电阻层析成像有限元模型优化
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摘要
为了提高电阻层析成像正问题计算精度,以有限元模型次最外层半径为变量,以敏感场均匀分布时模型均方根值的倒数为适应度函数,利用求解低维多峰值函数优化问题的改进遗传算法,优化模拟敏感场内电流线分布密度与分布形式的新型拓扑结构有限元模型,最后以各峰值点对应的中心流模型均方根值为误差函数,选择新型拓扑结构有限元模型次最外层半径的最优值.仿真实验结果表明,相同实验条件下,相比优化前新型拓扑结构有限元模型、传统按等间隔原理剖分的有限元模型及其改进模型,优化后有限元模型在敏感场均匀分布时模型均方根值分别降低了32.002 5%、83.395 8%和44.760 5%,有效提高了电阻层析成像正问题计算精度与图像重建质量.
Aiming to improve the accuracy of solving the forward problem in electrical resistance tomography(ERT),the new topological finite element model was optimized in this paper. Using the radius of the second outermost layer of the model as a variable,and the reciprocal of the root mean square value of a homogeneous sensitive field distribution as a fitness function,the improved genetic algorithm for solving low-dimension multi-peak function optimization problem was adopted to optimize the new topological finite element model which simulated the current line density and distribution of the sensitive field. Finally,the root mean square value of the core flow model corresponding to each peak point was used as an error function to determine the optimal value of the radius of the second outermost layer of the model. Simulation results demonstrate that,compared to the unoptimized topological finite element model,the conventional finite element model based on uniformly-spaced dissection and its modified version,the optimized model reduce the root mean square value of a homogeneous sensitive field distribution by 32.002 5%,83.395 8% and 44.760 5%,effectively improves both the accuracy of solving the forward problem and the quality of image reconstruction under the same experimental conditions.
Aiming to improve the accuracy of solving the forward problem in electrical resistance tomography(ERT),the new topological finite element model was optimized in this paper. Using the radius of the second outermost layer of the model as a variable,and the reciprocal of the root mean square value of a homogeneous sensitive field distribution as a fitness function,the improved genetic algorithm for solving low-dimension multi-peak function optimization problem was adopted to optimize the new topological finite element model which simulated the current line density and distribution of the sensitive field. Finally,the root mean square value of the core flow model corresponding to each peak point was used as an error function to determine the optimal value of the radius of the second outermost layer of the model. Simulation results demonstrate that,compared to the unoptimized topological finite element model,the conventional finite element model based on uniformly-spaced dissection and its modified version,the optimized model reduce the root mean square value of a homogeneous sensitive field distribution by 32.002 5%,83.395 8% and 44.760 5%,effectively improves both the accuracy of solving the forward problem and the quality of image reconstruction under the same experimental conditions.
引文
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[12]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 Xiaoyan,Zhang Jing.Using threshold correction method to improve the image quality of EIT[J].Chinese Journal of Biomedical Engineering,2011,30(4):481-486(in Chinese).
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[14]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 Wuliang,Wang Ben,Wang Huaxiang.Digital demodulation based on half-period sampling in electromagnetic tomography[J].Journal of Tianjin University,2011,44(12):1118-1123(in Chinese).
[15]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.
[16]王超,张军青,徐传进.基于FPGA的EMT系统设计[J].天津大学学报,2011,44(2):95-100.Wang Chao,Zhang Junqing,Xu Chuanjin.Design of an electromagnetic tomography(EMT)system based on FPGA[J].Journal of Tianjin University,2011,44(2):95-100(in Chinese).
[17]Xiao Liqing,Wang Huaxiang,Xu Xiaoju.Research on improved genetic algorithm for low-dimension and multimodal function optimization[C]//IEEE Chinese Control and Decision Conference.Mianyang,China,2011:3918-3922.
[18]Xue Qian,Wang Huaxiang,Cui Ziqiang,et al.Electrical capacitance tomography using an accelerated proximal gradient algorithm[J].Review of Scientific Instruments,2012,83(4):1-7.
[2]陈德运,陈宇,王莉莉,等.基于改进GaussNewton的电容层析成像图像重建算法[J].电子学报,2009,37(4):739-743.Chen Deyun,Chen Yu,Wang Lili,et al.A novel Gauss-Newton image reconstruction algorithm for electrical capacitance tomography system[J].Acta Electronica Sinica,2009,37(4):739-743(in Chinese).
[3]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 Jiangtao,Liu Shi.Statistical estimation of ensemble Kalman filter fusion based on priori information approach in electrical capacitance tomography[J].Chemical Engineering,2012,40(4):36-39(in Chinese).
[4]Yang W Q,Beck M S,Byars M.Electrical capacitance tomography-from design to applications[J].Measurement&Control,1995,28(9):261-266.
[5]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 Liqing,Wang Huaxiang,Cheng Honglin,et al.Topology optimization of ERT finite element model based on improved GA[J].Chinese Journal of Scientific Instrument,2012,33(7):1490-1496(in Chinese).
[6]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 Liqing,Wang Huaxiang,Han Chengchun.A new topology structure finite element model of electrical resistance tomography system[J].Proceedings of the CSEE,2011,31(20):100-106(in Chinese).
[7]张玲玲,王化祥,范文茹.基于1范数的电阻层析成像图像重建算法[J].天津大学学报,2011,44(9):786-790.Zhang Lingling,Wang Huaxiang,Fan Wenru.Image reconstruction algorithm based on 1-norm for electrical resistance tomography[J].Journal of Tianjin University,2011,44(9):786-790(in Chinese).
[8]Daily W,Ramirez A.Electrical resistance tomography[J].Society of Exploration Geophysicists,2004,23(5):438-442.
[9]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 Shouxiao,Wang Huaxiang,Fan Wenru,et al.Improved regularization reconstruction algorithm based on3D model for ERT system[J].Journal of Tianjin University,2012,45(3):215-220(in Chinese).
[10]Dong Feng,Xu Yanbin.Application of electrical resistance tomography in two-phase flow measurement[J].Journal of Engineering Thermophysics,2006,27(5):791-794.
[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 Huaxiang,Huang Wenrui,Fan Wenru.Measurement pattern for 3D electrical impedance tomography[J].Journal of Tianjin University,2012,45(8):729-734(in Chinese).
[12]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 Xiaoyan,Zhang Jing.Using threshold correction method to improve the image quality of EIT[J].Chinese Journal of Biomedical Engineering,2011,30(4):481-486(in Chinese).
[13]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.
[14]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 Wuliang,Wang Ben,Wang Huaxiang.Digital demodulation based on half-period sampling in electromagnetic tomography[J].Journal of Tianjin University,2011,44(12):1118-1123(in Chinese).
[15]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.
[16]王超,张军青,徐传进.基于FPGA的EMT系统设计[J].天津大学学报,2011,44(2):95-100.Wang Chao,Zhang Junqing,Xu Chuanjin.Design of an electromagnetic tomography(EMT)system based on FPGA[J].Journal of Tianjin University,2011,44(2):95-100(in Chinese).
[17]Xiao Liqing,Wang Huaxiang,Xu Xiaoju.Research on improved genetic algorithm for low-dimension and multimodal function optimization[C]//IEEE Chinese Control and Decision Conference.Mianyang,China,2011:3918-3922.
[18]Xue Qian,Wang Huaxiang,Cui Ziqiang,et al.Electrical capacitance tomography using an accelerated proximal gradient algorithm[J].Review of Scientific Instruments,2012,83(4):1-7.