Faculty Profiles - ENDO Tomohiro

MISC - ENDO Tomohiro

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Implementation of Random Sampling for ACE-format Cross Sections using FRENDY and Application to Uncertainty Reduction Reviewed International journal

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

Proc. M&C2019 page： 1493 - 1502 2019.8

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

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.

Calculation Method of Estimated Criticality Lower-limit Multiplication Factor using the Bootstrap Method Reviewed International journal

T. Hayashi, T. Endo, A. Yamamoto

Proc. M&C2019 page： 1874 - 1885 2019.8

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

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.

A Resonance Calculation Method using Energy Expansion Bases based on a Reduced Order Model Reviewed International journal

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

Proc. M&C2019 page： 1081 - 1092 2019.8

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

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 U238. Comparisons of the results obtained by the present and the ultra-fine group (reference) methods show the fundamental validity of this method.

Data Assimilation using Subcritical Measurement of Prompt Neutron Decay Constant Reviewed International journal

T. Endo, A. Yamamoto

Proc. M&C2019 page： 1864 - 1873 2019.8

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

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 k_eff.The sensitivity coefficients of k_eff 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 k_eff due to the 56 group SCALE covariance data can be reduced. The experimental value of α contributes to improving nuclear data of fission spectrum χ and total fission neutron number ν via strong correlations between χ and prompt χ_p and between ν and prompt ν_p.

Uncertainty Quantification/Reduction of BWR Core Characteristics considering Cross Section and Thermal- hydraulics Uncertainties Reviewed International journal

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

Trans. Am. Nucl. Soc. Vol. 120 page： 851 - 854 2019.6

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

The uncertainty quantification of the critical eigenvalue of BWR is performed considering uncertainties of cross sections and thermal-hydraulics using the random sampling method. Using the quantified results, the uncertainty reduction of predicted critical eigenvalues is carried out using the bias factor (BF) or the physics-guided coverage mapping (PCM) method. The dominant contributor to the uncertainty for critical eigenvalue is the cross section, followed by the void fraction. Uncertainties of the rated thermal power and the core flow have a smaller impact than those of the cross section and void fraction. By applying the BF or the PCM method, bias of the predicted critical eigenvalue can be reduced. However, reduced uncertainty seems to be too small, suggesting there are still missing uncertainties that should be taken into account. The measurement error and the modeling approximation error would be the candidates for additional uncertainties.

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

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

The Proceedings of the International Conference on Nuclear Engineering (ICONE) Vol. 2019.27 page： 1022 - 0 2019.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Society of Mechanical Engineers (ASME)

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

Scopus

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

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

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

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

A simplified treatment for offset fuel assemblies due to bowing is proposed. In the present method, nominal (nonoffset) geometry is used while cross section of the gap region is corrected to incorporate the variation of gap size. Verification results in the single assembly geometries and the 5x5 assembly geometry indicate that the present method accurately reproduces the reference results obtained by explicit consideration of the deformed geometry. Since the present method does not require geometry change, it will be a convenient candidate for high-fidelity core simulators that explicitly consider the heterogeneous geometry. In the present summary, validity of the proposed method is verified by a typical situation. Verification in other conditions (e.g., use of different energy group structures, transport or diffusion method) will be a future task.

Transport Consistent Diffusion Coefficient for CMFD Acceleration Reviewed International journal

A. Yamamoto, T. Endo, A. Giho

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

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

The transport consistent diffusion (TCD) coefficient is derived using the even-parity transport equation and the twonode problem in one-dimensional geometry. TCD depends on the optical mesh size and shows similar behavior with the effective diffusion (EffD) and the artificial grid diffusion (AGD) coefficients. Since EffD and AGD coefficients can contribute to the stabilization of the CMFD/GCMR acceleration for MOC calculation, TCD coefficient will be also useful for the CMFD acceleration.

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

M. Matsushita, T. Endo, A. Yamamoto

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

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

A surrogate model (ROM) for severe accident analysis (SBO) is developed using the low-rank approximation with SVD in order to reduce the calculation costs of a severe accident code for safety margin analysis. ROM can rapidly reconstruct many accident progression results using 25 samples obtained by the RELAP5/SCDAPSIM. Only 9 bases out of 25 bases are used to construct the surrogate model. The boundary between the core damage and core intact regions estimated by ROM reproduces that obtained by the RELAP5/SCDAPSIM within the accuracy of approximately 300 s. In order to improve the accuracy, two issues will be addressed. The first one is the improvement on interpolation of expansion coefficients. The second one is the optimum number of samples and sampling methods to reach sufficient reproduction accuracy.

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

M. Yamamoto, T. Endo, A. Yamamoto

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

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

Reduction of cross section table size is tried by applying the dimensionality reduction technique with the singular value decomposition. The pin-by-pin multi-group cross sections obtained by a single assembly calculation are considered in this study. The accuracy of the reconstructed cross section is verified by comparison with the original cross section. In the present study, approximately 78% reduction in cross section table size is possible while keeping the accuracy of k-infinity higher than 1e−4. As the future study, the impact of the reconstructed cross section on the spatial distribution of neutron flux should be investigated. For example, assembly or core calculation using the reconstructed and original cross sections are carried out and their results will be compared. Finally, the validity of the present method should be verified in an actual core analysis.

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

A. Nonaka, T. Endo, A. Yamamoto

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

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

In this paper, the estimation method of subcriticality in dollar units based on the integral method for arbitrary state changes in a subcritical system is newly proposed. To confirm the applicability of the proposed method in a three dimension geometry, verification calculations of the virtual numerical experiments were carried out for the modified LMW benchmark problem. As a result, it was confirmed that the proposed method can roughly estimate the subcriticality in dollar units after the step-wise transient of state-change and the accuracy depends on the measuring region of neutrons. Therefore, in order to accurately estimate the subcriticality of a whole core, the spatial correction will be necessary. In the future study, the subcritical experiments using the proposed method at actual nuclear experimental facilities will be carried out. Treatment of measurement signals by a plurality of neutron detectors located at different positions will be an issue to be resolved.

Estimation of Subcriticality using Particle Filter Method Reviewed International journal

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

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

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

In this summary, the applicability of the Particle Filter (PF) method to estimate the subcriticality was investigated. Through the experimental result at the Kindai University reactor (UTR-KINKI), the estimated reactivity using the PF method is almost the same as that using the conventional inverse kinetics method (IKM) within the range of ±2σ. In case of the retrieval of fuel debris at Fukushima Daiichi Nuclear Power Station (1F-NPS), it is supposed that the temporal variations of (-ρ, Λ, βeff) could be occurred at the same time by changing H/U ratio due to the submersing and the drilling operations. As one of the future studies, the applicability of the PF method for the simultaneous estimation not only (-ρ) but also (Λ, βeff) will be investigated.

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

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

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

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

In the present study, an estimation method of modeling approximation error using the Kriging and the the principal component analysis (PCA) is developed and verified. The difference between the results obtained by a deterministic lattice physics code and a continuous-energy Monte Carlo code can be estimated by the proposed surrogate model. In the present study, the accuracy of the surrogate model is verified in a simple geometry. Verifications with more complicated and practical conditions are the future tasks.

Cache Efficient Flux Region Assignment for the Method of Characteristics Reviewed International journal

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2018 page： 788 - 799 2018.4

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

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.

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

T. Endo, A. Yamamoto

Proc. PHYSOR2018 page： 1240 - 1253 2018.4

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

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.

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

S. Sugaya, T. Endo, A. Yamamoto

Proc. PHYSOR2018 page： 2632 - 2643 2018.4

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

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.

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

A. Nonaka, T. Endo, A. Yamamoto

Proc. PHYSOR2018 page： 3271 - 3282 2018.4

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

A subcriticality measurement method using the integral method is developed for any step-wise 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 Region-Wise Even-Parity Discontinuity Factor for MOC Through Iterative Procedure Reviewed International journal

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2018 page： 1892 - 1903 2018.4

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

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.

Development of the Uncertainty Quantification Method of Activation in Reactor Structures using Reduced-Order Modeling Reviewed International journal

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

Proc. PHYSOR2018 page： 1793 - 1804 2018.4

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

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.

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

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

Proc. PHYSOR2018 page： 3042 - 3053 2018.4

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

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.

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MISC - ENDO Tomohiro