consider a two-group diffusion problem in an infinite medium, which has a solution in a closed form. We employ automatic differentiation in conjunction with the sandwich formula for uncertainty propagation in three ways. Firstly, by evaluating the analytical expression for the multiplication factor using dual number arithmetic. Then, by solving the diffusion problem with the power iteration algorithm and the algebra of dual matrices. Finally, automatic differentiation is used to calculate the partial derivatives of the production and loss operators in the perturbation formula from the adjoint-weighted technique. The numerical solution of the diffusion problem is verified against the analytical formulas and the results of the uncertainty calculations are compared with those from the global sensitivity analysis approach. The uncertainty values obtained in this work differ from values given in the literature by less than 1?10?5.

scholarly journals Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation

2021 ◽  
Vol 36 (2) ◽  
pp. 107-115
Author(s):  
Pavel Bokov ◽  
Danniell Botes ◽  
Suzanne Groenewald
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Automatic Differentiation ◽  
Uncertainty Propagation ◽  
Diffusion Problem ◽  
Iteration Algorithm ◽  
Dual Number ◽  
Analytical Formulas ◽  
Cross Section Uncertainty ◽  
Neutron Cross Sections

This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analysis. As an illustration, we consider a two-group diffusion problem in an infinite medium, which has a solution in a closed form. We employ automatic differentiation in conjunction with the sandwich formula for uncertainty propagation in three ways. Firstly, by evaluating the analytical expression for the multiplication factor using dual number arithmetic. Then, by solving the diffusion problem with the power iteration algorithm and the algebra of dual matrices. Finally, automatic differentiation is used to calculate the partial derivatives of the production and loss operators in the perturbation formula from the adjoint-weighted technique. The numerical solution of the diffusion problem is verified against the analytical formulas and the results of the uncertainty calculations are compared with those from the global sensitivity analysis approach. The uncertainty values obtained in this work differ from values given in the literature by less than 1?10?5.

scholarly journals BETA EFFECTIVE SENSITIVITY TO NUCLEAR DATA WITHIN THE APOLLO3® NEUTRONIC PLATFORM

2021 ◽  
Vol 247 ◽  
pp. 15003
Author(s):  
G. Valocchi ◽  
P. Archier ◽  
J. Tommasi
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Uncertainty Propagation ◽  
Direct Calculation ◽  
Nuclear Data ◽  
The Core ◽  
Nuclear Data Library ◽  
Lattice Core ◽  
Effective Sensitivity ◽  
Data Library

In this paper, we present a sensitivity analysis of the beta effective to nuclear data for the UM17x17 experiment that has been performed in the EOLE reactor. This work is carried out using the APOLLO3® platform. Regarding the flux calculation, the standard two-step approach (lattice/core) is used. For what concerns the delayed nuclear data, they are processed to be directly used in the core calculation without going through the lattice one. We use the JEFF-3.1.1 nuclear data library for cross-sections and delayed data. The calculation of k-effective and beta effective is validated against a TRIPOLI4® one while the main sensitivities are validated against direct calculation. Finally, uncertainty propagation is performed using the COMAC-V2.0 covariance library.

scholarly journals Asymptotic Analysis for the Variance-Based Global Sensitivity Indices

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Pavel M. Bokov
Keyword(s):  
Sensitivity Analysis ◽  
Asymptotic Analysis ◽  
Covariance Matrix ◽  
Cross Sections ◽  
Uncertainty Propagation ◽  
Laplace Approximation ◽  
Asymptotic Formulas ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
The Impact

We discuss the estimation of the uncertainty and sensitivity parameters for a model response under the assumption that the input variables are normally distributed and block-wise correlated with the covariance matrix, which is small in some norm. These conditions may arise when considering the impact of the group-wise neutron cross-sections' uncertainties on the uncertainty of some reactor parameters such as the neutron multiplication factor. The variance-based global sensitivity analysis, considered in our work, involves the calculation of multidimensional integrals. When the input uncertainties are small, the values of these integrals can be estimated using an asymptotic analysis method called the Laplace approximation. The asymptotic formulas for the output variance and for the global sensitivity indices have been obtained using the Laplace approximation method. It is demonstrated that the asymptotic formula for uncertainty propagation matches the uncertainty propagation formula being used in the local sensitivity analysis. The applicability of the obtained asymptotic approximations was successfully demonstrated on a test problem with realistic cross-section and covariance matrix values.

Sensitivity Analysis of Nuclide Importance to One-Group Neutron Cross Sections

2001 ◽  
Vol 138 (3) ◽  
pp. 279-294
Author(s):  
Hiroshi Sekimoto ◽  
Atsushi Nemoto ◽  
Yoshikane Yoshimura
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Neutron Cross Sections

A New Method to Evaluate the Correlation Coefficients Between Nuclides in Uncertainty and Sensitivity Analysis

2017 ◽  
Author(s):  
Xu Jia Yi ◽  
Ma Xu Bo ◽  
Shen Jing Wen ◽  
Liu Jia Yi ◽  
Chen Yi Xue
Keyword(s):  
Sensitivity Analysis ◽  
Correlation Coefficient ◽  
Cross Section ◽  
Cross Sections ◽  
Correlation Coefficients ◽  
Atomic Density ◽  
Pressurized Water Reactor ◽  
Pressurized Water ◽  
Uncertainty And Sensitivity Analysis ◽  
Cross Section Uncertainty

Uncertainty and sensitivity analysis is an essential component of nuclear engineering calculations. Uncertainties in the cross-section input data directly affect uncertainties in the results. The covariance values between different types of cross-sections are considered in the NJOY covariance library. However, the correlation coefficient between isotopes can depend on the specific problem. The correlation coefficient between 235U and 238U in a pressurized water reactor (PWR) might be different from that in a fast reactor. In this study, a new Monte Carlo-based method is proposed for calculating this effect. The correlation coefficients between different isotopes are calculated using a problem-dependent fraction parameter. The correlation coefficients between the capture cross-sections of 235U, 238U, 239Pu, and 241Pu are calculated. The same method can be extended to other reaction types. The correlation coefficients as a function of the isotopic atomic density uncertainty and the average one-group microscopic cross-section uncertainty are also studied. It is shown that the correlation coefficients vary very little with the uncertainty in the average one-group microscopic cross-section. The correlation coefficient of an isotope pair changes slightly over the course of a cycle because of atomic density and microscopic cross-section changes.

scholarly journals Undergraduate Measurements of Neutron Cross Sections

2015 ◽  
Vol 66 ◽  
pp. 641-648 ◽  
Author(s):  
S.F. Hicks ◽  
J.R. Vanhoy ◽  
A.J. French ◽  
Z.C. Santonil ◽  
B.P. Crider ◽  
...  
Keyword(s):  
Cross Sections ◽  
Neutron Cross Sections
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