﻿ 航空发动机中气液两相流的可视化检测<sup>*</sup>
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Visible measurement of gas-liquid two-phase flow in aircraft engine
ZHAO Yu, YUE Shihong, ZHANG Yangyang, WANG Huaxiang
School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China
Received: 2017-02-13; Accepted: 2017-05-19; Published online: 2017-03-30 09:59
Foundation item: National Natural Science Foundation of China (61174014)
Corresponding author. YUE Shihong, E-mail: shyue1999@tju.edu.cn
Abstract: This paper focuses on the lack of the sensitivity coefficient information and the low utilization of the measurement voltage in FCM clustering algorithm in electrical impedance tomography (EIT) technology, and proposes a new imaging algorithm. In the new algorithm, sensitivity matrix information is introduced to correct the voltage of each subdivision unit. And at the same time, we propose to handle the measurement voltage according to its weight coefficient in the total voltage value, and this method can be applied to all EIT classical inversion algorithms. Both the theoretical analysis and numerical simulation results demonstrate that the new algorithm is more accurate in locating two-phase flow patterns than the existing FCM clustering algorithm, the spatial resolution deviation of reconstructed image has been reduced by 5% to 15%, and the correlation coefficient has been increased by 5% to 20%.
Key words: electrical impedance tomography (EIT)     FCM clustering algorithm     measurement voltage     sensitivity matrix     two-phase flow patterns

1 研究背景及相关工作

 图 1 正问题/逆问题求解过程 Fig. 1 Solution procedure of forward/inverse problem
1.1 灵敏度系数矩阵

 (1)

1.2 EIT的FCM聚类算法

FCM聚类算法是一种应用广泛的聚类算法，是图像处理中典型的图像划分算法。在文献[11-12]中，把FCM聚类算法成功应用于EIT成像中。结果表明，EIT中FCM聚类算法具有成像速度快，参数鲁棒性强等特点，可以用作实时监测。以下称该算法为FCM-EIT算法。该算法的具体说明如下：

1) 根据等势线反投影(LBP)算法[13]求得每个剖分单元16次激励后的电压均值，生成矩阵u(812×1)。

2) 根据每个剖分单元的位置信息将u矩阵转换为灰度共生矩阵G(32×32)。

3) 求得灰度共生矩阵G的方差矩阵d(812×1)，则D=[u, d]作为FCM聚类算法的特征值进行聚类成像。

4) 求得隶属度矩阵U(812×2)，则每个像素点的灰度值P(i)=max(U(i, :))。

2 基于FCM-EIT的优化算法

2.1 测量数据权系数计算

 (2)

 (3)

 图 2 测量数据权系数化说明 Fig. 2 Weight coefficient of measurement data

UemptyiUfulli (i=1, 2, …, 208)依次对应，进行上述一次归一化，得到权系数处理后电压的2种不同形式：

 (4)

 图 3 权系数化前后的测量值 Fig. 3 Measured values before and after coefficient weighting
2.2 灵敏度系数的应用

 (5)

S修正后所得的V矩阵计算的均值和方差作为输入特征值用于FCM-EIT算法的计算。

3 仿真实验和结果

 图 4 流型分布 Fig. 4 Distribution of flow patterns
3.1 仿真结果

3.1.1 优化后FCM-EIT算法性能测试

 模型序号 两相流模型 LBP算法 FCM-EIT算法 优化后FCM-EIT算法 1 2 3 4

3.1.2 测量数据的权系数化对其他算法的作用

 泡状介质分布模型 Landweber/Tikhonov算法成像 权系数法处理后成像

3.2 评价参数

3.2.1 相关系数

 (6)

 模型序号 LBP算法 原始FCM算法 优化后FCM算法 1 0.414 1 0.364 7 0.415 4 2 0.373 8 0.295 9 0.390 2 3 0.166 9 0.877 7 0.922 2 4 0.345 5 0.405 1 0.568 4

 图 5 LBP、原始图像和优化后图像的相关系数对比 Fig. 5 Comparison among correlation coefficient of LBP, original image and optimized image

3.2.2 相对误差

 (7)

 模型序号 LBP算法 原始FCM算法 优化后FCM算法 1 0.173 4 0.276 3 0.201 1 2 0.207 7 0.267 8 0.163 9 3 0.859 8 0.072 8 0.050 5 4 0.301 2 0.297 8 0.219 5

 图 6 LBP、原始图像、优化后图像的相对误差对比 Fig. 6 Comparison among relative errors of LBP, original image and optimized image

4 结论

1) 充分利用了灵敏度系数的信息以及对测量电压值进行更高效率的利用，提高了聚类算法的精度。图像相关系数提高了近5%~20%，相对误差降低了约5%~15%。数值仿真结果验证了优化后的算法在成像领域具有更好的性能。

2) 本文提出的边界电压权系数处理方法在其他成像算法中也进行了部分模型验证，均得到了较好的成像效果。

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#### 文章信息

ZHAO Yu, YUE Shihong, ZHANG Yangyang, WANG Huaxiang

Visible measurement of gas-liquid two-phase flow in aircraft engine

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(11): 2345-2351
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0060