Time reversal for crack identification

Amitt, Eyal; Givoli, Dan; Turkel, Eli

doi:10.1007/s00466-014-0996-2

Cited by 22 publications

(25 citation statements)

References 36 publications

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“…In [1] an approach is considered for 2D scalar wave propagation problems, both forward and backward steps are assumed to take place in the cracked configuration of the medium. While for the forward step it is assumed that solution is obtained, or measured, for the correct cracked configuration, for the backward step a variety of cracked patterns is assumed, for each of them a wave propagation simulation is necessary, while the estimated cracked configuration is the one which gives the best refocusing on the source point.…”

Section: Damage Identificationmentioning

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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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: Damage Identificationmentioning

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

“…This uses a procedure for incorporating multiple time measurements and a new optimization method for identifying scatterers [28][29][30]. This approach was applied to timedependent acoustics in [28], using a finite element (FE) spatial discretization, and to elastodynamics in [29], using finite differences in space and time.…”

Section: Introductionmentioning

confidence: 99%

“…This approach was applied to timedependent acoustics in [28], using a finite element (FE) spatial discretization, and to elastodynamics in [29], using finite differences in space and time. In [30] a variant of the method was applied to the identification of cracks in membranes, whose behavior is governed by the scalar wave equation.…”

Section: Introductionmentioning

confidence: 99%

“…However, many of the papers mentioned above, including [28][29][30], do not involve a physical lab experiment to produce the data. Instead, the data in these papers are generated numerically.…”

Section: Introductionmentioning

confidence: 99%

“…Mathematically, the inverse problem to be solved is governed by the equations of linear 2D elastodynamics. In contrast to [28][29][30], which was purely numerical and employed only synthesized data, now an experimental system with displacement sensors is used to provide physical measurements at the sensor locations. We demonstrate the performance of the system by considering two problems involving a thin metal plate in a plane stress state.…”

Section: Introductionmentioning

confidence: 99%

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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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Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

Rabinovich

Givoli

Bielak³

et al. 2021

Num Anal Meth Geomechanics

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The problem of identifying an obstacle (scatterer) in the form of a cavity in a 2D geophysical medium is considered. This is posed as an inverse wave problem, where the location of the cavity is sought based on measurements of the elastic waves recorded by sensors located at certain points in the domain. The sensor measurements are noisy, and are generated synthetically as a first step. The inverse problem is solved by seeking the minimum of a specially designed cost functional, based on a computational time reversal (TR) procedure, where waves are radiated back in time from the sensors. The cost functional is defined to measure, for each scatterer candidate in the search space, the quality of the refocusing of the backward‐propagating waves on the given wave source at the end of the TR process. While the basic idea has appeared in previous publications, here it is applied to a 2D heterogeneous geophysical model (albeit a relatively simple one), and is enhanced by using several auxiliary techniques. These include (a) an “augmentation” technique, which is used to strengthen the coherent information (and thus to weaken the noncoherent information) by solving an elliptic problem at each time step; (b) experimentation with both instantaneous (impact) sources and time‐harmonic sources of finite duration; (c) combining the identification results of several sources and several source wavelengths to enhance identification; (d) reducing the size of the search space by a special “zooming in” technique; and (e) defining a performance index to assess the method's success and to provide a measure of confidence in the identification result in each specific case. Several numerical experiments are presented that demonstrate the performance of the proposed schemes. The sensitivity of the identification process to various parameters of the scatterer, the measurements, and the medium is investigated.

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Time reversal for crack identification

Cited by 22 publications

References 36 publications

Time Reversal in Elastodynamics and Applications to Structural Health Monitoring

Time Reversal in Elastodynamics and Applications to Structural Health Monitoring

Computational Time Reversal for NDT Applications Using Experimental Data

Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

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