Non-destructive imaging using the time domain topological energy method

Domínguez, N.; Gibiat, Vincent

doi:10.1016/j.ultras.2009.08.014

Cited by 76 publications

(94 citation statements)

References 9 publications

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“…Thus, the results will exclusively rely on multiple-reflected waves. The method can deal with ballistic waves like in the previous experimental applications [6], [7], [8] but suppressing them allows to demonstrate that they are not necessary when investigating a reverberating medium. The transducer is a 5 mm in diameter piezoelectric sensor adhesively bonded to one side of the plate at the position .…”

Section: Experimental Applications Locating a Defect In A Simple Platmentioning

confidence: 99%

“…Both wave fields are usually obtained with numerical simulations and are referred to as the solutions of the direct and the adjoint problem, respectively. Using a reference medium as close as possible to the experimental medium and an appropriate numerical tool, the method is experimentally applied with traditional emitter/receiver transducers and leads to accurate location and imaging of various objects [6], [7], [8]. So far, the method has been applied with infinite or semi-infinite reference media, as well as by taking into account the first reflections at the edge of a bounded domain [9].…”

Section: Introductionmentioning

confidence: 99%

“…The study is here restricted to the normal displacement at the surface of the plate. Plotting the function gives an image in the plane [6], [7], [8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Locating damages in a complex structure using one or two fixed ultrasonic transducers

Rodríguez¹,

Veidt²,

Castaings³

et al. 2016

AIP Conference Proceedings

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Section: Experimental Applications Locating a Defect In A Simple Platmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Locating damages in a complex structure using one or two fixed ultrasonic transducers

Rodríguez¹,

Veidt²,

Castaings³

et al. 2016

AIP Conference Proceedings

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“…Plotting the function Tðx; yÞ gives an image in the plane ðx; yÞ. [7][8][9] Let us assume that a punctual source is located at the point ðx 0 ; y 0 Þ. Knowing, in the absence of defect, the acoustic impulse response hðx; y; tÞ associated to this source, the two fields u and v can be expressed, respectively, by uðx; y; tÞ ¼ hðx; y; tÞ Ã u s ðtÞ; (2a) vðx; y; tÞ ¼ hðx; y; tÞ Ã rðÀtÞ;…”

Section: -mentioning

confidence: 99%

“…Using a reference medium as close as possible to the experimental medium and an appropriate numerical tool, the method is experimentally applied with traditional emitter/receiver transducers and leads to accurate location and imaging of various defects. [7][8][9] So far, the method has been applied with infinite or semi-infinite reference media, as well as by a)…”

mentioning

confidence: 99%

One channel defect imaging in a reverberating medium

Rodríguez

Veidt

Castaings

et al. 2014

Applied Physics Letters

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A noniterative reconstruction method for the inverse potential problem with partial boundary measurements

Fernandez

Novotny

Prakash

2019

Math Methods in App Sciences

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In this paper, a noniterative reconstruction method for solving the inverse potential problem is proposed. The forward problem is governed by a modified Helmholtz equation. The inverse problem consists in the reconstruction of a set of anomalies embedded into a geometrical domain from partial or total boundary measurements of the associated potential. Since the inverse problem is written in the form of an ill‐posed boundary value problem, the idea is to rewrite it as a topology optimization problem. In particular, a shape functional measuring the misfit between the solution obtained from the model and the data taken from the boundary measurements is minimized with respect to a set of ball‐shaped anomalies by using the concept of topological derivatives. It means that the shape functional is expanded asymptotically and then truncated up to the desired order term. The resulting truncated expansion is trivially minimized with respect to the parameters under consideration that leads to a noniterative second order reconstruction algorithm. As a result, the reconstruction process becomes very robust with respect to the noisy data and independent of any initial guess. Finally, some numerical experiments are presented showing the capability of the proposed method in reconstructing multiple anomalies of different sizes and shapes by taking into account complete or partial boundary measurements.

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Non-destructive imaging using the time domain topological energy method

Cited by 76 publications

References 9 publications

Locating damages in a complex structure using one or two fixed ultrasonic transducers

Locating damages in a complex structure using one or two fixed ultrasonic transducers

One channel defect imaging in a reverberating medium

A noniterative reconstruction method for the inverse potential problem with partial boundary measurements

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