State estimation in process tomography—reconstruction of velocity fields using EIT

Abstract

In this paper, we consider imaging of moving fluids with electrical impedance tomography (EIT). In EIT, the conductivity distribution is reconstructed on the basis of electrical boundary measurements. In the case of time-varying targets—such as moving fluids in process industry—it is advantageous to formulate the reconstruction problem as a state-estimation problem, because the state-estimation approach allows incorporation of target evolution models in the reconstruction. The reconstruction algorithms consist of recursions in which the state predictions given by the evolution model are updated with the information provided by measurements. When monitoring single-phase flow, the evolution of the substance concentration can be described with the convection–diffusion model. The convection–diffusion model includes the fluid velocity field. In our previous studies, we have assumed that the velocity field is known. In this paper, we extend the approach to cases of unknown velocity fields. The velocity field is reconstructed simultaneously with the conductivity distribution by using an extended Kalman filter. The numerical results indicate that estimating the velocity field from EIT measurements is possible—at least to some extent.