电阻成像系统成像算法研究
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摘要
近十几年来,电阻层析成像(ERT)技术逐步进入到了工业应用研究阶段,它根据物体内部介质的电阻率(或电导率)的不同,通过对物体表面电流、电压的施加、测量来获知物体内部电导率的分布,进而重建出反应物体内部结构的图像,和传统的过程参数检测技术相比,具有非侵入,无辐射,成本低等许多的优点。因此它在生产过程监测,环境监测等诸多的领域存在着巨大的潜力,成为了国内外研究的热点。
电阻层析成像技术(Electrical Resistance Tomography,ERT)是基于电阻传感机理的过程成像技术。它具有非侵入性、成本低、结构简单、实时性好等优点,可获取过程参数的二维/三维图像信息。研究报告显示该项技术在工业过程检测与控制中具有广阔应用前景。
本文主要以电阻层析成像技术在两相流动生产过程中的可视化监测应用和浓度测量为研究背景,对ERT图像重建算法进行了较为深入的研究。本文的主要工作总结如下:
(1)对ERT系统的基本原理、系统构成、基本特点和应用范围进行了较为详尽的分析,对它的应用现状和发展前景做了较全面的总结,阐述了ERT技术独特的优点和应用前景。
(2)编制了ERT仿真软件包,它支持圆形场域剖分,剖分精度可调,多种流型设置,有限元方法计算,灵敏度计算,支持多种成像算法。
(3)对国内外目前常用的几种ERT图像重建算法进行深入研究,包括等位线反投影算法,灵敏度系数算法,单步基洪诺夫算法(Tikhonov Regularization),Landweber算法,牛顿拉弗逊(Newton-Raphson)算法,多元线性回归算法。比较各种成像算法的特点,为改进算法打下基础。
(4)通过LBP算法和MLRR算法的仿真对比,提出了一种改进的迭代算法,即以线性回归作为迭代初值的迭代算法。
(5)目前,还没有可靠的迭代终止规则,只能靠固定迭代次数来终止迭代过程。对五种典型流型按照占空比,空间图像误差不同分别进行迭代次数的优化研究,减少迭代次数意味着减少了图像重建的时间,为实时成像提供了可能。
(6)用经典的Landweber迭代算法和Newton-Raphson迭代算法以及MLRR迭代算法分别进行图像重建,用空间图像误差作为重建质量的评价指标,结果表明MLRR迭代算法对流型2、流型3、流型4、流型5重建时,重建图像质量明显好于Landweber迭代算法和Newton-Raphson迭代算法,为流型辨识提供了依据和方便。
(7)当测量数据施加噪声干扰时,仿真结果表明MLRR迭代算法重建质量好于Landweber迭代算法和Newton-Raphson迭代算法,但MLRR迭代算法对噪声干扰的敏感程度高于Landweber迭代算法和Newton-Raphson迭代算法。
(8)用实际测量数据进行图像重建对比,结果表明MLRR迭代算法成像效果明显要于其它算法,MLRR迭代算法完全可以应用于实时成像。
In the recent decades,Electrical Resistance Tomography technology has been developing rapidly and now has come to the stage of industrial applications. It reconstructs the internal conductivity(or impedance) profile of an object from boundary measurements of voltages and the corresponding current fluxes. ERT has several advantages over other traditional process-parameter-measurement techniques, such as its non-invasion,low cost, lack of radiation, visualization, Now the application research of the ERT technique has been considered as a research focus all over the world.
Electrical Resistance Tomography (ERT), which is based on resistance sensing principle, is a promising technology of process tomography. It has the advantage of being non-intrusive, low cost, simple structure and fast response, which can acquire 2D/3D image information of process parameters. Research reports have showed that the technique has a broad application prospect for the detection and control of industrial process.
This thesis focuses on the research of ERT image reconstruction algorithm, which based on the visible monitor and concentration measuring of ERT technology in the process of two-phase flow. The main contributions and conclusions of this thesis are as follows:
(1) Carried on a exhaustive analysis on the basic principle,the system composition, the essentialfeature and the application scope of the ERT system. Make the comprehensive summary on the present application situation and the prospects for development and elaborate the merit and the application prospect of the ERT technology.
(2) A simulating software of Electrical Resistance Tomography of industrial processing pipe. It has many functions as follows:auto finite element mesh of circular area,precision-adjusted mesh,multi-type of flow,Finite Element Method(FEM) , calculating sensitive and supporting many Image Reconstruction methods.
(3) Conduct the deep research to the present commonly used several kind of ERT image reconstruction algorithm, including Linear Back Projection algorithm, Sensitivity Theorem method algorithm,Tikhonov Regularization algorithm,Landweber algorithm,Newton-Raphson algorithm, MLRR algorithm.Compared with each kind of image formation algorithm characteristic, build the foundation for the improvement algorithm.
(4) Comparing of simulation experiment for LBP algorithm and MLRR algorithm, an ameliorated iterative algorithm is proposed whose first iterative step value comes from MLRR algorithm.
(5) For the moment, there aren't reliable rules to stop the iterative step. So, we have to stop it by certain iterative times. This thesis simulates the five typical flow regimes but different occupied special ratio to optimize iterative times. Decreasing the iterative times means the image reconstruction time is short and it provides the probability for real time image reconstruction.
(6) This thesis makes a contrast between the popular Landweber iterative and the Newton-Raphson iterative as the MLRR iterative. Numerical simulation results show that MLRR iterative is much better than the Landweber iterative and Newton-Raphson iterative for No.2 flow regime, No.3 flow regime, No.4 flow regime and No.5 flow regime, which provides the gist and convenience for the flow regime identification.
(7) When the measurement data are perturbed, numerical simulation results show that MLRR iterative is better than the Landweber iterative and Newton-Raphson iterative. But the sensitivities of MLRR iterative to such perturb are higher than Landweber iterative and Newton-Raphson iterative.
(8) Contrasted image reconstruction with the actual measurement data, the results show that MLRR iterative is better than other algorithms. MLRR iterative algorithm can be applied to real-time imaging.
电阻层析成像技术(Electrical Resistance Tomography,ERT)是基于电阻传感机理的过程成像技术。它具有非侵入性、成本低、结构简单、实时性好等优点,可获取过程参数的二维/三维图像信息。研究报告显示该项技术在工业过程检测与控制中具有广阔应用前景。
本文主要以电阻层析成像技术在两相流动生产过程中的可视化监测应用和浓度测量为研究背景,对ERT图像重建算法进行了较为深入的研究。本文的主要工作总结如下:
(1)对ERT系统的基本原理、系统构成、基本特点和应用范围进行了较为详尽的分析,对它的应用现状和发展前景做了较全面的总结,阐述了ERT技术独特的优点和应用前景。
(2)编制了ERT仿真软件包,它支持圆形场域剖分,剖分精度可调,多种流型设置,有限元方法计算,灵敏度计算,支持多种成像算法。
(3)对国内外目前常用的几种ERT图像重建算法进行深入研究,包括等位线反投影算法,灵敏度系数算法,单步基洪诺夫算法(Tikhonov Regularization),Landweber算法,牛顿拉弗逊(Newton-Raphson)算法,多元线性回归算法。比较各种成像算法的特点,为改进算法打下基础。
(4)通过LBP算法和MLRR算法的仿真对比,提出了一种改进的迭代算法,即以线性回归作为迭代初值的迭代算法。
(5)目前,还没有可靠的迭代终止规则,只能靠固定迭代次数来终止迭代过程。对五种典型流型按照占空比,空间图像误差不同分别进行迭代次数的优化研究,减少迭代次数意味着减少了图像重建的时间,为实时成像提供了可能。
(6)用经典的Landweber迭代算法和Newton-Raphson迭代算法以及MLRR迭代算法分别进行图像重建,用空间图像误差作为重建质量的评价指标,结果表明MLRR迭代算法对流型2、流型3、流型4、流型5重建时,重建图像质量明显好于Landweber迭代算法和Newton-Raphson迭代算法,为流型辨识提供了依据和方便。
(7)当测量数据施加噪声干扰时,仿真结果表明MLRR迭代算法重建质量好于Landweber迭代算法和Newton-Raphson迭代算法,但MLRR迭代算法对噪声干扰的敏感程度高于Landweber迭代算法和Newton-Raphson迭代算法。
(8)用实际测量数据进行图像重建对比,结果表明MLRR迭代算法成像效果明显要于其它算法,MLRR迭代算法完全可以应用于实时成像。
In the recent decades,Electrical Resistance Tomography technology has been developing rapidly and now has come to the stage of industrial applications. It reconstructs the internal conductivity(or impedance) profile of an object from boundary measurements of voltages and the corresponding current fluxes. ERT has several advantages over other traditional process-parameter-measurement techniques, such as its non-invasion,low cost, lack of radiation, visualization, Now the application research of the ERT technique has been considered as a research focus all over the world.
Electrical Resistance Tomography (ERT), which is based on resistance sensing principle, is a promising technology of process tomography. It has the advantage of being non-intrusive, low cost, simple structure and fast response, which can acquire 2D/3D image information of process parameters. Research reports have showed that the technique has a broad application prospect for the detection and control of industrial process.
This thesis focuses on the research of ERT image reconstruction algorithm, which based on the visible monitor and concentration measuring of ERT technology in the process of two-phase flow. The main contributions and conclusions of this thesis are as follows:
(1) Carried on a exhaustive analysis on the basic principle,the system composition, the essentialfeature and the application scope of the ERT system. Make the comprehensive summary on the present application situation and the prospects for development and elaborate the merit and the application prospect of the ERT technology.
(2) A simulating software of Electrical Resistance Tomography of industrial processing pipe. It has many functions as follows:auto finite element mesh of circular area,precision-adjusted mesh,multi-type of flow,Finite Element Method(FEM) , calculating sensitive and supporting many Image Reconstruction methods.
(3) Conduct the deep research to the present commonly used several kind of ERT image reconstruction algorithm, including Linear Back Projection algorithm, Sensitivity Theorem method algorithm,Tikhonov Regularization algorithm,Landweber algorithm,Newton-Raphson algorithm, MLRR algorithm.Compared with each kind of image formation algorithm characteristic, build the foundation for the improvement algorithm.
(4) Comparing of simulation experiment for LBP algorithm and MLRR algorithm, an ameliorated iterative algorithm is proposed whose first iterative step value comes from MLRR algorithm.
(5) For the moment, there aren't reliable rules to stop the iterative step. So, we have to stop it by certain iterative times. This thesis simulates the five typical flow regimes but different occupied special ratio to optimize iterative times. Decreasing the iterative times means the image reconstruction time is short and it provides the probability for real time image reconstruction.
(6) This thesis makes a contrast between the popular Landweber iterative and the Newton-Raphson iterative as the MLRR iterative. Numerical simulation results show that MLRR iterative is much better than the Landweber iterative and Newton-Raphson iterative for No.2 flow regime, No.3 flow regime, No.4 flow regime and No.5 flow regime, which provides the gist and convenience for the flow regime identification.
(7) When the measurement data are perturbed, numerical simulation results show that MLRR iterative is better than the Landweber iterative and Newton-Raphson iterative. But the sensitivities of MLRR iterative to such perturb are higher than Landweber iterative and Newton-Raphson iterative.
(8) Contrasted image reconstruction with the actual measurement data, the results show that MLRR iterative is better than other algorithms. MLRR iterative algorithm can be applied to real-time imaging.
引文
1.魏颖.电阻层析成象技术及其在两相流测量中的应用研究[D],沈阳东北大学,2001.
2.邹璐.电阻层析成像系统仿真建模研究[D],北京清华大学,2002.
3.徐苓安等.过程层析成像技术的研究现状和发展趋势[J],中国仪器仪表学会过程检测控制分会第三届年会论文集,过程控制仪表及系统,1995:63-72.
4.马艺馨,徐苓安,姜常珍.电阻层析成像技术的研究[J],仪器仪表学报,2001,22(4):195-198.
5.D.C.Barber and B.H.Brown.Applied potential tomography[J],Journal Physics E:Science Instrument,1984,17(3):723-733.
6.Y Yan and J Ma.Measurement of particulate velocity under stack-flow conditions[J],Meas.Sci.Technol.,2001,162(2):59-65.
7.R.B Scheler et al.Advanced Profile Gauge for Multiphase Systems[J],1st World Congress on industrial Process Tomography,Buxton,Greater Manchester,2008,45(2)14-17.
8.刘铁军.工程电导测试技术及其应用[D],杭州浙江大学,2006.
9.何永勃.电阻抗双模态层析成像技术研究[D],天津大学,2006.
10.冯慈璋著.《电磁场》[M],北京:人民教育出版社,1979,23-56.
11.倪光正,钱秀英.《电磁场数值计算》[M],北京:高等教育出版社,1996,12-35.
12.余金华,黄志尧,李海青.电阻层析成像有限元分析若干技巧[J],仪器仪表学报,2003,24(4):687-689.
13.邓娟,王妍,任超世.EIT图像重建算法的进展研究[J],中国医学装备,2007,4(6):1-4.
14.魏颖,夏靖波,王师.电阻层析成像敏感场的仿真计算[J],沈阳东北大学学报(自然科学版),2000,21(4):372-375.
15.甘庆玉,电容电阻复合成像系统敏感场特性分析及重建研究[D],南宁广西大学,2005.
16.李英.电阻层析成像技术软场特性及图像重建算法研究[D],杭州浙江大学,2003.
17.丁永维,董峰.电阻层析成像技术图像重建算法概述[J],仪器仪表学报,2006,13(6):195-198.
18.FADIL SANTOSA and MICHAEL VOGELIUS,A Backprojection Algorithm for Electrical Impedance Imaging[J],SIAM J.APPL.MATH.1990,Vol50,No.1:216-243.
19.Tin-Su Pan and Andrew E.Yagle,Numerical Study of Multigrid Implementations of some Iterative Image Reconstruction Algorithms[J],IEEE TRANSACTIONS ON MEDICAL IMAGING,1991,10(4):758-769.
20.Juliusz B.Gajewski.Monitoring electrostatic flow noise for mass flow and mean velocity measurement in pneumatic transport[J].Journal of Electrostatics 1996,37(3):261-276.
21.Y.Yan and J Ma.Design and evaluation of electrostatic sensors for the measurement of velocity of pneumatically conveyed solids[J].Flow.Meas.Inst,2000,11(3):195-204.
22.黄嵩.电阻抗静态成像中正则化算法研究[D],重庆大学,2005.
23.W Q Yang and M S Beck.A Combined Capacitance Electrodynamic Transducer for Oil Pipeline Flow Velocity Measurement[J],IST,nchester,2001,46(2):13-25.
24.Wuliang Yin and Huaxiang Wang.An Image Reconstruction Algorithm Based on Matrix Direct Inverse for Electrical Resistance Tomography.Instrumentation and Measurement Technology Conference,May 2008,21(5):41-43.
25.马艺馨,董峰.迭代法求矩阵广义逆的ERT图像重建算法[J],自然科学进展,2001,11(4):409-413.
26.Tin-Su Pan and Andrew Eyagle,Acceleration of Landweber-Type Algorithms by Suppression of Projection on the Maximum Singular Vector[J],IEEE TRANSACTIONS ON MEDICAL IMAGING,1992,11(4):268-279.
27.王化祥,王超,陈磊.基于Landweber迭代的图像重建算法[J],信号处理,2000,16(4):354-356.
28.张军.求解不适定问题的快速Landweber迭代法[J],南京理工大学,数学杂志,2005,25(3):333-337.
29.崔晓会.电阻层析成像算法研究及其应用软件设计[D],天津大学,2005.
30.李英,黄志尧,冀海峰,李海青.两相流参数测量ERT图像重建算法的研究[J],浙江大学学报(工学版),2003,37(4):282-285.
2.邹璐.电阻层析成像系统仿真建模研究[D],北京清华大学,2002.
3.徐苓安等.过程层析成像技术的研究现状和发展趋势[J],中国仪器仪表学会过程检测控制分会第三届年会论文集,过程控制仪表及系统,1995:63-72.
4.马艺馨,徐苓安,姜常珍.电阻层析成像技术的研究[J],仪器仪表学报,2001,22(4):195-198.
5.D.C.Barber and B.H.Brown.Applied potential tomography[J],Journal Physics E:Science Instrument,1984,17(3):723-733.
6.Y Yan and J Ma.Measurement of particulate velocity under stack-flow conditions[J],Meas.Sci.Technol.,2001,162(2):59-65.
7.R.B Scheler et al.Advanced Profile Gauge for Multiphase Systems[J],1st World Congress on industrial Process Tomography,Buxton,Greater Manchester,2008,45(2)14-17.
8.刘铁军.工程电导测试技术及其应用[D],杭州浙江大学,2006.
9.何永勃.电阻抗双模态层析成像技术研究[D],天津大学,2006.
10.冯慈璋著.《电磁场》[M],北京:人民教育出版社,1979,23-56.
11.倪光正,钱秀英.《电磁场数值计算》[M],北京:高等教育出版社,1996,12-35.
12.余金华,黄志尧,李海青.电阻层析成像有限元分析若干技巧[J],仪器仪表学报,2003,24(4):687-689.
13.邓娟,王妍,任超世.EIT图像重建算法的进展研究[J],中国医学装备,2007,4(6):1-4.
14.魏颖,夏靖波,王师.电阻层析成像敏感场的仿真计算[J],沈阳东北大学学报(自然科学版),2000,21(4):372-375.
15.甘庆玉,电容电阻复合成像系统敏感场特性分析及重建研究[D],南宁广西大学,2005.
16.李英.电阻层析成像技术软场特性及图像重建算法研究[D],杭州浙江大学,2003.
17.丁永维,董峰.电阻层析成像技术图像重建算法概述[J],仪器仪表学报,2006,13(6):195-198.
18.FADIL SANTOSA and MICHAEL VOGELIUS,A Backprojection Algorithm for Electrical Impedance Imaging[J],SIAM J.APPL.MATH.1990,Vol50,No.1:216-243.
19.Tin-Su Pan and Andrew E.Yagle,Numerical Study of Multigrid Implementations of some Iterative Image Reconstruction Algorithms[J],IEEE TRANSACTIONS ON MEDICAL IMAGING,1991,10(4):758-769.
20.Juliusz B.Gajewski.Monitoring electrostatic flow noise for mass flow and mean velocity measurement in pneumatic transport[J].Journal of Electrostatics 1996,37(3):261-276.
21.Y.Yan and J Ma.Design and evaluation of electrostatic sensors for the measurement of velocity of pneumatically conveyed solids[J].Flow.Meas.Inst,2000,11(3):195-204.
22.黄嵩.电阻抗静态成像中正则化算法研究[D],重庆大学,2005.
23.W Q Yang and M S Beck.A Combined Capacitance Electrodynamic Transducer for Oil Pipeline Flow Velocity Measurement[J],IST,nchester,2001,46(2):13-25.
24.Wuliang Yin and Huaxiang Wang.An Image Reconstruction Algorithm Based on Matrix Direct Inverse for Electrical Resistance Tomography.Instrumentation and Measurement Technology Conference,May 2008,21(5):41-43.
25.马艺馨,董峰.迭代法求矩阵广义逆的ERT图像重建算法[J],自然科学进展,2001,11(4):409-413.
26.Tin-Su Pan and Andrew Eyagle,Acceleration of Landweber-Type Algorithms by Suppression of Projection on the Maximum Singular Vector[J],IEEE TRANSACTIONS ON MEDICAL IMAGING,1992,11(4):268-279.
27.王化祥,王超,陈磊.基于Landweber迭代的图像重建算法[J],信号处理,2000,16(4):354-356.
28.张军.求解不适定问题的快速Landweber迭代法[J],南京理工大学,数学杂志,2005,25(3):333-337.
29.崔晓会.电阻层析成像算法研究及其应用软件设计[D],天津大学,2005.
30.李英,黄志尧,冀海峰,李海青.两相流参数测量ERT图像重建算法的研究[J],浙江大学学报(工学版),2003,37(4):282-285.