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Maruyama, Shuhei; Yamamoto, Akio*; Endo, Tomohiro*
Annals of Nuclear Energy, 205, p.110591_1 - 110591_13, 2024/09
Times Cited Count：0 Percentile：0.00(Nuclear Science & Technology)Fujita, Tatsuya
Proceedings of Best Estimate Plus Uncertainty International Conference (BEPU 2024) (Internet), 14 Pages, 2024/05
The uncertainty analysis of PWR depletion test problem on the OECD/NEA/NSC LWR-UAM benchmark Phase II based on JENDL-5 was performed as a preliminary investigation. The random sampling was used to quantify the uncertainty of k-infinity and nuclide inventories, the cross section (XS), the fission product yield (FPY), the decay constant, and the decay branch ratio were randomly perturbed, and several times of SERPENT 2.2.1 calculations were performed. XSs in the ACE file were perturbed by the ACE file perturbation tool using FRENDY with the 56-group covariance matrix generated by NJOY2016.72. The perturbation quantity of independent FPY was evaluated using the FPY covariance matrix prepared in JENDL-5, and the perturbed cumulative FPY was reconstructed based on the relationship between the independent and cumulative FPYs. The decay constant was independently perturbed for each nuclide. To perturb the decay branch ratios, the covariance matrix was generated by applying the generalized least square method and randomly perturbed based on this covariance matrix in the same manner as the independent FPY. In general, the influence due to decay data was an order of magnitude smaller than the influences due to XS and FPY uncertainties. For the uncertainty of k-infinity and transuranic nuclide inventories, the influence due to XS uncertainty was dominant, and that due to FPY and decay data uncertainties was one or a few orders of magnitude smaller. On the other hand, for the uncertainty of FP nuclide inventories, the influence due to FPY uncertainty was almost the same or larger than that due to XS uncertainty. It was also confirmed that the influence due to either XS or FPY uncertainty became different for each FP nuclide. In future studies, the influence due to XS uncertainty on FP nuclides will be discussed because it was not prepared in JENDL-5 and not considered in the present paper.
Fujita, Tatsuya
Proceedings of International Conference on Physics of Reactors (PHYSOR 2024) (Internet), p.718 - 727, 2024/04
The convergence process of the k-infinity uncertainty during random-sampling-based uncertainty quantification was compared between several efficient sampling techniques. The k-infinity uncertainty was evaluated by statistically processing several times of SERPENT 2.2.1 calculations using perturbed ACE files based on JENDL-5 cross-section covariance data. The antithetic sampling (AS), the Latin hypercube sampling (LHS), the control variates (CV), and the combination approaches of them were focused on in the present paper. In PWR-UO
fuel assembly geometry without the nuclide depletion, as discussed in past studies, AS and LHS showed higher efficient convergence than nominal sampling without any efficient sampling techniques. In terms of CV, though a stand-alone application did not have a large impact on the k-infinity uncertainty convergence, its performance was improved in combination with AS, as discussed in the past study. In addition, a new combined approach of LHS and CV (CV+LHS) was proposed in the present paper. CV+LHS improved the k-infinity uncertainty convergence and was more efficient than CV+AS. The main reason for this improvement was that the convergence for the mean value of alternative parameters in CV was enhanced by applying LHS. Consequently, this study proposed the new combined approach of CV+LHS and confirmed its efficiency performance for the random-sampling-based uncertainty quantification in the PWR-UO fuel assembly geometry. The applicability of CV+LHS for the nuclide-depletion calculations will be confirmed in future studies.
Katano, Ryota; Yamamoto, Akio*; Endo, Tomohiro*
Nuclear Science and Engineering, 196(10), p.1194 - 1208, 2022/10
Times Cited Count：1 Percentile：18.18(Nuclear Science & Technology)In this study, we propose the ROM-Lasso method that enables efficient evaluation of sensitivity coefficients of neutronics parameters to cross-sections. In the proposed method, a vector of sensitivity coefficients is expanded by subspace bases, so-called Active Subspace (AS) based on the idea of Reduced Order Modeling (ROM). Then, the expansion coefficients are evaluated by the Lasso linear regression between cross-sections and neutronics parameters obtained by the random sampling. The proposed method can be applied in the case where the adjoint method is difficult to be applied since the proposed method uses only forward calculations. In addition, AS is an effective subspace that can expand the vector of sensitivity coefficients with the lower number of dimension. Thus, the number of unknows is reduced from the original number of input parameters and the calculation cost is dramatically improved compared to the Lasso regression without AS. In this paper, we conducted ADS burnup calculations as a verification. We have shown how AS bases are obtained and the applicability of the proposed method.
Katano, Ryota; Yamamoto, Akio*; Endo, Tomohiro*
Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) (Internet), p.2032 - 2041, 2022/05
We have proposed the ROM-Lasso method to perform an efficient evaluation of the sensitivity coefficients of ADS core parameters to cross sections without major modification of the core analysis system. In the ROM-Lasso method, the sensitivity coefficient vector is expanded via the subspace bases so-called Active Subspace (AS), and the effective number of unknowns is reduced. Then, the expansion coefficients are determined via the penalized linear regression with the core parameters obtained by the random sampling, and the sensitivity coefficient vector is estimated. Owing to the AS, the required number of the core calculations is dramatically reduced in the ROM-Lasso method. In this work, we take the sensitivity coefficient evaluation of the coolant void reactivity at the end of the cycle for example and demonstrate how estimation accuracy depends on the number of samples and the AS.
Iwamoto, Hiroki; Meigo, Shinichiro
Journal of Nuclear Science and Technology, 57(3), p.276 - 290, 2020/03
Times Cited Count：2 Percentile：19.64(Nuclear Science & Technology)This paper presents an approach to uncertainty estimation of spallation particle multiplicity of lead (
Pb), primarily focusing on proton-induced spallation neutron multiplicity (
) and its propagation to a neutron energy spectrum. The uncertainty is estimated from experimental proton-induced neutron-production double-differential cross sections (DDXs) and model calculations with the Particle and Heavy Ion Transport code System (PHITS). Uncertainties in multiplicities for 
, 
, and 
reactions are then inferred from the estimated uncertainty and the PHITS calculation. Using these uncertainties, uncertainty in a neutron energy spectrum produced from a thick Pb target bombarded with 500 MeV proton beams, measured in a previous experiment, is quantified by a random sampling technique, and propagation to the neutron energy spectrum is examined. Relatively large uncertainty intervals (UIs) were observed outside the lower limit of the measurement range, which is prominent in the backward directions. Our findings suggest that a reliable assessment of spallation neutron energy spectra requires systematic DDX experiments for detector angles and incident energies below 100 MeV as well as neutron energy spectrum measurements at lower energies below 
1.4 MeV with an accuracy below the quantified UIs.
Katano, Ryota; Endo, Tomohiro*; Yamamoto, Akio*; Tsujimoto, Kazufumi
Journal of Nuclear Science and Technology, 55(10), p.1099 - 1109, 2018/10
Times Cited Count：4 Percentile：34.86(Nuclear Science & Technology)In this study, we propose the penalized regression "adaptive smooth-lasso" for the estimation of sensitivity coefficients of the neutronics parameters. The proposed method estimates the sensitivity coefficients of the neutronics parameters using the variation of the microscopic cross sections and the neutronics parameter obtained by random sampling. The proposed method utilizes only the forward calculations. Thus, the proposed method can be applied for the complex reactor analysis for which the application of the adjoint method is difficult. In this study, we proposed a penalty term considering the characteristics of the sensitivity coefficients of the neutronics parameter to the microscopic multi-group cross sections. Through verification calculation, we show that the proposed method achieves high accuracy with less computational cost compared to the method based on random sampling proposed in the previous studies.
