Time domain linear sampling method for qualitative identification of buried cavities from elastodynamic over-determined boundary data

Khaji, N.; Manshadi, S.H. Dehghan

doi:10.1016/j.compstruc.2015.02.011

Cited by 6 publications

(6 citation statements)

References 30 publications

(34 reference statements)

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“…For simplicity, we consider the scattering of acoustic waves due to an inhomogeneity of compact support D ⊂ R 3 . The generalization to elastic wave scattering is relatively straightforward and has been considered in [10], for example. We assume the inhomogeneity is modeled by a variable wave speed c = c(x), with c(x) > 0 for all x ∈ D, and that the wave speed is a positive constant c = c 0 for all x ∈ R 3 \ D, where D denotes the closure of D. For a point source located at x s ∈ R 3 , let u be the total wave that satisfies the initial-value problem…”

Section: Overview Of the Time-domain Linear Sampling Methodsmentioning

confidence: 99%

“…With the time-domain approach, however, came an ambiguous time parameter that strongly influences the ability of the method to faithfully reconstruct the support of the scatterer. In particular, the literature to date indicates that 'an appropriate time shift' must be chosen to obtain an image of the scatterer [7][8][9][10], yet no information is offered on how this parameter should be chosen. We have found that a clear and precise analysis of the time parameter and its influence on the reconstruction process has yet to be provided.…”

Section: Introductionmentioning

confidence: 99%

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Theory of the linear sampling method for time-dependent fields

Prunty

Snieder

2019

Inverse Problems

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The linear sampling method seeks to localize the unknown source of an observed, time-dependent field. The unknown source could be, for example, a scatterer embedded within a medium, or an impulsive excitation such as an earthquake or explosion. The source of the observed field is localized by means of solving the so-called near-field equation and mapping the obtained solutions through an indicator functional over a test region assumed to contain the source. In its current formulation, however, the linear sampling method suffers from an ambiguous time parameter that strongly influences its ability to localize the unknown source. Our paper consists of two fundamental results central to the theoretical understanding of the linear sampling method and its numerical implementation. First, we prove the so-called blowup behavior of solutions to the near-field equation for a general source function that is separable in space and time. Second, we show that the linear sampling method can be formulated such that the ambiguous time parameter is irrelevant. We demonstrate that a dependence of the linear sampling method on the time parameter arises from an incorrect implementation of a convolution-type operator found in the near-field equation. When the operator is implemented correctly, the dependence on the time parameter vanishes. We provide detailed algorithms for efficient and proper implementations of the convolutional operator in both the time and frequency domains. The crucial result of the improved implementations is that they allow the linear sampling method to be completely automated, as one does not need to know the space-time dependence of the unknown source. We demonstrate the effectiveness of the improved time-and frequency-domain implementations using several numerical examples applied to imaging scatterers.

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Section: Overview Of the Time-domain Linear Sampling Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theory of the linear sampling method for time-dependent fields

Prunty

Snieder

2019

Inverse Problems

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“…𝐷 𝑖 = 𝑒 𝑖𝑘𝑙 𝑠 𝑘𝑙 + 𝜀 𝑖𝑘 𝐸 𝑘 (8) where 𝑠 𝑖𝑗 is the strain tensor, 𝐸 𝑘 is the electric field,𝐶 𝑖𝑗𝑘𝑙 is the fourth-order elasticity tensor measured in a constant electric field, 𝑒 𝑘𝑖𝑗 is the piezoelectric stress constant and 𝜀 𝑖𝑗 is the dielectric tensor measured at constant strains.…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

“…These efforts have led to the conceptually distinct class of inverse solutions, known as "qualitative methods." These methods are based on non-iterative flaw detection from boundary measurements and may be classified as probe or sampling methods such as linear sampling method (LSM) [6][7][8][9][10][11], topological sensitivity (TS) [12][13][14], factorization method (FM) [15], the probe method [16], and point source method [17]. Among these methods, the LSM and the FM, which have been introduced in the inverse scattering literature of far-field acoustics, are particularly attractive.…”

Section: Introductionmentioning

confidence: 99%

Flaw identification in Plane Linear Piezoelastic Media Using Linear Sampling Method

Manshadi

2023

Preprint

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In this paper, the linear sampling method is introduced for cavity detection in a two dimensional (2D) piezoelastic media using measurement of data on the boundary. This method is categorized as a qualitative approach to image the geometrical features of unknown targets. Although this method has been used in the context of inverse problems such as acoustics, electromagnetism and elastostatic, there is no specific attempt to apply this method to identification of cavities in piezoelastic media. This study emphasizes the implementation of the linear sampling method coupled with the finite element method (FEM). A set of numerical simulations on two-dimensional problems is presented to highlight many effective features of the proposed qualitative identification method.

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“…By assuming a linear array containing N elements, the calculation process of the multistatic response matrix in this paper is as follows: Firstly, after the acquisition of the FMC data, an N × N matrix is provided, whose (m,n)th element is actually the recorded time-domain signal from mth transmitter to nth receiver, where 1 m N and 1 n N ; then, the FFT of each element in this N × N matrix is calculated; after that, the complex value of the FFT result at frequency w of (m,n)th element is used as the (m,n)th entry of the F (w). For other time domain implementations of the related sampling methods the reader is referred to [28], [29], [30], [25] for details.…”

Section: B Inverse Scateringmentioning

confidence: 99%

The Application of the Factorization Method to the Subsurface Imaging of Surface-Breaking Cracks

Zhang

Huthwaite

Lowe

2018

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Abstract-A common location for cracks to appear is at the surface of a component; at the near surface, many nondestructive evaluation (NDE) techniques are available to inspect for these, but at the far surface this is much more challenging. Ultrasonic imaging is proposed to enable far surface defect detection, location and characterisation. One specific challenge here is the presence of a strong reflection from the backwall, which can often mask the relatively small response from a defect. In this paper, the Factorization Method (FM) is explored for the application of subsurface imaging of the surface-breaking cracks. In this application, the component has two parallel surfaces, the crack is initiated from the far side and the phased array is attached on the near side. Ideally, the pure scattered field from a defect is needed for the correct estimation of the scatterer through the FM algorithm. However, the presence of the backwall will introduce a strong specular reflection into the measured data which should be removed before applying the FM algorithm. A novel subtraction method was developed to remove the backwall reflection. The performance of the FM algorithm and this subtraction method were tested with the simulated and experimental data. The experimental results showed a good consistency with the simulated results. It is shown that the FM algorithm can generate high quality images to provide a good detection of the crack and an accurate sizing of the crack length. The subtraction method was able to provide a good backwall reflection removal in the case of small cracks (1-3 wavelengths).

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Time domain linear sampling method for qualitative identification of buried cavities from elastodynamic over-determined boundary data

Cited by 6 publications

References 30 publications

Theory of the linear sampling method for time-dependent fields

Theory of the linear sampling method for time-dependent fields

Flaw identification in Plane Linear Piezoelastic Media Using Linear Sampling Method

The Application of the Factorization Method to the Subsurface Imaging of Surface-Breaking Cracks

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