Identification of material damage in two-dimensional domains using the SQUID-based nondestructive evaluation system

Banks, Harvey Thomas; Kojima, Fumio

doi:10.1088/0266-5611/18/6/324

Cited by 14 publications

(29 citation statements)

References 23 publications

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“…The infimum in the right-hand side of (48) is indeed attained, by the Banach-Alaoglu theorem and since the kernel of A is weak- * closed. When S and Q satisfy the conditions of Lemma 2.3, then this kernel consists of S-silent magnetizations and M(µ 0 ) is just M (µ 0 ) defined in (4). But when these conditions are not satisfied (for instance if S is smooth compact surface), then the two quantities may not coincide.…”

Section: Regularization By Penalizing the Total Variationmentioning

confidence: 99%

Inverse Potential Problems for Divergence of Measures with Total Variation Regularization

et al. 2019

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We study inverse problems for the Poisson equation with source term the divergence of an R 3 -valued measure; that is, the potential Φ satisfies ∆Φ = div µ, and µ is to be reconstructed knowing (a component of) the field grad Φ on a set disjoint from the support of µ. Such problems arise in several electro-magnetic contexts in the quasi-static regime, for instance when recovering a remanent magnetization from measurements of its magnetic field. We develop methods for recovering µ based on total variation regularization. We provide sufficient conditions for the unique recovery of µ, asymptotically when the regularization parameter and the noise tend to zero in a combined fashion, when it is uni-directional or when the magnetization has a support which is sparse in the sense that it is purely 1-unrectifiable.Numerical examples are provided to illustrate the main theoretical results.

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Section: Regularization By Penalizing the Total Variationmentioning

confidence: 99%

Inverse Potential Problems for Divergence of Measures with Total Variation Regularization

et al. 2019

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“…Our focus in this paper is in the identification of electromagnetic material parameters and the emphasis is on one dimensional scattering of a dielectric slab. Although prior work exists using nonlinear least square methods [2,3,4,5,6], it is well known that the problem mentioned above has many solutions due to the fact that it is ill-posed. Recently, interest has grown in stochastic inversion using Markov Chain Monte Carlo (MCMC) methods [7,8].…”

Section: Subject Termsmentioning

confidence: 99%

Inverse Problem for Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method (Preprint)

Knopp¹,

Kojima²

2012

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information ABSTRACTThis paper is concerned with a stochastic inverse methodology arising in electromagnetic imaging. Nondestructive testing using guided microwaves covers a wide range of industrial applications including early detection of anomalies in conducting materials. The focus of this paper is the identification of electromagnetic material parameters and emphasis is on one dimensional scattering of a dielectric slab. The direct problem can be solved numerically using the finitedifference time-domain method (FDTD). The Markov Chain Monte Carlo method (MCMC) is applied to the inversion problem. Some successful results of computational experiments are demonstrated in order to show the feasibility and applicability of the proposed method. SUBJECT TERMS

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“…The nonlinear least square identification (OLSI) is a conventional inverse methodology and there have been so many efforts in variety of industrial applications. For OLSI related to electromagnetic inversion, we refer [3][4] [5][6] [7]. However,it is well known that the problem mentioned above has many solutions due to the fact it is ill-posed.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Evaluation for Two-dimensional Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method

Kojima

Knopp

2012

Stochastic Systems Theory and its Applications (SSS)

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Motivated by quantitative evaluation of aging properties of electrical cables, a computational method for identifying physical parameters of dielectric materials is considered. First, a nondestructive testing using microwaveguide is described by electric and magnetic fields defined on the problem. Secondly, an inversion technique based on Markov Chain Monte Carlo method (MCMC) is employed for solving the electromagnetic interrogation treated here. Finally, a numerical scheme of the direct problem is developed using the finitedifference time-domain method (FDTD) in two spatial dimensions. Applying Metropolis-Hasting algorithm to the inversion presented here, results on computational experiments are demonstrated in order to show the feasibility and applicability of the proposed method.

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Identification of material damage in two-dimensional domains using the SQUID-based nondestructive evaluation system

Cited by 14 publications

References 23 publications

Inverse Potential Problems for Divergence of Measures with Total Variation Regularization

Inverse Potential Problems for Divergence of Measures with Total Variation Regularization

Inverse Problem for Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method (Preprint)

Quantitative Evaluation for Two-dimensional Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method

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