摘要
摘要
多相流广泛存在于动力、石油、化工、核能、食品和医学等多个领域。与单相流动相比，多相流动相间存在着界面效应和相间速度，其流动特性更加复杂多变，因此要建立可靠的多相流动力学模型，并对多相流动过程进行预测、设计及控制。电阻抗成像(Electrical Impedance Tomography, EIT)技术是电学层析成像技术的一种，可以通过非接触的方式，将物体的内部结构特性通过电特性反应出来。本文旨在对于电阻抗层析成像技术的主要原理、图像重建算法进行研究，为电阻抗层析成像技术在多相流检测中的应用提供理论基础。
EIT技术的研究主要分为两方面，即正问题的研究与逆问题的研究。EIT正问题(Forward Problem)采用有限元方法(FEM)求解，基于变分原理，建立有限元方程。EIT逆问题(Inverse problem)是非线性问题，主要工作是对图像重建的研究，EIT技术有多种图像重建算法，本次毕业设计主要通过Matlab仿真软件对Landweber算法、正则化算法、STM算法等进行图像重建。通过图像重建结果，比较不同算法的优缺点。
关键词:EIT技术；正问题；逆问题；有限元法；图像重建
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燕山大学本科生毕业设计(论文)
Abstract
Multiphase flow widely exists in many fields, such as power, petroleum, chemical, nuclear energy, food and medicine etc. Compared with the singlephase, multiphase flow have interface effect and the existence of phase velocity, the flow characteristics is more complex. Therefore, it?s important to establish a reliable multiphase flow dynamics model, so do the multiphase flow process prediction, design and control. Electrical impedance tomography technology(EIT) is a kind of electrical tomography technology, which can react the internal structure characteristics of object through electrical charcterstics by non contact mode. This paper aims to study the main principle of EIT and electrical impedance tomography image reconstruction algorithm what provide a theoretical basis for EIT technology in multiphase flow detection application.
The study of EIT technology is mainly divided into twoaspects, namely the forward problem and inverse problem. The forward problem of EIT was solved by using the finite element method (FEM) solution, which based on the variational principle, and established the finite element equations. The inverse problem of EIT is a nonlinear problem, the main work is the study of image reconstruction. EIT technology has a variety of image reconstruction algorithm. This graduation design mainly study Landweber algorithm, STM algorithm, regularization algorithm through Matlab simulation. Through image reconstruction results, comparing the advantages and disadvantages of different algorithms.
Keywords:Electrical Impedance Tomography; Forward Problem; Inverse Problem; Finite Element Method;Image Reconstruction
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目 录
摘要 ....................................................................................................................... I Abstract ................................................................................................................ II 第1章 绪论 ........................................................................................................ 1
1.1 课题背景知识 ....................................................................................... 1 1.2 EIT图像重建技术研究现状 ................................................................. 1 1.2.1 EIT技术国内外研究现状 .............................................................. 2 1.2.2 EIT技术国内外研究成果 .............................................................. 2 1.3 课题研究内容及论文安排 ................................................................... 4 第2章 电阻抗层析成像技术综述 .................................................................... 5
2.1 引言 ....................................................................................................... 5 2.2 过程层析成像技术简介 ....................................................................... 5 2.3 EIT技术理论基础 ................................................................................. 8 2.3.1 EIT技术生物学基础 ...................................................................... 9 2.3.2 EIT技术基本原理 ........................................................................ 10 2.3.3 EIT技术相关参数介绍 ................................................................. 11 2.4 EIT系统简介 ....................................................................................... 14 2.5 本章小结 ............................................................................................. 15 第3章 EIT技术数学模型及有限元建模 ....................................................... 16
3.1 引言 ..................................................................................................... 16 3.2 传输管道三维建模的EIT技术数学模型 ......................................... 16 3.2.1 EIT技术数学模型理论基础 ........................................................ 16 3.2.2 用于传输管道三维建模的EIT数学模型 .................................. 17 3.3 用于传输管道多相流检测的EIT求解路线 ..................................... 18 3.4 有限元法求解EIT正问题 ................................................................. 19 3.4.1 EIT正问题 .................................................................................... 19 3.4.2 有限元法基本原理 ...................................................................... 21
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3.4.3 有限元模型 .................................................................................. 22 3.4.4 使用EIDORS 3.4进行ERT正问题求解 .................................. 24 3.5 本章小结 ............................................................................................. 25 第4章 EIT技术图像重建算法 ....................................................................... 26
4.1 引言 ..................................................................................................... 26 4.2 EIT逆问题 ........................................................................................... 26 4.3 几种常见的图像重建算法研究 ......................................................... 27 4.3.1 灵敏度系数算法研究 .................................................................. 27 4.3.2 Landweber算法研究 .................................................................... 28 4.3.3 Tikhonov正则化算法研究 .......................................................... 30 4.3.4 不同算法图像重建效果对比 ...................................................... 32 4.4 本章小结 ............................................................................................. 34 结论 .................................................................................................................... 35 参考文献 ............................................................................................................ 35 致谢 .................................................................................................................... 39 附录1 开题报告 附录2 中期报告 附录3 外文文献 附录4 外文翻译
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