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Journal Articles

Deterministic sampling method using simplex ensemble and scaling method for efficient and robust uncertainty quantification

Endo, Tomohiro*; Maruyama, Shuhei; Yamamoto, Akio*

Journal of Nuclear Science and Technology, 61(3), p.363 - 374, 2024/03

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.

Journal Articles

Uncertainty reduction of sodium void reactivity using data from a sodium shielding experiment

Maruyama, Shuhei; Endo, Tomohiro*; Yamamoto, Akio*

Journal of Nuclear Science and Technology, 61(1), p.31 - 43, 2024/01

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.

Journal Articles

Convergence behavior of statistical uncertainty in probability table for cross section in unresolved resonance region

Tada, Kenichi; Endo, Tomohiro*

Journal of Nuclear Science and Technology, 60(11), p.1397 - 1405, 2023/11

 Times Cited Count:0 Percentile:75.85(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.

Journal Articles

An Estimation method for an unknown covariance in cross-section adjustment based on unbiased and consistent estimator

Maruyama, Shuhei; Endo, Tomohiro*; Yamamoto, Akio*

Journal of Nuclear Science and Technology, 60(11), p.1372 - 1385, 2023/11

Journal Articles

Impact of nuclear data revised from JENDL-4.0 to JENDL-5 on PWR spent fuel nuclide composition

Watanabe, Tomoaki; Tada, Kenichi; Endo, Tomohiro*; Yamamoto, Akio*

Journal of Nuclear Science and Technology, 60(11), p.1386 - 1396, 2023/11

 Times Cited Count:0 Percentile:96.85(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$$_{2}$$O affected the nuclide compositions of PWR spent fuels.

Journal Articles

Comparison of neutronic characteristics of BWR burnup fuel between JENDL-4.0 and JENDL-5

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$$_{inf}$$ 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$$_{inf}$$. Above 20 GWd/t, the difference in k$$_{inf}$$ 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$$_{inf}$$ by performing burnup calculations with replacing nuclear data of individual nuclides from JENDL-4.0 to JENDL-5.

Journal Articles

Development of ACE file perturbation tool using FRENDY

Tada, Kenichi; Kondo, Ryoichi; Endo, Tomohiro*; Yamamoto, Akio*

Journal of Nuclear Science and Technology, 60(6), p.624 - 631, 2023/06

 Times Cited Count:1 Percentile:56.43(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.

Journal Articles

Statistical uncertainty quantification of probability tables for unresolved resonance cross sections

Tada, Kenichi; Endo, Tomohiro*

EPJ Web of Conferences, 284, p.14013_1 - 14013_4, 2023/05

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.

Journal Articles

Applicability evaluation of Akaike's Bayesian information criterion to covariance modeling in the cross-section adjustment method

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.

Journal Articles

Development of a robust nuclear data adjustment method to outliers

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.

Journal Articles

Development of nuclear data processing code FRENDY version 2

Tada, Kenichi; Yamamoto, Akio*; Kunieda, Satoshi; Konno, Chikara; Kondo, Ryoichi; Endo, Tomohiro*; Chiba, Go*; Ono, Michitaka*; Tojo, Masayuki*

Journal of Nuclear Science and Technology, 10 Pages, 2023/00

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.

Journal Articles

Impact of uncertainty reduction on lead-bismuth coolant in accelerator-driven system using sample reactivity experiments

Katano, Ryota; Oizumi, Akito; Fukushima, Masahiro; Pyeon, C. H.*; Yamamoto, Akio*; Endo, Tomohiro*

Nuclear Science and Engineering, 20 Pages, 2023/00

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.

Journal Articles

Implementation of resonance upscattering treatment in FRENDY nuclear data processing system

Yamamoto, Akio*; Endo, Tomohiro*; Chiba, Go*; Tada, Kenichi

Nuclear Science and Engineering, 196(11), p.1267 - 1279, 2022/11

 Times Cited Count:0 Percentile:33.72(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.

Journal Articles

Sensitivity coefficient evaluation of an accelerator-driven system using ROM-Lasso method

Katano, Ryota; Yamamoto, Akio*; Endo, Tomohiro*

Nuclear Science and Engineering, 196(10), p.1194 - 1208, 2022/10

 Times Cited Count:0 Percentile:33.72(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.

Journal Articles

Development of nuclear data processing code FRENDY version 2

Tada, Kenichi; Yamamoto, Akio*; Endo, Tomohiro*; Chiba, Go*; Ono, Michitaka*; Tojo, Masayuki*

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) (Internet), 10 Pages, 2022/05

Nuclear data processing is an important interface between an evaluated nuclear data library and nuclear transport calculation codes. JAEA has developed a new nuclear data processing code FRENDY from 2013. FRENDY version 1 generates ACE files which are used for the continuous-energy Monte Carlo codes including PHITS, Serpent, and MCNP; it was released as an open-source software under the 2-clause BSD license in 2019. After FRENDY version 1 was released, many functions are developed: the multi-group neutron cross-section library generation, the statistical uncertainty quantification for the probability tables for unresolved resonance cross-section, the perturbation of the ACE file, and the modification of the ENDF-6 formatted nuclear data file, etc. We released FRENDY version 2 including these functions. This presentation explains the overview of FRENDY and features of the new functions implemented in FRENDY version 2.

Journal Articles

Proposal and application of ROM-Lasso method for sensitivity coefficient evaluation

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.

Journal Articles

Adaptive setting of background cross sections for generation of effective multi-group cross sections in FRENDY nuclear data processing code

Yamamoto, Akio*; Endo, Tomohiro*; Tada, Kenichi

Journal of Nuclear Science and Technology, 58(12), p.1343 - 1350, 2021/12

 Times Cited Count:0 Percentile:16.97(Nuclear Science & Technology)

An adaptive setting method of background cross sections is implemented to FRENDY/MG, which is a multi-group neutron cross section generation code. In the present adaptive setting method, the range of background cross section is initially divided into 10 equal intervals and unnecessary background cross section points, at which self-shielding factors or reaction rates can be accurately interpolated, are eliminated. If the interpolation accuracy in an interval is not sufficient, the interval is successively halved until sufficient interpolation accuracy is obtained. For accurate interpolation of self-shielding factor or reaction rates, the monotone cubic interpolation is used. Verification calculations are carried out for all isotopes in JENDL-4.0 and -4.0u. Calculation results indicate that typical numbers of background cross sections are from 10 to 25 when the monotone cubic interpolation and error tolerance of 0.01 for self-shielding factors are used.

Journal Articles

Multi-group neutron cross section generation capability for FRENDY nuclear data processing code

Yamamoto, Akio*; Tada, Kenichi; Chiba, Go*; Endo, Tomohiro*

Journal of Nuclear Science and Technology, 58(11), p.1165 - 1183, 2021/11

 Times Cited Count:7 Percentile:85.57(Nuclear Science & Technology)

The multi-group cross section generation capability for neutrons is implemented in the FRENDY nuclear data processing code. ACE-formatted files are used as the source of nuclear data instead of ENDF-formatted files since FRENDY already has the capability to generate pointwise cross sections in the ACE format. Verification calculations of the newly implemented capability are carried out through the comparison with the NJOY nuclear data processing code. Cross section generations for all nuclides in JENDL-4.0, -4.0u, -5$$alpha$$4, ENDF/B-VII.1, -VIII.0, JEFF-3.3, and TENDL-2019 are carried out without unexpected processing issue, except for Pu-238 of TENDL-2019 that includes inconsistent data. The verification results indicate that the multi-group cross sections generated by FRENDY are consistent with those generated by NJOY or the calculation results by MCNP.

Journal Articles

Verification of the multi-group generation capability of FRENDY nuclear data processing code for recent nuclear data through comparison of one-group reaction rates

Yamamoto, Akio*; Tada, Kenichi; Chiba, Go*; Endo, Tomohiro*

Transactions of the American Nuclear Society, 124(1), p.544 - 547, 2021/06

Verification calculations for the capability of multi-group cross section generation in FRENDY (FRENDY/MG) are carried out through the comparison of one-group reaction rates using the multi-group cross sections obtained by FRENDY/MG and NJOY2016. Three different neutron spectra (LWR, FR, and 1/E) are used to calculate one-group reaction rates. The discrepancies of one-group reaction rates are small for most cases, showing the validity of FRENDY/MG. The FRENDY/MG will be released as the part of FRENDY nuclear data processing system in the near future.

Journal Articles

Multi-group cross section library generation by FRENDY for fast reactor neutronics calculations

Chiba, Go*; Yamamoto, Akio*; Tada, Kenichi; Endo, Tomohiro*

Transactions of the American Nuclear Society, 124(1), p.556 - 558, 2021/06

The FRENDY nuclear data processing code has been used to generate multi-group cross section libraries for the CBZ reactor physics code system. The newly generated libraries have been applied to neutronics calculations of a fast reactor core MET-1000, and several neutronics parameters are calculated. Calculations with other libraries generated by NJOY2016 have been also conducted, and differences in obtained neutronics parameters between the FRENDY-based library and the NJOY-based library have been quantified. Generally reasonable agreement between them has been obtained, so it has been demonstrated that the multi-group libraries for fast reactor neutronics calculations can be generated successfully by FRENDY. Detailed investigation on the impact of the difference in the processing codes on k-effective has been also carried out with a help of the perturbation theory, and the causes of the differences have been identified.

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