The objective of the Electrical Impedance and Diffuse Optical Reconstruction Software project is to develop freely available software that can be used to reconstruct electrical or optical material properties from boundary measurements. Nonlinear and ill posed problems such as electrical impedance and optical tomography are typically approached using a finite element model for the forward calculations and a regularized nonlinear solver for obtaining a unique and stable inverse solution. Most of the commercially available finite element programs are unsuitable for solving these problems because of their conventional inefficient way of calculating the Jacobian, and their lack of accurate electrode modelling. A complete package for the two-dimensional EIT problem was officially released by Vauhkonen et al at the second half of 2000. However most industrial and medical electrical imaging problems are fundamentally three-dimensional. To assist the development we have developed and released a free toolkit of Matlab routines which can be employed to solve the forward and inverse EIT problems in three dimensions based on the complete electrode model along with some basic visualization utilities, in the hope that it will stimulate further development. We also include a derivation of the formula for the Jacobian (or sensitivity) matrix based on the complete electrode model.

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This study addresses the issue of structural damage identification and location in carbon fiber reinforced polymer plates using electrical measurements. Electrical resistance tomography is presented as a method for structural damage localization in composite parts. A set of electrodes is fixed on the edges of the part and combinations of DC current injections and voltage measurements are applied to the system. The change of voltage between different times in the part’s service life (e.g. start and degraded) are monitored. These sets of measurements are used as input to inversely calculate conductivity maps for the complete composite part and thus indirectly assess its structural health. Such processes are inherently ill-posed. Data post-processing approaches are proposed here to diminish this uncertainty and to conclude to an optimally converge solution of the inverse problem. To assist the process, a material-originating mathematical constraint is introduced. The method is applied on carbon fiber reinforced polymer plates for different damage modes. Experimental recordings show that the analysis of electrical fields allows detecting the presence of damage. Discontinuities as small as 0.1% of the inspected area can be sensed. The proposed data post-processing techniques were applied and conductivity maps were calculated. The results show that using these techniques locating damage is possible with less than 10% error. Material-based constraints greatly enhance the prediction of the data post-processing techniques. It is believed that by overcoming certain implementation issues, electrical resistance tomography could evolve in the direction of a non-destructive evaluation or a structural health monitoring technique for composite structures.

An approach for damage inspection of composite structures utilizing carbon nanotubes (CNT) networks is investigated. CNT are dispersed in an epoxy using a processing technique compatible with commonly employed composite manufacturing techniques and subsequently used as matrix for a structural glass fiber reinforced composite. The developed electrical conductivity of the composite system is verified experimentally. The electrically conductive CNT network within the GFRP is exploited through distributed electrical voltage measurements to sense and, ultimately, locate damage in the plane of the composite plate. Damage in the form of cracks or delamination interrupts the continuity of the CNT network separating and isolating regions of the conductive network. Employing electric potential fields these changes can become measurable and can provide information for inversely locating the damage. Electrical Resistance Tomography (ERT) is formulated and experimentally applied to measure changes in the potential fields and deliver electrical conductivity change maps which are used to identify and locate changes in the CNT networks. These changes are correlated to capture the damage in the composite. Different damage modes are studied to assess the capabilities of the technique. The technique shows sensitivity to very small damages; less than 0.1% of the inspected area. The solution of the inverse ERT problem delivers a conductivity change maps which offers an effective localization with nearly 10% error and an inspection area suppression of around 75%. The proposed methodology to create CNT networks enables the application of ERT for Non-Destructive Evaluation of composite materials, previously not possible due to lack of conductivity, thus offering damage sensing and location capabilities even in-situ.

Abstract-In this paper, we review some numerical techniques based on the linear Krylov subspace iteration that can be used for the efficient calculation of the forward and the inverse electrical impedance tomography problems. Exploring their computational advantages in solving large-scale systems of equations, we specifically address their implementation in reconstructing localized impedance changes occurring within the human brain. If the conductivity of the head tissues is assumed to be real, the preconditioned conjugate gradients (PCGs) algorithm can be used to calculate efficiently the approximate forward solution to a given error tolerance. The performance and the regularizing properties of the PCG iteration for solving ill-conditioned systems of equations (PCGNs) is then explored, and a suitable preconditioning matrix is suggested in order to enhance its convergence rate. For image reconstruction, the nonlinear inverse problem is considered. Based on the Gauss-Newton method for solving nonlinear problems we have developed two algorithms that implement the PCGN iteration to calculate the linear step solution. Using an anatomically detailed model of the human head and a specific scalp electrode arrangement, images of a simulated impedance change inside brain's white matter have been reconstructed. Index Terms-Brain activity, computational efficiency, conjugate gradients, electrical impedance tomography, regularization.