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Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.

In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.

This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.

The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

The purpose of this paper is to establish a cheap but accurate approximation of the forward map in electrical capacitance tomography in order to approach robust real‐time inversion in the framework of Bayesian statistics based on Markov chain Monte Carlo (MCMC) sampling.

Existing formulations and methods to reduce the order of the forward model with focus on electrical tomography are reviewed and compared. In this work, the problem of fast and robust estimation of shape and position of non‐conducting inclusions in an otherwise uniform background is considered. The boundary of the inclusion is represented implicitly using an appropriate interpolation strategy based on radial basis functions. The inverse problem is formulated as Bayesian inference, with MCMC sampling used to efficiently explore the posterior distribution. An affine approximation to the forward map built over the state space is introduced to significantly reduce the reconstruction time, while maintaining spatial accuracy. It is shown that the proposed approximation is unbiased and the variance of the introduced additional model error is even smaller than the measurement error of the tomography instrumentation. Numerical examples are presented, avoiding all inverse crimes.

Provides a consistent formulation of the affine approximation with application to imaging of binary mixtures in electrical tomography using MCMC sampling with Metropolis‐Hastings‐Green dynamics.

The proposed cheap approximation indicates that accurate real‐time inversion of capacitance data using statistical inversion is possible.

The proposed approach demonstrates that a tolerably small increase in posterior uncertainty of relevant parameters, e.g. inclusion area and contour shape, is traded for a huge reduction in computing time without introducing bias in estimates. Furthermore, the proposed framework – approximated forward map combined with statistical inversion – can be applied to all kinds of soft‐field tomography problems.

The investigation of the influence of the modeling error on the solution of the inverse problem given uncertain measured data in electrical capacitance tomography (ECT).

The solution of the nonlinear inverse problem in ECT and hence, the obtainable accuracy of the reconstruction result, highly depends on the numerical modeling of the forward map and on the required regularization. The inherent discretization error propagates through the forward map, the solution of the inverse problem, the subsequent calculation of process parameters and properties and may lead to a substantial estimation error. Within this work different finite element meshes are compared in terms of obtainable reconstruction accuracy. In order to characterize the reconstruction results, two error measures are introduced, a relative integral error and the relative error in material fraction. In addition, the influence of the measurement noise given different meshes is investigated from the statistical point of view using repeated measurements.

The modeling error, the degree of regularization, and measurement uncertainties are the determining and limiting factors for the obtainable reconstruction accuracy of electrical tomography systems. The impact of these key influence factors on the calculation of process properties given both synthetic as well as measured data is quantified. Practical implications – The obtained results show that especially for measured data, the variability in calculated parameters strongly depends on the efforts put on the forward modeling, i.e. on an appropriate finite element mesh size. Hence, an investigation of the modeling error is highly recommended when real‐world tomography problems have to be solved.

The results presented in this work clearly show how the modeling error as well as inherent measurement uncertainties influence the solution of the inverse problem and the posterior calculation of certain parameters like void fraction in process tomography.

Crystallization is the process widely used for components separation and solids purification. The systems for crystallization process evaluation applied so far, involve numerous non-invasive tomographic measurement techniques which suffers from some reported problems. The purpose of this paper is to show the abilities of three-dimensional Electrical Capacitance Tomography (3D ECT) in the context of non-invasive and non-intrusive visualization of crystallization processes. Multiple aspects and problems of ECT imaging, as well as the computer model design to work with the high relative permittivity liquids, have been pointed out.

To design the most efficient (from a mechanical and electrical point of view) 3D ECT sensor structure, the high-precise impedance meter was applied. The three types of sensor were designed, built, and tested. To meet the new concept requirements, the dedicated ECT device has been constructed.

It has been shown that the ECT technique can be applied to the diagnosis of crystallization. The crystals distribution can be identified using this technique. The achieved measurement resolution allows detecting the localization of crystals. The usage of stabilized electrodes improves the sensitivity of the sensor and provides the images better suitable for further analysis.

The dedicated 3D ECT sensor construction has been proposed to increase its sensitivity in the border area, where the crystals grow. Regarding this feature, some new algorithms for the potential field distribution and the sensitivity matrix calculation have been developed. The adaptation of the iterative 3D image reconstruction process has also been described.

The purpose of this paper is to conduct a review of types of tomographic systems that have been widely researched within the past 10 years. Decades of research on non-invasively and non-intrusively visualizing and monitoring gas-liquid multi-phase flow in process plants in making sure that the industrial system has high quality control. Process tomography is a developing measurement technology for industrial flow visualization.

A review of types of tomographic systems that have been widely researched especially in the application of gas-liquid flow within the past 10 years was conducted. The sensor system operating fundamentals and assessment of each tomography technology are discussed and explained in detail.

Potential future research on gas-liquid flow in a conducting vessel using ultrasonic tomography sensor system is addressed.

The authors would like to undertake that the above-mentioned manuscript is original, has not been published elsewhere, accepted for publication elsewhere or under editorial review for publication elsewhere and that my Institute’s Universiti Teknologi Malaysia representative is fully aware of this submission.

The purpose of this paper is to calculate the two‐dimensional (2D) centre position of objects with known shapes based on the reconstruction image of a square sensing area estimated with simulated and measured data by using electrical capacitance tomography (ECT).

A 2D electrostatic finite element model is used to calculate the capacitances between electrode pairs. A reconstruction algorithm with low computation time provides suitable images for subsequent image processing techniques. The results based on numerical data are verified by measurements.

It is possible to calculate the centre position of up to four rods (cross‐sectional area about 5 per cent of the measuring area) with an accuracy of 3 per cent in both coordinate directions related to the dimensions of the measuring area.

The paper presents an efficient method for position determination of several objects with known shape and uniform permittivity distribution by using ECT measurements with low‐cost electronic for industrial application.

There are demands from the industry to have a modern application of Electrical Capacitance Tomography (ECT) system which is mobile and agile. One of the factors why such system is needed in the industry is because of the requirement to install the measurement sensors in a hostile and harsh environment which demands a special kind of ECT system. This paper will discuss the features of mobile or portable ECT which is more practical to be implemented in the harsh environment. Besides, the implementation of cloud computing and wireless technology in the portable ECT systems is also discussed. This review outlines some key features of portable or in another word mobile ECT as a complete system.

There are demands from the industry to have a modern application of ECT system which is mobile and agile. One of the factors why such system is needed in the industry is due to the requirement to install the measurement sensors in hostile and harsh environment which demands a special kind of ECT systems. This paper will discuss the features of mobile or portable ECT which is more practical to be implemented in the harsh environment. Besides, the implementation of cloud computing and wireless technology in the portable ECT systems is also being discussed. This review outlines some key features of portable or in another word mobile ECT as a complete system.

This review outlines some key features of portable or in another word mobile ECT as a complete system. A lot of improvement can be done to realize a reliable and stable ECT system. It is seems that in the near future, machine to machine communication will become the main stream.

This paper fulfils an identified need to study improvement that can be done to develop a portable ECT system which is reliable and stable. Besides, the implementation of cloud computing and wireless technology in the portable ECT systems is also discussed.

The purpose of this paper is to demonstrate improvement of the accuracy of electrical tomography reconstruction by incorporation of a priori knowledge into the inverse problem solution.

The fusion of two different inversion algorithms capable of real‐time operation is discussed, namely a non‐iterative monotonicity‐based approach, determining the a priori knowledge and an iterative Gauss‐Newton (GN)‐based reconstruction algorithm. Furthermore, the method is compared with the unmodified algorithms themselves by means of reconstructions from simulated inclusions at different noise levels.

The accuracy of the inverse problem reconstructions, especially at the boundary regions of the unknown inclusions, benefit from the investigations of incorporating a priori knowledge about material values and can be considerable improved. The monotonicity method itself, which has low complexity, provides remarkable reconstruction results in electrical tomography.

The paper is applied to simulated discrete two‐phase scenarios, e.g. gas/oil mixtures. In a further step the method would be tested with measured data. Moreover, investigations have to be carried out in order to make the monotonicity‐based reconstruction principle more robust against disturbing artifacts.

The fusion of the non‐iterative monotonicity‐based method with the GN‐based algorithm demonstrates a novel approach of improving the reconstruction accuracy in electrical tomography.

The purpose of this paper is to introduce a significant modification of the sensitivity maps calculation process using electric field distribution analysis. A sensitivity matrix is typically a crucial part of a deterministic image reconstruction process in a three-dimensional capacitance tomography (3D ECT) and strictly decides about a final image quality. Commonly used sensitivity matrix computation methods mostly provide acceptable results and additionally allow to perform a recalculation of sensitivity maps according to the changing permittivity distribution.

The new “tunnel-based” algorithm is proposed which traces the surfaces constructed along the electric field lines. The new solution is developed and tested using experimental data.

To fully validate the new technique both linear and non-linear image reconstruction processes were performed and the criteria of image error estimation were discussed. This paper discusses some preliminary results of the image reconstruction process using the new proposed algorithm. As a result of this research, an increased accuracy of the new method is proved.

The presented results of image reconstruction with new sensitivity matrix in comparison with the classic matrix proved that the new solution is able to improve the convergence and stability of image reconstruction process for 3D ECT imaging.

Rectangular fluidised beds are commonly used in industry, e.g. circulating fluidised bed (CFB) boilers. Apparently, no one has tried to imagine rectangular fluidised beds by electrical capacitance tomography (ECT). The purpose of this paper is to design a rectangular ECT sensor to understand the behaviour of a rectangular CFB riser.

A rectangular sensor with eight electrodes is adopted to obtain the capacitance data. The sensitivity map is simulated to calculate the grey level of pixels for visualisation using the linear back‐projection algorithm.

Experiments showed that the position of the objects in the riser can be obviously indicated and the central region of the object(s) has significantly higher grey level than other regions in the images using the rectangular ECT sensor.

It has a limitation in providing a higher resolution image.

The results obtained by the rectangular ECT sensor show that it is promising to study the characteristics of flow non‐uniformity in the fast fluidisation regime of CFB.

Without using square and circular ECT sensors, this is the first time a rectangular ECT sensor has been developed to study the unique problems of the characteristics of flow non‐uniformity in a rectangular CFB riser.