电磁层析成像中有限元技术的研究

发布时间：2018-01-07 16:16

本文关键词：电磁层析成像中有限元技术的研究　出处：《沈阳师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：电磁层析成像技术(MIT)是电学层析成像(ET)的一种,MIT技术类似于其它ET技术的操作方法,并且根据阻抗检测技术的改进来修复电容层析成像和电阻层析成像的缺陷。MIT技术以法拉第电磁感应定律为基础,针对不同物质的电导率和磁导率,根据磁偶极子的特性,测量不同投影方向的检测值,从而重现物场空间内部分布,使所测量的敏感场分布实现可视化。MIT技术分为正问题和逆问题的研究,本文的主要研究内容为:1.构建MIT技术的物理模型,描述了该系统的工作原理,依据麦克斯韦方程组推导出电磁感应成像的数学模型。2.通过分析对比多种解决MIT数学模型方法:线性逼近法、分析方法和有限元法等,针对MIT系统的特性,采用有限元法。总结不同有限元剖分方法的特点:三角形单元具有较好的形状、算法较为简单,单元的边界适应性强,运用灵活,可以适用于各种离散不规则区域,而矩形单元比较适合离散矩形区域,相比之下单元的精度要低于四边形单元。因此,根据MIT物场空间的形状和计算需求,对目标场域中心部分进行三角形剖分,四周进行四边形剖分的三角形-四边形有限元剖分方法。给出了物场空间的有限元剖分结果和灵敏度图例。3.通过正则化方法、Landweber迭代法和共轭梯度算法进行图像重建,与被测物场对比,利用图像误差和相关性等指标评价重建图像,得出结论:三角形-四边形有限元剖分方法符合MIT物场空间特点,灵敏度图表符合电磁场规律,基于有限元方法的正则化重建算法重建图像质量比较高。
[Abstract]:Electromagnetic tomography (MIT) in electrical tomography (ET) is a kind of operation method, MIT technology is similar to other ET technology,.MIT technology and defect detection technology based on the improved impedance to repair electrical capacitance tomography and electrical resistance tomography based on Faraday's law of electromagnetic induction, according to different material conductivity and permeability. And according to the characteristic of the magnetic dipole, measuring different projection value, so as to reproduce the distribution of interior field space, so that the measurement of the sensitivity field visualization technology of.MIT is divided into forward problem and inverse problem research, the main contents of this paper are: 1. physical model construction of MIT technology, the working principle of the system described, according to the.2. mathematical model of Maxwell equations derived from electromagnetic induction imaging by comparative analysis of different methods to solve the mathematical model of MIT: linear approximation method, analysis method and The finite element method, according to the characteristics of the MIT system, using the finite element method. Summarize the characteristics of different finite element mesh method: triangular element has good shape, the algorithm is simple, the cell boundary adaptability, flexibility, can be applied to a variety of discrete and irregular region, and more suitable for discrete rectangle rectangular element in contrast, the accuracy of unit is lower than the quadrilateral element. Therefore, according to the shape and the computational requirements of MIT field space, the target field center part of the triangulation around the quadrangle triangle and quadrilateral finite element mesh finite element method. Then the field space differentiation. Methods through regular results and sensitivity of legend.3., Landweber iterative method and the conjugate gradient algorithm for image reconstruction, and the measured field comparison, using the image error and the correlation index of image reconstruction, it is concluded that The triangle quadrilateral finite element method is consistent with the MIT field characteristics, and the sensitivity chart is consistent with the electromagnetic field rule. The reconstructed image quality based on finite element method regularization algorithm is relatively high.

【学位授予单位】：沈阳师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O441;TP391.41

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