Tuomo Savolainen

Simultaneous reconstruction of electrode contact impedances and internal electrical properties: I. Theory

In electrical impedance tomography (EIT) currents are applied through the electrodes attached on the surface of the object and the resulting voltages are measured using the same or additional electrodes. The internal admittivity distribution is estimated based on the current and voltage data. When the voltages are measured on the current carrying electrodes the contact impedance that exists in the electrode–surface interface causes a voltage drop. In some cases this effect of the electrodes is known. However, this is not always the case and the contact impedance has to be taken into account in the image reconstruction. In this paper we propose an approach for estimating the contact impedance of the electrodes simultaneously with the estimation of the admittivity of the object. The complete electrode model (CEM) is used in the estimation procedure. We compare the proposed approach to a simple method which is based on the well known definition of the sample resistivity. The proposed approach is tested with real measurements by estimating the admittivity of isotonic saline solution in a cylindrical test cell and with simulations in a three-dimensional cylindrical domain. The CEM-based approach is shown to produce results that are similar to the results obtained with the simple approach in the test cell case. The advantage of the CEM-based approach over the simple approach is that the complete electrode model does not have any geometrical constraints, which makes it possible to utilize it in EIT studies. The results show that the CEM-based approach works well and can be used in practical contact impedance estimation with real measurements. This will be further studied in part II of this paper.

Suitability of a PXI platform for an electrical impedance tomography system

There are many different electrical impedance tomography (EIT) systems which are either non-commercial (in-house products) or commercial products. However, these systems are usually designed for specific applications and therefore the functionality of the systems might be limited. Nowadays there are commercially available many low-cost, efficient and accurate multifunctional components for data acquisition and signal processing. Therefore, it should be possible to construct an EIT system which is mainly built from commercially available components. The main goal of this work was to study the performance of a PXI-based EIT system. In this work, a PXI-based EIT system with 16 independent current injection channels and 80 independent measurement channels was constructed and tested. The results indicate that an EIT system can be constructed using a PXI platform which decreases the construction time of the system. Moreover, the system is efficient, accurate, modular, and it is not limited to any predetermined measurement protocols.

Real time three-dimensional electrical impedance tomography applied in multiphase flow imaging

In many industrial applications the aim is to obtain information on three-dimensional (3D) material distribution within the process vessels. With standard two-dimensional (2D) techniques only vague cross-sectional information can be obtained. It could be possible to carry out several 2D reconstructions on different layers and in this way to obtain 3D information. However, in this approach errors are induced since no real 3D information is utilized in the image reconstruction. In this paper we describe an approach to measure, reconstruct and visualize three-dimensional electrical impedance tomography images in real time. The reconstruction is based on a difference imaging scheme. An efficient current injection and voltage measurement protocol is used in order to increase the sensitivity and reduce the data collection time. The proposed approach can produce and visualize up to 15 3D EIT images per second when 80 measurement electrodes are used. Imaging results from a stirred vessel and a flow loop will be shown. The reconstructions show, for example, that 3D air/liquid distribution in the stirred vessel can reliably be visualized in real time and material flow can be monitored in a 3D section of the flow loop. Reconstructions can be visualized and analysed in many different ways in order to produce essential information on the behaviour of the processes.

Modelling of internal structures and electrodes in electrical process tomography

Classical electrical impedance tomography is an imaging modality in which the internal impedivity distribution is reconstructed from the known injected currents and voltages measured on the surface of the object. However, in many industrial cases there are a priori known internal structures inside the vessels which could be used as internal electrodes in tomographical imaging. In this paper we consider modelling of certain types of internal structures and using them as internal electrodes in two-dimensional electrical process tomography. We also propose an inversion approach in which directional smoothness of the resistivity distribution can be taken into account. Simulations and laboratory experiments show that, by utilizing internal structural information and using these internal structures as additional electrodes, we can achieve significant improvements in image reconstruction. Improvements are shown for the cases in which the electrodes are placed at the centre of the object and are surrounded by a resistive layer.

Detection of faults in resistive coatings with an impedance-tomography-related approach

In this paper we propose a method for detecting faults in resistive thin films and coatings with an electrical-impedance-tomography-related approach. The motivation of our study is the need to develop methods for the evaluation of coating properties and quality of implants. The method is based on the complete electrode model. We model the coating as one electrode with spatially varying contact impedance. Using a set of current and voltage measurements in a specially developed measurement cell including the coating and additional electrodes, we estimate the spatially varying contact impedance on the coating. The estimated contact impedance distribution can be regarded as a measure of the condition of the coating; that is, low contact impedance indicates a fault in the coating. The necessary modifications of the complete electrode model are given. The suggested method is tested with simulations and real measurements and it is shown that, with feasible regularization, faults in the coating can be detected with good precision.

Static Three-Dimensional Electrical Impedance Tomography

Abstract: In electrical impedance tomography, an approximation for the internal resistivity distribution is computed based on the knowledge of the voltages and currents on the surface of the body. Usually, it is assumed that the injected currents stay at the two‐dimensional (2D) electrode plane and the reconstruction is based on 2D assumptions. However, the currents spread out in three dimensions (3D) and therefore the structures out of the current injection plane may have significant effect on the reconstructed images. We have studied possibilities of a finite element‐based method to reconstruct static 3D images from real measurements made on a saline‐filled tank. We show that the 3D static images obtained from simple experiments are better than the 2D difference images obtained from the same object. We further show that the static images obtained with 2D calculations are much worse than the images obtained with 3D calculations. We also discuss the effects of the boundary shape error on the reconstructed static 3D images.

Fast Adaptive 3-D Nonstationary Electrical Impedance Tomography Based on Reduced-Order Modeling

Computational cost of image reconstruction in electrical impedance tomography (EIT) is generally very high. Time consumption of data processing can be prohibitive particularly in systems intended for continuous monitoring of time-varying targets in various applications. Recently, two promising approximate computational approaches have been proposed to reduce the computational cost of image reconstruction. These approaches are based on reduced-order approximation of the associated computational models. In this paper, we utilize these techniques to reduce the computational cost of 3-D nonstationary EIT imaging when high image reconstruction rate is required due to rapid changes or instabilities in the target of interest. The feasibility of the proposed reduced-order approach is evaluated in simulation and experimental studies. The results show that computational cost in nonstationary image reconstruction can be decreased significantly with reduced-order modeling, and in addition, with an appropriate reduced-order representation of the system state, the effects on the accuracy are very small.

Thermal Tomography Using Experimental Measurement Data

Experimental measurement data is used to test the feasibility of thermal tomography. The 3D distributed thermal conductivity, heat capacity and surface heat transfer coefficient of a mortar target containing an air hole are estimated using measurement data obtained with a prototype thermal tomography measurement device.Copyright