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 il-posed and nonlinear inverse problem of ECT image reconstruction, a new ECT image reconstruction method based on fast lin-earized 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 in-dicate that the proposed algorithm can fulfil the real-time requirement of ECT systems in the application.     

应用电容层析成像对多相流的动态可视化(英文)

Identifying the flow patterns is vital for understanding the complicated physical mechanisms in multiphase flows.For this purpose,electrical capacitance tomography(ECT) technique is considered as a promising visualization method for the flow pattern identification,in which image reconstruction algorithms play an important role.In this paper,a generalized dynamic reconstruction model,which integrates ECT measurement information and physical evolution information of the objects of interest,was presented.A generalized objective functional that simultaneously considers the spatial constraints,temporal constraints and dynamic evolution information of the objects of interest was proposed.Numerical simulations and experiments were implemented to evaluate the feasibility and efficiency of the proposed algorithm.For the cases considered in this paper,the proposed algorithm can well reconstruct the flow patterns,and the quality of the reconstructed images is improved,which indicates that the proposed algorithm is competent to reconstruct the flow patterns in the visualization of multiphase flows.     

基于小波网络的非线性动态过程建模和在环氧氯丙烷生产过程中的应用

A type of wavelet neural network, in which the scale function is adopted only,is proposed in this paper for non-linear dynamic process modelling.Its network size is decreased significantly and the weight coefficients can be estimated by a linear algorithm.The wavelet neural network holds some advantages supeiior to other types of neural networks.First, its network structure is easy to specify based on its theoretical analysis and intuition.Secondly, network training does not rely on stochastic gradient type techniques and avoidd the problem of poor convergence or undesirable local minima.The excellent statistic properties of the weight parameter estimations can be proven here.Both theoretical analysis and simulation study show that the identification method is robust and reliable. Furthermore,a hybrid network structure incorporating first-principle knowledge and wavelet network is developed to solve a commonly existing problem in chemical production processes.Applications of the hybrid network to a practical production process demonstrates that model generalisation capability is significantly improved.     

Sensor monitoring and online measurement correction in electric capacitance tomography system

The recalibration of electrical capacitance tomography (ECT) system is one of the key problems in keeping the system running steadily. However, for engineering application in solids/gas transport, online calibration can not be implemented and the data from this sensor may be unreliable due to the sensor pipe interior wall abrasion during pneumatic transport, so the solids concentration calculated from the reconstructed image based on these data will be highly inaccurate. The simulations show that, the inter-electrode relative capacitance variation of electrode pair spacing 1 is the most sensitive to the abrasion of sensor pipe interior wall, so this relative capacitance variation when the sensor is filled with air can be used as an indicator demanding offline system recalibration when the wall abrasion goes significant. Furthermore, while the pipe interior wall abrasion is not very serious, online correcting measured inter-electrode capacitance with wall capacitance variation can improve the accuracy of concentration calculation.     

电容层析成像技术在分离器料腿浓度测量中的应用

Accurate solid concentration measurement plays a key role in the process industry. Measurements analyzed offline can be used to estimate process efficiencies, to identify problems in a flow, and to validate computational models. Online measurements can be used for active control. Electrical capacitance tomography (ECT) is a unique measuring technique with great potential in multiphase flow measurement. Experimental studies are carried out on a solid concentration measurement in a cyclone separator dipleg, using ECT. In this experiment eight electrodes are selected for the ECT sensor that is placed on the straight tube of the dipleg. The fluctuating characteristics according to the screw feeder and the effect of the airflow rate from the top of the cyclone are analyzed. The feasibility and reliability of the method are verified by the experimental results.     

输入训练神经网络的维数约简算法及其在化工过程建模中的应用

Many applications of principal component analysis （PCA） can be found in dimensionality reduction. But linear PCA method is not well suitable for nonlinear chemical processes. A new PCA method based on improved input training neural network （IT-NN） is proposed for the nonlinear system modelling in this paper. Momentum factor and adaptive learning rate are introduced into learning algorithm to improve the training speed of IT-NN. Contrasting to the auto-associative neural network （ANN）, IT-NN has less hidden layers and higher training speed. The effectiveness is illustrated through a comparison of IT-NN with linear PCA and ANN with experiments. Moreover, the IT-NN is combined with RBF neural network （RBF-NN） to model the yields of ethylene and propylene in the naphtha pyrolysis system. From the illustrative example and practical application, IT-NN combined with RBF-NN is an effective method of nonlinear chemical process modelling.     

PVC生产过程故障传感器的检测与重构

Based on principal component analysis, this paper presents an application of faulty sensor detection and reconstruction in a batch process, polyvinylchloride (PVC) making process. To deal with inconsistency in process data, it is proposed to use the dynamic time warping technique to make the historical data synchronized first,then build a consistent multi-way principal component analysis model. Fault detection is carried out based on squared prediction error statistical control plot. By defining principal component subspace, residual subspace and sensor validity index, faulty sensor can be reconstructed and identified along the fault direction. Finally, application results are illustrated in detail by use of the real data of an industrial PVC making process.     

基于粒子群优化算法和非线性盲源信号分离测量两相流速度(英文)

In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method.Because of the nonlinear relationship between the output signals of capacitance sensors and fluid in pipeline,nonlinear blind source separation is applied.In nonlinear blind source separation,the odd polynomials of higher order are used to fit the nonlinear transformation function,and the mutual information of separation signals is used as the evaluation function.Then the parameters of polynomial and linear separation matrix can be estimated by mutual information of separation signals and particle swarm optimization algorithm,thus the source signals can be separated from the mixed signals.The two-phase flow signals with noise which are obtained from upstream and downstream sensors are respectively processed by nonlinear blind source separation method so that the noise can be effectively removed.Therefore,based on these noise-suppressed signals,the distinct curves of cross correlation function and the transit times are obtained,and then the velocities of two-phase flow can be accurately calculated.Finally,the simulation experimental results are given.The results have proved that this method can meet the measurement requirements of two-phase flow velocity.     

An Improved Hybrid Genetic Algorithm for Chemical Plant Layout Optimization with Novel Non-overlapping and Toxic Gas Dispersion Constraints

New approaches for facility distribution in chemical plants are proposed including an improved non-overlapping constraint based on projection relationships of facilities and a novel toxic gas dispersion constraint. In consideration of the large number of variables in the plant layout model, our new method can significantly reduce the number of variables with their own projection relationships. Also, as toxic gas dispersion is a usual incident in a chemical plant, a simple approach to describe the gas leakage is proposed, which can clearly represent the constraints of potential emission source and sitting facilities. For solving the plant layout model, an improved genetic algorithm （GA） based on infeasible solution fix technique is proposed, which improves the globe search ability of GA. The case study and experiment show that a better layout plan can be obtained with our method, and the safety factors such as gas dispersion and minimum distances can be well handled in the solution.     

Improvement in growth yield of single-walled carbon nanotubes with narrow chirality distribution by pulse plasma CVD

A pulse plasma chemical vapor deposition (CVD) technique was developed for improving the growth yield of single-walled carbon nanotubes (SWNTs) with a narrow chirality distribution. The growth yield of the SWNTs could be improved by repetitive short duration pulse plasma CVD, while maintaining the initial narrow chirality distribution. Detailed growth dynamics is discussed based on a systematic investigation by changing the pulse parameters. The growth of SWNTs with a narrow chirality distribution could be controlled by the difference in the nucleation time required using catalysts comprising relatively small or large particles as the key factor. The nucleation can be controlled by adjusting the pulse on/ofF time ratio and the total processing time.     

一种新的电容层析成像电极组合激励测量模式

电容层析成像图像重建为非线性不适定反问题,其敏感场分布不均匀,可获得的测量数据有限,中心处物体的成像效果不佳。增加电极数目,可获得更多的电容测量数据,减小其不定性,同时改善敏感场分布。但同时导致电容测量值变小,测量精度下降。在保证电容测量精度的前提下,提出了24电极组合式电容层析成像传感器结构,研究了两种激励测量方案,并与传统12电极电容层析成像传感器进行了对比分析,包括电容测量值的大小及其动态测量范围、灵敏场分布的均匀性以及不同流型下的重建图像。仿真结果表明,与12电极电容层析成像传感器相比,采用24电极组合式电容层析成像传感器,其电容测量值大,可较好地保证测量精度,其灵敏度分布更加均匀,对中心处物体的成像质量明显提高。     

基于数据驱动的卷积神经网络电容层析成像图像重建

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。     

Investigation of gas–solid bubbling fluidized beds using ECT with a modified Tikhonov regularization technique

Electrical capacitance tomography (ECT) provides a non‐intrusive means to visualize cross‐sectional material distribution of gas–solid bubbling fluidized beds. Successful application of ECT strongly depends on the image reconstruction algorithm used. For on‐line measurements of bubbling fluidized beds, employing an algorithm that can produce high‐quality images without extensive computation is necessary. Using the conventional Tikhonov regularization algorithm, image quality in the central area is basically satisfied but suffers from artifacts in the near‐wall region. To solve this problem, a similar division operation learned from linear back projection was introduced to modify the conventional Tikhonov algorithm. Both numerical simulations and experiments were performed to evaluate the modified technique. The results indicate that the artifacts can be effectively removed and the reconstructed image quality is similar to Landweber method with dozens of iterations. Furthermore, the modified Tikhonov technique shows high accuracy when obtaining important hydrodynamic parameters in gas–solid bubbling fluidized beds. © 2017 American Institute of Chemical Engineers AIChE J, 63: 29–41, 2018     

一种用于在线测量的电容层析成像图像重建算法

提出了一种新的、快速的电容层析成像算法。在分析极小范数解的基础之上针对ECT逆问题的特点对其进行改进，并利用奇异值分解定理证明这种改进的数值稳定作用，从而从极小范数解的角度解决了ECT逆问题数值解的唯一性和稳定性问题；在此基础上从最优化的角度推导出进一步提高重建图像质量的公式；数值实验表明这种改进是有效的，其图像重建时间近似LBP，然而成像质量比LBP、Tikhonov和Landweber迭代法要好。     

ECT imaging of three-phase fluidized bed based on three-phase capacitance model

In this work, the electrical capacitance tomography (ECT) with neural network multi-criteria optimization image reconstruction technique (NN-MOIRT), early developed by the authors, is applied to imaging bubble column and three-phase fluidized bed systems in the real time manner. Air, norpar (paraffin) and glass-beads are used as the gas, liquid, and solid phases, respectively. A three-phase capacitance model coupled with a two-region model is proposed to attain the gas holdup and the solids fraction from the permittivity maps of the three-phase system. The two-region model assumes that the solids fraction in the emulsion phase in the no bubble region is the same as in the bubble region. The three-phase capacitance model combines series and parallel capacitance connections among gas, liquid and solid components to relate the three-phase permittivity to each phase holdup. A direct image calculation to obtain the gas holdup from the permittivity map of the three-phase system is also performed by determining the permittivity threshold for the gas bubbles. Comparisons of the gas holdup obtained by ECT with that obtained from liquid head measurement showed a good agreement, validating the applicability of the model and its associated image calculation.     

Neural network multi-criteria optimization image reconstruction technique (NN-MOIRT) for linear and non-linear process tomography

In this work, an analog neural network is utilized to develop a new image reconstruction technique for the linear as well as the non-linear process tomography. The ultrasonic computed tomography (CT) and the electrical capacitance tomography (ECT) are chosen to represent the linear and the non-linear tomography. The image reconstruction technique is based on a multi-criteria optimization, namely neural network multi-criteria optimization image reconstruction technique (NN-MOIRT). The optimization technique utilizes multi-objective functions: (a) the negative entropy function, (b) the function of the least weighted square error of projection (integral) values between the measured data and the estimated projection data from the reconstructed image, and (c) a smoothness function that gives a relatively small peakedness in the reconstructed image. The optimization image reconstruction problem is then solved using the Hopfield model with dynamic neural-network computing. The technique has been tested using simulated and measured data; this technique has shown significant improvement in accuracy and consistency compared with other available techniques for both linear and non-linear tomography.     

Measurement of real-time flow structures in gas–liquid and gas–liquid–solid flow systems using electrical capacitance tomography (ECT)

The real-time cross-sectional distributions of the gas holdups in gas–liquid and gas–liquid–solid systems are measured using electrical capacitance tomography. For the gas–liquid system, air as the gas phase and both Norpar 15 (paraffin) and Paratherm as the liquid phases are used. Polystyrene beads whose permittivity is similar to that of Paratherm are used as the solid phase in the gas–liquid–solid system. The three-phase system is essentially a dielectrically two-phase system enabling measurement of the gas holdup in the gas–liquid–solid system independent of the other two phases. A new reconstruction algorithm based on a modified Hopfield dynamic neural network optimization technique developed by the authors is used to reconstruct the tomographic data to obtain the cross-sectional distribution of the gas holdup. The real-time flow structure and bubbles flow behavior in the two- and three-phase systems are discussed along with the effects of the gas velocity and the solid particles.     

用于两相流流型显示和空隙率测量的电容层析成像技术

引　言两相流流型的实时显示和空隙率的在线测量对两相流系统的控制、运行乃至机理研究等均具有重要意义 ,一直是两相流领域中重要的研究方向 .现已提出多种实现流型显示和空隙率测量的方法 ,例如用于流型显示的核辐射线法和光学法 ,用于空隙率 (或浓度 )测量的机理估算法、核辐射线法、电学法、光学法、微波法、热学法和核磁共振法等 ,但是总的来讲还未能满足应用要求 ,实际应用的例子也较少[1] .电容层析成像 (ｅｌｅｃｔｒｉｃａｌｃａｐａｃｉｔａｎｃｅｔｏｍｏｇｒａｐｈｙ ,简记ＥＣＴ)技术由于可在不干扰流场的情况下获取反映两相流…     

Dynamics of spiral bubble plume motion in the entrance region of bubble columns and three-phase fluidized beds using 3D ECT

In this study, we have developed, for the first time in the field, a ‘dynamic’ three-dimensional image reconstruction technique for electrical capacitance tomography (ECT) imaging based on a neural-network multi-criterion optimization (NNMOIRT). This development enables a real time, 3D imaging of a moving object to be realized. The image reconstruction scheme of the 3D ECT is established by introducing a 3D sensitivity matrix into the NN-MOIRT algorithm, developed earlier by the authors. The sensitivity matrices employed are based on 6- and 12-electrode twin-plane cylindrical sensors. The NN-MOIRT algorithm reconstructs simultaneously the image voxels (volume pixels) on 20×20×20 resolutions from the capacitance data obtained using the twin-plane sensors which surrounds the 3D section of 8 cm in length in the cylindrical columns. The technique is successfully tested over a 3D simulated as well as actual experimental objects. The 3D ECT technique is used to investigate the transient phenomena in the entrance region of a 10 cm diameter column using a single nozzle gas distributor with paraffin liquid (Norpar), air, and glass-beads as flow media. Hydrodynamic characteristics of the gas-liquid and gas-liquid-solid flows, including 3D bubble plume spiral motion, 3D large scale liquid vortex dynamics and real time three-dimensional gas holdup distribution are studied.