Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

Image Reconstruction Using a Genetic Algorithm for Electrical Capacitance Tomography

Electrical capacitance tomography （ECT） has been used for more than a decade for imaging dielectric processes. However, because of its ill-posedness and non-linearity, ECT image reconstruction has always been a challenge. A new genetic algorithm （GA） developed for ECT image reconstruction uses initial results from a linear back-projection, which is widely used for ECT image reconstruction to optimize the threshold and the maximum and minimum gray values for the image. The procedure avoids optimizing the gray values pixel by pixel and significantly reduces the search space dimension. Both simulations and static experimental results show that the method is efficient and capable of reconstructing high quality images. Evaluation criteria show that the GA-based method has smaller image error and greater correlation coefficients. In addition, the GA-based method converges quickly with a small number of iterations.

Damage Detection for CFRP Based on Planar Electrical Capacitance Tomography

Due to the widespread use of carbon fiber reinforced polymer/plastic(CFRP),the nondestructive structural health monitoring for CFRP is playing an increasingly essential role.As a nonrad iative,noninvasive and nondestructive detection technique,planar electrical capacitance tomography(PECT)electrodes array is employed in this paper to reconstruct the damage image according to the calculated dielectric constant changes.The shape and duty ratio of PECT electro-des are optimized according to the relations between sensitivity distribution and the dielectric constant of different anisotropic degrees.The sensitivity matrix of optimized PECT sensor is more uniform as the result shows,because the sensitiv-ity of insensitivity area can be increased by adding rotation of optimized electro-des.The reconstructed image qualities due to different PECT arrays and different damage locations are investigated at last.The simulation results indicate that:PECT can be used to detect the surface damage of CFRP;the sensitivity matrix of PECT for CFRP is highly relevant with the degree of anisotropic dielectric con-stant;the rotatable PECT sensor with rotation has better performance in unifor-mity of sensitivity;for different damage locations,the rotatable sensor with rotation has better image quality in most cases.

Visualization detection of slurry transportation pipeline based on electrical capacitance tomography in mining filling

In the long distance transportation of slurry filled for mining filling,there exist complex variation rules of pressure and flow velocity,pipe distribution location and other influencing factors.Electrical capacitance tomography(ECT)is a technique for visualizing two-phase flow in a pipe or closed container.In this paper,a visual detection method was proposed by image reconstruction of core,laminar,bubble and annular flow based on ECT technology,which reflects distribution of slurry in deep filling pipeline and measures the degree of blockage.There is an error between the measured and the real two-phase flow distribution due to two factors,which are immature image reconstruction algorithm of ECT and difference of flow patterns leading to degrees of error.In this paper,convolutional neural networks(CNN)is used to recognize flow patterns,and then the optimal image is calculated by the improved particle swarm optimization(PSO)algorithm with weights using simulated annealing strategy,and the fitness function is improved based on the results of the shallow neural network.Finally,the reconstructed binary image is further processed to obtain the position,size and direction of the blocked pipe.The realization of this method provides technical support for pipeline detection technology.

Visualization Detection of Solid-Liquid Two-Phase Flow in Filling Pipeline by Electrical Capacitance Tomography Technology

During mine filling,the caking in the pipeline and the waste rock in the filling slurry may cause serious safety accidents such as pipe blocking or explosion.Therefore,the visualization of the innermine filling of the solid-liquid two-phase flow in the pipeline is important.This paper proposes a method based on capacitance tomography for the visualization of the solid-liquid distribution on the section of a filling pipe.A feedback network is used for electrical capacitance tomography reconstruction.This reconstruction method uses radial basis function neural network fitting to determine the relationship between the capacitance vector and medium distribution error.In the reconstruction process,the error in the linear back projection is removed;thus,the reconstruction problem becomes an accurate linear problem.The simulation results showthat the reconstruction accuracy of this algorithm is better than that of many traditional algorithms;furthermore,the reconstructed image artifacts are fewer,and the phase distribution boundary is clearer.This method can help determine the location and size of the caking and waste rock in the cross section of the pipeline more accurately and has great application prospects in the visualization of filling pipelines in mines.

Online monitoring of gas-solid two-phase flow using projected CG method in ECT image reconstruction

Electrical capacitance tomography （ECT） is a promising technique for multi-phase flow measurement due to its high speed, low cost and non-intrusive sensing. Image reconstruction for ECT is an inverse problem of finding the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. The conjugate gradient （CG） method is a popular image reconstruction method for ECT, in spite of its low convergence rate. In this paper, an advanced version of the CG method, the projected CG method, is used for image reconstruction of an ECT system. The solution space is projected into the Kryiov subspace and the inverse problem is solved by the CG method in a low-dimensional specific subspace. Both static and dynamic experiments were carried out for gas-solid two-phase flows. The flow regimes are identified using the reconstructed images obtained with the projected CG method. The results obtained indicate that the projected CG method improves the quality of reconstructed images and dramatically reduces computation time, as compared to the traditional sensitivity, Landweber, and CG methods. Furthermore, the projected CG method was also used to estimate the important parameters of the pneumatic conveying process, such as the volume concentration, flow velocity and mass flow rate of the solid phase. Therefore, the projected CG method is considered suitable for online gas-solid two-phase flow measurement,

An ECT System Based on Improved RBF Network and Adaptive Wavelet Image Enhancement for Solid/Gas Two-phase Flow

Electrical capacitance tomography(ECT) is a non-invasive imaging technique that aims at visualizing the cross-sectional permittivity distribution and phase distribution of solid/gas two-phase flow based on the measured capacitance.To solve the nonlinear and ill-posed inverse problem:image reconstruction of ECT system,this paper proposed a new image reconstruction method based on improved radial basis function(RBF) neural network combined with adaptive wavelet image enhancement.Firstly,an improved RBF network was applied to establish the mapping model between the reconstruction image pixels and the capacitance values measured.Then,for better image quality,adaptive wavelet image enhancement technique was emphatically analyzed and studied,which belongs to a space-frequency analysis method and is suitable for image feature-enhanced.Through multi-level wavelet decomposition,edge points of the image produced from RBF network can be determined based on the neighborhood property of each sub-band;noise distribution in the space-frequency domain can be estimated based on statistical characteristics;after that a self-adaptive edge enhancement gain can be constructed.Finally,the image is reconstructed with adjusting wavelet coefficients.In this paper,a 12-electrode ECT system and a pneumatic conveying platform were built up to verify this image reconstruction algorithm.Experimental results demonstrated that adaptive wavelet image enhancement technique effectively implemented edge detection and image enhancement,and the improved RBF network and adaptive wavelet image enhancement hybrid algorithm greatly improved the quality of reconstructed image of solid/gas two-phase flow [pulverized coal(PC)/air].

Field Sensing Characteristic Research of Carbon Fiber Smart Material

In order to research the field sensing characteristic of the carbon fiber smart material, the Tikhonov regularization principle and the modified Newton-Raphson(MNR) algorithm were adopted to solve the inverse problem of the electrical resistance tomography(ERT). An ERT system of carbon fiber smart material was developed. Field sensing characteristic was researched with the experiment. The experimental results show that the specific resistance distribution of carbon fiber smart material is highly consistent with the distribution of structural strain. High resistance zone responds to high strain area, and the specific resistance distribution of carbon fiber smart material reflects the distribution of sample strain in covering area. Monitoring by carbon fiber smart material on complicated strain status in sample field domain is realized through theoretical and experimental study.

基于非凸与不可分离正则化算法的电容层析成像图像重建

搅拌器内两相混合是化工生产中常见的现象,电容层析成像(ECT)技术主要对两相分布进行可视化重构,以达到监测的目的。受稀疏贝叶斯学习的启发,提出了一种非凸与不可分离正则化(NNR)算法重建ECT图像。在稀疏先验的基础上引入矩阵低秩特性,采用最大后验估计在潜在空间中提出一个新的优化问题,利用对偶变量将潜在空间的目标函数映射到原始空间进行迭代求解,用来恢复同时稀疏与低秩的矩阵。与凸近似L1范数相比,NNR算法可获得更准确的重建图像,同时比非凸可分离方法更容易收敛到全局最优解。为验证NNR算法的重建效果,通过数值仿真与静态实验的方法分别与其他5种算法进行重建对比。结果表明:NNR算法可以有效减少重建伪影,提升中心物体的重建质量,为搅拌器内两相分布提供了高质量的重建算法。

一种组合电极电容层析成像重建图像融合方法

提出一种基于电容层析成像(ECT)组合电极重建图像及层次聚类的ECT图像融合方法。首先,构建组合8电极及12电极ECT阵列传感器,研究2种组合传感器激励测量方案;其次,采用层次聚类法对两种组合电极ECT重建图像进行聚类,从而消除重建过程中产生的伪影;最后,将聚类后的2种图像再进行小波融合重建。实验结果表明,相较于原始重建图像,所提方法重建图像平均相对误差最小,最大降幅达到23.4%,平均相关系数最大,最大增幅达到10.56%。

基于改进正问题模型和模因算法的ECT图像重建

为提高电容层析成像的图像重建质量,提出了一种基于改进正问题模型和模因算法的图像重建算法,即Im-MA算法。通过对灵敏度矩阵进行平滑滤波和降维处理,改进正问题模型。使用L_(2)范数作为数据拟合的测度,并将全变差作为正则项,构建目标函数,将图像重建问题转化为最优化问题。采用麻雀搜索算法和天牛须搜索算法相结合的模因(memetic algorithm,MA)算法求解目标函数。仿真与实验结果表明:与常用的Landweber算法相比,Im-MA算法的重建误差更小,且重建图像与真实分布更加接近。Im-MA算法为解决ECT逆问题提供了一种有效的新方法。

基于非凸熵最小化与高斯混合模型聚类的电容层析成像图像重建

基于压缩感知原理提出了一种构建非凸熵(NE)函数作为正则化项的方法,在有效缓解电容层析成像(ECT)病态性逆问题的同时可保证解的稀疏性,并采用快速迭代阈值收缩算法(FISTA)求解以加快收敛速度。对所得解通过高斯混合模型(GMM)进行阈值寻优,采用期望最大化算法(E-M)更新模型参数,从而构建NE-GMM算法。仿真及实验结果均表明:与LBP、Landweber、迭代硬阈值(IHT)、ADMM-L1及NE算法进行了对比,该算法所得重建图像质量最优,对中心分布及多物体分布的保真度进一步提高,仿真实验重建图像的平均相对误差和相关系数分别为0.4611及0.8827,优于其他5种算法。

基于深层小波网络的电容层析成像图像重建

提出了一种基于深层小波网络的电容层析成像(ECT)图像重建算法,采用Landweber算法生成初始重建图像作为网络输入;以U-Net深度卷积神经网络模型为骨干模型,通过在上、下采样层引入小波变换提取不同层次的特征,以及采用跳跃连接方式搭建高频特征传递通道,保留更多的细节信息,充分利用特征图中的全局和局部信息特征。仿真及静态实验结果均表明,基于该算法的图像重建精度更高,仿真及静态实验重建图像的平均相对图像误差分别为0.1918及0.6570,平均相关系数分别为0.9685及0.8169。

基于FCM及快速迭代收缩阈值算法的平面ECT图像重建

为提高平面阵列电容成像系统的成像精度,提出一种基于模糊C均值聚类(FCM)进行数据优化的快速迭代收缩阈值算法(FISTA)。根据平面阵列电容数据的特点,首先利用FCM算法对测量电容值进行分类,保留有效电容值,实现电容向量降维;然后利用离散小波基(DWT)对灰度值进行稀疏表示,并建立L1正则化模型,采用FISTA进行求解,以实现图像重建;最后将FCM处理后的电容值分别用于Landweber算法、Tikhonov算法进行重建对比。仿真与实验结果表明,该算法重建图像的平均相对误差约为0.0527,平均相关系数约为0.9422,均优于其它算法,且重建图像伪影较少,更接近真实情况;因此,所提算法具有更好的重建效果。。

基于多尺度密集连接网络的电容层析成像图像重建

为求解电容层析成像中的非线性病态反问题,提出了一种多尺度密集连接网络(MD-Net)模型。该模型由多尺度特征融合模块和密集连接块组成,以通过融合多尺度特征进一步提高图像的重建精度。通过MATLAB仿真实验平台构建了流型数据集,利用密集连接网络的非线性映射能力,完成训练集的学习与训练,并利用测试集进行训练效果评价。在此基础上进行了静态实验。仿真与静态实验结果均表明:与LBP、Landweber迭代算法和其他深度学习方法相比,该方法的重建精度最高、抗噪能力强,并具有良好的泛化能力。

基于多尺度自适应网络的ECT图像重建

为求解电容层析成像(ECT)中的非线性病态反问题,提出了一种多尺度自适应网络(MSANet)模型,该模型实现了更精细维度上多尺度特征的融合,且模型参数量相对较小。通过在单个残差块内构建树状结构组成多尺度特征融合模块,MSANet实现了更好的鲁棒性和更低的计算参数量;采用加入自适应空间阈值模块方式,进一步提高了图像的重建精度。实验结果表明:与线性反投影(LBP)算法、Landweber迭代算法及常用深度学习方法相比,该方法平均相对误差最小且平均相关系数最大,分别为0.181及0.967。

嵌入式电容层析成像系统的成像加速方法研究

为了提高嵌入式系统设计中电容层析成像(ECT)的图像重构速度,研究了一种针对进阶精简指令集机器加上现场可编程门阵列(ARM+FPGA)硬件架构的图像重构算法加速技术。针对广泛应用且鲁棒的Landweber迭代算法(ILA),首先分析算法结构,然后基于FPGA的流水线特点,改进ILA涉及的循环结构,从而达到加速的效果。同时,针对ARM+FPGA架构的特点,讨论了ARM核与FPGA核各自的任务分配方式,进一步优化了算法速度。为了验证算法的有效性,分别在使用MATLAB编程和使用提出的加速方法搭建的ZYNQ平台进行了图像重构实验,从图像重构耗时、图像相对误差和图像相关系数3个指标论证提出方法的有效性。实验结果显示,使用搭建的ZYNQ平台进行Landweber算法成像时,每个图像的运行时间比使用MATLAB编程的运行时间减少了30%~40%。该研究在保持重构精度的同时有效提升了迭代算法的速度,对于ECT系统的硬件加速具有一定适用性。

基于二阶混联灵敏度矩阵的ECT图像重建

电容层析成像技术求解图像重建问题属于非线性问题。在灵敏度矩阵的推导过程中,通常只保留灵敏度系数的线性部分,但是被忽略的非线性部分同样包含重要的成像信息。为了提高图像重建精度,基于二阶灵敏度系数的数学定义,结合模糊C-均值聚类算法和电场中心线理论,建立了二阶混联灵敏度矩阵,并将矩阵引入到Landweber算法中,提出了二阶Landweber算法;最后,进行仿真和静态实验,并与传统的Tikhonov算法和一阶Landweber算法进行对比,结果表明,二阶混联灵敏度矩阵可以提高图像重建精度。

基于模拟退火粒子群优化算法的ECT图像重建方法研究

电容层析成像系统中,其反问题的“病态性”特点,导致传统图像重建算法的重建结果伪影现象严重。粒子群算法(Particles Swarm Optimization,PSO)作为智能算法的一种,具有易实现,收敛快等显著优点,缺点也很明显,即粒子易收敛于局部最优解。将模拟退火算法与粒子群搜索算法相结合,利用模拟退火算法中的概率突变能力,能够有一定概率跳出算法的局部最优解。设计了五种不同的典型流型并进行了仿真实验,利用所提算法与LBP算法、Tikhonov算法、Landweber迭代算法以及标准PSO算法分别对其进行了图像重建。仿真实验所得到的主观结果和客观数据均表明,所提算法可以有效减少重建图像中的伪影,明确图像形状,提高重建图像质量,使得图像重建结果更加接近原始流型。

基于改进Forword-Backword Spliting算法的ECT图像重建算法

针对电容层析成像技术图像重建问题的不适定性和实时性要求,提出了一种基于改进前后向分裂(Forword-Backword Spliting, FBS)算法的ECT图像重建算法。首先,建立基于FBS算法的ECT逆问题求解模型,提升ECT图像重建的速度;其次将GMC惩罚项代替L1范数应用于ECT图像重建中,提高重建解的稀疏度以获得更准确的特征信号;最后建立基于GMC惩罚项的FBS图像重建模型并求解。采用COMSOL5.3和MATLAB2014软件搭建联合仿真平台,仿真结果显示,改进的算法最高将核心流模型成像相关系数提升至0.934 5,成像时间最快达到0.094 5 s,相较于Tikhonov正则化算法和Landweber算法,在成像速度和质量两方面均有明显提高。并通过实际实验验证了改进算法具有更好的可靠性和实时性。