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A Fast Forward Modeling Method for High Precision Induced Magnetic Field of Ships
He Baowei, Sun Zhaolong, Liu Yuelin, Zhou Guohua, Tang Liezheng
School of Electrical Engineering Naval University of Engineering Wuhan 430033 China

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Abstract  

Mastering the distribution of a ship’s induced magnetic field is an important issue for implementing magnetic stealth technology, and the integral equation method is one of the main methods to calculate the ship’s induced magnetic field. Integral equation method only needs to discretize the ferromagnetic region and does not need to consider the boundary conditions, so it has been widely concerned and applied. The traditional vector integral equation for modeling induced magnetic fields has the problems of low efficiency and a large computational burden. Considering that there are many discrete elements of large ferromagnetic objects such as ships, the coupling coefficient between elements forms a huge asymmetric dense matrix, so the computing time and memory requirement will increase sharply with the increase of the number of elements. To address these issues, a scalar magnetic potential integral equation method based on surface elements is proposed, and multi-level adaptive cross approximation (MLACA) algorithm is introduced. Since the integral equation method needs to obtain the magnetic susceptibility of ferromagnetic materials, the equivalent magnetic susceptibility inversion model is established based on the forward algorithm.
Firstly, the scalar magnetic potential integral formula based on triangular surface elements is derived. According to the principle of linear interpolation, the scalar magnetic potential of the center point of discrete elements is expressed by interpolation function and node scalar magnetic potential, and the elements’ coupling coefficient matrix is obtained by establishing a local coordinate system. Therefore, the scalar integral method of surface elements for solving ship’s induced magnetic field is obtained. Secondly, to realize the modeling problem of the induced magnetic field of large ships, the MLACA algorithm is introduced, which not only guarantees the accuracy of magnetic field calculation but also greatly reduces the memory requirement and computing time of the computer. Finally, aiming at the problem that the magnetic parameters of ferromagnetic materials of ships are not easy to obtain, a magnetic susceptibility inversion model is established based on the measured magnetic field values and the forward coupling model, taking the magnetic field fitting degree, prior distribution of magnetic susceptibility and smooth constraint as the objective function. The spatial distribution of equivalent magnetic susceptibility has been optimized by simulated annealing (SA) algorithms.
A numerical simulation of the iron spherical shell shows that the proposed scalar magnetic potential coupling forward modeling method can obtain the ship’s induced magnetic field efficiently with high precision. For the same discrete elements, compared with the vector method, the scalar method can save about 97% of the memory consumption and 65% of the computing time, which verifies the effectiveness of the scalar magnetic potential integral equation method based on the MLACA algorithm. According to the inversion model, the equivalent magnetic susceptibility of the iron spherical shell is optimized by the SA algorithm, which is utilized to predict the spherical shell of other positions and the average relative error is only 2.2%. After using of smooth constraint condition, the equivalent magnetic susceptibility obtained is smoother.
In order to verify the practicability of the proposed forward modeling method and magnetic susceptibility inversion method in engineering, an experimental scheme was designed for a reduced-scale ship model with unknown magnetic parameters. Firstly, the equivalent magnetic susceptibility distribution of the ship model is obtained by measuring the magnetic field of the ship model at the z1 plane, and it is used to predict the induced magnetic field at the z2 plane. The magnetic field fitting error and prediction error of the ship are about 5.0%, indicating that the proposed forward modeling model of induced magnetic field and the inverse optimization model of equivalent magnetic susceptibility can be used for induced magnetic field modeling of large ships with high precision and can provide support for the implementation of magnetic stealth technology on ships.
Key words： Ship magnetic field      reduced scalar magnetic potential      multi-level adaptive approximate cross      simulated annealing method      equivalent magnetic susceptibility     
Received: 22 November 2022     
PACS: TM153  
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He Baowei
Sun Zhaolong
Liu Yuelin
Zhou Guohua
Tang Liezheng
Cite this article:   
He Baowei,Sun Zhaolong,Liu Yuelin等. A Fast Forward Modeling Method for High Precision Induced Magnetic Field of Ships[J]. Transactions of China Electrotechnical Society, 0, (): 129-129.
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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.222204     OR     https://dgjsxb.ces-transaction.com/EN/Y0/V/I/129
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