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Kondo, Ryoichi; Endo, Tomohiro*; Yamamoto, Akio*
Journal of Nuclear Science and Technology, 61(12), p.1536 - 1545, 2024/12
Times Cited Count：0 Percentile：0.00(Nuclear Science & Technology)In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution.
Kondo, Ryoichi; Endo, Tomohiro*; Yamamoto, Akio*
EPJ Web of Conferences, 302, p.04002_1 - 04002_10, 2024/10
In the recent study, we have developed an efficient flux distribution tallying method in the Monte Carlo calculation toward the high-fidelity, large scale multi-physics simulation. In this method, the proper orthogonal decomposition is applied to the flux distribution tallies. While the tallying method was implemented with the collision estimator in the previous study, the track length estimator is implemented in the present study to obtain the tally with lower statistical error. The implementation of the flux distribution tally with the track length estimator is compared with that of the collision estimator and the normal track length estimator in a one-dimensional problem. The numerical results reveal that the distribution tally using the POD with the track length estimator can obtain a more precise solution compared with that with the collision estimator. Therefore, in terms of the statistical error, the relationship between the distribution tally with track length and collision estimator is similar to that between the conventional track length and collision estimators.
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)Tada, Kenichi; Yamamoto, Akio*; Kunieda, Satoshi; Konno, Chikara; Kondo, Ryoichi; Endo, Tomohiro*; Chiba, Go*; Ono, Michitaka*; Tojo, Masayuki*
Journal of Nuclear Science and Technology, 61(6), p.830 - 839, 2024/06
Times Cited Count：3 Percentile：75.12(Nuclear Science & Technology)Nuclear data processing code is important to connect evaluated nuclear data libraries and radiation transport codes. The nuclear data processing code FRENDY version 1 was released in 2019 to generate ACE formatted cross section files with simple input data. After we released FRENDY version 1, many functions were developed, e.g., neutron multi-group cross section generation, explicit consideration of the resonance interference effect among different nuclides in a material, consideration of the resonance upscattering, ACE file perturbation, and modification of ENDF-6 formatted file. FRENDY version 2 was released including these new functions. It generates GENDF and MATXS formatted neutron multi-group cross section files from an ACE formatted cross section file or an evaluated nuclear data file. This paper explains the features of the new functions implemented in FRENDY version 2 and the verification of the neutron multigroup cross section generation function of this code.
Katano, Ryota; Oizumi, Akito; Fukushima, Masahiro; Pyeon, C. H.*; Yamamoto, Akio*; Endo, Tomohiro*
Nuclear Science and Engineering, 198(6), p.1215 - 1234, 2024/06
Times Cited Count：0 Percentile：0.00(Nuclear Science & Technology)In this study, we have demonstrated that data assimilation using lead and bismuth sample reactivities measured in the Kyoto University Critical Assembly A-core can successfully reduce the uncertainty of the coolant void reactivity in accelerator-driven systems derived from inelastic-scattering cross-sections of lead and bismuth. We re-evaluated and highlighted the experimental uncertainties and correlations of the sample reactivities for the data assimilation formula. We used the MCNP6.2 code to evaluate the sample reactivities and their uncertainties, and performed data assimilation using the reactor analysis code system MARBLE. The high-sensitivity coefficients of the sample reactivities to lead and bismuth allowed us to reduce the cross-section-induced uncertainty of the void reactivity of the accelerator-driven system from 6.3% to 4.8%, achieving a provisional target accuracy of 5% in this study. Furthermore, we demonstrated that the uncertainties arising from other dominant factors, such as minor actinides and steel, can be effectively reduced by using integral experimental data sets for the unified cross-section dataset ADJ2017.
Harada, Yoshinari*; Yamaguchi, Hibiki*; Endo, Tomohiro*; Yamamoto, Akio*; Tada, Kenichi
Transactions of the American Nuclear Society, 130(1), p.758 - 762, 2024/06
The data assimilation was performed using deterministic sampling to selectively reduce uncertainties caused by the thermal neutron scattering in light water. The prompt neutron decay constant 
of the water tank system was used for the data assimilation. The deterministic sampling method was applied to uncertainty quantification and data assimilation for light water thermal neutron scattering law data obtained by the CAB model. The uncertainty quantification results using the deterministic sampling method were comparable to those using the random sampling method.
Endo, Tomohiro*; Maruyama, Shuhei; Yamamoto, Akio*
Journal of Nuclear Science and Technology, 61(3), p.363 - 374, 2024/03
Times Cited Count：0 Percentile：0.00(Nuclear Science & Technology)Uncertainty quantification (UQ) of the neutron multiplication factor is important to investigate the appropriate safety margin for a target system. Although the random sampling method is a practical and useful UQ method, a large computational cost is required to reduce the statistical error of the estimated uncertainty. Furthermore, if an input variable follows a normal distribution with a large standard deviation, the perturbed input variable by the random sampling method may become a physically inappropriate or negative value. To address these issues for the efficient and robust UQ, a modified deterministic sampling method using the simplex ensemble and the scaling method is proposed. The features of the proposed method are summarized as follows: The sample size is (r+2), where r corresponds to the effective rank of the covariance matrix between the input variables; depending on a situation of target UQ, the amounts of perturbations for the input parameters can be arbitrarily given by the scaling factor method; the scaling factor can be updated to avoid physically inappropriate in the perturbed input variables. The effectiveness of the proposed method is demonstrated through the UQ of the neutron multiplication factor due to fuel manufacturing uncertainties for a typical PWR pin-cell burnup calculation.
Maruyama, Shuhei; Endo, Tomohiro*; Yamamoto, Akio*
Journal of Nuclear Science and Technology, 61(1), p.31 - 43, 2024/01
Times Cited Count：2 Percentile：59.55(Nuclear Science & Technology)This study investigated the feasibility of reducing the uncertainty associated with fast-reactor-core design by sharing an experimental database between different fields (e.g., reactor physics and radiation shielding) using data assimilation techniques. As the first step in this study, we focused on the ORNL sodium shielding experiment and investigated the possibility of using the experimental data to reduce the uncertainty in sodium void reactivity (SVR), which is the most important safety parameter for sodium-cooled fast reactors. A sensitivity analysis based on the Generalized Perturbation Theory was performed for the sodium shielding experiment. Using the sensitivity coefficients evaluated here and those of the sodium void reactivity previously evaluated by the JAEA, we showed that sodium shielding experimental data can contribute to the uncertainty reduction of SVR by adopting the cross-section adjustment method. Based on this study, the uncertainty reduction effect is expected to be significant, especially for SVR dominated by neutron-leakage phenomena. Although new reactor physics experimental data on SVR may be difficult to obtain, the results of this study suggest that data from sodium shielding experiments can partially substitute for this role. This study demonstrated the value of the mutual use of integral experimental data in fast reactor designs.
Watanabe, Tomoaki; Tada, Kenichi; Endo, Tomohiro*; Yamamoto, Akio*
Journal of Nuclear Science and Technology, 60(11), p.1386 - 1396, 2023/11
Times Cited Count：3 Percentile：75.12(Nuclear Science & Technology)The burnup calculations for estimating the nuclide composition of the spent fuel are highly dependent on nuclear data. Many nuclides in the latest version of the Japanese Evaluated Nuclear Data Library JENDL-5 were modified from JENDL-4.0 and the modification affects the burnup calculations. This study confirmed the validity of JENDL-5 in the burnup calculations. The PIE data of Takahama-3 was used for the validation. The effect of modifications of the parameters, e.g., cross sections and fission yields, from JENDL-4.0 to JENDL-5 on the nuclide compositions was quantitatively investigated. The calculation results showed that JENDL-5 has a similar performance to JENDL-4.0. The calculation results also revealed that the modifications of the cross sections of actinide nuclides, fission yields, and thermal scattering low data of hydrogen in H
O affected the nuclide compositions of PWR spent fuels.
Tada, Kenichi; Endo, Tomohiro*
Journal of Nuclear Science and Technology, 60(11), p.1397 - 1405, 2023/11
Times Cited Count：1 Percentile：35.82(Nuclear Science & Technology)The probability table method is a well-known method for addressing self-shielding effects in the unresolved resonance region. A long computational time is required to generate the probability table. The effective way to reduce the generation time of the probability table is the reduction of the number of ladders. The purpose of this study is the estimation of the optimal number of ladders using the statistical uncertainty in the probability table. To this end, the statistical uncertainty quantification method of the probability table was developed and the convergence behavior of the statistical uncertainty was investigated. The product of the probability table and the average cross section was considered the target of the statistical uncertainty. The convergence rate was affected by the average level spacing and reduced neutron width. The generation time of the probability table was less than half when the input parameter was changed from the number of ladders to the tolerance value.
Maruyama, Shuhei; Endo, Tomohiro*; Yamamoto, Akio*
Journal of Nuclear Science and Technology, 60(11), p.1372 - 1385, 2023/11
Times Cited Count：1 Percentile：35.82(Nuclear Science & Technology)Watanabe, Tomoaki; Tada, Kenichi; Endo, Tomohiro*; Yamamoto, Akio*
Proceedings of 12th International Conference on Nuclear Criticality Safety (ICNC2023) (Internet), 10 Pages, 2023/10
The latest Japanese nuclear data library, JENDL-5, was released in December 2021. In JENDL-5, nuclear reaction cross sections for Gd-155 and Gd-157 were modified in addition to many heavy nuclides such as U-235. Fission yields and decay data, which are essential to characterize burnup fuels, were completely revised. This study investigated the effects of the nuclear data revisions from JENDL-4.0 to JENDL-5 on the neutronic characteristics of burnup fuels to validate JENDL-5. Burnup calculations of the 9x9 STEP-3 BWR fuel assembly based on the OECD/NEA Phase III-C benchmark were performed using JENDL-4.0 and JENDL-5. As a result, the k
for JENDL-5 was smaller than that of JENDL-4.0 throughout the burnup, with a large difference of about 600 pcm at 12 GWd/t, around the peak of the k. Above 20 GWd/t, the difference in k increases with increasing burnup value, reaching nearly 600 pcm at 50 GWd/t. In addition, this study investigates which nuclear data contribute significantly to the difference in k by performing burnup calculations with replacing nuclear data of individual nuclides from JENDL-4.0 to JENDL-5.
Tada, Kenichi; Kondo, Ryoichi; Endo, Tomohiro*; Yamamoto, Akio*
Journal of Nuclear Science and Technology, 60(6), p.624 - 631, 2023/06
Times Cited Count：5 Percentile：69.23(Nuclear Science & Technology)The sensitivity analysis and the uncertainty quantification have an important role in improving the evaluated nuclear data library. The current computational performance enables us to the sensitivity analysis and uncertainty quantification using the continuous energy Monte Carlo calculation code. The ACE file perturbation tool was developed for these calculations using modules of FRENDY. This tool perturbs the microscopic cross section, the number of neutrons per fission, and the fission spectrum. The uncertainty quantification using the random sampling method is also available if the user prepares the covariance matrix. The uncertainty of the k-effective using the perturbation tool was compared to the current sensitivity analysis codes SCALE/TSUNAMI and MCNP/KSEN. The comparison results indicated that the random sampling method using this tool accurately estimates the uncertainty of k-effective.
Tada, Kenichi; Endo, Tomohiro*
EPJ Web of Conferences, 284, p.14013_1 - 14013_4, 2023/05
Times Cited Count：0 Percentile：0.00(Nuclear Science & Technology)The self-shielding effect in the unresolved resonance region has a large impact on the fast- and intermediate-spectrum reactors. The probability table method is widely used for continuous-energy Monte Carlo calculation codes to treat the effect. In this method, a table provides the probability distribution of the cross-section for a nuclide in the given energy grid points. The table is generated by averaging with a lot of "ladders" which represent pseudo resonance structures. Though many nuclear data processing codes require the number of ladders as an input parameter to generate the probability table, an optimal number of ladders has not been investigated. Our previous study revealed that the suitable number of ladders depends on the nuclide and its resonance parameters. This result indicates that it is very difficult for users to find the optimal number of ladders. We developed the calculation method of the statistical uncertainty for the probability table generation.
Maruyama, Shuhei; Endo, Tomohiro*; Yamamoto, Akio*
EPJ Web of Conferences, 281, p.00008_1 - 00008_9, 2023/03
The applicability of Akaike's Bayesian Information Criterion (ABIC) to covariance modeling in the cross-section adjustment method was investigated. One of the most important things for a reliable cross-section adjustment method is giving a suitable covariance matrix. However, since we cannot know the true covariance matrix in advance, we usually estimate and assume it. To judge the goodness of the covariance matrix modeling, a metric is desirable. As a candidate for this metric, we focus on ABIC which is one of the information criteria in Bayesian inference, because the cross-section adjustment method is often discussed within the framework of Bayesian inference. In the conventional cross-section adjustment method, incorporation of the analysis model uncertainty in a covariance matrix still requires ad hoc treatment. In JAEA, the integral experimental database for fast reactors has been developed and the adjusted cross-section set ADJ2017 has been created based on this database. Many of the core characteristics in the database have been analyzed by a deterministic method. Therefore, the predicted core characteristics have non-negligible uncertainties with correlations due to some numerical approximations. However, the evaluations of the uncertainties and their correlations are still challenging issues. In addition, there would be unknown uncertainties that experimenters and analysts of reactor physics experiments could not recognize. To judge the goodness of the covariance matrix related to these uncertainties, the applicability of ABIC to the cross-section adjustment method was investigated.
Fukui, Yuhei*; Endo, Tomohiro*; Yamamoto, Akio*; Maruyama, Shuhei
EPJ Web of Conferences, 281, p.00006_1 - 00006_9, 2023/03
We developed a new nuclear data adjustment method for experimental data containing outliers. This method mitigates the effect of outliers by applying M-estimation, a type of robust estimation, to the conventional nuclear data adjustment method using sensitivity coefficients. Based on the M-estimation, we derived a weighted nuclear data adjustment formula and developed a weight calculation method. The weighted nuclear data adjustment formula was derived by weighting the function to take the extremum of the conventional nuclear data adjustment. The weighting of each nuclear characteristic is calculated from the difference between the measured and calculated values of the nuclear characteristic. This weight calculation method can evaluate the validity of each nuclear characteristic by considering correlations between nuclear characteristics using singular value decomposition. The proposed method and the conventional method were compared and verified by twin experiments. In the twin experiments, the nuclear data were adjusted using experimental data that intentionally included outliers. As a result of twin experiments, it was confirmed that the nuclear data were adjusted robustly and appropriately even with the experimental data containing outliers.
Yamamoto, Akio*; Endo, Tomohiro*; Chiba, Go*; Tada, Kenichi
Nuclear Science and Engineering, 196(11), p.1267 - 1279, 2022/11
Times Cited Count：2 Percentile：35.75(Nuclear Science & Technology)The resonance upscattering effect (the thermal agitation effect) is incorporated in the generation capability of multi-group neutron cross sections of the FRENDY nuclear data processing system. The resonance upscattering effect is considered by (1) the variation of self-shielding factors (effective cross sections) due to the change in ultra-fine group spectrum and (2) the variation of group-to-group elastic scattering cross sections. In the verification calculations, impacts on the ultra-fine group spectrum, effective cross sections, and neutronics characteristics (the Doppler effect) are confirmed. The effect of energy group structure and the treatments of resonance upscattering on the Doppler effect through the variation of effective cross sections and the elastic scattering matrix are studied. The results indicate that the FRENDY can provide appropriate multi-group cross sections considering the resonance upscattering effect.
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.
Asano, Norikazu; Nishimura, Arashi; Takabe, Yugo; Araki, Daisuke; Yanai, Tomohiro; Ebisawa, Hiroyuki; Ogasawara, Yasushi; Oto, Tsutomu; Otsuka, Kaoru; Otsuka, Noriaki; et al.
JAEA-Technology 2021-045, 137 Pages, 2022/06
JAEA-Technology-2021-045.pdf:2.97MB
A collapse event of a cooling tower for secondary cooling system in the Japan Materials Testing Reactor (JMTR) was caused by the strong winds of Typhoon No.15 on September 9, 2019. As measures against the event, the working group for the renewal of the UCL (Utility Cooling Loop) cooling tower was established in the department of JMTR, and the integrity of the UCL cooling tower, which is the same type of wooden cooling tower as the secondary cooling tower in the JMTR, was investigated. As a result of this investigation, we have decided to replace the existing UCL cooling tower with a new cooling system. After investigations, in order to reduce the risk of collapse due to wood decay, the new cooling system was installed as a component of the air system to be managed as a performance maintenance facility after decommissioning. This report describes the design of and the evaluation results of the facility.
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.
