航空磁探中水下目标三维积分方程磁场建模
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摘要
为获取航空磁探中水下铁磁性目标的空间磁场分布,通过三维积分方程法的基本原理推导出空间磁场的解析式,根据矢量恒等式和高斯散度定理简化空间磁场计算式,建立水下铁磁性目标空间磁场预测模型。通过铁磁性长方体对模型进行理论验证,使用铯光泵磁力仪测量铁磁性长旋转椭球体的高空磁场;然后,基于预测模型推算铁磁性长旋转椭球体的磁场,根据实际测量的磁场数据和预测值进行比较。结果表明,预测模型的推算精度较高,平均绝对误差为0.320 5 nT,平均相对误差为12.368%。
To obtain the spatial distribution of the magnetic field of underwater ferromagnetic target in the aeromagnetic anomaly detection, the analytical equation of spatial magnetic field of the underwater ferromagnetic target was derived based on the fundamentals of the three dimensional integral equations method. The analytical equation of spatial magnetic field was simplified by the vector identity and the Gaussian divergence theorem, and the prediction model of the magnetic field of the underwater ferromagnetic target was established. The theoretical validation of the prediction model was performed using the ferromagnetic cuboid. The magnetic field of the ferromagnetic ellipsoid at high altitude was measured by the cesium vapour optically pumped magnetometer. Then the magnetic field of the ferromagnetic ellipsoid was calculated by the proposed prediction model. The prediction values and the measurement values were compared. The results showed that the prediction accuracy of the prediction model was good enough. The mean absolute error was 0.3205 nT, and the mean relative error was 12.368%.
To obtain the spatial distribution of the magnetic field of underwater ferromagnetic target in the aeromagnetic anomaly detection, the analytical equation of spatial magnetic field of the underwater ferromagnetic target was derived based on the fundamentals of the three dimensional integral equations method. The analytical equation of spatial magnetic field was simplified by the vector identity and the Gaussian divergence theorem, and the prediction model of the magnetic field of the underwater ferromagnetic target was established. The theoretical validation of the prediction model was performed using the ferromagnetic cuboid. The magnetic field of the ferromagnetic ellipsoid at high altitude was measured by the cesium vapour optically pumped magnetometer. Then the magnetic field of the ferromagnetic ellipsoid was calculated by the proposed prediction model. The prediction values and the measurement values were compared. The results showed that the prediction accuracy of the prediction model was good enough. The mean absolute error was 0.3205 nT, and the mean relative error was 12.368%.
引文
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[2]崔汉国.舰船磁场可视化技术的研究与实现[J].计算机仿真,2004,21(4):22-24.CUI HANGUO.Research and application of visualization technology for vessel’s magnetic field[J].Computer Simulation,2004,21(4):22-24.(in Chinese)
[3]SHEINKER A,FRUMKIS L,GINZBURG B.Magnetic anomaly detection using a three-axis magnetometer[J].IEEE Transactions on Magnetics,2009,45(1):160-167.
[4]熊雄,杨日杰,王鸿吉.海浪磁噪声背景中动目标航空磁异常检测算法[J].华中科技大学学报:自然科学版,2015,43(5):100-105.XIONG XIONG,YANG RIJIE,WANG HONGJI.Airborne magnetic anomaly detection algorithm for moving target under ocean wave generated magnetic noise[J].Journal of Huazhong University of Science and Technology:Natural Science Edition,2015,43(5):100-105.(in Chinese)
[5]林春生.舰船磁场信号检测与磁性目标定位[D].武汉:海军工程大学,1996.LIN CHUNSHENG.Signal detection of ship magnetic field and magnetic target location[D].Wuhan:Naval Engineering Institute,1996.(in Chinese)
[6]翁行泰,曹梅芬.磁异探潜中潜艇的数学模型[J].上海交通大学学报,1995,29(3):27-32.WENG XINGTAI,CAO MEIFEN.Submarine math model of magnetic abnormity detection[J].Journal of Shanghai Jiaotong University,1995,29(3):27-32.(in Chinese)
[7]DAMES P M,SCHWAGER M,SCHWAGER D.Active magnetic anomaly detection using multiple micro aerial vehicles[J].IEEE Robotics and Automation Letters,2016,1(1):153-160.
[8]SHEINKER A,MOLDWIN M B.Magnetic anomaly detection(MAD)of ferromagnetic pipelines using principal component analysis(PCA)[J].Measurement Science and Technology,2016,27(4):1-7.
[9]SONG L,BILLINGS S,PASION L,et al.Transient electromagnetic scattering of a metallic object buried in underwater sediments[J].IEEE Transactions on Geoscience and Remote Sensing,2016,54(2):1091-1102.
[10]LIU Y,ZHANG Y,YI H.The new magnetic survey method for underwater pipeline detection[J].Applied Mechanics and Materials,2013,239(2):338-343.
[11]高俊吉,刘大明,姚琼荟.舰船固定磁性分解方法研究[J].哈尔滨工程大学学报,2007,28(10):1164-1170.GAO JUNJI,LIU DAMING,YAO QIONGHUI.Decomposition of the permanent magnetic field of ships[J].Journal of Harbin Engineering University,2007,28(10):1164-1170.(in Chinese)
[12]杨明明,刘大明,刘胜道.采用边界积分方程和Tikhonov正则化方法延拓潜艇磁场[J].兵工学报,2010,31(9):1216-1221.YANG MINGMING,LIU DAMING,LIU SHENGDAO.Submarine’s magnetic field extrapolation using boundary element method and tikhonov regularization[J].Acta Armamentarii,2010,31(9):1216-1221.(in Chinese)
[13]郭成豹,肖昌汉,刘大明.基于积分方程法和奇异值分解的磁性目标磁场延拓技术研究[J].物理学报,2008,57(7):4182-4188.GUO CHENGBAO,XIAO CHANGHAN,LIU DAMING.Research on the continuations of magnetic field of magnetic object based on integral equation method and singular value decomposition[J].Acta Physica Sinica,2008,57(7):4182-4188.(in Chinese)
[14]翁行泰,曹梅芬.潜艇感应磁场的三维有限元法计算研究[J].上海交通大学学报,1994,28(5):69-76.WENG XINGTAI,CAO MEIFEN.A research on the calculation of the induced magnetic field of a submarine[J].Journal of Shanghai Jiaotong University,1994,28(5):69-76.(in Chinese)
[15]牛龙飞,李斌,张静.三磁偶极子磁体舰船磁场仿真[J].计算机仿真,2009,26(3):12-15.NIU LONGFEI,LI BIN,ZHANG JING.Simulation of warship magnetic field based on three magnetic dipole magnetic bodies[J].Computer Simulation,2009,26(3):12-15.(in Chinese)
[16]周家新,陈建勇,单志超,等.航空磁探中潜艇磁场建模方法分析[J].海军航空工程学院学报,2017,32(1):143-148.ZHOU JIAXIN,CHEN JIANYONG,SHAN ZHICHAO,et al.Analysis of submarine magnetic field modeling method for aerial magnetic detection[J].Journal of Naval Aeronautical and Astronautical University,2017,32(1):143-148.(in Chinese)
[17]周耀忠,张国友.舰船磁场分析计算[M].北京:国防工业出版社,2004:104-200.ZHOU YAOZHONG,ZHANG GUOYOU.Ship magnetic field analyze and compute[M].Beijing:National Defend Industry Press,2004:104-200.(in Chinese)
[18]OLIVIER C,COULOMB J,BONGIRAUD J.Recent improvements for solving inverse magnetostatic problem applied to thin shells[J].IEEE Transactions on Magnetics,2002,38(2):1005-1008.
[19]刘胜道,刘大明,肖昌汉,等.基于遗传算法的磁性目标磁模型[J].武汉理工大学学报,2008,32(6):1017-1020.LIU SHENGDAO,LIU DAMING,XIAO CHANGHAN,et al.Magnetic model of the magnetic object based on genetic algorithm[J].Journal of Wuhan University of Technology,2008,32(6):1017-1020.(in Chinese)