Multi-objective optimization of ship magnetic field modeling method

Dai Zhong-Hua; Zhou Sui-Hua; Zhang Xiao-Bing

doi:10.7498/aps.70.20210334

Abstract

Ship magnetic field modeling is not only beneficial to understanding the characteristics of ship magnetic field, but also can predict the space distribution of ship magnetic field, which has an important application in ship protection and underwater weapons. Aiming at the problems of low modeling accuracy and poor stability in establishing the ship magnetic field hybrid model, a method of establishing a high precision stablity model is proposed in this paper. A hybrid model of magnetic field of a ship is established by using a uniformly magnetized rotating ellipsoid and a magnetic dipole array. Since the number and positions of magnetic dipoles in the hybrid model have an important effect on the modeling accuracy and stability, the fitting error function representing the modeling accuracy and the coefficient matrix condition number function representing the stability of the model are constructed by taking the magnetic dipole parameters as unknown variables. The multi-objective function is constructed by combining the fitting error function with the coefficient matrix conditional number function, which indirectly transforms the modeling problem into a multi-objective optimization problem. The multi-objective function is solved by using the multi-objective particle swarm optimization algorithm, and an optional set of modeling solution results is obtained. In order to select the best results from the optional set, the corresponding selection rules are designed based on the modeling accuracy. The proposed method is validated by the measured data of three kinds of ship models, the modeling results show that the relative error of the model is less than 3%, and the conversion error is less than 6%, which verifies that the proposed method can effectively model the ship magnetic field. Though the measurement data error exists, the modeling solution results from the proposed method have the best stability, which verifies that the modeling method proposed in this work has good stability. Compared with the two existing modeling methods, the proposed method has very good modeling accuracy and stability. Finally, the actual data of a ship on the sea are used for modeling, and the modeling results further verify that the proposed method has high modeling accuracy and conversion accuracy, and can be effectively applied to the relevant projects.

Keywords:

ship magnetic field modeling /
multi-objective function /
multi-objective particle swarm optimizatialgorithm /
selection rule

Authors and contacts

Department of Weaponry Engineering, Naval University of Engineering, Wuhan 430033, China

Corresponding author: Dai Zhong-Hua, 602024288@qq.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51509252, 42074074)

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References

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[2]	林春生 1996 水雷战与舰船防护 3 54 Lin C S 1996 Mine Warfare & Ship Self-Defence 3 54
[3]	Ginzburg B, Frumkis L, Kaplan B Z 2002 Sens. Actuators, A 102 67 Google Scholar
[4]	Wahlström N, Gustafsson F 2014 IEEE Trans. Signal Process. 62 545 Google Scholar
[5]	姚振宁, 刘大明, 刘胜道 2014 物理学报 22 227502 Google Scholar Yao Z N, Liu D M, Liu S D 2014 Acta Phys. Sin. 22 227502 Google Scholar
[6]	张宏欣, 周穗华, 张伽伟 2017 自动化学报 43 822 Google Scholar Zhang H X, Zhou S H, Zhang J W 2017 Acta Autom. Sin. 43 822 Google Scholar
[7]	戴忠华, 周穗华, 张宏欣 2019 电子学报 47 2457 Google Scholar Dai Z H, Zhou S H, Zhang H X 2019 Acta Electron. Sin. 47 2457 Google Scholar
[8]	Sui Y, Leslie K, Clark D 2017 IEEE Magn. Lett. 8 1 Google Scholar
[9]	张晓峻, 康曦元, 樊黎明 2019 地球物理学报 62 1921 Google Scholar Zhang X J, Kang X Y, Fan L M 2019 Acta Geophys. Sin. 62 1921 Google Scholar
[10]	费春娇, 张群英, 吴佩霖 2018 电子与信息学报 11 2779 Google Scholar Fei C J, Zhang Q Y, Wu P L 2018 J. Electron. Inf. Technol. 11 2779 Google Scholar
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[12]	高俊杰, 刘大明, 姚琼 2006 兵工学报 27 869 Google Scholar Gao J J, Liu D M, Yao Q 2006 Acta Armamentarii 27 869 Google Scholar
[13]	郭成豹, 肖昌汉, 刘大明 2008 物理学报 07 4182 Google Scholar Guo C B, Xiao H C, Liu D M 2008 Acta Phys. Sin. 07 4182 Google Scholar
[14]	闫辉, 肖昌汉, 周国华 2008 兵工学报 07 839 Google Scholar Yan H, Xiao H C, Zhou G H 2008 Acta Armamentarii 07 839 Google Scholar
[15]	王德强, 余强 2014 舰船科学技术 36 1 Google Scholar Wang D Q, Yu Q 2014 Ship Sci. Technol. 36 1 Google Scholar
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[26]	郭成豹, 殷琦琦 2019 物理学报 68 114101 Google Scholar Guo C B, Yin Q Q 2019 Acta Phys. Sin. 68 114101 Google Scholar
[27]	Alqadah H F, Valdivia N P, Williams E G 2016 Prog. Electromagnet. Res. B 65 109 Google Scholar
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[29]	Coello C A C 2006 IEEE Comput. Intell. Mag. 1 28 Google Scholar
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[31]	Bandyopadhyay S, Saha S, Maulik U, Deb K 2008 IEEE Trans. Evol. Comput. 12 269 Google Scholar
[32]	Coello C A C, Pulido G T, Lechuga M S 2004 IEEE Trans. Evol. Comput. 8 256 Google Scholar
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Cited By

图 1 舰船磁场混合模型

Figure 1. Ship magnetic field mixing model.

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图 2 磁场测量

Figure 2. Magnetic field measurement.

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图 3 混合模型中磁偶极子分布范围

Figure 3. Distribution range of magnetic dipoles in the mixed model.

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图 4 测量模式

Figure 4. Measurement mode.

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图 5 小型舰船建模结果可选集分布

Figure 5. Selectable distribution of modeling results for small ships.

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图 7 大型舰船建模结果可选集分布

Figure 7. Selectable distribution of modeling results for large ships.

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图 6 中型舰船建模结果可选集分布

Figure 6. Selectable distribution of modeling results for medium-sized ships.

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图 8 小型舰船船模磁偶极子分布情况

Figure 8. Distribution of magnetic dipole of small ship model.

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图 9 中型舰船船模磁偶极子分布情况

Figure 9. Distribution of magnetic dipole of medium ship model

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图 10 大型舰船船模磁偶极子分布情况

Figure 10. Distribution of magnetic dipoles of large ship models.

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图 11 干扰下不同方法求解的小型舰船磁矩绝对误差　(a) x方向磁矩绝对误差$\Delta {m_x}$; (b) y方向磁矩绝对误差$\Delta {m_y}$; (c) z方向磁矩绝对误差$\Delta {m_z}$

Figure 11. Absolute errors of magnetic moment of small ships solved by different methods under disturbance: (a) Absolute errors of magnetic moment in x-direction; (b) absolute errors of magnetic moment in y-direction; (c) absolute errors of magnetic moment in z-direction.

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图 12 干扰下不同方法求解的中型舰船磁矩绝对误差　(a) x方向磁矩绝对误差$\Delta {m_x}$; (b) y方向磁矩绝对误差$\Delta {m_y}$; (c) z方向磁矩绝对误差$\Delta {m_z}$

Figure 12. Absolute error of magnetic moment of medium ship solved by different methods under disturbance: (a) Absolute errors of magnetic moment in x-direction; (b) absolute errors of magnetic moment in y-direction; (c) absolute errors of magnetic moment in z-direction.

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图 13 干扰下不同方法求解的大型舰船磁矩绝对误差　(a) x方向磁矩绝对误差$ \Delta {m_x}$; (b) y方向磁矩绝对误差$ \Delta {m_y}$; (c) z方向磁矩绝对误差$ \Delta {m_z}$

Figure 13. Absolute errors of magnetic moment of large ships solved by different methods under disturbance: (a) Absolute errors of magnetic moment in x-direction; (b) absolute errors of magnetic moment in y-direction; (c) absolute errors of magnetic moment in z-direction.

DownLoad: Full-Size Img PowerPoint

图 14 测量场景示意图

Figure 14. The schematic diagram of measurement scene.

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表 1 试验参数

Table 1. Test parameters.

目标	尺度参数/m		测量深度/m		航迹1/m	航迹2/m	航迹3/m
目标	L	W	${Z_0}$	${Z_1}$	航迹1/m	航迹2/m	航迹3/m
小型船模	57.2	8.6	8.6	17	X = –80:2:80, Y = –4.2	X = – 80:2:80, Y = 0	X = – 80:2:80, Y = 4.2
中型船模	76.5	8.5	12.75	20.5	X = –100:2.5:100, Y =–15	X = –100:2.5:100, Y = 0	X = –100:2.5:100, Y = 15
大型船模	153	17.3	17.2	28.8	X = –128:3.2:128, Y = –8.64	X = –128:3.2:128, Y = 0	X = –128:3.2:128, Y = 8.64

DownLoad: CSV

表 2 Z₀深度平面上的三种舰船船模建模结果

Table 2. Modeling results of three kinds of ships on the Z₀ depth plane.

目标	小型舰船	中型舰船	大型舰船
磁偶极子数	10	8	14
系数矩阵条件数	85.13	76.5	128.95
建模相对误差	0.0295	0.0290	0.0256

DownLoad: CSV

表 3 不同深度的建模相对误差和换算相对误差

Table 3. Modeling relative errors and converted relative errors of different depths.

目标	建模深度/m	换算深度/m	相对误差
小型舰船	8.6	8.6	0.0295
	8.6	17	0.0402
	17	8.6	0.0479
	17	17	0.0256
中型舰船	12.75	12.75	0.0290
	12.75	20.5	0.0323
	20.5	12.75	0.0387
	20.5	20.5	0.0201
大型舰船	17.2	17.2	0.0256
	17.2	28.8	0.0301
	28.8	17.2	0.0547
	28.8	28.8	0.0152

DownLoad: CSV

表 4 不同方法的建模相对误差和换算相对误差

Table 4. Modeling relative error and conversion relative error of different methods.

目标			文献[1]	文献[25]	本文方法
小型舰船	磁偶极子数		10	10	10
	系数矩阵条件数		1.28 × 10³	34.65	85.13
	建模相对误差	17 m	0.0464	0.1071	0.0295
	建模相对误差	8.6 m	0.0450	0.0458	0.0256
	换算相对误差	8.6 m→17 m	0.0609	0.0913	0.0402
	换算相对误差	17 m→8.6 m	0.1208	0.1523	0.0497
中型舰船	磁偶极子数		8	8	8
	系数矩阵条件数		709.8	28.02	76.5
	建模相对误差	20.5 m	0.0568	0.0619	0.0290
	建模相对误差	12.75 m	0.0655	0.0872	0.0201
	换算相对误差	12.75 m→20.5 m	0.077	0.1726	0.0323
	换算相对误差	20.5 m→12.75 m	0.129	0.1317	0.0387
大型舰船	磁偶极子数		14	14	14
	系数矩阵条件数		2.36 × 10³	78.29	128.95
	建模相对误差	28.8 m	0.0991	0.1302	0.0256
	建模相对误差	17.2 m	0.0525	0.0602	0.0152
	换算相对误差	17.2 m→28.8 m	0.0984	0.1033	0.0301
	换算相对误差	28.8 m→17.2 m	0.1769	0.1782	0.0547

DownLoad: CSV

表 5 干扰下不同方法的建模相对误差和换算误差

Table 5. Modeling relative errors and conversion errors of different methods under interference.

目标		相对误差
目标		文献[1]	文献[25]	本文方法
小型舰船	未加干扰	0.0464	0.1071	0.0295
小型舰船	加干扰	0.0850	0.1167	0.0378
中型舰船	未加干扰	0.0568	0.0619	0.0290
中型舰船	加干扰	0.1179	0.0754	0.0313
大型舰船	未加干扰	0.0991	0.1302	0.0256
大型舰船	加干扰	0.1256	0.1419	0.0303

DownLoad: CSV

表 6 真实舰船测量数据建模结果

Table 6. Modeling results of real ship measurement data.

航向	建模相对误差	换算误差
东航向	0.0243	0.0543
西航向	0.0257	0.0621
南航向	0.0236	0.0325
北航向	0.0276	0.0421

DownLoad: CSV

[1]	林春生, 龚沈光 2007 舰船物理场 (第2版) 第51页 Lin C S, Gong S G 2007 Ship Physical Field (2nd Ed.) (Beijing: Ordnance Industry Press) p51 (in Chinese)
[2]	林春生 1996 水雷战与舰船防护 3 54 Lin C S 1996 Mine Warfare & Ship Self-Defence 3 54
[3]	Ginzburg B, Frumkis L, Kaplan B Z 2002 Sens. Actuators, A 102 67 Google Scholar
[4]	Wahlström N, Gustafsson F 2014 IEEE Trans. Signal Process. 62 545 Google Scholar
[5]	姚振宁, 刘大明, 刘胜道 2014 物理学报 22 227502 Google Scholar Yao Z N, Liu D M, Liu S D 2014 Acta Phys. Sin. 22 227502 Google Scholar
[6]	张宏欣, 周穗华, 张伽伟 2017 自动化学报 43 822 Google Scholar Zhang H X, Zhou S H, Zhang J W 2017 Acta Autom. Sin. 43 822 Google Scholar
[7]	戴忠华, 周穗华, 张宏欣 2019 电子学报 47 2457 Google Scholar Dai Z H, Zhou S H, Zhang H X 2019 Acta Electron. Sin. 47 2457 Google Scholar
[8]	Sui Y, Leslie K, Clark D 2017 IEEE Magn. Lett. 8 1 Google Scholar
[9]	张晓峻, 康曦元, 樊黎明 2019 地球物理学报 62 1921 Google Scholar Zhang X J, Kang X Y, Fan L M 2019 Acta Geophys. Sin. 62 1921 Google Scholar
[10]	费春娇, 张群英, 吴佩霖 2018 电子与信息学报 11 2779 Google Scholar Fei C J, Zhang Q Y, Wu P L 2018 J. Electron. Inf. Technol. 11 2779 Google Scholar
[11]	陈路昭, 冯永强, 郭瑞杰 2020 电子与信息学报 42 573 Google Scholar Chen L Z, Feng Y Q, Guo R J 2020 J. Electron. Inf. Technol. 42 573 Google Scholar
[12]	高俊杰, 刘大明, 姚琼 2006 兵工学报 27 869 Google Scholar Gao J J, Liu D M, Yao Q 2006 Acta Armamentarii 27 869 Google Scholar
[13]	郭成豹, 肖昌汉, 刘大明 2008 物理学报 07 4182 Google Scholar Guo C B, Xiao H C, Liu D M 2008 Acta Phys. Sin. 07 4182 Google Scholar
[14]	闫辉, 肖昌汉, 周国华 2008 兵工学报 07 839 Google Scholar Yan H, Xiao H C, Zhou G H 2008 Acta Armamentarii 07 839 Google Scholar
[15]	王德强, 余强 2014 舰船科学技术 36 1 Google Scholar Wang D Q, Yu Q 2014 Ship Sci. Technol. 36 1 Google Scholar
[16]	Holmes J J 2006 Synth. Lect. Comput. Electromagnet. 1 1 Google Scholar
[17]	Holmes J J 2007 Synth. Lect. Comput. Electromagnet. 2 1 Google Scholar
[18]	杨明明, 刘大明, 刘胜道, 连丽婷 2010 兵工学报 9 1216 Yang M M, Liu D M, Liu S D, Lian L T 2010 Acta Armamentarii 9 1216
[19]	王金根, 龚沈光, 刘胜道 2001 海军工程大学学报 3 49 Google Scholar Wang J G, Gong S G, Liu S D 2001 J. Naval Univ. Eng. 3 49 Google Scholar
[20]	刘胜道, 刘大明, 肖昌汉 2008 武汉理工大学学报 (交通科学与工程版) 6 1017 Liu S D, Liu D M, Xiao H C 2008 J. Wuhan Univ. Technol.(Transp. Sci. Eng.) 6 1017
[21]	徐杰, 刘大明, 周国华 2009 舰船科学技术 01 156 Google Scholar Xu J, Liu D M, Zhou G H 2009 Ship Sci. Technol. 01 156 Google Scholar
[22]	王桓, 周耀忠, 周国华 2007 海军工程大学学报 01 105 Google Scholar Wang H, Zhou Y Z, Zhou G H 2007 J. Naval Univ. Eng. 01 105 Google Scholar
[23]	张朝阳, 肖昌汉, 徐杰 2010 华中科技大学学报(自然科学版) 11 124 Google Scholar Zhang C Y, Xiao H C, Xu J 2010 J. Huazhong Univ. Sci. Technol. (Nat. Sci. Edition) 11 124 Google Scholar
[24]	吴志东, 周穗华, 郭虎生 2013 武汉理工大学学报 09 67 Google Scholar Wu Z D, Zhou S H, Guo H S 2013 J. Wuhan Univ. Technol. 09 67 Google Scholar
[25]	戴忠华, 周穗华, 单珊 2018 电子学报 46 1524 Google Scholar Dai Z H, Zhou S H, Shan S 2018 Acta Electron. Sin. 46 1524 Google Scholar
[26]	郭成豹, 殷琦琦 2019 物理学报 68 114101 Google Scholar Guo C B, Yin Q Q 2019 Acta Phys. Sin. 68 114101 Google Scholar
[27]	Alqadah H F, Valdivia N P, Williams E G 2016 Prog. Electromagnet. Res. B 65 109 Google Scholar
[28]	Vuillermet Y, Chadebec O, Coulomb J L, Rouve L L, Cauffet G, Bongiraud J P, Demilier L 2008 IEEE Trans. Magn. 44 1054 Google Scholar
[29]	Coello C A C 2006 IEEE Comput. Intell. Mag. 1 28 Google Scholar
[30]	Dorigo M, Gambardella L M 1997 IEEE Trans. Evol. Comput. 1 53 Google Scholar
[31]	Bandyopadhyay S, Saha S, Maulik U, Deb K 2008 IEEE Trans. Evol. Comput. 12 269 Google Scholar
[32]	Coello C A C, Pulido G T, Lechuga M S 2004 IEEE Trans. Evol. Comput. 8 256 Google Scholar
[33]	公茂果, 焦李成, 杨咚咚, 马文萍 2009 软件学报 20 271 Google Scholar Gong M G, Jiao L C, Yang D D, Ma W P 2009 J. Software 20 271 Google Scholar
[34]	Kennedy J 1995 Process of IEEE International Conference on Neural Networks Perth Australia, November 27, 1995 4 1942

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Vol. 70, Issue 16 - 2021-08-20

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