An analytical boundary element integral approach to track the boundary of a moving cavity using electrical impedance tomography

Abstract

This paper is about locating the boundary of a moving cavity within a homogeneous background from the voltage measurements recorded on the outer boundary. An inverse boundary problem of a moving cavity is formulated by considering a two-phase vapor–liquid flow in a pipe. The conductivity of the flow components (vapor and liquid) is assumed to be constant and known a priori while the location and shape of the inclusion (vapor) are the unknowns to be estimated. The forward problem is solved using the boundary element method (BEM) with the integral equations solved analytically. A special situation is considered such that the cavity changes its location and shape during the time taken to acquire a full set of independent measurement data. The boundary of a cavity is assumed to be elliptic and is parameterized with Fourier series. The inverse problem is treated as a state estimation problem with the Fourier coefficients that represent the center and radii of the cavity as the unknowns to be estimated. An extended Kalman filter (EKF) is used as an inverse algorithm to estimate the time varying Fourier coefficients. Numerical experiments are shown to evaluate the performance of the proposed method. Through the results, it can be noticed that the proposed BEM with EKF method is successful in estimating the boundary of a moving cavity.

A sub-domain based regularization method with prior information for human thorax imaging using electrical impedance tomography

“…In general, it is not easy to have an analytical solution for the EIT forward problem, so often numerical methods are used. Numerical methods based on the finite difference method, boundary element method and finite element method (FEM) are used to solve the forward problem of EIT (Vauhkonen 1997, de Munck et al 2000, Khambampati et al 2012. In this paper, we have used FEM to obtain numerical solution.…”

Boundary element method to estimate the time-varying interfacial boundary in horizontal immiscible liquids flow using electrical resistance tomography

“…(60) and solving for the updates of the associated covariance matrices, recursive EKF algorithm is obtained, which consists of prediction and filtering steps [8,26,37] Prediction:…”

“…However, this method is computationally intensive as it needs to calculate the potential and fluxes on the interfacial boundary. An analytical computation of boundary integrals is proposed for BEM with CEM to locate anomalies in homogeneous background which is a closed boundary problem [25,26]. In [27,28], BEM is formulated for free surface and stratified flow problem to estimate the open interfacial boundary using ERT.…”

Image reconstruction using voltage–current system in electrical impedance tomography

“…The image reconstruction algorithms have become more sophisticated along with the development of medical EIT. Using the fact that there are only two distinct conductivities in gas-liquid two-phase flows, interesting algorithms such as the mesh-grouping (Cho et al, 2001;Kim et al, 2014) and the boundary estimation (Han and Prosperetti, 1999;Khambampati et al, 2012) have been suggested. On the other hand, the application of EIT has been widened to various two-phase measurements.…”