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Planar array capacitance imaging system has the characteristics of uneven distribution of sensitive field, serious ill posed problem and measurement data vulnerable to external interference, and these characteristics will make the image artifacts particularly serious, affect the quality of the reconstructed image, and even determine the number of defects with difficulty. In order to solve the problem that the edge electric field and ill conditioned characteristics of planar array electrode seriously affect the quality of capacitance image reconstruction, an improved image reconstruction algorithm based on adaptive Kalman filter is proposed to reduce the noise of capacitance data and dielectric constant matrix. On the basis of constructing the state model of planar array capacitance imaging with noise, the maximum likelihood criterion is used to estimate and modify the noise variance matrix of dielectric constant matrix on-line, and the noise variance matrix of dielectric constant matrix is modified in real time. In order to restrain the filtering divergence and accelerate the convergence speed, different weighting coefficients are provided for the error covariance matrix with time going by. Through designing four kinds of samples from simple to complex structure, the defect detection experiment of composite structure is carried out. The experimental results show that compared with linear back projection (LBP), Tikhonov regularization (TR) algorithm and Kalman filtering algorithm, the image error of adaptive Kalman filtering algorithm can be reduced by about 20%, the image correlation coefficient is as high as 0.79 and the convergence speed can be improved by about 15%, the image artifacts of the four samples are greatly reduced. The experimental data show that the proposed adaptive Kalman filter image reconstruction algorithm can effectively reduce the noise of capacitance and permittivity matrix, enhance the stability of planar array capacitance imaging, and reduce the image error, so that the quality of the image can be significantly improved. This study provides a strong technical basis for improving the quantization accuracy of planar array capacitance imaging detection. In the future, we will further consider the image reconstruction under the condition of complex object field.
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Keywords:
- planar array electrode /
- capacitance image reconstruction /
- adaptive Kalman filter /
- composite materials /
- maximum likelihood criterion
[1] 温银堂, 赵丽梅, 张玉燕, 潘钊, 王洪瑞 2015 仪器仪表学报 36 1783
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Google Scholar
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Google Scholar
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Google Scholar
Wen Y T, Cao P P, Tian H G, Zhang Y Y, Luo X Y 2020 Acta Metrol Sin. 41 231
Google Scholar
[13] 杨丽君, 田洪刚, 安立明, 温银堂 2017 兵工学报 38 2488
Google Scholar
Yang L J, Tian H G, An L M, Wen Y T, Luo X Y 2017 Acta armamentarii. 38 2488
Google Scholar
[14] 温银堂, 贾瑶, 张玉燕, 罗小元, 王洪瑞 2016 仪器仪表学报 37 1596
Google Scholar
Wen Y T, Jia Y, Zhang Y Y, Luo X Y, Wang H R 2016 Chin. J. Sci. Inst. 37 1596
Google Scholar
[15] 彭丁聪 2009 软件导刊 8 32
Peng D C 2009 Software Guide 8 32
[16] 王楠, 李文成, 李岩 2010 光机电信息 27 28
Wang N, Li W C, Li Y 2010 Ome Information 27 28
[17] 马龙 2020 测绘与空间地理信息 43 21
Google Scholar
Ma L 2020 Geomatics & Spatial Info. Technol. 43 21
Google Scholar
[18] Wang H, Lei T, Rong Y M 2020 J. Manuf. Processes 11 1526
[19] Mohamed A H, Schwarz K P 1999 J. Geodesy 73 193
Google Scholar
[20] Brown R G 1983 Introduction To Random Signals and Applied Kalman Filtering (Vol.3) (New York: John Wiley and Sons) pp302−312
[21] Gao B B, Gao S S, Hu G, Zhong Y M, Gu C F 2018 Aerosp. Sci. Technol. 73 184
Google Scholar
[22] 栗世涛, 肖永刚, 孙业功 2010 信息安全与通信保密 10 98
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Li S T, Xiao Y G, Sun Y G 2010 Info. Security & Comm. Privacy 10 98
Google Scholar
[23] 李佳 2016 硕士学位论文 (北京: 华北电力大学)
Li J 2016 M. S. Thesis (Beijing: North China Electric Power University) (in Chinese)
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图 1 平面阵列电容成像系统
Figure 1. Planar array capacitance imaging system.
图 2 平面阵列电容传感器
Figure 2. Planar array capacitance sensor.
图 3 无胶层状态
Figure 3. Sample without adhesion.
图 4 满胶层状态
Figure 4. Complete sample.
图 5 (a)传感器单元; (b)数据采集单元; (c) 图像重建单元实物图
Figure 5. (a) Sensor unit; (b) data acquisition unit; (c) physical image of image reconstruction unit
图 6 样件一(a)、二(b)、三(c)、四(d)示意图
Figure 6. Schematic diagram of sample I (a), II (b), III (c) and IV (d).
图 7 样件一电容差值折线图
Figure 7. Capacitance difference of sample I.
图 8 样件二电容差值折线图
Figure 8. Capacitance difference of sample II.
图 9 样件三电容差值折线图
Figure 9. Capacitance difference of sample III.
图 10 样件四电容差值折线图
Figure 10. Capacitance difference of sample IV.
图 11 样件一图像误差
Figure 11. Image error of sample I.
图 12 样件二图像误差
Figure 12. Image error of sample II.
图 13 样件三图像误差
Figure 13. Image error of sample III.
图 14 样件四图像误差
Figure 14. Image error of sample IV.
表 1 不同算法成像效果图
Table 1. Imaging effects of different algorithms.
算法 样件一 样件二 样件三 样件四 LBP 
TR正则化 
Kalman滤波 
自适应Kalman 
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表 2 不同算法图像误差对比
Table 2. Image error comparison of different algorithms.
算法 样件一 样件二 样件三 样件四 LBP 1.71 1.80 1.85 2.12 TR 1.65 1.69 1.62 2.01 KF 1.64 1.52 1.47 1.79 AKF 1.40 1.41 1.39 1.60
DownLoad: CSV
表 3 不同算法图像相关系数对比
Table 3. Comparison of image correlation coefficients of different algorithms.
算法 样件一 样件二 样件三 样件四 LBP 0.58 0.47 0.41 0.23 TR 0.61 0.59 0.61 0.25 KF 0.61 0.71 0.75 0.55 AKF 0.78 0.77 0.79 0.63
DownLoad: CSV
表 4 不同算法收敛速度对比
Table 4. Comparison of convergence speed of different algorithms.
KF算法 AKF算法 迭代次数 图像误差 迭代次数 图像误差 样件一 20 0.98 19 0.72 样件二 45 1.39 36 1.06 样件三 44 1.50 37 0.92 样件四 80 2.07 59 1.51
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[1] 温银堂, 赵丽梅, 张玉燕, 潘钊, 王洪瑞 2015 仪器仪表学报 36 1783
Google Scholar
Wen Y T, Zhao L M, Zhang Y Y, Pan Z, Wang H R 2015 Chin. J. Sci. Inst. 36 1783
Google Scholar
[2] Hu X, Yang W 2010 Senor Review. 30 24
Google Scholar
[3] Carl T C, Perez-Juste A J F, Manuchehr S 2018 IEEE Sens. J. 18 6263
Google Scholar
[4] Carl T C, Manuchehr S 2017 IEEE Sens. J. 17 8059
Google Scholar
[5] Liang P Y, Han Y, Zhang Y Y, Wen Y T, Gao Q F, Meng J 2021 Measurement 167 1084
[6] Taylor S H, Garimella S V 2016 Int. J. Heat Mass Transfer. 106 1251
[7] Ye Z, Wei H Y, Soleimani M 2015 Measurement 61 270
Google Scholar
[8] Krzysztof G 2017 IEEE Sens. J. 17 8242
Google Scholar
[9] Rashid W 2016 Sensor Rev. 36 64
Google Scholar
[10] Yan H, Wang Y, Wang Y F, Zhou Y G 2020 IET Sci. Meas. Technol. 14 367
Google Scholar
[11] Zhang Y Y, Sun Y R, Wen Y T 2021 Measurement 168 724
[12] 温银堂, 曹鹏鹏, 田洪刚, 张玉燕, 罗小元 2020 计量学报 41 231
Google Scholar
Wen Y T, Cao P P, Tian H G, Zhang Y Y, Luo X Y 2020 Acta Metrol Sin. 41 231
Google Scholar
[13] 杨丽君, 田洪刚, 安立明, 温银堂 2017 兵工学报 38 2488
Google Scholar
Yang L J, Tian H G, An L M, Wen Y T, Luo X Y 2017 Acta armamentarii. 38 2488
Google Scholar
[14] 温银堂, 贾瑶, 张玉燕, 罗小元, 王洪瑞 2016 仪器仪表学报 37 1596
Google Scholar
Wen Y T, Jia Y, Zhang Y Y, Luo X Y, Wang H R 2016 Chin. J. Sci. Inst. 37 1596
Google Scholar
[15] 彭丁聪 2009 软件导刊 8 32
Peng D C 2009 Software Guide 8 32
[16] 王楠, 李文成, 李岩 2010 光机电信息 27 28
Wang N, Li W C, Li Y 2010 Ome Information 27 28
[17] 马龙 2020 测绘与空间地理信息 43 21
Google Scholar
Ma L 2020 Geomatics & Spatial Info. Technol. 43 21
Google Scholar
[18] Wang H, Lei T, Rong Y M 2020 J. Manuf. Processes 11 1526
[19] Mohamed A H, Schwarz K P 1999 J. Geodesy 73 193
Google Scholar
[20] Brown R G 1983 Introduction To Random Signals and Applied Kalman Filtering (Vol.3) (New York: John Wiley and Sons) pp302−312
[21] Gao B B, Gao S S, Hu G, Zhong Y M, Gu C F 2018 Aerosp. Sci. Technol. 73 184
Google Scholar
[22] 栗世涛, 肖永刚, 孙业功 2010 信息安全与通信保密 10 98
Google Scholar
Li S T, Xiao Y G, Sun Y G 2010 Info. Security & Comm. Privacy 10 98
Google Scholar
[23] 李佳 2016 硕士学位论文 (北京: 华北电力大学)
Li J 2016 M. S. Thesis (Beijing: North China Electric Power University) (in Chinese)
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