﻿ 改进的内外映射法推算潜艇外部感应磁场
 舰船科学技术  2020, Vol. 42 Issue (6): 172-175    DOI: 10.3404/j.issn.1672-7649.2020.06.035 PDF

Extrapolation of submarine′s external induced magnetic field by improved internal and external reflection method
HE Bao-wei, LIU Sheng-dao, ZHAO Wen-chun, ZHOU Guo-hua
College of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: The key of submarine’s closed-loop degaussing system is external magnetic field extrapolation, whose precision decides the compensation effect of submarine’s induced magnetic field and parts of permanent magnetic field. For solving the present problem of low precision in extrapolation, an improved internal and external reflection method was put forward. Without considering the installation posture of internal magnetic sensors in submarine model, the related matrix between internal and external magnetic field was solved by measuring only four different groups of magnetic field. Through the related matrix, the external induced magnetic fields were extrapolated under different geomagnetic effect. In a verification experiment, the extrapolated results were compared to the measured results.The biggest relative root mean square error is 4.20%, which shows the feasibility of this improved algorithm.
Key words: closed-loop degaussing     magnetic field extrapolation     improved internal and external reflection method
0 引　言

1 外部磁场推算原理

 $\Delta {{{H}}_{{{wi}}}} = SF*\Delta {{{H}}_{ni}}\text{，}$ (1)

 ${{{B}}_n} = { K_n}* A*{{{B}}_e}\text{，}$ (2)
 ${{{B}}_w} = { K_w}*{{{B}}_e}\text{。}$ (3)

 ${{{B}}_w} = { K_w}{ A^{ - 1}}{ K_n}^{ - 1}{{{B}}_n}\text{，}$ (4)

 $K = { K_w}{A^{ - 1}}{ K_n}^{ - 1}\text{，}$ (5)

$K$ 为潜艇内外磁场之间的映射关系矩阵。与文献[10]中相比，该映射矩阵同时包含了内外磁场之间的数值关系和空间关系，因此该方法不需要对内部磁传感器进行坐标系调整。另外，一旦内部磁传感器的位置固定安装不同，该矩阵即为常数，不随潜艇航行时的磁状态改变而改变。

 ${{{B}}_w} = K*{{{B}}_n}\text{。}$ (6)

 $\left[ {\begin{array}{*{20}{c}} {{B_{wx}}} \\ {{B_{wy}}} \\ {{B_{wz}}} \end{array}} \right]{\kern 1pt} = \left[ {\begin{array}{*{20}{c}} {{k_{11}}}&{{k_{12}}}&{{k_{13}}} \\ {{k_{21}}}&{{k_{22}}}&{{k_{23}}} \\ {{k_{31}}}&{{k_{32}}}&{{k_{33}}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{B_{nx}}} \\ {{B_{ny}}} \\ {{B_{nz}}} \end{array}} \right]\text{，}$ (7)
 $\left\{ {\begin{array}{*{20}{c}} {{B_{wx}} = {k_{11}}{B_{nx}} + {k_{12}}{B_{ny}} + {k_{13}}{B_{nz}}}\text{，} \\ {{B_{wy}} = {k_{21}}{B_{nx}} + {k_{22}}{B_{ny}} + {k_{23}}{B_{nz}}}\text{，} \\ {{B_{wz}} = {k_{31}}{B_{nx}} + {k_{32}}{B_{ny}} + {k_{33}}{B_{nz}}}\text{。} \end{array}} \right.$ (8)

2 潜艇模型实验 2.1 实验设计

 图 1 潜艇模型内部磁传感器示意图 Fig. 1 The sketch map of internal magnetic sensors in submarine model

 图 2 地磁模拟空间 Fig. 2 Geomagnetic field simulation space

 图 3 潜艇模型外部磁探头示意图 Fig. 3 The sketch map of external magnetic sensors of submarine model

2.2 实验结果与误差分析

 $RMSE = \frac{{{{\left\| {{{{B}}_w}' - {{{B}}_w}} \right\|}_2}}}{{\sqrt n \cdot {B_{w\max }}}}\text{。}$ (10)

1）实验室磁环境相对复杂，长时间的实验前后地磁场会发生变化，并且实验设备距离磁探头的距离太近，会影响测量结果；

2）地球磁场是一个均匀磁场，但是实验室条件下地磁模拟线圈产生的磁场均匀度不够好，很难完全模拟地磁场的变化。

3 结　论

1）利用内外映射法的基本原理来建立潜艇内外磁场映射关系的数学模型是有效的。改进方法后推算值的最大均方根误差仅为4.20%，能够满足将来的工程需要；

2）不需要考虑潜艇内部磁传感器时的安装姿态也可由算法直接求解出映射矩阵 $K$ ，为将来给实际潜艇安装消磁系统降低工作量；

3）只需测量背景磁场和单独改变三分量地磁场后的潜艇模型内外磁场值，即可快速求解出较为准确的映射矩阵，减少了测量次数。

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