基于数据驱动的卷积神经网络电容层析成像图像重建

doi:10.11949/0438-1157.20200021

摘要/Abstract

摘要：

针对电容层析成像技术的图像重建问题，提出了基于数据驱动的卷积神经网络图像重建方法。根据气固两相流的流型特点，通过数值模拟的方法随机生成了60000组介质分布图像，并利用有限元法计算了与之对应的电容向量，从而建立了一个“电容向量-介质分布”数据集；然后根据电容层析成像图像重建特点建立了卷积神经网络模型，对数据集中的训练集进行学习和训练，并利用测试集对训练结果进行了验证与评价。在此基础上，对获得的ECT图像重建卷积神经网络模型进行了静态实验和流化床测试实验研究。模拟和实验结果表明：所建立的卷积神经网络能较好地实现ECT图像重建，可直接用于流化床内的颗粒浓度分布测量。

关键词: 卷积神经网络, 电容层析成像, 图像重建, 颗粒浓度分布

Abstract:

A data-driven image reconstruction method based on convolutional neural networks is proposed for electrical capacitance tomography(ECT). According to the characteristics of the flow patterns of gas-solid two-phase flow, 60000 sets of particle distribution images are randomly generated by numerical simulation and the corresponding capacitance vectors are calculated by the finite element method, thereby creating a “capacitance vector - particle distribution” dataset. Then a convolutional neural network model is developed to learn and train the training dataset. The training result is verified and evaluated with the testing dataset. Further, static experiments and fluidized bed measurement experiments are performed on the ECT image reconstruction with the obtained convolutional neural network model. Simulation and experimental results show that the established convolutional neural network can well reconstruct ECT images and can be directly used for particle concentration distribution measurement in a fluidized bed.

Key words: convolutional neural network, electrical capacitance tomography, image reconstruction, particle concentration distribution

中图分类号:

TK 313

孙先亮, 李健, 韩哲哲, 许传龙. 基于数据驱动的卷积神经网络电容层析成像图像重建[J]. 化工学报, 2020, 71(5): 2004-2016.

Xianliang SUN, Jian LI, Zhezhe HAN, Chuanlong XU. Data-driven image reconstruction of electrical capacitance tomography based on convolutional neural network[J]. CIESC Journal, 2020, 71(5): 2004-2016.

图/表 18

图1 管道截面网格剖分

Fig.1 Pipe cross-section meshing

图2 随机流型生成过程

Fig.2 Generation process of random flow pattern

图3 用于ECT图像重建的CNN网络结构

Fig.3 Modified CNN network structure for ECT image reconstruction

图4 网络模型损失函数随训练过程的变化

Fig.4 Loss function of network model changes with training process

图5 典型流型的成像效果

Fig.5 Image reconstruction for typical flow patterns

表1 典型流型的评价指标

Table 1 Evaluation indexes for typical flow patterns

流型	指标	LBP	Landweber	CNN
分层流	相对图像误差	11.22%	13.01%	1.43%
	相关系数	0.9183	0.8972	0.9886
	相含量误差	-3.91%	-3.77%	0.21%
环状流	相对图像误差	11.34%	1.94%	0.49%
	相关系数	0.8596	0.9735	0.9932
	相含量误差	-3.41%	-1.58%	0.23%
核心流	相对图像误差	37.76%	25.94%	1.58%
	相关系数	0.8616	0.8801	0.9877
	相含量误差	13.89%	-14.71%	-0.72%
双核流	相对图像误差	35.36%	41.33%	3.56%
	相关系数	0.7490	0.6824	0.9736
	相含量误差	-7.39%	-8.61%	0.80%

图6 随机流型的成像效果

Fig.6 Image reconstruction for random flow patterns

表2 随机流型的评价指标

Table 2 Evaluation indexes for random flow patterns

流型	指标	LBP	Landweber	CNN
1a	相对图像误差	1.25%	0.66%	0.32%
	相关系数	0.8340	0.9173	0.9680
	相含量误差	0.11%	0.51%	-0.09%
1b	相对图像误差	19.34%	16.76%	1.40%
	相关系数	0.8201	0.8833	0.9767
	相含量误差	0.37%	0.04%	-1.39%
2a	相对图像误差	5.11%	5.62%	0.96%
	相关系数	0.8761	0.8776	0.9777
	相含量误差	0.30%	0.30%	-0.24%
2b	相对图像误差	4.58%	7.85%	0.99%
	相关系数	0.8918	0.8689	0.9781
	相含量误差	-0.39%	-0.20%	-1.10%

表3 图像重建时间

Table 3 Time consumption of image reconstruction

重建方法	耗时/μs
LBP	117.2
Landweber	15806.1
CNN逐帧	10122.3
CNN批量	114.5

图7 CNN算法在不同信噪比时的重建结果

Fig.7 Image reconstruction of CNN at different SNR

表4 CNN算法在不同信噪比下的相对图像误差

Table 4 Relative image error of CNN at different SNR

流型	相对图像误差/%
流型	10 dB	20 dB	30 dB	40 dB	无噪声
1a	5.15	2.23	0.49	0.37	0.32
1b	61.93	12.33	1.75	1.56	1.40
2a	36.27	3.99	1.95	1.05	0.96
2b	37.59	7.19	1.65	1.24	0.99

图8 三种算法在不同信噪比下的重建效果

Fig.8 Image reconstruction of methods at different SNR

表5 三种算法在不同信噪比下的相对图像误差

Table 5 Relative image error of methods at different SNR

算法	相对图像误差/%
算法	10 dB	20 dB	30 dB	40 dB	无噪声
LBP	7.22	5.07	5.20	5.04	5.11
Landweber	53.97	9.50	6.02	5.62	5.62
CNN	36.27	3.99	1.95	1.05	0.96

图9 ECT静态实验系统

Fig.9 Setup of static experiment

图10 静态实验中CNN网络与Landweber算法成像效果

Fig.10 Reconstruction results with modified CNN network and Landweber in static experiments

图11 静态实验中两种算法的相关系数

Fig.11 Correlation coefficients of two algorithms in static experiments

图12 循环湍动流化床

Fig.12 Setup of cyclic turbulent fluidized bed

图13 不同床高下颗粒浓度分布重建结果

Fig.13 Particle concentration distribution at different feeding heights

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