电容层析成像图像重建算法研究及敏感场仿真分析
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摘要
电容层析成像技术是基于电容敏感的原理的过程层析成像技术。与其他的检测技术相比该技术具有非辐射、非侵入、结构简单、成本低、适用范围广、安全性能好等优点,就目前来说,已经成为层析成像技术发展的主要的研究方向之一,也是一种极具发展潜力的测量技术。
本课题的研究工作主要分为两个部分：其中之一就是对图像重建算法的研究,另外就是对电容传感器敏感场的仿真。主要研究工作和结果如下所示：
1.通过编写软件程序,实现了目前常见的几种算法的成像实验,例如：线性反投影算法、迭代算法、正则化优化修正算法等。将这几种成像算法得到的图像重建结果进行了对比,并分别对这几种算法在成像质量及速率等方面进行分析。
2.通过对目前成像算法的研究发现图像成像的质量还有待于进一步的提高,并在此基础上提出了一种基于QR分解的电容层析成像图像重建算法。这种方法是首先把成像系统的正问题的数学模型进行规范化和Tikhonov正则化处理后,再把QR分解的思想代入到成像方程的求解中,最终可以得到图像重建的结果。
3.使用ANSYS有限元仿真软件,利用其静电场的分析模块功能对ECT电容传感器的敏感场进行模拟仿真。通过仿真,得到了电容传感器模型的节点电位等值云分布图以及电场力矢量分布图,并对其仿真结果进行必要地分析。
通过图像重建实验,将得到的几种图像重建算法的实验结果进行对比,利用本文提出的图像重建算法得到的重建结果在图像质量以及图像重建速率上都有不同程度的改善。
对传感器进行仿真,可以得到传感器模型的电位分布和电场矢量结果图。仿真结果体现了传感器敏感场特性,即在激励电极附近灵敏度高,而中心区域离激励电极较远灵敏度就比较低。
Electrical capacitance tomography is based on the principle of capacitance-sensitive process tomography technology, it has the advantages of no radiation, non-invasive, simple structure, low cost, broad scope and better security, as in the current main research directions development on process tomography, is a great development potential measurement.
The research topic is divided into two parts:one of them is researching on the image reconstruction algorithms, the other is sensitive to the capacitance sensor field simulation. The research work and results are as follows:
1. By writing software programs, in the several imaging algorithms are studied in this paper：linear back projection algorithm, iterative algorithm, regularization optimal correction algorithm etc., for example. This several imaging algorithms of image reconstruction results will be compared on the imaging quality and speed.
2. By studying the imaging algorithm will be found that the picture quality to be improved, based on QR decomposition of a kind of imaging algorithm is proposed, This is the first issue of the imaging model is standardized and Tikhonov regularization treatment, QR decomposition of thinking then substituted into the equation of the imaging, Final results of image reconstruction can be
3. Application of finite element simulation software ANSYS, we can use its electrostatic field analysis module to simulate the capacitance sensor sensitive, we can get potential distribution and electric intensity distribution of the simulation model, and we can analyses them.
Through the image reconstruction experiment, experimental results show the algorithm has advantages as regards the quality of reconstruction image and the reconstruction rate.
Through the sensor simulation, we can get potential distribution and electric intensity distribution of the simulation model, the simulation results reflect the characteristics of the sensor sensitivity field, high sensitivity in the incentive electrode nearby, center area far from incentive electrode sensitivity is lower.
本课题的研究工作主要分为两个部分：其中之一就是对图像重建算法的研究,另外就是对电容传感器敏感场的仿真。主要研究工作和结果如下所示：
1.通过编写软件程序,实现了目前常见的几种算法的成像实验,例如：线性反投影算法、迭代算法、正则化优化修正算法等。将这几种成像算法得到的图像重建结果进行了对比,并分别对这几种算法在成像质量及速率等方面进行分析。
2.通过对目前成像算法的研究发现图像成像的质量还有待于进一步的提高,并在此基础上提出了一种基于QR分解的电容层析成像图像重建算法。这种方法是首先把成像系统的正问题的数学模型进行规范化和Tikhonov正则化处理后,再把QR分解的思想代入到成像方程的求解中,最终可以得到图像重建的结果。
3.使用ANSYS有限元仿真软件,利用其静电场的分析模块功能对ECT电容传感器的敏感场进行模拟仿真。通过仿真,得到了电容传感器模型的节点电位等值云分布图以及电场力矢量分布图,并对其仿真结果进行必要地分析。
通过图像重建实验,将得到的几种图像重建算法的实验结果进行对比,利用本文提出的图像重建算法得到的重建结果在图像质量以及图像重建速率上都有不同程度的改善。
对传感器进行仿真,可以得到传感器模型的电位分布和电场矢量结果图。仿真结果体现了传感器敏感场特性,即在激励电极附近灵敏度高,而中心区域离激励电极较远灵敏度就比较低。
Electrical capacitance tomography is based on the principle of capacitance-sensitive process tomography technology, it has the advantages of no radiation, non-invasive, simple structure, low cost, broad scope and better security, as in the current main research directions development on process tomography, is a great development potential measurement.
The research topic is divided into two parts:one of them is researching on the image reconstruction algorithms, the other is sensitive to the capacitance sensor field simulation. The research work and results are as follows:
1. By writing software programs, in the several imaging algorithms are studied in this paper：linear back projection algorithm, iterative algorithm, regularization optimal correction algorithm etc., for example. This several imaging algorithms of image reconstruction results will be compared on the imaging quality and speed.
2. By studying the imaging algorithm will be found that the picture quality to be improved, based on QR decomposition of a kind of imaging algorithm is proposed, This is the first issue of the imaging model is standardized and Tikhonov regularization treatment, QR decomposition of thinking then substituted into the equation of the imaging, Final results of image reconstruction can be
3. Application of finite element simulation software ANSYS, we can use its electrostatic field analysis module to simulate the capacitance sensor sensitive, we can get potential distribution and electric intensity distribution of the simulation model, and we can analyses them.
Through the image reconstruction experiment, experimental results show the algorithm has advantages as regards the quality of reconstruction image and the reconstruction rate.
Through the sensor simulation, we can get potential distribution and electric intensity distribution of the simulation model, the simulation results reflect the characteristics of the sensor sensitivity field, high sensitivity in the incentive electrode nearby, center area far from incentive electrode sensitivity is lower.
引文
[1]石慧娴.循环流化床流动特性PIV测试和数值模拟[D].杭州：浙江大学,2003.
[2]牛刚.管内油气两相流动空泡份额的检测及波动特性的研究[D].上海：上海交通大学,2004.
[3]刘仁学,金锋,陆增喜.高炉喷吹煤粉总管质量流量的在线连续测量[J].钢铁,2000,35(1)：9-12.
[4]Y Yan. Mass Flow Measurement of Bulk Solids in Pneumatic Pipelines[J]. Meas. Sci. Technol.,1996,7(12):1687-1706.
[5]林宗虎,王栋,王树众.多相流的近期工程应用趋向[J].西安交通大学学报,2001,35(9)：886-890.
[6]M S Beck, A Plaskowski. Cross Correlation Flowmeters:Their Design and Application[M]. Bristol:Adam Hilger,1987.
[7]S M Huang, A B Plaskowski, C G Xie. Tomographic Imaging of Two-component Flow Using Capacitance Sensor[J].Journal of Physics E:Science Instrument,1989, 22(2):173-177.
[8]C G Xie, S M Huang, B S Hoyle. Electrical Capacitance Tomography for Flow Imaging:System Model for Development of Image Reconstruction Algorithms and Design of Primary Sensors[J].IEE Proceedings-G,1992,1399(1):89-98.
[9]G E Fasching, N S Smith. A Capacitive System for Three-dimensional Imaging of Fluidized Beds [J]. Review of Science Instruments,1991,62(9):2243-2251.
[10]S. Liu, W.Q. Yang, H. Wang. Investigation of square fluidized beds using capacitance tomography:preliminary results. Meas. Sci. Technol.,2001,12:1120～ 1125.
[11]Chen De yun, Yu Xiao yang, Zhao Xia. The capacitance measuring circuit of oil-water two-phase flows for electrical capacitance tomography system. Journal of circuit and system,2004,9(4):107～109.
[12]彭黎辉.电容层析成像技术关键技术研究[D].北京：清华大学,1998.
[13]陈德运,杨从晶等.电容层析成像系统传感器场域新的剖分方法及图像重建.传感技术学报,2003,(4)：409--414.
[14]王化祥,张立峰,朱学明.电容层析成像系统阵列电极的优化设计[J].天津大学学报,2003,36(3)：307-310.
[15]颜华,邵富群.电容层析成像传感器的优化设计[J].仪器仪表学报,2000,21(2)：139-141,145.
[16]邵富群,章勇高.考虑交互作用的ECT传感器的参数优化设计[J].东北大学学报,2003,24(2)：103-106.
[17]郭红星,余胜生,冯纪先.多电极电容传感器的参数优化设计[J].武汉大学学报,2000,46(5)：637-640.
[18]W Q Yang. Modeling of Capacitance Tomography Sensors[J]. IEE Proc Sci. Meas. Technol.,1997,144(5):203-208.
[19]颜华,邵富群,王师等.电容层析成像传感器软场性能分析,东北大学学报(自然科学版),1999,20(5)：457-460.
[20]何世钧,王化祥.电容层析成像系统的研究与应用,2005,28-30.
[21]G T Herman. Image Reconstruction from Projections:the Fundamentals of Computerized Tomography[M]. New York:Academic,1980.
[22]董向元,郭淑青等.电容层析成像技术及其应用.河南：黄河水利出版社,2008,115(3)：26-28.
[23]黄志尧.层析成象技术在多相流检测中的应用,浙江大学博士学位论文,1995
[24]C G Xie, M S Beck, et al.8-electrode capacitance system for two-component flow identification, Pa rt1:Tomographic flow imaging, IEEP roc. A,1989,136(4),173-183.
[25]苏邦良,张以恒,彭黎辉等.同步迭代图像重建技术在电容层析成像系统中的应用.清华大学学报,2000,40(9)：9-92.
[26]李海青,黄志尧.特种检测技术及应用.杭州：浙江大学出版社,2000.
[27]傅鹏,刘石,杨五强.两相流测量中电容层析成像图像重建的广义逆最小模解与线性反投影和迭代法的比较.仪器仪表学报,2001,22(1)：7-84.
[28]P C Hansen. Rank-Deficient and Discrete Ⅰll-Posed Problems[M].Philadelphia: SIAM,1998.
[29]Tikhonov A N, Arsenin V Y. Solution of Ⅰll-posed Problems. New York:John Wiley. 1977.
[30][德]]Frideerkuhnert.陈杰译.广义逆矩阵与正则化方法.北京：高等教育出版社,1984.
[31]王延平.信号复原与重建.南京：东南大学出版社,1992.
[32]赵进创,傅文利,张锦雄,李陶深.正则化优化修正的电容层析成像图像重建算法.仪器仪表学报,2004,25(1)：1-4.
[33]W Q Yang, D M Spink, T A York, HMccann. An Image-reconstruction Algorithm Based on Land Weber's Iteration Method for Electrical capacitance tomography. Meas. Sci. Technol.,1999,10:1065～1069.
[34]Tapp H S, Kemsley E K, et al., Image improvement in soft-field tomography through the use of chemo metrics. Meas. Sci. Technol.,1998,9:592～598.
[35]赵进创.电容层析成像技术及在两相流可视化监测中的应用研究.东北大学博士学位论文,68-71.
[36]张力,孟春玲,张扬.有限元法及ANSYS程序应用基础.北京：科学出版社,2008.
[2]牛刚.管内油气两相流动空泡份额的检测及波动特性的研究[D].上海：上海交通大学,2004.
[3]刘仁学,金锋,陆增喜.高炉喷吹煤粉总管质量流量的在线连续测量[J].钢铁,2000,35(1)：9-12.
[4]Y Yan. Mass Flow Measurement of Bulk Solids in Pneumatic Pipelines[J]. Meas. Sci. Technol.,1996,7(12):1687-1706.
[5]林宗虎,王栋,王树众.多相流的近期工程应用趋向[J].西安交通大学学报,2001,35(9)：886-890.
[6]M S Beck, A Plaskowski. Cross Correlation Flowmeters:Their Design and Application[M]. Bristol:Adam Hilger,1987.
[7]S M Huang, A B Plaskowski, C G Xie. Tomographic Imaging of Two-component Flow Using Capacitance Sensor[J].Journal of Physics E:Science Instrument,1989, 22(2):173-177.
[8]C G Xie, S M Huang, B S Hoyle. Electrical Capacitance Tomography for Flow Imaging:System Model for Development of Image Reconstruction Algorithms and Design of Primary Sensors[J].IEE Proceedings-G,1992,1399(1):89-98.
[9]G E Fasching, N S Smith. A Capacitive System for Three-dimensional Imaging of Fluidized Beds [J]. Review of Science Instruments,1991,62(9):2243-2251.
[10]S. Liu, W.Q. Yang, H. Wang. Investigation of square fluidized beds using capacitance tomography:preliminary results. Meas. Sci. Technol.,2001,12:1120～ 1125.
[11]Chen De yun, Yu Xiao yang, Zhao Xia. The capacitance measuring circuit of oil-water two-phase flows for electrical capacitance tomography system. Journal of circuit and system,2004,9(4):107～109.
[12]彭黎辉.电容层析成像技术关键技术研究[D].北京：清华大学,1998.
[13]陈德运,杨从晶等.电容层析成像系统传感器场域新的剖分方法及图像重建.传感技术学报,2003,(4)：409--414.
[14]王化祥,张立峰,朱学明.电容层析成像系统阵列电极的优化设计[J].天津大学学报,2003,36(3)：307-310.
[15]颜华,邵富群.电容层析成像传感器的优化设计[J].仪器仪表学报,2000,21(2)：139-141,145.
[16]邵富群,章勇高.考虑交互作用的ECT传感器的参数优化设计[J].东北大学学报,2003,24(2)：103-106.
[17]郭红星,余胜生,冯纪先.多电极电容传感器的参数优化设计[J].武汉大学学报,2000,46(5)：637-640.
[18]W Q Yang. Modeling of Capacitance Tomography Sensors[J]. IEE Proc Sci. Meas. Technol.,1997,144(5):203-208.
[19]颜华,邵富群,王师等.电容层析成像传感器软场性能分析,东北大学学报(自然科学版),1999,20(5)：457-460.
[20]何世钧,王化祥.电容层析成像系统的研究与应用,2005,28-30.
[21]G T Herman. Image Reconstruction from Projections:the Fundamentals of Computerized Tomography[M]. New York:Academic,1980.
[22]董向元,郭淑青等.电容层析成像技术及其应用.河南：黄河水利出版社,2008,115(3)：26-28.
[23]黄志尧.层析成象技术在多相流检测中的应用,浙江大学博士学位论文,1995
[24]C G Xie, M S Beck, et al.8-electrode capacitance system for two-component flow identification, Pa rt1:Tomographic flow imaging, IEEP roc. A,1989,136(4),173-183.
[25]苏邦良,张以恒,彭黎辉等.同步迭代图像重建技术在电容层析成像系统中的应用.清华大学学报,2000,40(9)：9-92.
[26]李海青,黄志尧.特种检测技术及应用.杭州：浙江大学出版社,2000.
[27]傅鹏,刘石,杨五强.两相流测量中电容层析成像图像重建的广义逆最小模解与线性反投影和迭代法的比较.仪器仪表学报,2001,22(1)：7-84.
[28]P C Hansen. Rank-Deficient and Discrete Ⅰll-Posed Problems[M].Philadelphia: SIAM,1998.
[29]Tikhonov A N, Arsenin V Y. Solution of Ⅰll-posed Problems. New York:John Wiley. 1977.
[30][德]]Frideerkuhnert.陈杰译.广义逆矩阵与正则化方法.北京：高等教育出版社,1984.
[31]王延平.信号复原与重建.南京：东南大学出版社,1992.
[32]赵进创,傅文利,张锦雄,李陶深.正则化优化修正的电容层析成像图像重建算法.仪器仪表学报,2004,25(1)：1-4.
[33]W Q Yang, D M Spink, T A York, HMccann. An Image-reconstruction Algorithm Based on Land Weber's Iteration Method for Electrical capacitance tomography. Meas. Sci. Technol.,1999,10:1065～1069.
[34]Tapp H S, Kemsley E K, et al., Image improvement in soft-field tomography through the use of chemo metrics. Meas. Sci. Technol.,1998,9:592～598.
[35]赵进创.电容层析成像技术及在两相流可视化监测中的应用研究.东北大学博士学位论文,68-71.
[36]张力,孟春玲,张扬.有限元法及ANSYS程序应用基础.北京：科学出版社,2008.