非规则结构电容层析成像填补法测量的敏感场特性及重构算法改进

doi:10.11949/0438-1157.20200300

摘要/Abstract

摘要：

利用填补的方式将不规则区域转为规则成像区，可拓展电容层析成像的测量范围。首先分析了填补法对应的敏感场特性，然后分别研究了敏感场、归一化电容、填充区介电常数和图像重构算法对填补法成像的影响。并利用特定的填充区边界条件对Landweber算法进行改进，提出两种改进方法:变换矩阵和拆分矩阵的Landweber图像重构方法。结果表明，填充区使电容信号绝对值增强，非线性程度增加。不同背景的敏感场对成像影响较小，但填充区充满时的敏感场可强化环状流成像。去除填充区噪声的归一化电容矩阵有利于图像重构。填充物质的介电常数与测量区高介电常数相近时成像最佳。拆分矩阵法降低了求解维度，缩短了计算时间，对各种流型成像整体效果较好，基于松弛因子改进还可进一步优化重构图像。最后，在一般非规则结构中对改进方法的可靠性进行了测试验证。研究表明，改进方法可以用于一般性不规则结构的相分布测量，未来还可以用于因高温、腐蚀等无法直接进行电极安装的工业场合中，具有改进多相流测量方法的普遍意义。

关键词: 电容层析成像, 重构算法, 非规则结构, 两相流, 测量

Abstract:

The measurement range of electrical capacitance tomography(ECT) can be extended by transforming the irregular area into regular imaging area by the filling method. First, the characteristics of the sensitive field corresponding to the filling method are analyzed, and then the effects of the sensitive field, the normalized capacitance, the dielectric constant of the filling area and the image reconstruction algorithm on the imaging of the filling method are studied. The Landweber algorithm was improved using the specific boundary conditions of the filling area, and two improved methods were proposed: the transformation matrix method and the split matrix method. The results show that the absolute value of capacitance signal is enhanced and the nonlinearity degree is increased using the filling method. The sensitive field with different background has little influence on the imaging, but the sensitive field with full filling area can enhance the annular flow imaging. The normalized capacitance matrix is benefit for image reconstruction. The reconstruction image changes to be the best when the dielectric constant of the filling material is close to the higher one of the measuring area. The split matrix method reduces the solution dimension, shortens the calculation time, and has a good overall effect on all kinds of flow pattern imaging. Finally, the reliability of the improved method is verified in the general irregular structure. The results show that the improved method can be used to measure the phase holdup distribution in the general irregular structure. It can also be used in the industrial occasions where the electrode cannot be directly installed due to high temperature and corrosion in the future, which has the general significance of improving the multiphase flow measurement method.

Key words: electrical capacitance tomography, reconstruction algorithm, irregular structure, two-phase flow, measurement

中图分类号:

O 359.1

陈昭, 陈猛, 王江江, 常家兴, 刘马林. 非规则结构电容层析成像填补法测量的敏感场特性及重构算法改进[J]. 化工学报, 2020, 71(8): 3469-3479.

Zhao CHEN, Meng CHEN, Jiangjiang WANG, Jiaxing CHANG, Malin LIU. Sensitive field characteristics and reconstruction algorithm improvement of ECT measurement with filling method in irregular structure[J]. CIESC Journal, 2020, 71(8): 3469-3479.

图/表 14

图1 不规则结构填补法ECT测量一般性原理(a)及填补法应用于多环斜孔式流化床入口处测量示意图(b)

Fig.1 General schematic diagram of ECT measurement of irregular structure with filling method (a) and instrumentation plan of filling method applied to multi-ring slope-hole fluidized bed inlet (b)

图2 ECT测量几何建模及网格划分

Fig.2 Schematic diagram of simplified geometric modeling and mesh generation

图3 不同背景下敏感场计算结果对比

Fig.3 Comparison of sensitivity map of different background

表1 本文研究案例定义

Table 1 Case definition in this study

项目	内容
敏感场S	1：标准敏感场；2：填充区满，测量区空；3：填充区满，测量区满
归一化电容矩阵中的C_L的选择	a：填充区空，测量区空；b：填充区满，测量区空
图像重构算法	甲：LBP；乙：Landweber；丙：Tikhonov；丁：改进1，变换矩阵法；戊：改进2，拆分矩阵法

图4 不同敏感场下成像质量和重构图像

Fig.4 Imaging quality and reconstruction images under different sensitivity maps

图5 不同归一化电容下成像质量和重构图像

Fig.5 Imaging quality and reconstruction images under different normalized capacitance

图6 半管流和核心流在不同填充区介电常数下的图像重构效果

Fig.6 Reconstruction images of half-tube flow and core flow with different permittivity in filling area

图7 不同函数下的变换矩阵重构结果

Fig.7 Reconstruction results of transformation matrix with different functions

图8 不同算法针对填补法成像的结果

Fig.8 Results of different algorithms for thick wall imaging

表2 各重构算法的计算所需要的运行时间

Table 2 Running time of each reconstruction algorithm

流型	运行时间/s
流型	LBP	Landweber	Tikhonov	变换矩阵	拆分矩阵
半管流	0.001331	0.082503	1.271096	2.72222	0.04930
核心流	0.001168	0.085205	1.525173	2.65924	0.04975
环状流	0.001076	0.117534	1.263974	2.67614	0.05122
双管流	0.001137	0.105980	1.345436	2.62670	0.04871
三管流	0.001099	0.083032	1.348390	2.64398	0.07876

图9 不同算法的图像误差

Fig.9 Image error of different algorithms

图10 不同算法的相关系数

Fig.10 Correlation coefficient of different algorithms

图11 不同c1下的半管流成像、不同c2下的双管流成像及三管流优化过程

Fig.11 Half-tube flow at different c1, double tube flow at different c2 and optimization of triple tube flow

图12 针对非规则结构的填补法下的图像重构结果和图像重构评价指标

Fig.12 Image reconstruction based on filling method for irregular structure and evaluation of image reconstruction

参考文献 32

1	Guo Q, Meng S, Wang D, et al. Investigation of gas-solid bubbling fluidized beds using ECT with a modified Tikhonov regularization technique[J]. AIChE Journal, 2017, 64(1): 29-41.
2	Mao M X, Ye J M, Wang H G, et al. Investigation of gas-solids flow in a circulating fluidized bed using 3D electrical capacitance tomography[J]. Measurement Science and Technology, 2016, 27(9): 095401.
3	Ge R H, Ye J M, Wang H G, et al. Investigation of gas-solids flow characteristics in a conical fluidized bed dryer by pressure fluctuation and electrical capacitance tomography[J]. Drying Technology, 2016, 34(11): 1359-1372.
4	罗琴, 赵银峰, 叶茂, 等. 电容层析成像在气固流化床测量中的应用[J]. 化工学报, 2014, 65(7): 2504-2512.
	Luo Q, Zhao Y F, Ye M, et al. Application of electrical capacitance tomography for gas-solid fluidized bed measurement[J]. CIESC Journal, 2014, 65(7): 2504-2512.
5	Li Y, Yang W Q, Xie C G, et al. Gas/oil/water flow measurement by electrical capacitance tomography[J]. Measurement Science and Technology, 2013, 24(7): UNSP 074001.
6	Wang H G, Qiu G Z, Ye J M, et al. Investigation of the fluidized bed coating process by process tomogrpahy and mathematical modeling[J]. Journal of Engineering Thermophysics, 2015, 36(5): 1015-1018.
7	Yang W Q, Ren Z, Takei M, et al. Medical applications of electrical tomography[C]//IEEE International Conference on Imaging Systems and Techniques. Krakow Poland: IEEE, 2018: 368-373.
8	Huang K, Meng S H, Guo Q, et al. High-temperature electrical capacitance tomography for gas-solid fluidised beds[J]. Measurement Science and Technology, 2018, 29(10): 104002.
9	陆海峰, 郭晓镭, 陶顺龙, 等. 电容层析成像在煤粉料仓下料中的应用[J]. 化工学报, 2014, 65(2): 422-429.
	Lu H F, Guo X L, Tao S L, et al. Application of electrical capacitance tomography in hopper discharge of pulverized coal[J]. CIESC Journal, 2014, 65(2): 422-429.
10	Che H Q, Ye J M, Tu Q Y, et al. Investigation of coating process in Wurster fluidised bed using electrical capacitance tomography[J]. Chemical Engineering Research & Design, 2018, 132: 1180-1192.
11	Yang W Q. Design of electrical capacitance tomography sensors[J]. Measurement Science and Technology, 2010, 21(4): 042001.
12	Ye J M, Wang H G, Yang W Q. Image reconstruction for electrical capacitance tomography based on sparse representation[J]. IEEE Transactions on Instrumentation and Measurement, 2015, 64(1): 89-102.
13	Ye J M, Li Y, Wang H G, et al. Concentric-annulus electrical capacitance tomography sensors[J]. Measurement Science and Technology, 2013, 24(9): 095403.
14	李伟. 电容层析成像反问题求解与图像融合方法研究[D]. 哈尔滨: 哈尔滨理工大学, 2014.
	Li W. Research on inverse problem solving and image fusion of electrical capacitance tomography[D]. Harbin: Harbin University of Science and Technology, 2014.
15	Peng L H, Mou C H, Yao D Y, et al. Determination of the optimal axial length of the electrode in an electrical capacitance tomography sensor[J]. Flow Measurement and Instrumentation, 2005, 16(2/3): 169-175.
16	Sun J T, Yang W Q. Fringe effect of electrical capacitance and resistance tomography sensors[J]. Measurement Science and Technology, 2013, 24(7): 074002.
17	张立峰, 王化祥. 一种新的电容层析成像电极组合激励测量模式[J]. 化工学报, 2012, 63(3): 860-865.
	Zhang L F, Wang H X. A new excitation measurement model of electrical capacitance tomography electrode combination[J]. CIESC Journal, 2012, 63(3): 860-865.
18	Wu M, Ye J M, Wang H G, et al. Evaluation of excitation strategy for a large-scale ECT sensor with internal-external electrodes[J]. IEEE Sensors Journal, 2017, 17(24): 8091-8098.
19	刘马林. 流化床-化学气相沉积技术在先进核燃料制备中的应用进展[J]. 化工进展, 2019, 38(4): 1646-1653.
	Liu M L. Application of fluidized bed chemical vapor deposition in advanced nuclear fuel preparation[J]. Chemical Industry and Engineering Progress, 2019, 38(4): 1646-1653.
20	Liu M L, Chen Z, Chen M, et al. Scale-up strategy study of coating furnace for TRISO particle fabrication based on numerical simulations[J]. Nuclear Engineering and Design, 2020, 357: 110413.
21	Cui Z Q, Wang Q, Xue Q, et al. A review on image reconstruction algorithms for electrical capacitance/resistance tomography[J]. Sensor Review, 2016, 36(4): 429-445.
22	Li Y, Yang W Q. Image reconstruction by nonlinear Landweber iteration for complicated distributions[J]. Measurement Science and Technology, 2008, 19(9): 094014.
23	Yang W Q, Peng L H. Image reconstruction algorithms for electrical capacitance tomography[J]. Measurement Science and Technology, 2003, 14(1): 1-13.
24	谢黄骏, 陈虹, 高旭, 等. 应用于低温流体两相流测量的修正电容层析成像线性反演算法[J]. 化工学报, 2019, 70(9): 3320-3328.
	Xie H J, Chen H, Gao X, et al. Linear inversion algorithm of modified electrical capacitance tomography applied to measurement of two phase flow of low temperature fluid[J]. CIESC Journal, 2019, 70(9): 3320-3328.
25	牟昌华, 彭黎辉, 姚丹亚, 等. 一种基于电势分布的电容成像敏感分布计算方法[J]. 计算物理, 2006, 1 (1): 87-92.
	Mou C H, Peng L H, Yao D Y, et al. A method for calculating sensitivity distribution of capacitance imaging based on potential distribution[J]. Computational Physics, 2006, 1(1): 87-92.
26	Guo Q, Meng S H, Wang D H, et al. Investigation of gas-solid bubbling fluidized beds using ECT with a modified Tikhonov regularization technique[J]. AIChE J., 2018, 64(1): 29-41.
27	马敏, 范广永, 孙颖. 电容成像双共轭梯度图像重建改进算法[J]. 北京航空航天大学学报, 2019, 45(8): 1489-1494.
	Ma M, Fan G Y, Sun Y. An improved algorithm for double conjugate gradient image reconstruction in capacitive imaging[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(8): 1489-1494.
28	Lu G, Peng L H, Zhang B, et al. Precondition landweber iteration algorithm for electrical capacitance tomography[J]. Flow Measurement and Instrumentation, 2005, 16(2/3): 163-167.
29	Yang W Q, Spink D M, York T A, et al. An image-reconstruction algorithm based on Landweber􀆳s iteration method for electrical-capacitance tomography[J]. Measurement Science and Technology, 1999, 10(11): 1065-1069.
30	Liu S, Fu L, Yang W Q. Optimization of an iterative image reconstruction algorithm for electrical capacitance tomography[J]. Measurement Science and Technology, 1999, 10(7): 37-39.
31	Ramli M F, Tian W B, Yang W Q, et al. Image reconstruction with different sensitivity maps generated with different background[C]//IEEE International Conference on Imaging Systems and Techniques. Chania, Greece: IEEE, 2016: 543-548.
32	Tian W B, Sun J T, Ramli M F, et al. Adaptive selection of relaxation factor in Landweber iterative algorithm[J]. IEEE Sensors Journal, 2017, 17(21): 7029-7042.

[1]	肖明堃, 杨光, 黄永华, 吴静怡. 浸没孔液氧气泡动力学数值研究[J]. 化工学报, 2023, 74(S1): 87-95.
[2]	周绍华, 詹飞龙, 丁国良, 张浩, 邵艳坡, 刘艳涛, 郜哲明. 短管节流阀内流动噪声的实验研究及降噪措施[J]. 化工学报, 2023, 74(S1): 113-121.
[3]	江河, 袁俊飞, 王林, 邢谷雨. 均流腔结构对微细通道内相变流动特性影响的实验研究[J]. 化工学报, 2023, 74(S1): 235-244.
[4]	袁佳琦, 刘政, 黄锐, 张乐福, 贺登辉. 泡状入流条件下旋流泵能量转换特性研究[J]. 化工学报, 2023, 74(9): 3807-3820.
[5]	温凯杰, 郭力, 夏诏杰, 陈建华. 一种耦合CFD与深度学习的气固快速模拟方法[J]. 化工学报, 2023, 74(9): 3775-3785.
[6]	王玉兵, 李杰, 詹宏波, 朱光亚, 张大林. R134a在菱形离散肋微小通道内的流动沸腾换热实验研究[J]. 化工学报, 2023, 74(9): 3797-3806.
[7]	何松, 刘乔迈, 谢广烁, 王斯民, 肖娟. 高浓度水煤浆管道气膜减阻两相流模拟及代理辅助优化[J]. 化工学报, 2023, 74(9): 3766-3774.
[8]	邢雷, 苗春雨, 蒋明虎, 赵立新, 李新亚. 井下微型气液旋流分离器优化设计与性能分析[J]. 化工学报, 2023, 74(8): 3394-3406.
[9]	高燕, 伍鹏, 尚超, 胡泽君, 陈晓东. 基于双流体喷嘴的磁性琼脂糖微球的制备及其蛋白吸附性能探究[J]. 化工学报, 2023, 74(8): 3457-3471.
[10]	闫琳琦, 王振雷. 基于STA-BiLSTM-LightGBM组合模型的多步预测软测量建模[J]. 化工学报, 2023, 74(8): 3407-3418.
[11]	仪显亨, 周骛, 蔡小舒, 蔡天意. 光纤后向动态光散射测量纳米颗粒的浓度适用范围研究[J]. 化工学报, 2023, 74(8): 3320-3328.
[12]	牛超, 沈胜强, 杨艳, 潘泊年, 李熠桥. 甲烷BOG喷射器流动过程计算与性能分析[J]. 化工学报, 2023, 74(7): 2858-2868.
[13]	郭雨莹, 敬加强, 黄婉妮, 张平, 孙杰, 朱宇, 冯君炫, 陆洪江. 稠油管道水润滑减阻及压降预测模型修正[J]. 化工学报, 2023, 74(7): 2898-2907.
[14]	高金明, 郭玉娇, 鄂承林, 卢春喜. 一种封闭罩内顺流多旋臂气液分离器的分离特性研究[J]. 化工学报, 2023, 74(7): 2957-2966.
[15]	何宣志, 何永清, 闻桂叶, 焦凤. 磁液液滴颈部自相似破裂行为[J]. 化工学报, 2023, 74(7): 2889-2897.