# American Institute of Mathematical Sciences

February  2014, 8(1): 127-148. doi: 10.3934/ipi.2014.8.127

## Adaptive meshing approach to identification of cracks with electrical impedance tomography

 1 Department of Applied Physics, University of Eastern Finland, 70211 Kuopio, Finland, Finland 2 Department of Mathematics, University of Auckland, Private Bag 92019, Auckland Mail Centre, Auckland 1142, New Zealand

Received  March 2013 Revised  September 2013 Published  March 2014

Electrical impedance tomography (EIT) is a non-invasive imaging modality in which the internal conductivity distribution is reconstructed based on boundary voltage measurements. In this work, we consider the application of EIT to non-destructive testing (NDT) of materials and, especially, crack detection. The main goal is to estimate the location, depth and orientation of a crack in three dimensions. We formulate the crack detection task as a shape estimation problem for boundaries imposed with Neumann zero boundary conditions. We propose an adaptive meshing algorithm that iteratively seeks the maximum a posteriori estimate for the shape of the crack. The approach is tested both numerically and experimentally. In all test cases, the EIT measurements are collected using a set of electrodes attached on only a single planar surface of the target -- this is often the only realizable configuration in NDT of large building structures, such as concrete walls. The results show that with the proposed computational method, it is possible to recover the position and size of the crack, even in cases where the background conductivity is inhomogeneous.
Citation: Kimmo Karhunen, Aku Seppänen, Jari P. Kaipio. Adaptive meshing approach to identification of cracks with electrical impedance tomography. Inverse Problems & Imaging, 2014, 8 (1) : 127-148. doi: 10.3934/ipi.2014.8.127
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