A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements

Ammari, Habib; Kang, Hyeonbae; Kim, Eun-Joo; Louati, Kaouthar; Vogelius, Michael

doi:10.1007/s00211-007-0130-x

Cited by 46 publications

(55 citation statements)

References 17 publications

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“…Suppose that the wavelength λ = 2π/ω = 1−β (>> ) for some positive constant β, then the following asymptotic formula holds uniformly on Γ e for some positive constant α [3]:…”

Section: Asymptotic Expansionsmentioning

confidence: 99%

“…Rigorous derivations of asymptotic expansions can be found in [1][2][3]. The expansions (3.5) and (3.6) can be seen easily by expanding ω and v formally as…”

Section: Modal Parameter Measurementsmentioning

confidence: 99%

“…The inverse problem considered in the papers [1][2][3] is to detect the corrosive parts on the inaccessible boundary Γ i by means of the measurements on the accessible boundary Γ e . In particular, the aim is to detect the location and the size of the corrosive parts, and the corrosion coefficient γ s .…”

mentioning

confidence: 99%

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Detection of Internal Corrosion

2009

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Abstract. The purpose of this paper is to review recently developed algorithms for corrosion detection and to compare between them. IntroductionCorrosion detection is an important problem in the field of nondestructive evaluation (NDE) for an obvious practical reason, and new techniques are constantly being sought for the detection of hidden corrosion. In general corrosion is defect in various phenomena such as electrical defect or defect for the wave propagation or the guided wave. Therefore the methods of detecting corrosion can vary depending on the related physical phenomena. Quite recently various algorithms for corrosion detection are proposed and tested numerically in three different models: the electrostatic model [3], the ultrasound model [2], and the guided wave model [1]. The purpose of this paper is to review the results of these works and compare them. Mathematical modelsThe electrostatic model of corrosion of this paper is taken from [11], which we review briefly here. Let Ω be a bounded domain in R d , d = 2, 3, and suppose that a corrosion occurs on a part Γ of the boundary ∂Ω of Ω. Vogelius and Xu derived in [11] that the electrostatic potential u in the presence of corrosion is a solution of the following nonlinear Article published by EDP Sciences and available at http://www.edpsciences.org/proc or http://dx

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“…Suppose that the wavelength λ = 2π/ω = 1−β (>> ) for some positive constant β, then the following asymptotic formula holds uniformly on Γ e for some positive constant α [3]:…”

Section: Asymptotic Expansionsmentioning

confidence: 99%

“…Rigorous derivations of asymptotic expansions can be found in [1][2][3]. The expansions (3.5) and (3.6) can be seen easily by expanding ω and v formally as…”

Section: Modal Parameter Measurementsmentioning

confidence: 99%

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Detection of Internal Corrosion

2009

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“…Among them, the MUltiple SIgnal Classification (MUSIC) algorithm has been successfully applied to various problems such as the location search of small defects [3], anti-personnel mines [4], internal corrosion [5], and the shape identification of thin electromagnetic inhomogeneities and perfectly conducting cracks [6,17,19,21]. However, in most of the studies that we mentioned above, the MUSIC algorithm has been applied only in full-view inverse scattering problems.…”

Section: Introductionmentioning

confidence: 99%

Properties of Music-Type Algorithm for Imaging of Thin Dielectric Inhomogeneity in Limited-View Inverse Scattering Problem

Park

2014

PIER M

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Abstract-It is well known that a Multiple Signal Classification (MUSIC)-type algorithm yields good results in the imaging of thin dielectric inhomogeneity for full-view inverse scattering problems. In contrast, it yields a poor result in limited-view inverse scattering problems. In this paper, we verify the reason for the above by establishing a relationship between a MUSIC-type imaging function and the Bessel functions of the integer order of the first kind. This verification is based on the asymptotic expansion formula for thin dielectric inhomogeneity. Various numerical examples are discussed for confirming our verification.

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“…Previous numerical investigations have concentrated on time independent equations with full data -see for example, [6,7,12]. This article is based on three sources: the Hilbert Uniqueness Method (HUM) formulated by Lions -see [30]; the numerical application of the above method to exact boundary control of the wave equation by Glowinski et al -see [26]; the theoretical results of the problem of detection for the wave equation by Ammari -see [2].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

Asch¹,

Darbas²,

Duval³

2010

ESAIM: COCV

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Abstract.We consider the numerical solution, in two-and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of "limited-view" data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing the centers of the imperfections. Numerical results, in 2-and 3-D, show the robustness and accuracy of the approach for retrieving randomly placed imperfections from both complete and partial boundary measurements.Mathematics Subject Classification. 35R30, 35L05, 65M60.

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A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements

Cited by 46 publications

References 17 publications

Detection of Internal Corrosion

Detection of Internal Corrosion

Properties of Music-Type Algorithm for Imaging of Thin Dielectric Inhomogeneity in Limited-View Inverse Scattering Problem

Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

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