Sensitive field characteristics and reconstruction algorithm improvement of ECT measurement with filling method in irregular structure

doi:10.11949/0438-1157.20200300

Abstract

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

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

CLC Number:

O 359.1

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.

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.

Figures/Tables 14

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)

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

Fig.3 Comparison of sensitivity map of different background

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

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

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

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

Fig.7 Reconstruction results of transformation matrix with different functions

Fig.8 Results of different algorithms for thick wall imaging

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

Fig.9 Image error of different algorithms

Fig.10 Correlation coefficient of different algorithms

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

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

References 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.

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