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

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.

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

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.

QUANTIFICATION OF NUCLEAR DATA AND MANUFACTURING UNCERTAINTIES IN VERA

Uncertainty quantification (UQ) was performed using the Consortium for the Advanced Simulation of Light Water Reactors (CASL) multiphysics core simulator VERA. Typically, only nuclear data cross sections are considered when trying to obtain uncertainty information in reactor simulation applications. In this paper, uncertainty in both nuclear cross section data and fuel manufacturing processes is analyzed using VERA. Uncertainties due to cross sections was determined by generating one thousand perturbed cross section libraries using the cross section covariance data provided in the evaluated nuclear data library. Uncertainty due to manufacturing was also determined using stochastic sampling and VERA. The use of similar stochastic sampling techniques for the same problems allows for the direct comparison of uncertainty stemming from the two sources of uncertainty. Sample size is considered due to the potentially large computational cost of stochastic sampling techniques, as is demonstrated in a full core depletion. It was found that for the Pressurized Water Reactor (PWR) pincell case at Hot Zero Power (HZP), the standard deviation in the neutron multiplication factor produced by material uncertainty was 101 pcm, while the standard deviation in the neutron multiplication factor produced by cross section uncertainty was 730 pcm. While the uncertainty in neutron multiplication factor due to cross section uncertainty is larger than uncertainty due to manufacturing uncertainties, neglecting manufacturing uncertainties may be an unacceptable oversight in certain high-precision simulation applications.

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

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.

Impact of Thorium Capture Cross Section Uncertainty on the Thorium Utilized ADS Reactivity Calculation

Recently, the researches on fast neutron spectrum system utilized thorium fuel are widely conducted. However, the recent thorium cross section libraries are limited compared to uranium cross section libraries. The impact of thorium cross section uncertainty on thorium fuel utilized accelerator driven system (ADS) reactivity calculation is estimated in this study. The uncertainty of thekeffcaused by232Th capture cross section of JENDL-4.0 is about 1.3%. The uncertainty of JENDL-4.0 is needed to be enhanced to provide more reliable results on reactivity calculation for the fast system. The impact of uncertainty of 232Th capture cross section of ENDF/B-VII is small (0.1%). Therefore, it will cause no significant impact of the thorium cross section library on the thorium utilized ADS design calculation.