电学层析成像形状重建方法研究

发布时间：2018-06-16 05:55

本文选题：电学层析成像 + 逆问题　；参考：《天津大学》2014年博士论文

【摘要】：电学层析成像技术是一种非侵入或非接触的过程可视化技术。它通过在物场边界处施加激励，获取物场的电学响应特性，进而反演计算出场内电学参数（电阻率、电容率、磁导率等）的分布信息，实现场内介质的二维或三维可视化测量。自问世以来，该技术以响应速度快、安全无辐射、结构简单、价格低廉等优点，在石油、化工、冶金、医药、食品等领域备受关注，得到了快速地发展，并被成功地应用于多相流过程参数检测、地质勘探、环境监测、工业安全监测、医疗监护、以及混合、沉淀、流化等过程的分析。但是，由于电学层析成像问题的非线性和不适定性，其重建结果的空间分辨率较低，难以满足现代工业生产的需求。目前，在电学层析成像技术中，被普遍采用的是基于区域剖分的像素重建算法。该类算法能够获取电学参数在离散像素点上的估计值，适合于连续电学参数分布的重建。在分块定常分布中，由于电学参数在介质边界处存在突变，基于区域剖分的重建算法很难得到关于介质边界的明确信息。针对该问题，论文对基于边界剖分的形状重建算法进行研究。该类算法充分利用电学参数分块定常分布这一先验信息，直接获取介质边界的几何轮廓，将重建电学参数分布的“图像重建”问题，转换为重建介质边界几何轮廓的“形状重建”问题，降低了问题的维数，减少了未知量的个数，改善了问题的不适定性，增强了重建结果的空间分辨率，可以用于定量分析。论文主要工作和研究成果如下：（1）采用边界元法对电学层析成像正问题进行求解，推导出闭合边界问题和开边界问题的最简边界积分方程，缩减所形成代数方程组的规模；并通过引入中间变量，简化代数方程组的构建过程，降低编程复杂度。（2）基于互易定理，推导出形状重建问题中的灵敏度计算公式，相比于现有方法，该方法具有更高的计算效率、更简洁的形式和更广的适用范围；研究形状重建问题中敏感场的分布规律，指出形状灵敏度在物体边界凹入部分较低，在凸出部分较高，在物体边界远离电极部分较低，在趋近电极部分较高。（3）提出基于傅里叶级数的二维内含物重建算法，，该算法在仿真和实验中均具有较高的速度和精度；依据形状灵敏度的分布规律，指出形状重建误差主要来源于边界凹入部分较低的灵敏度。（4）提出基于球谐函数和多级Levenberg-Marquardt搜索的三维内含物重建算法；设计并实现立方体电容层析成像传感器，构建三维电容层析成像实验平台；采用仿真和实验验证算法的有效性，由于形状敏感场的不均匀分布，重建物体在靠近电极时会在趋近电极方向发生形变。（5）提出基于贝塞尔函数的二维开界面形状重建算法，给出几何约束的添加方法；以气液两相层状流为例，分析电阻层析成像技术在不充分数据下的重建结果，指出导电流体液位高于四分之一管道直径的条件下，包含16个电极ERT系统能够精确的重建相界面的几何形状；分析电导率先验信息不准确时的形状重建结果，指出误差在2%之内，能够得到较好的重建结果。（6）提出基于贝塞尔曲面表征的三维开界面重建算法；针对不准确的介电常数先验值，提出同时重建介电常数和界面形状的重建算法；并采用仿真和实验数据，证明了算法的有效性。
[Abstract]:The electrical tomographic imaging technology is a non - invasive or non - contact process visualization technique . It is used in the fields of petroleum , chemical industry , metallurgy , medicine , food and so on . It has been successfully applied in the process of multi - phase flow process parameter detection , geological exploration , environmental monitoring , industrial safety monitoring , medical monitoring , mixing , precipitation , fluidization and so on .

At present , in the technology of electrical tomography , the pixel reconstruction algorithm based on region subdivision is commonly used . The algorithm can obtain the estimation value of electrical parameters on discrete pixel points , and is suitable for the reconstruction of continuous electrical parameter distribution . In the block constant distribution , because of the abrupt change of electrical parameters at the boundary of the medium , it is difficult to obtain clear information about the boundary of the media based on the reconstruction algorithm .

In order to solve the problem , the shape reconstruction algorithm based on boundary subdivision is studied . The algorithm makes full use of the prior information of the distribution of electrical parameters and directly obtains the geometric outline of the boundary of the medium . The problem of " shape reconstruction " of the reconstructed dielectric boundary geometry is solved , the dimension of the problem is reduced , the number of unknown quantities is reduced , the discomfort of the problem is improved , the spatial resolution of the reconstruction result is enhanced , and the method can be used for quantitative analysis .

The main work and research results of the thesis are as follows :

( 1 ) the boundary element method is adopted to solve the positive problem of the electrical tomographic imaging , and the simplest boundary integral equation of the closed boundary problem and the open boundary problem is deduced , and the size of the formed algebraic equation group is reduced ;
By introducing the intermediate variable , the construction process of algebraic equation group is simplified , and the programming complexity is reduced .

( 2 ) Based on the reciprocity theorem , the sensitivity calculation formula in the problem of shape reconstruction is derived . Compared with the existing method , the method has higher computational efficiency , simpler form and wider application range ;
The distribution rule of the sensitive field in the shape reconstruction is studied . It is pointed out that the shape sensitivity is lower in the concave part of the boundary of the object , and the shape sensitivity is higher in the convex part , and the part of the object is far away from the electrode part , and the part of the approaching electrode is higher .

( 3 ) A two - dimensional inclusion reconstruction algorithm based on Fourier series is proposed , which has higher speed and precision in simulation and experiment .
According to the distribution rule of shape sensitivity , it is pointed out that the shape reconstruction error is mainly derived from the lower sensitivity of the boundary concave part .

( 4 ) A three - dimensional inclusion reconstruction algorithm based on spherical harmonic function and multi - stage Levenberg - Marquardt search is proposed .
designing and implementing a cubic capacitance tomography sensor , and constructing a three - dimensional capacitance tomography experiment platform ;
By using the simulation and experimental verification algorithm , the shape - sensitive field is not evenly distributed , and the reconstructed object can deform in the direction of the approaching electrode when it is close to the electrode .

( 5 ) A two - dimensional open - interface shape reconstruction algorithm based on Bessel function is proposed , and the method of adding geometric constraints is given .
Taking the gas - liquid two - phase laminar flow as an example , the reconstruction results of the resistance tomography technique under the insufficient data are analyzed , and the geometric shape of the phase interface can be accurately reconstructed by the ERT system of 16 electrodes under the condition that the body fluid level of the conductive flow is higher than the diameter of the quarter pipe ;
The result of shape reconstruction when the prior information of conductivity is not accurate is analyzed , and it is pointed out that the error is within 2 % , and the better reconstruction result can be obtained .

( 6 ) proposing a three - dimensional open - interface reconstruction algorithm based on Bezier surface representation ;
A reconstruction algorithm for the reconstruction of dielectric constant and interface shape is proposed for the prior value of dielectric constant .
Simulation and experimental data are used to demonstrate the effectiveness of the algorithm .
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TP391.41;O441

【参考文献】