Faculty Profiles - YAMAMOTO, Akio

Burnup calculation using POD-based neutron spectrum reconstruction

Watanabe, T; Aizawa, N; Chiba, G; Tada, K; Fujita, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 63 ( 2 ) page： 166 - 186 2026.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

A fast burnup calculation method based on neutron spectrum reconstruction is proposed. The method employs a reduced-order model (ROM), constructed using proper orthogonal decomposition (POD) and regression models, to estimate neutron spectra experienced by fuel during burnup. The ROM is built from snapshot data generated through detailed burnup and neutron transport simulations under various conditions. During burnup calculations, the ROM is used to rapidly reconstruct neutron spectra at each burnup step. These reconstructed spectra are then used to compute one-group cross sections from multi-group effective cross sections derived using background cross sections. The proposed method significantly reduces computational time by avoiding repeated neutron transport simulations. Its performance is demonstrated using a PWR UO₂ fuel pin model. Results show that, with the 6th-order POD, the method predicts nuclide inventories with an average error within ± 5% compared to reference Monte Carlo calculations. Error analysis indicates that prediction accuracy is primarily limited by the regression models, rather than by the POD truncation or the multi-group cross section calculations.

DOI： 10.1080/00223131.2025.2560559

Sub-pin level distribution tallies and statistical error estimation with POD tallies in two-dimensional C5G7 benchmark

Kondo, R; Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 63 ( 2 ) page： 142 - 153 2026.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

The flux distribution tallies using proper orthogonal decomposition, called POD tallies, have been developed to address issues of high-fidelity Monte Carlo simulations. The POD tallies can reduce both dimensionality and statistical error. The present study verifies the applicability of the POD tallies to sub‑pin level flux distribution in the two‑dimensional C5G7 benchmark. Statistical error estimation is also proposed by applying the circular block bootstrap method to the POD tallies to estimate the statistical error of the flux distribution in a single Monte Carlo eigenvalue calculation. In the verification, the dimensionality of the finely discretized distribution is reduced by more than 90% compared with conventional cell tallies. The statistical error is reduced by more than half as the average value of all tally regions. It is confirmed that the statistical error of flux distribution can be properly estimated considering both the inter‑cycle correlation and the correlation between the expansion coefficients of different POD orders by the proposed approach.

DOI： 10.1080/00223131.2025.2554969

Absolute measurement of subcriticality in dollar units based on lag-1 autocovariance of zero-power reactor noise

Hirota, R; Moribe, T; Endo, T; Yamamoto, A; Watanabe, K; Wakabayashi, G; Shiga, H; Sakon, A; Oda, K; Kaneko, JH

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 63 ( 1 ) page： 54 - 65 2026.1

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

The zero-power reactor noise analysis is often utilized to measure a kinetic parameter of the prompt neutron decay constant (Formula presented.) for a target subcritical system in a steady state. There will be large uncertainties in the point kinetics parameters when detailed information on the target system is not available in advance. Therefore, if the subcriticality is converted from the measured (Formula presented.) value, the estimated subcriticality will inevitably have a large uncertainty. To address this problem, the present study aims to propose an absolute measurement technique of subcriticality in a steady state without the point kinetics parameters. The proposed method utilizes the lag-1 autocovariance of the reactor noise, which can emphasize the delayed neutron component better than the conventional reactor noise analysis methods such as the autocorrelation and Feynman- (Formula presented.) methods. By searching for the model parameters of the analytical formula of the lag-1 autocovariance for the measured values using the nonlinear least squares fitting method or Bayesian Monte Carlo, the subcriticality in dollar units can be inversely estimated together with the ratio of (Formula presented.). The validity of the proposed method is demonstrated for a zero-power reactor noise measurement at UTR-KINKI under a shutdown state.

DOI： 10.1080/00223131.2025.2530788

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

Yamamoto, A; Tsujita, K; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 63 ( 1 ) page： 45 - 53 2026.1

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

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

Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 63 ( 1 ) page： 120 - 127 2026.1

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

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

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 63 ( 1 ) page： 3 - 18 2026.1

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

Hybrid data assimilation methods for nuclear-data-induced uncertainties

Maruyama, S; Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 63 ( 1 ) page： 31 - 44 2026.1

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

This study proposes new hybrid data assimilation (DA) methods to effectively use experimental data represented in two different ways in the DA process for reducing nuclear-data-induced uncertainties. Conventional DA methods often assume a linear model, where data in a DA database are represented by their differential coefficients, i.e. nuclear data sensitivity coefficients. In contrast, more rigorous and versatile DA methods based on sampling techniques have been proposed recently. These sampling-based DA methods describe data for DA using results derived from direct transport calculations performed with perturbed nuclear data samples. The proposed hybrid DA methods simultaneously use both types of data described by sensitivity coefficients and sampling results and thus are called ‘hybrid.’ Two hybrid DA methods are proposed herein: the simple hybrid DA and efficient hybrid DA methods. Among these, the simple method is based on a straightforward concept that uses a random sampling technique. In contrast, the efficient method employs a more technical method that effectively combines a new deterministic sampling technique with sensitivity coefficients to reduce statistical uncertainties associated with the simple method. The efficient method is expected to be a candidate to achieve high precision and rigorous DA with a realistic sample size.

DOI： 10.1080/00223131.2025.2500579

Verification of in-core power distribution reconstruction based on POD for high-temperature gas-cooled reactors using ex-core detectors

Urase, Y; Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 63 ( 1 ) page： 66 - 81 2026.1

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

A reconstruction method of in-core power distribution using the proper orthogonal decomposition (POD) and the signal from ex-core detectors is proposed. POD can efficiently reconstruct the in-core power distribution from a small number of constraints (i.e. detectors) by expressing the power (≈ neutron flux) distribution in terms of a small number of POD bases and expansion coefficients. The number of unknowns required to reconstruct the power distribution is reduced from the number of spatial meshes in the core calculation to the number of POD expansion coefficients. A new method using the linear regression is proposed to calculate the POD expansion coefficients in addition to the method based on the generalized inverse matrix. In this study, the applicability of the in-core power distribution reconstruction method based on the ex-core detector signals and POD is verified in a two-dimensional system simulating the High-Temperature Engineering Test Reactor (HTTR). As a result of the verification, it was confirmed that the in-core power distribution can be reconstructed with a limited number of ex-core detector signals. The influence of statistical errors in the detector signals was also evaluated, and the in-core power distribution can be appropriately reconstructed when the order of the detector counts is approximately less than 3%. The linear regression method was numerically more stable than the generalized inverse matrix method in calculating POD expansion coefficients.

DOI： 10.1080/00223131.2025.2533530

Investigation of Thermal Cutoff Energy for Accurate Analysis of High-Temperature Engineering Test Reactor

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

JOURNAL OF NUCLEAR ENGINEERING AND RADIATION SCIENCE Vol. 11 ( 4 ) 2025.8

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Engineering and Radiation Science

This study investigates the appropriate thermal cutoff energy for neutron transport calculations in the High-Temperature Engineering Test Reactor (HTTR). Using the Monte Carlo calculation code mvp3.0, the impact of changing thermal cutoff energy on the multiplication factor was evaluated for the single fuel element geometry of HTTR, focusing on variations in fuel and moderator temperatures at the beginning of life (BOL) and end of life (EOL). In the default model of mvp3.0, resonance scattering is approximated by the free-monatomic-gas model with constant cross section. Therefore, the impact of using the exact model for resonance scattering was additionally examined. In the free-monatomic-gas model, a thermal cutoff energy of 30 eV is at least required to maintain the multiplication factor error within approximately ±50 pcm for both BOL and EOL. In addition, the results show that the impact of using the exact model instead of the free-monatomic-gas model on the multiplication factor is more than 200 pcm in the 30-40 eV range where U-238 has large resonance at 37 eV, and the impact becomes less than 50 pcm above 40 eV. These results indicate that a thermal cutoff energy of at least 30 eV is necessary without considering the effects of the exact model, and the energy range up to the 37 eV resonance needs to be considered in the case of applying the exact model to obtain the saturated results on multiplication factor for HTTR.

DOI： 10.1115/1.4067755

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

Kondo, R; Yamamoto, A; Endo, T

EPJ NUCLEAR SCIENCES & TECHNOLOGIES Vol. 11 2025.6

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

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 Vol. 214 2025.5

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

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

Oshima, Y; Endo, T; Yamamoto, A

NUCLEAR SCIENCE AND ENGINEERING Vol. 199 ( 4 ) page： 586 - 598 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：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 SP<sub>3</sub> 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 Vol. 62 ( 4 ) page： 366 - 378 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 62 ( 2 ) page： 179 - 196 2025.2

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

A Simple Resonance Calculation Method for Flexible Geometry Using Equivalence Relation and Point-wise Cross Sections (ERPX)

Discussion on the 3S for peaceful use of nuclear energy for future generations (1) Open Access

Yamamoto Akio

Journal of the Atomic Energy Society of Japan Vol. 67 ( 4 ) page： 218 - 221 2025

Yamamoto A., Endo T.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 544 - 553 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025

ERPX, a simple resonance calculation method that can incorporate space-dependent shelf-shielding is proposed. ERPX calculates space-dependent escape cross sections using the ultra-fine group (UFG) calculation in heterogeneous and homogeneous geometries with the narrow resonance (NR) approximation. Then the space-dependent escape cross sections and the explicit slowing down calculation in homogeneous geometry are then used to estimate the space-dependent effective cross section to mitigate the error caused by the NR approximation. The reduce-order model is and used in the UFG calculation in heterogeneous geometry to achieve short computation time. Verification developed calculation is carried out in 3x3 pin-cell geometry containing a large water region. The fuel pellet in focus is azimuthally and annularly divided. The calculation results indicated that the ERPX method can provide reasonable accuracy with practical computation time that can be used for the design calculations.

DOI： 10.13182/MC25-47330

Subcriticality Estimation without Point Kinetics Parameters Based on Autocovariance of Reactor Noise Using Delayed Neutron Components

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

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 2028 - 2037 2025

The reactor noise analysis method is useful as a passive measurement technique for a steady-state target subcritical system. When detailed information is not available in the target system, there are large uncertainties in the point kinetics parameters, such as the effective delayed neutron fraction and the neutron generation time. In this case, if the subcriticality measurement techniques using the point kinetics parameters (e.g., indirect conversion method from the measured prompt neutron decay constant to the subcriticality) are applied, the measured subcriticality will inevitably have a large uncertainty. To address this problem, the present study aims to investigate the absolute measurement of subcriticality without the point kinetics parameters by focusing on the delayed neutron components in the zero-power reactor noise. For this purpose, an analytical formula for the lag-1 autocovariance of the reactor noise is derived via the pair detection probability based on the fundamental mode approximation using the forward and adjoint K<inf>eff</inf>-eigenfunctions. The proposed method utilizes the nonlinear least squares fitting method for the measured autocovariance to determine the following three fitting parameters: the subcriticality in the dollar units; the ratio of β<inf>eff/</inf>Λ; and a proportional factor related to the Diven factor, the detection efficiency, and so on. Preliminary experimental analysis using the proposed method is demonstrated through the reactor noise measurement at UTR-KINKI (University Teaching and Research Reactor of Kindai University) under a shutdown state.

DOI： 10.13182/MC25-46579

Reactivity Estimation in Dollar Units Based on Bayesian Monte Carlo Using Autocovariance of Reactor Noise Measurement

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

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 2038 - 2047 2025

The reactor noise analysis method can measure the prompt neutron decay constant α using only time series data of neutron counts measured in a steady-state subcritical system. However, the point kinetics parameters such as the neutron generation time Λ and the effective delayed neutron fraction β<inf>eff</inf> are needed to estimate the reactivity in dollar units by conversion from the measured α value. To address the above-mentioned problem, this study aims to develop the estimation technique of the reactivity in dollar units ρ/β<inf>eff</inf>, by utilizing the delayed neutron component of reactor noise. To extract the delayed neutron components, this study focused on the lag-1 autocovariance for reactor noise. In addition, the Bayesian Monte Carlo (BMC) with merging particle filter (MPF) was applied as the data assimilation technique to estimate ρ/β<inf>eff</inf> from the measured variation of the autocovariance with respect to the counting gate width. As a result, the proposed method was validated through the reactor noise measurement at UTR-KINKI (University Teaching and Research Reactor of Kindai University).

DOI： 10.13182/MC25-46969

Fast Burnup Calculation Method Based on Neutron Spectrum Reconstruction with Proper Orthogonal Decomposition and Regression Model

Watanabe T., Aizawa N., Chiba G., Tada K., Yamamoto A.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 288 - 297 2025

A fast burnup calculation method based on neutron spectrum reconstruction using the proper orthogonal decomposition (POD) and regression model is studied. In this method, a large number of burnup-dependent multigroup neutron fluxes are prepared as snapshot data by detailed burnup calculations with randomly sampled parameter sets, such as fuel pin pitch and enrichment. Dimensionality reduction is applied to the neutron fluxes by POD and the regression models connecting the dimensionality-reduced neutron fluxes with the parameters are established. By substituting arbitrary input parameters into the regression models, the multigroup neutron flux is reconstructed and used to calculate one-group cross sections for burnup calculations. The above procedure performs burnup calculations with different sets of input parameters without calculating neutron spectra by neutron transport calculations at each burnup step. In this study, the feasibility of the method is examined by numerical calculations using a UO2 fuel pin-cell model of PWR. Results show that the nuclide inventories of randomly prepared target cases can be calculated with a prediction error of a few percent. The prediction error is dominated by the regression models in the present calculation condition.

DOI： 10.13182/MC25-46817

Correction Method of Few-Group Cross Sections for Core Analysis of High-Temperature Gas-Cooled Reactors

Haga A., Endo T., Yamamoto A., Chiba G.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 472 - 481 2025

To reduce the discretization error associated with the energy group collapsing, a correction method for few-group cross sections used in a core calculation of High-Temperature Gas-cooled Reactors (HTGRs) was investigated. It was confirmed that the correction of the removal scattering cross section as a function of the spectral index, which is the ratio of the fast and thermal group neutron fluxes, improves the calculation accuracy of the k-effective and the fuel compact-wise relative power distribution in the two-dimensional heterogeneous full core model of the High Temperature engineering Test Reactor (HTTR). The method of correcting the total scattering cross section, including the self-group scattering cross section, did not improve the accuracy. The method using the removal scattering cross section may be a candidate for a core design method of HTGRs.

DOI： 10.13182/MC25-47343

Effects of Self-shielding and Scattering Matrix Treatments in Detailed Burnup Calculation

Yamamoto A., Endo T., Watanabe T.

Transactions of the American Nuclear Society Vol. 133 ( 1 ) page： 698 - 701 2025

Theoretical Formula for Probability Generating Function of Neutron Counts in a Non-Multiplication System

Endo T., Ohashi R., Hirota R., Yamamoto A.

Transactions of the American Nuclear Society Vol. 133 ( 1 ) page： 426 - 429 2025

Study on Neutron Diffusion Calculation based on Particle Method for Multiphysics Simulation of Fuel Debris Retrieval

Kumita S., Tomohiro E., Yamamoto A.

Transactions of the American Nuclear Society Vol. 133 ( 1 ) page： 760 - 763 2025

Study on Core Analysis Models for HTGRs: VHTRC Analysis using MVP3

Kuroki Y., Yamamoto A., Endo T.

Transactions of the American Nuclear Society Vol. 133 ( 1 ) page： 632 - 635 2025

Nonlinear Diffusion Acceleration with Local Discontinuous Galerkin Method

Kasama R., Yamamoto A., Endo T.

Transactions of the American Nuclear Society Vol. 133 ( 1 ) page： 678 - 681 2025

Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations

Kondo, R; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 61 ( 12 ) page： 1536 - 1545 2024.12

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 61 ( 11 ) page： 1405 - 1414 2024.11

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 302 2024.10

Language：English Publishing type：Research paper (scientific journal) Publisher：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 2024.10

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 205 2024.9

Language：English Publishing type：Research paper (scientific journal) Publisher：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 2024.8

Language：English Publishing type：Research paper (scientific journal) Publisher：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 2024.7

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 Vol. 61 ( 6 ) page： 830 - 839 2024.6

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 198 ( 6 ) page： 1215 - 1234 2024.6

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 198 ( 5 ) page： 981 - 992 2024.5

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 61 ( 3 ) page： 354 - 362 2024.3

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 61 ( 3 ) page： 363 - 374 2024.3

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

Maruyama, S; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 61 ( 1 ) page： 31 - 43 2024.1

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

Report on the lecture of standard committee in the 2023 fall meeting entitled “Standardization Activities for Safe Long Term Operation” Open Access

Murakami Kenta, Onizawa Kunio, Yamamoto Akio

Journal of the Atomic Energy Society of Japan Vol. 66 ( 4 ) page： 199 - 202 2024

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 page： 1572 - 1580 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 78 - 86 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 1036 - 1047 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 1025 - 1035 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 1642 - 1651 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 1622 - 1631 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 1612 - 1621 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 2490 - 2499 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 97 - 106 2024

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

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 Vol. 131 ( 1 ) page： 1053 - 1056 2024

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 Vol. 2 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 131 ( 1 ) page： 299 - 302 2024

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 Vol. 131 ( 1 ) page： 292 - 295 2024

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

Kasama R., Yamamoto A., Endo T.

Transactions of the American Nuclear Society Vol. 130 ( 1 ) page： 1044 - 1047 2024

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 Vol. 130 ( 1 ) page： 758 - 762 2024

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

Yamamoto A., Endo T.

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 1032 - 1035 2024

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

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

Morishita, Y; Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 60 ( 12 ) page： 1573 - 1585 2023.12

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 60 ( 11 ) page： 1386 - 1396 2023.11

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

Maruyama, S; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 60 ( 11 ) page： 1372 - 1385 2023.11

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 60 ( 6 ) page： 624 - 631 2023.6

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

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 page： 88 - 96 2022

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 107 - 116 2022

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 3366 - 3375 2022

Language：English Publishing type：Research paper (scientific journal) Publisher：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 page： 2042 - 2051 2022

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 58 ( 12 ) page： 1343 - 1350 2021.12

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 58 ( 12 ) page： 1308 - 1317 2021.12

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 58 ( 11 ) page： 1165 - 1183 2021.11

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

Hayashi, T; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 58 ( 9 ) page： 1008 - 1017 2021.9

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

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

NUCLEAR SCIENCE AND ENGINEERING Vol. 195 ( 7 ) page： 694 - 716 2021.7

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Kosuke, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 58 ( 2 ) page： 173 - 183 2021.2

Evolutionary simulated annealing for fuel loading optimization of VVER-1000 reactor International coauthorship Open Access

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

ANNALS OF NUCLEAR ENERGY Vol. 151 2021.2

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Vol. 11 ( 1 ) 2021.1

Language：English Publishing type：Research paper (scientific journal) Publisher：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 Masato, Endo Tomohiro, Yamamoto Akio

NUCLEAR SCIENCE AND ENGINEERING Vol. 195 ( 1 ) page： 33 - 49 2021.1

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 Vol. 124 ( 1 ) page： 556 - 558 2021

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 Vol. 124 ( 1 ) page： 184 - 187 2021

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 Vol. 124 ( 1 ) page： 544 - 547 2021

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 Vol. 125 ( 1 ) page： 904 - 907 2021

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

Chiba G., Yamamoto A.

Transactions of the American Nuclear Society Vol. 125 ( 1 ) page： 934 - 937 2021

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 Vol. 125 ( 1 ) page： 900 - 903 2021

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 page： 1568 - 1576 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

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 page： 1719 - 1728 2021

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 page： 710 - 720 2021

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 page： 2219 - 2230 2021

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 page： 1982 - 1991 2021

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

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 page： 1840 - 1849 2021

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

Applicability of a reduced order model for a safety analysis code to statistical safety analysis Reviewed

Data Assimilation Using Subcritical Measurement of Prompt Neutron Decay Constant Open Access

Endo Tomohiro, Yamamoto Akio

NUCLEAR SCIENCE AND ENGINEERING Vol. 194 ( 11 ) page： 1089 - 1104 2020.11

Implementation of the unscented transformation with low rank approximation in uncertainty analysis during large-break loss of coolant accident International coauthorship

Foad Basma, Yamamoto Akio, Endo Tomohiro

ANNALS OF NUCLEAR ENERGY Vol. 146 2020.10

Uncertainty and regression analysis of the MSLB accident in PWR based on unscented transformation and low rank approximation International coauthorship

Foad Basma, Yamamoto Akio, Endo Tomohiro

ANNALS OF NUCLEAR ENERGY Vol. 143 2020.8

Matsushita Masaki, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY page： 1-12 2020.7

Efficient uncertainty quantification for PWR during LOCA using unscented transform with singular value decomposition International coauthorship Open Access

Foad Basma, Yamamoto Akio, Endo Tomohiro

ANNALS OF NUCLEAR ENERGY Vol. 141 2020.6

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

Oshima Yoshiki, Endo Tomohiro, Yamamoto Akio, Kodama Yasuhiro, Ohoka Yasunori, Nagano Hiroaki

NUCLEAR SCIENCE AND ENGINEERING Vol. 194 ( 6 ) page： 477 - 491 2020.6

Application of the multigrid amplitude function method for time-dependent MOC based on the linear source approximation Reviewed Open Access

Tsujita Kosuke, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2020.1

Subcriticality measurement using time-domain decomposition-based integral method for simultaneous reactivity and source changes Reviewed Open Access

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

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2020.1

A kinetic model for the direct response matrix method

Mitsuyasu Takeshi, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 57 ( 1 ) page： 90 - 99 2020.1

Recent Research Activities on Nuclear Reactor Physics Using the Computational Science Open Access

YAMAMOTO Akio

The Proceedings of Mechanical Engineering Congress, Japan Vol. 2020 ( 0 ) page： K08101 2020

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：The Japan Society of Mechanical Engineers

<p>Outline of the nuclear reactor core analysis and computational methods used in this analysis are described. Various techniques and approximations are used to perform core analysis with practical computational resources. Recent progress on computer hardware and numerical algorithms enabled us to use more precise and accurate analysis methods.</p>

DOI： 10.1299/jsmemecj.2020.k08101

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

CiNii Research

Tsujita K., Endo T., Yamamoto A.

Transactions of the American Nuclear Society Vol. 123 ( 1 ) page： 1349 - 1353 2020

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 Vol. 123 ( 1 ) page： 841 - 844 2020

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 Vol. 2020-March page： 152 - 161 2020

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：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 Vol. 2020-March page： 1736 - 1744 2020

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：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 Vol. 2020-March page： 2690 - 2697 2020

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：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 Vol. 122 page： 714 - 717 2020

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 Vol. 122 page： 458 - 461 2020

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

Ishiguro Satomi, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2019.12

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

Matsushita Masaki, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2019.12

Track 1: Severe Accident Phenomena, Fukushima Accident Analysis Open Access

Journal of the Society of Mechanical Engineers Vol. 122 ( 1211 ) page： 10 - 12 2019.10

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

Sasaki M., Sanada Y., Yamamoto A.

RADIATION PROTECTION DOSIMETRY Vol. 184 ( 3-4 ) page： 400-404 2019.10

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

Yamamoto Akio, Endo Tomohiro, Giho Akinori

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 56 ( 8 ) page： 716 - 723 2019.8

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

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

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 56 ( 6 ) page： 471 - 478 2019.6

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 Vol. 2019-May 2019.5

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：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.

DOI： 10.1299/jsmeicone.2019.27.1022

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

Endo Tomohiro, Yamamoto Akio, Yamanaka Masao, Pyeon Cheol Ho

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 56 ( 4 ) page： 322 - 336 2019.4

Comparison of theoretical formulae and bootstrap method for statistical error estimation of Feynman-alpha method Open Access

Endo Tomohiro, Yamamoto Akio

ANNALS OF NUCLEAR ENERGY Vol. 124 page： 606 - 615 2019.2

Inverse estimation methods of unknown radioactive source for fuel debris search Open Access

Sugaya Shinji, Endo Tomohiro, Yamamoto Akio

ANNALS OF NUCLEAR ENERGY Vol. 124 page： 49 - 57 2019.2

A New Interpretation of Discontinuity Factor Open Access

Yamamoto Akio, Endo Tomohiro

NUCLEAR SCIENCE AND ENGINEERING Vol. 193 ( 9 ) page： 991 - 997 2019

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

Yamamoto Akio, Giho Akinori, Endo Tomohiro

NUCLEAR SCIENCE AND ENGINEERING Vol. 193 ( 3 ) page： 253 - 268 2019

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) Vol. 2019.27 ( 0 ) page： 1022 2019

Language：English Publishing type：Research paper (scientific journal) Publisher：The Japan Society of Mechanical Engineers

DOI： 10.1299/jsmeicone.2019.27.1022

CiNii Research

Subcriticality - from basics to applications (1) Open Access

Endo Tomohiro, Tsujimoto Kazufumi, Yamamoto Akio

Journal of the Atomic Energy Society of Japan Vol. 61 ( 10 ) page： 734 - 738 2019

Mission of Reactor Physics Open Access

Chiba Go, Yamamoto Akio

Journal of the Atomic Energy Society of Japan Vol. 61 ( 4 ) page： 254 - 256 2019

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

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

Transactions of the American Nuclear Society Vol. 120 page： 851 - 854 2019

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 page： 1493 - 1502 2019

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019

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 Vol. 121 page： 1309 - 1312 2019

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 Vol. 121 page： 1316 - 1320 2019

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 Vol. 121 page： 979 - 982 2019

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 page： 1081 - 1092 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 page： 1534 - 1543 2019

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 page： 1874 - 1885 2019

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 Open Access

Endo T., Yamamoto A.

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

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.

DOI： 10.1080/00295639.2020.1720499

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

Hayashi Koji, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 55 ( 12 ) page： 1434 - 1458 2018.12

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

Mitsuyasu Takeshi, Aoyama Motoo, Yamamoto Akio

ANNALS OF NUCLEAR ENERGY Vol. 122 page： 146 - 154 2018.12

Sensitivity analysis of prompt neutron decay constant using perturbation theory Open Access

Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 55 ( 11 ) page： 1245 - 1254 2018.11

Surrogate Model of Severe Accident Analysis Code for SBO Aiming Probabilistic Safety Margin Analysis Reviewed

M. Matsushita, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 119 page： 900-903 2018.11

Reduction of Cross Section Table Size for Core Analysis Using Dimensionality Reduction Technique Reviewed

M. Yamamoto, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 119 page： 1226-1228 2018.11

A Simple Treatment of Bowed Assembly Gap Through Correction of Cross Section Reviewed

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

Trans. Am. Nucl. Soc. Vol. 119 page： 1199-1202 2018.11

Transport Consistent Diffusion Coefficient for CMFD Acceleration Reviewed

A. Yamamoto, T. Endo

Trans. Am. Nucl. Soc. Vol. 119 page： 1179-1181 2018.11

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

A. Nonaka, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 119 page： 1112-1115 2018.11

Estimation of Subcriticality using Particle Filter Method Reviewed

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

Trans. Am. Nucl. Soc. Vol. 118 page： 851-854 2018.6

Quantification of Modeling Approximation Error of Pin-Cell Calculation Using Kriging and Principal Component Analysis Reviewed

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

Trans. Am. Nucl. Soc. Vol. 118 page： 875－878 2018.6

Inverse Estimation Methods of Unknown Radioactive Source for Fuel Debris Search Reviewed

S. Sugaya, T. Endo, A. Yamamoto

Proc. PHYSOR201 page： [USB-DRIVE] 2018.4

Estimation of Subcriticality in Dollar Units using Integral Method for Subcritical System Reviewed

A. Nonaka, T. Endo, A. Yamamoto

Proc. PHYSOR2018 page： [USB-DRIVE] 2018.4

Cache Efficient Flux Region Assignment for the Method of Characteristics Reviewed

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2018 page： [USB-DRIVE] 2018.4

Estimation of Region-Wise Even-Parity Discontinuity Factor for MOC Through Iterative Procedure Reviewed

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2018 page： [USB-DRIVE] 2018.4

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 page： [USB-DRIVE] 2018.4

Sensitivity Coefficient Analysis of Omega-Eigenvalue based on First-Order Perturbation Theory Reviewed

page： [USB-DRIVE] 2018.4

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

Katano Ryota, Endo Tomohiro, Yamamoto Akio, Tsujimoto Kazufumi

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 55 ( 10 ) page： 1099 - 1109 2018

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

Koike Hiroki, Kirimura Kazuki, Yamaji Kazuya, Kosaka Shinya, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 55 ( 1 ) page： 41 - 65 2018

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

Yokoyama Kenji, Yamamoto Akio, Kitada Takanori

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 55 ( 3 ) page： 319 - 334 2018

Estimation of Sensitivity Coefficient based on Lasso-type Penalized Linear Regression Reviewed

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

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 55 page： 1099-1109 2018

Utilization of Region-wise Even-Parity Discontinuity Factor to Reduce Discretization Error of MOC Reviewed

A. Yamamoto, A. Giho, T. Endo

Nuclear Science and Engineering Vol. 193 page： 253-268 2018

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

A. Yamamoto, A. Giho, T. Endo

Nuclear Science and Engineering Vol. 192 page： 243-250 2018

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

Yamamoto Akio, Giho Akinori, Endo Tomohiro

NUCLEAR SCIENCE AND ENGINEERING Vol. 192 ( 3 ) page： 240 - 253 2018

Symposium Report on ASRAM2017 Open Access

Yamaguchi Akira, Yamamoto Akio, Narumiya Yoshiyuki

Journal of the Atomic Energy Society of Japan Vol. 60 ( 6 ) page： 362 - 363 2018

Research and development roadmap for reactor physics 2017:future of reactor physics projected by next generations Open Access

Yamamoto Akio, Chiba Go, Kirimura Kazuki, Miki Yosuke, Yokoyama Kenji

Journal of the Atomic Energy Society of Japan Vol. 60 ( 4 ) page： 241-245 2018

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 Vol. 119 page： 900 - 903 2018

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 Vol. Part F168384-3 page： 1892 - 1903 2018

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：International Conference on Physics of Reactors, PHYSOR 2018: Reactor Physics Paving the Way Towards More Efficient Systems

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 Vol. 119 page： 1112 - 1115 2018

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 Vol. Part F168384-5 page： 3271 - 3282 2018

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 Vol. 118 page： 851 - 854 2018

Estimation of subcriticality using particle filter method

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

AISTech - Iron and Steel Technology Conference Proceedings Vol. 2018-May page： 851 - 854 2018

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 Vol. Part F168384-4 page： 2632 - 2643 2018

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.

DOI： 10.1016/j.anucene.2018.09.022

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 Vol. 118 page： 875 - 878 2018

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 Vol. 2018-May page： 875 - 878 2018

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 Vol. 119 page： 1226 - 1228 2018

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 Vol. Part F168384-2 page： 1240 - 1253 2018

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.

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 Vol. Part F168384-3 page： 1793 - 1804 2018

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.

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 Vol. Part F168384-2 page： 788 - 799 2018

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 Vol. Part F168384-5 page： 3042 - 3053 2018

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.

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

Estimation of Modeling Approximation Error of Core Analysis Using the Surrogate Model with Kriging Reviewed

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

rans. Am. Nucl. Soc. Vol. 117 page： 1269-1272 2017.11

Application of the GENESIS Code to the Kobayashi 3D Benchmark Problem Reviewed

Akio Yamamoto, Akinori Giho, Tomohiro Endo

Trans. Am. Nucl. Soc. Vol. 117 page： 1403-1406 2017.11

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

Yamamoto Akio, Giho Akinori, Endo Tomohiro

NUCLEAR ENGINEERING AND TECHNOLOGY Vol. 49 ( 6 ) page： 1143 - 1156 2017.9

Uncertainty Quantification of Activation Due to Cross Section Data in Neutron Shielding Calculation Reviewed

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

Proc. 2017 International. Cogress on Advances in Nuclear Power Plants 2017.4

Development of Dynamic Probabilistic Risk Assessment Model for PWR using Simplified Plant Simulation Method Reviewed

Shohei Otsuki,Tomohiro Endo,Akio Yamamoto

Proc. 2017 International Cogress on Advances in Nuclear Power Plants 2017.4

Application of Bias Factor Method using Random Sampling Technique for Critical Eigenvalue Prediction of BWR Reviewed

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

Proc. 2017 International Cogress on Advances in Nuclear Power Plants 2017.4

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

Akio Yamamoto,Akinori Giho,Tomohiro Endo

Proc. Int. Conf. on Math. and Comp. Methods Applied to Nucl. Sci. & Eng. (M&C2017) 2017.4

Theoretical Discussion of Statistical Error of Variance-to-Mean Ratio Reviewed

Tomohiro Endo,Akio Yamamoto

Proc. Int. Conf. on Math. and Comp. Methods Applied to Nucl. Sci. & Eng. (M&C2017) 2017.4

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) 2017.4

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

Toshiki Kimura,Tomohiro Endo,Akio Yamamoto

Proc. Int. Conf. on Math. and Comp. Methods Applied to Nucl. Sci. & Eng. (M&C2017) 2017.4

Mitsuyasu Takeshi, Aoyama Motoo, Yamamoto Akio

ANNALS OF NUCLEAR ENERGY Vol. 102 page： 77 - 84 2017.4

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

Yamamoto Akio, Giho Akinori, Kato Yuki, Endo Tomohiro

NUCLEAR SCIENCE AND ENGINEERING Vol. 186 ( 1 ) page： 1 - 22 2017.4

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

Yamamoto Akio, Kinoshita Kuniharu, Endo Tomohiro

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 54 ( 4 ) page： 459 - 471 2017.4

Automated generation of burnup chain for reactor analysis applications

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

KERNTECHNIK Vol. 82 ( 2 ) page： 196 - 205 2017.4

Estimation of Modeling Approximation Errors using Data Assimilation with the Minimum Variance Approach Reviewed

A. Yamamoto,K. Kinoshita,T. Endo

J. Nucl. Sci. Technol. Vol. 54 page： 459-471 2017.2

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

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

Nucl. Sci. Eng. Vol. 186 page： 1-22 2017

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

A. Yamamoto,A. Giho,T. Endo

Nucl. Eng. Technol. Vol. 49 page： 1143-1156 2017

Automated Generation of Burnup Chain for Reactor Analysis Applications Reviewed

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

Kerntechnik Vol. 82 page： 196-205 2017

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

T. Mitsuyasu, M. Aoyama, A. Yamamoto

Ann. Nucl. Energy Vol. 102 page： 77-84 2017

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

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

Trans. Am. Nucl. Soc. Vol. 117 page： 804-807 2017

Estimation of Sensitivity Coefficients of Core Characteristics based on Reduced-order Modeling using Sensitivity Matrix of Assembly Characteristics Reviewed Open Access

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

J. Nucl. Sci. Technol. Vol. 54 page： 637-647 2017

Application of the GENESIS Code to the Kobayashi 3D Benchmark Problem Reviewed

Akio Yamamoto,Akinori Giho,Tomohiro Endo

Trans. Am. Nucl. Soc. Vol. 117 page： 1403-1406 2017

Estimation of Modeling Approximation Error of Core Analysis Using the Surrogate Model with Kriging Reviewed

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

Trans. Am. Nucl. Soc. Vol. 117 page： 1269-1272 2017

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

Okubo Takuya, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 54 ( 1 ) page： 30 - 38 2017

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

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

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 54 ( 6 ) page： 637-647 2017

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

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

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.

Estimation of modeling approximation error of core analysis using the surrogate model with kriging

Hanai T., Endo T., Kodama Y., Ohoka Y., Yamamoto A.

Transactions of the American Nuclear Society Vol. 117 page： 1269 - 1272 2017

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

Yamamoto A., Giho A., Endo T.

Transactions of the American Nuclear Society Vol. 117 page： 1403 - 1406 2017

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

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

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.