本文關鍵詞：電磁層析成像中有限元技術的研究　出處：《沈陽師范大學》2017年碩士論文　論文類型：學位論文

  更多相關文章： 電磁層析成像技術 正問題 有限元法 三角形剖分 四邊形剖分

【摘要】：電磁層析成像技術(MIT)是電學層析成像(ET)的一種,MIT技術類似于其它ET技術的操作方法,并且根據(jù)阻抗檢測技術的改進來修復電容層析成像和電阻層析成像的缺陷。MIT技術以法拉第電磁感應定律為基礎,針對不同物質(zhì)的電導率和磁導率,根據(jù)磁偶極子的特性,測量不同投影方向的檢測值,從而重現(xiàn)物場空間內(nèi)部分布,使所測量的敏感場分布實現(xiàn)可視化。MIT技術分為正問題和逆問題的研究,本文的主要研究內(nèi)容為:1.構建MIT技術的物理模型,描述了該系統(tǒng)的工作原理,依據(jù)麥克斯韋方程組推導出電磁感應成像的數(shù)學模型。2.通過分析對比多種解決MIT數(shù)學模型方法:線性逼近法、分析方法和有限元法等,針對MIT系統(tǒng)的特性,采用有限元法�？偨Y不同有限元剖分方法的特點:三角形單元具有較好的形狀、算法較為簡單,單元的邊界適應性強,運用靈活,可以適用于各種離散不規(guī)則區(qū)域,而矩形單元比較適合離散矩形區(qū)域,相比之下單元的精度要低于四邊形單元。因此,根據(jù)MIT物場空間的形狀和計算需求,對目標場域中心部分進行三角形剖分,四周進行四邊形剖分的三角形-四邊形有限元剖分方法。給出了物場空間的有限元剖分結果和靈敏度圖例。3.通過正則化方法、Landweber迭代法和共軛梯度算法進行圖像重建,與被測物場對比,利用圖像誤差和相關性等指標評價重建圖像,得出結論:三角形-四邊形有限元剖分方法符合MIT物場空間特點,靈敏度圖表符合電磁場規(guī)律,基于有限元方法的正則化重建算法重建圖像質(zhì)量比較高。
[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.

【學位授予單位】：沈陽師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O441;TP391.41

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本文編號：1393309