Useful and valuable measurement data obtained at the solid-moderated core for the development of accelerator-driven systems (ADSs) have been accumulated at the Kyoto University Critical Assembly ...(KUCA), and some of them have been open to the public. In order to efficiently utilize these data, experimental analyses with deterministic calculation procedures are helpful. In the present manuscript, a numerical benchmark problem is established. This benchmark problem can be utilized by users of the ADS-related measurement data obtained at the KUCA A-core to verify their own numerical tools devoted to experimental analyses. Material and geometrical specifications with reference solutions obtained by a continuous-energy Monte Carlo code MVP-II are provided.
In addition, numerical results obtained by a deterministic code system CBZ are also presented as an example. Through careful investigation about discretization on space and angle, guideline for proper discretization is provided. The CBZ results tend to underestimate the reference Monte Carlo solutions about 0.5%∆k/kk', and calculations of simplified core models suggest that this is caused by neutron leakage treatment in finite systems or resonance self-shielding treatment in CBZ.
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.
This open access book is a pedagogical text on nuclear reactor experiments, covering almost all the experiments that can be carried out at the University Training Reactor, Kindai University ...(UTR-KINKI) with respect to reactor physics and radiation detection, and additionally including academic materials of test and research reactors, nuclear instrumentation, nuclear laws and regulations, in this main body. The book is an excellent primer for students who are interested in reactor physics, radiation detection, nuclear laws and regulations at universities, and the best textbook for students who have started to study the nuclear energy related fields to understand the basic theories and principles of the experiments in the fields of reactor physics and radiation detection. UTR-KINKI has been used for educational reactor experiments and basic research in a wide range of fields related to the use of radiation (neutrons, gamma-ray, beta-ray, alpha-ray, and X-ray), including reactor physics, radiation detection, radiation health physics, activation analysis, radiation biology, medical applications and archaeology. Also, UTR-KINKI has been actively engaged in nuclear education with its long history of operation, and has gained extensive experience in educational activities for undergraduate and graduate students, elementary, junior high and high school teachers, junior high and high school students, and general audiences.
•The singular value decomposition (SVD) and the Unscented Transform (UT) algorithms are combined (SVD-UT).•The computational time is drastically reduced by revealing the active subspace thanks the to ...Low Rank Approximation (LRA) algorithm.•Both SVD-UT and LRA-UT results are compared with the random sampling technique.•The uncertainty quantification is performed during MSLB in PWR, where the response variables are computed by ATHLET thermal-hydraulic code.•The SCALE 6.2 code is used for calculating the reactivity coefficients and the covariance matrix.
The present studies focus on the quantification of uncertainty during the main steam line break accident scenario (MSLB) in PWR, assuming that there is a failure on the feed-water regulating valve of the broken steam generator. The scenario is characterized by the associated positive Doppler and coolant density reactivities which bring the core back to critical (return-to-power). Accordingly, the input uncertainty parameters are the Doppler and coolant density reactivities taking into account the correlation matrix among the input parameters, which is calculated by SCALE 6.2 code. The main safety parameters are the maximum cladding surface temperatures and average core power during the accident which are computed by ATHLET thermal-hydraulic code. The sampling-based uncertainty technique is considered to be the most dependable technique which can be applicable to any code, however it is computationally expensive. Therefore, it is important to develop efficient techniques which are capable of reducing the calculation time. The first approach is the SVD-UT where the Unscented Transform (UT) algorithm and singular value decomposition (SVD) are combined to generate a minimal sample points. In addition, due to the strong correlation between the input reactivities, the computational time can be further reduced by implementing the Low Rank Approximation (LRA) and revealing the active subspace.
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.
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.
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.
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.
Confidence interval estimation by the bootstrap method is investigated for the uncertainty quantification of neutronics calculation using the random sampling method. The random sampling method is a ...simple and practical technique to quantify an uncertainty (standard deviation) of the target parameter calculated by a core analysis code. It is noted that a statistical error is inevitably included in the estimated uncertainty because of the probabilistic method using random numbers. In order to estimate the statistical error of uncertainty, we focus on the bootstrap method. The bootstrap method is one of the resampling techniques to evaluate variance and confidence interval of a sample estimate (e.g. variance) without the assumption of normality. Through a lattice burnup calculation for a simplified boiling water reactor (BWR) fuel assembly, it is verified that the bootstrap method can reasonably estimate the confidence interval of uncertainty of infinite neutron multiplication factor (k
inf
) due to covariance data of JENDL-4.0. In the case of this problem, the distribution of k
inf
is well approximated by a normal distribution; thus, the confidence interval of uncertainty can be also estimated by the aid of chi-squared distribution. The merit using the bootstrap method is to simply estimate the confidence interval of uncertainty without the assumption of normality.
We observed that uncoated furosemide tablets turned yellow in a light-shielded automatic packaging machine and discoloration of the furosemide tablets was heterogeneity and occurred on the surface of ...the tablets only. The machine was equipped with an internal blower to maintain a constant temperature. Therefore, we investigated the effect of air flow on the discoloration of the furosemide tablets using a blower in a dark environment. The color difference (ΔE) of the furosemide tablets increased linearly as the blowing time increased. We performed structural analysis of the yellow compound in the furosemide tablets by LC-MS and identified the compound as a hydrolysate of furosemide. This suggested that furosemide hydrolysis was accelerated by the air flow. The furosemide tablets were prepared with the most stable furosemide polymorph, form I. X-Ray powder diffractometry and IR spectroscopy showed that during tablet preparation, no crystal transition occurred to an unstable furosemide polymorph. Furthermore, IR spectroscopy showed that the crystal form of furosemide in the yellow portion of the tablets was form I. To elucidate the factors producing the discoloration, we investigated the effect of humidity and atmosphere (air, oxygen, and nitrogen) on the discoloration of the furosemide tablets. The results suggested that the discoloration of the furosemide tablets was accelerated by oxidation, although humidity did not affect the hydrolysis. Therefore, we concluded that the discoloration of the furosemide tablets in the automatic packing machine was caused by acceleration of oxidative degradation by air flow.
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