Eddy current tomography based on a finite difference forward model with additive regularization
05 Mar 2010-Vol. 1211, Iss: 1, pp 782-789
TL;DR: In this paper, an inversion technique with an improved tradeoff between quality of the results, computational requirements and ease of implementation is presented, which is achieved by fully accounting for the nonlinear nature of the forward problem by means of a system of bilinear equations obtained through a finite difference modeling of the problem.
Abstract: Eddy current tomography is a nondestructive evaluation technique used for characterization of metal components. It is an inverse problem acknowledged as difficult to solve since it is both ill‐posed and nonlinear. Our goal is to derive an inversion technique with improved tradeoff between quality of the results, computational requirements and ease of implementation. This is achieved by fully accounting for the nonlinear nature of the forward problem by means of a system of bilinear equations obtained through a finite difference modeling of the problem. The bilinear character of equations with respect to the electric field and the relative conductivity is taken advantage of through a simple contrast source inversion‐like scheme. The ill‐posedness is dealt with through the addition of regularization terms to the criterion, the form of which is determined according to computational constraints and the piecewise constant nature of the medium. Therefore an edge‐preserving functional is selected. The performance of the resulting method is illustrated using 2D synthetic data examples.
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Dissertation•
14 Oct 2010TL;DR: Current tomography can be employed to caracterize flaws in metal plates in steam generators of nuclear power plants by adapting contrast source inversion (CSI) type methods to the chosen model and a new criterion was proposed.
Abstract: La tomographie par courants de Foucault peut etre utilisee pour evaluer la forme et le volume de defauts dans des plaques metalliques de generateur de vapeur de centrale nucleaire. L'objectif du travail presente est de cartographier la distribution d'une grandeur representative du defaut, ici la conductivite relative. Ce probleme est difficile a resoudre car mal-pose et non-lineaire. Afin de le resoudre un modele numerique est necessaire. Nos travaux ont tout d'abord consiste a etudier les modeles directs existants pour choisir le plus adapte a notre cas. Il s'est avere que les methodes differentielles, differences finies ou elements finis, etaient les plus adaptees a notre cas. Une fois que le modele direct a ete choisi, nous avons adapte les methodes de type contrast source inversion (CSI) a ce modele, puis propose un nouveau critere a minimiser. Les methodes de type CSI sont basees sur la minimisation de l'erreur quadratique ponderee des equations du modele, observation et couplage. Par construction, elles autorisent une erreur sur ces equations. Il apparait que les resultats de reconstruction s'ameliorent lorsque l'erreur sur l'equation de couplage diminue. Afin de contraindre cette equation en evitant des problemes de conditionnement, on a eu recours a une technique de Lagrangien augmente. Enfin, le caractere mal-pose de ce probleme peut etre contourne en introduisant des informations a priori adequates notamment sur la forme generale des defauts a reconstruire ainsi que sur les valeurs possibles de la conductivite relative. L'efficacite des methodes developpees est illustree avec des cas simules en 2D.
8 citations
Additional excerpts
...Cependant, ces dernières années, ces méthodes ont été adaptées pour utiliser un modèle basé sur une formulation différentielle (Abubakar et al., 2008a; Trillon et al., 2009) car les modèles intégraux nécessitent différentes conditions pour être utilisables....
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...Durant l’inversion, la bilinéarité est exploitée afin de faciliter et d’accélérer la résolution du problème (Trillon, 2009; Trillon et al., 2009) comme le font les méthodes de type MGM/CSI présentées au chapitre I....
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Dissertation•
30 May 2011
TL;DR: In this paper, an inversion algorithm based on the optimization of an objective function and two methods for the generation of generic surrogate models, both involving a sequential sampling strategy are discussed in detail.
Abstract: Electromagnetic Nondestructive Evaluation (ENDE) is applied in various industrial domains for the exploration of hidden in-material defects of structural components. The principal task of ENDE can generally be formalized as follows: an unknown defect affects a given host structure, interacting with a known electromagnetic field, and the response (derived from the electromagnetic field distorted by the defect) is measured using one or more receivers at known positions. This response contains some information on the electromagnetic constitutive parameters and the geometry of the defect to be retrieved. ENDE aims at extracting this information for the characterization of the defect, i.e., at the solution of the arising “inverse problem”. To this end, one has to be able to determine the electromagnetic field distorted by a defect with known parameters affecting a given host structure, i.e., to solve the “forward problem”. Practically, this is performed via the mathematical modeling (based on the Maxwell's equations) and the numerical simulation of the studied ENDE configuration. Such simulators can provide fine precision, but at a price of computational cost. However, the solution of an inverse problem often requires several runs of these “expensive-to-evaluate” simulators, making the inversion procedure firmly demanding in terms of runtime and computational resources. To overcome this challenge, “surrogate modeling” offers an interesting alternative solution. A surrogate model imitates the true model, but as a rule, it is much less complex than the latter. A way to construct such surrogates is to perform a couple of simulations and then to approximate the model based on the obtained data. The choice of the “prototype” simulations is usually controlled by a sophisticated strategy, drawn from the tools of “design-of-experiments”. The goal of the research work presented in this Dissertation is the improvement of ENDE methods by using surrogate modeling and design-of-experiments techniques. Three self-sufficient approaches are discussed in detail: an inversion algorithm based on the optimization of an objective function and two methods for the generation of generic surrogate models, both involving a sequential sampling strategy. All approaches presented in this Dissertation are illustrated by examples drawn from eddy-current nondestructive testing.
7 citations
Proceedings Article•
31 Aug 2011TL;DR: This paper focuses on the axisymmetric case and builds a PDE-based direct model with Dirichlet-to-Neumann boundary operators to describe the relationship between observed data and the inspected component and proposes an inverse algorithm of gradient descent shape optimization type involving a regularization technique by boundary differential operators.
Abstract: Eddy current testing (ECT) using coils is widely practised in in-service inspection of steam generators in nuclear power plants of pressurized water reactor type. In this paper, we consider the shape estimate problem of magnetic deposits given some ECT signals. The non-linearity and the ill-posedness of this inverse problem make it quite challenging. We focus on the axisymmetric case and build a PDE-based direct model with Dirichlet-to-Neumann boundary operators to describe the relationship between observed data and the inspected component. With this direct model, we propose an inverse algorithm of gradient descent shape optimization type involving a regularization technique by boundary differential operators. First numerical experiments are quite encouraging.
4 citations
Cites background or methods from "Eddy current tomography based on a ..."
...Due to the ill-posedness of the inverse problem (see for example [5]), the shape increment given by a first approach (see Section 4....
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...Rather than the contrast source inverse method that the preceding works used (see [5] and its references), we take the shape optimization approach to minimize the cost functional...
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