Anssi Lehikoinen

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.

Dynamical inversion of geophysical ERT data: state estimation in the vadose zone

The imaging of the evolution of conductive fluids in porous media with electrical resistance tomography (ERT) can be considered as a dynamic inverse problem, in which the time-dependent electrical conductivity distribution in the target region is inferred from voltage measurements at electrodes placed in boreholes or on the ground surface. A petrophysical relationship is then used to relate the electrical conductivity to water saturation. We consider a state estimation approach that combines the complete electrode model for simulating ERT measurements and a hydrological evolution model for unsaturated flow. To demonstrate the approach, we consider synthetic measurements from a simulated experiment in which water is injected from a point source into an initially dry soil. The purpose is to carry out a feasible study. In the studied simple cases, the proposed method provides improved estimates of the water saturation distribution compared to the traditional reconstruction approach, which does not employ an evolution model.

Importance sampling approach for the nonstationary approximation error method

The approximation error approach has previously been proposed to handle modelling, numerical and computational errors. This approach has been developed both for stationary and nonstationary inverse problems (Kalman filtering). The key idea of the approach is to compute the approximate statistics of the errors over the distribution of all unknowns and uncertainties and carry out approximative marginalization with respect to these errors. In nonstationary problems, however, information is accumulated over time, and the initial uncertainties may turn out to have been exaggerated. In this paper, we propose an algorithm with which the approximation error statistics can be updated during the accumulation of measurement information. The proposed algorithm is based on importance sampling. The recursions that are proposed here are, however, based on the (extended) Kalman filter and therefore do not employ the often exceedingly heavy computational load of particle filtering. As a computational example, we study an estimation problem that is related to a convection?diffusion problem in which the velocity field is not accurately specified.

Three-dimensional nonstationary electrical impedance tomography with a single electrode layer

In a tubular vessel equipping a single electrode layer, true three-dimensional electrical impedance tomography imaging is generally not considered possible. In a nonstationary setting, however, the accumulation of information over an epoch can possibly allow for 3D imaging if appropriate evolution models are available. Such an evolution model is the stochastic convection‐diffusion model if the flow field is such that the main flow is along the tube. A single electrode layer sensor would obviously be much cheaper and could be installed in locations in which a multi-layer sensor possibly could not be. In this paper, we assess this possibility both computationally and experimentally. The results show that a single electrode layer system is a potential technique in nonstationary estimation.

A reduced-order filtering approach for 3D dynamical electrical impedance tomography

Recently, it has been shown that the state estimation approach to process tomography can provide estimates that are significantly better than (a sequence of) conventional stationary snapshot estimates. One of the main obstacles of the adoption of the recursive state estimation algorithms, most commonly different versions of the Kalman filter, is the computational complexity. This is due to both the required large dimension for the state variable and the need to use iterative versions of the Kalman filter in such cases in which there are large contrasts or varying background. In this paper, we propose to use a reduced-order representation for the state variable. In particular, we propose to use the proper orthogonal decomposition-related basis for the state. We consider a simulation study with fluctuating background conductivity, and, in particular, with fluctuating contact impedances. We compare the proposed approach to three different versions of the Kalman filter having different computational complexities. We show that this approach allows the reduction of the dimension of the problem approximately by an order of magnitude and yields essentially as accurate estimates as the most accurate traditional Kalman filter version, the iterated extended Kalman filter.

An electrical impedance tomography-based approach to monitor in vitro sodium chloride dissolution from pharmaceutical tablets

An approach to monitor in vitro dissolution process from pharmaceutical tablets utilizing electrical impedance tomography (EIT) is introduced. In the demonstration, a tablet containing sodium chloride (NaCl) was dissolution tested using tap water as a dissolution medium within an apparatus similar to the United States Pharmacopoeia dissolution apparatus II. During the process, the three-dimensional sodium chloride concentration distribution was monitored with EIT measurements as a function of time. For EIT measurements, an array of electrodes was attached on the boundary of the dissolution vessel, a set of alternating electric currents was injected through the electrodes, and the resulting voltages were measured. With these data and by applying mathematical algorithms, an approximation for the spatial/temporal concentration distribution inside the vessel was computed. It was found that the computed distributions were relatively homogeneous. A NaCl release curve was computed by integrating the concentration distribution over the vessel volume, and the final value of the curve matched well with the reference point based on the weight loss of the tablet. Finally, EIT monitoring is suggested to be used for research and product development purposes.

Machine learning approach for locating phase interfaces using conductivity probes

We describe a technique to measure the locations of phase interfaces (bed levels) in industrial processes, such as in sedimentation or separation. The measurement approach is based on Electrical Impedance Tomography (EIT) type technology in which the conductivity distribution of the object is estimated based on the current–voltage data of the measurement device. In this article we discuss a novel probe technique that uses machine learning methodology to estimate the bed levels. We also introduce a way to prune the set of injection and measurement electrodes to the bare minimum which makes the measurement device considerably simpler – and consequently, cheaper – to build. Results obtained through a simulation study are reported and discussed.

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.

Process tomography and estimation of velocity fields

Abstract One of the most common end applications of process tomography is acquiring information of the related flow. Usually, the information is accessed indirectly by computing single time-lapse estimates of the parameter that is being imaged, such as conductivity, permittivity or density, and then the sequence of images is analysed to infer some characteristics of the flow. Sometimes correlation information on the measurement stream is also used to obtain information on the mean flow. In this chapter, we focus on the state estimation approach, which can be used to access information on the flow field based on explicit modelling of the related transport phenomena. The state estimation approach separates the model for the measurements and the model for the evolution of all time-varying quantities. As an example, we consider electrical impedance tomography as the imaging, modality and advection-diffusion and Navier–Stokes models as the model for the flow. The central topic here is how to derive the related stochastic versions of the measurement and evolution models. In particular, we consider the problems that are related to unknown boundary conditions and model reduction.

Importance Sampling Approach for the Nonstationary Approximation Error Method

The approximation error approach has been earlier proposed to handle modelling, numerical and computational errors in inverse problems. The idea of the approach is to include the errors to the forward model and compute the approximate statistics of the errors using Monte Carlo sampling. This can be a computationally tedious task but the key property of the approach is that the approximate statistics can be calculated off‐line before measurement process takes place. In nonstationary problems, however, information is accumulated over time, and the initial uncertainties may turn out to have been exaggerated. In this paper, we propose an importance weighing algorithm with which the approximation error statistics can be updated during the accumulation of measurement information. As a computational example, we study an estimation problem that is related to a convection‐diffusion problem in which the velocity field is not accurately specified.