Yanbin Xu

A high-performance digital system for electrical capacitance tomography

This paper describes a recently developed digital-based data acquisition system for electrical capacitance tomography (ECT). The system consists of high-capacity field-programmable gate arrays (FPGA) and fast data conversion circuits together with a specific signal processing method. In this system, digital phase-sensitive demodulation is implemented. A specific data acquisition scheme is employed to deal with residual charges in each measurement, resulting in a high signal-to-noise ratio (SNR) at high excitation frequency. A high-speed USB interface is employed between the FPGA and a host PC. Software in Visual C++ has been developed to accomplish operational functions. Various tests were performed to evaluate the system, e.g. frame rate, SNR, noise level, linearity, and static and dynamic imaging. The SNR is 60.3 dB at 1542 frames s−1 for a 12-electrode sensor. The mean absolute error between the measured capacitance and the linear fit value is 1.6 fF. The standard deviation of the measurements is in the order of 0.1 fF. The dynamic imaging test demonstrates the advantages of high temporal resolution of the system. The experimental results indicate that the digital signal processing devices can be used to construct a high-performance ECT system.

An integrated ECT/ERT dual modality sensor

Capacitance and resistance tomography systems have been developed for visualizing the distributions of materials in an industrial process. They offer certain advantages over other tomography modalities, such as low cost, rapid response, no radiation and being non-intrusive. Single modal tomography could provide a satisfactory solution in most process applications. However, in some more complex applications, additional information is required for comprehensive understanding of the process under investigation. ECT and ERT are two most researched electrical tomography techniques. Individual ECT and ERT systems has been combined for dual modal measurement in recent years, however, the two sensors were located at two different cross-sections of the process, resulting in poor sensor integration and data fusion. As a result of the present research an integrated tomography system with capacitive and resistive sensors located at the same cross-section of the process has been developed. In the integrated system the use of both resistive and capacitive electrodes help eliminate mutual interferences between the two modalities. Experimental work with water-gas two-phase flow on vertical and horizontal pipes shows that the integrated system can provide effective dual modal measurements. The reconstructed images together with the stacked images are used to deduce such process parameters as gas holdup and flow velocity.

A fast sparse reconstruction algorithm for electrical tomography

Electrical tomography (ET) has been widely investigated due to its advantages of being non-radiative, low-cost and high-speed. However, the image reconstruction of ET is a nonlinear and ill-posed inverse problem and the imaging results are easily affected by measurement noise. A sparse reconstruction algorithm based on L1 regularization is robust to noise and consequently provides a high quality of reconstructed images. In this paper, a sparse reconstruction by separable approximation algorithm (SpaRSA) is extended to solve the ET inverse problem. The algorithm is competitive with the fastest state-of-the-art algorithms in solving the standard L2−L1 problem. However, it is computationally expensive when the dimension of the matrix is large. To further improve the calculation speed of solving inverse problems, a projection method based on the Krylov subspace is employed and combined with the SpaRSA algorithm. The proposed algorithm is tested with image reconstruction of electrical resistance tomography (ERT). Both simulation and experimental results demonstrate that the proposed method can reduce the computational time and improve the noise robustness for the image reconstruction.

Separation of Gas–Liquid Two-Phase Flow Through Independent Component Analysis

Two-phase flow measurement has attracted a major interest in the past four decades due to its wide range of applications in industry. This paper introduces a new method to separate the gas phase from the liquid phase through a blind source separation algorithm, without a separate device, based on the assumption that the two phases are separated and their independence is reflected in the statistical relation between the electrical signals generated by the process. Experimental data are obtained from a gas-liquid two-phase flow rig through electrical resistance tomography (ERT). An independent component analysis (ICA) method is applied to separate the gas phase from the liquid phase. The efficiency of the ICA method with the ERT data is assessed through experiments. The independent components (ICs) are interpreted by comparing them with the reconstructed images by ERT. The comparative studies show that ICA is effective in extracting phase information of gas-liquid two-phase flow, particularly for stratified, slug, and wave flows. Based on the extracted ICs, the cross-correlation technique is adopted to estimate the mean velocity of the liquid phase in the central area, the gas phase at the interface, and the liquid phase around the pipe wall and the liquid slug. Through correlating ICs representing different spatially independent processes from the upstream and downstream planes after the elimination of cyclostationary characteristics of ICs, the mean velocity of different spatially processes is obtained.

Development of Single Drive Electrode Electrical Resistance Tomography System

A new data acquisition strategy, namely the single drive electrode method used in electrical resistance tomography (ERT) system, is introduced in this paper. The ERT system based on the method has been designed and the bi-directional pulse current is used in this system. The simulation studies have been done by ANSYS software and the results have been analyzed for the deep study. The experiments results and the reconstruction image are shown finally in order to testify the reliability of the new system and the feasibility of the new method

Application of electrical resistance tomography for slug flow measurement in gas/liquid flow of horizontal pipe

It is important to study the slug flow in a gas/liquid flow to achieve an in-depth understanding of the mixture flow and optimization of industrial processes. This paper presents a study of the slug flow measurement in gas/liquid flow of horizontal pipe. The application of ERT for slug flow measurement is demonstrated and described, including the visualization of slug size and shape. A novel method to obtain the liquid slug velocity is put forward. Independent component analysis (ICA) method has been applied to extract the liquid slug information. A good agreement between the independent component with the maximal kurtosis and liquid slug fluctuation of slug flow is observed. Through correlating independent component with the maximal kurtosis from upstream and downstream planes, the mean velocity and the length of liquid slug have been obtained. The comparison between the mean velocity from the ERT system and CCD camera is presented. The experimental results show the method is reasonable for the slug flow measurement in horizontal pipe.

An Lq–Lp optimization framework for image reconstruction of electrical resistance tomography

Image reconstruction in electrical resistance tomography (ERT) is an ill-posed and nonlinear problem, which is easily affected by measurement noise. The regularization method with L2 constraint term or L1 constraint term is often used to solve the inverse problem of ERT. It shows that the reconstruction method with L2 regularization puts smoothness to obtain stability in the image reconstruction process, which is blurry at the interface of different conductivities. The regularization method with L1 norm is powerful at dealing with the over-smoothing effects, which is beneficial in obtaining a sharp transaction in conductivity distribution. To find the reason for these effects, an Lq–Lp optimization framework (1 ≤ q ≤ 2, 1 ≤ p ≤ 2) for the image reconstruction of ERT is presented in this paper. The Lq–Lp optimization framework is solved based on an approximation handling with Gauss–Newton iteration algorithm. The optimization framework is tested for image reconstruction of ERT with different models and the effects of the Lp regularization term on the quality of the reconstructed images are discussed with both simulation and experiment. By comparing the reconstructed results with different p in the regularization term, it is found that a large penalty is implemented on small data in the solution when p is small and a lesser penalty is implemented on small data in the solution when p is larger. It also makes the reconstructed images smoother and more easily affected by noise when p is larger.

Digital signal processing in electrical capacitance tomography

This paper presents the design, implementation and performance of a 16-electrode electrical capacitance tomography in Tianjin University. Currently, electrical capacitance tomography systems are primarily based on analog hardware. However, there are some disadvantages for the analog devices, e.g. relatively narrow bandwidth and long settling time, which place limits to further improvements in both data acquisition rate and precision. With the advances in logic resource, lower cost and flexibility of FPGA, an FPGA based data acquisition scheme was chosen over the traditional analog signal processing method. Improvements in system performance are achieved by implementing most functions in digital rather than analog hardware. Logics realized within the FPGA perform the signal generation, phase-sensitive demodulation, micro-controller and data transfer functions, thus providing effective integration. Preliminary results show that the signal-to-noise ratio could be greater than 76 dB. The reconstructed images on the prototype are presented to illustrate the feasibility and potentiality of the FPGA based capacitance measurement system.

Sparse regularization for small objects imaging with electrical resistance tomography

Electrical resistance tomography (ERT) is a technique for reconstructing internal conductivity distribution of the field from electrical measurements on the surface. It is a nonlinear and ill-posed inverse problem which is easily affected by measurement noise. In order to improve the image quality of ERT, regularization methods are used to treat this ill-posedness. The Tikhonov method, which is based on L2 regularization, is generally used to solve this problem. However, it is not suitable when the conductivity has a sharp transition because it puts smoothness to obtain stability in the image reconstruction process. Recently, sparse regularization method with L1 norm shows its powerful effects for dealing with problem that has sharp transition in conductivity distribution. Thus image reconstruction results for small objects will be discussed in this paper with L1 regularization method and L2 regularization method. Simulation results show that L1 regularization method can effectively improve the image reconstruction results of small objects. It also shows L1 regularization method is less sensitive to measurement noise.

An adaptive total variation regularization method for electrical resistance tomography

Total variation (TV) regularization method is widely used to solve the inverse problem of Electrical resistance tomography (ERT), which is ill-posed. However, TV regularization often suffers the staircases effect. To reduce those staircases effect, a modified TV regularization, called adaptive total variation (ATV) regularization, is proposed in this paper, which automatically adjusts the regularization term by distinguishing between edges and ramps according to the image gradients. With adaptive regularization term, at block edges it behaves more like the TV functional (∫Ω|∇u|dΩ) to perverse the edges and in ramp regions it behaves more like the H1 functional (∫Ω|∇u|2dΩ) to avoid the staircase effect. Simulation and experimental results of ATV regularization and TV regularization are compared, which show that ATV regularization can avoid the staircase effect and endure a relatively high level of noise in the measured voltages.