# A Decoupled Calibration Method Based on the Multi-Output Support Vector Regression Algorithm for Three-Dimensional Electric-Field Sensors

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Coupling Calibration Principle of Three Dimensional Electric Field Sensor

## 3. Decoupled Calibration Method Based on Multi-Output Support Vector Regression (SVR)

#### 3.1. SVR Model

#### 3.2. ν-SVR Model

## 4. Calibration Devices and Experiment Methods

#### 4.1. Calibration Device

#### 4.2. Measurement of Coupling Coefficient between Poles of 3D Electric-Field Sensor

**P**and the prediction data to

**R**. The regression matrix

**Q**is solved according to

**PQ = R**.

## 5. Analysis of Experimental Result

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bazelyan, E.M.; Raizer, Y.P.; Aleksandrov, N.L. Non-stationary corona around multi-point system in atmospheric electric field: I. Onsetelectric field and discharge current. J. Atmos. Sol.-Terr. Phys.
**2014**, 109, 80–90. [Google Scholar] [CrossRef] - Chubb, J. Comparison of atmospheric electric field measurements by a pole mounted field-meter and by a horizontal wire antenna. J. Electrost.
**2015**, 73, 1–5. [Google Scholar] [CrossRef] - Chubb, J. The measurement of atmospheric electric fields using pole mounted electrostatic field meter. J. Electrost.
**2014**, 72, 295–300. [Google Scholar] [CrossRef] - Xing, H.Y.; He, G.X.; Ji, X.Y. Analysis on Electric Field Based on Three Dimensional Atmospheric Electric Field Apparatus. J. Electr. Eng. Technol.
**2018**, 4, 1696–1703. [Google Scholar] - Bateman, M.G.; Stewart, M.F.; Blakeslee, R.J. A low-noise, microprocessor-controlled, internally digitizing rotating-vane electric field mill for airborne platforms. J. Atmos. Ocean. Technol.
**2007**, 24, 1245–1255. [Google Scholar] [CrossRef] [Green Version] - Zhang, X.; Bai, Q.; Xia, S.H. Design and measurement of a miniaturized three dimensional electric field sensor. J. Electron. Inf. Technol.
**2007**, 29, 1002–1004. [Google Scholar] - Mach, D.M.; Koshak, W.J. General matrix inversion technique for the calibration of electric field sensor arrays on aircraft platforms. J. Atmos. Ocean. Technol.
**2007**, 24, 1576–1587. [Google Scholar] [CrossRef] [Green Version] - Lin, C.; Chen, X.N.; Zhang, H.T.; Gu, C.C.; Wang, S.M. Design of the air three dimensional atmospheric electric field directional detection system. In Journal of PLA University of Science and Technology (Natural Science Edition); Jie Fang Jun Li Gong Da Xue Xue Bao Bian Ji Bu: Nanjing, China, 2017. [Google Scholar]
- Cui, Y.; Yuan, H.; Song, X. Model, design, and testing of field mill sensors for measuring electric fields under high-voltage direct-current power lines. IEEE Trans. Ind. Electron.
**2017**, 65, 608–615. [Google Scholar] [CrossRef] - Cui, Y.; Yuan, H.; Zhao, L.X. Optimum design of calibration device for field mill type electric field sensor based on finite element method. J. Beijing Univ. Aeronaut. Astronaut.
**2015**, 41, 1807–1812. [Google Scholar] - Zakriya, M.; Waqas, A.G.; Mahmoud, R. Double Comb-Finger Design to eliminate Cross-axis Sensitivity in a Dual-axis Accelerometer. IEEE Sens. Lett.
**2017**, 1, 1–4. [Google Scholar] - Yang, P.F.; Peng, C.R.; Fang, D.M. Design fabrication and application of an SOI-based resonant electric field micro-sensor with coplanar comb-shaped electrodes. J. Micromech. Microeng.
**2013**, 23, 1–8. [Google Scholar] [CrossRef] - Ling, B.Y.; Wang, Y.; Peng, C.R. Single-chip 3D electric field micro-sensor. Front. Mech. Eng.
**2017**, 12, 581–590. [Google Scholar] [CrossRef] [Green Version] - Fang, Y.G.; Peng, C.R.; Fang, D.M.; Wang, Y.; Xia, S.H. Micro 3-dimensional folding electric field sensor. Transducer Microsyst. Technol.
**2017**, 35, 67–70. [Google Scholar] - Wen, X.L.; Peng, C.R.; Fang, D.M. Measuring method of three dimensional atmospheric electric field based on coplanar decoupling structure. J. Electron. Inf. Technol.
**2014**, 36, 2504–2508. [Google Scholar] - Zhou, S.; Liu, L.P.; Gao, J.Y.; Zhang, B.C. Research on static decoupling algorithm for 3-axis wrist force sensor. J. Electron. Meas. Instrum.
**2020**, 34, 181–187. [Google Scholar] - Li, B.; Peng, C.R.; Ling, B.Y. The decoupling calibration method based on genetic algorithm of three dimensional electric field sensor. J. Electron. Inf. Technol.
**2017**, 39, 2252–2258. [Google Scholar] - Liu, Y.H.; Dong, C.Y.; Li, J.; Wang, Y. LQR control of unmanned aerial vehicles lateral based on genetic algorithm. Comput. Meas. Control
**2013**, 21, 1544–1546. [Google Scholar] - Wu, G.F.; Cui, Y.; Liu, H.; Zhang, L. Decoupling Calibration Method of 3D Electric Field Sensor Based on Differential Evolution Algorithm. Trans. China Electrotech. Soc.
**2021**, 36, 3993–4001. [Google Scholar] - Prabakaran, G.; Vaithiyanathan, D.; Ganesan, M. FPGA based Effective Agriculture Productivity Prediction System Using Fuzzy Support Vector Machine. Fusion Eng. Des.
**2021**, 185, 1–16. [Google Scholar] [CrossRef] - Zhang, F.; Chen, H.W.; Li, Y.W. TDOA-DOA Mapping Using Multi-kernel Least-squares Support Vector Regression. J. Data Acquis. Process.
**2017**, 32, 540–549. [Google Scholar] - Li, Z.G.; Hou, J.; Wang, K. Application of fuzzy support vector machine on road type recognition. J. Data Acquis. Process.
**2014**, 29, 146–151. [Google Scholar] - Han, L.; Pu, X.J.; Liu, Q. FECG signal extraction based on multichannel v-SVR combined with TFBSS. Chin. J. Sci. Instrum.
**2015**, 36, 1381–1387. [Google Scholar]

**Figure 2.**Distribution of eletronic lines and potential cloud. (

**a**) Distribution of electronic lines; (

**b**) Potential cloud.

**Figure 6.**The amplitude of the induction electrodes output voltage; (

**a**) X axis direction; (

**b**) Y axis direction; (

**c**) Z axis direction.

**Figure 8.**Electric-field intensity, E (kV/m). (

**a**) X axis direction; (

**b**) Y axis direction; (

**c**) Z axis direction.

**Figure 9.**Relative Error in Electric field intensity (ε/%). (

**a**) X axis direction; (

**b**) Y axis direction; (

**c**) Z axis direction.

Regression Decision Function Model | Optimum Penalty Factors C | Number of Support Vectors | Constant d | Mean Square Error | Square Correlation Coefficient |
---|---|---|---|---|---|

${f}^{1}(x)$ | 8 | 16 | 0.0035 | 6.33 × 10^{−5} | 0.994 |

${f}^{2}(x)$ | 8 | 16 | 0.0074 | 6.31 × 10^{−5} | 0.992 |

${f}^{3}(x)$ | 16 | 20 | 0.0532 | 1.42 × 10^{−4} | 0.992 |

**Table 2.**The relative error between the calculated value of electric field and the theoretical value obtained by two decoupling calibration methods.

Electric Field Intensity | Traditional Least Squares Method for Solving Inverse Matrix | Method Proposed in This Paper | ||
---|---|---|---|---|

Maximum Relative Error | Mean Relative Error | Maximum Relative Error | Mean Relative Error | |

${E}_{x}$ | 13.9% | 8.2% | 4.83% | 3.27% |

${E}_{y}$ | 16.9% | 7.21% | 6.5% | 2.76% |

${E}_{z}$ | 17.8% | 7.77% | 4.55% | 1.88% |

${E}_{}$ | 16.3% | 5.87% | 4.58% | 2.72% |

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**MDPI and ACS Style**

Zhao, W.; Li, Z.; Zhang, H.; Yuan, Y.; Zhao, Z.
A Decoupled Calibration Method Based on the Multi-Output Support Vector Regression Algorithm for Three-Dimensional Electric-Field Sensors. *Sensors* **2021**, *21*, 8196.
https://doi.org/10.3390/s21248196

**AMA Style**

Zhao W, Li Z, Zhang H, Yuan Y, Zhao Z.
A Decoupled Calibration Method Based on the Multi-Output Support Vector Regression Algorithm for Three-Dimensional Electric-Field Sensors. *Sensors*. 2021; 21(24):8196.
https://doi.org/10.3390/s21248196

**Chicago/Turabian Style**

Zhao, Wei, Zhizhong Li, Haitao Zhang, Yuan Yuan, and Ziwei Zhao.
2021. "A Decoupled Calibration Method Based on the Multi-Output Support Vector Regression Algorithm for Three-Dimensional Electric-Field Sensors" *Sensors* 21, no. 24: 8196.
https://doi.org/10.3390/s21248196