一种舰船高精度感应磁场快速正演建模方法

doi:10.19595/j.cnki.1000-6753.tces.222204

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摘要

为了解决矢量积分方程法计算舰船感应磁场时效率较低和计算量较大的问题,提出一种基于简化标量磁位的积分方程正演模型,并引入了多层自适应交叉近似 (multi-level adaptive cross approximation, MLACA)算法,不仅能够保证磁场计算精度,还能大幅减少计算机的内存需求和计算时间。数值仿真表明使用基于MLACA的标量积分方程法能够快速获取高精度的铁磁物体感应磁场。针对舰船铁磁材料的磁性参数不易获取的问题,基于磁场实测值和正演耦合模型,以磁场拟合度、磁化率先验分布和光滑约束条件为目标函数建立了磁化率反演模型,并采用模拟退火(simulated annealing, SA)算法优化得到了等效磁化率的空间分布。球壳数值仿真和船模试验结果表明,磁化率反演优化模型有效可行,其中球壳磁场的预测误差为2.2%,船模磁场的预测误差约为4.8%。

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	何保委
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关键词 ：舰船磁场, 简化标量磁位, 多层自适应交叉近似, 模拟退火法, 等效磁化率

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

收稿日期: 2022-11-22

PACS:

TM153

基金资助:

国家自然科学基金资助项目（51377165, 52207020）

通讯作者: 刘月林女,1989年生,硕士,讲师,研究方向为电磁环境与防护技术。E-mail：mooncake1024@163.com

作者简介: 何保委男,1995年生,博士生,研究方向为电磁环境与防护技术。E-mail：hebaowei188@163.com

引用本文:

何保委, 孙兆龙, 刘月林, 周国华, 唐烈峥. 一种舰船高精度感应磁场快速正演建模方法[J]. 电工技术学报, 0, (): 129-129. He Baowei, Sun Zhaolong, Liu Yuelin, Zhou Guohua, Tang Liezheng. A Fast Forward Modeling Method for High Precision Induced Magnetic Field of Ships. Transactions of China Electrotechnical Society, 0, (): 129-129.

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