Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 51277176).
Received Date:15 February 2019
Accepted Date:12 March 2019
Available Online:01 June 2019
Published Online:05 June 2019
Abstract:Aiming at the problems of low accuracy and low adaptability of the existing ship magnetic field inversion modeling methods with equivalent sources, a new method of inversion modeling of magnetic monopole array of ship magnetic fields is proposed. Three-dimensional ship magnetic monopole array is arranged according to the ship ferromagnetic structure, and the inversion prediction model of ship magnetic fields is established by regularization technology. Three typical forms of magnetic monopole arrays are established: rectangular magnetic monopole array on the horizontal surface of the draft line, cuboid magnetic monopole array enclosing the ship hull, three-dimensional ship magnetic monopole array distributed according to the ship’s ferromagnetic structure. The theoretical analysis shows that the three-dimensional ship magnetic monopole array reduces the blindness of the equivalent magnetic source setting, and the obtained equivalent magnetic source is highly consistent with the real magnetic source, which can reproduce the complete magnetic field information of the ship to a greater extent. The magnetic field of a typical virtual ship is applied to the validation test. The results show that the proposed three-dimensional ship magnetic monopole array has higher precision and adaptability than the rectangular or cuboid magnetic monopole array. In particular, the proposed three-dimensional ship magnetic monopole array can realize the mutual conversion between the near and far magnetic fields, and between the magnetic fields above and below the ship. The proposed three-dimensional ship magnetic monopole array model has the unique advantages of small complexity, simple modeling and flexible layout, and it provides an alternative method for the high-precision data processing and explanation to the inversion modeling of ship magnetic fields, ship magnetic field positioning, et al. Keywords:magnetostatic field/ equivalent source method/ magnetic monopole/ ship’s magnetic signature
一艘舰船从一个水下磁传感器线阵上方通过(如图2所示), 每隔一定时间间隔进行一次磁场采样, 可认为是在舰船下方形成了一个虚拟的水下磁传感器长方形阵列(如图3所示). 图 2 铁磁舰船航行通过一个磁传感器线阵 Figure2. Ferromagnetic ship runs over a line array of magnetic sensors.
图 3 铁磁舰船及其下方的虚拟磁传感器长方形阵列 Figure3. Ferromagnetic ship stands over a virtual array of magnetic sensors.
针对上述舰船, 可采用一定的技术步骤得到最优化的磁单极子阵列分布, 如图4和图5所示, 并反演重建舰船的磁性参数. 图 4 舰船结构上的磁单极子阵列分布 Figure4. Magnetic monopole array in the geometry of ship.
图 5 机组和推进轴的磁单极子分布 Figure5. Magnetic monopoles for the engine block and the shaft.
当$\alpha \to 0$时, Tihhonov正则化解趋向于Moore-Penrose伪逆解. 采用L曲线法选择正则化参数, 能够深入探究所研究的问题, 有助于问题的解决, 如图6所示. 图 6 根据L曲线法得到正则化参数 Figure6. Regularization parameter obtained by the L-curve method.
根据已知的舰艇磁场测量值和线性测量矩阵, 采用Tikhonov正则化技术求解线性方程组所描述的逆问题, 可以得到所有磁源的正则化解Qα. 从而可以知道舰艇磁场的拟合计算值bα = AQα, 进而知道拟合误差berr-α=bα – b. 实际上根据拟合误差berr-α, 可以判断哪些测量点上的磁场测量值存在粗大误差, 需要重新测量以修正测量误差或排除该测量值, 实现舰艇磁场纠错的目的. 根据纠错后的舰艇磁场测量值, 再次进行正则化反演计算, 得到最接近真实的正则化解Qα. 根据该正则化解Qα可以得到其他测量点位置处的舰艇磁场预测值, 从而实现舰艇磁场的综合分析, 如图7所示. 图 7 舰船磁场预测值和测量值的对比 Figure7. Comparison of predicted and measured values of ship's magnetic field.
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4.1.磁单极子阵列设置
所采用的反演目标为按照实际舰船结构抽象出来的一艘虚拟典型舰船, 其中船长表示为L, 船宽表示为B, 船高表示为H. 不同的磁单极子分布形式具有不同的反演效果, 设置三种磁单极子阵列分布形式进行对比分析, 分别为: 1)水线平面上的长方形磁单极子阵列 (简称“长方形阵列”), 由L × B = 25 × 5 = 125个磁单极子构成, 如图8所示; 图 8 吃水线水平面上的长方形磁单极子阵列 Figure8. Rectangular magnetic monopole array on the horizontal surface of the draft line.
2)包围船体的长方体磁单极子阵列 (简称“长方体阵列”), 由L × B × H = 25 × 5 × 4 = 500个磁单极子构成, 如图9所示; 图 9 包围船体的长方体磁单极子阵列 Figure9. Cuboid magnetic monopole array enclosing the ship hull.
3)按照船体铁磁结构分布的三维船体阵列 (简称“三维船体阵列”), 由L × B × H = 347个磁单极子构成, 如图10所示. 图 10 按照船体铁磁结构分布的三维船体磁单极子阵列 Figure10. Three-dimensional ship magnetic monopole array distributed according to the ferromagnetic structure of the ship hull.
24.2.磁场测量点的配置 -->
4.2.磁场测量点的配置
磁场测量点配置为2L × 2B = 81 × 9 = 729的点阵, 分布范围为长2L、宽2B, 点的纵向间隔为L/40, 横向间隔0.25B, 如图11所示. 取5个测量深度平面: 吃水线下方+1B, +2B, +5B三个深度, 吃水线上方–2B, –5B两个深度, 如图12和图13所示. 此处未设置–1B深度平面, 因为舰船部分上层建筑高度较大, 与此深度平面存在结构冲突. 在舰船磁场测量领域, 一般取船首方向为x轴正向, 右舷方向为y轴正向, 垂直向下为z轴正向, 如图12和图13所示. 图 11 舰船磁场测量点分布俯视图 Figure11. Top view of the distribution of magnetic field measurement points on ship.
图 12 舰船磁场测量点分布侧视图 Figure12. Side view of distribution of magnetic field measurement points on ship.
图 13 舰船磁场测量点分布后视图 Figure13. Rear view of the distribution of magnetic field measurement points on ship.