Faculty Profiles - ENDO Tomohiro

MISC - ENDO Tomohiro

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2D Neutron Diffusion Calculation Based on Local/Global Iterations Using Proper Orthogonal Decomposition Reviewed International journal

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

Proceedings of the Reactor Physics Asia 2023 (RPHA2023) Conference 2023.10

Feasibility Study on Subcritical Rod Worth Measurement for UTR-KINKI Reviewed International journal

T. Endo, G. Chiba, K. Watanabe, C. H. Pyeon, G. Wakabayashi

Proceedings of the Reactor Physics Asia 2023 (RPHA2023) Conference 2023.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

In this study, we investigate the feasibility of the subcritical rod worth measurement (SRWM) to UTRKINKI (University Training Reactor, Kindai University) through a virtual numerical experiment.

Comparison of Neutronic Characteristics of BWR Burnup Fuel between JENDL-4.0 and JENDL-5 Reviewed International journal

Tomoaki Watanabe, Kenichi Tada, Tomohiro Endo, Akio Yamamoto

Proc. ICNC2023 2023.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

The present study investigated the effect of the nuclear data modification from JENDL-4.0 to JENDL-5 on the criticality characteristics of a typical 9×9 BWR burnup fuel. In JENDL-5, many nuclear data essential to characterize burnup fuels, such as the cross sections of Gd-155 and Gd-157, were modified. The depletion calculations showed that kinf of JENDL-5 was smaller than that of JENDL-4.0 at almost all burnup steps for 0–50 GWd/t. Significant burnup dependencies of the kinf difference between JENDL-4.0 and JENDL-5 were also found. For example, the kinf difference significantly increased around 12 GWd/t, and the kinf difference gradually increased as the burnup value increased. The direct sensitivity calculations were carried out to specify which nuclear data impacts the kinf difference. The specific nuclear data of interest was replaced from JENDL-4.0 to JENDL-5. The sensitivity calculation results showed that the kinf difference around 12 GWd/t was mainly caused by the modification of the cross sections of U-235, Gd-155, Gd-157, and TSL data of H in H2O. These modifications affected the composition of Gd-155 and Gd-157. The sensitivity calculation results also clarified that modifying the U-235 and Pu-239 cross sections and TSL data of H in H2O affected the increase in the kinf difference as the burnup value increased. The modifications of the TSL data for H in H2O also affected the composition of U-235.

Program of Reactor Physics Experiment to Measure Subcriticality for an Unknown System Reviewed International journal

Shunya Teratani, Yoshinari Harada, Kaito Mori, Yoshiki Yamashita, Tomohiro Endo, Go Chiba

Proc. ICNC2023 2023.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

In order to train human resources for the future nuclear field, we have been developing an advanced educational program for the reactor physics experiments by utilizing a Japanese educational reactor (University Training Reactor, Kindai University, UTR-KINKI) with recent measurement techniques. This paper summarizes the advanced reactor physics experiment program for training graduate students to tackle unknown problems. As a problem-based learning program (PBL) of reactor physics experiments, we focused on the subcriticality measurement for an unknown system without prior knowledge of the external neutron source intensity and the point kinetics parameters. In order to solve this challenging problem, the basic lectures and the interactive exercise were prepared to help graduate students better understand (1) the criticality approach based on the inverse multiplication and (2) the measurement of the prompt neutron decay constant by the Feynman-α method. Through the series of lectures, the instructors hope that graduate students will get an idea of how to determine the subcriticality for a target unknown system, e.g., by combining the inverse multiplication and the Feynman-α methods through the Simmons-King method. The combined method was demonstrated by the actual reactor physics experiment at UTR-KINKI.

Nuclear Data Sensitivity Analysis of a Sodium Shielding Experiment Based on Generalized Perturbation Theory for Data Assimilation Reviewed International journal

Shuhei Maruyama, Tomohiro Endo, Akio Yamamoto

Proc. ICNC2023 2023.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

This paper investigates the feasibility of uncertainty reduction by sharing the experimental database between different fields (e.g., reactor physics and radiation shielding) and using data assimilation techniques. To perform this study, we have developed a sensitivity analysis tool based on a transport generalized perturbation theory, which can be applied not only to the analysis of reactor physics experiments, but also to the analysis of shielding experiments. As the first step in this study, we focus on the ORNL sodium shielding experiments with Bonner Ball neutron detectors and perform a sensitivity analysis of these experiments. Using the sensitivity coefficients evaluated here and those of the fast reactor core characteristics evaluated to date by JAEA, we have shown that the sodium shielding experimental data can contribute to the uncertainty reduction of sodium void reactivity by adopting a data assimilation technique. Based on this preliminary study, the uncertainty reduction effect is expected to be significant, especially for sodium void reactivity dominated by the neutron leakage phenomena. Although new reactor physics experimental data on sodium void reactivity may be difficult to obtain, the results of this study suggest that the data from sodium shielding experiments can partially substitute for this role. This study demonstrates the value of the mutual use of integral experimental data in fast reactor design.

Efficient Uncertainty Quantification Using Deterministic Sampling Method with Simplex Ensemble and Scaling Method Reviewed International journal

Tomohiro Endo, Akio Yamamoto

Proc. ICNC2023 2023.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

In the field of criticality safety, the uncertainty quantification (UQ) of the neutron multiplication factor is important to investigate the appropriate safety margin for a target system. The random sampling method is a practical and useful method for the UQ. Note that, when using the random sampling method, the statistical error of the estimated uncertainty is inevitably caused. Therefore, a longer calculation time is required because of the larger sample size to reduce the statistical error. 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, this study proposes an improved deterministic sampling method using the simplex ensemble and the scaling method for efficient UQ. The features of the proposed method are summarized as follows: 1) the sample size is equal to (r+2), where r corresponds to the effective rank of the covariance matrix between the input variables; 2) the scaling method enables us to arbitrarily give a perturbation amount of the input parameters in the deterministic sampling method, thereby the weighted mean and covariance for the target output parameters are deterministically estimated depending on the weight by the scaling factor; 3) the scaling factor can be updated to prevent the negative values in the perturbed input variables. The effectiveness of the proposed method is demonstrated through the UQ due to fuel manufacturing uncertainties for a typical PWR pin-cell burnup calculation.

Data Assimilation Using Prompt Neutron Decay Constant for Water to Reduce Uncertainties due to Thermal Neutron Scattering Law Reviewed International journal

Yoshinari Harada, Hibiki Yamaguchi, Tomohiro Endo, Akio Yamamoto

Proc. ICNC2023 2023.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

In the neutronics analysis for a water-containing system, the thermal neutron scattering law (TSL) of water affects the calculated values of the neutronics parameters. In our previous study, we quantified the TSL data-induced uncertainty of the prompt neutron decay constant measured for water tank systems and evaluated the correlations between the different-sized water tank systems. Our previous study clarified that there were strong TSL data-induced correlations of ~0.9 in between the smallest and other water tank systems. Based on these strong correlations, it was suggested that the TSL data-induced uncertainties in the numerical predictions of for other water tank systems can be improved by the data assimilation using the experimental result of α for the smallest water tank. To demonstrate the uncertainty reduction using the experimental result of , this study aims to perform the data assimilation by the Bayesian Monte Carlo (BMC). To address the degeneracy problem in the conventional BMC, the merging particle filter was applied in this study. Consequently, the relative standard deviation of the TSL data-induced uncertainty of was reduced to 1/3. While the experimental results of existed within the 2σ-uncertainty range of the calculated values before the data assimilation, the calculated values of after the data assimilation were improved so that the experimental results were located within the posterior 1σ-uncertainty range.

Application of the RSE Method for the Resonance Treatment of HTGR Fuel with Double Heterogeneity Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Satoshi Takeda, Hiroki Koike, Kazuya Yamaji, Koji Asano

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

The resonance calculation using energy spectrum expansion (RSE) method is applied to realistic HTGR fuel elements containing the double heterogeneity. The pointwise disadvantage factor is used to spatially homogenize fuel particles in a fuel compact. The pointwise disadvantage factor is calculated using the method of characteristics coupled with the statistical geometry method. Verification calculations are carried out for a typical fuel compact cell of HTGR fuel. The ultra-fine group spectra, multi-group effective microscopic cross sections, and multi-group microscopic reaction rates are compared with the reference solution obtained by ultra-fine group (UFG) spectrum calculation. Differences between the RSE and UFG calculations are small and the difference in k-infinity due to the present resonance treatment is estimated to be 0.025% Δk.

Uncertainty Quantification of Prompt Neutron Decay Constant α due to Thermal Neutron Scattering Law of Water Reviewed International journal

Yoshinari Harada, Hibiki Yamaguchi, Tomohiro Endo, Akio Yamamoto

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

Thermal neutron scattering law (TSL) data for 1 H in H2O causes uncertainties of neutronics calculations for systems containing light water. As a preliminary study to improve the TSL data by the data assimilation using experimental data of prompt neutron decay constant for simple water tank systems, this study quantifies the TSL data-induced uncertainty of prompt neutron decay constant based on the random sampling method. In this study, 200 LEAPR formatted TSL data from TENDL-2021 is utilized as the randomly sampled TSL data for 1 H in H2O. For each TSL data, the numerical result of is calculated using an in-house deterministic code of eigenvalue calculation. As a result, this study clarifies that experimental results of exist within the 2 uncertainty range of the calculated values for four different sized water tank systems. Furthermore, TSL data-induced correlations of between different water tank sizes are also estimated. Consequently, there are strong positive correlations between them, i.e., correlation coefficients are greater than 0.9. This result implies that the TSL data for 1 H in H2O can be updated by the data assimilation using the measurement to reduce the TSL data-induced uncertainties of neutronics calculations for other systems that have the strong correlation due to the TSL data.

Study on a Data-Driven Neutron Transport Calculation Method Using Proper Orthogonal Decomposition Reviewed International journal

Shunya Teratani, Masato Ito, Tomohiro Endo, Akio Yamamoto

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

The proper orthogonal decomposition (POD) can reduce the dimension of the neutron flux distribution using a small number of POD bases and their expansion coefficients. POD can be directly applied to neutron diffusion calculations because the neutron diffusion equations can be discretized in a matrix form for the total neutron flux. However, application of POD to neutron transport calculations that rigorously treat the angular dependency of the neutron flux is difficult, because the transport calculation cannot be directly expressed by a matrix form equation for the total neutron flux. To address this problem, we propose a new POD transport calculation method based on a data-driven approach that utilizes multiple input and output data in transport calculations. As a feasibility study, the data-driven POD transport calculation method was implemented in a one-dimensional homogeneous slab geometry to verify the proposed method. Then, using a non-parametric way based on the Wilks' method, the upper tolerance limit (UTL) of the calculation error was statistically evaluated with the probability of 95% and the confidence level of 95%. Through this study, we demonstrate the proposed method can accurately calculate the total neutron flux, if "the number of input or output data used in the data-driven POD, " is larger than or equal to "the number of POD bases, " and is sufficiently large. In addition, we investigated the relationship between the contribution ratio of singular values for snapshot or data matrices and the UTL of relative root mean square error. Consequently, we observed the relationship of "(1−contribution ratio) ≈ UTL of rRMSE." Therefore, we expect that the number of POD bases can be determined based on the contribution ratio according to a target calculation accuracy.

Optimization of Nuclear Fuel Management for Multi-Module SMRs Reviewed International journal

Yoshiki Yamashita, Tomohiro Endo, Akio Yamamoto

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

A fuel management strategy for light water type Small Modular Reactors (SMRs) was studied assuming that multiple cores share nuclear fuels. Fuel management for two and three cores for the cases with and without fuel sharing and was considered. The optimization of power sharing of fuel batches was used for the optimization of fuel management instead of direct optimization of fuel loading patterns. The average discharge burnups and cycle lengths for various operating patterns were compared by changing the cycle length (the number of fresh fuel assemblies) of each core. As a result, it was found that the fuel cycle cost could be improved by sharing the nuclear fuels among multiple cores when their cycle lengths are different.

Evaluation of Neutron Flux Expansion Error by POD Bases Based on Wilks' Method Reviewed International journal

Masato Ito, Tomohiro Endo, Akio Yamamoto, Yasuhiro Kodama, Hiroaki Nagano

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

Proper orthogonal decomposition (POD) is a numerical analysis method to reduce the core analysis cost. In POD, orthonormal bases (POD bases) can be obtained by the data-driven approach to efficiently expand the spatial distribution of neutron flux. To ensure high accuracy of core analysis using POD, statistical evaluation of the upper tolerance limit (UTL) of neutron flux expansion error by POD bases is necessary. In the present study, the statistical evaluation for the expansion error is investigated using the non-parametric method based on the one-sided Wilks' formula. Using the first-order Wilks' method, the desired UTL with the target probability and confidence level can be estimated as the maximum value among the wilks random sampling results. In the verification for a pin-by-pin single UO2 fuel assembly without control rods, we investigate whether the UTL of the POD expansion error can be appropriately estimated using the Wilks' method. First, many estimated UTLs of the expansion error are estimated by randomly changing the calculation conditions. Next, each of the UTLs is tested whether it can be successfully estimated by checking the calculating probability using the estimated UTL is larger than or equal to the target probability. Finally, the confidence level is calculated as the ratio of the "successfully estimated UTLs" to the total UTLs. Consequently, the calculated confidence level calc includes the reference level ref within the range of statistical uncertainty. Therefore, this study demonstrates that the UTL of the expansion error can be appropriately estimated using the first-order Wilks' method.

Development of Real-Time 3D Fine Mesh Kinetics Calculation Method Based on POD Reviewed International journal

Kaito Ito, Akio Yamamoto, Tomohiro Endo, Kosuke Tsujita

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

A reduced order model using the proper orthogonal decomposition to reproduce 3D fine mesh kinetics calculations in real time is proposed and its applicability is verified through a benchmark calculation. The orthogonal basis is generated with the results of the 3D fine mesh calculation and a reduced order model is developed using the orthogonal basis. The results obtained by the 3D fine mesh kinetics model and the reduced order model are compared for a benchmark problem considering a control rod operation in the LMW benchmark problem. The relative root mean square error of the integrated core power is within 0.1%. The computation time per time step of the reduced order model is approximately 0.1 s, which confirms that the model is available for real-time application including on-line monitoring.

Deep Penetration Calculations Combining Proper Orthogonal Decomposition and Monte Carlo Methods Reviewed International journal

Kaito Mori, Akio Yamamoto, Tomohiro Endo

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

A deep penetration calculation method that combines a POD basis obtained by deterministic calculations and the expansion coefficients for the POD basis obtained by the continuous energy Monte Carlo method is proposed. The present method is applied to a simple deep penetration calculation of a slab geometry. By comparing the results obtained by the present method, the continuous energy Monte Carlo method, and the multigroup deterministic transport method, the statistical error of the continuous energy Monte Carlo method in deep penetration calculations and the systematic error of the multigroup deterministic transport method can be reduced by the present method.

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

Akio Yamamoto, Tomohiro Endo

Transactions of the American Nuclear Society Vol. 128 ( 1 ) page： 690 - 693 2023.6

Statistical Uncertainty Quantification of Probability Tables for Unresolved Resonance Cross Sections Reviewed International journal

Kenichi Tada, Tomohiro Endo

EPJ Web of Conferences Vol. 284 page： 14013 - 14013 2023.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

The probability table method is an important method to treat the self-shielding effect in the unresolved resonance region. A probability table is generated by using many “ladders” that represent pseudo resonance structures. This study developed a quantification method of the statistical uncertainty of a probability table. The product of the probability table and average cross section in each probability bin was considered as the target of the statistical uncertainty of the probability table. The central limit theorem (CLT), bootstrap method, and jackknife method were adopted to calculate the statistical uncertainty. The statistical uncertainties calculated using these methods were compared with the reference results. The calculation results showed that the statistical uncertainties obtained by CLT were similar to those of the other methods. Because the CLT calculation time was faster than that of the other methods, CLT was deemed as the best method for calculating the statistical uncertainty of the probability table. The statistical uncertainty quantification of the probability table developed in this study was implemented in nuclear data processing code FRENDY version 2. FRENDY version 2 can generate a probability table using the tolerance of the statistical uncertainty of the probability table.

DOI： 10.1051/epjconf/202328414013

Applicability evaluation of Akaike’s Bayesian information criterion to covariance modeling in the cross-section adjustment method Reviewed International journal

Shuhei Maruyama, Tomohiro Endo, Akio Yamamoto

EPJ Web of Conferences Vol. 281 page： 00008 2023.3

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

The applicability of Akaike’s Bayesian Information Criterion (ABIC) to the covariance modeling in the cross-section adjustment method has been investigated. In the conventional cross-section adjustment method, the covariance matrices are assumed to be true. However, this assumption is not always appropriate. To improve the reliability of the cross-section adjustment method, the estimation of the covariance model using the metric ABIC has been introduced, and the performance of ABIC has been investigated through simple numerical experiments. This paper derives the formula to efficiently evaluate ABIC which is represented by a lower rank matrix to enable numerical experiments with large samples in a realistic computation time. From the results of the numerical experiments, it has been confirmed that ABIC tends to select a covariance model with fewer hyperparameters and a smaller variance for the estimation error. However, it has also been found that this desirable property of ABIC will be lost when the structure of the covariance model is far from the true one.

DOI： 10.1051/epjconf/202328100008

Development of a robust nuclear data adjustment method to outliers Reviewed International journal

Yuhei Fukui, Tomohiro Endo, Akio Yamamoto, Shuhei Maruyama

EPJ Web of Conferences Vol. 281 page： 00006 2023.3

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

We developed a new nuclear data adjustment method for experimental data containing outliers. This method mitigates the effect of outliers by applying M-estimation, a type of robust estimation, to the conventional nuclear data adjustment method using sensitivity coefficients. Based on the M-estimation, we derived a weighted nuclear data adjustment formula and developed a weight calculation method. The weighted nuclear data adjustment formula was derived by weighting the function to take the extremum of the conventional nuclear data adjustment. The weighting of each nuclear characteristic is calculated from the difference between the measured and calculated values of the nuclear characteristic. This weight calculation method can evaluate the validity of each nuclear characteristic by considering correlations between nuclear characteristics using singular value decomposition. The proposed method and the conventional method were compared and verified by twin experiments. In the twin experiments, the nuclear data were adjusted using experimental data that intentionally included outliers. As a result of twin experiments, it was confirmed that the nuclear data were adjusted robustly and appropriately even with the experimental data containing outliers.

DOI： 10.1051/epjconf/202328100006

A New Approach for Resonance Treatment of Doubly Heterogeneous Fuel Using the RSE Method Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Satoshi Takeda, Hiroki Koike, Kazuya Yamaji, Koichi Ieyama, Koji Asano

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) page： 2042 - 2051 2022.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

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

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

Ryota Katano, Akio Yamamoto, Tomohiro Endo

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) page： 2032 - 2041 2022.5

Authorship：Last author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

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

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