本文選題：電學(xué)層析成像 + 逆問題��； 參考：《天津大學(xué)》2014年博士論文

【摘要】：電學(xué)層析成像技術(shù)是一種非侵入或非接觸的過程可視化技術(shù)。它通過在物場邊界處施加激勵，獲取物場的電學(xué)響應(yīng)特性，進(jìn)而反演計算出場內(nèi)電學(xué)參數(shù)（電阻率、電容率、磁導(dǎo)率等）的分布信息，實現(xiàn)場內(nèi)介質(zhì)的二維或三維可視化測量。自問世以來，該技術(shù)以響應(yīng)速度快、安全無輻射、結(jié)構(gòu)簡單、價格低廉等優(yōu)點，在石油、化工、冶金、醫(yī)藥、食品等領(lǐng)域備受關(guān)注，得到了快速地發(fā)展，并被成功地應(yīng)用于多相流過程參數(shù)檢測、地質(zhì)勘探、環(huán)境監(jiān)測、工業(yè)安全監(jiān)測、醫(yī)療監(jiān)護(hù)、以及混合、沉淀、流化等過程的分析。但是，由于電學(xué)層析成像問題的非線性和不適定性，其重建結(jié)果的空間分辨率較低，難以滿足現(xiàn)代工業(yè)生產(chǎn)的需求。 目前，在電學(xué)層析成像技術(shù)中，被普遍采用的是基于區(qū)域剖分的像素重建算法。該類算法能夠獲取電學(xué)參數(shù)在離散像素點上的估計值，適合于連續(xù)電學(xué)參數(shù)分布的重建。在分塊定常分布中，由于電學(xué)參數(shù)在介質(zhì)邊界處存在突變，基于區(qū)域剖分的重建算法很難得到關(guān)于介質(zhì)邊界的明確信息。 針對該問題，論文對基于邊界剖分的形狀重建算法進(jìn)行研究。該類算法充分利用電學(xué)參數(shù)分塊定常分布這一先驗信息，直接獲取介質(zhì)邊界的幾何輪廓，將重建電學(xué)參數(shù)分布的“圖像重建”問題，轉(zhuǎn)換為重建介質(zhì)邊界幾何輪廓的“形狀重建”問題，降低了問題的維數(shù)，減少了未知量的個數(shù)，改善了問題的不適定性，增強了重建結(jié)果的空間分辨率，可以用于定量分析。 論文主要工作和研究成果如下： （1）采用邊界元法對電學(xué)層析成像正問題進(jìn)行求解，推導(dǎo)出閉合邊界問題和開邊界問題的最簡邊界積分方程，縮減所形成代數(shù)方程組的規(guī)模；并通過引入中間變量，簡化代數(shù)方程組的構(gòu)建過程，降低編程復(fù)雜度。 （2）基于互易定理，推導(dǎo)出形狀重建問題中的靈敏度計算公式，相比于現(xiàn)有方法，該方法具有更高的計算效率、更簡潔的形式和更廣的適用范圍；研究形狀重建問題中敏感場的分布規(guī)律，指出形狀靈敏度在物體邊界凹入部分較低，在凸出部分較高，在物體邊界遠(yuǎn)離電極部分較低，在趨近電極部分較高。 （3）提出基于傅里葉級數(shù)的二維內(nèi)含物重建算法，，該算法在仿真和實驗中均具有較高的速度和精度；依據(jù)形狀靈敏度的分布規(guī)律，指出形狀重建誤差主要來源于邊界凹入部分較低的靈敏度。 （4）提出基于球諧函數(shù)和多級Levenberg-Marquardt搜索的三維內(nèi)含物重建算法；設(shè)計并實現(xiàn)立方體電容層析成像傳感器，構(gòu)建三維電容層析成像實驗平臺；采用仿真和實驗驗證算法的有效性，由于形狀敏感場的不均勻分布，重建物體在靠近電極時會在趨近電極方向發(fā)生形變。 （5）提出基于貝塞爾函數(shù)的二維開界面形狀重建算法，給出幾何約束的添加方法；以氣液兩相層狀流為例，分析電阻層析成像技術(shù)在不充分?jǐn)?shù)據(jù)下的重建結(jié)果，指出導(dǎo)電流體液位高于四分之一管道直徑的條件下，包含16個電極ERT系統(tǒng)能夠精確的重建相界面的幾何形狀；分析電導(dǎo)率先驗信息不準(zhǔn)確時的形狀重建結(jié)果，指出誤差在2%之內(nèi)，能夠得到較好的重建結(jié)果。 （6）提出基于貝塞爾曲面表征的三維開界面重建算法；針對不準(zhǔn)確的介電常數(shù)先驗值，提出同時重建介電常數(shù)和界面形狀的重建算法；并采用仿真和實驗數(shù)據(jù)，證明了算法的有效性。
[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 .
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TP391.41;O441

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 熊漢亮,董琰婷,王安文,徐苓安;電磁層析成像技術(shù)的物理機制與檢測極限[J];天津大學(xué)學(xué)報;1998年02期

2 王化祥,王超,陳磊;基于Landweber迭代的圖像重建算法[J];信號處理;2000年04期

本文編號：2025618