Dynamic Compensation of a Fluxgate Magnetometer Based on a Hybrid Optimizing Algorithm
Abstract
:Featured Application
Abstract
1. Introduction
2. Materials and Methods
2.1. Construction of the Dynamic Compensator for the Fluxgate Magnetometer
2.1.1. System Identification for the Fluxgate Magnetometer
2.1.2. Principle and Modeling of Dynamic Compensation
2.2. GA-SA Hybrid Optimization Algorithm
- Initialization: the simulation process of biological evolution.
- 2.
- Calculation of the fitness function:
- 3.
- Determine whether convergence criteria are met:
- 4.
- Perform replication, crossover, and variation operations on individuals. Generate the next generation population.
- 5.
- Simulated annealing searches are performed on each individual of the population.
- Take the first individual A1 in the population as an example:
- (1)
- Generate individual new states: where y is a zero random number with a bilateral symmetric distribution, and UB and LB are the upper and lower bounds of the solution range. For the current difference equation coefficients, take −10 and 10, respectively.
- (2)
- If , accept the new state of the individual, namely, . Otherwise, deny updating the new state.
- (3)
- Determine whether the Metropolis criterion is met. If ‘Yes’, go to Step 6. Otherwise, repeat Step 5.
- 6.
- Annealing:
- 7.
- Repeat Step 2 and Step 3 until the algorithm convergence rules are met and the current result is outputted.
3. Simulation and Signal Test
3.1. Simulation Results and Discussion
3.1.1. Comparison of Compensation Effects of Different Order Dynamic Compensators
3.1.2. Comparison of Compensation Effects of the Optimization Algorithm
3.2. Standard Signal Test Results and Discussion
3.2.1. Verification of the Step Magnetic Field Compensation Effect
3.2.2. Verification of Different Frequency Sinusoidal Magnetic Field Compensation Effects
4. Experiment and Discussion
4.1. Experimental Equipment and System
4.2. Experiment Process
4.2.1. Calibration of the Geomagnetic Background Field
4.2.2. Geomagnetic Dynamic Measurement
4.3. Result and Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Ambient Magnetic Field Parameter | Before Filter | After Filter |
---|---|---|
Standard deviation/nT | 44.41 | 1.07 |
Mean value/nT | −36.73 | 0.32 |
Peak-to-peak value/nT | 215.29 | 9.31 |
Order | Overshoot/% | Response Time/ms | Fitness |
---|---|---|---|
1 | 0.03 | 3.35 | |
2 | 0.27 | 1.95 | |
3 | 32.39 | 0.80 | |
4 | 62.66 | 6.20 | |
5 | 1.11 | 9.40 | |
6 | 1.01 | 9.10 | |
7 | divergency |
Overshoot/% | Response Time/ms | Fitness | |
---|---|---|---|
Before dynamic compensation | ---- | 10.70 | |
After GA compensation | 0.35 | 4.20 | |
After SA compensation | 0.92 | 2.10 | |
After GA-SA compensation | 0.17 | 1.95 |
Overshoot/% | Response Time/ms | |
---|---|---|
Before dynamic compensation | ---- | 10.91 |
After dynamic compensation | 4.3% | 0.63 |
Bx | By | Bz | |
---|---|---|---|
Calibration value/nT | 35,034.99 | −2819.58 | 34,061.87 |
Bx | By | Bz | ||
---|---|---|---|---|
Standard deviation/nT | Before compensation | 95.30 | 277.35 | 108.51 |
Static compensation | 62.90 | 107.96 | 79.95 | |
Dynamic compensation | 3.41 | 2.36 | 2.75 |
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Chen, Z.; Wang, Z.; Zhang, Q.; Liu, Z.; Pan, M.; Chen, D.; Xu, Y. Dynamic Compensation of a Fluxgate Magnetometer Based on a Hybrid Optimizing Algorithm. Appl. Sci. 2023, 13, 2830. https://doi.org/10.3390/app13052830
Chen Z, Wang Z, Zhang Q, Liu Z, Pan M, Chen D, Xu Y. Dynamic Compensation of a Fluxgate Magnetometer Based on a Hybrid Optimizing Algorithm. Applied Sciences. 2023; 13(5):2830. https://doi.org/10.3390/app13052830
Chicago/Turabian StyleChen, Zhuo, Zhenxiong Wang, Qi Zhang, Zhongyan Liu, Mengchun Pan, Dixiang Chen, and Yujing Xu. 2023. "Dynamic Compensation of a Fluxgate Magnetometer Based on a Hybrid Optimizing Algorithm" Applied Sciences 13, no. 5: 2830. https://doi.org/10.3390/app13052830
APA StyleChen, Z., Wang, Z., Zhang, Q., Liu, Z., Pan, M., Chen, D., & Xu, Y. (2023). Dynamic Compensation of a Fluxgate Magnetometer Based on a Hybrid Optimizing Algorithm. Applied Sciences, 13(5), 2830. https://doi.org/10.3390/app13052830