Quantitative assessment of non-destructive testing (NDT) capability often relies on probability of detection (POD) curves obtained by the â-a method that is commonly used in the recent POD analyses. However, practical guidance regarding the required number of flaws and their optimal size distribution remains limited. This study addresses this issue by exploring the influence of sample size and flaw size distribution on â-a POD estimation through Monte Carlo simulations. A known, nonlinear, saturating relationship between flaw size and signal amplitude obtained by numerical simulations of angle-beam ultrasonic inspection is adopted as a reference, and synthetic datasets are generated under various sampling conditions. The analysis shows that in the conventional â-a method, which performs a linear regression after variable transformation, POD estimates can become strongly biased and highly scattered when sampled flaws are not concentrated near the true (and unknown) flaw size of interest. In contrast, regression models applied without variable transformation, particularly a sigmoid model designed to reflect the saturation behavior of NDT signals, produce more stable estimates of flaw sizes of interest. These include a50 and a90, which are flaw sizes corresponding to 50% and 90% probabilities of detection, respectively. Furthermore, they exhibit substantially reduced dependence on the chosen flaw size range. These findings indicate that using regression functions consistent with the underlying signal physics can relax stringent requirements on flaw size distribution and enable reliable â-a POD studies with a comparatively small number of flawed specimens. They also underscore the importance of physics-based modeling and suggest that concepts developed in model-assisted POD (MAPOD) can be effectively leveraged even when simulation data are not directly used to construct POD curves.

This study proposes a novel approach for evaluating the probability of detection (POD) by considering the spatial distribution characteristics of measured signals, with a particular focus on its application in eddy current testing (ECT) under a low signal-to-noise ratio (SNR) situation. To simulate such a situation, eighteen welded austenitic stainless-steel plates were prepared, and seventy-three artificial slits were introduced parallel to their weld beads to simulate weld cracks. ECT signals were collected from the samples using a uniform eddy current probe. Experimental results revealed that evaluating flaw presence solely based on the maximum amplitude of measured signals, as employed in the conventional a-a approach, was quite misleading. In contrast, the proposed approach, which quantifies deviations in the one-dimensional spatial distributions of signals inspired by the Gini coefficient used in economics to assess income inequality, provided fewer false positives and false negatives. A multi-parameter POD model was then developed, formulating POD as a function of both the length and depth of a slit using these deviations, namely the Gini values. Decision thresholds, which are critical for POD estimation, were determined from the maximum signal features of the seven slit-free samples. The results demonstrate that the proposed Gini-based approach enables a simpler POD analysis while reducing false detections and mitigating the challenge of setting a proper decision threshold under a low SNR situation, in contrast to the conventional amplitude-based method.

This study aimed to probabilistically evaluate the size of a fatigue crack on a type 304 austenitic stainless steel flat plate using eddy current signals. Three fatigue cracks, with depths ranging from 2 mm to 5 mm, were introduced into the plates through a four-point bending test. After the starter notches for the test were removed, eddy current testing was conducted using a differential-type plus point probe at a frequency of 200 kHz to collect signals caused by the cracks. The fatigue crack was modeled as a rectangular continuous domain with a constant width and uniform electromagnetic properties. Since mechanical damage transforms the austenitic phase into the martensitic phase, both the conductivity and permeability of the domain were explicitly considered. The depth and length of the cracks were evaluated using a Bayesian-based inverse algorithm, assuming the electromagnetic properties of the crack were either known (equal to air) or unknown. When the crack was modeled as air, the evaluated crack sizes deviated considerably from the actual sizes. In contrast, assuming the electromagnetic properties to be unknown provided better evaluations with quantified uncertainty.

This study proposed a multi-parameter probability of detection (POD) model to probabilistically assess the capability of eddy current testing (ECT) for the inspection of divertor monoblock surfaces. The model assumes that a signal caused by the presence of a crack follows a probability density function with the depth, length, and position of the crack as variables. The parameters of the model are estimated by the combinational use of measured and experimental signals, and the probability that the signal exceeds a certain threshold is regarded as the probability of detection as the conventional a-a POD analysis. To demonstrate the model, sixty-three tungsten samples with an artificial slit were prepared to simulate the thermal fatigue cracking of the monoblock plasma-facing surface. The samples were measured using a differential plus-point ECT probe with a 1 mm lift-off and 500 kHz frequency. Correspondingly, numerical simulations of an eddy current simulator based on the A-phi formulation were performed. The difference between the normalized slit signals and a flawless signal, which is obtained with the aid of image processing, was considered as the signal response to mitigate the influence of large noise caused at the edges of monoblocks. The results show that the proposed model can evaluate POD much more reasonably than conventional models that represent a flaw using one or two parameters.

This study explores the applicability of guided microwave testing to assess the severity of partial circumferential pipe wall thinning (PWT). Numerical simulations revealed that the resonant frequency of reflected TM01 mode microwaves exhibited a negative correlation with the circumferential angle, depth, and length of PWT. Notably, high-order modes activated in the defect region produced frequency outliers, with corresponding frequencies decreasing as PWT depth or length increased. Experiments conducted using a 15 m long pipe yielded a frequency spectrum of the processed signals with a similar waveform to that of the simulation results, suggesting the feasibility of using simulation data to train the evaluation model. A one-dimensional convolutional neural network (1D CNN), built to automatically extract information from the frequency spectrum, achieved remarkable accuracy exceeding 96.7% in classifying the partial circumferential PWT severity in both simulated and experimental scenarios. Comparative analysis revealed that both 1D CNN and k-Nearest Neighbor classifiers, utilising full waveform information, outperformed traditional back-propagation neural networks relying on handcrafted frequency points. These findings highlight the critical importance of waveform information in PWT evaluation and present a novel approach for PWT severity assessment using guided microwave testing for long pipe inspection.

This study investigates the magnetic properties of F82H steel under weak magnetic fields to assess the applicability of eddy current testing to the non-destructive inspection of blanket cooling paths made of F82H steel. Sample plates made of F82H steel and three other types of steel were prepared and subjected to cold rolling to induce residual stress. Eddy current tests were performed to gather signals from the samples using a pancake-type eddy current testing probe. While cold rolling altered the eddy current signals for F82H plates, the changes were less pronounced than those observed in the other steels. Subsequently, the B-H curves of the samples were measured using a vibrating sample magnetometer. The results of the measurement clearly showed that the residual stress changes the magnetic properties of F82H steel. Change in relative permeability correlated with variations in the eddy current signal. The findings indicate that residual magnetization, rather than magnetic property changes induced by residual stress, is the primary source of noise in the eddy current signals.

This study proposes a numerical model to predict pipe failure based on periodic non-destructive inspections using electromagnetic acoustic resonance (EMAR). A total of 149 artificially corroded samples that simulated flow-assisted corrosion were prepared; 27 of them were plates, and others were from pipes of various dimensions. The samples were measured using EMAR, and the thicknesses of the samples were evaluated based on the fundamental resonance frequency. The results of the evaluations were compared with the actual thicknesses measured by a caliper gauge to quantify the uncertainty in pipe wall thickness evaluation. Numerical evaluations were performed to predict pipe failure probability in the future based on the results of periodic EMAR measurements. Three scenarios of pipe thickness reduction were considered, and each scenario assumed that pipe thickness measurements by EMAR were performed every five years. The actual pipe wall thickness, which is not necessarily the same as the EMAR evaluations, is estimated as a probability density function using the Bayesian approach proposed in an earlier study by the authors. Whereas this study considers only pipe rupture, the results of numerical simulations support the validity of the model especially when the corrosion rate is not constant.

This study proposed a data fusion method based on Bayesian estimation for flaw characterization using eddy current signals and evaluated its applicability using measured signals. The proposed method can fuse several measured data to define the likelihood function as multiplication of probabilistic distributions of eddy current signals and calculate posterior distribution based on the assumption that all signals are independent. Rectangular slits on austenitic stainless-steel plates were measured by plus-point and uniform eddy current probes with three frequencies: 50 kHz, 200 kHz, and 400 kHz. All combinations of probes and frequencies were utilized to estimate flaw size distribution. The results indicate that the proposed method can accurately evaluate the flaw size from the eddy current signals and probabilistically evaluate the error. Furthermore, variations in the importance of each data were found in the comparison of all combinations of probes and frequencies; therefore, the probabilistic sizing method could be used to determine the proper measurement conditions from the viewpoints of uncertainty of the evaluation.

This study evaluated the applicability of a high-frequency ultrasonic test to the inspection of the bonded interfaces between a divertor monoblock and a cooling pipe. This study prepared a tungsten block bonded with 1 mm of oxygen-free copper and 1.5 mm-thick CuCrZr plates, which simplifies one of the fundamental designs of a divertor: a tungsten monoblock bonded with a cooling pipe with a copper interlayer. The samples were fabricated using a high-temperature vacuum furnace for diffusion bonding. A high-frequency ultrasonic immersion test using a 30 MHz probe was performed from the CuCrZr surface to simulate inspecting the interface from inside the pipe. Ultrasonic images obtained by the test were consistent with the actual bonding condition revealed by sectioning the samples; whether a flaw exists on the interface between CuCrZr and the oxygen-free copper or that between the oxygen-free copper and tungsten was clearly distinguished. The results of this study also suggested the possibility of detecting the growth of crystal grains caused by improper bonding such as too high bonding temperature.

In this study, we evaluated the dependence of the heat transfer properties of a molten salt mixture (LiF-NaF-BeF2-Flinabe) on its composition ratio to determine its applicability as a coolant in a nuclear system. Specifically, we evaluated the density, specific heat, viscosity, and thermal conductivity of Flinabe using molecular dynamics simulation and calculated the Prandtl number and figure of merit heat transfer metrics. The calculated density, specific heat, and viscosity differed from the experimental values by approximately 20 %. Although we could not directly compare the calculated thermal conductivity of Flinabe due to a lack of accurate experimental measurements, we discovered a temperature dependence consistent with that of other salts. Overall, the findings of the present study revealed that light LiF-rich molten salts have favorable heat transfer characteristics. The ternary system LiF-NaF-BeF2 = 33-29-38 mol% has a relatively low Prandtl number and figure of merit compared to the binary system LiF-BeF2, and the melting point is 25 K lower than that of a binary salt. We concluded that LiF-NaF-BeF2 = 33-29-38 mol% is the optimal composition for a heat transfer medium for nuclear power systems.

This paper experimentally compares low-frequency and pulsed eddy current testing techniques in measuring plate thickness. The experimental setups for both methods were built using general commercial devices. A single polarity rectangular wave with a 10 Hz pulse repetition frequency and 50% duty was utilised as the excitation wave in pulsed eddy current testing. Ferromagnetic steel and nonferromagnetic aluminium alloy plates of 1, 3, 5, and 10 mm thicknesses were tested at various lift-off distances. Using peak amplitude, valley amplitude, time to attenuate, logarithmic slope, and reciprocal square root of the logarithmic slope as features, pulsed eddy current testing could effectively evaluate the steel plates thicker than 3 mm and all the aluminium alloy plates. In contrast, low-frequency eddy current testing using a 10 Hz excitation frequency could evaluate both steel and aluminium alloy plates using signal phase. This indicates that redundant frequency components may impair the effectiveness of pulsed eddy current testing. Moreover, low signal-to-noise ratio and simple signal processing methods struggle to detect minor signal variations. Additionally, the linearity of phase versus thickness for steel is better than for aluminium alloy, potentially indicating that ferromagnetic materials enhance the coupling between the coil and the plate.

This study evaluated the applicability of eddy current testing to the surface inspection of a divertor plasma-facing unit in a Tokamak fusion reactor. Artificial slits were introduced on the surfaces of some samples. The eddy current testing was performed to detect these slits. A quantitative detection evaluation method based on evaluating the distribution differences is proposed. The results reveal that the signals of slits near the edge are easily buried by the edge signals and difficult to detect directly from the signal amplitude image. With the aid of the proposed method, not only the slit in the middle of the sample surface but also the slits near the sample edges were successfully detected by eddy current testing.

In industry, natural cracks usually exist in complex forms such as adjacent, colony, irregular, and crossing. Mere magnetic field is inadequate to accurately evaluate the complex cracks using eddy current testing. In this study, an improved eddy current imaging method using the signal of rotating eddy current testing (RECT) was proposed to reconstruct the surface profile of complex cracks. A transformation method was adopted to transform the signals of RECT into those under uniform eddy current testing at the desired orientation. The deconvolution of the transformed signals and square current dipole was carried out to obtain eddy current images at eight orientations around complex cracks. By accumulating the eddy current images, the surface profile of the complex cracks was reconstructed. Simulations and experiments were carried out to illustrate, validate, and test the proposed method. The results indicated that the obtained surface profiles were clearer than those obtained by the previous method using uniform eddy current testing. The improved method was effective for artificial complex slits and irregular stress corrosion crack colonies. Moreover, its performance was stable for the cracks with different angles and depths.

Electromagnetic acoustic resonance method (EMAR) is promising for online monitoring of pipes wall thinning with corrosion during operation. However, the improvement of measurement accuracy is one of issues to be solved, although some signal processing methods such as superposition of nth compression method (SNC) have been proposed in order to improve the accuracy of wall thickness estimation. In this study, for the purpose of highly accurate evaluation of the wall thickness, the thickness of 51 corrosion specimens was measured and compared with the true thickness obtained by 3D laser scanner. The fundamental resonance frequency of EMAR signal spectrum was evaluated by discrete Fourier transform method (DFT) and SNC method, and the wall thickness was calculated. As a result, evaluated thickness by EMAR almost corresponded to the average of true thickness. The accuracy of the evaluated thickness by the SNC method depends on the method to set the postulated thickness for determining the number of compressions. It was found that using the evaluated thickness by the DFT method for determining the number of compressions improved the estimation accuracy of the evaluated thickness by the SNC method. In addition, it was confirmed the estimation accuracy of this evaluated thickness was higher than that of the evaluated thickness by the DFT method.

This study proposed a simple side-incident TE 11 mode microwave probe for the rapid and long-range inspection of cracks in metallic pipes. The probe feeds the microwaves to a metallic pipe, which works as a waveguide; the reflection signal provoked by a defect is measured for detection and localization. The probe enables the detection of both circumferentially and axially oriented cracks, unlike those reported in earlier studies. To achieve better performance, numerical simulations were conducted to evaluate the conversion efficiency and optimize the insertion length of the coaxial cable and the exposed length of the cable core wire. The simulation results suggest that the optimized probe configuration is feasible for pipes with various diameters by proportionally changing the current probe configuration. Although injected microwaves propagated in two directions, the ratio of microwaves to one direction could be controlled by adjusting the inclination angle and the exposed length of the cable core wire. Subsequently, three TE 11 probes fabricated according to the simulation results were used to detect circumferential and axial slits in a brass pipe. The results showed that circumferential slits in the vertical positions (parallel to the nontilted coaxial cable) and axial slits in the horizontal positions (perpendicular to the nontilted coaxial cable) caused large reflections, consistent with the electromagnetic field distribution of the TE 11 mode microwaves in a circular waveguide. Further experiments verified the feasibility of the designed probe for pipes with different diameters and for directional pipe inspection.

This study explores the applicability of microwave nondestructive testing to detect a metal pipe's inner crack. Three-dimensional finite element simulations were conducted to study the inspectability of cracks using microwaves in different modes and the dependency of the reflection characteristics of microwaves on crack size. The simulation results showed that microwaves in the TM01 and TE01 modes can detect circumferential and axial cracks, respectively. The positive relationship between crack size and intensity corresponding to the reflected microwaves was obtained in simulations and then verified by experiments. In both simulations and experiments, the axial crack length showed a small influence on the results, especially for shallow crack detection. In the experiments, circumferential and axial cracks with a width of 0.3 mm were detected using microwaves. The experimental results revealed that signal amplitudes decreased when a slit penetrated a pipe wall, probably due to a microwave leakage.

This study evaluated the effect of the grain size of the divertor's cooling pipe on the capability of high-frequency ultrasonic tests to evaluate the quality of the bonded interface between the divertor's cooling pipe and armor. First, simple oxygen-free copper and copper-chromium-zirconium block samples with different grain sizes were prepared and measured by an ultrasonic microscope with a 35 MHz probe. The results of the measurements confirmed that the non-uniformity of backwall echoes increased with the grain size of the samples. Samples with large grains provided distinctive signals that can be clearly confirmed on the ultrasonic C-scan images. Subsequently, two bonded samples consisting of 2.5 mm oxygen-free copper bonded with a block of pure tungsten that meets the material specifications of tungsten for ITER component which mimicked the basic design of a divertor's cooling pipe and a monoblock, were measured to evaluate their bonded interfaces. One of the bonded samples bonded at a high temperature provided distinctive signals due to the enlargement of the grain of the oxygen-free copper. Results confirmed that the grain enlargement is the reason for reduced defect detection capability of the high-frequency ultrasonic tests as was suggested previously. This study also revealed that the enlargement of grain caused by improper manufacturing would be non-destructively detectable by high-frequency ultrasonic tests.

This study reports a board game design that would be an effective tool for teaching and learning the best mix of national power sources in a class concerning energy and sustainability in higher education courses. A board game was developed to understand the characteristics of power sources from a Japanese viewpoint based on an earlier study of the authors. The purpose of the game is to satisfy electricity demands by choosing power sources and procuring the resources necessary for power generation to help develop a country. A total of 50 undergraduate and graduate students were asked to assess the game. The results of the questionnaire-based survey conducted after the game confirmed the students’ evaluation that the game was highly enjoyable and could serve as an effective tool for energy and environmental education in high schools or universities. In addition, the average of “the ratio of the power sources proper to win the game” given by the students was similar to Japanese power mix before the Fukushima disaster, although the game significantly simplified, and even excluded, various factors affecting the national policy of power sources.

Piping in nuclear power plants is subject to corrosion and erosion caused by the interaction with fluids it carries. In order to prevent accidents such as pipe rupture, it is necessary to non-destructively inspect the thickness of the pipe wall and predict the remaining pipe life. In contrast, signals obtained by non-destructive inspection are affected by various uncontrollable and unknown factors, which will result in uncertainty in evaluating pipe wall thickness. Ignoring the uncertainty would lead to a large error in the pipe reliability assessment. Therefore, it is important to develop a reasonable pipe wall thinning management that can takes the uncertainty of non-destructive testing into consideration. Based on this background, this study aimed to develop a piping wall thinning prediction model that accounts for the uncertainty in evaluating pipe wall thickness and to evaluate its applicability to ultrasonic testing. At first, ultrasonic tests were performed to measure the thickness of specimens simulating flow accelerated corrosion. The results of the measurements were statistically analysed to obtain a mathematical model correlating the evaluated and true thickness. A numerical model to predict the reduction of wall thinning with its uncertainty is developed. Compared to the conventional method, the proposed method is able to predict wall thickness with high accuracy.