Elastodynamic ray theory and asymptotic methods for direct and inverse scattering problems

Chen, Jer-Shi

doi:10.31274/rtd-180813-8605

Cited by 5 publications

(6 citation statements)

References 143 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result, without the absolute sign, agrees with the first term found in Chen's thesis [22] for the ratio between the "step" and the front delta response. Chen, actually employed elastodynamic ray theory to obtain two terms in the numerator of the expression for F3 which rendered it exact.…”

Section: "Asupporting

confidence: 90%

“…Even though the Born approximation is a long-wavelength, weak-scattering theory, it has also been successfully used for sizing strong volumetric scatterers like voids [48]. Chen [22], using elastodynamic ray theory, recently gave some exact results for voids that may help to explain this unexpected success of the Born approximation.…”

Section: Time Domain Resultsmentioning

confidence: 99%

“…give explicit expressions for the response of flaws to an ideal unit impulse function [13,17], Chen [22], in a recent thesis, has shown that the early arriving waves in this ideal response (leading edge response) contain significant information on flaw properties that can, in principle, be used for flaw sizing purposes. In Chapter Two, we will…”

Section: Scattering Theorymentioning

confidence: 99%

See 2 more Smart Citations

Ultrasonic flaw classification: an approach using modeling, signal processing, and adaptive learning

Koo

View full text Add to dashboard Cite

Section: "Asupporting

confidence: 90%

Section: Time Domain Resultsmentioning

confidence: 99%

Section: Scattering Theorymentioning

confidence: 99%

See 1 more Smart Citation

Ultrasonic flaw classification: an approach using modeling, signal processing, and adaptive learning

Koo

View full text Add to dashboard Cite

“…Since it would be difficult to obtain angles 8 > 45°in many practical situations, there is simply not enough leverage in the variation of F(8) to solve Equation(22). Although this negative result initially appears discouraging, the surprising fact that R,(B) = R,(OO)F(8) …”

mentioning

confidence: 85%

“…Equation (13) can be further evaluated by use of the method of stationary phase. In this case the far-field scattering amplitude is given by [22] Downloaded by [University of Auckland Library] at 18:00 27 November 2014 ( 14) where, x' is the position vector of the specular reflection point, and R, and R~are the principal radii of the curvature of S at x'. In fact, this represents the front surface specular reflection from the flaw, which is the most significant part of the scattering signal.…”

Section: Specular Reflection From An Inclusionmentioning

confidence: 99%

New Approaches to Ultrasonic Equivalent Sizing for Small Flaws

Song

Schmerr

1992

Nondestructive Testing and Evaluation

View full text Add to dashboard Cite

Ultrasonic equivalent flaw sizing methods size defects in a material by ohtaining a best-lit simple defect shape (such as an ellipsoid or ellipse) from relatively SIll,11I amounts of ultrasonic data. In these cquivulcnt flaw sizing methods. it is essential that the origin of time he determined precisely with respect 10 a fixed spatial location. Current methods for this determination arc not entirely adequate. leading to an important "zero-of-time" problem.In this work, two new approaches to equivalent Ilaw sizing for relatively smalillaws arc developed: (I) an amplitude-based equivalent (AilE) sizing method for obtaining best-lit equivalentllaws by the use of amplitude ratios measured at different transducer orientations, and (2) a first moment (FM) method for estimating the equivalent radius from a first moment calculation of the time domain flaw response. We show how these approaches can address the zero-of-time problem and demonstrate the performance of these methods with experiments.

show abstract

Surface Reconstruction of a Three-Dimensional Ultrasonic Flaw

Koo

1993

Inverse Problems in Engineering Mechanics

View full text Add to dashboard Cite

In three-dimensional inverse scattering problems, the reconstruction of a solid scatterer is often difficult, if not impossible, and computationally expensive due to the dimensionality. To obtain only the geometrical information, a surface reconstruction algorithm is nattwally more, desirable since no additional knowledge can be gained ft'ore doing the solid reconstruction and the computation is reduced to two dimensions. With the application of the first Born approximation, this paper proposes a simple surface reconstruction technique for a three-dimensional target. In general, this method is ill-posed. However, the numerical instability part of the ill-posedness is removable when the surface has a twofold symmetry with respect to a plane. To demonstrate this approach, three analytical examples are shown. I_q.tr.__octi?n Reconstruction of the geomeu3, of an embedded flaw has been one of the major areas in nondestructive evaluation (NDE) research. Some of the algorithms published in the last decade were based on the elastic wave inverse (gust) Born approximation, which is essentially a low frequency approximation to an isolated weak scatterer in an otherwise isotropic and homogeneous medium whose material properties are similar to the host's [ 1,2]. A key factor in the development of these inverse algorithms is the spatial-frequency function "shape factor" that appears in the formulation of the inverse Bom approximation. This shape, factor embodies all information about the size, shape, and orientation of the scatterer and, therefore, one can develop inverse procedures to extract the geomeu3, in terms of a characteristic function (which has the value 1 inside the scatterer and 0 outside). The direct approach to recovering this characteristic function requires three-dimensional information in the spatial-frequency domain [3], which is computationally expensive. However, the basic equation of the general three-dimensional inverse Born approximation c,'m be.further cast to form a set of equations for the surface of a three-dimensional flaw. As a consequence, one can develop a "surface reconstruction" algorithm based upon these equations. Since the surface of a three-dimensional flaw is two-dimensional, the algorithm requires o_tly 'knowledge of a two-dimensional hyper-plane of the shape factor instead of a !.

show abstract

Elastodynamic ray theory and asymptotic methods for direct and inverse scattering problems

Cited by 5 publications

References 143 publications

Ultrasonic flaw classification: an approach using modeling, signal processing, and adaptive learning

Ultrasonic flaw classification: an approach using modeling, signal processing, and adaptive learning

New Approaches to Ultrasonic Equivalent Sizing for Small Flaws

Surface Reconstruction of a Three-Dimensional Ultrasonic Flaw

Contact Info

Product

Resources

About