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10 pages, 4223 KiB  
Article
Detection of Sub-pT Field of Magnetic Responses in Metals and Magnetic Materials by Highly Sensitive Magnetoresistive Sensors
by Hyuna Ahn, Ayana Tanaka, Yuta Kono, Suko Bagus Trisnanto, Tamon Kasajima, Tomohiko Shibuya and Yasushi Takemura
Sensors 2025, 25(3), 776; https://doi.org/10.3390/s25030776 - 27 Jan 2025
Viewed by 397
Abstract
We developed a measurement system capable of detecting magnetic responses in various material samples. The system utilizes an excitation coil to apply an alternating magnetic field within the frequency range of 1–10 kHz. The magnetic field generated in the samples was detected using [...] Read more.
We developed a measurement system capable of detecting magnetic responses in various material samples. The system utilizes an excitation coil to apply an alternating magnetic field within the frequency range of 1–10 kHz. The magnetic field generated in the samples was detected using a highly sensitive magnetoresistive sensor. The system demonstrated a detection lower limit in the sub-pT range for magnetic fields arising from magnetic responses such as eddy currents and magnetization changes. The frequency dependence of the detected signal intensities correlated well with the physical mechanisms underlying the magnetic responses. Notably, the distance between the excitation coil and the magnetic sensor was maintained at 300 mm. These results, which demonstrate the detection of a sub-pT magnetic field using a highly sensitive magnetic sensor, have not been previously reported and provide valuable insights for advancing practical applications in non-destructive testing and clinical diagnostic imaging. Full article
(This article belongs to the Special Issue Sensors in Nondestructive Testing)
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Figure 1
<p>Schematic of the measurement system. The distance between the excitation coil and the sensing position of each MR sensor was 300 mm. An alternating magnetic field with an intensity of <span class="html-italic">H</span><sub>ex</sub> was applied to the measured sample. The MR sensor (left) detects the magnetic flux density, <span class="html-italic">B</span><sub>d</sub>, generated in the sample. The distance between the sample and the sensing position of the MR sensor was <span class="html-italic">x</span> = 20 mm for the aluminum, stainless-steel, and ferrite samples and <span class="html-italic">x</span> = 5 mm for the magnetic nanoparticle samples.</p>
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<p>Noise density spectrum of MR sensor (Nivio xMR sensor, TDK Corp.).</p>
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<p>Intensities of magnetic flux densities detected by the MR sensor are a function of the intensity of the applied magnetic field. The magnetic flux was generated in the aluminum, stainless-steel, and ferrite samples. The amplitude and frequency of the applied magnetic field were <span class="html-italic">H</span><sub>ex</sub> = 0.2–120 nT/μ<sub>0</sub> and <span class="html-italic">f</span> = 10 kHz, respectively. (<b>b</b>) provides an enlarged view of the weak-field range depicted in (<b>a</b>).</p>
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<p>Intensities of magnetic response signals measured from (<b>a</b>) aluminum (plate and foil) and (<b>b</b>) stainless-steel and ferrite samples as a function of the applied field frequency <span class="html-italic">f</span> = 1–10 kHz.</p>
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<p>Intensity of the magnetic flux density detected by the MR sensor as a function of the iron content (mg-Fe) in the MNP samples. The magnetic flux was generated by magnetization changes in the MNP samples. Measurements were conducted on 0.1 mL MNP samples containing 0.028–2.43 mg-Fe. The applied magnetic field had an amplitude of <span class="html-italic">H</span><sub>ex</sub> = 1.3 μT/μ<sub>0</sub> and <span class="html-italic">f</span> = 10 kHz. (<b>b</b>) provides an enlarged view of the weak-field range depicted in (<b>a</b>).</p>
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<p>Intensities of magnetic response signals measured from the MNP samples as a function of the applied field frequency <span class="html-italic">f</span> = 1–10 kHz. These intensities were calculated from the detected magnetic flux density normalized by the iron content in the samples. Measurements were conducted on 0.1 mL MNP samples containing 5.6, 11.2, and 16.8 mg-Fe.</p>
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<p>Imaginary parts of the magnetic susceptibility of the MNP samples as a function of the applied field frequency (frequency range of <span class="html-italic">f</span> = 0.1–10 kHz). The magnetic susceptibility was normalized by the iron content in the MNP samples. Measurements were conducted on 0.1 mL MNP samples containing 5.6, 11.2, and 16.8 mg-Fe.</p>
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23 pages, 18755 KiB  
Article
Extended Material Recovery from Municipal Solid Waste Incinerator Bottom Ash Using Magnetic, Eddy Current, and Density Separations
by Ida Bagus Gede Sumbranang Adhiwiguna, Keshalinni Ramalingam, Karl-Heinz Becker, Alexander Khoury, Ragnar Warnecke and Rüdiger Deike
Recycling 2025, 10(1), 16; https://doi.org/10.3390/recycling10010016 - 24 Jan 2025
Viewed by 709
Abstract
This research introduces an extended processing method for increasing the possibility of valorizing processed IBA (pr.IBA), which is currently only used as a construction material in landfill sites, considering its immense potential in valuable metal and mineral concentrations. Following a selective milling process, [...] Read more.
This research introduces an extended processing method for increasing the possibility of valorizing processed IBA (pr.IBA), which is currently only used as a construction material in landfill sites, considering its immense potential in valuable metal and mineral concentrations. Following a selective milling process, an extended material recovery sequence involving a magnetic, eddy current, and density separation sequence is developed. Based on the observations and outcomes explored in the present study, a substantially reliable and practical industrial approach is designed and tested to generate a cleaner mineral fraction and complementarily collect valuable metals from pr.IBA. Specifically, four enhanced valuable product streams can be anticipated, output mineral, high-magnetic, low-magnetic, and non-ferrous, which can be further utilized as alternative materials for cement clinker and concrete production coupled with iron, copper, and aluminum recovery in a conventional recycling operation. Therefore, in addition to introducing an additional perspective and moving one step closer to closing the waste management loop, this proposed method offers the opportunity to save primary materials and reduce carbon emissions by providing valuable alternative secondary resources. Full article
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<p>Metallography (stitching) of (<b>a</b>) MF010-Mag, (<b>b</b>) MF010-NE, and (<b>c</b>) MF010-Min.</p>
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<p>Metallography (stitching) of (<b>a</b>) CF010-Mag, (<b>b</b>) CF010-NE, and (<b>c</b>) CF010-Min.</p>
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<p>Metallography (stitching) of heaviest fraction from CF010-LFe after density separation at different particle classifications: (<b>a</b>) 0.50–0.71 mm, (<b>b</b>) 1.00–1.18 mm, and (<b>c</b>) 1.40–2.00 mm.</p>
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<p>Heavy fractions from CF010-NE after density separation at different particle classifications: (<b>a</b>) 0.50–0.71 mm, (<b>b</b>) 1.00–1.18 mm, and (<b>c</b>) 1.40–2.00 mm.</p>
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<p>Elemental mapping (EDS) from a mixed sample of heavy fractions from CF010-NE. The EDS mapping represents the particles in the red circle.</p>
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<p>Elemental mapping (EDS) from a mixed sample of light fractions from CF010-NE. The EDS mapping represents the particles in the red circle.</p>
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<p>Metallography (stitching) of heaviest fraction from CF010-Min after density separation at different particle classifications: (<b>a</b>) 1.18–1.40 mm and (<b>b</b>) 1.40–2.00 mm.</p>
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<p>The theoretical annual mass balance (tons) of IBA in Germany [<a href="#B4-recycling-10-00016" class="html-bibr">4</a>,<a href="#B19-recycling-10-00016" class="html-bibr">19</a>].</p>
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<p>The average theoretical annual mass (tons) of pr.IBA in Germany after milling [<a href="#B13-recycling-10-00016" class="html-bibr">13</a>].</p>
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<p>The expected annual mass (tons) separation output of 0–10 mm pr.IBA in Germany.</p>
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<p>The expected annual mass (tons) separation output of 10–32 mm pr.IBA in Germany.</p>
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<p>A visual comparison between (<b>a</b>) CF010-Min and (<b>b</b>) a typical natural aggregate for concrete production—the representation only shows the particle size range of 4.0–8.0 mm.</p>
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<p>Metallography (stitching) of (<b>a</b>) oversized and (<b>b</b>) undersized particles after grinding and sieving of light fraction from CF010-NE in <a href="#recycling-10-00016-f006" class="html-fig">Figure 6</a>.</p>
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<p>XRD results of MF010-Mag: part of magnetic fraction originated from middle fraction (MF) of selective-milled 0–10 mm pr.IBA after magnetic separation.</p>
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<p>XRD results of CF010-Mag: part of magnetic fraction originated from coarse fraction (CF) of selective-milled 0–10 mm pr.IBA after magnetic separation.</p>
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<p>XRD results of MF010-Min: part of output mineral originated from middle fraction (MF) of selective-milled 0–10 mm pr.IBA after magnetic and eddy current separations.</p>
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<p>XRDs result of CF010-Min: part of output mineral originated from coarse fraction (CF) of selective-milled 0–10 mm pr.IBA after magnetic and eddy current separations.</p>
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16 pages, 11828 KiB  
Article
A Precise Oxide Film Thickness Measurement Method Based on Swept Frequency and Transmission Cable Impedance Correction
by Yifan Li, Qi Xiao, Lisha Peng, Songling Huang and Chaofeng Ye
Sensors 2025, 25(2), 579; https://doi.org/10.3390/s25020579 - 20 Jan 2025
Viewed by 415
Abstract
Accurately measuring the thickness of the oxide film that accumulates on nuclear fuel assemblies is critical for maintaining nuclear power plant safety. Oxide film thickness typically ranges from a few micrometers to several tens of micrometers, necessitating a high-precision measurement system. Eddy current [...] Read more.
Accurately measuring the thickness of the oxide film that accumulates on nuclear fuel assemblies is critical for maintaining nuclear power plant safety. Oxide film thickness typically ranges from a few micrometers to several tens of micrometers, necessitating a high-precision measurement system. Eddy current testing (ECT) is commonly employed during poolside inspections due to its simplicity and ease of on-site implementation. The use of swept frequency technology can mitigate the impact of interference parameters and improve the measurement accuracy of ECT. However, as the nuclear assembly is placed in a pool for inspection, a cable several dozen meters in length is used to connect the ECT probe to the instrument. The measurement is affected by the transmission line and its effect is a function of the operating frequencies, resulting in errors for swept frequency measurements. This paper proposes a method for precisely measuring oxide film thickness based on the swept frequency technique and long transmission line impedance correction. The signals are calibrated based on a transmission line model of the cable, effectively eliminating the influence of the transmission cable. A swept frequency signal-processing algorithm is developed to separate the parameters and calculate oxide film thickness. To verify the feasibility of the method, measurements are conducted on fuel cladding samples with varying conductivities. It is found that the method can accurately assess oxide film thickness with varying conductivity. The maximum error is 3.42 μm, while the average error is 1.82 μm. The impedance correction reduces the error by 66%. The experimental results indicate that this method can eliminate the impact of long transmission cables, and the algorithm can mitigate the influence of material conductivity. This method can be utilized to measure oxide film thickness in nuclear power maintenance inspections following extensive testing and engineering optimization. Full article
(This article belongs to the Special Issue Intelligent Sensors and Signal Processing in Industry)
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<p>Typical structure of a fuel rod with an oxide film.</p>
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<p>Equivalent circuit model of a coil and transmission cable.</p>
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<p>A schematic diagram of the measurement circuit.</p>
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<p>The flowchart of the inversely calculation of the corrected impedance.</p>
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<p>The diagram of the thickness measurement algorithm.</p>
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<p>The schematic diagram of the probe.</p>
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<p>Frequency characteristic curve of the coil and the cable.</p>
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<p>Schematic diagram of the experimental system.</p>
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<p>Photograph of the experimental apparatus.</p>
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<p>Experiment results: voltage (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math>) vs. frequency, (<b>a</b>) in−phase component and (<b>b</b>) quadrature component.</p>
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<p>In−phase (<b>a</b>) and quadrature (<b>b</b>) components of impedance <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Z</mi> </mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </msub> </mrow> </semantics></math> after impedance correction.</p>
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<p>Comparison of thickness measurement results of zirconium alloy samples before and after impedance correction.</p>
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15 pages, 5542 KiB  
Article
Array Coil Design and Experimental Verification for Separation of Tower Grounding Pulsed Eddy Current Excitation and Response Magnetic Field Signals
by Zhiwu Zeng, Zheng Guo, Fan Gan, Yun Zuo, Xu Tian, Xinxun Wang, Zhichi Lin, Wanyi Zhu, Xiaotian Wang and Jingang Wang
Energies 2025, 18(2), 364; https://doi.org/10.3390/en18020364 - 16 Jan 2025
Viewed by 357
Abstract
Transmission line towers play an important role in power transmission, and the assessment of transmission line tower grounding by pulsed eddy current detection technology is conducive to the safe and reliable operation of power transmission. Aiming at the problem that the primary and [...] Read more.
Transmission line towers play an important role in power transmission, and the assessment of transmission line tower grounding by pulsed eddy current detection technology is conducive to the safe and reliable operation of power transmission. Aiming at the problem that the primary and secondary magnetic fields of the traditional pulsed eddy current transmitting coil structure overlap, resulting in the loss of shallow information, this paper first discusses the loss of shallow information caused by the aliasing of the magnetic field under the non-zero current shutdown effect, and then analyzes the traditional weak magnetic field coupling separation principle, and proposes the array coil structure of this paper based on the magnetic field vector destructive separation principle. Subsequently, the corresponding finite element simulation model was established, and the magnetic field distribution, magnetic field size, induced voltage, and mutual inductance coefficient of the array coil and the traditional center loop structure at the receiving coil were compared in the static field. In the transient field, the response signal of the array coil structure with or without the grounding body and the receiving coil is equidistant was simulated. The simulation results show that, under the same excitation, the vector coil array structure can greatly reduce the mutual inductance coefficient between the excitation and transmitting coils, reduce the influence of the primary magnetic field of the excitation coil on the receiving coil, and avoid the loss of shallow information. Finally, experimental tests were carried out on different tower grounding bodies. The experimental results at different measuring points prove that the array coil structure proposed in this paper can separate well the magnetic field generated by the excitation signal, improve the effective resolution time, avoid the loss of shallow information, and improve the operational stability of power transmission systems. Full article
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<p>Schematic diagram of pulsed eddy current grounding detection. (<b>a</b>) Schematic diagram of tower grounding. (<b>b</b>) Schematic diagram of pulsed eddy current detection signal and eddy currents.</p>
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<p>Weak magnetic coupling design. (<b>a</b>) Differential structure. (<b>b</b>) Co-centered zero flux coils. (<b>c</b>) Anti-flux coil design. (<b>d</b>) Eccentric coil design.</p>
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<p>Schematic diagram of N-turn rectangular multilayer coil.</p>
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<p>Schematic diagram of weak magnetic coupling array coil.</p>
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<p>Simulation results of magnetic field distribution under static field. (<b>a</b>) Magnetic field intensity distribution cloud diagram of array coil. (<b>b</b>) Magnetic field intensity vector diagram of the central loop. (<b>c</b>) Magnetic field strength vector diagram of array coil.</p>
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<p>The induced voltage of the primary magnetic field in the receiving coil.</p>
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<p>The relationship between the induced voltage, the strength of the magnetic field at the center point, and the excitation current.</p>
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<p>Analysis of the change in magnetic field strength under different excitation currents. (<b>a</b>) The change in magnetic field strength at the center point due to different distances between the grounding bodies. (<b>b</b>) The change trend of magnetic field strength in the area below the array coil.</p>
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<p>Schematic diagram of grounding body simulation. (<b>a</b>) Model diagram. (<b>b</b>) Schematic diagram of grounding magnetic field distribution.</p>
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<p>Comparison of induced voltage of array coil.</p>
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<p>Equidistant receiving coil simulation. (<b>a</b>) Schematic diagram of equidistant receiving coils. (<b>b</b>) Comparison of received signals under array coil.</p>
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<p>Experimental Schematic.</p>
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<p>Magnetic induction intensity at the center.</p>
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<p>Comparison of detection signals measured by center loop and array coil.</p>
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<p>Comparison of detection signals under different grounding steel bars.</p>
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<p>Detection signals and normalized curves measured by the center loop of P1 measuring point and array coil.</p>
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<p>Induced voltage profiles of the center loop and array coils. (<b>a</b>) Center loop; (<b>b</b>) Array coils.</p>
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17 pages, 3760 KiB  
Article
Method and Experimental Research of Transmission Line Tower Grounding Body Condition Assessment Based on Multi-Parameter Time-Domain Pulsed Eddy Current Characteristic Signal Extraction
by Yun Zuo, Jie Wang, Xiaoju Huang, Yuan Liu, Zhiwu Zeng, Ruiqing Xu, Yawen Chen, Kui Liu, Hongkang You and Jingang Wang
Energies 2025, 18(2), 322; https://doi.org/10.3390/en18020322 - 13 Jan 2025
Viewed by 392
Abstract
Pole tower grounding bodies are part of the normal structure of the power system, providing relief from fault currents and equalizing overvoltage channels. They are important devices; however, in the harsh environment of the soil, they are prone to corrosion or even fracture, [...] Read more.
Pole tower grounding bodies are part of the normal structure of the power system, providing relief from fault currents and equalizing overvoltage channels. They are important devices; however, in the harsh environment of the soil, they are prone to corrosion or even fracture, which in turn affects the normal utilization of the transmission line, so accurately assessing the condition of grounding bodies of the power grid is critical. To assess the operational status of a grounding body in a timely manner, this paper proposes a multi-parameter pulsed eddy current (PEC) time-domain characteristic signal corrosion classification method for the detection of the state of a pole tower grounding body. The method firstly theoretically analysed the influence of multi-parameter changes on the PEC response time-domain feature signal caused by grounding body corrosion and extracts the decay time constant (DTC), and the decay time constant stabilization value (DTCSV) and time to stabilization (TTS) were obtained based on the DTC time domain characteristics for describing the corrosion of the grounding body. Subsequently, DTCSV and TTS were used as inputs to a support vector machine (SVM) to classify the corrosion of the grounding body. A simulation model was constructed to investigate the effect of multiparameter time on the DTCSV and TTS of the tower grounding body based on the single-variable method, and the multiparameter time-domain characterization method used for corrosion assessment was validated. Four defects with different corrosion levels were classified using the optimized SVM model, with an accuracy rate of 95%. Finally, a PEC inspection system platform was built to conduct classification tests on steel bars with different degrees of corrosion, and the results show that the SVM classification model based on DTCSV and TTS has a better discriminatory ability for different corrosive grounders and can be used to classify corrosion in the grounders of poles towers to improve the stability of power transmission. Full article
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<p>Flowchart of DTC-SVM corrosion classification of grounded body based on DTCSV and TTS.</p>
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<p>The effect of different grounding body conductivities on the transient response signal. (<b>a</b>) The logarithmic curve of the response signal for different grounding body conductivities; (<b>b</b>) the decay time constant curve for different grounding body conductivities.</p>
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<p>The effect of different grounding body relative permeabilities on the transient response signal. (<b>a</b>) The logarithmic curve of the response signal for different grounding body relative permeabilities; (<b>b</b>) the decay time constant curve for different grounding body relative permeabilities.</p>
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<p>Relationship between α(<span class="html-italic">t</span>) and the relative permeability <span class="html-italic">μ<sub>r</sub></span> and conductivity <span class="html-italic">σ</span> of the grounding body.</p>
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<p>The effect of different grounding body loss thickness on the transient response signal. (<b>a</b>) The logarithmic curve of the response signal for different grounding body loss thicknesses; (<b>b</b>) the decay time constant curve for different grounding body loss thicknesses.</p>
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<p>The effect of different grounding body burial depths on the transient response signal. (<b>a</b>) The logarithmic curve of the response signal for different grounding body burial depths; (<b>b</b>) the DTCSV change caused by changes in burial depth and wall thickness.</p>
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<p>Grounding defect detection (<b>a</b>) the grounding defect model, (<b>b</b>) the decay time constant detection result of the grounding body defect.</p>
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<p>The curve of DTCSV with the change in grounding body parameters. (<b>a</b>) The DTCSV with defects when the relative permeabilities of the grounding body change; (<b>b</b>) the DTCSV with defects when the conductivities of the grounding body change.</p>
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<p>Schematic diagram of the pulsed eddy current testing experimental verification system classification results of four classifiers: (<b>a</b>) SVM, (<b>b</b>) GSSVM, (<b>c</b>) GASVM (<b>d</b>) PSOSVM.</p>
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<p>Schematic diagram of the pulsed eddy current testing experimental verification system classification results of four classifiers: (<b>a</b>) SVM, (<b>b</b>) GSSVM, (<b>c</b>) GASVM (<b>d</b>) PSOSVM.</p>
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<p>Schematic diagram of pulsed eddy current testing experimental verification system.</p>
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<p>Grounding body defect test and classification results. (<b>a</b>) the defect detection result based on the decay time constant, (<b>b</b>) the defect scatter plot based on TDC-PSOSVM.</p>
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12 pages, 12962 KiB  
Proceeding Paper
One Kind of Green New Method for Detection of Inside Layer Cracks of Aircraft Multilayer Structures
by Huabin Huang, Zhiwei Peng and Mao Xu
Eng. Proc. 2024, 80(1), 20; https://doi.org/10.3390/engproc2024080020 - 10 Jan 2025
Viewed by 306
Abstract
To address the technical challenges in detecting internal cracks within aircraft metallic multilayer structures, we have employed the environmentally friendly detection technique of remote-field eddy current (RFEC). Through theoretical analysis and experimental research, we have analyzed influencing factors such as frequency and phase, [...] Read more.
To address the technical challenges in detecting internal cracks within aircraft metallic multilayer structures, we have employed the environmentally friendly detection technique of remote-field eddy current (RFEC). Through theoretical analysis and experimental research, we have analyzed influencing factors such as frequency and phase, designed detection probes and reference blocks, and conducted research on the capability of detecting concealed defects within thick structures (greater than 10 mm). By testing the reference blocks, we have studied the changes in phase and amplitude caused by variations in frequency and damage, gaining insights into the detection capabilities and applicable scope of this method. Ultimately, we have obtained an effective method for detecting internal cracks within different thickness layers of metallic multilayer structures. Full article
(This article belongs to the Proceedings of 2nd International Conference on Green Aviation (ICGA 2024))
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<p>Schematic diagram of low-frequency eddy current detection principle.</p>
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<p>Schematic diagram of far-field eddy current effect.</p>
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<p>Principle of remote-field eddy current technology for flat panel multilayer structure.</p>
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<p>Structure diagram of far-field eddy current probe.</p>
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<p>Amplitude curve under different driving frequencies.</p>
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<p>Phase–frequency curve.</p>
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<p>Circular probe and sliding probe.</p>
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<p>Comparative test blocks for inspection tests.</p>
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<p>Scanning method of circular nail hole.</p>
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<p>Scanning method of sliding hole edge.</p>
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<p>Flat plate sliding scanning method of probe.</p>
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<p>Far-field eddy current detection results of Test Block 2.</p>
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<p>Far-field eddy current detection results of Test Block 3.</p>
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<p>Far-field eddy current detection results of Test Block 2 + Block 3.</p>
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<p>Far-field eddy current testing results of Test Block 5.</p>
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<p>Blocking board on the front of the comparison block.</p>
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<p>Blocking board on the back of the comparison block.</p>
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<p>Comparison of side end sections of test blocks.</p>
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<p>Far-field eddy current test results.</p>
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23 pages, 9410 KiB  
Article
Application of Reduced Order Surrogate Models in Compatible Determination of Material Properties Profiles by Eddy Current Method
by Volodymyr Y. Halchenko, Ruslana Trembovetska, Volodymyr Tychkov, Viacheslav Kovtun and Nataliia Tychkova
Electronics 2025, 14(1), 212; https://doi.org/10.3390/electronics14010212 - 6 Jan 2025
Viewed by 518
Abstract
A number of computer experiments have investigated the effectiveness in terms of accuracy of the method for simultaneously determining the distributions of electrical conductivity and magnetic permeability in the subsurface zone of planar conductive objects when modeling the process of eddy-current measurement testing [...] Read more.
A number of computer experiments have investigated the effectiveness in terms of accuracy of the method for simultaneously determining the distributions of electrical conductivity and magnetic permeability in the subsurface zone of planar conductive objects when modeling the process of eddy-current measurement testing by surface probes. The method is based on the use of surrogate optimization, which involves the use of a high-performance neural network proxy-model of probe by means of a deep learning as part of the target quadratic function. The surrogate model acts as a carrier and storage of a priori information about the object and takes into account the influence of all the main factors essential in the formation of the probe output signal. The problems of the surrogate model’s cumbersomeness and mitigation of the “curse of dimensionality” effect are solved by applying techniques for reducing the dimensionality of the design space based on the PCA algorithm. We investigated options for compromise solutions regarding the dimensionality of the PCA-space and the accuracy of obtaining the desired material properties profiles by the optimization method. The results of modeling the inverse measurement problem indicate a fairly high accuracy of profile reconstruction. Full article
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<p>Geometric model of the profile measuring task.</p>
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<p>Distributions of relative errors in calculating the amplitude and phase of the magnetic vector potential.</p>
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<p>General scheme of the method for determining material property profiles.</p>
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<p>Plots of MP and EC profiles of the training sample for the first sample.</p>
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<p>Plots of MP and EC profiles of the training sample for the second sample.</p>
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<p>Statistical evaluation of the quality of metamodels <span class="html-italic">n</span><sub>red</sub> = 66. Scatter plot of the metamodel rMLP-16-17-15-11-1.</p>
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<p>Statistical evaluation of the quality of metamodels <span class="html-italic">n</span><sub>red</sub> = 66. Scatter plot of the metamodel iMLP-16-17-16-13-1.</p>
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<p>Statistical evaluation of the quality of metamodels <span class="html-italic">n</span><sub>red</sub> = 66. Histogram of residuals of the metamodel rMLP-16-17-15-11-1.</p>
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<p>Statistical evaluation of the quality of metamodels <span class="html-italic">n</span><sub>red</sub> = 66. Histogram of residuals of the metamodel iMLP-16-17-16-13-1.</p>
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<p>Statistical evaluation of the quality of metamodels for <span class="html-italic">n</span><sub>red</sub> = 70. Scatter plot of the metamodel rMLP-16-17-16-14-1.</p>
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<p>Statistical evaluation of the quality of metamodels for <span class="html-italic">n</span><sub>red</sub> = 70. Scatter plot of the metamodel iMLP-16-16-15-12-1.</p>
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<p>Statistical evaluation of the quality of metamodels for <span class="html-italic">n</span><sub>red</sub> = 70. Histogram of the residuals of the metamodel rMLP-16-17-16-14-1.</p>
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<p>Statistical evaluation of the quality of metamodels for <span class="html-italic">n</span><sub>red</sub> = 70. Histogram of the residuals of the metamodel iMLP-16-16-15-12-1.</p>
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<p>Examples of the obtained profiles for the PCA space dimension equal to 63.</p>
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<p>Distributions of absolute errors module of profile reconstruction for test measurement 1 of magnetic permeability.</p>
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<p>Distributions of absolute errors module of profile reconstruction for test measurement 1 of electrical conductivity.</p>
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<p>Errors in determining MP profiles RMAE,% for two test measurements at different dimensions of PCA-spaces.</p>
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<p>Errors in determining EC profiles RMAE,% for two test measurements at different dimensions of PCA-spaces.</p>
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31 pages, 17373 KiB  
Article
Non-Destructive Evaluation of Reinforced Concrete Structures with Magnetic Flux Leakage and Eddy Current Methods—Comparative Analysis
by Paweł Karol Frankowski, Piotr Majzner, Marcin Mąka and Tomasz Stawicki
Appl. Sci. 2024, 14(24), 11965; https://doi.org/10.3390/app142411965 - 20 Dec 2024
Viewed by 610
Abstract
This article evaluates two essential non-destructive electromagnetic techniques, magnetic flux leakage (MFL) and eddy current (EC) methods, and their effectiveness in assessing the basic parameters of reinforced concrete (RC). The study compares both systems’ hardware and software components, emphasizing the adaptations implemented to [...] Read more.
This article evaluates two essential non-destructive electromagnetic techniques, magnetic flux leakage (MFL) and eddy current (EC) methods, and their effectiveness in assessing the basic parameters of reinforced concrete (RC). The study compares both systems’ hardware and software components, emphasizing the adaptations implemented to tailor the methods for evaluating RC structures. Subsequently, the measurement results are analyzed, and association rules are extracted to demonstrate the relationships between variations in the physical parameters of the tested structure and the features of the measured waveforms. Finally, similar identification models are implemented, and the obtained identification results are compared. The paper documents and details all phases of this research. The findings indicate that while the operational principles of both methods are similar, the techniques differ significantly in terms of their measurement systems’ complexity and usability. The eddy current (EC) method exhibits superior spatial resolution, whereas the magnetic method is more straightforward and offers a greater effective range and favorable association rules. Consequently, it is recommended that both techniques be utilized for different structures and in varying contexts. The techniques’ advantages, disadvantages, and limitations are discussed in this work and supported by the measurement results. Full article
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<p>Comparison of magnetic sensors based on sensitivity, bandwidth, and size [<a href="#B41-applsci-14-11965" class="html-bibr">41</a>]. GMR—giant magnetoresistance; AMR—anisotropic magnetoresistance; TMR—tunnel magnetoresistance; GMI—giant magnetoimpedance; MO—magneto-optical; SQUID—superconducting quantum interference device.</p>
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<p>Methodology for knowledge acquisition from NDT measurement data based on the CRISP-DM model.</p>
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<p>Development evolution of techniques for extracting features from waveforms.</p>
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<p>Attribute extraction process (equal dividing and characteristic points).</p>
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<p>Attribute extraction with equal intervals in the domain of amplitude method.</p>
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<p>The definitions of amplitude and offset: (<b>a</b>) amplitude, (<b>b</b>) offset.</p>
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<p>The algorithm for extracting association rules from NDT data.</p>
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<p>Samples: (<b>a</b>) 3D schematic presentation, (<b>b</b>) cross-section and parameters, (<b>c</b>) parameters.</p>
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<p>Example rebars used during supplementary measurements.</p>
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<p>Block diagram of eddy current system.</p>
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<p>EC transducers used in the experiments: (<b>a</b>) cross-section and description, (<b>b</b>) small T5 transducer, (<b>c</b>) medium T13 transducer, (<b>d</b>) large T20 transducer, (<b>e</b>) largest T25 transducer.</p>
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<p>Waveforms obtained from EC transducers: (<b>a</b>) absolute, (<b>b</b>) differential.</p>
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<p>The magnetic system, (<b>a</b>) block diagram, and (<b>b</b>) elements are arranged on the sample surface. M—magnet, S—sensor.</p>
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<p>Example eddy current measurements: (<b>a</b>) magnitude and phase shift vs. transducer position, (<b>b</b>) real (<span class="html-italic">Re</span>) and imaginary (<span class="html-italic">Im</span>) components vs. transducer position, (<b>c</b>) <span class="html-italic">Im</span> vs. <span class="html-italic">Re</span>.</p>
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<p>Example magnetic measurements with the use of AMR sensor; (<b>a</b>) <span class="html-italic">B</span><sub>x</sub>, (<b>b</b>) <span class="html-italic">B</span><sub>y</sub>, (<b>c</b>) <span class="html-italic">B<sub>z</sub></span>.</p>
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<p>Impact of concrete cover thickness on shape attributes; (<b>a</b>) <span class="html-italic">d</span><sub>90</sub>, (<b>b</b>) <span class="html-italic">d</span><sub>50</sub>, (<b>c</b>) <span class="html-italic">d</span><sub>10</sub>.</p>
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<p>Impact of concrete cover thickness on high-quality shape attributes; (<b>a</b>) <span class="html-italic">d</span><sub>x</sub>, (<b>b</b>) <span class="html-italic">d</span><sub>s</sub>.</p>
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<p>Process of <span class="html-italic">d</span><sub>x</sub> extraction from <span class="html-italic">B</span><sub>y</sub> and <span class="html-italic">B</span><sub>z</sub>.</p>
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<p>Linear approximation of measurement results (<span class="html-italic">d</span><sub>x</sub> attribute) for different transducers; (<b>a</b>) T5, (<b>b</b>) T13, (<b>c</b>) T20, (<b>d</b>) T25.</p>
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<p>EC transducer—waveforms obtained for different concrete cover thicknesses.</p>
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<p>Amplitude as a function of concrete cover thickness. (<b>a</b>) Eddy current method; (<b>b</b>) magnetic flux leakage method.</p>
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<p>EC—waveforms obtained for different rebar diameters; (<b>a</b>) raw data, (<b>b</b>) normalized data.</p>
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<p>MFL—waveforms obtained for different rebar diameters; (<b>a</b>) <span class="html-italic">B</span><sub>x</sub>, raw data; (<b>b</b>) <span class="html-italic">B</span><sub>y</sub>, raw data; (<b>c</b>) <span class="html-italic">B</span><sub>z</sub>, raw data; (<b>d</b>) <span class="html-italic">B</span><sub>x</sub>, normalized data; (<b>e</b>) <span class="html-italic">B</span><sub>y</sub>, normalized data; (<b>f</b>) <span class="html-italic">B</span><sub>z</sub>, normalized data.</p>
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<p>Results of rebar diameter identification derived from both methods across all transducers.</p>
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<p>EC—waveforms obtained for different rebar classes; (<b>a</b>) raw data, (<b>b</b>) normalized data.</p>
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<p>MFL—waveforms obtained for different reinforced steel classes; (<b>a</b>) <span class="html-italic">B</span><sub>x</sub>, raw data; (<b>b</b>) <span class="html-italic">B</span><sub>y</sub>, raw data; (<b>c</b>) <span class="html-italic">B</span><sub>z</sub>, raw data; (<b>d</b>) <span class="html-italic">B</span><sub>x</sub>, normalized data; (<b>e</b>) <span class="html-italic">B</span><sub>y</sub>, normalized data; (<b>f</b>) <span class="html-italic">B</span><sub>z</sub>, normalized data.</p>
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<p>Results of steel class identification derived from both methods across all transducers.</p>
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14 pages, 6448 KiB  
Article
Detecting the Corrosion of a Steel Rebar Using the Eddy Current Testing Method
by Dongfeng He
Standards 2024, 4(4), 286-299; https://doi.org/10.3390/standards4040014 - 19 Dec 2024
Viewed by 413
Abstract
The corrosion of the steel reinforcing bar (rebar) reduces the strength capacity of concrete structures. Corrosion detection at the early stage of steel rebar implementation is important for the maintenance of concrete structures. Using the eddy current testing method, we developed a portable [...] Read more.
The corrosion of the steel reinforcing bar (rebar) reduces the strength capacity of concrete structures. Corrosion detection at the early stage of steel rebar implementation is important for the maintenance of concrete structures. Using the eddy current testing method, we developed a portable system to evaluate the corrosion of steel rebars. An AC current was sent to the excitation coil to produce an AC magnetic field and an eddy current was induced in the steel rebar. A detection coil was used to detect the signal produced by the eddy current. A lock-in amplifier was used to obtain the same phase signal and a 90-degree phase difference signal and an X-Y graph was plotted. From the slope of the X-Y graph, the corrosion of the steel rebar or steel wire can be evaluated. We examined the effects of excitation frequency, coil type, and coil size on the experimental results to optimize the system. The signal-to-noise ratio and the detection depth were improved with a specially designed probe. Full article
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<p>(<b>a</b>) Steel rebar without corrosion. (<b>b</b>) Corroded steel rebar with black rust on the surface.</p>
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<p>Block diagram of steel rebar corrosion evaluation system using the eddy current testing method.</p>
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<p>Setup of the experiments.</p>
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<p>Excitation coil, detection coil, compensation coil, and the circuit in the probe.</p>
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<p>(<b>a</b>) Detected background signal without the compensation coil. (<b>b</b>) Detected signal with the compensation coil.</p>
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<p>Signals of the steel rebars with and without corrosion for different frequencies. (<b>a</b>) 10 kHz. (<b>b</b>) 40 kHz. (<b>c</b>) 80 kHz. (<b>d</b>) 150 kHz.</p>
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<p>Phase differences of the signals for the steel rebar with and without corrosion when the excitation frequency was 10 kHz, 40 kHz, 80 kHz, and 150 kHz.</p>
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<p>Excitation coil, detection coil, and compensation coil. (<b>a</b>) Excitation coil with a diameter of 3 cm. (<b>b</b>) Excitation coil with a diameter of 5 cm. (<b>c</b>) Excitation coil with a diameter of 7 cm. (<b>d</b>) Excitation coil with a diameter of 9 cm.</p>
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<p>(<b>a</b>). Signals for the excitation coil with the diameter of 3 cm. (<b>b</b>). Signals for the excitation coil with the diameter of 5 cm. (<b>c</b>). Signals for the excitation coil with the diameter of 7 cm. (<b>d</b>). Signals for the excitation coil with the diameter of 9 cm. The depth of the steel rebar was 25 mm.</p>
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<p>(<b>a</b>). Signals for the excitation coil with the diameter of 3 cm. (<b>b</b>). Signals for the excitation coil with the diameter of 5 cm. (<b>c</b>). Signals for the excitation coil with the diameter of 7 cm. (<b>d</b>). Signals for the excitation coil with the diameter of 9 cm. The depth of the steel rebar was 45 mm.</p>
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<p>Signal-to-noise ratios changed with the depths of the steel rebars for the excitation coils with diameters of 3 cm, 5 cm, 7 cm, and 9 cm.</p>
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<p>Differential detection coil with a Helmholtz excitation coil.</p>
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<p>Background signal with the differential detection coil.</p>
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<p>Signals for the differential detection coil with Helmholtz excitation coil when the depth of the steel rebar was 25 mm. (<b>a</b>). The diameter of the excitation was 3 cm. (<b>b</b>). The diameter of the excitation was 5 cm. (<b>c</b>). The diameter of the excitation was 7 cm.</p>
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<p>Signals for the differential detection coil with Helmholtz excitation coil when the depth of the steel rebar was 45 mm. (<b>a</b>). The diameter of the excitation was 3 cm. (<b>b</b>). The diameter of the excitation was 5 cm. (<b>c</b>). The diameter of the excitation was 7 cm.</p>
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<p>Signal-to-noise ratios changed with the depths of the steel rebars for the excitation coils with diameters of 3 cm, 5 cm, and 7 cm.</p>
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22 pages, 2326 KiB  
Review
Basic Theory and Applications of Oil and Gas Pipeline Non-Destructive Testing Methods
by Yuqin Wang, Fei Song, Qingshan Feng, Weibiao Qiao, Shaohua Dong, Yangyang Jiang and Qianli Ma
Energies 2024, 17(24), 6366; https://doi.org/10.3390/en17246366 - 18 Dec 2024
Viewed by 696
Abstract
In recent years, with the increasing construction mileage of oil and gas pipelines (OGPs), the aging problem of OGPs has become increasingly prominent, so, ensuring the safety of OGPs is of great significance. In addition, the safety of OGP transportation is also an [...] Read more.
In recent years, with the increasing construction mileage of oil and gas pipelines (OGPs), the aging problem of OGPs has become increasingly prominent, so, ensuring the safety of OGPs is of great significance. In addition, the safety of OGP transportation is also an important component of pipeline integrity. Therefore, to ensure the safety of OGP transportation, regular OGP inspections should be carried out. During this process, defects in the OGP and measured wall thickness information should be recorded to provide a basis for subsequent pipeline repair or replacement. This study analyzes the literature on pipeline testing and reviews approximately eighty articles. Based on these articles, we summarize the types of common OGP defects and review the basic principles of various non-destructive testing methods for pipelines, including electromagnetic acoustic transducer inspection, magnetic flux leakage testing, ultrasonic testing, and eddy current testing. We also provide a detailed introduction to the applications and innovative testing methods based on the above OGP inspection methods. Finally, an analysis and outlook on the future research focus of OGP inspection technology are presented. This research suggests that different detection methods should be used for different types of defects, such as using the magnetic leakage method for the internal detection of natural gas pipelines. Full article
(This article belongs to the Topic Oil and Gas Pipeline Network for Industrial Applications)
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<p>Non-destructive testing methods for pipelines.</p>
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<p>Proportion of oil pipeline failure types [<a href="#B11-energies-17-06366" class="html-bibr">11</a>].</p>
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<p>The working process of UT [<a href="#B4-energies-17-06366" class="html-bibr">4</a>].</p>
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<p>The working principle of EMAT [<a href="#B24-energies-17-06366" class="html-bibr">24</a>]: (<b>a</b>) transmitted wave; (<b>b</b>) reflected wave.</p>
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<p>The working principle of EC [<a href="#B25-energies-17-06366" class="html-bibr">25</a>].</p>
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<p>The basic theory of MFL [<a href="#B27-energies-17-06366" class="html-bibr">27</a>].</p>
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21 pages, 19203 KiB  
Article
Design and Study of Pulsed Eddy Current Sensor for Detecting Surface Defects in Small-Diameter Bars
by Lei Han, Yi Jiang and Ming Yuan
Sensors 2024, 24(24), 8063; https://doi.org/10.3390/s24248063 - 18 Dec 2024
Viewed by 500
Abstract
The design and study of pulsed eddy current sensors for detecting surface defects in small-diameter rods are highly significant. Accurate detection and identification of surface defects in small-diameter rods may be attained by the ongoing optimization of sensor design and enhancement of detection [...] Read more.
The design and study of pulsed eddy current sensors for detecting surface defects in small-diameter rods are highly significant. Accurate detection and identification of surface defects in small-diameter rods may be attained by the ongoing optimization of sensor design and enhancement of detection technologies. This article presents the construction of a non-coaxial differential eddy current sensor (Tx-Rx sensor) and examines the detection of surface defects in a small diameter bar. A COMSOL 3D model is developed to examine the variations in eddy current distribution and defect signal characteristics between the plate and rod components. The position of the excitation coil on the bar and the eddy current disruption around the defect are examined. Additionally, a Tx-Rx sensor has been developed and enhanced concerning coil dimensions, coil separation, and elevation height. An experimental system is established to detect bar structures with surface defects of varying depths, and a model correlating differential signal attenuation with defect depth is proposed, achieving a quantitative relative error of less than 5%, thereby offering a reference for the quantitative detection of bar surface defects. Full article
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<p>Pulsed eddy current Tx-Rx sensor detection schematic.</p>
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<p>Schematic diagram of pulsed eddy current testing model.</p>
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<p>Current density simulation cloud image of plate cross-section at different frequencies.</p>
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<p>Current density simulation cloud image of bar cross-section at different frequencies.</p>
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<p>Simulation cloud image of eddy current disturbance at defect under different excitation coil positions.</p>
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<p>Time-domain signal simulation results of induced voltage of bar and plate.</p>
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<p>Simulation cloud image of cross-section current density distribution of bar and plate without defect.</p>
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<p>Simulation results of differential time-domain signals of plate and bar.</p>
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<p>Simulation cloud image of cross-section current density distribution of bar and plate with defects.</p>
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<p>Differential signal simulation results of bar cross-sections with different depth defects.</p>
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<p>Eddy current distribution simulation cloud image of bar section at D<sub>dif</sub> time (t = 0.00502 s).</p>
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<p>Eddy current distribution simulation cloud image of bar cross-section under different depth defects at E<sub>dif</sub> time (t = 0.022 s).</p>
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<p>Tx-Rx sensor.</p>
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<p>The experimental results of sensors with different structures under varying lift-off.</p>
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<p>Experimental results of detection signals of different coil combinations.</p>
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<p>Experimental results under different coil spacing.</p>
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<p>Diagram of sensor position.</p>
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<p>Experimental results of differential signals at different positions.</p>
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<p>Pulsed eddy current test platform.</p>
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<p>Surface flat hole defect with a depth of 2 mm.</p>
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<p>Experimental normalization results of time-domain detection signal of induced voltage of bar and plate.</p>
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<p>Experimental results of pulsed eddy current testing of defective bars with different depths.</p>
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<p>The fitting curve of the relationship between differential signal and attenuation slope of different depth defects.</p>
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17 pages, 10949 KiB  
Article
Research on the Detection Method for Feeding Metallic Foreign Objects in Coal Mine Crushers Based on Reflective Pulsed Eddy Current Testing
by Benchang Meng, Zezheng Zhuang, Jiahao Ma and Sihai Zhao
Appl. Sci. 2024, 14(24), 11704; https://doi.org/10.3390/app142411704 - 15 Dec 2024
Viewed by 753
Abstract
In response to the difficulties and poor timeliness in detecting feeding metallic foreign objects during high-yield continuous crushing operations in coal mines, this paper proposes a new method for detecting metallic foreign objects, combining pulsed eddy current testing with the Truncated Region Eigenfunction [...] Read more.
In response to the difficulties and poor timeliness in detecting feeding metallic foreign objects during high-yield continuous crushing operations in coal mines, this paper proposes a new method for detecting metallic foreign objects, combining pulsed eddy current testing with the Truncated Region Eigenfunction Expansion (TREE) method. This method is suitable for the harsh working conditions in coal mine crushing stations, which include high dust, strong vibration, strong electromagnetic interference, and low temperatures in winter. A model of the eddy current field of feeding metallic foreign objects in the truncated region is established using a coaxial excitation and receiving coil with a Hall sensor. The full-cycle time-domain analytical solution for the induced voltage and magnetic induction intensity of the reflective field under practical square wave signals is obtained. Simulation and experimental results show that the effective time range, peak value, and time to peak of the received voltage and magnetic induction signals can be used to classify and identify the size, thickness, conductivity, and magnetic permeability of feeding metallic foreign objects. Experimental results meet the actual needs for removing feeding metallic foreign objects in coal mine sites. This provides core technical support for the establishment of a predictive fault diagnosis system for crushing equipment. Full article
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<p>Structure diagram of the open-pit coal mine crushing station (1—Mining Truck, 2—Ore Receiving Hopper, 3—Plate Feeder, 4—Protective Steel Structure, 5—Electrical Control Room, 6—Detection Probes Array, 7—Dual-roll Screening Crusher, and 8—Belt Conveyor).</p>
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<p>Structure diagram of the dual-roll screening crusher (1—Wear Plates for Front and Side Walls, 2—Crusher Tooth Rolls, 3—Drive Motor, 4—Hydraulic Coupling, 5—Reducer, and 6—Coupling).</p>
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<p>Side view of the truncated region of (<b>a</b>) the single-turn coil, and (<b>b</b>) the rectangular cross-section coaxial excitation and receiving coils with Hall sensors.</p>
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<p>Typical PEC signals with non-ferromagnetic metals; (<b>a</b>) receiving coil voltage signals; (<b>b</b>) magnetic induction signals of Hall sensor.</p>
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<p>Typical PEC signals with ferromagnetic metals; (<b>a</b>) receiving coil voltage signals; (<b>b</b>) magnetic induction signals of Hall sensor.</p>
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<p>Single-probe testing experiment; (<b>a</b>) experimental platform; (<b>b</b>) block diagram of the system.</p>
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<p>Detailed view of single-probe and samples; (<b>a</b>) bottom view of the single-probe; (<b>b</b>) seven test samples for experiment.</p>
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<p>PEC differential signals of alloy steel 42CrMo with different thicknesses; (<b>a</b>) receiving coil differential voltage signals; (<b>b</b>) magnetic induction differential signals of Hall sensor.</p>
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<p>Relationship between key characteristic quantities of PEC differential signals and the thicknesses of alloy steel 42CrMo; (<b>a</b>) peak voltage and its corresponding time to peak; (<b>b</b>) peak magnetic inductance and its corresponding time to peak.</p>
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<p>Three-dimensional surface plots between key characteristics of pulsed eddy current differential voltage signals and the conductivity and thickness of non-ferromagnetic metals; (<b>a</b>) peak voltage; (<b>b</b>) time to peak.</p>
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<p>Three-dimensional surface plots between key characteristics of pulsed eddy current differential magnetic inductance signals and the conductivity and thickness of non-ferromagnetic metals; (<b>a</b>) peak magnetic inductance; (<b>b</b>) time to peak.</p>
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<p>Field experiment platform with the multi-probe array.</p>
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<p>Dual <span class="html-italic">Y</span>-axis plot of PEC differential signals and time for the effective detection interval in the field experiment.</p>
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21 pages, 3464 KiB  
Article
Modeling of a Novel T-Core Sensor with an Air Gap for Applications in Eddy Current Nondestructive Evaluation
by Siquan Zhang
Sensors 2024, 24(24), 7931; https://doi.org/10.3390/s24247931 - 11 Dec 2024
Viewed by 546
Abstract
Multi-layer conductive structures, especially those with features like bolt holes, are vulnerable to hidden corrosion and cracking, posing a serious threat to equipment integrity. Early defect detection is vital for implementing effective maintenance strategies. However, the subtle signals produced by these defects necessitate [...] Read more.
Multi-layer conductive structures, especially those with features like bolt holes, are vulnerable to hidden corrosion and cracking, posing a serious threat to equipment integrity. Early defect detection is vital for implementing effective maintenance strategies. However, the subtle signals produced by these defects necessitate highly sensitive non-destructive testing (NDT) techniques. Analytical modeling plays a critical role in both enhancing defect-detection capabilities and guiding the design of highly sensitive sensors for these complex structures. Compared to the finite element method (FEM), analytical approaches offer advantages, such as faster computation and high accuracy, enabling a comprehensive analysis of how sensor and material parameters influence defect detection outcomes. This paper introduces a novel T-core eddy current sensor featuring a central air gap. Utilizing the vector magnetic potential method and a truncated region eigenfunction expansion (TREE) method, an analytical model was developed to investigate the sensor’s interaction with multi-layer conductive materials containing a hidden hole. The model yielded closed-form expressions for the induced eddy current density and coil impedance. A comparative study, implemented in Matlab, analyzed the eddy current distribution generated by T-core, E-core, I-core, and air core sensors under identical conditions. Furthermore, the study examined how the impedance of the T-core sensor changed at different excitation frequencies between 100 Hz and 10 kHz when positioned over a multi-layer conductor with a hidden air hole. These findings were then compared to those obtained from E-core, I-core, and air-core sensors. The analytical results were validated through finite element simulations and experimental measurements, exhibiting excellent agreement. The study further explored the influence of T-core design parameters, including the air gap radius, dome radius, core column height, and relative permeability of the T-core material, on the inspection sensitivity. Finally, the proposed T-core sensor was used to evaluate crack and hole defects in conductors, demonstrating its superior sensitivity compared to I-core and air core sensors. Although slightly less sensitive than the E-core sensor, the T-core sensor offers advantages, including a more compact design and reduced material requirements, making it well-suited for inspecting intricate and confined surfaces of the target object. This analytical model provides a valuable tool for designing advanced eddy current sensors, particularly for applications like detecting bolt hole defects or measuring the thickness of non-conductive coatings in multi-layer conductor structures. Full article
(This article belongs to the Topic Advances in Non-Destructive Testing Methods, 2nd Edition)
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<p>Cross-sectional illustrations of (<b>a</b>) an I-core, (<b>b</b>) a T-core, and (<b>c</b>) an E-core ECT sensors, each featuring an air gap within the ferrite core.</p>
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<p>T-core ECT sensors consisting of (<b>a</b>) a filamentary coil and (<b>b</b>) a multi-turn coil positioned above a layered conductor with a hole in its second layer. Numbers 1–8 represent different regions.</p>
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<p>Numerical calculation scheme of the analytical model.</p>
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<p>Axially symmetric (<b>a</b>) E-core and (<b>b</b>) I-core ECT sensors positioned above a layered conductor with a hidden hole in the second layer. Numbers 1–8 represent different regions.</p>
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<p>Configuration for the experiment.</p>
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<p>E-core, T-core, I-core, and coil used in the experiments.</p>
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<p>Real component of the eddy current density at a depth of 0.2 mm beneath the surface of the layered conductor, across varying distances from the coil’s central axis.</p>
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<p>Magnetic flux density distributions generated by sensors of four different core types: (<b>a</b>) E-core, (<b>b</b>) T-core, (<b>c</b>) I-core, and (<b>d</b>) air-core. All sensors were positioned above the same layered conductor and subjected to the same excitation.</p>
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<p>Normalized changes in (<b>a</b>) resistance and (<b>b</b>) reactance caused by the layered conductor of E-core, T-core, I-core (with a relative permeability of 2500), and air-core (with a relative permeability of 1) sensors, as a function of frequency.</p>
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<p>Normalized changes in (<b>a</b>) resistance and (<b>b</b>) reactance caused by an air hole in the second-layer conductor of E-core, T-core, I-core (with a relative permeability of 2500), and air-core (with a relative permeability of 1) sensors, as a function of frequency.</p>
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<p>Investigating the correlation between variations in T-core coil resistance caused by a hole in the second-layer conductor and the radius of the T-core air gap.</p>
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<p>Investigation of the correlation between the variation in resistance of the T-core coil, caused by the presence of a hole in the second-layer conductor, and the radius of the T-core’s upper circular plate.</p>
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<p>Investigating the correlation between variation in T-core coil resistance caused by a hole in the second-layer conductor and the T-core’s column height.</p>
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<p>Investigating the correlation between variations in coil (<b>a</b>) resistance and (<b>b</b>) reactance caused by a hole in the second-layer conductor and the T-core’s relative permeability.</p>
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<p>The correlation between variations in coil (<b>a</b>) resistance and (<b>b</b>) reactance and the distance from the crack’s center line during scanning with various core sensors.</p>
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<p>The correlation between variations in coil (<b>a</b>) resistance and (<b>b</b>) reactance and the distance from the hole’s center during the scanning process of various core sensors through the hole.</p>
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<p>The relationship between the change in (<b>a</b>) resistance and (<b>b</b>) reactance of the T-core coil and the excitation frequency; the distance between the coil axis and the crack centerline is 10 mm.</p>
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<p>Refinement of the low-frequency area of <a href="#sensors-24-07931-f017" class="html-fig">Figure 17</a>: (<b>a</b>) resistance and (<b>b</b>) reactance.</p>
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14 pages, 5323 KiB  
Article
Modeling and Simulation of Eddy Current Dissipation Magnetic Acceleration Noise of Space Inertial Sensors
by Pengxuan Li, Zhiyin Sun, Wei Gao, Bingzhang Cao, Yunzhao Li, Liyi Li and Lei Wang
Sensors 2024, 24(23), 7723; https://doi.org/10.3390/s24237723 - 3 Dec 2024
Viewed by 556
Abstract
The magnetic acceleration noise (MAN) that stems from the eddy current dissipation of a test mass (TM) serves as an important source of noise for space inertial sensors. Given the problem that the eddy current dissipation magnetic acceleration noise (ECDMAN) of a cubic [...] Read more.
The magnetic acceleration noise (MAN) that stems from the eddy current dissipation of a test mass (TM) serves as an important source of noise for space inertial sensors. Given the problem that the eddy current dissipation magnetic acceleration noise (ECDMAN) of a cubic TM defies analytical solutions, an analytical model of ECDMAN for a spherical TM, which has the same volume as the cubic TM, is systematically derived on the basis of the principles of electromagnetism and the fluctuation-dissipation theorem, and this model can be used as an approximate analytical model for the evaluation of this noise term. Based on the approximate analytical model, with the TM of the LISA Pathfinder (LPF) as the research object, this paper obtains a modification coefficient using the approach of combining the analytical method with the finite element method (FEM), and establishes a semi-analytical model of ECDMAN for the cubic TM. Using the parameters of the LPF’s TM, the calculation error of the semi-analytical model is reduced by about 4.64% compared with the approximate analytical model. Finally, a generalized modeling approach for the semi-analytical model of ECDMAN is put forward, which is applicable to TMs with different parameters and can realize the real-time and rapid evaluation of ECDMAN during in-orbit experiments. Full article
(This article belongs to the Section Physical Sensors)
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<p>Schematic diagram of the induced eddy current of a spherical TM under the action of AUMF. The red dotted lines represent the eddy current, and the arrows point to their flow direction.</p>
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<p>Schematic diagram of the equivalent process of eddy current formation.</p>
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<p>The eddy current loss of a spherical TM.</p>
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<p>The simulation result of the two processes of the generation of eddy current loss.</p>
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<p>The displacement curve of the TM.</p>
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<p>Simulation result of the equivalence of damping loss and eddy current loss.</p>
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<p>Comparison of eddy current loss between spherical TM and cubic TM.</p>
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<p>The ratio of the eddy current loss of the cubic TM to the spherical TM.</p>
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<p>A generalized process for establishing the semi-analytical model of ECDMAN.</p>
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15 pages, 9185 KiB  
Article
Research and Analysis of Carbon Fiber-Reinforced Polymer Prepreg Detection Based on Electromagnetic Coil Sensors
by Sichang Zhang, Shouqi Cao and Meiling Wang
Appl. Sci. 2024, 14(23), 10807; https://doi.org/10.3390/app142310807 - 22 Nov 2024
Viewed by 653
Abstract
In response to the challenges posed by the complexity and potential hazards of traditional chemical methods for detecting the surface density of carbon fiber prepreg materials, this paper explores the use of eddy current testing principles. It establishes the relationship between coil impedance [...] Read more.
In response to the challenges posed by the complexity and potential hazards of traditional chemical methods for detecting the surface density of carbon fiber prepreg materials, this paper explores the use of eddy current testing principles. It establishes the relationship between coil impedance variation and the surface density of carbon fiber prepreg materials and designs a quadrupolar excitation eddy current detection probe. This probe can detect the surface density of both single-line and woven carbon fiber prepreg structures. The overall structure and dimensions of the designed quadrupolar probe were optimized using finite element simulation software. The results show that the number of coil turns significantly affects the sensor performance, with more turns leading to increased sensitivity. Moreover, with the same number of coil turns, smaller inner diameters and larger outer diameters of the coil enhance sensor sensitivity. A comprehensive comparison between unidirectional and woven carbon fiber models suggests that woven structures have superior electrical conductivity at identical excitation frequencies, while unidirectional models show more pronounced electrical anisotropy. These findings provide valuable insights for analyzing electrical properties, numerical simulations, and eddy current testing in composite materials. Full article
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<p>Simulation model illustration depicting four T_coils, one R_coil, and a CFRP model.</p>
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<p>Top view of quadrupolar structure. O1–O4 denote the centers of the four transmitting coils and the arrows indicate the current directions.</p>
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<p>Model mesh generation.</p>
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<p>Current density of the measured material. (<b>a</b>) Current density of isotropic materials. (<b>b</b>) Current density of anisotropic materials.</p>
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<p>The relationship between the excitation frequency, the number of coil turns, and the coil impedance.</p>
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<p>Distribution map of magnetic flux density magnitude: (<b>a</b>) 1 MHz magnetic flux density magnitude; (<b>b</b>) 10 MHz magnetic flux density magnitude.</p>
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<p>The inner diameter (d) of the coil. The relationship between the lift-off distance, the inner diameter (d) of the coil, and the coil impedance.</p>
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<p>The outer diameter (D) of the coil. The relationship between the lift-off distance, the outer diameter (D) of the coil, and the coil impedance.</p>
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<p>The height (H) of the coil. The relationship among the lift-off distance, the height (H) of the coil, and the coil impedance.</p>
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<p>Simulation model of carbon fiber materials. (<b>a</b>) Woven carbon fiber model, (<b>b</b>) unidirectional carbon fiber model.</p>
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<p>Distribution map of conductive current density. (<b>a</b>–<b>c</b>) Conductive current density of unidirectional carbon fiber model; (<b>d</b>–<b>f</b>) conductive current density of woven carbon fiber model.</p>
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<p>The relationship among the excitation frequency, coil impedance, and the modulus of current density. (<b>a</b>) The relationship among the excitation frequency and coil impedance. (<b>b</b>) The relationship among the excitation frequency and the modulus of current density.</p>
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<p>The relationship between the real part of the coil impedance and the modulus of the current density.</p>
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