A dynamic volume imaging based on the principle of electrical capacitance tomography (ECT), namely, electrical capacitance volume tomography (ECVT), has been developed in this study. The technique generates, from the measured capacitance, a whole volumetric image of the region enclosed by the geometrically three-dimensional capacitance sensor. This development enables a real-time, 3-D imaging of a moving object or a real-time volume imaging (4-D) to be realized. Moreover, it allows total interrogation of the whole volume within the domain (vessel or conduit) of an arbitrary shape or geometry. The development of the ECVT imaging technique primarily encloses the 3-D capacitance sensor design and the volume image reconstruction technique. The electrical field variation in three-dimensional space forms a basis for volume imaging through different shapes and configurations of ECT sensor electrodes. The image reconstruction scheme is established by implementing the neural-network multicriterion optimization image reconstruction (NN-MOIRT), developed earlier by the authors for the 2-D ECT. The image reconstruction technique is modified by introducing into the algorithm a 3-D sensitivity matrix to replace the 2-D sensitivity matrix in conventional 2-D ECT, and providing additional network constraints including 3-to-2-D image matching function. The additional constraints further enhance the accuracy of the image reconstruction algorithm. The technique has been successfully verified over actual objects in the experimental conditions.Index Terms-3-D ECT, dynamic volume imaging, electrical capacitance volume tomography, Hopfield analog neural network.

This article reports recent advances and progress in the field of electrical capacitance volume tomography (ECVT). ECVT, developed from the two-dimensional electrical capacitance tomography (ECT), is a promising non-intrusive imaging technology that can provide real-time three-dimensional images of the sensing domain. Images are reconstructed from capacitance measurements acquired by electrodes placed on the outside boundary of the testing vessel. In this article, a review of progress on capacitance sensor design and applications to multi-phase flows is presented. The sensor shape, electrode configuration, and the number of electrodes that comprise three key elements of three-dimensional capacitance sensors are illustrated. The article also highlights applications of ECVT sensors on vessels of various sizes from 1 to 60 inches with complex geometries. Case studies are used to show the capability and validity of ECVT. The studies provide qualitative and quantitative real-time three-dimensional information of the measuring domain under study. Advantages of ECVT render it a favorable tool to be utilized for industrial applications and fundamental multi-phase flow research.

This article describes the recent progress in research and development on electrical capacitance tomography (ECT). Specifically, the article highlights several aspects of ECT including the electrical capacitance volume tomography (ECVT), 3D sensor design, 3D neural network multicriterion image reconstruction technique (3D-NN-MOIRT), multimodal imaging based on ECT and ECVT sensors, static-charge effects and the scheme of their elimination in the ECT image reconstruction, and multiphase flow imaging applications. The multimodal capability that enables permittivity and conductivity imaging to be simultaneously conducted is illustrated. The simulation and experimental results are presented to provide quantitative and/or qualitative assessment of the significance of various ECT techniques. The employment of ECVT in conjunction with using electrical capacitance based imaging sensors is shown to represent a favorable tool for industrial multiphase flow imaging.

A combined multilayer feed-forward neural network (MLFF-NN) and analogue Hopfield network is developed for nonlinear image reconstruction of electrical capacitance tomography (ECT). The (nonlinear) forward problem in ECT is solved using the MLFF-NN trained with a set of capacitance data from measurements based on a back-propagation training algorithm with regularization. The inverse problem is solved using an analogue Hopfield network based on a neural-network multi-criteria optimization image reconstruction technique (HN-MOIRT). The nonlinear image reconstruction based on this combined MLFF-NN + HN-MOIRT approach is tested on measured capacitance data not used in training to reconstruct the permittivity distribution. The performance of the technique is compared against commonly used linear Landweber and semi-linear image reconstruction techniques, showing superiority in terms of both stability and quality of reconstructed images.

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