Design and Optimization of Multi-Stage TMR Sensors for Power Equipment AC/DC Leakage Current Detection
<p>Multi-stage open-loop TMR sensor structure diagram.</p> "> Figure 2
<p>Simulation model of multi-stage TMR sensor front-end.</p> "> Figure 3
<p>Variation of magnetic field magnitude with current at the measurement point.</p> "> Figure 4
<p>Sensitivity of the magnetic field measurement at the measurement point as the current changes.</p> "> Figure 5
<p>Magnetic field characteristics at the measurement point under the change of the new multi-stage size structure: (<b>a</b>) The magnitude of the magnetic field at the air gap as <span class="html-italic">h</span> varies; (<b>b</b>) The magnitude of the magnetic field at the air gap as d varies; (<b>c</b>) The magnitude of the magnetic field at the measurement point that varies synchronously with <span class="html-italic">r</span><sub>1</sub> and <span class="html-italic">p</span>.</p> "> Figure 6
<p>Interference position placement diagram.</p> "> Figure 7
<p>Schematic diagram of the TMR front-end anti-magnetic interference performance with and without the magnetic ring structure at different angles of interference: (<b>a</b>) Under Interference A; (<b>b</b>) Under Interference B; (<b>c</b>) Under Interference C; (<b>d</b>) Under Interference D.</p> "> Figure 7 Cont.
<p>Schematic diagram of the TMR front-end anti-magnetic interference performance with and without the magnetic ring structure at different angles of interference: (<b>a</b>) Under Interference A; (<b>b</b>) Under Interference B; (<b>c</b>) Under Interference C; (<b>d</b>) Under Interference D.</p> "> Figure 8
<p>Effect of height h and opening gap d on magnetic interference immunity of TMR front-end: (<b>a</b>) With the variation of height <span class="html-italic">h</span>; (<b>b</b>) With the variation of the opening slit <span class="html-italic">d</span>.</p> "> Figure 9
<p>Analysis of TMR front-end anti-magnetic interference performance with the same ring thickness and different N-stage settings.</p> "> Figure 10
<p>ACGWO-BP-NSGA-II design block diagram.</p> "> Figure 11
<p>The effect of ACGWP-BP fitting under each disturbance: (<b>a</b>) Under interference A; (<b>b</b>) Under interference B (<b>c</b>) Under interference C; (<b>d</b>) Under interference D.</p> "> Figure 12
<p>Pareto Frontier Diagram.</p> "> Figure 13
<p>Experimental test platform: (<b>a</b>) AC characteristics experimental platform; (<b>b</b>) DC characteristics experiment platform.</p> "> Figure 14
<p>Sensor range and linearity.</p> "> Figure 15
<p>Sensor frequency response characteristics.</p> "> Figure 16
<p>Comparison of TMR sensor input and output AC characteristic curves under no interference: (<b>a</b>) Under multi-stage magnetic ring structure; (<b>b</b>) Under monostage magnetic ring structure.</p> "> Figure 17
<p>Comparison of the input and output AC characteristics of TMR sensors under interference: (<b>a</b>) Under multi-stage magnetic ring structure; (<b>b</b>) Under monostage magnetic ring structure.</p> "> Figure 18
<p>Comparison of TMR sensor input and output DC characteristic curves under no interference: (<b>a</b>) Under multi-stage magnetic ring structure; (<b>b</b>) Under monostage magnetic ring structure.</p> "> Figure 19
<p>Comparison of the input and output DC characteristics of TMR sensors under interference: (<b>a</b>) Under multi-stage magnetic ring structure; (<b>b</b>) Under monostage magnetic ring structure.</p> ">
Abstract
:1. Introduction
- The method possesses excellent front-end magnetic field measurement sensitivity and anti-magnetic interference performance;
- The method can increase the accuracy and stability of microampere level current sensor measurements without increasing the size of the sensor or the processing complexity of the circuit;
- An improved non-dominated ranking genetic algorithm (ACGWO-BP-NSGA-II) is proposed for nonlinear mapping to assure the optimal performance of the front-end magnetic measurement of the sensor with the smallest possible size.
2. Multi-Stage Open-Loop TMR Sensor Characterization
2.1. Multi-Stage Open-Loop TMR Sensor Structure
2.2. Magnetic Sensitivity Analysis
2.3. Analysis of Anti-Magnetic Capacity
3. Dimensional Optimization Design of ACGWO-BP-NSGA-II
3.1. Optimization Target Establishment
3.2. ACGWO-BP-NSGA-II Optimization Process
- (1)
- Build the multi-stage magnetic ring structure model. Determine the model dimensions r1 = 10 mm, d = 4 mm, h = 10 mm, the number of stages N = 3, initialize p = th1 = th2 = th3 = 1 mm, and perform relevant material and boundary settings and meshing.
- (2)
- Set the scan range of optimized dimension parameters. Set the scan range of the first stage size p to 6–15 mm; the variation range of th1 and th2 to 1–10 mm.
- (3)
- Solve the calculation. Set the interference current I′ to 1–1000 mA, and change p, th1, and th2 to obtain the magnetic field measurement error MC1(X)–MC4(X) obtained for sample X under four interferences according to the setting in Equation (2), then the fitted sample for mapping MCj() is (X, MCj(X)).
3.2.1. ACWGO-BP Nonlinear Fitting Algorithm
- (a)
- Chaos mapping initialization. Tent chaos mapping is introduced in the initialization to ensure the uniformity of the initial population distribution and the diversity of the populations, and to speed up the convergence of the GWO algorithm in the exploration space.The sequence of Tent chaos mapping is shown in Equation (16)
- (b)
- Then, the initial position sequence of gray wolf is is shown in Equation (17).
- (c)
- Adaptive descent strategy. Since the path of GWO in the process of finding the optimal solution, exploring the optimal search itself is not linearly convergent. The traditional convergence path presents linear convergence as shown in Equation (11), and cannot reflect the actual optimization approach and release the inherent ability of GWO’s superior search. The adaptive descent strategy as shown in Equation (18) is introduced to ensure its balance in local and global search.
- (d)
- Location update correction. Finally, inspired by the literature [38], a similar correction was made to the location update formula to play and use individual information to guide the individual search capabilities of wolves.
3.2.2. ACGWO-BP-NSGA-II Optimization Framework
3.3. Results Validation and Analysis
4. Experimental Verification
4.1. AC Characteristics Experiment
4.1.1. No External Interference Situation
4.1.2. External Magnetic Interference Situation
4.2. DC Characteristics Experiment
4.3. Performance Comparison Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
TMR | Tunneling magnetoresistive |
AMR | Anisotropic magnetoresistive |
GMR | Giant magnetoresistive |
A | Magnetic field measurement sensitivity |
MC | Relative error of magnetic field measurement |
M | Combined error of magnetic field measurement |
C | The total thickness of the magnetic ring |
F | Fitting the mapping |
ACGWO | Adaptive Gray Wolf Algorithm |
ACGWO-BP-NSGA-II | The improved non-dominated ranking genetic algorithm |
R2 | The goodness-of-fit |
MAE | The mean absolute error |
B | Magnetic induction strength magnitude |
N | Number of stages of multi-stage magnetic ring |
h | Height of multi-stage magnetic ring |
p | Thickness of inner stage polymagnetic layer |
r | Radius of lead wire |
r1 | Inner radius of multi-stage magnetic ring |
thi | Thickness of attenuation layer at each level |
d | Width of air gap of magnetic ring opening |
I′i (i = A–D) | Interference current in four directions |
δ | Non-linear error |
τ | The electromagnetic propagation coefficient |
μ | Permeability |
α | Dielectric constant |
β | Phase constant |
σ | Electrical conductivity |
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Material Name | Relative Permeability |
---|---|
Permalloy | 50,000 |
Aluminum | 1 |
Copper | 1 |
Model Label Name | Size (mm) |
---|---|
r | 2 |
r1 | 10 |
h | 10 |
d | 8 |
p | 10 |
th1–thN−1 | 2 |
Level N | Size Setting |
---|---|
1 | p = 10 mm |
2 | p = 5 mm, th1 = 15 mm |
3 | p = 3 mm, th1 = 3 mm, th2 = 4 mm |
4 | p = 2.5 mm, th1 = 2.5 mm, th2 = 2.5 mm, th3 = 2.5 mm |
5 | p = 2 mm, th1 = 2 mm, th2 = 2 mm, th3 = 2 mm, th4 = 2 mm |
6 | p = 1.6 mm, th1 = 1.6 mm, th2 = 1.6 mm, th3 = 1.6 mm, th4 = 1.6 mm, th5 = 2 mm |
Training Process |
---|
|
Interference A | ||||
Algorithm Name | R2train | MAEtrain | R2test | MAEtest |
Random forest | 0.94 | 0.38 | 0.87 | 0.6 |
GRNN | 0.98 | 0.2 | 0.95 | 0.35 |
Bipolar rational fractions | 0.84 | 0.69 | 0.82 | 0.7 |
BP | 0.89 | 0.54 | 0.87 | 0.58 |
ACGWO-BP | 0.99 | 0.10 | 0.97 | 0.12 |
Interference B | ||||
Algorithm name | R2train | MAEtrain | R2test | MAEtest |
Random forest | 0.88 | 0.8 | 0.78 | 1.16 |
GRNN | 0.99 | 0.25 | 0.77 | 1 |
Bipolar rational fractions | 0.74 | 1.5 | 0.707 | 1.43 |
BP | 0.8 | 1.28 | 0.72 | 1.41 |
ACGWO-BP | 0.97 | 0.14 | 0.92 | 0.17 |
Interference C | ||||
Algorithm name | R2train | MAEtrain | R2test | MAEtest |
Random forest | 0.97 | 3.25 | 0.88 | 4.42 |
GRNN | 0.98 | 1.01 | 0.96 | 2.81 |
Bipolar rational fractions | 0.95 | 4.46 | 0.94 | 4.62 |
BP | 0.96 | 3.50 | 0.92 | 3.80 |
ACGWO-BP | 0.99 | 1.48 | 0.96 | 1.69 |
Interference D | ||||
Algorithm name | R2train | MAEtrain | R2test | MAEtest |
Random forest | 0.93 | 3.31 | 0.88 | 4.06 |
GRNN | 0.99 | 0.7 | 0.93 | 3.02 |
Bipolar rational fractions | 0.96 | 4.50 | 0.95 | 4.40 |
BP | 0.98 | 2.8 | 0.97 | 3.02 |
ACGWO-BP | 0.99 | 1.25 | 0.98 | 1.24 |
p (mm) | th1 (mm) | th2 (mm) | M (%) (NSGA-II) | M (%) (Multi-Stage Magnetic Ring) | M (%) (Single Magnetic Ring) |
---|---|---|---|---|---|
6.6 | 1 | 8.5 | 18.32 | 16.7 | 104 |
6 | 1 | 8.7 | 19.23 | 16.6 | 122 |
6 | 1 | 8.4 | 20.08 | 19.1 | 105 |
6 | 1 | 8.3 | 20.69 | 19.0 | 138 |
6 | 1 | 8 | 22.03 | 19.8 | 142 |
6 | 1 | 7.9 | 22.88 | 20.0 | 138 |
6 | 1 | 7.6 | 25.19 | 23.6 | 139 |
6 | 1 | 7.5 | 26.02 | 24.5 | 120 |
p (mm) | th1 (mm) | th2 (mm) | A (Multi-Stage Magnetic Ring) | A (Single Magnetic Ring) |
---|---|---|---|---|
We a6.6 | 1 | 8.5 | 15.0 | 15.2 |
6 | 1 | 8.7 | 15.1 | 15.3 |
6 | 1 | 8.4 | 15.0 | 15.2 |
6 | 1 | 8.3 | 15.0 | 15.3 |
6 | 1 | 8 | 15.0 | 15.3 |
6 | 1 | 7.9 | 15.0 | 15.3 |
6 | 1 | 7.6 | 15.0 | 15.2 |
6 | 1 | 7.5 | 15.0 | 15.3 |
Parameter | This Work | [32] | [31] | [30] | [40] |
---|---|---|---|---|---|
Sensor technology | TMR | TMR | TMR | GMR | GMR |
Sensor setup sensitivity | 57.30 V/A | 10.52 V/A | 10 V/A | 0.0392 V/A | 0.2319 V/A |
Measurement range | ±60 mA | ±300 mA | ±200 mA | ±200 mA | ±300 mA |
Detection limit | AC: 85 μA DC: 50 μA | AC: 280 μA | / | 10 mA | AC: 100 to 300 μA DC: 100 μA |
Bandwidth | 80 kHz | 10 kHz | / | 1 MHz | 50 kHz |
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Hu, X.; Duan, X.; Zhang, W.; Fu, Y.; Li, Y.; Zhao, P.; Deng, X.; Yu, C.; Wang, J. Design and Optimization of Multi-Stage TMR Sensors for Power Equipment AC/DC Leakage Current Detection. Sensors 2023, 23, 4749. https://doi.org/10.3390/s23104749
Hu X, Duan X, Zhang W, Fu Y, Li Y, Zhao P, Deng X, Yu C, Wang J. Design and Optimization of Multi-Stage TMR Sensors for Power Equipment AC/DC Leakage Current Detection. Sensors. 2023; 23(10):4749. https://doi.org/10.3390/s23104749
Chicago/Turabian StyleHu, Xiaoxu, Xuetao Duan, Wei Zhang, Yameng Fu, Yongfu Li, Pengcheng Zhao, Xudong Deng, Chuanxiang Yu, and Jingang Wang. 2023. "Design and Optimization of Multi-Stage TMR Sensors for Power Equipment AC/DC Leakage Current Detection" Sensors 23, no. 10: 4749. https://doi.org/10.3390/s23104749