Determination of surface and interior cracks from electrostatic measurements using Schwarz-Christoffel transformations

Elcrat, Alan R.; Hu, Chenglie

doi:10.1016/0020-7225(96)00011-0

Cited by 6 publications

(12 citation statements)

References 7 publications

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“…In the projected line-search, all negative entries of σ and z are replaced by a very small positive value. This assures that the estimates fulfill the positivity constraints in (17).…”

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confidence: 82%

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Adaptive meshing approach to identification of cracks with electrical impedance tomography

Karhunen¹,

Seppänen²,

Kaipio³

2014

IPI

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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.2010 Mathematics Subject Classification. Primary: 65N21, 62F15; Secondary: 65N50.

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“…In the projected line-search, all negative entries of σ and z are replaced by a very small positive value. This assures that the estimates fulfill the positivity constraints in (17).…”

mentioning

confidence: 82%

“…The crack identification based on this framework has also excited numerous other studies, see e.g. [20,9,29,17,6,5]. Further, a Bayesian (statistical) inversion approach to crack identification was proposed in [4], and a level set method in [3].…”

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confidence: 96%

Adaptive meshing approach to identification of cracks with electrical impedance tomography

Karhunen¹,

Seppänen²,

Kaipio³

2014

IPI

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“…The crack identification based on the aforementioned principles has also excited numerous other studies, see e.g. [161][162][163][164][165][166][167][168][169][170][171][172].…”

Section: Crack Identification With Adaptive Meshing Approachmentioning

confidence: 96%

Electrical Resistance Tomography imaging of concrete

Karhunen¹,

Seppänen²,

Lehikoinen³

et al. 2010

Cement and Concrete Research

217

135

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Cracking and deterioration of concrete are the leading causes of a premature failing of reinforced concrete structures. To assess the condition of concrete, a variety of destructive and non-destructive testing methods have been developed. From these two methods, the non-destructive testing (NDT) is a more favorable (albeit more challenging) option since the tested target is left undamaged. The NDT modalities include acoustic, electromagnetic and radiation based techniques. In this thesis, the feasibility of electrical resistance tomography (ERT) for NDT of concrete is studied. In ERT, electric currents are injected into the target through electrodes that are are attached to the boundary of the target. The resulting voltages between the electrodes are measured and this boundary voltage data is then used to reconstruct the internal conductivity distribution of the target. The reconstruction of the internal conductivity distribution of concrete is expected to provide valuable information about the condition of the structure so that appropriate repairs can be taken in time. The difficulty in ERT, as is in any other diffuse tomography modality, is that the problem has a nature of an ill-posed inverse problem. This implies that the solutions of the problem are unstable and nonunique in the classical sense. As a consequence, extra attention must be directed to the mathematical modeling of the measurements as well as to the reconstruction methods. Furthermore, concrete is strongly heterogeneous material composed of cement matrix, aggregate and different chemical compounds that create a challenging target for electrical modalities. Previous studies have shown that ERT is a potential tool for NDT of concrete, but the quality of the reconstruction was not yet sufficient for practical applications. In this thesis, especially localizing reinforcing bars and crack identification are considered. To meet those aims, novel computational methods for the image reconstruction are developed. For the crack identification and localizing reinforcing bars, a novel adaptive meshing approach was developed. In the new approach cracks and reinforcing bars are modeled as internal structures. The results show that by employing accurate mathematical models and statistical inversion techniques based on the Bayesian framework, ERT can become an applicable tool for practical NDT of concrete.

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“…Starting from 1980's, Schwarz-Christoffel maps have also been used for Grid Generation, which is a crucial step for numerically solving some nonlinear partial differential equations on irregular domains (see Sridhar and Davis [1985]). The package, however, may also be modified (by rewriting routine DSCFUN) to solve some so-called generalized accessory parameter problems, in which some equations in the nonlinear system are formulated using nongeometrical conditions associated with a particular problem (see Elcrat and Hu [1996] and Trefethen [1989a]). …”

Section: Examplesmentioning

confidence: 99%

“…Daeppen's code, however, is not available in the public domain. Based on Daeppen's idea, which is an extension of Trefethen's treatment for computing Schwarz-Christoffel mapping for simply connected domains to doubly connected regions, we independently explored many details of implementing (1.1) and developed a robust, portable, well-structured, and well-documented Fortran 77 package, which has been well tested by numerous examples and some nontrivial applications (see Elcrat and Hu [1996], Elcrat et al [1997], andHu [1995]). Compared to the results reported by Daeppen [1988], we achieved, with our code, the better results in terms of accuracy, speed, and being user friendly for the same test problems.…”

Section: Introductionmentioning

confidence: 99%

Algorithm 785

1998

ACM Trans. Math. Softw.

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A software package implementing Schwarz-Christoffel Conformal transformation (or mapping) of doubly connected polygonal regions is fully described in this article from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is reflected by the flexibility in choosing the accuracy of the parameters to be computed, the speed of computation, the ability of mapping "difficult" regions (to be specified in Section 2), and being user friendly. Several examples are presented to demonstrate the capabilities of the package.

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Determination of surface and interior cracks from electrostatic measurements using Schwarz-Christoffel transformations

Cited by 6 publications

References 7 publications

Adaptive meshing approach to identification of cracks with electrical impedance tomography

Adaptive meshing approach to identification of cracks with electrical impedance tomography

Electrical Resistance Tomography imaging of concrete

Algorithm 785

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