| ID | 101 |
| Title | Design of a dual-port, side-incident microwave probe for detection of in-pipe damage |
| Author | Guanren Chen, Takuya Katagiri, Noritaka Yusa, Hidetoshi Hashizume, |
| Published in | Measurement Science and Technology 31 (2020), 125001. |
| Keywords | electromagnetic non-destructive inspection, side-incident, in-pipe damage, mode converter |
| Abstract | This study reports a dual-port, side-incident microwave probe dedicated to the non-destructive inspection of metal pipes. Two types of side-incident probes (LJ and JL) are proposed to emit TM01 and TM02 mode microwaves into the pipe under test, and each type of probe has two ports used to inspect two opposite directions. Numerical simulations are conducted to study the dimensional parameters affecting the transmission characteristic of the probe and optimize the probe to obtain better mode purity and transmission directivity. The simulation results also suggest that the optimal probe dimensions for one inner pipe diameter can be applied to another diameter by multiplying the dimensions by a factor that is determined by the ratio of two diameters. Two LJ-type, side-incident probes with an inner diameter of 19 mm or 39 mm are fabricated according to the simulation results. The experimental verification is subsequently carried out to test the detection directivity of the probes by detecting the short pipes with partially milled damage situated on both sides of each probe. Experimental results show that the proposed dual-port, side-incident probe can effectively detect the in-pipe damage on either side of the probe using the corresponding port and thus realize the directional pipe inspection. Furthermore, this method shows a prospect of being applied to various inner pipe diameters. |
| ID | 102 |
| Title | エネルギーに対する意識と個人属性の関連性に関する調査研究 |
| Author | 遊佐訓孝 |
| Published in | エネルギー環境教育研究 15 (2021), 61-68. |
| Keywords | |
| Abstract | エネルギーに対する意識と個人属性の関連性評価のためのアンケート調査を実施した．インターネット上でのクラウドソーシングサービスを利用 し，3742名からエネルギー問題に対する関心の度合い，石油，石炭，ガス，水力，太陽光，風力，原子力を30年後どの程度使用するべきかなどの 問いに対する回答を，性別，年代，学歴，年収，居住環境，エネルギーに関する知識，婚姻状況，そして専攻/経歴の文系/理系の度合いに関するもの とともに収集した．同一回答者に対して短期間に2回の同一調査を実施し，回答の一貫性が乏しい回答者を除外して集計することでエネルギーに対する 意識と個人属性の関連性はより明瞭となった．全体的に，年代，収入，知識量が高い/大きいほどエネルギー問題に対し関心を持ち，エネルギー問題を 重要視しており，エネルギーの選択において意見を持っていた．また，女性は男性に比べ，高年齢層は低年齢層に比べ，また再生可能エネルギーを正し く理解している回答者はそうでない回答者に比べ，化石燃料及び原子力に対してより否定的であった．また，婚姻状況および居住環境による回答差異は 確認されなかった． |
| ID | 103 |
| Title | Demonstration of detection of the multiple pipe wall thinning defects using microwaves |
| Author | Takuya Katagiri, Guanren Chen, Noritaka Yusa, Hidetoshi Hashizume |
| Published in | Measurement 64 (2020), 465-472. |
| Keywords | Electromagnetic nondestructive testing, pipeline, multiple defects, signal processing, microwaves |
| Abstract | In this study, the applicability of a nondestructive method using microwaves to the detection of multiple pipe wall thinning defects was investigated. In numerical simulation, a single full circumferential defect was introduced into a straight pipe of 19 mm inner diameter, and the effect of the defect on transmitted waves was investigated. The transmitted energy ratio of the TM01 mode to the emitted wave was found to be 93% in average even in the presence of a 1-mm depth thinning. After that, experimental measurements were performed using a flanged brass tube with two artificial thinning defects. By applying signal processing to the measured S-parameters, clear reflections from the two defects were observed. By comparing the signals, we confirmed that the first full circumferential defect provides at most 12% amplitude attenuation of the reflected signal from the second defect, which should be related to the distance and size of the defects. |
| ID | 104 |
| Title | A detection sensitivity analysis model for structural health monitoring to inspect wall thinning considering random sensor location |
| Author | Haicheng Song, Noritaka Yusa |
| Published in | Research in Nondestructive Evaluation 32 (2021), 74-87. |
| Keywords | finite element simulation, probability of detection, sensor placement |
| Abstract | Structural health monitoring (SHM), which allows the detection of defects at an early stage by attaching sensors to the target, is an effective method of enhancing the reliability and the safety of important engineering structures. One of the practical difficulties of SHM is that usually a large area must be monitored using a limited number of sensors fixed at certain locations. And the sensor placement is a decisive contributor to the detection capability of SHM because measured signals are generally dependent on the location of a defect with respect to a sensor. In order to quantify the detection sensitivity more reasonably, this study proposes an analytical method based on a closed-form probability density function and a numerical method based on Monte-Carlo simulation to quantify the detection sensitivity, taking into account the randomness of sensor location. The effectiveness of the proposed detection sensitivity analysis model has been examined using simulated inspection signals of low frequency electromagnetic monitoring for detecting full circumferential pipe wall thinning. |
| ID | 105 |
| Title | Inverse analysis of low frequency electromagnetic signals for sizing local wall thinning using a multivariate probabilistic model |
| Author | Haicheng Song, Noritaka Yusa |
| Published in | NDT&E International119 (2021), 102417. |
| Keywords | nondestructive inspection, multi-frequency signal, inverse analysis |
| Abstract | Local wall thinning is a common form of degradation in carbon steel pipes, and a low frequency electromagnetic method is proposed in this study to inspect such wall thinning defects. In addition, an appropriate method needs to be developed to solve the inverse problem, which is to estimate defect size based on the inspection signal. Resolving the inverse problem of nondestructive inspection usually involves a machine learning algorithm and training data should be large and realistic to enable the algorithm to produce an accurate and reliable estimate of defect size. However, the acquisition of such training data is sometimes time-consuming and costly. Therefore, this study aims to estimate the size of local wall thinning based on the inspection signal by developing a new method to generate training data for a machine learning algorithm. With the aid of signals obtained from numerical simulation, a multivariate probabilistic model is proposed to infer a joint distribution over features extracted from measured multi-frequency signals from the low frequency electromagnetic inspection method. The joint distribution is subsequently leveraged to quickly generate sufficient training data for a Gaussian process regression algorithm that uses the signal features as the input to estimate defect size. The multivariate probabilistic model is proved able to reasonably characterize the joint distribution over the features. Moreover, the trained algorithm has been validated by experimental data and it is confirmed it can be used to estimate the residual thickness of a pipe wall with errors within tolerance and high reliability even when the lift-off is changed. |
| ID | 106 |
| Title | Frequency component mixing of pulsed or multi-frequency eddy current testing for nonferromagnetic plate thickness measurement using a multi-gene genetic programming algorithm |
| Author | Jiuhao Ge, Noritaka Yusa, Mengban Fan |
| Published in | NDT&E International 120 (2021), 102423. |
| Keywords | eddy current testing, Gini coefficient, linearity, genetic programming |
| Abstract | For the efficient use of frequency components, a frequency mixed feature for pulsed eddy current testing (PECT) or multi-frequency eddy current testing (MultiECT) was proposed for measuring nonferromagnetic plate thickness measurement. An evolutionary algorithm, multigene genetic programming, was employed to mix the frequency components using the best linearity as a target. Time domain and frequency domain finite element simulations of PECT and MultiECT were conducted. The simulation results revealed that, for in terms of thickness measurement, a mixed feature comprising two or three frequencies was more linear and accurate than the traditional peak time and decay coefficient of PECT. Experiments were conducted to validate the results of the simulations and to test the mixed feature in aluminum plate thickness evaluations. The experimental results also revealed that the use of more frequencies did not always increase the accuracy of thickness evaluations. Proper frequency component selection was more efficient than blindly addingincreasing frequency numbers. |
| ID | 107 |
| Title | Experimental investigation on bend-region crack detection using TE11 mode microwaves |
| Author | Guanren Chen, Takuya Katagiri, Noritaka Yusa, Hidetoshi Hashizume |
| Published in | Nondestructive Testing and Evaluation (accepted for publication) |
| Keywords | Non-destructive testing, metal pipe, mode conversion, bend, microwave probe |
| Abstract | This study experimentally investigates the efficacy of TE11 mode microwaves in detecting bend-region cracks. Three types of bends with different dimensions were deployed in a 3 m piping system and then tested, with an axial or circumferential slit machined at different angular positions to simulate a crack. The TE11 mode microwaves were excited using self-designed TE11 mode microwave probes and utilised for crack detection. The experimental results show clear reflection peaks at the bend position, demonstrating the feasibility of applying TE11 mode microwaves in the detection of bend-region cracks. Furthermore, the peak location of reflection is in accordance with the angular position of the slit. The findings also indicate that the peak amplitude of reflection is affected by the factors of mode conversion of microwaves at a bend. In addition, the experimental results also manifest an excellent signal-to-noise ratio to both two types of slits, suggesting that the microwave NDT is a powerful tool for bend-region inspection. |
| ID | 108 |
| Title | Probabilistic evaluation of EMAR signals to evaluate pipe wall thickness and its application to pipe wall thinning management, |
| Author | Noritaka Yusa, Haicheng Song, Daiki Iwata, Tetsuya Uchimoto, Toshiyuki Takagi, Makoto Moroi |
| Published in | NDT&E International122 (2021), 102475. |
| Keywords | periodic non-destructive inspection, electromagnetic non-destructive testing, electromagnetic acoustic transducer, pipe inspection, probability of detection, corrosion rate |
| Abstract | In this study an approach is proposed to probabilistically evaluate wall thickness and the probability of pipe failure when subjected to wall thinning based on the results of periodic non-destructive evaluations. Electromagnetic acoustic resonance (EMAR) has been adopted as a specific non-destructive method to evaluate pipe wall thickness. A probabilistic model correlating the true and evaluated thicknesses was proposed on the basis of the results of laboratory experiments to measure 38 artificially corroded carbon steel plates. A Bayesian approach was proposed to estimate the probability of true thickness and the probability of failure from results of multiple non-destructive evaluations at certain time intervals. The approach was applied to the analyses of several virtual periodic EMAR evaluations of pipe wall thickness that gradually became thinner, whose results demonstrate that the proposed approach is effective regardless of the variability of corrosion rates. |
| ID | 109 |
| Title | Evaluation of detection capability of eddy current probes with stochastic decision threshold for inspecting pits on austenitic stainless steel |
| Author | Jing Wang, Haicheng Song, Takuma Tomizawa, Noritaka Yusa, Yuanjing Ling |
| Published in | International Journal of Applied Electromagnetics and Mechanics67 (2021), 19-33. |
| Keywords | |
| Abstract | |
| ID | 110 |
| Title | Probability of detection model based on hit/miss data considering multiple signal features and multiple flaw parameters from eddy current testing suffering low signal to noise ratio |
| Author | Takuma Tomizawa, Haicheng Song, Noritaka Yusa, Hideki Yuya |
| Published in | Nondestructive Testing Diagnosis |
| Keywords | Weld, Cladding, Stainless steel, Corrosion pit, Non-destructive testing |
| Abstract | This study developed a probabilistic method based on hit/miss analysis to evaluate the detection capability of eddy current testing (ECT) under low signal-to-noise (S/N) ratio, taking into consideration multiple signal features and multiple flaw parameters. Realistic corrosion pits on stainless steel clads were prepared and eddy current inspection was conducted to gather flaw signal and noise. The proposed method was applied to the experimental data. Hit/miss of flaw signals were judged by the threshold using multiple signal features. The Hit/miss results were fitted to the selected function of probability of detection (POD) based on extended information criteria. The POD's 95% upper confidence bounds were generated by bootstrap method. Experimental results, generated POD contours, and 95% upper confidence bounds indicate that the proposed method allows for reasonable evaluation of the detection capability. |
| ID | 111 |
| Title | エネルギーベストミックス学習のためのボードゲーム開発 |
| Author | 遊佐訓孝，浜田良樹 |
| Published in | エネルギー環境教育15 (2021), 21-28. |
| Keywords | |
| Abstract | エネルギー環境教育における重要な課題の一つと位置付けられているエネルギーのベストミックスについて学ぶための4人用ボードゲームを開発した． 当該ボードゲームでは各プレイヤーはある国の電力供給を担う最高責任者となり，発電設備と資源を用いて発電し，必要量の電力を供給することで自国 を発展させることを目的とする．発展と共に必要電力も上昇するが，資源価格の変動や発電に伴う温室効果ガス排出量の制限，そして特定の発電設備が 有利/不利になるランダムイベント等があるため，各電源の特徴を考慮した上での選択が必要となるという特徴を有している．最終的に自国を最も発展 させたプレイヤーが勝利者となる．ゲーム未経験者12名による評価結果は，当該ボードゲームは市販のボードゲームと同程度のゲーム性を有しつつ も，電源特性及びそれを踏まえたエネルギーミックスの理解のために有効であると考えられるとのものであった． |
| ID | 112 |
| Title | Inspection of pitting corrosions on weld overlay cladding using uniform eddy current testing and rotating eddy current testing |
| Author | Jiuhao Ge, Fanwei Yu, Takuma Tomizawa, Haicheng Song, Noritaka Yusa |
| Published in | IEEE Transactions on Instrumentation & Measurement70 (2021), 6010410. |
| Keywords | Reactor pressure vessel, artificial pit, corrosion evaluation, RECT |
| Abstract | This study investigated the applicability of detecting pitting corrosions on stainless steel weld overlay cladding using uniform eddy current testing, which is insensitive to surface undulation, and rotating eddy current testing, which can be considered a superposition of uniform eddy current testing in orthogonal directions. The performance of the two techniques in detecting artificial pitting corrosions on and next to weld beads was compared. The signal distributions revealed that only rotating eddy current testing was capable of describing the surface profiles of pitting corrosions. The results of uniform eddy current testing could not distinguish between pitting corrosions and cracks. The probability of detection curves drawn to quantitatively indicate the detection capabilities of the two techniques revealed that uniform eddy current testing with induced eddy currents parallel and perpendicular to weld beads was better than rotating eddy current testing in detecting pitting corrosions on and next to weld beads, respectively. Scanning twice by uniform eddy current testing at orthogonal orientations may be a better process for detecting pitting corrosion on weld overlay cladding compared with using rotating eddy current testing. The measured signals of the two techniques in normal direction were located around the edges of the pitting corrosions, which only indicated the depth around edges. The results suggest that uniform and rotating eddy current testing with normal direction magnetic field signals may be inadequate for evaluating the maximum depth of pitting corrosions or large corrosions. |
| ID | 113 | |
| Title | Multivariate Probability of Detection (POD) Analysis Considering the Defect Location for Long-Range, Non-Destructive Pipe Inspection Using Electromagnetic Guided Wave Testing | |
| Author | Guanren Chen, Yijin Guo, Takuya Katagiri, Haicheng Song, Takuma Tomizawa, Noritaka Yusa, Hidetoshi Hashizume | |
| Published in | NDT&E International 124 (2021), 102539. | |
| Keywords | 2D POD, microwave NDT, pipe wall thinning, TM01, multivariate
regression |
|
| Abstract |
|
| ID | 114 |
| Title | Transformation of rotating eddy current testing signal at desired eddy current orientation |
| Author | Jiuhao Ge, Chenkai Yang, Fanwei Yu, Noritaka Yusa |
| Published in | NDT&E International 125 (2022), 102551 |
| Keywords | Rotating field; Phase rotation; Welds noise decreasing |
| Abstract | The results of rotating eddy current testing can be regarded as the results superposed by the uniform eddy current testing in orthogonal directions. However, in the case of the directional nondestructive testing problem, such as welds detection, only the results from the induced current that is perpendicular to the crack have the greatest sensitivity. In contrast, the results from other induced current orientations may contain a large amount of noise generated by welds. In this work, a brief method is proposed to transform the results of rotating eddy current testing into the results of uniform eddy current testing at the desired eddy current orientation. The experiments indicate that both the signal distribution and the signal amplitude of the transformed results well match the results of uniform eddy current testing. Moreover, an application of the proposed method in welds detection is conducted. The results reveal that the welds noise significantly decreased and that the indication of slits can be obviously identified. The results validate that the proposed method can improve the detection ability and expand the application of the rotating eddy current testing technique. |
| ID | 115 |
| Title |
Whether "rich in frequency" means "rich in information" in pulsed
eddy current testing to evaluate plate thickness: A numerical
investigation |
| Author | Noritaka Yusa, Jiuhao Ge, Mengbao Fan |
| Published in | Materials Transactions 63 (2022), 529-538. |
| Keywords | electromagnetic nondestructive evaluation, finite element method,
inverse problem, ill-posedness, thickness evaluation |
| Abstract | This study investigated whether it is really reasonable to insist
that being "rich in frequency" represents an advantage of pulsed
eddy current testing when compared with conventional eddy current
testing. More specifically, this study compared the capabilities of
pulsed eddy current testing and conventional eddy current testing in
evaluating the thickness of non-ferromagnetic plates with
thicknesses of 1?20 mm. To avoid any instrumentation effect, the
investigations were performed based on signals obtained by finite
element simulations, and the correlations between the thickness and
a scalar feature value extracted from measured signals were
discussed. This study considered two typical excitation waveforms, a
Gaussian pulse and a step function simulating the sudden termination
of the excitation currents, and four simple and conventional scaler
feature values: peak amplitude, time to peak, time to attenuate the
signal into a certain level, and logarithmic slope of the signal
attenuation. Narrowing the Gaussian pulse led to difficulty in terms
of the thickness evaluation, although it should make the pulse
richer in frequency. Subsequent analyses compared the capabilities
of the pulsed and conventional eddy current testing to evaluate
plate thickness under the assumption that they have the same
signal-to-noise ratio. The results revealed that the error in the
thickness evaluation using the pulsed eddy current testing was
somewhat larger than the error using the conventional eddy current
testing with three frequencies. Whereas the target of this study was
limited to the thickness evaluation of non-ferromagnetic plates, the
results of this study point out that what is important is using
frequencies in a proper range as well known in the conventional eddy
current testing. They also indicate that it is not reasonable to
postulate that "richness in frequency" always leads to a better
nondestructive evaluation when using the pulsed eddy current
testing. |
| ID | 116 |
| Title | Application of high-frequency ultrasonic test to the non-destructive inspection of W-Cu bonded interface |
| Author | Noritaka Yusa, Ryouji Suzuki, Takashi Furukawa, Masayuki Tokitani, Suguru Masuzaki |
| Published in | Plasma and Fusion Research 17 (2022), 2405013. |
| Keywords | non-destructive testing, divertor, cooling channel, diffusion
bonding, solid state bonding, imaging, thermography |
| Abstract | This study evaluated the applicability of high-frequency
ultrasonic tests to the non-destructive inspection of the bonded
interface between a cooling pipe and a divertor monoblock. Samples
prepared in this study were an ITER-grade tungsten block bonded with
a 2.5 mm-thick oxygen-free copper using diffusion bonding. The
high-frequency ultrasonic test was performed using an acoustic
microscope. A probe, operated in pulse-echo mode, scanned the copper
surface of the sample two-dimensionally. Five probes with operating
frequencies ranging from 15 to 50 MHz were used. The measured
ultrasonic signals were converted into ultrasonic images on the
assumption that the samples had a uniform and isotropic speed of
sound to evaluate reflections from the interface. Whereas an
interface without any artificial flaw partly reflected ultrasonics,
setting the decision threshold properly, based on the distribution
of the surface echo amplitudes, enabled the smallest flaw to be
detected clearly. Ultrasonic signals measured around 30 MHz showed
the best signal-to-noise ratio in detecting an artificial flaw
introduced at the bonding layer. The results of the ultrasonic tests
were consistent with those of subsequent lock-in thermography and
destructive test. However the thermography test could not detect
small flaws that the high-frequency ultrasonic test confirmed. |
| ID | 117 |
| Title | Demonstration of quantitative evaluation of pipe wall thinning
defects using microwave NDT |
| Author | Yijin Guo, Guanren Chen, Takuya Katagiri, Noritaka Yusa, Hidetoshi Hashizume, |
| Published in | Nondestructive Testing and Evaluation 37 (2022), 737-753 |
| Keywords | microwaves, signal processing, resonant frequency, back
propagation neural network |
| Abstract | This study investigated the applicability of microwave
nondestructive testing, which has been proved effective in quickly
detecting the defect location in a long pipe, to the size evaluation
of wall thinning defects. Artificial wall thinning defects with
different sizes (depths and lengths) and edge profiles were
introduced to a flanged brass pipe with a total length of 15 m, and
reflected microwave signals were measured in experiments. A signal
processing method combining windowing and dispersion compensation
was proposed to extract the defect-related reflection signals in the
frequency domain. Resonant frequencies, at which the amplitude of
extracted signals dropped significantly, decreased with the increase
of either wall thinning depth or length. In addition, the results
demonstrate that wall thinning location and pipe end conditions have
little influence on resonant frequencies after signal processing. A
back propagation neural network was trained by simulation data,
using resonant frequencies as the input, to simultaneously evaluate
defect depth and length, and the performance was validated by
experiments. Maximum prediction errors of depth and length of wall
thinning were 0.06 mm and 0.57 mm, respectively, which indicated the
feasibility of proposed method to evaluate the wall thinning defect
sizes. |
| ID | 118 |
| Title | Surface
profile reconstruction of complex cracks using the signals of
rotating eddy current testing through eddy current image method |
| Author | Jiuhao Ge, Baowang Hu, Chenkai Yang, Fanwei Yu, Noritaka Yusa |
| Published in | IEEE Transactions on Industrial Electronics 70 (2023), 9632-9641. |
| Keywords | crack colony, current dipole, eddy current imaging, stress
corrosion crack |
| Abstract | 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. |
| ID | 119 |
| Title | Probe design for the eddy current inspection of cooling tubes in the blanket of a DEMO fusion reactor |
| Author | Mizuki Kako, Takuma Tomizawa, Jiuhao Ge, Takashi Nozawa, Noritaka Yusa |
| Published in | Plasma and Fusion Research 17 (2022), 2405102. |
| Keywords | ECT, F82H, blanket, prototype reactor, cooling tube,
ferromagnetic, bobbin probe |
| Abstract | This study investigated the applicability of eddy current testing
(ECT) to the non-destructive inspection of cooling tubes in the
blanket of a fusion DEMO reactor. Pipes made of F82H steel with
inner and outer diameters of 9 and 11 mm, respectively, were
prepared, and slits imitating cracks were fabricated on the pipe
surfaces. ECT was performed using a differential type bobbin probe
having one exciting and two detecting coils designed in this study.
The results of the inspections and subsequent three-dimensional
finite element simulations revealed that a bobbin probe is effective
in detecting cracks appearing on the inner surface of a pipe.
Moreover, the detectability does not deteriorate significantly when
cracks oriented in the circumferential directions are targeted,
unlike in the case of ECT of the heat exchanger tubes of the steam
generators of the pressurized water reactors. This indicates that a
probe with a more complicated structure, such as a plus-point probe,
would be unnecessary to detect flaws on the inner surface of a pipe.
In contrast, the ECT signals from a non-penetrating slit on the
outer surface were buried in noise even though the slit was as deep
as 0.9 mm. |
| ID | 120 |
| Title | Integration of multiple wall thinning parameters into the
probability of detection analysis for the long-range pipe inspection
using microwaves |
| Author | Yijun Guo, Takuma Tomizawa, Fanwei Yu, Noritaka Yusa, Hidetoshi
Hashizume |
| Published in | NDT&E International 133 (2023), 102763. |
| Keywords | multiple size parameters, circumferential angle, defect location,
TM01, multivariate regression |
| Abstract | A three-dimensional probability of detection (POD) model
integrating the depth, circumferential angle, and location of pipe
wall thinning (PWT) was proposed for the probabilistic analysis of
long-range pipe inspection using microwaves. Microwaves in TM01 mode
were used to detect PWT with different sizes and locations (up to
13.5 m). The microwave signals reflected from the PWT were measured
and processed, and their amplitudes were extracted and treated as
the signal response. The results showed that the signal response was
rarely influenced by the axial length of the PWT, while its natural
logarithm was proportional to the natural logarithm of the PWT depth
and circumferential angle. In addition, the signal response
decreased exponentially with the PWT location. Subsequently, a
multivariate regression model was established, and the related
coefficients were estimated using the maximum likelihood method. The
POD calculated from the regression model suggests that a small PWT
at a far distance (e.g., 36.0 m) can be reliably detected using
microwaves. Compared with a two-dimensional POD model that considers
only the PWT cross-section area as the size parameter, the proposed
POD model clearly shows that the POD is more dependent on the
circumferential angle than on the depth of the PWT. |