电学成像算法及气固两相流研究
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摘要
电学层析成像技术是一种非侵入可视化测量技术，由于该技术具有响应快、无损伤、成本低廉等优点，在医学临床监护和工业多相流检测等领域具有广阔的前景。
本课题主要对电学成像的图像重建算法、电极优化及气固两相流的流动参数测量展开讨论，本文的主要工作及结果简单总结如下：
1、在深入讨论图像成像算法的基础上，提出一种基于三维模型的改进正则化的电阻成像算法（HTIK）。针对迭代Tikhonov算法系数选择问题，提出基于同伦映射的方法，并利用非线性函Sigmoid调节正则化参数，以获得的图像灰度值作为迭代Tikhonov法的初始值进行迭代，重建敏感场图像。仿真及实验结果表明，该方法有效地改进了电阻层析成像的成像质量。
2、为提高电学成像系统重建图像质量，提出基于图像融合的电学成像方法。通过电磁场有限元仿真软件COMSOL构建ECT传感器模型进行仿真研究，分别通过共轭梯度算法和奇异值分解算法重建图像，运用基于小波变换的图像融合方法对图像进行处理。仿真及实验结果表明该方法有效改进了ECT成像质量。然后用COMSOL建立ERT模型，运用小波融合算法进行融合，经过仿真和实验证明该方法可以提高ERT成像质量。
3、为了估计电极数与成像质量之间的关系，通过COMSOL分别建立4、8、12、16、20、24、28个电极的电阻层析成像的三维模型，然后分别通过Landweber算法、共轭梯度算法和截断奇异值算法进行成像仿真。通过结果对比表明，12个电极的三维电阻层析成像模型为最佳选择。
4、将主成分分析方法应用于气固两相流的测量中。首先为了对电学成像的仿真图像进行识别，提出了一种基于PCA的2D流型图像的特征提取方法。然后提出基于PCA的气力输送中脉动流的识别方法。通过与共轭梯度算法所成图像进行对比，证明该方法可以测量管道中的脉动流。最后提出一种基于PCA的ECT相关测速新方法。将ECT上下截面得到的原始数据运用PCA进行处理，运用相关原理，对水平管道中的粉煤灰进行流速测量。
Electrical tomography is one kind of nonintrusive and visible measurementtechnique.Electrical tomography has wide applications in clinical monitoring andindustrial multi-phase flow measurement for the advantages of being fast in response,nondestructive and low cost.
In this thesis, image reconstruction algorithms for electrical tomography,optimum design for electrodes and gas/solid two-phase flow measurement, have beeninvestigated. The main works and results are briefly listed as follows:
1. Image reconstruction algorithms are deeply studied. An improvedregularization reconstruction algorithm(HTIK)based on3D model is presented. Ingeneral, the regularization coefficient of iterative Tikhonov algorithm is difficult tochoose. Homotopic mapping is adopted to solve the problem. A quasi-Sigmoidmethod is used to adjust the regularization parameter. Thereafter sensitive field imagecan be reconstructed by deploying the resultant image vector as the initial value ofiteration Tikhonov algorithm. Both simulation and experimental results demonstratethat the proposed method can improve imaging quality obviously.
2. In order to improve the image quality of electrical tomography, an algorithmbased on the wavelet fusion method is proposed. Simulations are done by constructingan ECT sensor model using the finite element analysis software COMSOL. Theconjugate gradient and singular value decomposition algorithms are utilized toimplement image reconstruction.Then the wavelet-transform-based image fusionmethod is used for image processing. Both simulation and experimental resultsdemonstrate that the method can improve image quality of ECT obviously.Thensimulations are done by constructing an ERT sensor model using COMSOL. Thewavelet-transform-based image fusion method is used for image processing. Bothsimulation and experimental results demonstrate that the proposed method canimprove image quality of ERT.
3. To investigate the effect of the number of electrodes on the quality ofreconstructed images, simulations are done by constructing3D ERT sensors withdifferent number of electrodes,4,8,12,16,20,24and32, using the finite elementanalysis software COMSOL. The Landweber, conjugate gradient and truncated singular value decomposition algorithms are utilized to implement imagereconstruction. The simulation results demonstrate that the3D ERT modeling with12electrodes is the best choice.
4. The principal component analysis method is applied to gas/solid two phaseflow measurement. In order to identify simulation images,2D image processingmethod based on the principal component analysis is used. Then using PCA method,raw ECT data are used to identify the slug flow in pneumatic conveying system, andthese are confirmed through images reconstructed by conjugate gradient algorithm.Finally, this thesis presents a novel method of calculating the solid velocity based onPCA using cross correlation of twin-plane ECT data.The capacitance signals capturedfrom up-stream and down-stream electrodes are processed by principal componentanalysis. Then the velocity of coal ash in a horizontal tube can be calculated by thecross-correlation method.
本课题主要对电学成像的图像重建算法、电极优化及气固两相流的流动参数测量展开讨论，本文的主要工作及结果简单总结如下：
1、在深入讨论图像成像算法的基础上，提出一种基于三维模型的改进正则化的电阻成像算法（HTIK）。针对迭代Tikhonov算法系数选择问题，提出基于同伦映射的方法，并利用非线性函Sigmoid调节正则化参数，以获得的图像灰度值作为迭代Tikhonov法的初始值进行迭代，重建敏感场图像。仿真及实验结果表明，该方法有效地改进了电阻层析成像的成像质量。
2、为提高电学成像系统重建图像质量，提出基于图像融合的电学成像方法。通过电磁场有限元仿真软件COMSOL构建ECT传感器模型进行仿真研究，分别通过共轭梯度算法和奇异值分解算法重建图像，运用基于小波变换的图像融合方法对图像进行处理。仿真及实验结果表明该方法有效改进了ECT成像质量。然后用COMSOL建立ERT模型，运用小波融合算法进行融合，经过仿真和实验证明该方法可以提高ERT成像质量。
3、为了估计电极数与成像质量之间的关系，通过COMSOL分别建立4、8、12、16、20、24、28个电极的电阻层析成像的三维模型，然后分别通过Landweber算法、共轭梯度算法和截断奇异值算法进行成像仿真。通过结果对比表明，12个电极的三维电阻层析成像模型为最佳选择。
4、将主成分分析方法应用于气固两相流的测量中。首先为了对电学成像的仿真图像进行识别，提出了一种基于PCA的2D流型图像的特征提取方法。然后提出基于PCA的气力输送中脉动流的识别方法。通过与共轭梯度算法所成图像进行对比，证明该方法可以测量管道中的脉动流。最后提出一种基于PCA的ECT相关测速新方法。将ECT上下截面得到的原始数据运用PCA进行处理，运用相关原理，对水平管道中的粉煤灰进行流速测量。
Electrical tomography is one kind of nonintrusive and visible measurementtechnique.Electrical tomography has wide applications in clinical monitoring andindustrial multi-phase flow measurement for the advantages of being fast in response,nondestructive and low cost.
In this thesis, image reconstruction algorithms for electrical tomography,optimum design for electrodes and gas/solid two-phase flow measurement, have beeninvestigated. The main works and results are briefly listed as follows:
1. Image reconstruction algorithms are deeply studied. An improvedregularization reconstruction algorithm(HTIK)based on3D model is presented. Ingeneral, the regularization coefficient of iterative Tikhonov algorithm is difficult tochoose. Homotopic mapping is adopted to solve the problem. A quasi-Sigmoidmethod is used to adjust the regularization parameter. Thereafter sensitive field imagecan be reconstructed by deploying the resultant image vector as the initial value ofiteration Tikhonov algorithm. Both simulation and experimental results demonstratethat the proposed method can improve imaging quality obviously.
2. In order to improve the image quality of electrical tomography, an algorithmbased on the wavelet fusion method is proposed. Simulations are done by constructingan ECT sensor model using the finite element analysis software COMSOL. Theconjugate gradient and singular value decomposition algorithms are utilized toimplement image reconstruction.Then the wavelet-transform-based image fusionmethod is used for image processing. Both simulation and experimental resultsdemonstrate that the method can improve image quality of ECT obviously.Thensimulations are done by constructing an ERT sensor model using COMSOL. Thewavelet-transform-based image fusion method is used for image processing. Bothsimulation and experimental results demonstrate that the proposed method canimprove image quality of ERT.
3. To investigate the effect of the number of electrodes on the quality ofreconstructed images, simulations are done by constructing3D ERT sensors withdifferent number of electrodes,4,8,12,16,20,24and32, using the finite elementanalysis software COMSOL. The Landweber, conjugate gradient and truncated singular value decomposition algorithms are utilized to implement imagereconstruction. The simulation results demonstrate that the3D ERT modeling with12electrodes is the best choice.
4. The principal component analysis method is applied to gas/solid two phaseflow measurement. In order to identify simulation images,2D image processingmethod based on the principal component analysis is used. Then using PCA method,raw ECT data are used to identify the slug flow in pneumatic conveying system, andthese are confirmed through images reconstructed by conjugate gradient algorithm.Finally, this thesis presents a novel method of calculating the solid velocity based onPCA using cross correlation of twin-plane ECT data.The capacitance signals capturedfrom up-stream and down-stream electrodes are processed by principal componentanalysis. Then the velocity of coal ash in a horizontal tube can be calculated by thecross-correlation method.
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