研究者詳細 - 山本　章夫

Collapsed energy group structure for analysis of prismatic high-temperature gas-cooled reactor with uranium fuel

Takeda, S; Kitada, T; Yamamoto, A; Yamaji, K; Koike, H; Asano, K

ANNALS OF NUCLEAR ENERGY 214 巻 2025年5月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

Considering computational costs, it is practical to use collapsed energy group structures with less than several tens of groups of the core analysis of High-Temperature Gas-cooled Reactors (HTGRs). This study evaluates the performance of several existing energy group structures and newly optimized 15-group and 25-group structures for prismatic HTGRs with uranium fuel. Both multi-element and two-dimensional core geometries were used to account for neutron spectrum interference effects caused by the presence of control rods, differences in graphite temperature, and variations in the amount of surrounding graphite. The optimization calculations were performed using Genetic algorithm and Particle swarm optimization. Among the group structures with around 15 groups, the newly optimized 15-group structure showed relatively good agreement with the reference solution. For the group structures with around 25 groups, while the newly optimized 25-group structure showed slightly better performance under certain conditions, the existing 26-group structure consistently demonstrated stable and good performance.

DOI： 10.1016/j.anucene.2025.111238

Treatment of corner crossing ray-traces in CMFD acceleration of MOC

Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2025年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

Treatment of corner crossing ray traces in the coarse-mesh finite-difference (CMFD) acceleration of a method of characteristics (MOC) transport calculation is discussed. The contribution of the corner crossing ray trace at a CMFD mesh is independently tallied as partial current at the corner of the CMFD mesh to reduce computational burden during transport sweeps in MOC. The tallied partial current at the corner is distributed to the partial currents at the sides of CMFD meshes. Some details of implementations in rectangular and triangular CMFD meshes are explained. The present method is implemented to the GENESIS neutron transport code, and its validity is confirmed through the 3 (Formula presented.) 3 square cells and the hexagonal cell geometries. The calculation results indicate that the present method resolves the issue of corner crossing ray trace in the CMFD acceleration of MOC.

DOI： 10.1080/00223131.2025.2490832

Impact of nuclear data updates from JENDL-4.0 to JENDL-5 on burnup calculations of light-water reactor fuels

Watanabe, T; Tada, K; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2025年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

This study investigated the impact of nuclear data updates from JENDL-4.0 (J4) to JENDL-5 (J5) on the light-water reactor fuel burnup calculations. Burnup calculations were conducted with J4 and J5 for pressurized water reactor pin-cell and boiling water reactor (BWR) fuel assembly geometries. The calculation results revealed significant burnup-dependent differences in the neutron multiplication factor (k<inf>inf</inf>). Across the burnup range of 0–50 GWd/t, k<inf>inf</inf> values of J5 were consistently smaller than those of J4 and the difference gradually increased as burnup progressed. Direct sensitivity calculations, in which each nuclide data was replaced from J4 to J5, indicated that updates to the cross-sections of U-235, U-238, and Pu-239 and the thermal scattering law data of H in H<inf>2</inf>O notably impacted the k<inf>inf</inf> differences. For the BWR assembly geometry containing Gd fuels, large k<inf>inf</inf> differences were observed in the burnup range of 10–15 GWd/t. This difference was primarily attributed to updates in the cross-sections of U-235, Gd-155, Gd-157, and thermal scattering law data of H in H<inf>2</inf>O. Furthermore, we investigated how the nuclear data updates affected the k<inf>inf</inf> differences by examining nuclide number densities, the energy-dependent sensitivities, and the neutron spectra.

DOI： 10.1080/00223131.2025.2486798

Development of Multigroup Monte Carlo Neutron Transport Method with Regionwise Even-Parity Discontinuity Factor

Oshima, Y; Endo, T; Yamamoto, A

NUCLEAR SCIENCE AND ENGINEERING 199 巻 ( 4 ) 頁： 586 - 598 2025年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

The multigroup Monte Carlo (MC) neutron transport method with a regionwise even-parity discontinuity factor (REPDF), i.e. the discontinuity factor (DF)–MC method, is developed with the aim to provide a reference solution for deterministic transport calculations with DF. Applying the analogy with optics, neutrons are transmitted or reflected at a region surface during random walks. The probability of transmission or reflection is determined by REPDFs in adjacent regions. The DF is traditionally used in deterministic neutron transport methods to reduce the discretization error due to spatial homogenization and energy condensation. The DF-MC method can treat DF in the framework of the multigroup MC method. In this paper, the weight cancellation technique based on the closest pair of points using the divide-and-conquer algorithm is used because negative weights appear due to the neutron reflection. The REPDF is calculated by the method of characteristics (MOC). The verification calculations are carried out in the pin-by-pin homogenized and assembly homogenized KAIST-2A core geometry. The DF-MC calculation can reproduce the results of the MOC with the REPDF. These results demonstrate the principle of the DF-MC method and extend the application of the DF to the probabilistic neutron transport method.

DOI： 10.1080/00295639.2024.2383102

Reduced order SP3 core calculation based on local/global iterations using proper orthogonal decomposition

Ito, M; Endo, T; Yamamoto, A; Takeishi, T; Kodama, Y; Hyoudou, H

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 62 巻 ( 4 ) 頁： 366 - 378 2025年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

For an efficient heterogeneous neutron transport calculation, this study newly proposes a reduced order core calculation method by applying proper orthogonal decomposition (POD) to the simplified P<inf>3</inf> (SP<inf>3</inf>) calculation with the local/global iterations. The fine mesh SP<inf>3</inf> calculation (local calculation) for each single assembly can be efficiently solved using POD, thanks to the matrix form-based SP<inf>3</inf> equation and the relatively small system of linear equations. By reconstructing the fine mesh distribution of neutron flux and partial neutron currents from the POD bases and the expansion coefficients estimated by the local calculation, the partial current-based coarse mesh finite difference (p-CMFD) calculation is applied to the coarse mesh calculation (global calculation). Using the global calculation results, each local boundary condition can be updated. These local and global calculations are iterated until convergence. Through a two-dimensional UO<inf>2</inf>-MOX whole core calculation with different fuel loading patterns, the proposed method is verified in comparison with the reference result by the conventional fine mesh SP<inf>3</inf> calculation. The calculation results show that the proposed method accurately reconstructs the fine mesh distribution of neutron flux.

DOI： 10.1080/00223131.2024.2436958

Verification of direct coupling code system using FRENDY version 2 and GENESIS for light water reactor lattices

Fujita, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 62 巻 ( 2 ) 頁： 179 - 196 2025年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

This study newly established a direct coupling code system consisting of the nuclear data processing code FRENDY version 2, and the three-dimensional heterogeneous transport code GENESIS (FRENDY-V2/GENESIS) for easy implementation of the random-sampling-based uncertainty quantification considering the implicit effect due to nuclear cross-section (XS) perturbations. The multi-group macroscopic XSs prepared for GENESIS were generated by FRENDY version 2, where the Dancoff factor was calculated by the neutron current method. Then the background XSs were evaluated based on the Carlvik two-term rational approximation. The infinite multiplication factor (k-infinity) and the fission reaction rate distribution in UO<inf>2</inf> and MOX lattice geometries were compared with MVP3 to verify the calculation accuracy of FRENDY-V2/GENESIS. The sensitivity analyses on the discretization conditions such as the ray tracing of the method of characteristics were also carried out. Through several comparisons between FRENDY-V2/GENESIS and MVP3, FRENDY-V2/GENESIS with the SHEM 361-group structure calculates the k-infinity within approximately 50 pcm and the fission reaction rate distribution within approximately 0.1% by the root mean square, respectively. Consequently, the applicability of FRENDY-V2/GENESIS was verified, and FRENDY-V2/GENESIS can be used to discuss the implicit effect due to multi-group XS perturbations.

DOI： 10.1080/00223131.2024.2410918

将来世代のための原子力の平和利用の3Sに関する討議 1

山本章夫

日本原子力学会誌ATOMOΣ 67 巻 ( 4 ) 頁： 218 - 221 2025年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本原子力学会

Safety, Security, Safeguards(3S)の一つである原子力安全(Safety)の概念について，(1)原子力安全の目的，(2)安全目標，(3)深層防護，(4)安全設計・安全評価，(5)「欠け」と想定外事象対応を解説する。また，Safety, Security, Safeguardsはお互いに関連するため，Safetyの観点から相補的あるいは相反的な点について留意事項を説明する。本稿は2024年日本原子力学会秋の大会における核不拡散・保障措置・核セキュリティ連絡会と学生連絡会との合同企画セッションの内容がベースになっており，この分野にあまりなじみのない「将来世代」の読者を想定している。

DOI： 10.3327/jaesjb.67.4_218

Fundamental properties and characteristics of flux distribution tallies using proper orthogonal decomposition

Kondo R., Yamamoto A., Endo T.

EPJ Nuclear Sciences and Technologies 11 巻 2025年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：EPJ Nuclear Sciences and Technologies

The flux distribution tallies using the proper orthogonal decomposition (POD) called the POD tallies have been developed in our previous study. The POD tallies can achieve dimensionality and statistical uncertainty reduction for a finely discretized flux distribution. Some characteristics of the POD tallies, which are left by our previous work, are revealed in the present study. Firstly, the POD tallies with the track length estimator are newly implemented. Since the statistical uncertainty of the POD tallies is reduced compared with the cell tallies, the POD tallies with the track length estimator can obtain the most precise result among the present implantations. Secondly, the basis vectors obtained by the deterministic and the stochastic methods are compared. The statistical uncertainty of the snapshot data invokes the degradation of the extracted basis vectors. This result indicates that the deterministic method might be more efficient for the snapshot calculation. Finally, the impact of the covariances of expansion coefficients on the statistical uncertainty of expanded flux distribution is investigated. The reconstructed statistical uncertainty considering only the variances of the expansion coefficients differs from the reference. This result reveals that the covariances of the expansion coefficients are important to estimate the statistical uncertainty of the local flux in the flux distribution.

DOI： 10.1051/epjn/2025019

A deterministic transport calculation method of α-eigenvalue for non-multiplying system using framework of k-eigenvalue calculation

Yamamoto A., Tsujita K., Endo T.

Journal of Nuclear Science and Technology 2025年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

A new α-eigenvalue calculation method for a non-multiplying system using the framework of conventional k-eigenvalue calculation of a deterministic transport code is proposed. The time-derivative or the time-absorption term in α-eigenvalue calculation is moved to the right-hand side of the transport equation and is considered as a virtual fission source. The present method is applied to a simple three-dimensional problem with the one-group cross-section and a small water tank system with the 252-group cross-section. The calculation results indicate that the present method provides accurate α-eigenvalue with rapid convergence and no numerical instability.

DOI： 10.1080/00223131.2025.2507866

Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations

Kondo, R; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 61 巻 ( 12 ) 頁： 1536 - 1545 2024年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and 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.

DOI： 10.1080/00223131.2024.2365445

Limited linear source approximation with edge detection for convergence stability of method of characteristics

Yamamoto, A; Endo, T; Chiba, G

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 61 巻 ( 11 ) 頁： 1405 - 1414 2024年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

A new implementation of the limited linear source approximation (LLSA) is proposed. The LLSA was previously proposed to eliminate local negative source in flux regions to mitigate numerical instability of the method of characteristics (MOC) with linear source approximation (LSA). In the present LLSA implementation, the convex edges of flux regions are used to check the local negative source to decrease the computational load. The present method is implemented in the transport code GENESIS, and its effectiveness is verified through the two dimensional C5G7 benchmark problem and the simplified two-dimensional high-temperature engineering test reactor core. The calculation results indicate that the present LLSA implementation efficiently mitigates the numerical instability of MOC with LSA. Additional computational time is less than 1% of total computation time.

DOI： 10.1080/00223131.2024.2341776

Implementation of track length estimator for flux distribution tallies using proper orthogonal decomposition in one-dimensional geometry Open Access

Kondo R., Endo T., Yamamoto A.

EPJ Web of Conferences 302 巻 2024年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：EPJ Web of Conferences

In a 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 proper orthogonal decomposition 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 estimators is similar to that between the conventional track length and collision estimators.

DOI： 10.1051/epjconf/202430204002

Resonance Treatment of Double-Heterogeneous Fuel Using a Deterministic Statistical Geometry Method in Heterogeneous Transport Calculation Code GALAXY-Z

Yamaji, K; Koike, H; Asano, K; Takeda, S; Yamamoto, A

NUCLEAR SCIENCE AND ENGINEERING 2024年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

A resonance calculation using a deterministic statistical geometry (DSTG) method has been developed to efficiently treat the double heterogeneity of coated fuel particles loaded in a high-temperature gas-cooled reactor. Using the DSTG method, neutron flux spatial distribution can be calculated in a heterogeneous geometry containing the randomly dispersed fuel particles and surrounding graphite matrix, which is consistent with statistical geometry in a Monte Carlo method. We applied the DSTG method to resonance calculations based on the equivalence theory and the ultra-fine-group energy treatment in the heterogeneous transport calculation code GALAXY-Z developed by Mitsubishi Heavy Industries, Ltd. In the GALAXY-Z code, DSTG can directly treat the heterogeneity of dispersed fuel particles in fuel compacts. The ultra-fine-group fixed-source DSTG calculation is applied to a high-energy range beyond 30 eV in which upscattering can be ignored. The fixed-source DSTG calculation is applied to a Dancoff-factor calculation for the equivalence theory in a low-energy range of less than 30 eV. In the low-energy range, the SHEM 361-group structure is applied, and the energy grids are detailed enough to allow a continuous treatment of the neutron spectrum. In other words, the upscattering effects and the resonance self-shielding effects are automatically considered in the multigroup transport calculation. The homogenized and collapsed multigroup cross sections of fuel particles are provided to lattice calculations of fuel elements. The comparison of reaction rates (effective cross sections) between GALAXY-Z and the continuous-energy Monte Carlo code MVP is carried out for fuel particles within a fuel element of the high-temperature engineering test reactor. The numerical results indicate that the present method well reproduces the fuel particle’s effective cross sections, k-infinity, and fission rate distribution calculated by MVP.

DOI： 10.1080/00295639.2024.2397259

Quantifying uncertainty induced by scattering angle distribution using maximum entropy method

Maruyama, S; Yamamoto, A; Endo, T

ANNALS OF NUCLEAR ENERGY 205 巻 2024年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

This study developed a new method for evaluating the uncertainty in reactor core/shielding characteristics attributable to the scattering angle distribution in the combined method of the continuous energy Monte Carlo (CEMC) transport calculations and the random sampling (RS) technique based on nuclear data covariances. Recent advances in computer performance have made it possible to evaluate the nuclear data-induced uncertainty with high accuracy using the Monte Carlo method. The total Monte Carlo (TMC) method is a typical uncertainty quantification method that relies entirely on the Monte Carlo method. Another representative Monte Carlo-based uncertainty quantification method is the combination method of the RS technique based on nuclear data covariances and CEMC transport calculations (CEMC-RS). CEMC-RS has the advantage that the uncertainty can be quantified even if one is not familiar with nuclear data measurement and evaluation, as long as the nuclear data covariances are available. However, no method has been established to quantify the uncertainty in CEMC-RS, despite the fact that the uncertainty due to the scattering angle distribution is non-negligible in fast reactor core analysis and shielding analysis. This study introduces a new approach for uncertainty quantification related to scattering angle distribution in CEMC-RS, utilizing the maximum entropy method. The effectiveness of this method was verified through comparison with results from the classical deterministic uncertainty quantification approach based on generalized perturbation theory. Overall, this method offers a more accurate tool for nuclear engineers and researchers in evaluating and managing uncertainties in reactor design and safety analysis.

DOI： 10.1016/j.anucene.2024.110591

Simplified Treatment of Coating Layers in TRISO Fuel in Statistical Geometry Method in Monte Carlo Calculation

Yamamoto, A; Endo, T; Takeda, S; Yamaji, K; Koike, H; Asano, K

NUCLEAR SCIENCE AND ENGINEERING 2024年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

An improved sampling method for flight distance is proposed for Monte Carlo analysis of TRISO fuel particles using the statistical geometry (STG) method. The statistically uniform distribution of fuel particles, which is usually assumed as a default sampling method of flight distance of a neutron between fuel particles, shows considerable bias on k-infinity when coating layers of a TRISO fuel particle are homogenized with a graphite matrix. The proposed new sampling method almost resolves the difference between the no-coating-layer model (coating layers are homogenized with a graphite matrix) and the explicit-coating-layer model (explicitly considers coating layers, reference). By adopting the present method, the no-coating-layer model can be used without significant loss of accuracy in the STG method of a Monte Carlo analysis. The computation time with a continuous energy Monte Carlo code for a typical fuel compact cell of a high-temperature gas-cooled reactor is reduced to one-seventh of the explicit-coating-layer model when the no-coating-layer model is used.

DOI： 10.1080/00295639.2024.2384236

Uncertainty reduction of sodium void reactivity using data from a sodium shielding experiment (vol 61, pg 31, 2024)

Maruyama, S; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2024年7月

Development of nuclear data processing code FRENDY version 2

Tada, K; Yamamoto, A; Kunieda, S; Konno, C; Kondo, R; Endo, T; Chiba, G; Ono, M; Tojo, M

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 61 巻 ( 6 ) 頁： 830 - 839 2024年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

Nuclear data processing 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, adaptive setting of the background cross sections, consideration of the resonance upscattering, ACE file perturbation, statistical uncertainty quantification of probability table, 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.

DOI： 10.1080/00223131.2023.2278600

Impact of Uncertainty Reduction on Lead-Bismuth Coolant in Accelerator-Driven System Using Sample Reactivity Experiments

Katano, R; Oizumi, A; Fukushima, M; Pyeon, CH; Yamamoto, A; Endo, T

NUCLEAR SCIENCE AND ENGINEERING 198 巻 ( 6 ) 頁： 1215 - 1234 2024年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

In this study, we have demonstrated that data assimilation (DA) 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 (ADSs) derived from inelastic scattering cross sections of lead and bismuth. We reevaluated and highlighted the experimental uncertainties and correlations of the sample reactivities for the DA formula. We used the MCNP6.2 code to evaluate the sample reactivities and their uncertainties and performed DA 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 ADS 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.

DOI： 10.1080/00295639.2023.2246779

Deterministic Transport Calculation Method for Statistical Geometry with Small Fuel Particles

Yamamoto, A; Endo, T; Takeda, S; Koike, H; Yamaji, K; Asano, K

NUCLEAR SCIENCE AND ENGINEERING 198 巻 ( 5 ) 頁： 981 - 992 2024年5月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

A deterministic transport calculation method is proposed for the treatment of dispersed fuel particles in a fuel compact/fuel pebble of a typical high-temperature gas-cooled reactor fuel. The random distribution of fuel particles was considered using the statistical geometry (STG) method, which is widely used in the Monte Carlo method. A long-ray trace, which represents a neutron flight path, was considered, and the segment lengths and material distributions on the ray trace were randomly sampled using STG. Then a conventional transport sweep, as used in the method of characteristics, was performed along the ray trace. The proposed deterministic statistical geometry (DSTG) method can calculate the flux spatial distribution in a heterogeneous geometry containing randomly dispersed fuel particles and the surrounding graphite matrix, which is consistent with the STG in a Monte Carlo method. The validity of the DSTG method was confirmed through sensitivity calculations and comparisons with a multigroup Monte Carlo method that utilizes STG. The proposed method can be used for the homogenization of heterogeneous structures inside a fuel compact or fuel pebble as an alternative to conventional deterministic unit cell calculations that consider fuel particles and the surrounding matrix in high-temperature gas-cooled reactor fuels.

DOI： 10.1080/00295639.2023.2230414

Application of neutron current method for Dancoff factor estimation of fuel particles in double-heterogeneous fuel

Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 61 巻 ( 3 ) 頁： 354 - 362 2024年3月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

An evaluation method of Dancoff factors of fuel particles in a typical fuel element of a high-temperature gas-cooled reactor (HTGR) is proposed based on the neutron current method that is widely used for lattice physics calculations of light water reactors. The first level of heterogeneity, i.e. dispersed fuel particles in graphite matrix, is treated by the deterministic statistical geometry (DSTG) method. The homogenized cross-sections of dispersed fuel particles are provided to the second level of heterogeneity, i.e. fuel compacts in a fuel element or a fuel pebble. The validity of the present method is confirmed through the comparison with the reference Dancoff factor obtained by the Monte Carlo and the neutron current methods, which explicitly treats the double heterogeneity. The comparison is carried out for a fuel element simulating the High Temperature Engineering Test Reactor (HTTR), which adopts a typical prismatic fuel element. The numerical results indicate that the present method well reproduces the reference Dancoff factor under various packing fractions. Since the present method can handle flexible geometry and its computation time is short, the present method will be a candidate for the Dancoff factor evaluation method in design calculations of HTGR.

DOI： 10.1080/00223131.2023.2231462

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

Endo, T; Maruyama, S; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 61 巻 ( 3 ) 頁： 363 - 374 2024年3月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and 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 (Formula presented.), where (Formula presented.) 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.

DOI： 10.1080/00223131.2023.2231931

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

Maruyama, S; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 61 巻 ( 1 ) 頁： 31 - 43 2024年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and 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.

DOI： 10.1080/00223131.2023.2244512

標準委員会2023年秋の大会企画セッション「安全な長期運転に向けた標準化活動」の報告

村上健太, 鬼沢邦雄, 山本章夫

日本原子力学会誌ATOMOΣ 66 巻 ( 4 ) 頁： 199 - 202 2024年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本原子力学会

原子力学会標準委員会は，高経年化対策実施基準の改定を通して長期運転にかかる活動をリードしてきたが，最近の法・規制の変更を踏まえて，引き続き重要な貢献をする必要があると考えている。本稿は，2023年秋の大会で実施された企画セッションにおける議論を再構成し，安全な長期運転に向けた取り組みとその標準化における留意点を解説したものである。重要な点として，(1)時間の経過に伴って見いだされる知識を有効に活用すること，(2)オブソレッセンスを含む安全への影響が大きな新知見を見逃さないこと，(3)安全への影響と発現可能性の大きさを踏まえて対応に重要度をつけること，(4)国際的な知識基盤構築へ貢献すること，などが挙げられる。

DOI： 10.3327/jaesjb.66.4_199

Verification of Neutronics Analysis Method using CBZ and GENESIS for a Prismatic High-Temperature Gas-Cooled Reactor

Yamamoto A., Chiba G.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 1572 - 1580 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

A neutronics calculation method for prismatic-type high-temperature gas-cooled reactors is developed using a general neutronics analysis code CBZ and a 2D/3D multi-group neutron transport code GENESIS.Fuel element and a simplified two-dimensional core of the high-temperature engineering test reactor (HTTR) is considered as the benchmark problems and the calculation results of CBZ and GENESIS are compared with those obtained by the continuous energy Monte Carlo code MVP.K-effective, fuel element/fuel compact-wise power distributions are compared.The results of the comparison indicate that CBZ and GENESIS accurately reproduce the reference results obtained by MVP.

DOI： 10.13182/PHYSOR24-43456

Statistical Error Estimation of Autocorrelation Method using Circular Block Bootstrap Method

Hirota R., Endo T., Yamamoto A., Watanabe K., Kaneko J.H.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 78 - 86 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

The autocorrelation method is a subcriticality measurement technique based on the reactor noise analysis method. In this method, the prompt neutron decay constant can be obtained from the exponential decay of the autocorrelation of successively detected neutron counts in a target subcritical system. To simply estimate the statistical error of the prompt neutron decay several measurements of the reactor noise are required, although the total measurement time is inevitably long constant, for typical systems where the reactor noise analysis method is applied. Therefore, the purpose of this study is to investigate the applicability of the circular block bootstrap method in order to estimate the statistical error of the prompt neutron decay constant obtained by the autocorrelation method using a single reactor noise measurement. The bootstrap-based statistical error estimation method is validated using the time series data of reactor noise measurements at UTR-KINKI in a shutdown state with the inherent neutron source in the uranium-aluminum fuel. Consequently, this study demonstrates that the circular block bootstrap method can be also utilized for the autocorrelation method, to estimate the confidence interval of the prompt neutron decay constant as the statistical error. Namely, a single reactor noise measurement can be effectively reused for error estimation instead of multiple measurements.

DOI： 10.13182/PHYSOR24-43468

Simplified Treatment of Coating Layers in TRISO Fuel in Statistical Geometry Method in Monte Carlo Calculation

Yamamoto A., Endo T., Takeda S., Yamaji K., Koike H., Asano K.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 1036 - 1047 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

An improved sampling method for flight distance is proposed for Monte Carlo analysis of TRISO fuel particles using the statistical geometry method.The statistically uniform distribution of fuel particles, which is usually assumed as a default sampling method of flight distance of a neutron in graphite matrix, shows considerable bias on neutronics property when coating layers of a TRISO fuel particle are homogenized with graphite matrix.The proposed new sampling method almost resolves the difference between the homogenized coating model and the reference model that explicitly considers coating layers.By adopting the present method, the homogenized coating model can be used without significant loss of accuracy in the statistical geometry method.Computation time for a typical HTTR fuel compact cell with a continuous energy Monte Carlo code is reduced to 1/7 when the homogenized coating model is used.

DOI： 10.13182/PHYSOR24-43318

Resonance Treatment of Double-Heterogeneous Fuel using a Deterministic Statistical Geometry Method in Heterogeneous Transport Calculation Code GALAXY-Z

Yamaji K., Koike H., Asano K., Takeda S., Yamamoto A.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 1025 - 1035 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

A resonance calculation using a deterministic statistical geometry (DSTG) method has been developed to efficiently treat double heterogeneity of coated fuel particles loaded in a high temperature gas-cooled reactor (HTGR). By the DSTG method, neutron flux spatial distribution can be calculated in a heterogeneous geometry containing randomly dispersed fuel particles and surrounding graphite matrix, which is consistent with STG in a Monte Carlo method. We applied the DSTG method to resonance calculations based on the equivalence theory and the ultra-fine-group energy treatment in the heterogeneous transport calculation code GALAXY-Z developed by Mitsubishi Heavy Industries, Ltd. (MHI). In the GALAXY-Z code, DSTG can directly treat heterogeneity of dispersed fuel particles in fuel compacts. The ultra-fine-group fixed-source DSTG calculation is applied to high-energy range beyond 30eV, in which up-scattering can be ignored. The fixed-source DSTG calculation is applied to Dancoff factor calculation for the equivalence theory in low-energy range less than 30eV. In the low-energy range, the SHEM 361-group structure is applied, and the energy grids are detailed enough to allow a continuous treatment of the neutron spectrum. In other word, the up-scattering effects and the resonance self-shielding effects are automatically considered in multi-group transport calculation. The homogenized and collapsed multi-group cross-sections of fuel particles are provided to lattice calculations of fuel elements. The comparison of reaction rates (effective cross-sections) between GALAXY-Z and the continuous-energy Monte Carlo code MVP is carried out for fuel particles within a fuel element of the High Temperature Engineering Test Reactor (HTTR). The numerical results indicated that the present method well reproduces fuel particle's reaction rates (effective cross-sections) calculated by MVP.

DOI： 10.13182/PHYSOR24-43462

Reconstruction of In-core Power Distribution Based on POD Using Ex-core Detector Signals

Urase Y., Endo T., Yamamoto A.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 1642 - 1651 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

A reconstruction method of in-core power distribution using the proper orthogonal decomposition (POD) and the signal from ex-core detectors is developed.In the present method, the neutron flux distribution is expanded in a small number of POD bases and expansion coefficients.Neutron transport calculations were performed with several calculation conditions to perturb the neutron flux distributions in the reactor core and the POD bases were obtained using the multiple neutron flux distributions as the snapshot data.The neutron counts of ex-core detectors were evaluated from in-core neutron flux distributions and the detector response coefficients.Considering the neutron the counts of ex-core detectors as measured signals, the expansion coefficients of POD that represent the in-core neutron flux distributions were determined.Assuming a simple two-dimensional core with nine regions, the reconstruction accuracy of in-core neutron flux distribution was verified for several conditions.The results indicate that the in-core neutron flux distributions can be reconstructed by the ex-core detector signals when the distance between the detectors and the core is appropriately chosen.

DOI： 10.13182/PHYSOR24-43478

Real-Time 3D Fine Spatial Mesh Kinetics Simulator using POD for Coupled Core

Ito K., Tsujita K., Endo T., Yamamoto A.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 1622 - 1631 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

Toward the development of the digital triplets to effectively educate the reactor physics experiment, the present study develops a real-time 3D fine spatial mesh kinetics simulator based on the proper orthogonal decomposition (POD).Our developed simulator, called Ikaros3D, was specifically designed for a coupled core to promote students' better understanding of the complicated behavior of the spatial variation of the dynamic reactivity depending on the neutron detector position.Through a verification test, we confirmed that the reduced order model (ROM) using POD was able to accurately and quickly simulate the variation in the total core power due to the operation of two different control rods, thanks to the pre-tabulated compressed coefficient matrices for the POD-based kinetics calculation.

DOI： 10.13182/PHYSOR24-43834

Preliminary Study on Two-Dimensional SP3 Calculation Based on POD-Local/Global Iterations

Ito M., Yamamoto A., Endo T., Takeishi T., Kodama Y., Nagano H.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 1612 - 1621 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

As a preliminary study for an efficient heterogeneous neutron transport calculation, this study newly proposes a reduced order core calculation method by applying proper orthogonal decomposition (POD) to the SP3 calculation with the global/local iterations.The fine mesh SP3 calculation (local calculation) for each single assembly can be efficiently solved using POD, thanks to the matrix form-based SP3 equation and the relatively small scale of the simultaneous equations.By reconstructing the fine mesh distribution of neutron flux and partial neutron currents from the POD bases and the expansion coefficients estimated by the local calculation, the p-CMFD calculation is applied to the coarse mesh calculation (global calculation).These local and global calculations are iterated until convergence.Through the two-dimensional small and large UO2-MOX core calculations, our proposed method is verified by comparing with the reference result by the conventional fine mesh SP3 calculation.

DOI： 10.13182/PHYSOR24-43629

Loading Pattern Optimization for LWRs using Monte Carlo Tree Search

Kasama R., Yamamoto A., Endo T.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 2490 - 2499 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

Inspired by recent breakthroughs in AI for games, we transform the fuel loading pattern optimization problem into a game tree search problem and adopt Monte Carlo Tree Search (MCTS) to solve it. The performance of MCTS is compared with the conventional optimization methods, such as the random search and simulated annealing (SA), for the loading pattern optimization of a typical pressurized water reactor. The results demonstrate the superior efficiency of MCTS over the conventional methods. MCTS consistently produces high-quality patterns and effectively avoids the common problem of falling into local minima. By using techniques rooted in AI, we are opening up a new way of solving complex problems in nuclear engineering, offering the prospect of more reliable and efficient core designs. This innovative approach will not only benefit the nuclear field, but also serve as a bridge between optimization and artificial intelligence.

DOI： 10.13182/PHYSOR24-43466

Investigation of Subcriticality Monitoring Method using Improved Simplest Reactivity Estimator with Bilateral Filter

Moribe T., Endo T., Yamamoto A., Kaneko J.H.

Proceedings of the International Conference on Physics of Reactors Physor 2024 頁： 97 - 106 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors Physor 2024

In the retrieval of fuel debris from the Fukushima Daiichi nuclear power plant, there are the following issues: lack of information needed to inversely estimate the subcriticality; and the limitation of neutron detector size. In order to address these issues, we propose a reactivity estimation method that combines the improved simplest reactivity estimator (SRE) and the least squares inverse kinetics method. This study aims to estimate the reactivity in dollar units in a data-driven manner only from the measured neutron count rate without point kinetics parameters. Furthermore, the usefulness of the bilateral filter in combination with the median for the count rate is also investigated to mitigate statistical errors in the reactivity estimation results due to the statistical fluctuation and outlier in the measured count rate data. To verify our proposed method, point kinetics calculation is performed to simulate the time series data of the neutron count rate during a stepwise transient from a deep subcritical state to the shallower state. Here, the magnitude of the count rate at the initial state is parametrically varied to investigate the effect of the statistical count rate fluctuation on the estimated reactivity. As a result, it is observed that the estimated reactivity tends to be overestimated (i.e., closer to critical) as lower count rate data are used in our proposed method. Thus, our proposed method is considered practical from the perspective of criticality control. Moreover, it is clarified that the combinational use of the bilateral filter and the median can effectively reduce the error of the estimated reactivity due to the statistical of the count rate. Consequently, this feasibility study demonstrates our proposed method for monitoring the fluctuation reactivity change even under the low neutron count rate condition.

DOI： 10.13182/PHYSOR24-43487

THERMAL CUT-OFF ENERGY FOR ACCURATE ANALYSIS OF PRISMATIC HIGH-TEMPERATURE GAS-COOLED REACTOR

Takeda S., Kitada T., Yamamoto A., Yamaji K., Koike H., Asano K.

Proceedings of 2024 31st International Conference on Nuclear Engineering ICONE 2024 2 巻 2024年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of 2024 31st International Conference on Nuclear Engineering ICONE 2024

In this study, the appropriate thermal cut-off energy for neutron transport calculations in High-Temperature Gas-cooled Reactor (HTGR) is investigated. The research employs the Monte Carlo calculation code MVP3.0 to evaluate the impact of changing thermal cut-off energy on the multiplication factor in the single fuel element geometries, focusing on variations in fuel and moderator temperatures at both the Beginning Of Life (BOL) and End Of Life (EOL). Up-scattering effect mainly caused by graphite used in HTGR as moderator has strong relation to the thermal cut-off energy. The findings show that when the thermal cut-off energy is set at 20 eV, the multiplication factor tends to be underestimated, especially at high fuel temperature. Furthermore, the study confirms that when the thermal cut-off energy is at or above 30 eV, the variations in multiplication factors remain within approximately ±50 pcm.

DOI： 10.1115/ICONE31-130801

Study on Fusion Safety Concept Based on Nuclear Safety (2) Defense in Depth in Fusion Safety

Yamahista Y., Endo T., Yamamoto A., Ino T.

Transactions of the American Nuclear Society 131 巻 ( 1 ) 頁： 299 - 302 2024年

Study on Fusion Safety Concept Based on Nuclear Safety (1) Fusion Safety Objective and Principles

Yamahista Y., Endo T., Yamamoto A., Ino T.

Transactions of the American Nuclear Society 131 巻 ( 1 ) 頁： 292 - 295 2024年

Loading Pattern Optimization with Deep Learning and Monte-Carlo Tree Search

Kasama R., Yamamoto A., Endo T.

Transactions of the American Nuclear Society 130 巻 ( 1 ) 頁： 1044 - 1047 2024年

Data Assimilation Using Deterministic Sampling Method to Selectively Reduce Uncertainty due to Thermal Neutron Scattering Law for Light Water

Harada Y., Yamaguchi H., Endo T., Yamamoto A., Tada K.

Transactions of the American Nuclear Society 130 巻 ( 1 ) 頁： 758 - 762 2024年

A Simple Resonance Calculation Approach for Space-dependent Self-shielding

Yamamoto A., Endo T.

Transactions of the American Nuclear Society 131 巻 ( 1 ) 頁： 1032 - 1035 2024年

2D Cylindrical SP3 Transport Calculation Using Finite Volume Method with Cross-Diffusion Treatment for Unstructured Meshes

Endo T., Yamamoto A.

Transactions of the American Nuclear Society 131 巻 ( 1 ) 頁： 1053 - 1056 2024年

THERMAL CUT-OFF ENERGY FOR ACCURATE ANALYSIS OF PRISMATIC HIGH-TEMPERATURE GAS-COOLED REACTOR

Takeda, S; Kitada, T; Yamamoto, A; Yamaji, K; Koike, H; Asano, K

PROCEEDINGS OF 2024 31ST INTERNATIONAL CONFERENCE ON NUCLEAR ENGINEERING, VOL 2, ICONE31 2024 2024年

Sensitivity analysis of risk assessment for continuous Markov process Monte Carlo method using correlated sampling method

Morishita, Y; Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 60 巻 ( 12 ) 頁： 1573 - 1585 2023年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

The correlated sampling method is applied to the continuous Markov-chain Monte-Carlo (CMMC) method to efficiently perform sensitivity analysis of input parameters such as the failure rate of safety components. In the correlated sampling method, the original and the perturbed samples are assumed to trace an identical accident sequence, but the weight of the perturbed sample is adjusted to incorporate the variation of input data. The present method is applied to the sensitivity analysis of the safety evaluation of spent fuel pools. The result indicates that the sensitivity analysis for the CMMC coupling method can be efficiently carried out using the correlated sampling method.

DOI： 10.1080/00223131.2023.2231464

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

Watanabe, T; Tada, K; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 60 巻 ( 11 ) 頁： 1386 - 1396 2023年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and 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<inf>2</inf>O affected the nuclide compositions of PWR spent fuels.

DOI： 10.1080/00223131.2023.2201603

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

Maruyama, S; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 60 巻 ( 11 ) 頁： 1372 - 1385 2023年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

A new estimation method of an unknown covariance in the cross-section adjustment method for the development of an application library is proposed. The unknown covariance is defined by the difference between the true covariance (the population covariance) and a prior covariance assumed by an analyst. The unknown covariance is estimated using an empirical covariance consistent with the observed data. To estimate the unknown covariance, an unbiased and consistent estimator in regression analysis has been incorporated into the conventional cross-section adjustment. This estimator does not require assumptions for the probability distribution of the observation data. The statistical properties of this estimator were numerically verified. In addition, the effectiveness of the proposed method was confirmed by another numerical test using actual integral experimental data. In the second numerical test, the modeling uncertainty (covariance) due to the deterministic analysis method was assumed to be unknown. The results show that the proposed method can practically estimate the unknown covariance and adjusted cross-sections using only prior information on covariances.

DOI： 10.1080/00223131.2023.2203707

Development of ACE file perturbation tool using FRENDY

Tada, K; Kondo, R; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 60 巻 ( 6 ) 頁： 624 - 631 2023年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

The sensitivity analysis and the uncertainty quantification play an important role in improving the evaluated nuclear data library. The current computational performance enables us to perform sensitivity analysis and uncertainty quantification using continuous energy Monte Carlo calculation codes. 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 matrices. The uncertainty of k<inf>eff</inf> using the ACE file 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<inf>eff</inf>. The ACE file perturbation tool is included in the current version of FRENDY.

DOI： 10.1080/00223131.2022.2130463

Comparison of internal boundary conditions for optical diffusion calculations considering reflection and refraction Open Access

Amano T., Endo T., Yamamoto A.

Optics Continuum 2 巻 ( 7 ) 頁： 1540 - 1560 2023年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Optics Continuum

A method to treat the internal boundary condition in an optical diffusion calculation is proposed and is compared with the conventional methods. One of the existing internal boundary conditions is Haskel’s method, which uses the effective reflection coefficient for partial currents. However, Haskel’s method ignores incoming partial currents from the adjacent mesh in its derivation. As a result, the accuracy at the internal boundary is lower. This paper proposes a method to improve the accuracy by iteratively updating the effective reflection coefficient for partial current. The proposed method was applied to the benchmark calculations on a one-dimensional slab geometry and its accuracy was confirmed by comparing it with the reference solution obtained by the Monte Carlo code MCML, along with the previously proposed Haskel’s method and Aronson’s method. As a result, it was confirmed that the proposed method is more accurate than Haskel’s method at the internal boundary and gives the same result as Aronson’s method. The convergence of the effective reflection coefficient using iterative calculations in the proposed method was good.

DOI： 10.1364/OPTCON.492445

Efficient reduced order model based on the proper orthogonal decomposition for time-dependent MOC calculations

Tsujita, K; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 60 巻 ( 3 ) 頁： 343 - 357 2023年3月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

An efficient reduced order model (ROM) for time-dependent transport calculations using the method of characteristics (MOC) is proposed. In the present ROM, the flux distributions and the net neutron currents between the adjacent unstructured mesh regions are taken from the MOC solution. Then, the coefficient matrices for the MOC-equivalent diffusion equation are reconstructed from them. The proper orthogonal decomposition (POD) is applied for the MOC-equivalent diffusion equation to reduce the degree of freedoms (DOFs) using the orthogonal bases obtained by the singular value decomposition (SVD) for the sampled MOC solution. The accuracy and computation time of the present ROM are verified in the C5G7-TD 2D benchmark problem. The calculation results show that the present ROM enables us approximately 5000–6000 times faster computation than the full order model (FOM) for kinetic calculations itself in the present calculation condition. The present method can be substituted as real-time simulations without the spatial homogenization when typical flux distributions and the net neutron currents of a target problem can be precalculated.

DOI： 10.1080/00223131.2022.2097963

Nuclear data adjustment using a deterministic sampling method with unscented transformation

Fukui, Y; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 60 巻 ( 3 ) 頁： 238 - 250 2023年3月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

A nuclear data adjustment method using a deterministic sampling method based on an unscented transform was developed, and its validity was confirmed through a twin experiment using a critical benchmark problem. Conventional nuclear data adjustment methods require sensitivity analysis using generalized perturbation theory or many forward calculations using stochastically sampled nuclear data. To address this issue, this study focused on unscented transform-based sampling (UTS), which is used in uncertainty quantification. Based on the UTS, perturbed nuclear data can be deterministically sampled to reproduce the population covariance matrix with minimum sample size. Therefore, UTS can significantly reduce the computational cost compared to conventional nuclear data adjustment using random sampling (RS). Furthermore, the UTS was improved to prevent the sampling of negative nuclear data while accurately reproducing the population covariance matrix. The proposed method was applied to the numerical experiment of Godiva, and the adjusted nuclear data were compared with those obtained using conventional methods. Consequently, it was demonstrated that UTS can adjust nuclear data at a lower computational cost than RS.

DOI： 10.1080/00223131.2022.2095051

Theoretical Derivation of a Unique Combination Number Hidden in the Higher-Order Neutron Correlation Factors Using the Pal-Bell Equation Open Access

Endo, T; Nishioka, F; Yamamoto, A; Watanabe, K; Pyeon, CH

NUCLEAR SCIENCE AND ENGINEERING 197 巻 ( 2 ) 頁： 176 - 188 2023年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

The Pál-Bell equation is a backward-type master equation that describes the probability generating function (PGF) of neutron counts in a neutron multiplication system. Thanks to the Pál-Bell equation with the two-forked and the fundamental mode approximations, an analytical solution of PGF of neutron counts in a source-driven subcritical system can be theoretically derived. This theoretical derivation clarifies that the unique combination number of double factorial (2n−3)!! does exist in the ratio of the higher-order neutron correlation factors measured in a critical state even for any kind of fissile and moderator materials. Additionally, the unique combination numbers are experimentally validated for the order 3 ≤ n ≤ 6 through reactor noise measurements in actual subcritical systems. This knowledge can be used to judge whether a target system is in a deep subcritical state or to roughly estimate the magnitude of subcriticality, based on the factorial moments of the measured reactor noise in a zero-power state.

DOI： 10.1080/00295639.2022.2049992

ACE-FRENDY-CBZ: a new neutronics analysis sequence using multi-group neutron transport calculations

Chiba, G; Yamamoto, A; Tada, K

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 60 巻 ( 2 ) 頁： 132 - 139 2023年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

We propose a new neutronics analysis sequence using multi-group neutron transport calculations named ACE-FRENDY-CBZ. This sequence is free from uses of any application libraries; with the ACE files as the starting point, multi-group cross sections of media comprising a target system are calculated with the FRENDY code, and multi-group neutron transport calculations are performed with modules of the CBZ code system. The ACE-FRENDY-CBZ sequence was tested against the eight fast neutron systems, and good agreement in the neutron multiplication factors with the reference Monte Carlo results was obtained within 20 pcm differences in the bare systems and within 60 pcm differences in the reflected systems. It was also found that the adoption of the consistent P approximation increases the errors. In order to investigate this issue, we adopted the sub-group method to calculate spatially-dependent current-weighted total cross sections in the reflector regions, and it was suggested that the uses of the spatially-dependent cross sections with the consistent P approximation has a possibility to further improve the numerical accuracy.

DOI： 10.1080/00223131.2022.2087783

Application of Equivalent Dancoff Factor Method for Resonance Calculation of Double Heterogeneous Fuel

Yamamoto A., Endo T.

Transactions of the American Nuclear Society 128 巻頁： 690 - 693 2023年

新型燃料の導入に向けた道筋 ―安全評価技術の継続的向上の視点から―

村上健太, 山本章夫

日本原子力学会誌ATOMOΣ 65 巻 ( 10 ) 頁： 606 - 607 2023年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本原子力学会

新型燃料の場合，海外で実績があるとしても，メーカ毎の設計の違いが解析結果に与える影響を評価することが必要である。商業機密に留意しながらも，代表的な製品に対する試験結果を外挿するような判断の仕組みを整えることが好ましい。統計的安全評価コードは，個々の要因がパフォーマンスに与える影響を詳細に分析するためのプラットフォームの役割を果たす。その普及には，95/95値に代表される評価基準を関係者の共通理解とする必要がある。核燃料の場合，過渡・事故時の挙動の評価が特に重要である。材料試験炉という基盤インフラが危機的な状況にあるなか，安全機能と物理現象の関係を丁寧に整理し，個々の試験の意義を明確に定義する姿勢が求められる。

DOI： 10.3327/jaesjb.65.10_606

Implementation of Resonance Up-scattering Treatment in FRENDY Nuclear Data Processing System

Yamamoto, A; Endo, T; Chiba, G; Tada, K

NUCLEAR SCIENCE AND ENGINEERING 196 巻 ( 11 ) 頁： 1267 - 1279 2022年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

The resonance upscattering effect (the thermal agitation effect) is implemented in the generation capability of multigroup 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 the ultra-fine group spectrum and (2) the variation of group-to-group elastic scattering cross sections. Since the upscattering effect is considered in the ultra-fine group spectrum calculation, an iteration calculation is necessary to consider the upscattering. The impacts of the iteration strategy (Jacobi or Gauss-Seidel), as well as the number of iterations, are discussed. 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 impact of resonance upscattering treatments on the Doppler effect through the variation of effective cross sections and the elastic scattering matrix are investigated. The results indicate that FRENDY can provide appropriate multigroup cross sections considering the resonance upscattering effect.

DOI： 10.1080/00295639.2022.2087833

Sensitivity Coefficient Evaluation of an Accelerator-Driven System Using ROM-Lasso Method

Katano, R; Yamamoto, A; Endo, T

NUCLEAR SCIENCE AND ENGINEERING 196 巻 ( 10 ) 頁： 1194 - 1208 2022年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

We propose the use of reduced-order modeling to improve the sensitivity coefficient evaluation method based on Lasso-type penalized linear regression. In this method, cross sections of interest are uniformly randomly sampled, and corresponding perturbed core analyses are performed. The sensitivity coefficients of the higher-dimensional model are expanded by the active subspace (AS) attained by the lower-dimensional model, and the expansion coefficients are estimated by the Lasso regression. In addition, AS bases can be flexibly chosen according to neutronics parameters of interest. We conducted a verification calculation for an accelerator-driven system and clarified that the proposed method successfully reduces the calculation cost by a couple of orders of magnitude compared with the direct method. The proposed method can be used to practically evaluate the sensitivity coefficients of various parameters.

DOI： 10.1080/00295639.2022.2067447

Application of dynamic mode decomposition to Rossi-α method in a critical state using file-by-file moving block bootstrap method

Endo, T; Nishioka, F; Yamamoto, A; Watanabe, K; Pyeon, CH

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 59 巻 ( 9 ) 頁： 1117 - 1126 2022年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

Prompt neutron decay constant (Formula presented.) in a critical state is useful information to validate the numerically predicted ratio of the point kinetics parameters (Formula presented.), where (Formula presented.) and (Formula presented.) are the effective delayed neutron fraction and prompt neutron lifetime, respectively. To directly measure (Formula presented.) in a target critical system, this study proposes the application of the dynamic mode decomposition (DMD) to the reactor noise analysis based on the Rossi- (Formula presented.) method. The DMD-based Rossi- (Formula presented.) method enables us to robustly estimate the fundamental mode component of (Formula presented.) from the Rossi- (Formula presented.) histograms measured using multiple neutron detectors. Furthermore, the file-by-file moving block bootstrap method is newly proposed for the statistical uncertainty quantification of (Formula presented.) to prevent huge memory usage when the neutron count rate is high and/or the total measurement time is long. A critical experiment has been conducted at Kyoto University Critical Assembly to demonstrate the proposed method. As a result, the proposed method can uniquely determine the (Formula presented.) value of which the statistical uncertainty is smallest. By utilizing this experimental result of (Formula presented.), numerical results of (Formula presented.) ratio using the continuous energy Monte Carlo code MCNP6.2 with recent nuclear data libraries, which are processed by the nuclear data processing code FRENDY, are validated.

DOI： 10.1080/00223131.2022.2030260

Improvements in Computational Efficiency for Resonance Calculation Using Energy Spectrum Expansion Method

Kondo, R; Endo, T; Yamamoto, A; Takeda, S; Koike, H; Yamaji, K; Asano, K

NUCLEAR SCIENCE AND ENGINEERING 196 巻 ( 7 ) 頁： 769 - 791 2022年7月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

Improvements in computational efficiency for the Resonance calculation using energy Spectrum Expansion (RSE) method are proposed in order to increase the applicability of the method for core nuclear analyses. First, efficient treatment of the neutron source for the RSE method has been newly developed. This is a balanced approach from the viewpoints of computation time and memory size, in comparison with the other approaches mentioned in a previous study [R. KONDO et al., “A New Resonance Calculation Method Using Energy Expansion Based on a Reduced Order Model,” Nucl. Sci. Eng., 195, 694 (2021)]. Second, low-rank approximation has been applied to the RSE method considering the deficit ratio of the singular value for the orthogonal basis. Computation time was reduced by ~68% while maintaining sufficient accuracy of effective cross sections. Third, the impacts of the discretization parameters in the method of characteristics on the RSE method have been investigated, and coarser conditions of the parameters were found to be appropriate from the viewpoints of computation time and accuracy of effective cross sections. Finally, RSE calculations with these improvements have been performed for the fuel assembly geometry of a light water reactor. The computation time was reduced by ~70%, and the data size of the scattering cross-section moments was approximately 3900 times smaller in comparison with the RSE calculation without the improvements.

DOI： 10.1080/00295639.2021.2025297

Impact of Angular and Spatial Source Distribution Approximations on Convergence Performance of Nonlinear Acceleration Methods for MOC in Slab Geometry

Oshima, Y; Endo, T; Yamamoto, A

NUCLEAR SCIENCE AND ENGINEERING 196 巻 ( 4 ) 頁： 379 - 394 2022年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

The convergence performance of nonlinear acceleration methods for the method of characteristics (MOC) with flat source (FS) approximation (FS MOC) or linear source (LS) approximation (LS MOC) is numerically investigated by focusing on the spatial and angular approximations in the acceleration calculations. The convergence of nonlinear acceleration depends on the consistency of the calculation models between the higher-order and lower-order (acceleration) methods. The convergence of four acceleration methods is evaluated to clarify the relationship between model consistency and convergence performance. These methods consist of FS or LS for the spatial source distribution and P1 or discrete angle for the angular distribution, i.e., (1) FS analytic coarse mesh finite difference (ACMFD) acceleration (FS ACMFD), (2) LS ACMFD, (3) FS angular-dependent discontinuity factor MOC (ADMOC) acceleration (FS ADMOC), and (4) LS ADMOC. The ACMFD and ADMOC accelerations are based on P1 and discrete angle approximations, respectively. The FS MOC and LS MOC are considered higher-order methods. The FS MOC and LS MOC with five acceleration methods, i.e., the aforementioned four acceleration methods and the conventional coarse mesh finite difference acceleration method, are used to perform fixed-source calculations in one-group one-dimensional homogeneous slab geometry, and the spectral radii are numerically evaluated. The numerical results indicate that (1) the nonlinear acceleration methods that are unconditionally stable for FS MOC also show similar convergence properties for LS MOC in one-dimensional slab geometry; (2) better convergence is observed when the consistency of higher- and lower-order models is high; and (3) when a coarse mesh is optically thick, the spatial homogenization degrades the convergence performance, even if spatial and angular approximations are consistent between the higher- and lower-order models.

DOI： 10.1080/00295639.2021.1982549

Transport consistent diffusion coefficient for CMFD acceleration and comparison of convergence properties (vol 56, pg 716, 2019)

Yamamoto, A; Endo, T; Giho, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 59 巻 ( 3 ) 頁： 407 - 407 2022年3月

Applicability of Dynamic Mode Decomposition to Estimate Fundamental Mode Component of Prompt Neutron Decay Constant from Experimental Data

Nishioka, F; Endo, T; Yamamoto, A; Yamanaka, M; Pyeon, CH

NUCLEAR SCIENCE AND ENGINEERING 196 巻 ( 2 ) 頁： 133 - 143 2022年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

To robustly estimate the fundamental mode component of prompt neutron decay constant α in a subcritical system, dynamic mode decomposition (DMD) is applied to time-series data obtained by the pulsed-neutron source (PNS) and Rossi-α methods. For the statistical uncertainty quantification of α by DMD, randomly sampled virtual data are used for the DMD procedure. The applicability of DMD is demonstrated by analyzing the experimental results by the PNS and Rossi-α methods, which are performed at the Kyoto University Critical Assembly (KUCA). When applying the DMD to the PNS and Rossi-α experimental data, a constant signal was added to the experimental data to remove the background constant component. The application results indicate that DMD enables one to robustly estimate the fundamental mode component of α in the PNS and Rossi-α methods.

DOI： 10.1080/00295639.2021.1968225

外的事象に対する原子力発電所の安全対策とリスクマネジメント

倫理規程制定20年を迎えて　第4回

山本章夫

日本原子力学会誌ATOMOΣ 64 巻 ( 3 ) 頁： 176 - 176 2022年

村上健太, 山本章夫

日本原子力学会誌ATOMOΣ 64 巻 ( 5 ) 頁： 272 - 274 2022年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本原子力学会

フォローアップセミナーでは，企画セッションで抽出された2つの論点について，講演者に2名のパネリストを加えて議論した。リスク評価を含む知見の不確かさを踏まえながら迅速な意思決定を行うという論点では，ハザード評価の確からしさに関する認識の相違が更に浮き彫りになると共に，得られた知見に対して「規制基準に照らして判断する」という議論と，不確かさを有することを前提に対策を決めることの違いが指摘された。また外的事象に対するプラントのパフォーマンスを評価するという論点では，地震PRAを十分に活用して，設計基準レベルを超えたときのプラントの挙動を把握することの重要性が強調された。

DOI： 10.3327/jaesjb.64.5_272

組織横断的な原子力教育基盤の構築に向けて

黒﨑健, 小崎完, 中島宏, 小原徹, 若林源一郎, 卞哲浩, 松山成男, 阿部博志, 宇埜正美, 山本章夫

日本原子力学会誌ATOMOΣ 64 巻 ( 9 ) 頁： 520 - 524 2022年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本原子力学会

文部科学省が支援する国際原子力人材育成イニシアティブ事業において，未来社会に向けた先進的原子力教育コンソーシアム(Advanced Nuclear Education Consortium for the Future Society：ANEC)が2020年度に設立された。本稿では，ANEC設立の背景や経緯，運営体制，人材育成の取り組み状況，将来展望等を紹介する。

DOI： 10.3327/jaesjb.64.9_520

Proposal and Application of ROM-Lasso Method for Sensitivity Coefficient Evaluation

Katano R., Yamamoto A., Endo T.

Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022 頁： 2032 - 2041 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022

We propose a novel method for evaluating sensitivity coefficients of neutronics parameters to cross sections, so-called the ROM-Lasso. In this method, cross sections of interest are randomly sampled, and corresponding perturbed core analyses are performed. Then, the sensitivity coefficient vector of the higher-level model is expanded via the active subspace bases obtained with the lower-level model whose dimensional complexity is smaller than that of the higher-level model, and the expansion coefficients are estimated by the lasso regression. A unique feature of the ROM-Lasso method allows the use of different bases optimized for each neutronics parameter. We conducted a verification calculation for an accelerator-driven system and demonstrated that the ROM-Lasso method can reproduce the sensitivity coefficients with a much smaller number of forward calculations than the direct method. The proposed method can be used to practically evaluate the sensitivity coefficients.

DOI： 10.13182/PHYSOR22-37557

Neutron Diffusion Calculation in Heterogeneous Geometry Based on Local/Global Iteration Using Proper Orthogonal Decomposition

Ito M., Endo T., Yamamoto A., Masaoka Y., Kodama Y., Nagano H.

Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022 頁： 503 - 512 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022

This study newly proposes a heterogeneous core calculation method based on local/global iteration using proper orthogonal decomposition (POD). By using the singular value decomposition (SVD) and the low-rank approximation, appropriate POD bases for expanding the neutron flux can be obtained from snapshot data of the neutron flux obtained by fine mesh calculations. By projection using the POD bases, the dimension of the target equation (e.g., discretized neutron diffusion equation) can be dramatically reduced. In the proposed method, POD is effectively applied to each single assembly calculation (local calculation). Furthermore, using the local/global iteration, the effective neutron multiplication factor and the neutron flux distribution in the whole core geometry can be obtained by combining the numerical results of the local calculation for each fuel assembly and the global calculation for the whole core. As a feasibility study, the proposed method is applied to a one-dimensional heterogeneous core analysis, and the accuracy is investigated by changing the total number of POD bases.

DOI： 10.13182/PHYSOR22-37693

Investigation of the Impact of Difference Between FRENDY and NJOY2016 on Neutronics Calculations

Ono M., Tojo M., Tada K., Yamamoto A.

Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022 頁： 88 - 96 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022

A nuclear data library is used as a starting input for all subsequent neutronics calculations. NJOY has been used worldwide as a nuclear data processing code to create cross section libraries for a long time. For verification of NJOY method and providing an alternative nuclear data processing tool, JAEA has been developed the new nuclear library processing code FRENDY. In this paper, nuclear calculations were performed using the ACE files and the multigroup libraries created by both FRENDY and NJOY, and the impacts on the neutronics characteristics due to nuclear data processing were investigated using those libraries. MCNP was used to compare the ACE files by calculating many benchmark problems including ICSBEP and it was confirmed that the k-eff values generally agree with each other within the range of statistical errors. The multigroup cross sections are verified by the BWR design codes LANCR/AETNA through calculation of a commercial BWR5 equilibrium core loaded with 9x9 fuels. It was confirmed that fuel assembly and core characteristics are consistent with each other. From the above investigations, it was confirmed that FRENDY can provide comparable continuous/multi-group neutron cross sections with NJOY.

DOI： 10.13182/PHYSOR22-37287

Development of Nuclear Data Processing Code FRENDY Version 2

Tada K., Yamamoto A., Endo T., Chiba G., Ono M., Tojo M.

Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022 頁： 107 - 116 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022

Nuclear data processing is an important interface between an evaluated nuclear data library and neutronics calculation codes. JAEA has been developed the new nuclear data processing code FRENDY from 2013. FRENDY version 1 generates the ACE files used for the continuous-energy Monte Carlo codes including PHITS, Solomon, Serpent, and MCNP and it was released as the open-source software under the 2-clause BSD license in 2019. After we released FRENDY version 1, many functions, e.g., the multi-group neutron cross-section library generation, the statistical uncertainty quantification of 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, are developed. We released FRENDY version 2 including these functions. The present paper explains the overview of FRENDY and features of new functions implemented in FRENDY version 2.

DOI： 10.13182/PHYSOR22-37299

AREA RATIO METHOD USING DYNAMIC MODE DECOMPOSITION

Endo T., Nishioka F., Yamamoto A., Yamanaka M., Pyeon C.H.

Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022 頁： 3366 - 3375 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022

To reduce the higher mode effects on the subcriticality estimation using the pulsed neutron source without the aid of a high-fidelity neutron transport calculation, we propose a new area ratio method based on a data-driven approach using the dynamic mode decomposition (DMD) with the neutron count data measured by multiple neutron detectors. Thanks to eigenvalues and eigenvectors based on DMD, the fundamental mode of the prompt neutrons and the background component due to delayed neutrons are extracted from the measured neutron count data matrix. The effectiveness of the proposed method is demonstrated via experimental analysis for a pulsed neutron source measurement performed at Kyoto University Critical Assembly.

DOI： 10.13182/PHYSOR22-37184

A New Approach for Resonance Treatment of Doubly Heterogeneous Fuel using the RSE method

Yamamoto A., Endo T., Takeda S., Koike H., Yamaji K., Ieyama K., Asano K.

Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022 頁： 2042 - 2051 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022

A new resonance calculation method for the doubly-heterogeneous (DH) fuels such as high-temperature gas-cooled reactor fuel is proposed based on the Resonance calculation based on Spectral Expansion (RSE) method. The concept of pointwise disadvantage factor for fuel grain is taken into account to treat the DH fuels. The verification calculation is carried out for simplified single fuel cell and fuel compact consisting of five fuel cells and graphite moderator. The calculation results indicate that the present method can appropriately handle the space-dependent self-shielding effect for DH fuels.

DOI： 10.13182/PHYSOR22-37251

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

Yamamoto, A; Endo, T; Tada, K

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 58 巻 ( 12 ) 頁： 1343 - 1350 2021年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

An adaptive setting method of background cross sections is implemented to FRENDY/MG, which is a multi-group neutron cross section generation module, for accurate interpolation of self-shielding factors with a minimum number of background cross sections. Since the dependence of self-shielding factors on background cross section is significantly different among energy group, reaction type, and nuclide, appropriate setting of background cross sections usually requires considerable works. 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 are eliminated. Then interpolation accuracy at each interval is tested. 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. Calculation results indicate that the present method provides an appropriate set of background cross sections while satisfying input error tolerance for self-shielding factors or reaction rates. 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.

DOI： 10.1080/00223131.2021.1944930

Application of continuous Markov-chain Monte-Carlo method to multi-unit risk evaluations considering interdependence of accident progression among multiple units

Sawada, K; Yamamoto, A; Endo, T; Sato, C; Maeda, K; Jang, S

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 58 巻 ( 12 ) 頁： 1308 - 1317 2021年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

The accident in Fukushima Dai-ichi nuclear power plants reconfirms the necessity of the safety assessment considering multiple nuclear reactor units. However, consideration of the interdependency among safety systems or events in multiple units as well as the time dependency of accident progressions is difficult in the conventional event tree method, which is widely used in probabilistic risk assessments. Recently, the continuous Markov-chain Monte-Carlo (CMMC) method coupled with a plant safety analysis or a severe accident analysis code has been paid attention to address these issues. In the present study, the CMMC coupling method is applied to the risk assessment of multiple units to clarify the benefits and issues to be resolved of this method. Since the CMMC coupling method requires many executions of an accident analysis code, a meta-model that simplifies systems and physical phenomena in accidents is used in this study to reduce computational cost. Furthermore, the inverse transform sampling method is newly adapted. Numerical analyses of BWR accident under station blackout with loss of cooling capability are carried out considering the correlation among the availabilities of mitigation systems. The results suggested that the CMMC coupling method can quantitatively treat the interdependency and time dependency among events in multiple units.

DOI： 10.1080/00223131.2021.1940341

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

Yamamoto, A; Tada, K; Chiba, G; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 58 巻 ( 11 ) 頁： 1165 - 1183 2021年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and 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. The several distinguished features are implemented for the multi-group generation capability, e.g. explicit consideration of resonance interference effect among nuclides, enhanced resonance treatment for various nuclear reactions, and accurate numerical integration of thermal cross sections. 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, - (Formula presented.), ENDF/B-VII.1, -VIII.0, JEFF-3.3, and TENDL-2019 are carried out without unexpected processing issues, 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. Now FRENDY can generate not only the pointwise cross sections for continuous energy Monte-Carlo codes but also the multi-group cross sections for deterministic neutronics analysis codes.

DOI： 10.1080/00223131.2021.1921631

Proposal and applicability of estimated criticality lower-limit multiplication factor using the bootstrap method

Hayashi, T; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 58 巻 ( 9 ) 頁： 1008 - 1017 2021年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

To judge whether an application system is a subcritical state or not based on numerical results of the effective neutron multiplication factor (Formula presented.), an evaluation method of the estimated criticality lower-limit multiplication factor (ECLLMF) using the bootstrap method is newly proposed. By utilizing numerical results of (Formula presented.) for critical benchmark-problems that are selected depending on neutronic similarity to the application system, the ECLLMF should be carefully and conservatively estimated based on uncertainties of (Formula presented.) due to a criticality safety analysis code, experimental uncertainty, and covariance matrix of the nuclear data library. Furthermore, the frequency distribution of (Formula presented.) for these problems does not necessarily obey an ideal normal distribution. Using a resampling technique called ‘bootstrap method,’ the proposed method can reasonably estimate the ECLLMF considering the uncertainties and nuclear data-induced correlation between each critical benchmark-problem without the assumption of normality. To investigate the applicability of the proposed method, the approach-to-criticality experiment was carried out at the Kyoto University Critical Assembly (KUCA). Comparison of numerical results of (Formula presented.) and the ECLLMF using the bootstrap method indicated that the proposed method was able to judge an actual subcritical core as subcritical state.

DOI： 10.1080/00223131.2021.1902416

A New Resonance Calculation Method Using Energy Expansion Based on a Reduced Order Model

Kondo, R; Endo, T; Yamamoto, A; Takeda, S; Koike, H; Yamaji, K; Sato, D

NUCLEAR SCIENCE AND ENGINEERING 195 巻 ( 7 ) 頁： 694 - 716 2021年7月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

A Resonance calculation using energy Spectrum Expansion (RSE) method is newly proposed in this paper. In this method, ultra-fine-group (UFG) spectra appearing in a resonance calculation are expanded by orthogonal bases on energy, which are extracted from the UFG spectra obtained in homogeneous geometry with various background cross sections using singular value decomposition and low-rank approximation. Namely, this method is based on the concept of a reduced order model. A neutron transport equation for flux moments (expansion coefficients) similar to the conventional one is derived and is numerically solved. This method applies to two benchmark problems in which a resonance interference effect and spatial self-shielding effect can appear. The results indicate that this method accurately predicts the reference effective cross sections and reaction rates obtained from direct UFG calculation in heterogeneous geometry.

DOI： 10.1080/00295639.2020.1863066

Fast reproduction of time-dependent diffusion calculations using the reduced order model based on the proper orthogonal and singular value decompositions

Tsujita, K; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 58 巻 ( 2 ) 頁： 173 - 183 2021年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

An efficient reduced order model (ROM) for time-dependent diffusion calculations using the proper orthogonal decomposition (POD) is proposed. Employing the singular value decomposition (SVD) and low-rank approximation (LRA) for the flux distributions sampled from the detail full order model (FOM) solutions, the orthogonal basis suitable for a target problem is numerically obtained. In the present ROM, flux distribution is expanded with an orthogonal basis on space. Then, the dimensionality reduction is performed for the neutron diffusion equation using the orthogonal basis, and the equation for the expansion coefficients is obtained. Since any flux distributions can be used to construct the orthogonal bases, different orthogonal bases calculated from different flux distribution sets are tested. The accuracy and computation time of the present ROM are verified in the TWIGL benchmark problem. The calculation results show that the present ROM is approximately 100 times faster than the FOM for kinetic calculations in the present conditions. The present method can be substituted as real-time FOM simulations when typical flux distributions of a target problem can be precalculated to represent the solution space with less degree of freedom (DOF).

DOI： 10.1080/00223131.2020.1814891

Evolutionary simulated annealing for fuel loading optimization of VVER-1000 reactor 国際共著

Tran, VP; Phan, GTT; Hoang, VK; Ha, PNV; Yamamoto, A; Tran, HN

ANNALS OF NUCLEAR ENERGY 151 巻 2021年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

An evolutionary simulated annealing (ESA) method has been developed for the problem of fuel loading optimization of VVER-1000 reactor. The ESA method improves original simulated annealing by using crossover and mutation operators to generate new trial loading patterns (LPs). A core physics calculation code for fuel LP optimization of VVER reactors (LPO-V) has been developed and verified based on a VVER-1000 MOX benchmark core in comparison with MCNP4c calculations. Calculations for optimizing fuel LP of the VVER-1000 MOX core have been conducted using the ESA method in comparison with simulated annealing (SA) and adaptive simulated annealing (ASA). Statistical differences between these methods were also evaluated based on the Mann–Whitney U test. The results show that the ESA method is advantageous over the SA and ASA.

DOI： 10.1016/j.anucene.2020.107938

New method for visualizing the dose rate distribution around the Fukushima Daiichi Nuclear Power Plant using artificial neural networks Open Access

Sasaki, M; Sanada, Y; Katengeza, EW; Yamamoto, A

SCIENTIFIC REPORTS 11 巻 ( 1 ) 2021年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Scientific Reports

This study proposes a new method of visualizing the ambient dose rate distribution using artificial neural networks (ANNs) from airborne radiation monitoring results. The method was applied to the results of the airborne radiation monitoring which was conducted around the Fukushima Daiichi Nuclear Power Plant by an unmanned aerial vehicle. Much of the survey data obtained in the past were used as the training data for building a network. The number of training cases was related to the error between the ground and converted values by the ANN. The quantitative evaluation index (the root-mean-square error) between the ANN-converted value and the ground-based survey result converged at 200 training cases. This number of training case was considered a rough criterion of the required number of training cases. The reliability of the ANN method was evaluated by comparison with the ground-based survey data. The dose rate map created by the ANNs method reproduced ground-based survey results better than traditional methods.

DOI： 10.1038/s41598-021-81546-4

Compression of Cross-Section Data Size for High-Resolution Core Analysis Using Dimensionality Reduction Technique

Yamamoto, M; Endo, T; Yamamoto, A

NUCLEAR SCIENCE AND ENGINEERING 195 巻 ( 1 ) 頁： 33 - 49 2021年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

Compression of cross-section data used for high-resolution core analysis is performed using a dimensionality reduction technique based on the singular value decomposition (SVD) and low-rank approximation. The size of cross-section data can be a significant issue in high-resolution core analysis using detailed energy and spatial resolutions. This study addresses this issue focusing on the similarity of multigroup cross sections among different spatial regions. A data compression method using the SVD and low-rank approximation is applied for the multigroup microscopic cross sections of heterogeneous material regions obtained by a lattice physics calculation with burnup and branch calculations. Weighting by nuclide number densities and neutron spectra is considered to improve the efficiency of compression for cross sections. Single-assembly transport calculations with the method of characteristics are carried out using the original cross sections and the reconstructed cross sections after data compression. The accuracy of data compression for cross sections is evaluated by comparing the multiplication factor and multigroup scalar fluxes. The results indicate that the present data compression for microscopic cross sections can reduce approximately 99.7% of the original cross-section data size under the present calculation condition.

DOI： 10.1080/00295639.2020.1781482

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

Chiba G., Yamamoto A., Tada K., Endo T.

Transactions of the American Nuclear Society 124 巻 ( 1 ) 頁： 556 - 558 2021年

Perturbation-theory-based sensitivity analysis of prompt neutron decay constant for water-only system

Endo T., Noguchi A., Yamamoto A., Tada K.

Transactions of the American Nuclear Society 124 巻 ( 1 ) 頁： 184 - 187 2021年

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 A., Tada K., Chiba G., Endo T.

Transactions of the American Nuclear Society 124 巻 ( 1 ) 頁： 544 - 547 2021年

Application of Regionwise Even-Parity Discontinuity Factor to the Multigroup Analog Monte-Carlo Method

Oshima Y., Endo T., Yamamoto A., Aizawa N.

Transactions of the American Nuclear Society 125 巻 ( 1 ) 頁： 904 - 907 2021年

Verification of Medium-Wise Multi-Group Cross Section Calculation Capability of FRENDY/MG

Chiba G., Yamamoto A.

Transactions of the American Nuclear Society 125 巻 ( 1 ) 頁： 934 - 937 2021年

Dimension-reduced Nuclear Data Adjustment Method based on the Bayesian Monte-Carlo Method

Fukui Y., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 125 巻 ( 1 ) 頁： 900 - 903 2021年

THEORETICAL DERIVATION OF UNIQUE COMBINATION-NUMBER FOR HIGHER ORDER NEUTRON CORRELATION FACTORS BASED ON PÁL-BELL EQUATION

Endo T., Yamamoto A.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 1568 - 1576 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

The Pál-Bell equation is a master equation to describe the probability generating function (PGF) of neutron counts in the neutron multiplication system. Thanks to the Pál-Bell equation with the two-forked and the fundamental mode approximations, an analytical solution of PGF of neutron counts in a source-driven subcritical system can be theoretically derived. Thereby, the unique combination numbers for the higher-order neutron-correlation factors for a near-critical state can be theoretically clarified. This knowledge is useful to judge whether a target system is a near-critical state or not using only a histogram (or factorial moments) of neutron counts.

DOI： 10.13182/M&C21-33627

S2 Consistent Analytic CMFD Acceleration for Method of Characteristics

Oshima Y., Yamamoto A., Endo T.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 1840 - 1849 2021年

A coarse mesh finite-difference (CMFD) acceleration consistent with the S2 discrete ordinate method using the step-characteristics is proposed. The analytically derived finite-difference formulation for diffusion theory (ACMFD), which is theoretically consistent with the discrete ordinate method in one-dimensional slab geometry with the S2 Gauss-Legendre quadrature, is used for the acceleration of a transport calculation. Our numerical calculations in simple geometry revealed that the consistent treatment of scattering source distribution in the ACMFD acceleration has a significant impact on the convergence property. Further, the linearized Fourier analysis of ACMFD acceleration shows the same convergence property as numerical calculations. These numerical and theoretical analyses show that the S2- consistent ACMFD acceleration is unconditionally stable without any correction to the diffusion coefficient.

DOI： 10.13182/M&C21-33737

DEVELOPMENT OF ESTIMATION METHOD FOR PROMPT NEUTRON DECAY CONSTANT USING DYNAMIC MODE DECOMPOSITION

Nishioka F., Fukui Y., Endo T., Yamamoto A., Yamanaka M., Pyeon C.H.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 1719 - 1728 2021年

To estimate the prompt neutron decay constant α corresponding to the fundamental mode in a subcritical system, we try applying the Dynamic Mode Decomposition (DMD) to time-series data of neutron counts obtained by the pulsed-neutron source (PNS) method. In this study, we newly develop an estimation method of α with the statistical uncertainty by the DMD and the random sampling method. The applicability of the proposed method is demonstrated by analyzing a PNS experiment carried out at the Kyoto University Critical Assembly (KUCA).

DOI： 10.13182/M&C21-33631

FRENDY/MG: A MULTI-GROUP CROSS SECTION GENERATION MODULE USING ACE POINTWISE CROSS SECTIONS

Yamamoto A., Endo T., Foad B., Chiba G., Tada K.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 710 - 720 2021年

A generation capability of neutron multi-group cross sections is being implemented to the FRENDY nuclear data processing code, as FRENDY/MG. FRENDY/MG generates neutron multi-group cross sections for deterministic core analysis codes considering an arbitrary energy group structure. Distinguished features of FRENDY/MG are 1) use of ACE pointwise cross sections as the source of nuclear data (no evaluated nuclear data file is directly used), 2) treatment of a compound material consisting of multiple nuclides to explicitly consider the resonance interference effect. Various verifications are being carried out through the comparison with the multi-group cross sections generated by NJOY.

DOI： 10.13182/M&C21-33679

FUEL ASSEMBLY ANALYSES WITH RESONANCE CALCULATION USING ENERGY SPECTRUM EXPANSION METHOD

Kondo R., Endo T., Yamamoto A., Takeda S., Koike H., Yamaji K., Sato D.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 2219 - 2230 2021年

Efficient numerical algorithms for a Resonance calculation using energy Spectrum Expansion (RSE) method were proposed for a large and complicated geometry such as a fuel assembly. The RSE method can treat complicated heterogeneous geometry considering resonance interference effect among different regions. Calculation procedure of the RSE method is composed of (1)generation of ultra-fine group spectra from ultra-fine group calculations in homogeneous geometry, (2)expansion of the spectra by orthogonal basis on energy based on singular value decomposition, (3)transport calculation for expansion coefficients and (4)reconstruction of ultra-fine group spectra in target heterogeneous regions by the expansion coefficients and the orthogonal basis. In this study, the efficient numerical algorithms for the RSE method were developed and applied. The algorithms are composed of (i)scattering source calculation by the combination of conventional slowing down and moment-to-moment transfer calculations, and (ii)matrix exponential generation in transport calculation of the RSE method with method of characteristics by diagonalization using eigenvalue decomposition. Through numerical verification, it was confirmed that effective multi-group cross sections by the RSE method with the new algorithms are well agreed with those by direct ultra-fine group calculation in the fuel assembly geometry. The RSE method with the new algorithms is applicable to the fuel assembly analysis.

DOI： 10.13182/M&C21-33621

IMPLEMENTATION OF A RESONANCE CALCULATION USING ENERGY SPECTRUM EXPANSION METHOD INTO HETEROGENEOUS TRANSPORT CALCULATION CODE GALAXY-Z

Yamaji K., Koike H., Ieyama K., Sato D., Yamamoto A., Takeda S.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 1982 - 1991 2021年

A resonance calculation using the energy spectrum expansion (RSE) method has been developed in order to efficiently treat complicated heterogeneous geometry and resonance interference effect among both nuclides and regions. The three-dimensional (3D) heterogeneous transport calculation code GALAXY-Z developed by Mitsubishi Heavy Industries Ltd. uses the RSE method as resonance calculation method. In this study, resonane calculations of the GALAXY-Z code using the RSE method were performed and showed good agreements of nuclear characteristics with the ultra-fine-group method in wide range of moderator density for actual PWR fuel specifications. The GALAXY-Z code using the RSE method is applicable with high accuracy to generation of nuclear constants in normal operations and accident conditions including low moderator density conditions and can siginificantly reduce computational memory in comparison with the ultra-fine-group method.

DOI： 10.13182/M&C21-33788

Data Assimilation Using Subcritical Measurement of Prompt Neutron Decay Constant

Endo, T; Yamamoto, A

NUCLEAR SCIENCE AND ENGINEERING 194 巻 ( 11 ) 頁： 1089 - 1104 2020年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

The prompt neutron decay constant (Formula presented.) in a steady-state subcritical system can be directly measured using a reactor noise analysis method such as the Feynman- (Formula presented.) method. To reduce the nuclear data–induced uncertainty of (Formula presented.) for a target system, this study investigates the applicability of data assimilation techniques, i.e., the bias factor method and the cross-section adjustment method, based on a subcritical measurement of (Formula presented.) conducted at Kyoto University Critical Assembly (KUCA). The sensitivity coefficients of (Formula presented.) and (Formula presented.) with respect to the nuclear data were efficiently estimated using a deterministic S<inf>N</inf> transport code with first-order perturbation theory. As a result, the a priori relative uncertainty of (Formula presented.) due to the 56-group SCALE covariance data can be reduced if there is strong correlation between the measured (Formula presented.) and the target (Formula presented.). The experimental value of (Formula presented.) contributes to improving the nuclear data of total fission spectrum (Formula presented.) and total fission neutron number (Formula presented.) via strong correlations between (Formula presented.) and prompt (Formula presented.) and between (Formula presented.) and prompt (Formula presented.), by utilizing the sensitivity coefficients of (Formula presented.) with respect to prompt (Formula presented.) and (Formula presented.).

DOI： 10.1080/00295639.2020.1720499

Implementation of the unscented transformation with low rank approximation in uncertainty analysis during large-break loss of coolant accident 国際共著

Foad, B; Yamamoto, A; Endo, T

ANNALS OF NUCLEAR ENERGY 146 巻 2020年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

The Low Rank Approximation (LRA) and Unscented Transform (UT) are integrated to produce a new algorithm having the capability to decrease the time required for the uncertainty quantification during Loss of coolant accident (LOCA) in Pressurized Water Reactors (PWR). The LRA is an efficient technique used in reducing computational cost due to its ability to perform dimensionality reduction by revealing the active or important degrees of freedom and calculate the basis of the so-called active subspace basing on the Singular Value Decomposition (SVD). For further reduction in the computational time; the UT algorithm is also implemented to generate a set of sigma points, these sigma points are the representatives of the whole probability distribution (the UT is restricted to Gaussian distribution). The main safety parameter is the maximum cladding temperatures during the accident which are computed by ATHLET thermal-hydraulic code. The reactivity coefficients and the covariance matrix are calculated using the SCALE 6.2 code. The present calculation model has 14-dimensions, therefore the number of sigma points needed for the SVD/UT technique is 29, and can be minimized to 5 sigma points only if the LRA/UT is used where two singular values are sufficient to reproduce/span the space thanks to the strong correlations between the reactivity coefficients.

DOI： 10.1016/j.anucene.2020.107614

Uncertainty and regression analysis of the MSLB accident in PWR based on unscented transformation and low rank approximation 国際共著

Foad, B; Yamamoto, A; Endo, T

ANNALS OF NUCLEAR ENERGY 143 巻 2020年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

The present studies focus on the quantification of uncertainty during the main steam line break accident scenario (MSLB) in PWR, assuming that there is a failure on the feed-water regulating valve of the broken steam generator. The scenario is characterized by the associated positive Doppler and coolant density reactivities which bring the core back to critical (return-to-power). Accordingly, the input uncertainty parameters are the Doppler and coolant density reactivities taking into account the correlation matrix among the input parameters, which is calculated by SCALE 6.2 code. The main safety parameters are the maximum cladding surface temperatures and average core power during the accident which are computed by ATHLET thermal-hydraulic code. The sampling-based uncertainty technique is considered to be the most dependable technique which can be applicable to any code, however it is computationally expensive. Therefore, it is important to develop efficient techniques which are capable of reducing the calculation time. The first approach is the SVD-UT where the Unscented Transform (UT) algorithm and singular value decomposition (SVD) are combined to generate a minimal sample points. In addition, due to the strong correlation between the input reactivities, the computational time can be further reduced by implementing the Low Rank Approximation (LRA) and revealing the active subspace.

DOI： 10.1016/j.anucene.2020.107493

Applicability of a reduced order model for a safety analysis code to statistical safety analysis 査読有り

Matsushita Masaki, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 頁： 1-12 2020年7月

Efficient uncertainty quantification for PWR during LOCA using unscented transform with singular value decomposition 国際共著

Foad, B; Yamamoto, A; Endo, T

ANNALS OF NUCLEAR ENERGY 141 巻 2020年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

This paper discusses one of the most important issues facing the regulatory body while performing the uncertainty analysis of the nuclear reactor parameter during accident conditions. This problem is the long computational time required by the statistical sampling methods to compute the uncertainty. We overcome this problem by introducing the Unscented Transform (UT) algorithm and singular value decomposition (SVD). Where both algorithms are combined (SVD/UT) to generate a set of sigma points, these sigma points are the representatives of whole probability distribution. The uncertainty quantification is performed during Loss of coolant accident in Pressurized Water Reactor (PWR), where the input variable of uncertainty is the coolant density reactivity. The SCALE 6.2 code is used for calculating the reactivity coefficients and the covariance matrix. The response variables are the peak cladding temperatures during the accident which are computed by ATHLET thermal-hydraulic code. The results obviously confirm the efficiency of the SVD/UT sampling in predicting the new mean values, and assure its ability to reduce the sampling size leading to a dramatic reduction of computational cost.

DOI： 10.1016/j.anucene.2020.107341

Impact of Various Parameters on Convergence Performance of CMFD Acceleration for MOC in Multigroup Heterogeneous Geometry

Oshima, Y; Endo, T; Yamamoto, A; Kodama, Y; Ohoka, Y; Nagano, H

NUCLEAR SCIENCE AND ENGINEERING 194 巻 ( 6 ) 頁： 477 - 491 2020年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

The impact of various parameters in the coarse mesh finite difference (CMFD) acceleration method on overall convergence behavior is investigated through numerical calculations using the method of characteristics (MOC). Four parameters appearing in the CMFD acceleration with MOC, i.e., scalar flux distribution in flat flux regions (FFRFlux), the scalar flux distribution in CMFD meshes (CMFDFlux), homogenized cross sections (HXSs) in CMFD meshes, and current correction factors (CCFs), are considered. Parts of these four parameters are fixed to the converged values throughout iterations in order to estimate their impact on convergence. Numerical calculations are carried out for Korea Advanced Institute of Science and Technology’s (KAIST’s) benchmark problem KAIST-2A, which is a heterogeneous and multigroup problem, and the number of outer iterations to reach convergence is evaluated. The impact of geometric heterogeneity and cross-section homogenization in the CMFD acceleration has not been considered in linearized Fourier analysis so far. The calculation results indicate that (1) convergence of HXS has little impact on the overall convergence, (2) convergence of FFRFlux is dominant followed by CCF when a CMFD mesh is optically thin, and (3) convergence of FFRFlux is dominant when a CMFD mesh is optically thick and contains many flat flux regions.

DOI： 10.1080/00295639.2020.1722512

A kinetic model for the direct response matrix method

Application of the multigrid amplitude function method for time-dependent MOC based on the linear source approximation 査読有り

Tsujita Kosuke, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2020年1月

Subcriticality measurement using time-domain decomposition-based integral method for simultaneous reactivity and source changes 査読有り

Endo Tomohiro, Nonaka Asahi, Imai Sho, Yamamoto Akio, Sakon Atsushi, Hashimoto Kengo

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2020年1月

Mitsuyasu, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 57 巻 ( 1 ) 頁： 90 - 99 2020年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

An accurate analysis model for transient reactor behavior is necessary to keep sufficient safety margins of nuclear power plants to prevent cliff edge effects. In this study, the direct response matrix (DRM) method is applied to the kinetic domain and the transient analysis is enabled based on the transport equation. The kinetic DRM model introduces the time delay to four sub-response matrices. The time delay can be evaluated by a Monte Carlo calculation. The model is evaluated in homogeneous and heterogeneous problems. The Doppler feedback is considered in the heterogeneous problem and the calculation results are compared with the experimental data. The calculation results indicate that the calculation step 1.0E-7 s is sufficient for the model and the model provides results in good agreement with the experimental data. It is concluded that the present model with the DRM method can be used for transient analysis.

DOI： 10.1080/00223131.2019.1659874

Fast reproduction of time-dependent MOC calculations using the reduced order model based on the proper orthogonal and singular value decompositions

Tsujita K., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 123 巻 ( 1 ) 頁： 1349 - 1353 2020年

Subcriticality estimation using unscented Kalman filter for reactivity- And source-transients

Endo T., Yamamoto A., Yamanaka M., Pyeon C.H.

Transactions of the American Nuclear Society 123 巻 ( 1 ) 頁： 841 - 844 2020年

計算科学を活用した炉物理研究の最先端

山本章夫

年次大会 2020 巻 ( 0 ) 頁： K08101 2020年

A resonance calculation method using energy expansion based on a reduced order model: Use of ultra-fine group spectrum calculation and application to heterogeneous geometry

Kondo R., Endo T., Yamamoto A., Takeda S., Koike H., Yamaji K., Ieyama K., Sato D.

International Conference on Physics of Reactors: Transition to a Scalable Nuclear Future, PHYSOR 2020 2020-March 巻頁： 152 - 161 2020年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：International Conference on Physics of Reactors: Transition to a Scalable Nuclear Future, PHYSOR 2020

A Resonance calculation using energy Spectral Expansion (RSE) method has been recently proposed in order to efficiently treat complicated heterogeneous geometry and resonance interference effect. In the RSE method, ultra-fine group spectra are generated from ultra-fine group calculations in homogeneous geometry, and the spectra are expanded by the orthogonal basis on energy based on the singular value decomposition. Then the transport calculation for expansion coefficients is numerically performed, and the ultra-fine group spectra in the target heterogeneous regions are reconstructed by the expansion coefficients and the orthogonal basis. In this study, the RSE method is applied to multi-cell geometries including UO2, MOX and water cells, in which the resonance interference effect between UO2 and MOX fuel cells appears. The validity of the RSE method is confirmed through comparison with the reference effective multi-group cross sections obtained from the direct ultra-fine group calculation in the target heterogeneous geometry.

DOI： 10.1051/epjconf/202124702006

Experiment of unique combination number due to the third-order neutron-correlation

Endo T., Imai S., Watanabe K., Yamamoto A., Sakon A., Hashimoto K., Yamanaka M., Pyeon C.H.

International Conference on Physics of Reactors: Transition to a Scalable Nuclear Future, PHYSOR 2020 2020-March 巻頁： 1736 - 1744 2020年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：International Conference on Physics of Reactors: Transition to a Scalable Nuclear Future, PHYSOR 2020

From zero-power reactor noise measurement, the second- and third-order neutron correlation factors Y and y3 can be evaluated by analyzing mean, variance, the third-order central moment of neutron count data. Theoretically, it is expected that the neutron-correlation ratio Y3/Y2 converges to the unique combination number “3” at a near-critical state in an arbitrary system without depending on the fissile material and the neutron-energy spectrum of core, as the neutron counting gate width T increases sufficiently. Thus, the information about the difference between y3/Y2 and “3” has the potential to judge whether a target unknown system is critical or not and to roughly guess the absolute value of subcriticality. In this study, the detector dead-time effect on y3/Y2 is theoretically investigated based on the heuristic method using the single-, pair-, and trio-detection probabilities with the fundamental mode approximation. As a result, it is clarified that the saturation value of y3/Y2 converges to “3” independent of the dead time, when a target system is a critical state. For validation, actual experimental results are presented for a non-multiplication system driven by 252Cf spontaneous source, and shallow and deep subcritical systems at Japanese experimental facilities (UTR-KINKI and KUCA) under the shutdown state. Consequently, it is demonstrated that y3/Y2 shows a significant difference from “3” in the non-multiplication system. In the case of subcritical systems driven by inherent neutron sources, it is confirmed that the ratios y3/Y2 are close to the unique combination number “3,” and the slight difference from “3” is measurable by the long-time reactor noise measurement for the deep subcritical system.

DOI： 10.1051/epjconf/202124709004

Estimated criticality lower-limit multiplication factor of low-enriched uranium dioxide-concrete system using the bootstrap method

Hayashi T., Nishioka F., Endo T., Yamamoto A.

International Conference on Physics of Reactors: Transition to a Scalable Nuclear Future, PHYSOR 2020 2020-March 巻頁： 2690 - 2697 2020年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：International Conference on Physics of Reactors: Transition to a Scalable Nuclear Future, PHYSOR 2020

The present paper aims to evaluate the estimated criticality lower-limit multiplication factor of fuel debris in a form of uranium dioxide-concrete mixture for a study of criticality control on the fuel debris generated through the molten core concrete interaction in a severe accident of a light water reactor. The estimated criticality lower-limit multiplication factor is evaluated using the bootstrap method where the assumption of the normal distribution is not necessary. In addition, it is calculated taking into account correlation coefficients that represent the degrees of neutronic similarity between the target system and benchmark critical experiment systems, experimental uncertainties of benchmark data, and statistical uncertainties of calculated effective multiplication factor by a continuous energy Monte Carlo code. This paper shows that the estimated criticality lower-limit multiplication factor using the bootstrap method can be comparable with a baseline upper-subcritical-limit which is evaluated by Whisper-1.1 without margins of subcriticality for uncertainties from nuclear covariance data and undetected errors in software.

DOI： 10.1051/epjconf/202124717001

Development of FRENDY nuclear data processing code: Generation capability of multi-group cross sections from ace file

Yamamoto A., Endo T., Tada K.

Transactions of the American Nuclear Society 122 巻頁： 714 - 717 2020年

Application of bootstrap method to estimated criticality lower-limit multiplication factor considering nuclear data-induced uncertainty

Hayashi T., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 122 巻頁： 458 - 461 2020年

Loading pattern optimization for a PWR using Multi-Swarm Moth Flame Optimization Method with Predator 査読有り

Ishiguro Satomi, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2019年12月

Development of a reduced order model for severe accident analysis codes by singular value decomposition aiming probabilistic safety margin analysis 査読有り

Matsushita Masaki, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2019年12月

破損・堆積現象の解明を目指して(<特集>廃炉国際ワークショップ FDR2019)

倉田正輝, 山本章夫, 溝上伸也

日本機械学会誌 122 巻 ( 1211 ) 頁： 10 - 12 2019年10月

APPLICATION OF THE FOREST SHIELDING FACTOR TO THE MAXIMUM-LIKELIHOOD EXPECTATION MAXIMIZATION METHOD FOR AIRBORNE RADIATION MONITORING 査読有り

Sasaki M., Sanada Y., Yamamoto A.

RADIATION PROTECTION DOSIMETRY 184 巻 ( 3-4 ) 頁： 400-404 2019年10月

Transport consistent diffusion coefficient for CMFD acceleration and comparison of convergence properties

Yamamoto, A; Endo, T; Giho, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 56 巻 ( 8 ) 頁： 716 - 723 2019年8月

A simple treatment of increased gap due to fuel assembly bowing through correction of cross sections

Yamamoto, A; Endo, T; Nagano, H; Ohoka, Y; Yamamoto, K

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 56 巻 ( 6 ) 頁： 471 - 478 2019年6月

Development of assembly bowing model for pin-by-pin core calculations

Yamamoto K., Ohoka Y., Nagano H., Yamamoto A., Endo T.

International Conference on Nuclear Engineering, Proceedings, ICONE 2019-May 巻 2019年5月

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：International Conference on Nuclear Engineering, Proceedings, ICONE

Calculation capability of the pin-power distribution considering the variation of the assembly gap size due to assembly bowing was implemented in the pin-by-pin core calculation code SCOPE2. The previous studies show that the perturbation of geometry can be treated by the perturbation of macroscopic cross-section or atomic number density of the region instead of explicit consideration of geometry deformation. This methodology was applied to the assembly gap region: the variation of the gap size was treated by the correction on the macroscopic cross-section of the gap water. The correction model for the cross-section of gap water was implemented in SCOPE2 since it treats pin-by-pin cross-sections in a transport calculation. The correction was made according to the variation in the gap size. This implemented model has an advantage that the modification of the cross-section tables used in the core calculation is not necessary to consider the variation of gap size. For single assembly and multi-assemblies geometries, the assembly bowing model implemented in SCOPE2 was verified by comparing with the reference results using the assembly calculation code AEGIS, where the gap size perturbation was explicitly considered by varying the geometry of the gap region. It was confirmed that the variation of pin-power distribution due to the assembly bowing can be appropriately treated by SCOPE2 with the assembly bowing model.

Experimental validation of unique combination numbers for third- and fourth-order neutron correlation factors of zero-power reactor noise

Endo, T; Yamamoto, A; Yamanaka, M; Pyeon, CH

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 56 巻 ( 4 ) 頁： 322 - 336 2019年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

Zero-power reactor noise is useful for subcriticality measurements. Based on the nuclear reactor physics and the theory of neutron detection, this paper theoretically clarifies that the third- and fourth-order neutron correlation factors Y <inf>3</inf> and Y <inf>4</inf> can be expressed as functions of the second-order neutron correlation factor Y. In particular, if the neutron-counting gate width is sufficiently large, the saturation values Y <inf>3</inf> /Y 2 and Y <inf>4</inf> /Y 2 are almost equal to the unique combination numbers, ‘3’ and ‘15,’ for a source-driven subcritical system, where the subcriticality is less than 10,000 pcm. These unique combination numbers, ‘3’ and ‘15,’ for Y <inf>3</inf> /Y 2 and Y <inf>4</inf> /Y 3 were validated using actual zero-power reactor noise measurements carried out at the Kyoto University Criticality Assembly. In this study, the estimation of statistical errors and correlations between different gate widths owing to the bunching method was achieved by the moving block bootstrap method. For a sufficiently long measured reactor noise in a steady and unperturbed state, a statistical test for the evaluation of the critical state and the absolute measurement of subcriticality can be carried out by statistically quantifying the difference between the measurement value of Y <inf>3</inf> /Y 2 and the unique combination number.

DOI： 10.1080/00223131.2019.1580625

Comparison of theoretical formulae and bootstrap method for statistical error estimation of Feynman-α method

Endo, T; Yamamoto, A

ANNALS OF NUCLEAR ENERGY 124 巻頁： 606 - 615 2019年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

This paper discusses the statistical error of the variance-to-mean ratio, or the Y value in the Feynman-α method, from a single measurement of reactor noise. As a theoretical approach, two practical theoretical formulae are derived to estimate the statistical error of Y: one is based on the propagation of uncertainty with unbiased estimators for the third- and fourth-order central moments; the other is a simplified formula that reuses the Y value under the fundamental mode approximation, where the subcriticality is approximately less than 10,000 pcm. As a numerical approach, the bootstrap method is improved to efficiently estimate the correlations of Y between different counting gate widths, or covariance matrix Σ<inf>Y</inf>, due to the bunching method. Through an actual reactor noise experiment at the Kyoto University Criticality Assembly, the statistical errors of Y using the theoretical formulae and the bootstrap method are validated by comparing the reference statistical errors that are estimated from the multiple experiments of reactor noise. Furthermore, the impact of Σ<inf>Y</inf> on the statistical error of the prompt neutron decay constant α is numerically investigated. Consequently, in the case of this experimental analysis, it was confirmed that the bootstrap method with the correlations of Y seems to be slightly better from the viewpoint of the coverage probability of the estimated confidence intervals of α although the fitting error method without the correlation of Y could be useful for the order estimation of the statistical error of α.

DOI： 10.1016/j.anucene.2018.10.032

Inverse estimation methods of unknown radioactive source for fuel debris search

Sugaya, S; Endo, T; Yamamoto, A

ANNALS OF NUCLEAR ENERGY 124 巻頁： 49 - 57 2019年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

To identify the distribution of fuel debris remaining in the reactor vessel and/or the containment vessel of Fukushima Daiichi NPS, we focused on the inverse estimation of radioactive source distribution using the measured radiation counts. The Maximum Likelihood-Expectation Maximization (ML-EM) and the Moore-Penrose Matrix Inverse (MPMI) methods are examined. The ML-EM method has been used for the image reconstruction of computed tomography, and the MPMI method is one of the solution methods for simultaneous linear equations with the underdetermined condition. A simple calculation model simulating a containment vessel was constructed including detectors and radiation sources. In an actual situation, a sufficient number of radiation measurement positions would not be available owing to the complexity of structures inside the containment vessel. Thus, the number of radiation measurement points (number of constraints) is smaller than that of radiation source positions. It means that an underdetermined inverse problem should be solved. The detection probability of radiation (neutron or photon) is calculated by the adjoint transport calculation since the detection probability is used as the coupling coefficient between radiation counts at a detector and a radioactive source. The result of estimation using the ML-EM or the MPMI method indicates that the accuracy of estimation depends on the distance between a radiation source and a detector, and measurement positions of radiation count. The ML-EM and the MPMI methods show different prediction accuracy depending on the prediction condition. It is found that reasonable prediction accuracy would be obtained when the detectors are placed at the vicinity of radiation sources of interest.

DOI： 10.1016/j.anucene.2018.09.022

A New Interpretation of Discontinuity Factor

Yamamoto, A; Endo, T

NUCLEAR SCIENCE AND ENGINEERING 193 巻 ( 9 ) 頁： 991 - 997 2019年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

A new interpretation of the discontinuity factor (DF) for scalar flux, partial current, and angular flux is discussed. Conventionally, the DF is considered as the discontinuous condition of scalar flux, partial current, or angular flux at an interface. In the new interpretation, the DF is considered as the refractive index of materials for partial current or angular flux that conserves odd-parity or odd-moment angular flux at an interface of different materials. It is related to the transmission and reflection of partial current or angular flux at an interface where different materials are adjacent. Using the present interpretation, a fundamental issue of neutron balance (i.e., artificial loss or production of neutrons at an interface due to discontinuous condition), which would appear in the conventional interpretation of DF, can be resolved.

DOI： 10.1080/00295639.2019.1579514

Utilization of Regionwise Even-Parity Discontinuity Factor to Reduce Discretization Error of MOC

Yamamoto, A; Giho, A; Endo, T

NUCLEAR SCIENCE AND ENGINEERING 193 巻 ( 3 ) 頁： 253 - 268 2019年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

To reduce angular and spatial discretization error of the method of characteristics with a coarse calculation condition, the regionwise even-parity discontinuity factor (EPDF) for transport calculations is evaluated through an iterative procedure using only the regionwise scalar flux, i.e., without the odd-parity angular flux, the partial current, or the net current at the region boundary. The regionwise EPDF is evaluated in a single-assembly geometry with the reflective boundary condition. The evaluated EPDF is applied to a 2 × 2 colorset assembly and core configurations, and the performance is compared to that of the conventional superhomogenization (SPH) method. The calculation results indicate that (1) no convergence issue is observed during the iteration process to estimate the EPDF, (2) the performance of the regionwise EPDF is better than that of the conventional SPH method, and (3) the normalization of the EPDF is necessary to incorporate different surface scalar flux levels among different types of fuel assemblies.

DOI： 10.1080/00295639.2018.1516961

DEVELOPMENT OF ASSEMBLY BOWING MODEL FOR PIN-BY-PIN CORE CALCULATIONS

Yamamoto Kento, Ohoka Yasunori, Nagano Hiroaki, Yamamoto Akio, Endo Tomohiro

The Proceedings of the International Conference on Nuclear Engineering (ICONE) 2019.27 巻 ( 0 ) 頁： 1022 2019年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：The Japan Society of Mechanical Engineers

DOI： 10.1299/jsmeicone.2019.27.1022

基礎から分かる未臨界

遠藤知弘, 辻本和文, 山本章夫

日本原子力学会誌ATOMOΣ 61 巻 ( 10 ) 頁： 734 - 738 2019年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本原子力学会

臨界管理や原子炉の運転等において，体系の中性子実効増倍率は最も基本的な概念の一つである。実効増倍率が1のときを臨界，1未満のときを未臨界と呼ぶことは良く知られているが，実は両者は大きく異なる状態である。本連載講座では，核燃料サイクル施設の臨界安全，原子炉施設の臨界管理や福島第一原子力発電所のデブリ取り出し等で重要となる未臨界状態について，臨界状態の原子炉との違い，炉物理的な特徴，未臨界状態であることを評価・測定する手法などを解説する。第1回では，臨界・未臨界の炉物理的な違いについて紹介する。

DOI： 10.3327/jaesjb.61.10_734

Uncertainty quantification/reduction of BWR core characteristics considering cross section and thermal-hydraulics uncertainties

炉物理の使命

千葉豪, 山本章夫

日本原子力学会誌ATOMOΣ 61 巻 ( 4 ) 頁： 254 - 256 2019年

Ito M., Yamamoto A., Endo T., Ama T.

Transactions of the American Nuclear Society 120 巻頁： 851 - 854 2019年

Resonance calculation using energy spectral expansion based on reduced order model: Application to heterogeneous geometry

Yamamoto A., Kondo R., Endo T., Takeda S., Koike H., Yamaji K., Sato D.

Transactions of the American Nuclear Society 121 巻頁： 1316 - 1320 2019年

A resonance calculation method using energy expansion bases based on a reduced order model

Yamamoto A., Endo T., Takeda S., Koike H., Yamaji K., Ieyama K., Sato D.

International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 頁： 1081 - 1092 2019年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019

A Resonance calculation using energy Spectral Expansion bases (the RSE method) is newly proposed. In the present method, an ultra-fine group spectrum appeared in a resonance calculation is expanded by expansion bases on energy. The transport equation for the expansion coefficients is derived, which is the simultaneous first order differential equation for the expansion coefficients. The present method is applied to a one-dimensional slab geometry composed of 238U. Comparisons of the results obtained by the present and the ultra-fine group (reference) methods show the fundamental validity of this method.

Application of various superhomogenization (SPH) methods for the method of characteristics

Sawada K., Endo T., Yamamoto A.

International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 頁： 1534 - 1543 2019年

To reduce the error due to the difference between the fine and the coarse calculation conditions in a transport calculation using method of characteristics (MOC), the superhomogenization (SPH) method has been widely used. However, the conventional SPH method has a problem with numerical stability in the iterative calculations for the estimation of SPH factors, especially when local strong absorbers exist in a calculation geometry. To address this problem, improvements of the SPH methods were tested to reduce the angular and spatial discretization error of the MOC. The performances of the various SPH methods were confirmed in pressurized water reactor (PWR) 2 × 2 fuel assembly geometries and in a PWR core geometry. The results of verification indicate that in a core geometry the improved SPH methods provide better accuracy than that of the conventional SPH.

Calculation method of estimated criticality lower-limit multiplication factor using the bootstrap method

Hayashi T., Endo T., Yamamoto A.

International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 頁： 1874 - 1885 2019年

The present paper describes a calculation method of the estimated criticality lower-limit multiplication factor (ECLLMF) using the bootstrap method, which is an uncertainty evaluation method. In the conventional method, the normal distribution is assumed for a probability distribution with respect to calculation biases of effective multiplication factors (keff) to evaluate ECLLMF. To propose a methodology without the assumption of the normal distribution, an estimation method of ECLLMF is newly developed using the bootstrap method, where the assumption of the normal distribution is not necessary. From the verification results, it is confirmed that the estimation result using the non-parametric bootstrap method is more reasonable than that using the conventional method, when a probability distribution of keff does not obey the normal distribution.

Data assimilation using subcritical measurement of prompt neutron decay constant

Endo T., Yamamoto A.

International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 頁： 1864 - 1873 2019年

The prompt neutron decay constant α can be directly measured by the reactor noise analysis method (e.g., the Feynman-α method) in a steady-state subcritical system. In this study, the applicability of the data assimilation techniques (i.e., the bias factor and cross section adjustment methods) using a subcritical measurement of α conducted at the Kyoto University Critical Assembly (KUCA) was investigated to reduce the nuclear data-induced uncertainty of keff.The sensitivity coefficients of keff and α with respect to the nuclear data were efficiently estimated using a deterministic SN transport code with the first-order perturbation theory. As a result, a priori relative uncertainty of keff due to the 56 group SCALE covariance data can be reduced. The experimental value of α contributes to improving nuclear data of fission spectrum X and total fission neutron number v via strong correlations between X and prompt Xp and between v and prompt vp.

Development of efficient data sampling method to construct surrogate model of severe accident analysis code for SBO aiming probabilistic safety margin analysis

Matsushita M., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 121 巻頁： 979 - 982 2019年

Implementation of random sampling for ace-format cross sections using frendy and application to uncertainty reduction

Kondo R., Endo T., Yamamoto A., Tada K.

International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 頁： 1493 - 1502 2019年

For uncertainty quantification and reduction using the random sampling technique through a continuous energy Monte Carlo method, the perturbation capability of nuclear data libraries for MCNP is developed using a nuclear data processing system FRENDY, which is being developed by JAEA. The implemented capability is applied to uncertainty quantification using the random sampling method and to uncertainty reduction of kinetic parameter based on the bias factor method. Validity of the implemented capability is confirmed through comparison with the results obtained by the conventional sandwich formula using SCALE and MCNP.

Reduction of macroscopic and microscopic cross section table size for heterogeneous core calculation using dimensionality reduction

Yamamoto M., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 121 巻頁： 1309 - 1312 2019年

Underestimation of statistical uncertainty of local tallies in Monte Carlo eigenvalue calculation for simple and LWR lattice geometries

Hayashi, K; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 55 巻 ( 12 ) 頁： 1434 - 1458 2018年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

A prediction method of the true variance of local tally in a Monte Carlo (MC) critical calculation is developed. In the MC calculation, the effective multiplication factor ((Formula presented.)) and the fission rate distribution are estimated by simulating fission chain reactions. The statistical uncertainty of calculation result is commonly estimated by the standard error based on the central limit theorem. However, the evaluated statistical uncertainty would be underestimated when the inter-cycle correlation is not appropriately taken into account. In this study, a theoretical formula of the underestimation ratio (UR) of the statistical uncertainty for a local tally is derived using the eigenfunction expansion and the Autoregressive model. Note that the UR is defined by the ratio of uncertainty estimated by a MC calculation to the true statistical uncertainty. The proposed method is applied to one-dimensional slab and multi-assembly geometries with reflective boundary conditions. In the one-dimensional slab geometry, the prediction results of UR show reasonable agreement with the reference. In the multi-assembly geometry, on the other hand, the prediction results of UR are agreement with the reference regarding the relative spatial shape but there are considerable differences in the absolute values of UR.

DOI： 10.1080/00223131.2018.1513875

Subchannel void distribution correction model for the two-stage core analysis method in boiling water reactors

Mitsuyasu, T; Aoyama, M; Yamamoto, A

ANNALS OF NUCLEAR ENERGY 122 巻頁： 146 - 154 2018年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

The two-stage core analysis method is widely used for BWR core analysis. The purpose of this study is to develop a subchannel void distribution correction model for the two-stage core analysis method using an assembly-based thermal-hydraulics calculation in the core analysis stage. The model assumes two kinds of subchannel void distribution gradients along with the two diagonal lines in the horizontal cross section of a BWR fuel assembly. The model appends and tabulates the difference of the subchannel perturbation condition from the base condition in the lattice physics, and evaluates the tilts within the 2D lattice physics scheme, and couples those results with 3D subchannel analysis which evaluates the thermal-hydraulics characteristics within the coolant flow area divided as some subchannel regions. The developed model is evaluated using a heterogeneous and a small core problem. The model gives a better power distribution compared with that of the authors’ previous model. As a result, the model can incorporate the subchannel effect into the current two-stage core calculation method.

DOI： 10.1016/j.anucene.2018.08.041

Sensitivity analysis of prompt neutron decay constant using perturbation theory

Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 55 巻 ( 11 ) 頁： 1245 - 1254 2018年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

Experimental results of prompt neutron decay constant α is useful information to validate numerical results of ω-eigenvalue for spatial and energetic fundamental mode. In order to accomplish the data assimilation technique using α, it is desirable to establish an efficient numerical calculation method for sensitivity coefficient analysis of α For this purpose, the numerical calculation method using the first-order perturbation theory is investigated. A specific theoretical formula is derived to evaluate the sensitivity coefficient of α to nuclear data. The derived rigorous formula utilizes forward and adjoint eigenfunctions which consist of neutron flux and delayed neutron precursor densities. Using the prompt approximation, the derived formula can be simplified without the term involving the delayed neutron precursor densities. By calculating α using the multi-energy-group neutron transport code for an ICSBEP benchmark problem, the derived formula for sensitivity analysis using the perturbation theory is verified by comparing with the reference results using the direct method. Consequently, the efficient numerical procedures for uncertainty quantification of α can be established by the aid of the sensitivity coefficients based on the perturbation theory.

DOI： 10.1080/00223131.2018.1491902

Estimation of sensitivity coefficient based on lasso-type penalized linear regression

Reduction of Cross Section Table Size for Core Analysis Using Dimensionality Reduction Technique 査読有り

M. Yamamoto, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. 119 巻頁： 1226-1228 2018年11月

A Simple Treatment of Bowed Assembly Gap Through Correction of Cross Section 査読有り

A. Yamamoto, T. Endo, K. Yamamoto, Y. Ohoka, H. Nagano

Trans. Am. Nucl. Soc. 119 巻頁： 1199-1202 2018年11月

Transport Consistent Diffusion Coefficient for CMFD Acceleration 査読有り

A. Yamamoto, T. Endo

Trans. Am. Nucl. Soc. 119 巻頁： 1179-1181 2018年11月

Estimation of Subcriticality in Dollar Units Based on Integral Method for Arbitrary State-Change in Subcritical System 査読有り

A. Nonaka, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. 119 巻頁： 1112-1115 2018年11月

Surrogate Model of Severe Accident Analysis Code for SBO Aiming Probabilistic Safety Margin Analysis 査読有り

M. Matsushita, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. 119 巻頁： 900-903 2018年11月

Estimation of Subcriticality using Particle Filter Method 査読有り

T. Ikeda, T. Kimura, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. 118 巻頁： 851-854 2018年6月

Quantification of Modeling Approximation Error of Pin-Cell Calculation Using Kriging and Principal Component Analysis 査読有り

T.Hanai, A. Yamamoto, T. Endo, K. Yamamoto, Y. Ohoka, H. Nagano

Trans. Am. Nucl. Soc. 118 巻頁： 875－878 2018年6月

Inverse Estimation Methods of Unknown Radioactive Source for Fuel Debris Search 査読有り

S. Sugaya, T. Endo, A. Yamamoto

Proc. PHYSOR201 頁： [USB-DRIVE] 2018年4月

Estimation of Subcriticality in Dollar Units using Integral Method for Subcritical System 査読有り

A. Nonaka, T. Endo, A. Yamamoto

Proc. PHYSOR2018 頁： [USB-DRIVE] 2018年4月

Cache Efficient Flux Region Assignment for the Method of Characteristics 査読有り

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2018 頁： [USB-DRIVE] 2018年4月

Estimation of Region-Wise Even-Parity Discontinuity Factor for MOC Through Iterative Procedure 査読有り

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2018 頁： [USB-DRIVE] 2018年4月

Development of Reduced Order Model of Severe Accident Analysis Code for Probabilistic Safety Margin Analysis

M. Matsushita, T. Endo, A. Yamamoto, T. Kitao

Proc. PHYSOR2018 頁： [USB-DRIVE] 2018年4月

Sensitivity Coefficient Analysis of Omega-Eigenvalue based on First-Order Perturbation Theory 査読有り

頁： [USB-DRIVE] 2018年4月

Katano, R; Endo, T; Yamamoto, A; Tsujimoto, K

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 55 巻 ( 10 ) 頁： 1099 - 1109 2018年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

We proposed the penalized regression ‘adaptive smooth-lasso’ for the estimation of sensitivity coefficients of the neutronics parameters. The proposed method utilizes the variation of the microscopic cross-sections and the neutronics parameters obtained by random sampling. The weighted penalty term of the proposed method is more appropriate for the estimation of the sensitivity of neutronics parameters to the microscopic cross-section than that of the conventional methods. In a numerical verification calculation, sensitivity coefficients of k<inf>eff</inf> of an accelerator-driven system are estimated using the proposed method, the conventional penalized regression, and the direct method. Comparison of these results indicates that the proposed method is superior to the conventional penalized linear regression from the viewpoint of reproduction of the reference sensitivity coefficients obtained by the direct method. Through the verification calculations, the proposed method can be a candidate for a practical method to estimate the sensitivity coefficients with low calculation cost.

DOI： 10.1080/00223131.2018.1479988

Radially and azimuthally dependent resonance self-shielding treatment for general multi-region geometry based on a unified theory

Koike, H; Kirimura, K; Yamaji, K; Kosaka, S; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 55 巻 ( 1 ) 頁： 41 - 65 2018年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

A unified resonance self-shielding method, which can treat general sub-divided fuel regions, is developed for lattice physics calculations in reactor physics field. In a past study, a hybrid resonance treatment has been developed by theoretically integrating equivalence theory and ultra-fine-group slowing-down calculation. It can be applied to a wide range of neutron spectrum conditions including low moderator density ranges in severe accident states, as long as each fuel region is not sub-divided. In order to extend the method for radially and azimuthally sub-divided multi-region geometry, a new resonance treatment is established by incorporating the essence of sub-group method. The present method is composed of two-step flux calculation, i.e. ‘coarse geometry + fine energy’ (first step) and ‘fine geometry + coarse energy’ (second step) calculations. The first step corresponds to a hybrid model of the equivalence theory and the ultra-fine-group calculation, and the second step corresponds to the sub-group method. From the verification results, effective cross-sections by the new method show good agreement with the continuous energy Monte-Carlo results for various multi-region geometries including non-uniform fuel compositions and temperature distributions. The present method can accurately generate effective cross-sections with short computation time in general lattice physics calculations.

DOI： 10.1080/00223131.2017.1384704

Dimension-reduced cross-section adjustment method based on minimum variance unbiased estimation

Yokoyama, K; Yamamoto, A; Kitada, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 55 巻 ( 3 ) 頁： 319 - 334 2018年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

A new formulation of the cross-section adjustment methodology with the dimensionality-reduction technique has been derived in the light of the fact that it is often used under the condition of ill-posed problem, where the number of integral experimental quantities is less than the number of adjusted nuclear data parameters. This new formulation is proposed as the dimension-reduced conventional cross-section adjustment method (DRCA). The derivation of DRCA is based on the minimum variance unbiased estimation (MVUE), and the assumption of normal distribution is not used. The result of DRCA depends on a user-defined matrix that determines the dimension-reduced feature subspace. We examined three variations of DRCA, namely, DRCA1, DRCA2, and DRCA3, which employ (1) the nuclear data covariance matrix as the user-defined matrix, (2) the sensitivity coefficient matrix postmultiplied by the nuclear data covariance matrix, and (3) the sensitivity coefficient matrix, respectively. Mathematical investigation and numerical verification revealed that DRCA2 is equivalent to the currently widely used cross-section adjustment method. Moreover, DRCA3 is found to be identical to the cross-section adjustment method based on MVUE, which has been proposed in the previous study.

DOI： 10.1080/00223131.2017.1397563

Flux Region Assignment Method Using Ray Trace Information for the Method of Characteristics to Improve Cache Efficiency

Estimation of Sensitivity Coefficient based on Lasso-type Penalized Linear Regression 査読有り

R. Katano, T. Endo, A. Yamamoto, K. Tsujimoto

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 55 巻頁： 1099-1109 2018年

Utilization of Region-wise Even-Parity Discontinuity Factor to Reduce Discretization Error of MOC 査読有り

A. Yamamoto, A. Giho, T. Endo

Nuclear Science and Engineering 193 巻頁： 253-268 2018年

Flux Region Assignment Method using Ray Trace Information for the Method of Characteristics to Improve Cache Efficiency

A. Yamamoto, A. Giho, T. Endo

Nuclear Science and Engineering 192 巻頁： 243-250 2018年

Yamamoto, A; Giho, A; Endo, T

NUCLEAR SCIENCE AND ENGINEERING 192 巻 ( 3 ) 頁： 240 - 253 2018年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

A flux region assignment algorithm to increase cache efficiency for the method of characteristics (MOC) is proposed. In order to minimize the stride of memory access, flux region identifications are assigned based on the ray trace sequence during the MOC calculation. The present method is implemented in the three-dimensional transport code GENESIS and its performance is confirmed through verification calculations ranging from single pressurized water reactor (PWR) fuel assembly to PWR full-core benchmark problems. Quantitative comparison of cache efficiency is carried out and the present method shows improved cache efficiency, which results in a reduction in computation time. The present method can reduce computational time by improving cache efficiency while suppressing memory requirement.

DOI： 10.1080/00295639.2018.1501978

リスク評価とマネジメントに関するアジアシンポジウム開催報告

山口彰, 山本章夫, 成宮祥介

日本原子力学会誌ATOMOΣ 60 巻 ( 6 ) 頁： 362 - 363 2018年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：一般社団法人日本原子力学会

リスクに関する国際シンポジウムは，日中韓を中心に横浜で開催された。20年ほど前に日韓で始まった日韓PSAワークショップにその起源をおくもので，原子力施設に関するリスク評価の専門家が一堂に会し，充実した意見交換，議論が行われた。リスクの本格活用に臨む我が国としては多くの知見を得たシンポジウムとなった。

DOI： 10.3327/jaesjb.60.6_362

原子炉物理分野の研究開発ロードマップ2017:次世代が考える炉物理の未来

山本章夫, 千葉豪, 桐村一生, 三木陽介, 横山賢治

日本原子力学会誌ATOMOΣ 60 巻 ( 4 ) 頁： 241-245 2018年

記述言語：英語掲載種別：研究論文（学術雑誌）

炉物理部会の傘下に設置された「炉物理ロードマップ調査・検討」WGにおけるロードマップ策定の概要を紹介する。本ロードマップの特徴は，①次世代を担う若手の技術者・研究者を中心に議論・策定を進めたこと，②現状から類推して課題を設定するフォアキャストアプローチに加え，原子炉物理分野のビジョンとミッションを検討し，これらを達成するために解決すべき課題をバックキャストアプローチにより設定したこと，にある。本ロードマップの詳細は，報告書として炉物理部会のホームページより閲覧可能である。

DOI： 10.3327/jaesjb.60.4_241

Surrogate model of severe accident analysis code for SBO aiming probabilistic safety margin analysis

Matsushita M., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 119 巻頁： 900 - 903 2018年

Cache efficient flux region assignment for the method of characteristics

Yamamoto A., Giho A., Endo T.

International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems Part F168384-2 巻頁： 788 - 799 2018年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems

A flux region assignment algorithm to increase cache efficiency for the method of characteristics is proposed. In order to minimize the stride of memory access, flux region IDs are assigned based on the ray trace sequence during the method of characteristics calculation. The present method is implemented in the three-dimensional transport code GENESIS and its performance is confirmed through verification calculations ranging from single PWR fuel assembly to PWR full core benchmark problems. The present method can reduce computational time by improving cache efficiency while suppressing memory requirement.

Development of reduced order model of severe accident analysis code for probabilistic safety margin analysis

Matsushita M., Endo T., Yamamoto A., Kitao T.

International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems Part F168384-5 巻頁： 3042 - 3053 2018年

For probabilistic safety margin analysis, we developed a reduced order model (ROM) that reconstruct calculation results of typical severe accident progressions obtained by the severe accident analysis code, MAAP. The ROM is applied for fast reconstruction of time series plant parameters (e.g., pressure and temperature) obtained by the MAAP code. The ROM is applied to two severe accident scenarios, i.e., the station black out (SBO) with loss of all feed water capabilities and the large break loss of coolant accident (large break LOCA) without the emergency core cooling system (ECCS) capability. Verification results indicate that the ROM reasonably reproduces temporal variation of plant parameters with a few bases obtained by the ROM, which enables very fast reconstruction of complicated accident progression of a severe accident.

Development of the uncertainty quantification method of activation in reactor structures using reduced-order modeling

Yokoi K., Endo T., Yamamoto A., Hayashi K., Mizuno R., Kimura Y.

International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems Part F168384-3 巻頁： 1793 - 1804 2018年

Uncertainty quantification of activation in structure materials around a nuclear reactor is important for efficient planning of decommissioning. In order to quantify the uncertainty of activation in reactor structures, neutron shielding calculations are necessary. Since the neutron shielding calculation is performed for spatially large regions around a reactor, it requires a lot of computation time especially in the case of multi-dimensional geometry. In this study, the reduced-order modeling (ROM) is applied to the sensitivity and uncertainty analysis of activation in reactor structures to reduce computation time. The ROM can reduce calculation cost for evaluation of sensitivity coefficients by identifying important or sensitive subspace (active subspace, AS) in input data. In this study, an AS is constructed by the several sensitivity coefficients in reactor structures which are evaluated by the perturbation theory (PT). Sensitivity coefficients of activation throughout reactor structures are estimated using the AS and the uncertainty of activation is evaluated by the "sandwich formula." The calculation results indicate that the uncertainty of the activation in reactor structures can be reproduced with low calculation cost (approximately 30 neutron transport calculations) using the ROM in one-dimensional geometry of a 500 MWe class BWR.

Estimation of region-wise even-parity discontinuity factor for MOC through iterative procedure

Yamamoto A., Giho A., Endo T.

International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems Part F168384-3 巻頁： 1892 - 1903 2018年

To reduce angular and spatial discretization error of MOC with a coarse calculation condition, region-wise even-parity discontinuity factor (EPDF) for transport calculations is evaluated through an iterative procedure using only region-wise scalar flux, i.e., without odd parity angular flux, partial-, or net-current at region boundary. Region-wise EPDF is evaluated in a single assembly geometry with reflective boundary condition. The evaluated EPDFs are applied to a 2x2 colorset assembly configuration and its performance is compared to the conventional superhomogenization (SPH) method. The calculation results indicate that 1) no convergence issue is observed during the iteration process to estimate EPDF, 2) performance of the region-wise EPDF is better than that of the conventional SPH method.

Estimation of subcriticality in dollar units based on integral method for arbitrary state-change in subcritical system

Nonaka A., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 119 巻頁： 1112 - 1115 2018年

Estimation of subcriticality in dollar units using integral method for subcritical system

Nonaka A., Endo T., Yamamoto A.

International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems Part F168384-5 巻頁： 3271 - 3282 2018年

A subcriticality measurement method using the integral method is developed for any stepwise transient. The integral method usually applied to a negative reactivity insertion using the rod-drop and the source-jerk methods. In this study, it is clarified that the integral method can be applied to measure positive reactivity insertion. During refueling of a reactor, not only reactivity but also neutron source intensity and neutron generation time simultaneously change. In order to accurately monitor the subcriticality under these conditions, variations of these parameters must be taken into consideration. Therefore, a subcriticality measurement method is developed, which is applicable to not only variation of reactivity but also simultaneous variations of neutron source intensity and neutron generation time. Furthermore, the present method utilizes only measurement value of neutron count rate, thus the proposed method is practical. Verification calculations are carried out for a step-wise change of reactivity, neutron source intensity, and neutron generation time. The results indicate that reactivity is accurately predicted for the change of the neutron source intensity, which is difficult to achieve by the neutron source multiplication method. On the other hand, although the change of the neutron generation time has considerable impacts on the estimated result of subcriticality, the predicted error is less than 10% for very large variation of neutron generation time.

Estimation of subcriticality using particle filter method

Ikeda T., Kimura T., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 118 巻頁： 851 - 854 2018年

Estimation of subcriticality using particle filter method

Ikeda T., Kimura T., Endo T., Yamamoto A.

AISTech - Iron and Steel Technology Conference Proceedings 2018-May 巻頁： 851 - 854 2018年

Inverse estimation methods of unknown radioactive source for fuel debris search

Sugaya S., Endo T., Yamamoto A.

International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems Part F168384-4 巻頁： 2632 - 2643 2018年

To identify distribution of fuel debris remaining in the reactor vessel and/or the containment vessel of Fukushima Daiichi NPS, we focused on the inverse estimation of radioactive source distribution using measured values of radiation counts. The Maximum Likelihood-Expectation Maximization (ML-EM) method and the Moore-Penrose Matrix Inverse (MPMI) method are examined. The ML-EM method has been used for image reconstruction of computed tomography, and the MPMI method is one of the solution methods for simultaneous linear equations. A simple calculation model simulating the containment vessel were constructed including detectors and radiation sources. In actual situation, sufficient number of radiation measurement positions would not be available owing to the complexity of structures inside the containment vessel. Thus, the number of radiation measurement points (number of constraints) are smaller than positions of radiation source. It means that an underdetermined inverse problem should be solved. The detection probability of radiation (neutron or photon) is calculated by the adjoint transport calculation since the detection probability is used as the coupling coefficient between a radiation count at a detector and a radioactive source. Result of estimation using the ML-EM or the MPMI method indicates that the accuracy of estimation depends on the distance between a radiation source and a detector, and radiation count measurement positions. The ML-EM and the MPMI methods show different prediction accuracy depending on the calculation condition. It is found that the detectors should be placed at vicinity of radiation sources of interest and that the applicability of the inverse estimation does not strongly depend on the radioactivity distribution.

Quantification of modeling approximation error of pin-cell calculation using kriging and principal component analysis

Hanai T., Yamamoto A., Endo T., Yamamoto K., Ohoka Y., Nagano H.

Transactions of the American Nuclear Society 118 巻頁： 875 - 878 2018年

Quantification of modeling approximation error of pin-cell calculation using kriging and principal component analysis

Hanai T., Yamamoto A., Endo T., Yamamoto K., Ohoka Y., Nagano H.

AISTech - Iron and Steel Technology Conference Proceedings 2018-May 巻頁： 875 - 878 2018年

Reduction of cross section table size for core analysis using dimensionality reduction technique

Yamamoto M., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 119 巻頁： 1226 - 1228 2018年

Sensitivity coefficient analysis of omega-eigenvalue based on first-order perturbation theory

Endo T., Yamamoto A.

International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems Part F168384-2 巻頁： 1240 - 1253 2018年

Experimental results of prompt neutron decay constant α is useful information to validate numerical results of ω -eigenvalue for spatial and energetic fundamental mode. In order to accomplish the data assimilation technique using α, it is desirable to establish an efficient numerical calculation method for sensitivity coefficient analysis of ω -eigenvalue. For this purpose, the numerical calculation method using the standard first-order perturbation theory is investigated. A specific theoretical formula is derived to evaluate the sensitivity coefficient of ω to nuclear data. The derived formula utilizes forward and adjoint eigenfunctions which consist of neutron flux and delayed neutron precursor densities. Through a feasibility study based on the multi-group diffusion calculation, the derived formula is verified by comparing with the reference results using the direct method. In addition, it is confirmed that the prompt approximation is applicable to the evaluation of sensitivity coefficient of α for a subcritical state where α is sufficiently larger than decay constants of delayed neutron precursors.

Estimation of Modeling Approximation Error of Core Analysis Using the Surrogate Model with Kriging 査読有り

Tomomi Hanai, Tomohiro Endo, Yasuhiro Kodama, Yasunori Ohoka, Akio Yamamoto

rans. Am. Nucl. Soc. 117 巻頁： 1269-1272 2017年11月

Application of the GENESIS Code to the Kobayashi 3D Benchmark Problem 査読有り

Akio Yamamoto, Akinori Giho, Tomohiro Endo

Trans. Am. Nucl. Soc. 117 巻頁： 1403-1406 2017年11月

Recent developments in the GENESIS code based on the Legendre polynomial expansion of angular flux method Open Access

Yamamoto, A; Giho, A; Endo, T

NUCLEAR ENGINEERING AND TECHNOLOGY 49 巻 ( 6 ) 頁： 1143 - 1156 2017年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Engineering and Technology

This paper describes recent development activities of the GENESIS code, which is a transport code for heterogeneous three-dimensional geometry, focusing on applications to reactor core analysis. For the treatment of anisotropic scattering, the concept of the simplified Pn method is introduced in order to reduce storage of flux moments. The accuracy of the present method is verified through a benchmark problem. Next, the iteration stability of the GENESIS code for the highly voided condition, which would appear in a severe accident (e.g., design extension) conditions, is discussed. The efficiencies of the coarse mesh finite difference and generalized coarse mesh rebalance acceleration methods are verified with various stabilization techniques. Use of the effective diffusion coefficient and the artificial grid diffusion coefficients are found to be effective to stabilize the acceleration calculation in highly voided conditions.

DOI： 10.1016/j.net.2017.06.016

Estimation of modeling approximation errors using data assimilation with the minimum variance approach

Uncertainty Quantification of Activation Due to Cross Section Data in Neutron Shielding Calculation 査読有り

Kimihiro Yokoi,Tomohiro Endo,Akio Yamamoto,Ryoji Mizuno,Yoshio Kimura

Proc. 2017 International. Cogress on Advances in Nuclear Power Plants 2017年4月

Application of Bias Factor Method using Random Sampling Technique for Critical Eigenvalue Prediction of BWR 査読有り

Motohiro Ito,Tomohiro Endo,Akio Yamamoto,Yusuke Kuroda,Takashi Yoshii

Proc. 2017 International Cogress on Advances in Nuclear Power Plants 2017年4月

Development of Dynamic Probabilistic Risk Assessment Model for PWR using Simplified Plant Simulation Method 査読有り

Shohei Otsuki,Tomohiro Endo,Akio Yamamoto

Proc. 2017 International Cogress on Advances in Nuclear Power Plants 2017年4月

Development of GENESIS, a Three-dimensional Heterogeneous Transport Code based on the LEAF Method 査読有り

Akio Yamamoto,Akinori Giho,Tomohiro Endo

Proc. Int. Conf. on Math. and Comp. Methods Applied to Nucl. Sci. & Eng. (M&C2017) 2017年4月

Theoretical Discussion of Statistical Error of Variance-to-Mean Ratio 査読有り

Tomohiro Endo,Akio Yamamoto

Proc. Int. Conf. on Math. and Comp. Methods Applied to Nucl. Sci. & Eng. (M&C2017) 2017年4月

Inverse Estimation of Unknown Radioactive Source using Detection Probability by Adjoint Calculation

Shinji Sugaya,Tomohiro Endo,Akio Yamamoto

Proc. Int. Conf. on Math. and Comp. Methods Applied to Nucl. Sci. & Eng. (M&C2017) 2017年4月

Uncertainty Quantification of Bell Factor for Sjöstrand Method due to Cross-section Data for MA core 査読有り

Toshiki Kimura,Tomohiro Endo,Akio Yamamoto

Proc. Int. Conf. on Math. and Comp. Methods Applied to Nucl. Sci. & Eng. (M&C2017) 2017年4月

Yamamoto, A; Kinoshita, K; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 54 巻 ( 4 ) 頁： 459 - 471 2017年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

In this paper, we estimate prediction errors owing to approximations in calculation models (modeling approximation error) using the data assimilation method. Correlations between the modeling approximation error and neutronics parameters obtained through calculations are evaluated in test configurations and then the evaluated correlations are used to predict the modeling approximation errors in design configuration. Formulae to estimate the modeling approximation error using the correlations are derived based on the minimum variance approach and the physical interpretation of the formulae is discussed through simple cases. The proposed method is applied in 2 × 2 and 3 × 3 fuel assembly geometries using specifications of the KAIST benchmark problem. The correlation between the modeling approximation error and parameters (neutron leakage in each fuel assembly) is estimated in 2 × 2 fuel assemblies and then the modeling approximation error in 3 × 3 fuel assemblies is predicted using the correlation. The calculation results not only indicate feasibility of the present method, but also suggest a need for further investigation on the assumptions used in the present study, i.e. applicability and robustness of the correlation among different geometries.

DOI： 10.1080/00223131.2017.1286271

Automated generation of burnup chain for reactor analysis applications

Tran, VP; Tran, HN; Yamamoto, A; Endo, T

KERNTECHNIK 82 巻 ( 2 ) 頁： 196 - 205 2017年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Kerntechnik

This paper presents the development of an automated generation of burnup chain for reactor analysis applications. Algorithms are proposed to reevaluate decay modes, branching ratios and effective fission product (FP) cumulative yields of a given list of important FPs taking into account intermediate reactions. A new burnup chain is generated using the updated data sources taken from the JENDL FP decay data file 2011 and Fission yields data file 2011. The new burnup chain is output according to the format for the SRAC code system. Verification has been performed to evaluate the accuracy of the new burnup chain. The results show that the new burnup chain reproduces well the results of a reference one with 193 fission products used in SRAC. Burnup calculations using the new burnup chain have also been performed based on UO<inf>2</inf> and MOX fuel pin cells and compared with a reference chain th2cm6fp193bp6T.

DOI： 10.3139/124.110671

A coupling model for the two-stage core calculation method with subchannel analysis for boiling water reactors

Mitsuyasu, T; Aoyama, M; Yamamoto, A

ANNALS OF NUCLEAR ENERGY 102 巻頁： 77 - 84 2017年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

The two-stage core analysis method is widely used for BWR core analysis. The purpose of this study is to develop a core analysis model coupled with subchannel analysis within the two-stage calculation scheme using an assembly-based thermal-hydraulics calculation in the core analysis. The model changes the 2D lattice physics scheme, and couples with 3D subchannel analysis which evaluates the thermal-hydraulics characteristics within the coolant flow area divided as some subchannel regions. In order to couple with these two analyses, some BWR fuel assembly parameters are assumed and verified. The developed model is evaluated for the heterogeneous problem with and without a control rod. The present model is especially effective for the control rod inserted condition. The present model can incorporate the subchannel effect into the current two-stage core calculation method.

DOI： 10.1016/j.anucene.2016.11.045

GENESIS: A Three-Dimensional Heterogeneous Transport Solver Based on the Legendre Polynomial Expansion of Angular Flux Method

Yamamoto, A; Giho, A; Kato, Y; Endo, T

NUCLEAR SCIENCE AND ENGINEERING 186 巻 ( 1 ) 頁： 1 - 22 2017年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

A heterogeneous transport solver in three-dimensional (3-D) geometry, GENESIS, is developed incorporating recent developments in the method of characteristics (MOC) in 3-D geometry. The Legendre Polynomial Expansion of Angular Flux (LEAF) method is implemented in the GENESIS code, in which neutron transport is calculated in two-dimensional (2-D) characteristics planes rather than in one-dimensional characteristics lines adopted in the conventional approach of 3-D MOC. Unlike the planar MOC method that combines 2-D MOC calculations through axial leakages, the GENESIS code explicitly considers angular and spatial dependence of outgoing and incoming angular fluxes between axial planes. Thus, the GENESIS code eliminates a crucial approximation used in the planarMOC method: No approximation is used for axial leakage treatment. The GENESIS code can handle flexible shapes of objects in rectangular or hexagonal geometry. A two-level, multigroup generalized coarse mesh rebalance acceleration method is adopted for efficient convergence of neutron transport calculation. Performance of the GENESIS code is verified through various benchmark calculations. The calculation results indicate the fidelity of the GENESIS code based on the LEAF method.

DOI： 10.1080/00295639.2016.1273002

An efficient execution of Monte Carlo simulation based on delta-tracking method using GPUs

Estimation of Modeling Approximation Errors using Data Assimilation with the Minimum Variance Approach 査読有り

A. Yamamoto,K. Kinoshita,T. Endo

J. Nucl. Sci. Technol. 54 巻頁： 459-471 2017年2月

GENESIS - A Three-dimensional Heterogeneous Transport Solver based on the Legendre Polynomial Expansion of Angular Flux Method 査読有り

A. Yamamoto,A. Giho,Y. Kato,T. Endo

Nucl. Sci. Eng. 186 巻頁： 1-22 2017年

Automated Generation of Burnup Chain for Reactor Analysis Applications 査読有り

V. P. Tran,H. N. Tran,A. Yamamoto,T. Endo

Kerntechnik 82 巻頁： 196-205 2017年

A Coupling Model for the Two-stage Core Calculation Method with Subchannel Analysis for Boiling Water Reactors 査読有り

T. Mitsuyasu, M. Aoyama, A. Yamamoto

Ann. Nucl. Energy 102 巻頁： 77-84 2017年

Recent developments in the GENESIS code based on the Legendre polynomial expansion of angular flux method 査読有り

A. Yamamoto,A. Giho,T. Endo

Nucl. Eng. Technol. 49 巻頁： 1143-1156 2017年

Estimation of Sensitivity Coefficients of Core Characteristics based on Reduced-order Modeling using Sensitivity Matrix of Assembly Characteristics 査読有り

R. Katano,T. Endo,A. Yamamoto,M. Abdo,H. Abdel-Khalik

J. Nucl. Sci. Technol. 54 巻頁： 637-647 2017年

Application of the GENESIS Code to the Kobayashi 3D Benchmark Problem 査読有り

Akio Yamamoto,Akinori Giho,Tomohiro Endo

Trans. Am. Nucl. Soc. 117 巻頁： 1403-1406 2017年

Estimation of Modeling Approximation Error of Core Analysis Using the Surrogate Model with Kriging 査読有り

Tomomi Hanai,Tomohiro Endo,Yasuhiro Kodama,Yasunori Ohoka,Akio Yamamoto

Trans. Am. Nucl. Soc. 117 巻頁： 1269-1272 2017年

Application of the Bias Factor Method Using the Random Sampling Technique for Prediction Accuracy Improvement of Neutronics Parameters of BWR 査読有り

Motohiro Ito,Tomohiro Endo,Akio Yamamoto,Yusuke Kuroda,Takashi Yoshii

Trans. Am. Nucl. Soc. 117 巻頁： 804-807 2017年

Estimation of sensitivity coefficients of core characteristics based on reduced-order modeling using sensitivity matrix of assembly characteristics

Katano Ryota, Endo Tomohiro, Yamamoto Akio, Abdo Mohammad, Abdel-Khalik Hany

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 54 巻 ( 6 ) 頁： 637-647 2017年

Okubo, T; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 54 巻 ( 1 ) 頁： 30 - 38 2017年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

An efficient execution method for Monte Carlo simulation using graphic processing unit (GPU) is proposed. The delta-tracking method is used since the delta-tracking method can reduce conditional branches and complexity of code implementation, which degrade computational performance on GPUs. In order to improve parallel efficiency in the eigenvalue calculation, generated fission neutrons are recorded using the atomic operation which avoids the data race in GPUs. We also propose a method to efficiently tally neutron flux in a region. The present method is based on the atomic operation and use of fixed-point type number instead of common floating-point type number. The verification calculations using the C5G7 benchmark problem show effectiveness of the proposed numerical algorithms on GPUs through comparison with calculations using central processing units.

DOI： 10.1080/00223131.2016.1202793

Uncertainty quantification of activation due to cross section data in neutron shielding calculation

Yoko K., Endo T., Yamamoto A., Mizuno R., Kimura Y.

2017 International Congress on Advances in Nuclear Power Plants, ICAPP 2017 - A New Paradigm in Nuclear Power Safety, Proceedings 2017年

記述言語：日本語掲載種別：研究論文（学術雑誌）出版者・発行元：2017 International Congress on Advances in Nuclear Power Plants, ICAPP 2017 - A New Paradigm in Nuclear Power Safety, Proceedings

Quantification of activation in structure materials around a nuclear reactor using results of neutron shielding calculations is necessary for efficient planning of decommissioning. In this study, the random sampling method is applied to the neutron shielding calculation in order to estimate uncertainties of neutron flux and activation of 59Co in structure materials due to cross section covariance. The calculation results indicate that the magnitude of uncertainty of activation of 59Co due to cross section data is approximately 15∼30% inside structure materials.

Evaluation of the n/γ discrimination performance of the neutron detector with eu doped TRUST-LiCaAlF6

Maeno K., Endo T., Yamamoto A.

2017 International Congress on Advances in Nuclear Power Plants, ICAPP 2017 - A New Paradigm in Nuclear Power Safety, Proceedings 2017年

The n/γ discrimination performance of the prototype neutron detector using Eu doped TRUST-LiCaAlF6 is quantitatively investigated, in order to confirm its applicability to the subcriticality monitoring in the decommissioning works at Fukushima Daiichi Nuclear Power Plant units 1-3, especially focusing on removal of fuel debris. In this paper, the experimental results of pulse-height distribution measurement using 252Cf at the Nagoya University Cobalt 60 irradiation facility are shown. Additionally, in order to investigate the applicability to the reactor noise analysis, preliminary experimental results of the Feynman-α method are also shown.

Application of the genesis code to the Kobayashi 3D benchmark problem

Yamamoto A., Giho A., Endo T.

Transactions of the American Nuclear Society 117 巻頁： 1403 - 1406 2017年

Development of dynamic probabilistic risk assessment model for PWR using simplified plant simulation method

Otsuki S., Endo T., Yamamoto A.

2017 International Congress on Advances in Nuclear Power Plants, ICAPP 2017 - A New Paradigm in Nuclear Power Safety, Proceedings 2017年

The CMMC (Continuous Markov Monte Carlo) coupling method is proposed for quantifying accident scenarios that have time-dependence in accident progression and inter-dependence of individual events. In order to analyze large number of samples within realistic computing time, we developed a simplified accident progression analysis model and coupled the simplified model to the CMMC method. Large number of samples for station black out in PWR were analyzed using the random sampling method based on the CMMC method considering uncertainty of decay heat from a core. As a result, uncertainties of event initiation time and FPs release ratio to the atmosphere are estimated.

Effective use of engineering reactor simulator for education of nuclear safety

Yamamoto A., Endo T.

2017 International Congress on Advances in Nuclear Power Plants, ICAPP 2017 - A New Paradigm in Nuclear Power Safety, Proceedings 2017年

Effective use of a reactor simulator to lecture nuclear safety for undergraduate/master's course students majoring nuclear engineering is discussed. Various scenarios from normal operating to severe accident conditions are used for an exercise of a few days' course. Through discussions on plant behaviors of various scenarios within a small group and among class members, participants can understand physics behind responses of a nuclear power plant.