Ship Magnetic Field Modeling and Extrapolation Based on a Convolutional Neural Network

Abstract

Accurate modeling of ship magnetic fields is important for predicting their spatial distribution to improve the magnetic stealth effect of ships. This study proposes an extrapolation model for ship magnetic fields based on genetic algorithms and convolutional neural networks (CNNs). The magnetic probe position matrix of the traditional equivalent source is utilized as input, and the three-directional components of the magnetic field measured by the probes are employed as output. The extrapolation model for ship magnetic fields is obtained through iterative training and fitting with CNNs. Variables such as the number of magnetic dipoles, the distance between magnetic dipoles, the size and quantity of convolutional kernels, batch size, learning rate, and L2 regularization coefficient are optimized to boost the accuracy of the extrapolation model for magnetic fields. The fitting accuracy of the extrapolation model for ship magnetic fields is used as the optimization objective. Based on a finite element simulation model of ship magnetic fields, the accuracy and robustness of the CNN algorithm under different magnetic field conditions are validated using the known standard depth plane, the unknown depth at 1.125 times the standard depth plane, and the unknown depth at 1.25 times the standard depth plane. Results show that, after optimization, the fitting error for the magnetic field extrapolation model based on CNN is 1.50% for the standard depth plane, 1.63% for the unknown depth at 1.125 times the standard depth plane, and 2.36% for the unknown depth at 1.25 times the standard depth plane. The error remains below 5% under varying magnetic field conditions. When a random measurement error of 0%–5% is introduced for the magnetic probes, the prediction error at 1.25 times the standard depth plane is 2.30%; with a random error of 0%–10%, the prediction error is 4.95%. This approach significantly improves the accuracy and robustness of magnetic field extrapolation, which makes it an effective and feasible method for ship magnetic field modeling.

Keywords

Shipboard magnetic field / Convolutional neural network / Genetic algorithm / Equivalent source method / Magnetic field extrapolation

References

[1] BirsanM. Simulation of a ship’s deperming process using the Jiles-Atherton model. IEEE Transactions on Magnetics, 2021, 5767300407

[2] ChenYF, YangQX, LiYJ, ZhangH, ZhangCG. Data-driven deep convolutional neural networks for electromagnetic field estimation of transformers. IEEE Transactions on Applied Superconductivity, 2024, 3485500805

[3] DaiZH, ZhouSH, ZhangXB. Multi-objective optimization of ship magnetic field modeling method. Acta Physica Sinica, 2021, 7016164101

[4] DengB, WangJ, XuX, YiG. Individual prediction of electric field induced by deep-brain magnetic stimulation with CNN-Transformer. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2024, 32: 2143-2152

[5] GaoJJ, LiuDM, YaoQH, ZhouGH, YanHC. Verifying the mathematics model of submarine magnetic field extrapolation with boundary element method through experiment. Acta Armamentarii, 2006, 27(5): 869-872

[6] GaoJJ, WangPZ, ZhuXL. Calculation and verification of ship magnetic field based on boundary integral-iterative method. 2021 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), 202115

[7] HanZX, HuJC, LiZN, MaPC, PengQJ, WangQ, ZhengZZ, ZhuHW. Magnetic field simulation of reactor based on deep neural networks. IEEE Transactions on Power Delivery, 2023, 38(3): 2224-2227

[8] HuaC, HuangC, ZuoY, WangW, YangJ. Research on low frequency magnetic field test and equivalent modeling method of ship equipment. 6th Global Electromagnetic Compatibility Conference (GEMCCON), 202013

[9] HuiY, XiC, YeKQ. The application of recursive algorithm on ship’s magnetic field extrapolation. Acta Armamentarii, 2010, 31: 1200-1203

[10] JakubiukK, ZimnyP, WolszynM. Multidipoles model of ship’s magnetic field. 15th International Symposium on Applied Eleetromagneties and Meehanies, 201245

[11] JiaW, LinC. Improved Euler method for preventing failure of positioning magnetic target magnetic Gradiometer. Journal of Navigation University of Engineering, 2018, 30(3): 37-42

[12] JinHH, WangH, ZhuangZH. A new simple method to design degaussing coils using magnetic dipoles. Journal of Marine Science and Engineering, 2022, 10101495

[13] KhanA, GhorbanianV, LowtherD. Deep learning for magnetic field estimation. IEEE Transactions on Magnetics, 2019, 5567202304

[14] LinPF, ZhangN, ChangM, XuL. Research on the model and the location method of ship shaft-rate magnetic field based on rotating magnetic dipole. IEEE Access, 2020, 8: 162999-163005

[15] LiuQ, SunZ, JiangR, WuX, LeiY. A signal reconstruction and conversion method for magnetic field under a ship. Journal of Electrical Engineering, 2022, 37(15): 3723-3732

[16] MenanaH. 3D FEM-BEM coupling for the magnetic field computation in thin shells: Application to the evaluation of ship magnetic signature. IEEE Transactions on Magnetics, 2021, 5767402206

[17] PengQJ, SimaWX, SunJQ, WangJS, YangM, ZouDX. Calculation method of transformer space dynamic magnetic field acceleration taking into account core nonlinearity. Journal of Electrotechnology, 2025, 40(5): 1559-1574

[18] SasakiH, IwataK, SatoT, SatoY. Prediction of motor characteristic maps via deep operator networks for topology optimization. IEEE Transactions on Magnetics, 2024, 60128206205

[19] SheinkerA, GinzburgB, SalomonskiN, YanivA, PerskyE. Estimation of ship’s magnetic signature using multi-dipole modeling method. IEEE Transactions on Magnetics, 2021, 5756500408

[20] SynnesSA. Representing elongated magnetic sources by prolate spheroidal harmonics developed on an optimized coordinate system. IEEE Transactions on Magnetics, 2008, 44(10): 2277-2282

[21] TarnawskiJ, CichockiA, RutkowskiTA, BuszmanK, WoloszynM. Improving the quality of magnetic signature reproduction by increasing flexibility of multi-dipole model structure and enriching measurement information. IEEE Access, 2020, 8: 190448-190462

[22] TarnawskiJ, RutkowskiTA, WoloszynM, CichockiA, BuszmanK. Magnetic signature description of ellipsoid-shape vessel using 3D multi-dipole model fitted on cardinal directions. IEEE Access, 2022, 10: 16906-16930

[23] WangY, WangD, ChiC, YuZT, LiJW, YuL. Ship shaft-rate electric field signal denoising method based on VMD-MSS. Journal of Marine Science and Engineering, 2024, 124544

[24] WoloszynM, JankowskiP. Simulation of ship’s deperming process using Opera 3D. 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering (ISEF) Book of Abstracts, 201712

[25] YanJResearch on magnetic modeling simulation technology of marine target, 2020, Harbin. Harbin Institute of Technology. 4146

[26] ZateevAA, IvanovYM, SemenovVG. Enhancing the precision of measurements of a ship’s magnetic moment in the far field. Measurement Techniques, 2021, 64(8): 681-688

[27] ZhangZ, YuW, YiJ. Equivalent source forecast method for bad points’ field on ship’s magnetic field measuring. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2018, 46(4): 63-67

[28] ZhouG, XiaoC, LiuS, GaoJ. 3D Magnetostatic Field Computation With Hexahedral Surface Integral Equation Method. Diangong Jishu Xuebao, 2009, 24(3): 1-7

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Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature

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