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多目标优化的舰船磁场建模方法

戴忠华 周穗华 张晓兵

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多目标优化的舰船磁场建模方法

戴忠华, 周穗华, 张晓兵

Multi-objective optimization of ship magnetic field modeling method

Dai Zhong-Hua, Zhou Sui-Hua, Zhang Xiao-Bing
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  • 针对舰船磁场混合模型建模中存在的建模精度不高和稳定性差的问题, 提出一种高精度稳定模型建立方法, 结合混合模型中磁偶极子参数与舰船结构的相关性, 以建模精度和模型稳定性为目标构造了多目标函数, 通过对多目标函数优化获得合理的磁偶极子参数, 间接地将建模求解问题转化为多目标函数优化问题.利用多目标粒子群优化算法进行求解, 得到了建模问题求解结果的可选集, 以建模精度为基准设计了从可选集中选取最佳结果的选择规则. 三种类型的舰船船模实测数据建模结果表明: 本文方法所建模型相对误差小于3%, 换算误差小于6%, 能够有效对舰船磁场进行建模; 当存在测量数据误差时, 本文方法建模求解结果稳定, 验证了文本方法建模具有较好的稳定性. 海上的某型舰船实测数据建模结果表明, 本文方法建模具有较高的建模精度和换算精度, 能够有效地在相关的工程中应用.
    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.
      通信作者: 戴忠华, 602024288@qq.com
    • 基金项目: 国家自然科学基金(批准号: 51509252, 42074074)资助的课题
      Corresponding author: Dai Zhong-Hua, 602024288@qq.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51509252, 42074074)
    [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 67Google Scholar

    [4]

    Wahlström N, Gustafsson F 2014 IEEE Trans. Signal Process. 62 545Google Scholar

    [5]

    姚振宁, 刘大明, 刘胜道 2014 物理学报 22 227502Google Scholar

    Yao Z N, Liu D M, Liu S D 2014 Acta Phys. Sin. 22 227502Google Scholar

    [6]

    张宏欣, 周穗华, 张伽伟 2017 自动化学报 43 822Google Scholar

    Zhang H X, Zhou S H, Zhang J W 2017 Acta Autom. Sin. 43 822Google Scholar

    [7]

    戴忠华, 周穗华, 张宏欣 2019 电子学报 47 2457Google Scholar

    Dai Z H, Zhou S H, Zhang H X 2019 Acta Electron. Sin. 47 2457Google Scholar

    [8]

    Sui Y, Leslie K, Clark D 2017 IEEE Magn. Lett. 8 1Google Scholar

    [9]

    张晓峻, 康曦元, 樊黎明 2019 地球物理学报 62 1921Google Scholar

    Zhang X J, Kang X Y, Fan L M 2019 Acta Geophys. Sin. 62 1921Google Scholar

    [10]

    费春娇, 张群英, 吴佩霖 2018 电子与信息学报 11 2779Google Scholar

    Fei C J, Zhang Q Y, Wu P L 2018 J. Electron. Inf. Technol. 11 2779Google Scholar

    [11]

    陈路昭, 冯永强, 郭瑞杰 2020 电子与信息学报 42 573Google Scholar

    Chen L Z, Feng Y Q, Guo R J 2020 J. Electron. Inf. Technol. 42 573Google Scholar

    [12]

    高俊杰, 刘大明, 姚琼 2006 兵工学报 27 869Google Scholar

    Gao J J, Liu D M, Yao Q 2006 Acta Armamentarii 27 869Google Scholar

    [13]

    郭成豹, 肖昌汉, 刘大明 2008 物理学报 07 4182Google Scholar

    Guo C B, Xiao H C, Liu D M 2008 Acta Phys. Sin. 07 4182Google Scholar

    [14]

    闫辉, 肖昌汉, 周国华 2008 兵工学报 07 839Google Scholar

    Yan H, Xiao H C, Zhou G H 2008 Acta Armamentarii 07 839Google Scholar

    [15]

    王德强, 余强 2014 舰船科学技术 36 1Google Scholar

    Wang D Q, Yu Q 2014 Ship Sci. Technol. 36 1Google Scholar

    [16]

    Holmes J J 2006 Synth. Lect. Comput. Electromagnet. 1 1Google Scholar

    [17]

    Holmes J J 2007 Synth. Lect. Comput. Electromagnet. 2 1Google 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 49Google Scholar

    Wang J G, Gong S G, Liu S D 2001 J. Naval Univ. Eng. 3 49Google 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 156Google Scholar

    Xu J, Liu D M, Zhou G H 2009 Ship Sci. Technol. 01 156Google Scholar

    [22]

    王桓, 周耀忠, 周国华 2007 海军工程大学学报 01 105Google Scholar

    Wang H, Zhou Y Z, Zhou G H 2007 J. Naval Univ. Eng. 01 105Google 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 124Google Scholar

    Zhang C Y, Xiao H C, Xu J 2010 J. Huazhong Univ. Sci. Technol. (Nat. Sci. Edition) 11 124Google Scholar

    [24]

    吴志东, 周穗华, 郭虎生 2013 武汉理工大学学报 09 67Google Scholar

    Wu Z D, Zhou S H, Guo H S 2013 J. Wuhan Univ. Technol. 09 67Google Scholar

    [25]

    戴忠华, 周穗华, 单珊 2018 电子学报 46 1524Google Scholar

    Dai Z H, Zhou S H, Shan S 2018 Acta Electron. Sin. 46 1524Google Scholar

    [26]

    郭成豹, 殷琦琦 2019 物理学报 68 114101Google Scholar

    Guo C B, Yin Q Q 2019 Acta Phys. Sin. 68 114101Google Scholar

    [27]

    Alqadah H F, Valdivia N P, Williams E G 2016 Prog. Electromagnet. Res. B 65 109Google Scholar

    [28]

    Vuillermet Y, Chadebec O, Coulomb J L, Rouve L L, Cauffet G, Bongiraud J P, Demilier L 2008 IEEE Trans. Magn. 44 1054Google Scholar

    [29]

    Coello C A C 2006 IEEE Comput. Intell. Mag. 1 28Google Scholar

    [30]

    Dorigo M, Gambardella L M 1997 IEEE Trans. Evol. Comput. 1 53Google Scholar

    [31]

    Bandyopadhyay S, Saha S, Maulik U, Deb K 2008 IEEE Trans. Evol. Comput. 12 269Google Scholar

    [32]

    Coello C A C, Pulido G T, Lechuga M S 2004 IEEE Trans. Evol. Comput. 8 256Google Scholar

    [33]

    公茂果, 焦李成, 杨咚咚, 马文萍 2009 软件学报 20 271Google Scholar

    Gong M G, Jiao L C, Yang D D, Ma W P 2009 J. Software 20 271Google Scholar

    [34]

    Kennedy J 1995 Process of IEEE International Conference on Neural Networks Perth Australia, November 27, 1995 4 1942

  • 图 1  舰船磁场混合模型

    Fig. 1.  Ship magnetic field mixing model.

    图 2  磁场测量

    Fig. 2.  Magnetic field measurement.

    图 3  混合模型中磁偶极子分布范围

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

    图 4  测量模式

    Fig. 4.  Measurement mode.

    图 5  小型舰船建模结果可选集分布

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

    图 7  大型舰船建模结果可选集分布

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

    图 6  中型舰船建模结果可选集分布

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

    图 8  小型舰船船模磁偶极子分布情况

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

    图 9  中型舰船船模磁偶极子分布情况

    Fig. 9.  Distribution of magnetic dipole of medium ship model

    图 10  大型舰船船模磁偶极子分布情况

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

    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$\Delta {m_z}$

    Fig. 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.

    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$\Delta {m_z}$

    Fig. 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.

    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}$

    Fig. 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.

    图 14  测量场景示意图

    Fig. 14.  The schematic diagram of measurement scene.

    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
    LW${Z_0}$${Z_1}$
    小型船模57.28.6 8.617X = –80:2:80,
    Y = –4.2
    X = – 80:2:80,
    Y = 0
    X = – 80:2:80,
    Y = 4.2
    中型船模76.58.5 12.7520.5X = –100:2.5:100,
    Y =–15
    X = –100:2.5:100,
    Y = 0
    X = –100:2.5:100,
    Y = 15
    大型船模15317.3 17.228.8X = –128:3.2:128,
    Y = –8.64
    X = –128:3.2:128,
    Y = 0
    X = –128:3.2:128,
    Y = 8.64
    下载: 导出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10814
    系数矩阵条件数85.1376.5128.95
    建模相对误差0.02950.02900.0256
    下载: 导出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8.68.60.0295
    170.0402
    178.60.0479
    170.0256
    中型舰船12.7512.750.0290
    20.50.0323
    20.512.750.0387
    20.50.0201
    大型舰船17.217.20.0256
    28.80.0301
    28.817.20.0547
    28.80.0152
    下载: 导出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101010
    系数矩阵条件数1.28 × 10334.6585.13
    建模相对误差17 m0.04640.10710.0295
    8.6 m0.04500.04580.0256
    换算相对误差8.6 m→17 m0.06090.09130.0402
    17 m→8.6 m0.12080.15230.0497
    中型舰船磁偶极子数888
    系数矩阵条件数709.828.0276.5
    建模相对误差20.5 m0.05680.06190.0290
    12.75 m0.06550.08720.0201
    换算相对误差12.75 m→20.5 m0.0770.17260.0323
    20.5 m→12.75 m0.1290.13170.0387
    大型舰船磁偶极子数141414
    系数矩阵条件数2.36 × 10378.29128.95
    建模相对误差28.8 m0.09910.13020.0256
    17.2 m0.05250.06020.0152
    换算相对误差17.2 m→28.8 m0.09840.10330.0301
    28.8 m→17.2 m0.17690.17820.0547
    下载: 导出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
    文献[1]文献[25]本文方法
    小型舰船未加干扰0.04640.10710.0295
    加干扰0.08500.11670.0378
    中型舰船未加干扰0.05680.06190.0290
    加干扰0.11790.07540.0313
    大型舰船未加干扰0.09910.13020.0256
    加干扰0.12560.14190.0303
    下载: 导出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0.02430.0543
    西航向0.02570.0621
    南航向0.02360.0325
    北航向0.02760.0421
    下载: 导出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 67Google Scholar

    [4]

    Wahlström N, Gustafsson F 2014 IEEE Trans. Signal Process. 62 545Google Scholar

    [5]

    姚振宁, 刘大明, 刘胜道 2014 物理学报 22 227502Google Scholar

    Yao Z N, Liu D M, Liu S D 2014 Acta Phys. Sin. 22 227502Google Scholar

    [6]

    张宏欣, 周穗华, 张伽伟 2017 自动化学报 43 822Google Scholar

    Zhang H X, Zhou S H, Zhang J W 2017 Acta Autom. Sin. 43 822Google Scholar

    [7]

    戴忠华, 周穗华, 张宏欣 2019 电子学报 47 2457Google Scholar

    Dai Z H, Zhou S H, Zhang H X 2019 Acta Electron. Sin. 47 2457Google Scholar

    [8]

    Sui Y, Leslie K, Clark D 2017 IEEE Magn. Lett. 8 1Google Scholar

    [9]

    张晓峻, 康曦元, 樊黎明 2019 地球物理学报 62 1921Google Scholar

    Zhang X J, Kang X Y, Fan L M 2019 Acta Geophys. Sin. 62 1921Google Scholar

    [10]

    费春娇, 张群英, 吴佩霖 2018 电子与信息学报 11 2779Google Scholar

    Fei C J, Zhang Q Y, Wu P L 2018 J. Electron. Inf. Technol. 11 2779Google Scholar

    [11]

    陈路昭, 冯永强, 郭瑞杰 2020 电子与信息学报 42 573Google Scholar

    Chen L Z, Feng Y Q, Guo R J 2020 J. Electron. Inf. Technol. 42 573Google Scholar

    [12]

    高俊杰, 刘大明, 姚琼 2006 兵工学报 27 869Google Scholar

    Gao J J, Liu D M, Yao Q 2006 Acta Armamentarii 27 869Google Scholar

    [13]

    郭成豹, 肖昌汉, 刘大明 2008 物理学报 07 4182Google Scholar

    Guo C B, Xiao H C, Liu D M 2008 Acta Phys. Sin. 07 4182Google Scholar

    [14]

    闫辉, 肖昌汉, 周国华 2008 兵工学报 07 839Google Scholar

    Yan H, Xiao H C, Zhou G H 2008 Acta Armamentarii 07 839Google Scholar

    [15]

    王德强, 余强 2014 舰船科学技术 36 1Google Scholar

    Wang D Q, Yu Q 2014 Ship Sci. Technol. 36 1Google Scholar

    [16]

    Holmes J J 2006 Synth. Lect. Comput. Electromagnet. 1 1Google Scholar

    [17]

    Holmes J J 2007 Synth. Lect. Comput. Electromagnet. 2 1Google 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 49Google Scholar

    Wang J G, Gong S G, Liu S D 2001 J. Naval Univ. Eng. 3 49Google 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 156Google Scholar

    Xu J, Liu D M, Zhou G H 2009 Ship Sci. Technol. 01 156Google Scholar

    [22]

    王桓, 周耀忠, 周国华 2007 海军工程大学学报 01 105Google Scholar

    Wang H, Zhou Y Z, Zhou G H 2007 J. Naval Univ. Eng. 01 105Google 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 124Google Scholar

    Zhang C Y, Xiao H C, Xu J 2010 J. Huazhong Univ. Sci. Technol. (Nat. Sci. Edition) 11 124Google Scholar

    [24]

    吴志东, 周穗华, 郭虎生 2013 武汉理工大学学报 09 67Google Scholar

    Wu Z D, Zhou S H, Guo H S 2013 J. Wuhan Univ. Technol. 09 67Google Scholar

    [25]

    戴忠华, 周穗华, 单珊 2018 电子学报 46 1524Google Scholar

    Dai Z H, Zhou S H, Shan S 2018 Acta Electron. Sin. 46 1524Google Scholar

    [26]

    郭成豹, 殷琦琦 2019 物理学报 68 114101Google Scholar

    Guo C B, Yin Q Q 2019 Acta Phys. Sin. 68 114101Google Scholar

    [27]

    Alqadah H F, Valdivia N P, Williams E G 2016 Prog. Electromagnet. Res. B 65 109Google Scholar

    [28]

    Vuillermet Y, Chadebec O, Coulomb J L, Rouve L L, Cauffet G, Bongiraud J P, Demilier L 2008 IEEE Trans. Magn. 44 1054Google Scholar

    [29]

    Coello C A C 2006 IEEE Comput. Intell. Mag. 1 28Google Scholar

    [30]

    Dorigo M, Gambardella L M 1997 IEEE Trans. Evol. Comput. 1 53Google Scholar

    [31]

    Bandyopadhyay S, Saha S, Maulik U, Deb K 2008 IEEE Trans. Evol. Comput. 12 269Google Scholar

    [32]

    Coello C A C, Pulido G T, Lechuga M S 2004 IEEE Trans. Evol. Comput. 8 256Google Scholar

    [33]

    公茂果, 焦李成, 杨咚咚, 马文萍 2009 软件学报 20 271Google Scholar

    Gong M G, Jiao L C, Yang D D, Ma W P 2009 J. Software 20 271Google Scholar

    [34]

    Kennedy J 1995 Process of IEEE International Conference on Neural Networks Perth Australia, November 27, 1995 4 1942

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出版历程
  • 收稿日期:  2021-02-20
  • 修回日期:  2021-03-12
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-08-20

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