Anil Kumar Khambampati

Unscented Kalman filter approach to tracking a moving interfacial boundary in sedimentation processes using three-dimensional electrical impedance tomography

The monitoring of solid–fluid suspensions under the influence of gravity is widely used in industrial processes. By considering sedimentation layers with different electrical properties, non-invasive methods such as electrical impedance tomography (EIT) can be used to estimate the settling curves and velocities. In recent EIT studies, the problem of estimating the locations of phase interfaces and phase conductivities has been treated as a nonlinear state estimation problem and the extended Kalman filter (EKF) has been successfully applied. However, the EKF is based on a Gaussian assumption and requires a linearized measurement model. The linearization (or derivation of the Jacobian) is possible when there are no discontinuities in the system. Furthermore, having a complex phase interface representation makes derivation of the Jacobian a tedious task. Therefore, in this paper, we explore the unscented Kalman filter (UKF) as an alternative approach for estimating phase interfaces and conductivities in sedimentation processes. The UKF uses a nonlinear measurement model and is therefore more accurate. In order to justify the proposed approach, extensive numerical experiments have been performed and a comparative analysis with the EKF is provided.

An oppositional biogeography-based optimization technique to reconstruct organ boundaries in the human thorax using electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive imaging modality which has been actively studied for its industrial as well as medical applications. However, the performance of the inverse algorithms to reconstruct the conductivity images using EIT is often sub-optimal. Several factors contribute to this poor performance, including high sensitivity of EIT to the measurement noise, the rounding-off errors, the inherent ill-posed nature of the problem and the convergence to a local minimum instead of the global minimum. Moreover, the performance of many of these inverse algorithms heavily relies on the selection of initial guess as well as the accurate calculation of a gradient matrix. Considering these facts, the need for an efficient optimization algorithm to reach the correct solution cannot be overstated. This paper presents an oppositional biogeography-based optimization (OBBO) algorithm to estimate the shape, size and location of organ boundaries in a human thorax using 2D EIT. The organ boundaries are expressed as coefficients of truncated Fourier series, while the conductivities of the tissues inside the thorax region are assumed to be known a priori. The proposed method is tested with the use of a realistic chest-shaped mesh structure. The robustness of the algorithm has been verified, first through repetitive numerical simulations by adding randomly generated measurement noise to the simulated voltage data, and then with the help of an experimental setup resembling the human chest. An extensive statistical analysis of the estimated parameters using OBBO and its comparison with the traditional modified Newton-Raphson (mNR) method are presented. The results demonstrate that OBBO has significantly better estimation performance compared to mNR. Furthermore, it has been found that OBBO is robust to the initial guess of the size and location of the boundaries as well as offering a reasonable solution when the a priori knowledge of the conductivity of the organs is not very accurate.

Image reconstruction with an adaptive threshold technique in electrical resistance tomography

In electrical resistance tomography, electrical currents are injected through the electrodes placed on the surface of a domain and the corresponding voltages are measured. Based on these currents and voltage data, the cross-sectional resistivity distribution is reconstructed. Electrical resistance tomography shows high temporal resolution for monitoring fast transient processes, but it still remains a challenging problem to improve the spatial resolution of the reconstructed images. In this paper, a novel image reconstruction technique is proposed to improve the spatial resolution by employing an adaptive threshold method to the iterative Gauss–Newton method. Numerical simulations and phantom experiments have been performed to illustrate the superior performance of the proposed scheme in the sense of spatial resolution.

Moving interfacial boundary estimation in stratified flow of two immiscible liquids using electrical resistance tomography

This work is concerned with the interfacial boundary estimation in stratified flows of two immiscible liquids using electrical resistance tomography. The interfacial boundary is parametrized with front points and the unknown positions of the front points are estimated based on the relationship between the injected currents and the induced boundary potentials. It is assumed that the interfacial boundary moves during the time taken to collect a full set of independent measurement data. In order to find the unknown interface, the front point locations are treated as state variables, which are tracked through the extended Kalman filter approach. Numerical experiments are successfully conducted for the verification of the proposed approach.

Electrical resistance imaging of a time-varying interface in stratified flows using an unscented Kalman filter

In this paper, we estimate a time-varying interfacial boundary in stratified flows of two immiscible liquids using electrical resistance tomography. The interfacial boundary is approximated with front points spaced discretely along the interface. The design variables to be estimated are the locations of the front points, which are varying with the moving interface. The inverse problem is treated as a stochastic nonlinear state estimation problem with the nonstationary phase boundary (state) being estimated with the aid of an unscented Kalman filter. Numerical experiments are performed to evaluate the performance of an unscented Kalman filter. Specifically, a detailed analysis has been done on the effect of the number of front points and contrast ratio on the reconstruction performance. The reconstruction results show that an unscented Kalman filter is better suited for estimation in comparison to the conventional extended Kalman filter.

Phase boundary estimation in electrical impedance tomography using the Hooke and Jeeves pattern search method

In industrial processes, monitoring of heterogeneous phases is crucial to the safety and operation of the engineering structures. Particularly, the visualization of voids and air bubbles is advantageous. As a result many studies have appeared in the literature that offer varying degrees of functionality. Electrical impedance tomography (EIT) has already been proved to be a hallmark for process monitoring and offers not only the visualization of the resistivity profile for a given flow mixture but is also used for detection of phase boundaries. Iterative image reconstruction algorithms, such as the modified Newton–Raphson (mNR) method, are commonly used as inverse solvers. However, their utility is problematic in a sense that they require the initial solution in close proximity of the ground truth. Furthermore, they also rely on the gradient information of the objective function to be minimized. Therefore, in this paper, we address all these issues by employing a direct search algorithm, namely the Hooke and Jeeves pattern search method, to estimate the phase boundaries that directly minimizes the cost function and does not require the gradient information. It is assumed that the resistivity profile is known a priori and therefore the unknown information will be the size and location of the object. The boundary coefficients are parameterized using truncated Fourier series and are estimated using the relationship between the measured voltages and injected currents. Through extensive simulation and experimental result and by comparison with mNR, we show that the Hooke and Jeeves pattern search method offers a promising prospect for process monitoring.

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

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.

EM algorithm applied for estimating non-stationary region boundaries using electrical impedance tomography

EIT has been used for the dynamic estimation of organ boundaries. One specific application in this context is the estimation of lung boundaries during pulmonary circulation. This would help track the size and shape of lungs of the patients suffering from diseases like pulmonary edema and acute respiratory failure (ARF). The dynamic boundary estimation of the lungs can also be utilized to set and control the air volume and pressure delivered to the patients during artificial ventilation. In this paper, the expectation-maximization (EM) algorithm is used as an inverse algorithm to estimate the non-stationary lung boundary. The uncertainties caused in Kalman-type filters due to inaccurate selection of model parameters are overcome using EM algorithm. Numerical experiments using chest shaped geometry are carried out with proposed method and the performance is compared with extended Kalman filter (EKF). Results show superior performance of EM in estimation of the lung boundary.

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

Electrical impedance tomography (EIT) is a non-invasive imaging technique that can be used as a bed-side monitoring tool for human thorax imaging. EIT has high temporal resolution characteristics but at the same time it suffers from poor spatial resolution due to ill-posedness of the inverse problem. Often regularization methods are used as a penalty term in the cost function to stabilize the sudden changes in resistivity. In human thorax monitoring, with conventional regularization methods employing Tikhonov type regularization, the reconstructed image is smoothed between the heart and the lungs, that is, it makes it difficult to distinguish the exact boundaries of the lungs and the heart. Sometimes, obtaining structural information of the object prior to this can be incorporated into the regularization method to improve the spatial resolution along with helping create clear and distinct boundaries between the objects. However, the boundary of the heart is changed rapidly due to the cardiac cycle hence there is no information concerning the exact boundary of the heart. Therefore, to improve the spatial resolution for human thorax monitoring during the cardiac cycle, in this paper, a sub-domain based regularization method is proposed assuming the lungs and part of background region is known. In the proposed method, the regularization matrix is modified anisotropically to include sub-domains as prior information, and the regularization parameter is assigned with different weights to each sub-domain. Numerical simulations and phantom experiments for 2D human thorax monitoring are performed to evaluate the performance of the proposed regularization method. The results show a better reconstruction performance with the proposed regularization method.

Particle swarm optimization technique for elliptic region boundary estimation in electrical impedance tomography

In this study we consider the recovery of smooth elliptic region boundary in electrical impedance tomography (EIT). The assumption made is that the resistivity profile is known a priori but some of the geometric information is missing. This missing information may for example be shape, size and location. This leads to a nonlinear ill‐posed inverse problem. In this study we propose a population based parallel evolutionary computation technique, particle swarm optimization (PSO). We formulate the forward problem as mapping of a set of Fourier coefficients representing boundary shapes to the resistivity profile in the domain. Then PSO is used to iteratively seek the boundary configuration minimizing a cost functional. The final goal of this study is to recover the region boundary with only one measurement data (i.e., one current pattern) contaminated with measurement noise along with a very high contrast ratio. The simulation results are also provided to assess the merit of PSO technique.