Faculty Profiles - YAMAMOTO, Akio

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

Amano T., Endo T., Yamamoto A.

Optics Continuum Vol. 2 ( 7 ) page： 1540 - 1560 2023.6

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Open Access

Tsujita, K; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 60 ( 3 ) page： 343 - 357 2023.3

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 60 ( 3 ) page： 238 - 250 2023.3

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 197 ( 2 ) page： 176 - 188 2023.2

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 60 ( 2 ) page： 132 - 139 2023.2

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 128 page： 690 - 693 2023

Roadmap towards the introduction of new design fuels as well as the continuous improvement of safety evaluation (5) Open Access

Murakami Kenta, Yamamoto Akio

Journal of the Atomic Energy Society of Japan Vol. 65 ( 10 ) page： 606 - 607 2023

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

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

NUCLEAR SCIENCE AND ENGINEERING Vol. 196 ( 11 ) page： 1267 - 1279 2022.11

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 196 ( 10 ) page： 1194 - 1208 2022.10

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Open Access

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

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 59 ( 9 ) page： 1117 - 1126 2022.9

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 196 ( 7 ) page： 769 - 791 2022.7

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 196 ( 4 ) page： 379 - 394 2022.4

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 59 ( 3 ) page： 407 - 407 2022.3

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

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

NUCLEAR SCIENCE AND ENGINEERING Vol. 196 ( 2 ) page： 133 - 143 2022.2

Language：English Publishing type：Research paper (scientific journal) Publisher：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

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

Safety measures and risk management of nuclear power plants against external events (4) Open Access

Murakami Kenta, Yamamoto Akio

Journal of the Atomic Energy Society of Japan Vol. 64 ( 5 ) page： 272 - 274 2022

倫理規程制定20年を迎えて　第4回 Open Access

山本章夫

日本原子力学会誌ATOMOΣ Vol. 64 ( 3 ) page： 176 - 176 2022

Toward construction of cross-organizational education system for nuclear engineering Open Access

Kurosaki Ken, Kozaki Tamotsu, Nakashima Hiroshi, Obara Toru, Wakabayashi Genichiro, Pyeon Cheolho, Matsuyama Shigeo, Abe Hiroshi, Uno Masayoshi, Yamamoto Akio

Journal of the Atomic Energy Society of Japan Vol. 64 ( 9 ) page： 520 - 524 2022

Katano R., Yamamoto A., Endo T.

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

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 503 - 512 2022

Language：English Publishing type：Research paper (scientific journal) Publisher：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