基于有限元法的水下航行器地磁异常模拟研究

doi:10.12305/j.issn.1001-506X.2024.07.03

摘要/Abstract

摘要：

为改进水下航行器磁异常探测技术中磁异常实测数据难获得、现有磁体模型计算精度不高等问题, 基于有限元仿真探讨建立无需区分近、远场的高精度混合磁体模型方法。应用有限元数值方法仿真复杂结构水下航行器的空间磁异常分布, 以磁场数值解为收敛目标, 建立以偶极子阵元数目、位置及磁矩为参数的均匀磁化椭球体与偶极子阵列混合的航行器磁异常解析模型, 采用非线性最小二乘算法求解模型系数。仿真结果表明, 基于该模型得到磁异常计算值与全空间内数值解的拟合度较高, 测试平面平均误差为3%。该模型在磁场延拓、高精度建模等方面可以进一步应用。

关键词: 航空磁异常探测, 有限元仿真, 磁体模拟, 数值拟合

Abstract:

To overcome the difficulties of obtaining the magnetic anomaly data of underwater vehicles and the low calculation precision of existing magnet simulation models, a high-precision hybrid analytical model suitable in both near-field and far-field based on finite element method is introduced. The spatial signature of magnetic anomaly of an underwater vehicle with complex structure is analyzed by the finite element method. Then, an analytical model combined with uniformly-magnetized spheroid and a dipole array is proposed with the numerical results as the convergence goal. This analytical model consists of several parameters, including the number of array elements, the positions of each element, and magnetic moments, which are solved by nonlinear least-square algorithm. The simulation results show that the magnetic anomaly calculated from this model has good consistencies with the numerical solution in full space, giving an average error of 3% at the measurement plane. This model could be potentially extended to applications like magnetic field continuation and high-precision modeling.

Key words: airborne magnetic anomaly detection, finite element method (FEM), magnet simulation, numerical fitting

中图分类号:

O411.3

赵高阳, 刘勇, 朱平杰, 向冰, 周洪娟. 基于有限元法的水下航行器地磁异常模拟研究[J]. 系统工程与电子技术, 2024, 46(7): 2191-2200.

Gaoyang ZHAO, Yong LIU, Pingjie ZHU, Bing XIANG, Hongjuan ZHOU. Simulation of geomagnetic anomaly of underwater vehicle based on finite element method[J]. Systems Engineering and Electronics, 2024, 46(7): 2191-2200.

图/表 14

图1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

表1

图12

图13

参考文献 30

1	宋保维, 潘光, 张立川, 等. 自主水下航行器发展趋势及关键技术[J]. 中国舰船研究, 2022, 17 (5): 27- 44.
	SONG B W , PAN G , ZHANG L C , et al. Development trend and key technologies of autonomous underwater vehicles[J]. Chinese Journal of Ship Research, 2022, 17 (5): 27- 44.
2	WELLER R A , LEVIN L A , GATES A R . Global observing needs in the deep ocean[J]. Frontiers in Marine Science, 2019, 6 (6): 167218016.
3	WANG C , CUI Y , SONG X , et al. A novel underwater target detection method based on low-frequency magnetic signal generated by portable transmitter[J]. IEEE Sensors Journal, 2023, 23 (8): 8459- 8465. doi: 10.1109/JSEN.2023.3253708
4	SANCHEZ P , PAPAELIAS M , MARQUEZ F . Autonomous underwater vehicles: instrumentation and measurements[J]. IEEE Instrumentation and Measurement Magazine, 2020, 23 (2): 105- 114. doi: 10.1109/MIM.2020.9062680
5	鞠建波, 郁红波, 范赵鹏, 等. 吊放声呐扩展螺旋阵搜潜效能评估改进方法[J]. 水下无人系统学报, 2020, 28 (4): 434- 439.
	JU J B , YU H B , FAN Z P , et al. An improved method for evaluation the submarine searching effectiveness with extension spiral array of dipping sonar[J]. Journal of Unmanned Undersea Systems, 2020, 28 (4): 434- 439.
6	胡平, 顾雪峰, 刘凯, 等. 国外航空反潜装备现状及发展趋势[J]. 舰船电子工程, 2022, 42 (9): 10-12, 86.
	HU P , GU X F , LIU K , et al. Current situation and development trend of foreign aviation anti-submarine equipment[J]. Ship Electronic Engineering, 2022, 42 (9): 10-12, 86.
7	BRUNOTTE X, MEUNIER G, BONGIRAUD J. Ship magnetizations modelling by finite element method[C]//Proc. of the IEEE Conference on Electromagnetic Field Computation, 1992.
8	WANG J X , REN Q . A 3-D hybrid maxwell's equations finite-difference time-domain (ME-FDTD)/wave equation finite-element time-domain (WE-FETD) method[J]. IEEE Trans.on Antennas and Propagation, 2023, 71 (6): 5212- 5220. doi: 10.1109/TAP.2023.3268732
9	CHADEBEC O , COULOMB J L , BONGIRAUD J P , et al. Recent improvements for solving inverse magnetostatic problem applied to thin shells[J]. IEEE Trans.on Magnetics, 2002, 38 (2): 1005- 1008. doi: 10.1109/20.996258
10	IOANNIDIS G . Identification of a ship or submarine from its magnetic signature[J]. IEEE Trans.on Aerospace&Electronic Systems, 1977, 13, 327- 329.
11	曲晓慧, 杨日杰, 单志超. 潜艇磁场建模方法的分析与比较[J]. 舰船科学技术, 2011, 33 (3): 7- 11. doi: 10.3404/j.issn.1672-7649.2011.03.002
	QU X H , YANG R J , SHAN Z C . Analysis and comparison on magnetic field modeling method of submarine[J]. Ship Science and Technology, 2011, 33 (3): 7- 11. doi: 10.3404/j.issn.1672-7649.2011.03.002
12	林春生. 舰船磁场深度换算中的单列椭球体和磁偶极子混合模型[J]. 水雷战与舰船防护, 1996, 1996 (3): 54- 58.
	LIN C S . Hybrid model of single-row ellipsoid and magnetic dipole in ship magnetic field depth conversion[J]. Mine Warfare & Ship Self-defence, 1996, 1996 (3): 54- 58.
13	HOFFMANN A . Spin hall effects in metals[J]. IEEE Trans.on Magnetics, 2013, 49 (10): 5172- 5193. doi: 10.1109/TMAG.2013.2262947
14	徐杰. 基于遗传算法的潜艇三维模型及其磁场延拓方法[J]. 舰船电子工程, 2009, 29 (7): 188- 191. doi: 10.3969/j.issn.1627-9730.2009.07.054
	XU J . Application of genetic algorithm in continuation of magnetic field of submarines in high areas[J]. Ship Electronic Engineering, 2009, 29 (7): 188- 191. doi: 10.3969/j.issn.1627-9730.2009.07.054
15	招妙妍. 基于模拟退火算法的航向实测磁场数据建模分析[J]. 舰船电子工程, 2019, 39 (9): 188- 190. doi: 10.3969/j.issn.1672-9730.2019.09.043
	ZHAO M Y . Modeling and analysis of directional field data based on simulated annealing algorithm[J]. Ship Electronic Engineering, 2019, 39 (9): 188- 190. doi: 10.3969/j.issn.1672-9730.2019.09.043
16	NARA T , SUZUKI S , ANDO S . A closed form formula for magnetic dipole localizati-on by measurement of its magnetic field and spatial gradients[J]. IEEE Trans.on Magnetics, 2006, 42 (10): 3291- 3293. doi: 10.1109/TMAG.2006.879151
17	QIN Y J , LI K Y , YAO C , et al. Magnetic anomaly detection using full magnetic gradient orthonormal basis function[J]. IEEE Sensors Journal, 2020, 20 (21): 12928- 12940. doi: 10.1109/JSEN.2020.3003680
18	张志东. 磁性材料的磁结构、磁畴结构和拓扑磁结构[J]. 物理学报, 2015, 64 (6): 5- 21.
	ZHANG Z D . Magnetic structures, magnetic domains and topological magnetic textures of magnetic materials[J]. Acta Physica Sinica, 2015, 64 (6): 5- 21.
19	JILES D , KIARIE W . An integrated model of magnetic hysteresis, the magnetomechanical effect, and the barkhausen effect[J]. IEEE Trans.on Magnetics, 2023, 57 (2): 1- 11.
20	CHUNG H J , YANG C S , JUNG W J . A magnetic field separation technique for a scaled model ship through an earth's magnetic field simulator[J]. Journal of Magnetics, 2015, 20 (1): 62- 68. doi: 10.4283/JMAG.2015.20.1.062
21	HALGEDAH F . The dependence of magnetic domain structure upon magnetization state with emphasis upon nucleation as a mechanism for pseudo-single-domain behavior[J]. Journal of Geophysical Research, 1983, 6505- 6522.
22	XIN Z, XU Q, LI Q, et al. An orthonormalized basis function based narrowband filtering algorithm for magnetic anomaly detection[C]//Proc. of the International Congress on Image & Signal Processing, 2016.
23	孙晓永, 张琦, 潘孟春, 等. 基于COMSOL Multiphysics的目标磁特性仿真分析[J]. 中国测试, 2017, 43 (1): 122- 126.
	SUN X Y , ZHANG Q , PAN M C , et al. Simulation analysis of the magnetic properties based on COMSOL multiphysics[J]. China Measurement&Test, 2017, 43 (1): 122- 126.
24	RUBIO J D J . Stability analysis of the modified levenberg-marquardt algorithm for the artificial neural network training[J]. IEEE Trans.on Neural Networks and Learning Systems, 2020, 32 (8): 3510- 3524.
25	ANDREI N . Steepest descent methods[J]. Springer Optimization and its Applications, 2022, 195 (1): 81- 107.
26	HANSEN E R , GREENBERG R I . An interval Newton method[J]. Applied Mathematics & Computation, 1983, 12 (2/3): 89- 98.
27	VASIN V V . Solving nonlinear inverse problems based on the regularized modified Gauss-Newton method[J]. Doklady Mathe- matics, 2022, 105 (3): 175- 177. doi: 10.1134/S1064562422030103
28	GE J , WANG S Q , DONG H B , et al. Real-time detection of moving magnetic target using distributed scalar sensor based on hybrid algorithm of particle swarm optimization and Gauss-Newton method[J]. IEEE Sensors Journal, 2020, 20 (18): 10717- 10723. doi: 10.1109/JSEN.2020.2994324
29	YANG J , ZOU J . Parameter estimation of a horizontally multilayered soil with a fast evaluation of the apparent resistivity and its derivatives[J]. IEEE Access, 2020, 8, 52652- 52662. doi: 10.1109/ACCESS.2020.2980875
30	戴忠华, 张晓兵, 周穗华. 舰船磁场磁偶极子阵列模型的适用性研究[J]. 武汉理工大学学报, 2020, 42 (4): 99- 104.
	DAI Z H , ZHANG X B , ZHOU S H . Applicability of magnetic dipole array model for ship magnetic field[J]. Journal of Wuhan University of Technology, 2020, 42 (4): 99- 104.

评价参数	表达式	模型标号	模型误差评价
评价参数	表达式	模型标号	B_x	B_y	B_z	B
R²	$R^2=1-\frac{\sum\limits_{i=1}^m\left(B_i-B_i^{\prime}\right)^2}{\sum\limits_{i=1}^m\left(B_i-\bar{B}_i\right)^2}$	Ⅰ	0.869 4	0.949 7	0.959 4	0.577 3
		Ⅱ	0.970 4	0.994 0	0.990 9	0.987 0
		Ⅲ	0.970 9	0.991 4	0.989 8	0.983 8
RMSE	$\mathrm{RMSE}=\sqrt{\frac{1}{m} \sum\limits_{i=1}^m\left(B_i-B_i^{\prime}\right)^2}$	Ⅰ	0.069 9	0.030 4	0.059 3	0.093 7
		Ⅱ	0.033 3	0.010 5	0.028 0	0.016 4
		Ⅲ	0.033 0	0.012 6	0.029 6	0.018 3
RSS	$\mathrm{RSS}=\sum\limits_{i=1}^m\left(B_i-B_i^{\prime}\right)^2$	Ⅰ	49.905 1	9.441 2	35.821 5	89.484 5
		Ⅱ	11.319 8	1.125 1	8.000 5	2.749 6
		Ⅲ	11.115 0	1.616 3	8.952 3	3.420 1

[1]	金煌煌, 庄志洪, 付梦印, 郭健, 王宏波. 最简多磁偶极子等效建模方法[J]. 系统工程与电子技术, 2021, 43(8): 2066-2075.
[2]	李腾达, 冯刚, 刘少伟, 时建明, 范成礼. 铜基复合型四极轨道电磁特性仿真分析[J]. 系统工程与电子技术, 2021, 43(11): 3054-3063.