Eddy Current Measurement for Planar Structures
<p>Metallic plate measured using a probe with transmitting and receiving coils.</p> "> Figure 2
<p>Comparison between the plate term <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>z</mi> <msup> <mi>e</mi> <mrow> <mi>i</mi> <mi>θ</mi> </mrow> </msup> </mrow> </semantics></math> and sensor term <math display="inline"><semantics> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> together with its approximation function <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 3
<p>Relationship between the spatial frequency and radius, for the measurement of a finite-size plate.</p> "> Figure 4
<p>Eddy current performance using an accelerated FEM solver: (<b>a</b>) Color map; (<b>b</b>) quiver map [<a href="#B42-sensors-22-08695" class="html-bibr">42</a>].</p> "> Figure 5
<p>The relative residual with different mesh elements [<a href="#B22-sensors-22-08695" class="html-bibr">22</a>].</p> "> Figure 6
<p>Cross-sectional view of tilted Tx-Rx coils, other dimensions similar as the counterparts without tilt angle.</p> "> Figure 7
<p>Primary issues of parameter inversion.</p> "> Figure 8
<p>Generic block diagram of EM instruments.</p> "> Figure 9
<p>Self-designed and constructed EC testing instrument.</p> "> Figure 10
<p>System architecture of the customized EC testing instrument.</p> "> Figure 11
<p>Frequency responses of eddy current probes.</p> "> Figure 12
<p>Terminal arrangement of commercial impedance analyzers for: (<b>a</b>) impedance measurement of DUT; (<b>b</b>) mutual inductance measurement between the excitation and detection coils.</p> "> Figure 13
<p>Calibration with a current sensing transformer.</p> "> Figure 14
<p>Categories of the eddy-current probes.</p> "> Figure 15
<p>Measurement configuration for lift-off compensation employing triple-coil probe.</p> "> Figure 16
<p>Lift-off invariance features: (<b>a</b>) Phase invariance phenomenon; (<b>b</b>) lift-off invariance inductance; (<b>c</b>) conductivity invariance phenomenon; (<b>d</b>) permeability invariance phenomenon; (<b>e</b>) lift-off invariance frequency.</p> "> Figure 17
<p>Key factors estimating the defect information.</p> "> Figure 18
<p>(<b>a</b>) Experimental setup of EC system; (<b>b</b>) diagram of defect scanning.</p> "> Figure 19
<p>Geometric features of the Lissajous curve in the impedance plane. <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>1</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </semantics></math> are clustered centers of a variety of impedance curves.</p> "> Figure 20
<p>Various scanning modes where A-Scan is the pulse response of a single point; <math display="inline"><semantics> <mi>x</mi> </semantics></math>, <math display="inline"><semantics> <mi>y</mi> </semantics></math>, and <math display="inline"><semantics> <mi>ζ</mi> </semantics></math> indicate the width, length, and depth of a rectangular plate, respectively [<a href="#B154-sensors-22-08695" class="html-bibr">154</a>].</p> "> Figure 21
<p>(<b>a</b>) Comparison between the measured magnetic field signal (experimental data) and HG<sub>0.1</sub> pattern (simulated data) [<a href="#B155-sensors-22-08695" class="html-bibr">155</a>]; (<b>b</b>) shape of defect; (<b>c</b>) normalized sum of Eddy current density distributions [<a href="#B147-sensors-22-08695" class="html-bibr">147</a>].</p> ">
Abstract
:1. Introduction
2. Computational Models
2.1. Analytical Models
2.1.1. Dodd and Deeds and Associated Simplified Models
2.1.2. Model for the Finite-Size Plate
2.2. Finite Element Method
2.3. Tilted Structure Measurement
2.4. Multivariable Inversion
3. Measurement System
3.1. Impedance Measurement System
3.1.1. Overview of EC Testing Instruments
3.1.2. Customized EC Testing Instrument
3.1.3. Commercial Impedance Analyzers
3.1.4. Calibration
3.2. Probe Design
4. Planar Structure Measurements and Applications
4.1. Reducing the Lift-Off Effects
4.1.1. Lift-Off Compensation Using Multiple Measurements
4.1.2. Lift-Off Compensating Algorithms
4.1.3. Lift-Off Invariance Phenomenon
4.2. Defect Scanning
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Element Number | Calculation Time of the Method without Acceleration (s) | Calculation Time of the Proposed Method (s) | Accelerated Rate (Times) | Calculation Deviation (%) |
---|---|---|---|---|
10 k | 7.69 | 2.03 | 3.79 | 2.56 |
51 k | 57.74 | 3.56 | 16.22 | 3.22 |
139 k | 306.79 | 8.96 | 34.24 | 3.56 |
# | Copper | Aluminium |
---|---|---|
Inductance trajectory |
Algorithm | Updating Direction, | Convergence Rate | Stability |
---|---|---|---|
Gradient descent | Slow | High | |
Conjugate gradient | +, | Fast | Medium |
Newton method | Fast | Low | |
LM | Medium | Medium | |
PSO | is an inertial constant, and are step length, and are random variables, and as well as indicate the estimated local and global optimum.) | Medium | High |
Researcher | Controller | Applied Excitation Frequency | SNR | Software | Main Application |
---|---|---|---|---|---|
M. Kekelj et al. [91] | Cyclone V SoC | 100~400 kHz | Up to 56 dB | MATLAB | Pipe defects |
M. Hamel et al. [92] | NI DAQ | 50~150 kHz | - | LabVIEW | Plate with crack |
N. Zhang et al. [93] | NI DAQ | 0.1~1 kHz | - | MATLAB | Cylindrical samples |
A. K. Soni et al. [94] | NI DAQ with lock-in amplifier | 0.5~80 kHz | 38 dB | LabVIEW | Plate with crack |
D. E. Aguiam et al. [95] | ADSP | Up to 10 MHz | - | LabVIEW | Block with crack |
G. Zhang et al. [96] | NI DAQ with lock-in amplifier | 50 kHz | - | LabVIEW | Plate with crack |
G. Dingley et al. [97] | AVR MCU | 0.1~100 kHz | Up to 90 dB | - | EMT |
- | Basic Accuracy | Frequency Range | Impedance Range | Data Speed | No. of Channels |
---|---|---|---|---|---|
Zurich MFIA | 0.05% | 1 mHz to 500 kHz/5 MHz | 1 mΩ to 1 TΩ | 20 msec/point for f > 10 kHz | 1 Current, 1 Voltage |
Solartron 1260A impedance analyzer | 0.1%, 0.1° | 10 µHz to 32 MHz | 100 mΩ to 100 TΩ | No specified | 1 Current, 2 Voltage |
Coil Structure | Magnetic Field Distribution, | Coil Structure | Magnetic Field Distribution, |
---|---|---|---|
Pancake coil | Spiral coil | ||
Solenoid coil | U-shaped (ferrite core) coil | ||
Tangential coil (rectangular) | Rotating field coils | (Varying with time) |
Probe Type | Plate Materials | Applied Frequency for Estimation | Lift-Off (mm) | Estimated Variables and Range | Relative Error of Estimation |
---|---|---|---|---|---|
Triple-coil [100] | Al | Peak frequency | Up to 6 | Thickness (22~100 um) | <5% |
Triple-coil [132] | DP 800, DP 1000 | Zero-crossing frequency | Up to 4 | <2% | |
Triple-coil [133] | DP 600, Cr-Mo | Dual frequency | Up to 20 | <4.5% | |
Triple-coil [126] | Al, Cu | Single frequency (16 kHz) | Up to 5 | Thickness (~66 um) | <5% |
Triple-coil [99] | Al, Cu | Single frequency (200 kHz) | Up to 4 | Thickness (0.4, 0.5 mm) | <3% |
Phenomenon | Plate Materials | Applied Frequency for Estimation | Lift-Off (mm) | Estimated Variables and Range | Relative Error of Estimation |
---|---|---|---|---|---|
Phase invariance phenomenon [143] | Al, Cu | 100~1 MHz | - | Thickness (22 μm~5 mm) | <3% |
Lift-off invariance inductance [24] | DP 600, DP 800 | Single frequency depending on material | Up to 12 | <1% | |
Lift-off invariance inductance [144] | DP 600, LC-Mild, Cr-Mo | Single frequency depending on material | Up to 5 | <1% | |
Conductivity invariance phenomenon [139] | DP 600, DP 800, DP 1000 | Single frequency (90 kHz) | 1.9 | <3% | |
Permeability- independent frequency [141] | Al, Al alloy, SUS304 | 4~200 kHz | - | Thickness (1~8 mm) | - |
Slope of lift-off curve [136] | Cu, Al, SS, Ti | 1 MHz | 0.04 to 0.4 | Thickness (~100 um) | <3% |
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Xia, Z.; Huang, R.; Chen, Z.; Yu, K.; Zhang, Z.; Salas-Avila, J.R.; Yin, W. Eddy Current Measurement for Planar Structures. Sensors 2022, 22, 8695. https://doi.org/10.3390/s22228695
Xia Z, Huang R, Chen Z, Yu K, Zhang Z, Salas-Avila JR, Yin W. Eddy Current Measurement for Planar Structures. Sensors. 2022; 22(22):8695. https://doi.org/10.3390/s22228695
Chicago/Turabian StyleXia, Zihan, Ruochen Huang, Ziqi Chen, Kuohai Yu, Zhijie Zhang, Jorge Ricardo Salas-Avila, and Wuliang Yin. 2022. "Eddy Current Measurement for Planar Structures" Sensors 22, no. 22: 8695. https://doi.org/10.3390/s22228695