Time Reversal and Imaging for Structures

Panagiotopoulos, Christos G.; Petromichelakis, Yiannis; Tsogka, Chrysoula

doi:10.1007/978-3-319-56136-3_9

Cited by 4 publications

(6 citation statements)

References 21 publications

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“…in seismology for epicenter localization, while the second is the scatterer localization problem that has been used e.g. for the localization of subsurface objects [10,11] in geosciences or damaged areas within structures [12,13] in Structural Health Monitoring (SHM). In this paper, we reserve the abbreviation TR to indicate computational Time-Reversal.…”

Section: Introductionmentioning

confidence: 99%

Signal-to-Noise Ratio analysis for time-reversal based imaging techniques in bounded domains

2018

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We consider the problem of localizing small material defects in rectangular bounded domains. The scalar acoustic equation is used to model wave propagation in this context. Our data is the scattered field collected at one or more receivers and due to impulsive excitations at one or more source positions. To localize the defect we use an imaging method that consists in back-propagating the recorded field in the domain of interest. The back-propagation is performed numerically using a model for the Green's function in the bounded medium. For the source localization problem this imaging technique is equivalent to computational Time Reversal (TR). We study in this paper the quality of imaging in terms of the Signal to Noise Ratio (SNR) both for the source and the defect localization problems. SNR here is defined as the value of the image at the true source (defect) location, divided by the maximal value of the image outside a small region around the true source (defect) location. Our theoretical analysis carried out for the simpler one-dimensional case allows us to correctly predict the performance of the method. Our results indicate that for the source localization problem the SNR increases linearly with the number of receivers while for the defect localization its maximal value is 2 and can only be attained by

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Section: Introductionmentioning

confidence: 99%

Signal-to-Noise Ratio analysis for time-reversal based imaging techniques in bounded domains

2018

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“…In the case of switching time reversal approaches, based on the reciprocal statement of Equation ( 10), we expected to observe wave refocusing on the part of the initial disturbance which produced the forward wave propagation motion. Such an approach could lead to interesting time reversal computational tools [32,33]. A usual choice of such a disturbance would be a concentrated impulsive load on point x s given by q(x, t)=δ(x − x s )δ(t) resulting in motion u(x, t).…”

Section: Switching Time Reversalmentioning

confidence: 99%

“…Following previous work [33,36], our choice here is to assumef of zero values components or units when it corresponds to some u r component. Evolutionf (t) = u(t * ) is the reversed in time component of vector u, actually being the solution of the forward problem of Equation (18).…”

Section: The Time Reversal or Backward Stepmentioning

confidence: 99%

“…Of crucial importance is the choice of quantity to be monitored in order to observe refocusing during the backward step. Such refocusing on appropriate discrete time step [33] or time averaged [37] will indicate the spatial location of original source point of the forward step. As for monitoring quantity, we consider here the value of some DOF, its time derivative, some appropriate norm (e.g., Euclidean) or even some energetic quantity, as would be the density of elastic, kinetic or total energy.…”

Section: The Time Reversal or Backward Stepmentioning

confidence: 99%

“…By this, one avoids the need to establish the appropriate time step of a refocusing snapshot. The imaging functional for our case is given as [33]:…”

Section: Imaging In Frequency Domainmentioning

confidence: 99%

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A Numerical Study on Computational Time Reversal for Structural Health Monitoring

Panagiotopoulos

Stavroulakis

2021

Signals

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Structural health monitoring problems are studied numerically with the time reversal method (TR). The dynamic output of the structure is applied, time reversed, as an external loading and its propagation within the deformable medium is followed backwards in time. Unknown loading sources or damages can be discovered by means of this method, focused by the reversed signal. The method is theoretically justified by the time-reversibility of the wave equation. Damage identification problems relevant to structural health monitoring for truss and frame structures are studied here. Beam structures are used for the demonstration of the concept, by means of numerical experiments. The influence of the signal-to-noise ratio (SNR) on the results was investigated, since this quantity influences the applicability of the method in real-life cases. The method is promising, in view of the increasing availability of distributed intelligent sensors and actuators.

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Finite element method based computational time reversal in elastodynamics: Refocusing, reconstruction and its numerical sensitivity

Mračko

Kober

Kolman

et al. 2021

Mathematics and Computers in Simulation

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Time Reversal and Imaging for Structures

Cited by 4 publications

References 21 publications

Signal-to-Noise Ratio analysis for time-reversal based imaging techniques in bounded domains

Signal-to-Noise Ratio analysis for time-reversal based imaging techniques in bounded domains

A Numerical Study on Computational Time Reversal for Structural Health Monitoring

Finite element method based computational time reversal in elastodynamics: Refocusing, reconstruction and its numerical sensitivity

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