Time domain topological gradient and time reversal analogy: an inverse method for ultrasonic target detection

Domínguez, N.; Gibiat, Vincent; Esquerre, Y.

doi:10.1016/j.wavemoti.2004.09.005

Cited by 94 publications

(78 citation statements)

References 22 publications

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“…Recently, topological sensitivity analysis [10][11][12][13][14][15][16] has been developed as an effective means of defect imaging based on signals originating from multiple reflections from an object. In the imaging method, wave fields for time-reversed incident waves from array sensors in objects with and without defects are calculated first, and then the space function obtained from the difference of the wave fields gives the defect images.…”

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confidence: 99%

“…In the imaging method, wave fields for time-reversed incident waves from array sensors in objects with and without defects are calculated first, and then the space function obtained from the difference of the wave fields gives the defect images. 10,11 Rodriguez et al created images of artificial defects in bulky media and plates by accelerating the calculation speed in the topological imaging. 12 They also proposed the application of topological imaging to defect imaging in a complex geometry where there is no straight path from an ultrasonic transducer to a particular region of interest.…”

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confidence: 99%

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Imaging defects in a plate with complex geometries

Hayashi

2016

Applied Physics Letters

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This paper discusses a defect imaging technique using signals containing multiple reflected waves, for a plate with complex geometries, in which direct waves from a generating point to a receiving point cannot be measured. This technique utilizes a characteristic of flexural vibrations wherein the amplitude of the received signals is approximately inversely proportional to the thickness of the source of the elastic wave when a laser pulse is applied to the surface of the plate. First, a theoretical modal analysis elucidated that the amplitude distributions obtained by scanning the laser source of the elastic waves consist of thickness distributions and spurious distributions caused by multiple reflections in the plate. The amplitude distributions were then experimentally obtained for a complex-shaped plate with an artificial defect. The distributions were found to consist of a defect image as well as spurious images, and this agreed well with the theoretical discussions. Clearer defect images with small spurious images were obtained even for a plate with complex geometries by taking an average of the images obtained at multiple frequencies.

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confidence: 99%

Imaging defects in a plate with complex geometries

Hayashi

2016

Applied Physics Letters

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“…Soon after its emergence [24], the idea was embraced for imaging of diametrically small anomalies [18] and inverse scattering problems; see, for example, [2,4,15,22,23,25,27] and articles cited therein.…”

Section: Introductionmentioning

confidence: 99%

Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions

Wahab

2015

SIAM J. Imaging Sci.

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The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of scattered magnetic field at a fixed frequency. The inverse problem of inclusion detection is formulated as an optimization problem in terms of a filtered discrepancy functional and the topological derivative based imaging functional obtained therefrom. The sensitivity and resolution analysis of the imaging functional is rigorously performed. It is substantiated that the Rayleigh resolution limit is achieved. Further, the stability of the reconstruction with respect to measurement and medium noises is investigated and the signal-to-noise ratio is evaluated in terms of the imaginary part of free space fundamental magnetic solution.

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“…Moreover, analogies between TD and time reversal have been investigated [29,54]. On the other hand, only scattered studies have so far been devoted to crack identification, including [10] for 2D potential problems, [7] and [9] for the 2D and 3D Helmholtz equation, respectively, and [32] in 2D elastostatics.…”

Section: Introductionmentioning

confidence: 99%

Qualitative identification of cracks using 3D transient elastodynamic topological derivative: Formulation and FE implementation

Bellis

Bonnet

2013

Computer Methods in Applied Mechanics and Engineering

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To cite this version:Cédric Bellis, Marc Bonnet. Abstract A time-domain topological derivative (TD) approach is developed for transient elasticwave imaging of buried cracks. The TD, which quantifies the sensitivity of the misfit cost functional to the creation at a specified location of an infinitesimal trial crack, is expressed in terms of the time convolution of the free field and an adjoint field as a function of that specified location and of the trial crack shape. Following previous studies on cavity identification in similar conditions, the TD field is here considered as a natural and computationally efficient approach for defining a crack location indicator function. This study emphasizes the implementation and exploitation of TD fields using the standard displacement-based FEM, a straightforward exploitation of the relevant sensitivity formulation established here. Results on several numerical experiments on 3D elastodynamic and acoustic configurations are reported and discussed, allowing to assess and highlight many features of the proposed TD-based fast qualitative crack identification, including its ability to identify multiple cracks and its robustness against data noise.

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Time domain topological gradient and time reversal analogy: an inverse method for ultrasonic target detection

Cited by 94 publications

References 22 publications

Imaging defects in a plate with complex geometries

Imaging defects in a plate with complex geometries

Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions

Qualitative identification of cracks using 3D transient elastodynamic topological derivative: Formulation and FE implementation

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