ERT新型拓扑结构有限元模型优化
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摘要
为了提高电阻层析成像正问题计算精度,提出一种新型拓扑结构有限元模型:模型内部区域采取非均匀分布形式,模型外部区域模拟敏感场均匀分布时电流线的分布形式与分布密度,并以模型外部区域的起始层数和模型各层半径为变量(最外层除外),利用改进遗传算法优化新型拓扑结构有限元模型。实验结果表明:敏感场均匀分布时,优化后新型拓扑结构有限元模型相比传统按等间隔原理剖分的有限元模型及其改进模型,模型均方根值分别降低了84.175%、23.643%、20.943%,有效提高了正问题计算精度,降低了图像相对误差。
In order to improve the solution accuracy of the forward problem in electrical resistance tomography( ERT),a finite element model with novel topology is proposed. The inner region of the finite element model is subdivided non-uniformly,and the outer region simulates the distribution and density of the current lines in uniformly distributed sensitivity field. Besides,the initial number of layers in the outer region and the radius of each layer( except for the outermost layer) are taken as variables,the modified genetic algorithm( GA) is adopted to optimize the finite element model with novel topology. Experiment results show that for homogeneous sensitivity field,the optimized finite element model with novel topology reduces the root mean square( RMS) value of the model by 84. 175%,23. 643% and 20. 943% compared with the conventional equally-spaced finite element model and its improved version,thus enhances the solution accuracy of the forward problem effectively,and reduces the relative image error.
In order to improve the solution accuracy of the forward problem in electrical resistance tomography( ERT),a finite element model with novel topology is proposed. The inner region of the finite element model is subdivided non-uniformly,and the outer region simulates the distribution and density of the current lines in uniformly distributed sensitivity field. Besides,the initial number of layers in the outer region and the radius of each layer( except for the outermost layer) are taken as variables,the modified genetic algorithm( GA) is adopted to optimize the finite element model with novel topology. Experiment results show that for homogeneous sensitivity field,the optimized finite element model with novel topology reduces the root mean square( RMS) value of the model by 84. 175%,23. 643% and 20. 943% compared with the conventional equally-spaced finite element model and its improved version,thus enhances the solution accuracy of the forward problem effectively,and reduces the relative image error.
引文
[1]YIN W,PEYTON A J.A planar EMT system for the detection of faults on thin metallic plates[J].Measurement Science&Technology,2006,17(8):2130-2135.
[2]李柳,邵富群.电磁层析成像图像重建中的修正共轭梯度算法[J].仪器仪表学报,2010,31(3):655-658.LI L,SHAO F Q.Modified conjugate gradient algorithm for image reconstruction of electromagnetic tomography[J].Chinese Journal of Scientific Instrument,2010,31(3):655-658.
[3]尹武良,王奔,王化祥.电磁层析成像中基于半周期采样的数字解调方法[J].天津大学学报,2011,44(12):1118-1123.YIN W L,WANG B,WANG H X.Digital demodulation based on half-period sampling in electromagnetic tomography[J].Journal of Tianjin University,2011,44(12):1118-1123.
[4]刘泽,薛芳其,杨国银,等.电磁层析成像灵敏度矩阵实验测试方法[J].仪器仪表学报,2013,34(9):1982-1988.LIU Z,XUE F Q,YANG G Y,et al.Experimental measurement method of sensitivity matrix for electromagnetic tomography[J].Chinese Journal of Scientific Instrument,2013,34(9):1982-1988.
[5]MA X,PEYTON A J,HIGSON S R,et al.Hardware and software design for an electromagnetic induction tomography(EMT)system for high contrast metal process applications[J].Measurement Science&Technology,2006,17(1):111-118.
[6]DONG F,XU Y B.Application of electrical resistance tomography in two-phase flow measurement[J].Journal of Engineering Thermophysics,2006,27(5):791-794.
[7]李守晓,王化祥,范文茹,等.基于三维模型的改进正则化ERT成像算法[J].天津大学学报,2012,45(3):215-220.LI SH X,WANG H X,FAN W R,et al.Improved regularization reconstruction algorithm based on 3D model for ERT system[J].Journal of Tianjin University,2012,45(3):215-220.
[8]肖理庆,王化祥,韩成春.一种新型拓扑结构的电阻层析成像有限元模型[J].中国电机工程学报,2011,31(20):100-106.XIAO L Q,WANG H X,HAN CH CH.A new topology structure finite element model of electrical resistance tomography system[J].Proceedings of the CSEE,2011,31(20):100-106.
[9]肖理庆,王化祥.电阻层析成像有限元模型优化[J].天津大学学报,2014,47(1):54-60.XIAO L Q,WANG H X.Optimization of finite element model for electrical resistance tomography[J].Journal of Tianjin University,2014,47(1):54-60.
[10]陈晓艳,张静.采用阈值修正法改善电阻抗图像质量[J].中国生物医学工程学报,2011,30(4):481-486.CHEN X Y,ZHANG J.Using threshold correction method to improve the image quality of EIT[J].Chinese Journal of Biomedical Engineering,2011,30(4):481-486.
[11]王化祥,黄文瑞,范文茹.三维电阻抗成像的测量模式[J].天津大学学报,2012,45(8):729-734.WANG H X,HUANG W R,FAN W R.Measurement pattern for 3D electrical impedance tomography[J].Journal of Tianjin University,2012,45(8):729-734.
[12]陈德运,高明,李伟,等.新型ECT数据采集系统设计与实现[J].电机与控制学报,2013,17(5):87-92.CHEN D Y,GAO M,LI W,et al.Design and implementation of data acquisition system for the electrical capacitance tomography[J].Electric Machines and Control,2013,17(5):87-92.
[13]赵玉磊,郭宝龙,闫允一.电容层析成像技术的研究进展与分析[J].仪器仪表学报,2012,33(8):1909-1920.ZHAO Y L,GUO B L,YAN Y Y.Latest development and analysis of electrical capacitance tomography technology[J].Chinese Journal of Scientific Instrument,2012,33(8):1909-1920.
[14]陈江涛,刘石.融合电容层析成像先验信息的集合卡尔曼滤波统计估计[J].化学工程,2012,40(4):36-39.CHEN J T,LIU SH.Statistical estimation of ensemble Kalman filter fusion based on priori information approach in electrical capacitance tomography[J].Chemical Engineering,2012,40(4):36-39.
[15]CHEN Q,LIU S.Flame imaging in meso-scale porous media burner using electrical capacitance tomography[J].Chinese Journal of Chemical Engineering,2012,20(2):329-336.
[16]肖理庆,王化祥,程红林,等.改进遗传算法的ERT有限元模型拓扑结构优化[J].仪器仪表学报,2012,33(7):1490-1496.XIAO L Q,WANG H X,CHENG H L,et al.Topology optimization of ERT finite element model based on improved GA[J].Chinese Journal of Scientific Instrument,2012,33(7):1490-1496.
[17]陈德运,陈宇,王莉莉,等.基于改进Gauss-Newton的电容层析成像图像重建算法[J].电子学报,2009,37(4):739-743.CHEN D Y,CHEN Y,WANG L L,et al.A novel Gauss-Newton image reconstruction algorithm for electrical capacitance tomography system[J].Acta Electronica Sinica,2009,37(4):739-743.
[18]郭志恒,律德才,邵富群.基于差分灵敏度模型的电容层析成像图像重建方法[J].中国电机工程学报,2012,32(23):75-82.GUO ZH H,LV D C,SHAO F Q.Image reconstruction method for electrical capacitance tomography based on the difference sensitivity model[J].Proceedings of the CSEE,2012,32(23):75-82.
[19]范文茹,王化祥,郝魁红.基于两步迭代TV正则化的电阻抗图像重建算法[J].仪器仪表学报,2012,33(3):625-630.FAN W R,WANG H X,HAO K H.Two-step iterative TV regularization algorithm for image reconstruction of electrical impedance tomography[J].Chinese Journal of Scientific Instrument,2012,33(3):625-630.
[20]王莉莉,陈宇,陈德运,等.基于改进信赖域的电容层析成像图像重建算法[J].仪器仪表学报,2010,31(5):1076-1081.WANG L L CHEN Y,CHEN D Y,et al.Improved trust region based image reconstruction algorithm for electrical capacitance tomography system[J].Chinese Journal of Scientific Instrument,2010,31(5):1076-1081.
[21]杨琳,徐灿华,付峰,等.一种基于加权频差阻尼最小二乘的准静态EIT算法[J].仪器仪表学报,2013,34(8):1879-1885.YANG L,XU C H,FU F,et al.Quasi-static EIT algorithm based on weighted frequency difference damped least square[J].Chinese Journal of Scientific Instrument,2013,34(8):1879-1885.
[22]XUE Q,WANG H X,CUI Z Q,et al.Electrical capacitance tomography using an accelerated proximal gradient algorithm[J].Review of Scientific Instruments,2012,83(4):1-7.
[23]闵锐,杨倩倩,皮亦鸣,等.基于正则化正交匹配追踪的SAR层析成像[J].电子测量与仪器学报,2012,26(12):1069-1073.MIN R,YANG Q Q,PI Y M,et al.SAR tomography imaging based on regularized orthogonal matching pursuit[J].Journal of Electronic Measurement and Instrument,2012,26(12):1069-1073.
[2]李柳,邵富群.电磁层析成像图像重建中的修正共轭梯度算法[J].仪器仪表学报,2010,31(3):655-658.LI L,SHAO F Q.Modified conjugate gradient algorithm for image reconstruction of electromagnetic tomography[J].Chinese Journal of Scientific Instrument,2010,31(3):655-658.
[3]尹武良,王奔,王化祥.电磁层析成像中基于半周期采样的数字解调方法[J].天津大学学报,2011,44(12):1118-1123.YIN W L,WANG B,WANG H X.Digital demodulation based on half-period sampling in electromagnetic tomography[J].Journal of Tianjin University,2011,44(12):1118-1123.
[4]刘泽,薛芳其,杨国银,等.电磁层析成像灵敏度矩阵实验测试方法[J].仪器仪表学报,2013,34(9):1982-1988.LIU Z,XUE F Q,YANG G Y,et al.Experimental measurement method of sensitivity matrix for electromagnetic tomography[J].Chinese Journal of Scientific Instrument,2013,34(9):1982-1988.
[5]MA X,PEYTON A J,HIGSON S R,et al.Hardware and software design for an electromagnetic induction tomography(EMT)system for high contrast metal process applications[J].Measurement Science&Technology,2006,17(1):111-118.
[6]DONG F,XU Y B.Application of electrical resistance tomography in two-phase flow measurement[J].Journal of Engineering Thermophysics,2006,27(5):791-794.
[7]李守晓,王化祥,范文茹,等.基于三维模型的改进正则化ERT成像算法[J].天津大学学报,2012,45(3):215-220.LI SH X,WANG H X,FAN W R,et al.Improved regularization reconstruction algorithm based on 3D model for ERT system[J].Journal of Tianjin University,2012,45(3):215-220.
[8]肖理庆,王化祥,韩成春.一种新型拓扑结构的电阻层析成像有限元模型[J].中国电机工程学报,2011,31(20):100-106.XIAO L Q,WANG H X,HAN CH CH.A new topology structure finite element model of electrical resistance tomography system[J].Proceedings of the CSEE,2011,31(20):100-106.
[9]肖理庆,王化祥.电阻层析成像有限元模型优化[J].天津大学学报,2014,47(1):54-60.XIAO L Q,WANG H X.Optimization of finite element model for electrical resistance tomography[J].Journal of Tianjin University,2014,47(1):54-60.
[10]陈晓艳,张静.采用阈值修正法改善电阻抗图像质量[J].中国生物医学工程学报,2011,30(4):481-486.CHEN X Y,ZHANG J.Using threshold correction method to improve the image quality of EIT[J].Chinese Journal of Biomedical Engineering,2011,30(4):481-486.
[11]王化祥,黄文瑞,范文茹.三维电阻抗成像的测量模式[J].天津大学学报,2012,45(8):729-734.WANG H X,HUANG W R,FAN W R.Measurement pattern for 3D electrical impedance tomography[J].Journal of Tianjin University,2012,45(8):729-734.
[12]陈德运,高明,李伟,等.新型ECT数据采集系统设计与实现[J].电机与控制学报,2013,17(5):87-92.CHEN D Y,GAO M,LI W,et al.Design and implementation of data acquisition system for the electrical capacitance tomography[J].Electric Machines and Control,2013,17(5):87-92.
[13]赵玉磊,郭宝龙,闫允一.电容层析成像技术的研究进展与分析[J].仪器仪表学报,2012,33(8):1909-1920.ZHAO Y L,GUO B L,YAN Y Y.Latest development and analysis of electrical capacitance tomography technology[J].Chinese Journal of Scientific Instrument,2012,33(8):1909-1920.
[14]陈江涛,刘石.融合电容层析成像先验信息的集合卡尔曼滤波统计估计[J].化学工程,2012,40(4):36-39.CHEN J T,LIU SH.Statistical estimation of ensemble Kalman filter fusion based on priori information approach in electrical capacitance tomography[J].Chemical Engineering,2012,40(4):36-39.
[15]CHEN Q,LIU S.Flame imaging in meso-scale porous media burner using electrical capacitance tomography[J].Chinese Journal of Chemical Engineering,2012,20(2):329-336.
[16]肖理庆,王化祥,程红林,等.改进遗传算法的ERT有限元模型拓扑结构优化[J].仪器仪表学报,2012,33(7):1490-1496.XIAO L Q,WANG H X,CHENG H L,et al.Topology optimization of ERT finite element model based on improved GA[J].Chinese Journal of Scientific Instrument,2012,33(7):1490-1496.
[17]陈德运,陈宇,王莉莉,等.基于改进Gauss-Newton的电容层析成像图像重建算法[J].电子学报,2009,37(4):739-743.CHEN D Y,CHEN Y,WANG L L,et al.A novel Gauss-Newton image reconstruction algorithm for electrical capacitance tomography system[J].Acta Electronica Sinica,2009,37(4):739-743.
[18]郭志恒,律德才,邵富群.基于差分灵敏度模型的电容层析成像图像重建方法[J].中国电机工程学报,2012,32(23):75-82.GUO ZH H,LV D C,SHAO F Q.Image reconstruction method for electrical capacitance tomography based on the difference sensitivity model[J].Proceedings of the CSEE,2012,32(23):75-82.
[19]范文茹,王化祥,郝魁红.基于两步迭代TV正则化的电阻抗图像重建算法[J].仪器仪表学报,2012,33(3):625-630.FAN W R,WANG H X,HAO K H.Two-step iterative TV regularization algorithm for image reconstruction of electrical impedance tomography[J].Chinese Journal of Scientific Instrument,2012,33(3):625-630.
[20]王莉莉,陈宇,陈德运,等.基于改进信赖域的电容层析成像图像重建算法[J].仪器仪表学报,2010,31(5):1076-1081.WANG L L CHEN Y,CHEN D Y,et al.Improved trust region based image reconstruction algorithm for electrical capacitance tomography system[J].Chinese Journal of Scientific Instrument,2010,31(5):1076-1081.
[21]杨琳,徐灿华,付峰,等.一种基于加权频差阻尼最小二乘的准静态EIT算法[J].仪器仪表学报,2013,34(8):1879-1885.YANG L,XU C H,FU F,et al.Quasi-static EIT algorithm based on weighted frequency difference damped least square[J].Chinese Journal of Scientific Instrument,2013,34(8):1879-1885.
[22]XUE Q,WANG H X,CUI Z Q,et al.Electrical capacitance tomography using an accelerated proximal gradient algorithm[J].Review of Scientific Instruments,2012,83(4):1-7.
[23]闵锐,杨倩倩,皮亦鸣,等.基于正则化正交匹配追踪的SAR层析成像[J].电子测量与仪器学报,2012,26(12):1069-1073.MIN R,YANG Q Q,PI Y M,et al.SAR tomography imaging based on regularized orthogonal matching pursuit[J].Journal of Electronic Measurement and Instrument,2012,26(12):1069-1073.