用正交多项式进行平面磁场拟合的一种新方法
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摘要
提高现代舰艇磁隐身能力的前提是准确地了解和掌握舰艇空间磁场分布,和舰艇所处地区的地磁场分布情况.针对目前磁场插值或拟合中存在的精度不够高,需要网格化等问题,本文提出了一种基于正交多项式的平面磁场拟合方法.不同于一维正交多项式的拟合方法,此方法首先从一般的完备二维多项式族出发,然后用Gram-Schmidt正交化过程将此完备二维多项式族正交化,得到数值正交基底,然后以此正交基进行平面磁场拟合.为了解决分块拟合问题,又提出了紧支的概念,通过与拉格朗日二维插值的船模试验及仿真比较,发现此方法拟合精度比较高,能够较准确的反映平面磁场的分布,有一定的工程实用价值.
The premise that improves the magnetic-concealed ability of modern naval vessels is to understand and master the space magnetic distributing of the vessels,and the geomagnetism distributing where the vessels are lying.Aiming at the problem of low precision in magnetic field interpolating and fitting,and the problem of gridding,a method of plane magnetic field fitting based on orthogonal polynomials was brought forward.Differing from the fitting by orthogonal polynomial of one dimension,this method was based on the generic maturity polynomial groups of two dimensions,and the generic maturity polynomial groups of two dimensions were orthogonalized based on the method of Gram-Schmidt.So the numerical base functions were gotten,and the fitting of the magnetic field with the base functions was carried out.For the problem of subsection in fitting,the concept of compact support was put forward,through testing with ship model,simulating and comparing with the Lagrange fitting of two dimensions,it is found that this method has the virtues of high precision and could reflect the distributing of plane magnetic field exactly.
The premise that improves the magnetic-concealed ability of modern naval vessels is to understand and master the space magnetic distributing of the vessels,and the geomagnetism distributing where the vessels are lying.Aiming at the problem of low precision in magnetic field interpolating and fitting,and the problem of gridding,a method of plane magnetic field fitting based on orthogonal polynomials was brought forward.Differing from the fitting by orthogonal polynomial of one dimension,this method was based on the generic maturity polynomial groups of two dimensions,and the generic maturity polynomial groups of two dimensions were orthogonalized based on the method of Gram-Schmidt.So the numerical base functions were gotten,and the fitting of the magnetic field with the base functions was carried out.For the problem of subsection in fitting,the concept of compact support was put forward,through testing with ship model,simulating and comparing with the Lagrange fitting of two dimensions,it is found that this method has the virtues of high precision and could reflect the distributing of plane magnetic field exactly.
引文
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[2]郭良辉,孟小红,郭志宏.位场数据网格化的反插值法[J].地球物理学报,2006,49(4):1183~1190.
[3]钟伟,杨宝俊,张智.多项式拟合技术在强噪声地震资料中的应用研究[J].地球物理学进展,2006,21(1):184~189.
[4]何汉林,魏汝祥,李卫军.数值分析[M].武汉:湖北科学技术出版社,1999,198~202.
[5]李庆扬,王能超,易大义.数值分析[M].武汉:华中理工大学出版社,1998,97~105.
[6]罗家洪.矩阵分析引论[M].广州:华南理工大学出版社,2003,39~42.
[7]Lancaster P,Salkauskas K.Surfaces generated by moving leastsquares methods[J].Mathematics of computation,1981,37(155):141~158.
[8]曾清红,卢德堂.基于移动最小二乘法的曲线曲面拟合[J].工程图学学报,2004,(1):84~89.
[9]陈森,苏洁南.正交多项式的应用[J].中南林业调查规划,1997,16(2):56~60.
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