电阻层析成像（ERT）技术及其在两相流检测中的应用
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摘要
电阻层析成像技术（Electrical Resistance Tomography）是电学过程层析成像技术的一种，其理论基础为电磁场的似稳场理论。ERT技术具有低成本、无放射性、非侵入、可视化等特点。近年来，随着ERT技术在医疗、地质勘探、工业过程、多相流检测等领域的迅猛发展，它已经成为可视化检测领域的代表技术和研究热点。
在众多检测领域中，ERT技术在两相流检测中的应用，是最具前景的研究课题。但是，ERT技术发展至今，仍有一些理论难点和技术瓶颈制约着ERT技术在两相流检测中的发展和工程应用。例如：（1）对ERT敏感场的研究大多集中在二维模型，对三维模型的研究甚少。（2）对ERT传感器的频率特性研究，大多停留在理论分析层面，特别是“连接阻抗”对电阻/电导测量结果的影响，很少有量化的实验研究。（3）针对ERT系统的非线性特点，提出有效的传感器优化方法。在优化方法中急需解决在复杂流型中各优化指标之间的不可比性与矛盾性。（4）开发快速高精度的图像重建算法，特别是对人工智能算法的开发。（5）如何提高ERT系统的信噪比与实时性。针对上述问题，本文在前人研究的基础上，以ERT技术在气/液两相流检测中的应用为工程背景，以有限元仿真结果与实际测试数据为依据，对ERT技术进行了一系列的研究。本文的主要工作和贡献如下：
1.针对二维敏感场的局限性，通过Comsol软件建立三维模型，深入地探讨了改变电极尺寸对三维敏感场分布的影响，并对“边缘效应”作了量化的分析。另外，利用作者开发的ERT系统仿真软件，从灵敏度的角度对ERT敏感场的“软场”特性进行详细研究。
2.对电极的等效电路进行频率分析，设计了点电极阵列和矩形电极阵列两种ERT传感器，并借助于英国Manchester大学的“基于阻抗分析仪的ERT测试平台”在牛奶流中进行了频率特性测试。测试结果表明：改变电极面积，将直接改变电极的电池常数，从而影响对电阻/电导测量的结果。另外增加电极面积可以减小“连接阻抗”的影响，获得更稳定的频率特性。上述研究，为传感器的优化设计和图像重建的解释提供了依据和便利，更为电阻层析成像技术在食品检测领域的应用进行了有益的探索。
3.提出一种将正交设计与模糊分析相结合的ERT传感器的多指标优化方法。该方法运用模糊数学的思想通过定义ERT指标满意度（ERTIS）和ERT指标综合满意度（ERTIOS）的概念及构造它们的满意度函数，建立一种新的科学合理的模糊评价方法。它把量纲、物理意义完全不同的ERT传感器的各项指标，统一为对ERT指标的满意度，并在满意程度上具有可比性。通过ERTIOS对多指标正交实验中ERT传感器各性能指标进行模糊分析，将多指标正交实验问题转化为单指标的正交实验问题。选择ERT传感器的均匀性指标和相关系数指标作为优化目标，采用多指标正交设计安排实验。实验因素包括三维ERT传感器结构的三个主要参数，即：电极的高度、宽度以及电极数目。利用ERT指标综合满意度（ERTIOS）对实验结果进行模糊分析，从而得出优化的ERT传感器结构参数。实验结果表明：经过优化的ERT传感器可以同时获得分布较为均匀的敏感场和更高质量的图像，使ERT传感器的ERTIOS提高13.75%以上。与全面搭配法相比，实验次数减少66%。该方法实验因素主次顺序可知，实验结果直观可靠，具有很强的实用性。
4.为提高图像重建算法的精度，提出一种改进的粒子群算法用于ERT图像重建。该算法使用最小二乘支持向量机对若干典型流型的图像样本进行训练，进而预测由灵敏度矩阵产生的测量电压误差。基于该电压误差构建粒子群优化的适应度函数，为避免粒子群陷入局部最优，采用惯性因子的非线性动态调整方法和粒子速度的变异操作对标准粒子群优化进行改进。利用这个改进的粒子群优化算法搜索重建图像的最优解。仿真实验结果表明，本算法与Landweber算法相比，图像精度可提高近50%，对于一些典型流型，图像误差可降至20%以下。
5.为了提高ERT系统的信噪比和实时性，提出了一个基于双极性脉冲电流激励下的ERT传感器测量模型，用于电极化表面的暂态过程分析。分析发现由于电极化效应，在激励电极对之间产生大量积累电荷。这部分残留电势在高频激励时将产生巨大的测量噪声，它的衰减速度大大影响了ERT系统的实时性。因此设计了一种新的高速放电电路，用于消除这部分残留电势所产生的测量噪声。该电路具有放电速度快，放电门限可调，自动判别电荷极性等优点。最后，对该电路的去噪效果进行了理论推导和仿真实验。实验结果表明：该电路可以有效地消除激励电极间的残留电势，提高了ERT系统的信噪比。更重要的，该技术的应用显著的提高了ERT系统的实时性，对ERT技术实现工业在线检测具有重大意义。
6.设计并研发了一套基于双极性脉冲激励下的ERT实验系统。该实验系统采用16电极ERT传感器构成传感器单元，以单片机为核心构造测量与数据采集单元。在每个单元中，给出了各电路模块设计的指导性原则和需注意的问题，并提供了各电路模块的调试程序。最后采用乒乓球模拟气泡，给出了该实验系统在气/液两相流检测中的静态实验结果。
ERT (Electrical Resistance Tomography) is one of the electrical processtomography technologies and theoretically supported by the theory of the quasi-staticfield. ERT is characterized by lower costs, non-radioactive, non-invasive andvisualization, etc. In recent years, with the roaring development of ERT in medical,geological exploration, industrial process and multiphase flow detection fields, itbecomes a representative technology and a research hot-spot in the visualizationdetection field.
The application of ERT technology on two-phase flow is the most promisingresearch subject in many detection fields. However, during the development of ERTtechnology, there are some difficulties in theory and bottlenecks in technology, whichhave been hampering the development of ERT technology in two-phase flow detectionand engineering application. For example,(1) Research on sensing field of ERT hasmainly been focusing on two-dimensional model, with little research on threedimensional models.(2) Research on frequency characteristic of ERT sensor has beenempty of experimental support, most of which has been considered as theoreticalanalysis to a certain extent, especially the influence of “contact impedance” onresistance/conductance measurement result has hardly been subjected to quantitativeexperimental research.(3) Sensor optimization method is presented according tononlinear characteristic of ERT system. The incomparability and inconsistency betweenoptimized indexes for complex flow pattern are in need of solution.(4) The high speedand high precision algorithm for image reconstruction should be developed, with focuson development of artificial&intelligent algorithm.(5) How to improve theperformance of ERT system in terms of SNR and real time. For the subjects mentionedabove, based on the previous research, taking application of ERT technology onvapor/liquid two-phase flow detection as engineering background, using finite elementsimulation results and experimental data as reference, this paper presents a series ofresearch on ERT technology. The main work and contribution of this paper are asfollows:
1. Due to the limitations of2D sensing field, the author establishes athree-dimensional model with Comsol software. The model is used to discuss the effecton3D sensing field distribution by changing the electrode size, and make a quantitativeanalysis on "edge effect". In addition, through applying the ERT system simulation software developed by the author, detailed researches on the “Soft field” characteristicof ERT sensing field especially in the angle of sensitivity are made.
2. This paper presents frequency analysis of equivalent electric circuit ofelectrode and designs two ERT sensors with point electrode array and rectangularelectrode array and carries out testing of frequency characteristic in milk adopting ERTtesting platform based on impedance analyzer of Manchester University, the testingresult shows that change of electrode area shall directly change the cell constant ofelectrode so as to influence the results of resistance/conductance measurement. Inaddition, increase in electrode area shall reduce the influence on “Contact impedance”and ensure more stable frequency characteristic. The above mentioned researchprovides a basis and convenience for optimized design of sensors and illustrations ofimages reconstruction, and it can be considered as a useful exploration of theapplication of ERT technology for food detection.
3. A multiple index optimization method for ERT sensors is put forward whichcombines an orthogonal design and fuzzy analysis. This method first establishes a newscientific and proper fuzzy evaluation method using fuzzy mathematics to define ERTindex satisfaction (ERTIS) and ERT index overall satisfaction (ERTIOS) to create therelated satisfaction functions. It completes the unification of all ERT sensor indices,even those with completely different dimensions and physical meaning, by determiningthe comparable satisfaction of each of the ERT indices. Through using a fuzzy analysisagainst the satisfaction of a set of multiple index orthogonal experiments, the ERTIOSanalysis is developed which allows a set of multiple index orthogonal experiments to betransferred into a single index orthogonal experiment, where, the uniformity index andthe correlation coefficient index of the ERT sensor are set as the optimization objectives.The experiments are set up based on multi-index orthogonal design. The experimentalresults indicate that the method can derive an evenly distributed sensitivity field and abetter image with the optimized sensors, and improve the ERTIOS of the ERT sensorsby13.75%. Compared with the full collocation method, the numbers of experiments isreduced by66%. The primary and secondary orders of the parameters in this experimentcan also determined by this method, and the experimental results are intuitive, reliable,and practical.
4. In order to improve the precision of image reconstruction algorithm, animproved particle swarm optimization for ERT image reconstruction algorithm is putforward. Group image samples of some typical flow regimes are trained with the leastsquares support vector, and then it is forecasted that the voltage deviation generated by the approximate of the sensitivity matrix. On the basis of the deviation, the fitnessfunction in particle swarm optimization is established. Not only the nonlinearadjustment method for inertia factor but also the mutation operation of particles speed isused in the standard particle swarm optimization. The improved PSO algorithm is usedto search the optimal solution of the reconstructed image. The simulation result showsthat compared with Landweber algorithm, the image precision of new algorithm canimprove nearly50%, and the image error can decrease to less than20%for some typicalflow regimes.
5. In order to improve the real-time performance of ERT system, this paper putforward an ERT sensor model based on dual-polarity pulse current excitation, for thetransient time process analysis of electrode-electrolyte surface. It is found by analysisthat due to electrode polarization, a large number of accumulated charges would beproduced between excitation electrodes. This part of residual potentials is bound toproduce a huge measuring noise at a high frequency excitation. Its attenuation speedwill greatly affect the real-time performance of ERT system. Therefore, the authordesigns a new high-speed discharge circuit to eliminate the measuring noise generatedby this part of residual potentials. The circuit has such features as fast discharge speed,adjustable discharge threshold, and automatic discrimination of charge polarity etc. Atlast, a theory analysis and a simulation experiment are made on the denoising effect ofthe circuit. The results show that: the circuit can effectively eliminate the residualpotentials between excitation electrodes, to improve the signal to noise ratio of ERTsystem. More importantly, this technology can be applied to significantly improve theERT system in real-time performance, with great significances in on-line industrydetection to ERT technology.
6An ERT experimental system on the basis of dual-polarity pulse currentexcitation is developed. This system adopts a sensor unit comprised of16-electrodeERT sensors and takes Single-Chip Microcomputer as the core part to construct themeasurement and data collection unit. In each cell, the author provides each circuitmodule the design principles and problems to notice, which also tells how to debug eachcircuit module. Finally, the author gives static experimental results of the vapor/liquidtwo phase liquid detection of this system with tennis ball simulated air bubbles.
在众多检测领域中，ERT技术在两相流检测中的应用，是最具前景的研究课题。但是，ERT技术发展至今，仍有一些理论难点和技术瓶颈制约着ERT技术在两相流检测中的发展和工程应用。例如：（1）对ERT敏感场的研究大多集中在二维模型，对三维模型的研究甚少。（2）对ERT传感器的频率特性研究，大多停留在理论分析层面，特别是“连接阻抗”对电阻/电导测量结果的影响，很少有量化的实验研究。（3）针对ERT系统的非线性特点，提出有效的传感器优化方法。在优化方法中急需解决在复杂流型中各优化指标之间的不可比性与矛盾性。（4）开发快速高精度的图像重建算法，特别是对人工智能算法的开发。（5）如何提高ERT系统的信噪比与实时性。针对上述问题，本文在前人研究的基础上，以ERT技术在气/液两相流检测中的应用为工程背景，以有限元仿真结果与实际测试数据为依据，对ERT技术进行了一系列的研究。本文的主要工作和贡献如下：
1.针对二维敏感场的局限性，通过Comsol软件建立三维模型，深入地探讨了改变电极尺寸对三维敏感场分布的影响，并对“边缘效应”作了量化的分析。另外，利用作者开发的ERT系统仿真软件，从灵敏度的角度对ERT敏感场的“软场”特性进行详细研究。
2.对电极的等效电路进行频率分析，设计了点电极阵列和矩形电极阵列两种ERT传感器，并借助于英国Manchester大学的“基于阻抗分析仪的ERT测试平台”在牛奶流中进行了频率特性测试。测试结果表明：改变电极面积，将直接改变电极的电池常数，从而影响对电阻/电导测量的结果。另外增加电极面积可以减小“连接阻抗”的影响，获得更稳定的频率特性。上述研究，为传感器的优化设计和图像重建的解释提供了依据和便利，更为电阻层析成像技术在食品检测领域的应用进行了有益的探索。
3.提出一种将正交设计与模糊分析相结合的ERT传感器的多指标优化方法。该方法运用模糊数学的思想通过定义ERT指标满意度（ERTIS）和ERT指标综合满意度（ERTIOS）的概念及构造它们的满意度函数，建立一种新的科学合理的模糊评价方法。它把量纲、物理意义完全不同的ERT传感器的各项指标，统一为对ERT指标的满意度，并在满意程度上具有可比性。通过ERTIOS对多指标正交实验中ERT传感器各性能指标进行模糊分析，将多指标正交实验问题转化为单指标的正交实验问题。选择ERT传感器的均匀性指标和相关系数指标作为优化目标，采用多指标正交设计安排实验。实验因素包括三维ERT传感器结构的三个主要参数，即：电极的高度、宽度以及电极数目。利用ERT指标综合满意度（ERTIOS）对实验结果进行模糊分析，从而得出优化的ERT传感器结构参数。实验结果表明：经过优化的ERT传感器可以同时获得分布较为均匀的敏感场和更高质量的图像，使ERT传感器的ERTIOS提高13.75%以上。与全面搭配法相比，实验次数减少66%。该方法实验因素主次顺序可知，实验结果直观可靠，具有很强的实用性。
4.为提高图像重建算法的精度，提出一种改进的粒子群算法用于ERT图像重建。该算法使用最小二乘支持向量机对若干典型流型的图像样本进行训练，进而预测由灵敏度矩阵产生的测量电压误差。基于该电压误差构建粒子群优化的适应度函数，为避免粒子群陷入局部最优，采用惯性因子的非线性动态调整方法和粒子速度的变异操作对标准粒子群优化进行改进。利用这个改进的粒子群优化算法搜索重建图像的最优解。仿真实验结果表明，本算法与Landweber算法相比，图像精度可提高近50%，对于一些典型流型，图像误差可降至20%以下。
5.为了提高ERT系统的信噪比和实时性，提出了一个基于双极性脉冲电流激励下的ERT传感器测量模型，用于电极化表面的暂态过程分析。分析发现由于电极化效应，在激励电极对之间产生大量积累电荷。这部分残留电势在高频激励时将产生巨大的测量噪声，它的衰减速度大大影响了ERT系统的实时性。因此设计了一种新的高速放电电路，用于消除这部分残留电势所产生的测量噪声。该电路具有放电速度快，放电门限可调，自动判别电荷极性等优点。最后，对该电路的去噪效果进行了理论推导和仿真实验。实验结果表明：该电路可以有效地消除激励电极间的残留电势，提高了ERT系统的信噪比。更重要的，该技术的应用显著的提高了ERT系统的实时性，对ERT技术实现工业在线检测具有重大意义。
6.设计并研发了一套基于双极性脉冲激励下的ERT实验系统。该实验系统采用16电极ERT传感器构成传感器单元，以单片机为核心构造测量与数据采集单元。在每个单元中，给出了各电路模块设计的指导性原则和需注意的问题，并提供了各电路模块的调试程序。最后采用乒乓球模拟气泡，给出了该实验系统在气/液两相流检测中的静态实验结果。
ERT (Electrical Resistance Tomography) is one of the electrical processtomography technologies and theoretically supported by the theory of the quasi-staticfield. ERT is characterized by lower costs, non-radioactive, non-invasive andvisualization, etc. In recent years, with the roaring development of ERT in medical,geological exploration, industrial process and multiphase flow detection fields, itbecomes a representative technology and a research hot-spot in the visualizationdetection field.
The application of ERT technology on two-phase flow is the most promisingresearch subject in many detection fields. However, during the development of ERTtechnology, there are some difficulties in theory and bottlenecks in technology, whichhave been hampering the development of ERT technology in two-phase flow detectionand engineering application. For example,(1) Research on sensing field of ERT hasmainly been focusing on two-dimensional model, with little research on threedimensional models.(2) Research on frequency characteristic of ERT sensor has beenempty of experimental support, most of which has been considered as theoreticalanalysis to a certain extent, especially the influence of “contact impedance” onresistance/conductance measurement result has hardly been subjected to quantitativeexperimental research.(3) Sensor optimization method is presented according tononlinear characteristic of ERT system. The incomparability and inconsistency betweenoptimized indexes for complex flow pattern are in need of solution.(4) The high speedand high precision algorithm for image reconstruction should be developed, with focuson development of artificial&intelligent algorithm.(5) How to improve theperformance of ERT system in terms of SNR and real time. For the subjects mentionedabove, based on the previous research, taking application of ERT technology onvapor/liquid two-phase flow detection as engineering background, using finite elementsimulation results and experimental data as reference, this paper presents a series ofresearch on ERT technology. The main work and contribution of this paper are asfollows:
1. Due to the limitations of2D sensing field, the author establishes athree-dimensional model with Comsol software. The model is used to discuss the effecton3D sensing field distribution by changing the electrode size, and make a quantitativeanalysis on "edge effect". In addition, through applying the ERT system simulation software developed by the author, detailed researches on the “Soft field” characteristicof ERT sensing field especially in the angle of sensitivity are made.
2. This paper presents frequency analysis of equivalent electric circuit ofelectrode and designs two ERT sensors with point electrode array and rectangularelectrode array and carries out testing of frequency characteristic in milk adopting ERTtesting platform based on impedance analyzer of Manchester University, the testingresult shows that change of electrode area shall directly change the cell constant ofelectrode so as to influence the results of resistance/conductance measurement. Inaddition, increase in electrode area shall reduce the influence on “Contact impedance”and ensure more stable frequency characteristic. The above mentioned researchprovides a basis and convenience for optimized design of sensors and illustrations ofimages reconstruction, and it can be considered as a useful exploration of theapplication of ERT technology for food detection.
3. A multiple index optimization method for ERT sensors is put forward whichcombines an orthogonal design and fuzzy analysis. This method first establishes a newscientific and proper fuzzy evaluation method using fuzzy mathematics to define ERTindex satisfaction (ERTIS) and ERT index overall satisfaction (ERTIOS) to create therelated satisfaction functions. It completes the unification of all ERT sensor indices,even those with completely different dimensions and physical meaning, by determiningthe comparable satisfaction of each of the ERT indices. Through using a fuzzy analysisagainst the satisfaction of a set of multiple index orthogonal experiments, the ERTIOSanalysis is developed which allows a set of multiple index orthogonal experiments to betransferred into a single index orthogonal experiment, where, the uniformity index andthe correlation coefficient index of the ERT sensor are set as the optimization objectives.The experiments are set up based on multi-index orthogonal design. The experimentalresults indicate that the method can derive an evenly distributed sensitivity field and abetter image with the optimized sensors, and improve the ERTIOS of the ERT sensorsby13.75%. Compared with the full collocation method, the numbers of experiments isreduced by66%. The primary and secondary orders of the parameters in this experimentcan also determined by this method, and the experimental results are intuitive, reliable,and practical.
4. In order to improve the precision of image reconstruction algorithm, animproved particle swarm optimization for ERT image reconstruction algorithm is putforward. Group image samples of some typical flow regimes are trained with the leastsquares support vector, and then it is forecasted that the voltage deviation generated by the approximate of the sensitivity matrix. On the basis of the deviation, the fitnessfunction in particle swarm optimization is established. Not only the nonlinearadjustment method for inertia factor but also the mutation operation of particles speed isused in the standard particle swarm optimization. The improved PSO algorithm is usedto search the optimal solution of the reconstructed image. The simulation result showsthat compared with Landweber algorithm, the image precision of new algorithm canimprove nearly50%, and the image error can decrease to less than20%for some typicalflow regimes.
5. In order to improve the real-time performance of ERT system, this paper putforward an ERT sensor model based on dual-polarity pulse current excitation, for thetransient time process analysis of electrode-electrolyte surface. It is found by analysisthat due to electrode polarization, a large number of accumulated charges would beproduced between excitation electrodes. This part of residual potentials is bound toproduce a huge measuring noise at a high frequency excitation. Its attenuation speedwill greatly affect the real-time performance of ERT system. Therefore, the authordesigns a new high-speed discharge circuit to eliminate the measuring noise generatedby this part of residual potentials. The circuit has such features as fast discharge speed,adjustable discharge threshold, and automatic discrimination of charge polarity etc. Atlast, a theory analysis and a simulation experiment are made on the denoising effect ofthe circuit. The results show that: the circuit can effectively eliminate the residualpotentials between excitation electrodes, to improve the signal to noise ratio of ERTsystem. More importantly, this technology can be applied to significantly improve theERT system in real-time performance, with great significances in on-line industrydetection to ERT technology.
6An ERT experimental system on the basis of dual-polarity pulse currentexcitation is developed. This system adopts a sensor unit comprised of16-electrodeERT sensors and takes Single-Chip Microcomputer as the core part to construct themeasurement and data collection unit. In each cell, the author provides each circuitmodule the design principles and problems to notice, which also tells how to debug eachcircuit module. Finally, the author gives static experimental results of the vapor/liquidtwo phase liquid detection of this system with tennis ball simulated air bubbles.
引文
[1].李海青，两相流参数检测及应用，浙江大学出版社，1991.
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