Dual modality ECT–MIT multi-phase flow imaging

Three-phase flow imaging is a very challenging problem in industrial process tomography. A particular interest here is three phase flow including both conductive and non-conductive phases. Currently there is no robust solution to this problem. Electrical capacitance tomography (ECT) has been applied to visualize the permittivity distribution by measuring inter-capacitance between electrodes around sensing area. Magnetic inductance tomography (MIT) is a technique to image the conductivity distribution through the inductance measurements over the coils around the sensing area. In this paper, the three-phase flow is classified into two scenarios: air background and water background. A dual-modality method of ECT and MIT is proposed to image both the conductive and dielectric components under test. As a result of this experiment, the dual-modality method is able to solve air-background three-phase flow imaging, but a problem has been raised in the water-background scenario. The static experiment results are promising for such contactless three phase flow imaging.     

Imaging conductive materials with high frequency electrical capacitance tomography

Electrical capacitance tomography (ECT) is known as an imaging technique for dielectric permittivity imaging. A novel ECT sensor model at a high excitation frequency is proposed to examine the capability of the ECT system to image both conductivity and permittivity contrasts. The proposed model uses a complex impedance forward model for the ECT system. This new model indicates that in higher excitation frequency both conductive and dielectric imaging may be feasible. Normally, capacitance tomography is designed for the measurements of imaginary part and resistance tomography is used to take the measurements of real part. The drawback of a typical capacitance tomography at a low excitation frequency, such as 200 kHz is that it cannot be used to measure the conductive phase of a conductive/dielectric mixed fluid, e.g. the gas/water flow. By increasing the excitation frequency, the capacitive impedance of the conductive material decreases and dielectric phenomena of the conductive fluid dominates so that it is possible to use capacitance tomography to characterise the dielectric/conductive flows. This paper presents a development of capacitance tomography with a high excitation frequency in measuring the gas/liquid mixture i.e. gas/water and gas/oil multiphase distributions. Both theoretical and experimental results are presented to verify this feasibility study.     

3D ECT reconstruction by an improved Landweber iteration algorithm

Electrical capacitance tomography (ECT) is a relatively mature non-invasive imaging technique that attempts to map dielectric permittivity of materials. Recently, 3D ECT has gained interest because of its potential to generate volumetric images. The study of a fast and accurate image reconstruction algorithm is a challenge task, especially for 3D reconstruction. In this paper, we propose an improved Landweber iteration algorithm. We incorporate an additional acceleration term into the cost function and apply an adaptive threshold operation to the image obtained in each iteration for reducing artefacts. The algorithm proposed is tested by the noise-free and noise-contaminated capacitance data. Sensitivity matrixes and capacitance data of a 3D ECT sensor are obtained by using the finite element (FE) method. Extensive simulations in 3D reconstruction are carried out. The results verify the effectiveness of these improvements. Both the reconstruction time and the artefacts in the reconstructed image are reduced obviously. The experimental results of 3D reconstruction of objects in the shape of letters U and L confirm the effectiveness of the proposed algorithm further.     

Preconditioned Landweber iteration algorithm for electrical capacitance tomography

Electrical capacitance tomography (ECT) has been used to obtain the cross-section images of processes with different dielectric materials inside. Image reconstruction with ECT is to retrieve the permittivity distribution of materials inside the sensor from the capacitance measurements. Algorithms for ECT image reconstruction should be both precise and fast in order to satisfy the requirements of real-time monitoring of the dynamic behavior of processes. Several algorithms have been developed for ECT image reconstruction. The Landweber iteration is the most precise one. However, the low convergence rate of the Landweber iteration limits its application for on-line imaging.This paper introduces an iterative algorithm based on the Landweber method with preconditioning for ECT image reconstruction. A preconditioner, which is equivalent to a filter, is applied to the Landweber iteration. The convergence of this algorithm is analyzed. Its performance is evaluated by using simulated and experimental data corresponding to certain typical permittivity distributions. Preliminary numerical and experimental results show that this algorithm converges more rapidly than the Landweber iteration without preconditioning. Therefore, image reconstruction iteration can be accelerated, which makes on-line quantitative image reconstruction possible.     

Application of ECT and relative change ratio of capacitances in probing anomalous objects in water

Nowadays electrical capacitance tomography (ECT) is mainly adopted for detecting dielectrics of low permittivity in chemical and petroleum industries. In these fields, to meet the demand of measuring capacitances within the range of low values, ECT still needs relatively high requirements of designing its system. In this work, an ECT system is simplified to probe anomalous objects in water with high permittivity. Additionally, the relative change ratio (RCR) of capacitances is presented for image reconstruction in terms of the high permittivity background. RCR is the change value of a capacitance divided by its background value. To verify the effectiveness of the simplification of an ECT system and the method of RCR for image reconstruction, simulations and experiments associated with media of high permittivity (i.e. water) were conducted. The obtained results demonstrate that the simplified ECT system based on RCRs of simulated and measured capacitances is capable of effectively probing anomalous objects in tap-water and sodium chloride solutions with different concentrations. Therefore the RCR is recommended when the sensing domain of ECT is of the high permittivity background. Besides the simplification of ECT systems can be appealing and beneficial to introduced ECT into other fields associated with water flows, such as hydrology, hydrogeology, hydroponics, environment science, etc.     

Nonlinear image reconstruction using a GA-ECT technique in electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive measurement technique that estimates the dielectric permittivity distribution of an inhomogeneous object from the boundary potentials at floating electrodes or mutual capacitances. In this paper, a stochastic inverse technique based on genetic algorithm (GA-ECT) is developed, which is adapted to the two different methods, i.e. potential measurement and capacitance measurement. Numerical simulation results are presented to evaluate the inverse technique both for noise free and noisy data and the results show that quantitative image can be reconstructed not only with the low permittivity contrast but also with the high contrast. Furthermore, the influence of a priori knowledge to image reconstruction is discussed.     

基于MCMC方法的电容成像图像重构算法

研究基于概率统计的电容成像图像重构算法,以马尔科夫随机场的方式给出介电常数分布的先验概率,利用电容成像(electrical capacitance tomography,ECT)线性模型得到似然函数,通过马尔科夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)方法对介电常数分布的后验概率密度进行采样,马尔科夫链的转移核利用Metropolis-Hastings方法得到,结合嵌套迭代提高计算效率。仿真结果表明,嵌套迭代-MCMC方法在正则化参数设置合适的条件下,可以得到较好的图像质量,基于MCMC方法图像重构算法为解决ECT图像重构问题提供一种新思路。     

ITS Reconstruction Tool-Suite: An inverse algorithm package for industrial process tomography

Electrical resistance tomography (ERT) and electrical capacitance tomography (ECT) are two established process tomography techniques that can be applied into various indsutries. ERT can monitor the electrical conductivity changes in the process whereas ECT can detect the electrical dielectric materials. Due to their high-speed and low cost features, they are particularly attractive to industrial applications which require real time conditional monitoring. For the past decades, 2D linear back projection (LBP) has been the standard technique for both commercialised ERT and ECT systems because of its simplicity and fast reconstruction speed. In this paper, ITS Plc has released a 'Reconstruction Tool-Suite' software that allows industrial users to utilise different reconstruction algorithms to further understand their processes. Different algorithms are integrated into this software package including the single step Tikhonov method and the iterative Landweber method. In the latest version of the software, the full-field 3D tomography reconstruction scheme is also included, which allows the users to perform 3D reconstruction for their processes. A series of experiments are conducted to validate the pros and cons of different methods.     

基于极限学习机求解正问题的 ECT 图像重建

在电容层析成像(ECT)图像重建迭代类算法中,通常采用线性正问题求解,以加快重建速度,由此产生重建误差。针对这一问题,提出了基于极限学习机(ELM)的非线性ECT正问题求解方法,ELM网络输入为介电常数分布,其输出为预测的电容测量值。将该方法与传统的Landweber迭代算法相结合构成ELM-Landweber迭代算法进行图像重建。为使样本具有较好的代表性,物体分布位置及大小均随机生成,并计算相应的归一化电容值作为ELM网络训练及测试样本,对ELM-Landweber迭代算法进行了仿真与静态实验,并与传统Landweber迭代算法进行比较。实验结果表明,相较于传统Landweber迭代算法,采用ELM-Landweber迭代算法,其算法收敛速度显著提高,重建图像质量得到明显改善。训练样本的平均图像相对误差由0.728减小至0.504,测试样本的平均图像相对误差由0.596减小至0.475。     

Window function-based regularization for electrical capacitance tomography image reconstruction

Image reconstruction for electrical capacitance tomography (ECT) is to retrieve the permittivity distribution of materials inside the sensor from the capacitance measurements outside. It is a typical inverse problem and has long been a challenge for its nonlinearity and ill-posedness. This paper discusses the application of Tikhonov regularization, widely used for ill-posed problems, to the image reconstruction for electrical capacitance tomography. Two methods using different regularizations are investigated, which are the standard Tikhonov regularization and the Tikhonov regularization based on the second order derivative operator. Particularly, a combined method using the linear back projection (LBP) result as the prior constraint for the Tikhonov regularization with the second order derivative operator is suggested. Simulation and experiment results show that this combined method takes advantages from both the linear back projection and the Tikhonov regularization and provides reconstructions better than those from the LBP and the Tikhonov regularization. In addition, considering the essence that the Tikhonov regularization can be described as a spectral filter characterized by its corresponding window function, we propose the possibility of applying other window functions to the ECT image reconstruction, which include the Gauss window, the Hanning window, the Blackman window, and the cosine window. Results also show the feasibility of using window functions as regularization, which presents a new strategy for the regularization of ECT image reconstruction.     

Image reconstruction of electrical capacitance tomography based on optimal simulated annealing algorithm using orthogonal test method

Electrical capacitance tomography (ECT) is a visualization measurement method for two-phase flow. Imaging permittivity distributions using electrical capacitance tomography has always been one of the most significant issues studied by scholars, and the algorithm will have a great impact on the accuracy of image reconstruction result. This paper applies simulated annealing (SA) algorithm to image reconstruction in ECT. However, some parameters of SA algorithm need to be optimized in order to obtain better reconstructed images in ECT. The influence of different parameter values in SA algorithm for image reconstruction in ECT is studied, and a set of optimal parameters of the SA algorithm is obtained based on the orthogonal experimental design method in this paper. At the same time, simulation and static experiments are conducted. Reconstructed images by SA algorithm with optimized parameter are compared with the linear back projection (LBP) and Landweber iterative algorithms. The results show that better images can be obtained for typical oil-gas two-phase flow using SA algorithm. The quality and shape fidelity of reconstructed image for the central object are obviously improved.     

基于互易原理磁感应成像中灵敏度矩阵的计算

磁感应成像(MIT)是一种利用线圈传感器重建所测物体内部电导率分布的成像方法.MIT中的灵敏度矩阵为所测感应电压对物体电导率变化的函数,是反演成像的关键.基于有限元方法和互易原理,提出一种有效计算MIT灵敏度矩阵的方法,在所建立测量模型基础上,运用该方法进行了实验与分析.实验结果表明,该方法可以快速求解MIT中的灵敏度矩阵,应用在高斯一步牛顿算法中可以实现图像重建,为MIT逆问题提供了更有效的解决方案.     

基于加权奇异值分解截断共轭梯度的电容层析图像重建

针对电容层析成像技术(ECT)中的"软场"效应和病态问题,提出了一种基于加权奇异值分解(SVD)截断共轭梯度的电容层析(ECT)图像重建算法。阐述了电容层析成像工作原理,提出了12电极ECT系统的测量方法。在分析灵敏度矩阵的奇异值分解理论的基础上,推导出了加权SVD截断共轭梯度的数学模型,并利用Tikhonov方法进行正则化加权处理。最后,分析了算法的收敛性,并将其应用于电容层析成像系统的图像重建中。实验结果表明,对于层流,截断共轭梯度算法的平均误差能达到27.54%,全部流型平均迭代步数达到13步,与LBP、Landweber和CG算法比较,该算法具有成像效果好,成像速度快,易于实现等特点。     

Visualisation of gas–oil two-phase flows in pressurised pipes using electrical capacitance tomography

Electrical capacitance tomography (ECT) was used to image various two-phase gas–oil horizontal flows on a 7.62 cm (3 in.) pressurised test loop. ECT is a novel non-invasive technique for imaging mixtures of electrically non-conducting substances. One of its most promising applications is the visualisation of gas–oil flows. This work presents a series of imaging experiments using a pressure-resistant ECT sensor. By varying the oil and gas flow rates, different flow regimes were established in the test loop. ECT images were obtained for each case and compared with (a) the flow observed through a transparent section in the loop and (b) the prediction of the Taitel–Duckler flow map. The results confirm the suitability of ECT for imaging gas–oil flows.     

非闭合电极电容层析成像传感器在冻土测试中的应用

为了实现电容层析成像技术对冻土冻结冰峰面的在线、非侵入测试,研制出了满足冻土测试要求的非闭合电极电容层析成像传感器,并对该种传感器的电容分布特性进行了实测;确定出了适合冻土测试的的高、低介电常数的标定物质;搭建了冻土一维冻结实验系统.对含水量8%的湿土样冻结过程的冰峰面迁移进行了电容层析成像测试,并利用IMNSNOF图像重建算法重建出了冻结过程各时刻的冻结截面物质分布图像,由图像可确定出冻土中已冻土、未冻区以及冰峰面的位置.电容层析成像测试结果与温度测试结果相吻合.     

Adaptive calibration of a capacitance tomography system for imaging water droplet distribution

A highly sensitive electrical capacitance tomography (ECT) system based on an HP4284 impedance analyser has been developed and used to quantify low concentration multi-phase flows in wet gas separation processes. The system hardware provides high accuracy (0.05%) and high resolution (10⁻¹⁷ F). The sensor was calibrated in an environmental chamber with solid samples of known permittivity over ranges of temperature and humidity. Adaptive calibration and adjacent electrode pair correction techniques were applied to image very low concentration profiles. This paper describes the techniques used and presents the experimental results obtained from a test flow rig called Twister, which has been designed to separate liquid droplets from wet gas streams. The test results over a range of operating conditions (20–95% humidity) demonstrate that the ECT system is capable of reconstructing clear images of the droplet distribution inside Twister. Changes as small as 1 gWater/kgAir in the form of liquid droplets were detectable. It has also been shown that the concentration of the condensable phase can be estimated quantitatively within 20% in comparison with the reference measurements.     

Dynamic imaging method using the low n-rank tensor for electrical capacitance tomography

Imaging objects in electrical capacitance tomography (ECT) measurement are often in a dynamic evolution process, and exploiting the spatial–temporal properties of the dynamic reconstruction objects is crucial for the improvement of the reconstruction quality. Based on the multiple measurement vectors, in this paper a robust dynamic reconstruction model that incorporates the ECT measurement information and the dynamic evolution information of a dynamic object, in which a series of dynamic images is cast as a third-order tensor that the first two dimensions are space and the third is time, is proposed. Under the considerations of the two-dimensional spatial structure property of a difference image and the spatial–temporal property of a third-order image tensor, a new objective functional that fuses the ECT measurement information, the dynamic evolution information, the temporal constraint, the spatial constraint, the low rank constraint of a difference image and the low n-rank constraint of a third-order tensor is proposed, where the images are reconstructed by a batching pattern. The split Bregman iteration (SBI) algorithm is developed for solving the proposed objective functional. Numerical simulations are implemented to demonstrate the advantages of the proposed algorithm on improving the reconstruction quality and the robustness.     

Decoupling the joint effect of moisture and mass in dense phase pneumatic conveying

Electric capacitance tomography (ECT) is advantageous for online imaging of pneumatic conveying of solids. From the ECT images, the spatial distribution of the mass of the material can be displayed at a very fast speed. However, as the mass distribution and the permittivity of the solids simultaneously affect the values of the measured capacitance arrays, they cause a coupled effect on the ECT images. In situations where the permittivity of the solids is influenced by the moisture, and this influence cannot be separated from the influence of the mass, or cannot be accounted for by an appropriate means, the measurement will be erroneous, as ECT images are usually interpreted as the distribution of the mass alone. This study aims to tackle the problem by an attempt to decouple the combined influence of the mass and the permittivity. A sensor of narrow electrodes is designed for the purpose of detecting only the variations in the permittivity. Simulation and experimental results both demonstrated that the influence of the permittivity and the mass of the solids can be decoupled under certain conditions, which provide a mechanism to correct the possible errors due to the unknown variation of the solids permittivity, or moisture.     

Split Bregman iteration based image reconstruction algorithm for electrical capacitance tomography

Practical applications of the electrical capacitance tomography (ECT) rely mainly on the effectiveness of reconstruction algorithms. In this paper the solution of the inverse problem with the focus on the ECT imaging is reformulated to be an optimization problem by introducing a new loss function with regularizes encoding multiple features of solution. An iterative scheme that decomposes a complex optimization problem into several simpler sub-problems is developed to solve the proposed loss function, in which the linearization approximation and the acceleration strategy are introduced to improve numerical performances. Numerical experiments validate the effectiveness of the proposed imaging method in tackling the ECT inverse problem.     

Maximum entropy regularization method for electrical impedance tomography combined with a normalized sensitivity map

Electrical impedance tomography (EIT) aims to estimate the electrical properties at the interior of an object from current–voltage measurements on its boundary. To overcome ill-posedness, regularization techniques such as Tikhonov regularization as well as some iterative methods were developed. In difference imaging between two different conductivity distributions, a conductivity change can be seen relatively non-negative to the medium with lower conductivity through some safeguard techniques. Therefore, the concept of maximum entropy from information theory and statistic mechanics can be used for this purpose. Furthermore, because the sensing field is “soft-field” and non-uniform, the same anomaly may produce different reconstruction signatures depending on its location within the image plane. Therefore, in this paper, maximum entropy based on general Tikhonov regularization, combined with normalized sensitivity map, is proposed to solve the inverse problem of EIT. Image reconstruction was carried out by maximum entropy regularization (MER) with a normalized sensitivity map and compared with the results from conjugate gradient method (CG), Tikhonov regularization, and CG with a normalized sensitivity map accordingly. Simulation and experiment results indicate that reconstructed images with higher quality can be obtained by MER with a normalized sensitivity map.