Time Reversal as a Computational Tool in Acoustics and Elastodynamics

Givoli, Dan

doi:10.1142/s0218396x14300011

Cited by 34 publications

(23 citation statements)

References 72 publications

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“…In [16], and some references therein, the wave is rebroadcasted through appropriate initial conditions. Alternatively, one can follow the approach used in [13] or [12] for acoustic waves, and adapt it to the case of linear elasticity that consists in solving the problem,…”

Section: The Time Reversal Processmentioning

confidence: 99%

“…Wave paths that were traversed in the forward propagation step are now reproduced in the backward one [3]. Ideal conditions for the time reversal process would be those corresponding to the case where receivers fill the whole medium (or its entire boundary), recording the field and its derivatives [15], without any noise [16]. The time reversibility is based on the spatial reciprocity (symmetry in engineering) and the time reversal invariance (under the transformation t→ − t) of linear wave equations.…”

Section: Introductionmentioning

confidence: 99%

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Time Reversal in Elastodynamics and Applications to Structural Health Monitoring

Panagiotopoulos¹,

Petromichelakis²,

Tsogka³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. In structural health monitoring, detection of localized damage can be achieved by exploiting recorded signals at a limited number of sensors within the structure. Here we propose the localization of damage using an array of sensors as a computational time-reversal mirror (TRM). Time reversal (TR) is a physical process that exploits the time reversibility of wave equations and achieves re-focusing of the wave on the source of its origin by sending back, reversed in time, the signals recorded on an array of transducers. TR was originally introduced by Mathias Fink and his group and has several applications ranging from medical imaging to telecommunications [14].In the present work, we perform time reversal numerically in order to effectively detect and localize defects in a bounded two-dimensional elastic domain. This is a generalization of a respective time-reversal implementation in an acoustic medium [12]. The solid contains a number of N r sensors which can act as sources as well. Our data is the response matrix of the scattered field, that is, the difference between the total field obtained in the damaged structure and the incident field corresponding to the response in the healthy structure.Numerical solution of the wave propagation problem is performed using a mixed finite element formulation in terms of the velocity and stress fields [6]. In order to dissociate the response caused by N d different defects, we apply the singular value decomposition (SVD) of the response matrix, while back-propagation of the projection of each singular vector corresponding to a non-zero singular value is performed in order to highlight each defect separately.

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Section: The Time Reversal Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time Reversal in Elastodynamics and Applications to Structural Health Monitoring

Panagiotopoulos¹,

Petromichelakis²,

Tsogka³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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show abstract

“…Since that seminal paper, TR has been of considerable interest in the computational mechanics literature. It was shown by Fink and others that TR can be utilized also as a computational tool for source or obstacle identification …”

Section: Introductionmentioning

confidence: 99%

“…It was shown by Fink and others that TR can be utilized also as a computational tool for source or obstacle identification. 8 The research done on obstacle identification using the TR technique is extensive. However, many of these identification algorithms are not developed for the identification of bulky-like obstacles in the unbounded domain.…”

Section: Introductionmentioning

confidence: 99%

Obstacle identification using the TRAC algorithm with a second‐order ABC

Levin

Turkel

Givoli

2019

Numerical Meth Engineering

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Summary We consider obstacle identification using wave propagation. In such problems, one wants to find the location, shape, and size of an unknown obstacle from given measurements. We propose an algorithm for the identification task based on a time‐reversed absorbing condition (TRAC) technique. Here, we apply the TRAC method to time‐dependent linear acoustics, although our methodology can be applied to other wave‐related problems as well, such as elastodynamics. There are two main contributions of our identification algorithm. The first contribution is the development of a robust and effective method for obstacle identification. While the original paper presented criteria for accepting or rejecting regions that enclose the obstacle, we use these criteria to develop an algorithm that automatically identifies the location of the obstacle. The second contribution is the utilization of an improved absorbing boundary condition (ABC) for the identification. We use the second‐order Engquist‐Majda ABC, and we implement it with a finite element scheme. To our knowledge, this is the first time that the second‐order Engquist‐Majda ABC is employed with the finite element method, as this boundary condition does not naturally fit in finite element schemes in its original form. Numerical experiments for the algorithms are presented.

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“…One should distinguish between physical TR, which is the original TR procedure invented by Fink et al [20], and computational TR, which has been developed later; see the review paper [21]. It is the latter which concerns us in the context of model-based NDT.…”

Section: Introductionmentioning

confidence: 99%

Computational Time Reversal for NDT Applications Using Experimental Data

et al. 2017

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A model-based non destructive testing (NDT) method is proposed for damage identification in elastic structures, incorporating computational time reversal (TR) analysis. Identification is performed by advancing elastic wave signals, measured at discrete sensor locations, backward in time. In contrast to a previous study, which was purely numerical and employed only synthesized data, here an experimental system with displacement sensors is used to provide physical measurements at the sensor locations. The performance of the system is demonstrated by considering two problems of a thin metal plate in a plane stress state. The first problem, which represents passive damage identification, consists in finding the location of a small impact region from remote measurements. The second problem is the identification of the location of a square hole in the plate. The difficulties one encounters in applying this identification method and ways to overcome them are described. It is concluded that while this is a viable model-based identifica-

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Time Reversal as a Computational Tool in Acoustics and Elastodynamics

Cited by 34 publications

References 72 publications

Time Reversal in Elastodynamics and Applications to Structural Health Monitoring

Time Reversal in Elastodynamics and Applications to Structural Health Monitoring

Obstacle identification using the TRAC algorithm with a second‐order ABC

Computational Time Reversal for NDT Applications Using Experimental Data

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