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In this paper, we present an efficient method to simulate multilayered anisotropic composite material with effective medium theory. Effective permittivity, permeability and orientation angle for a layered anisotropic composite medium are extracted with this equivalent model. We also derive analytical expressions for effective parameters and orientation angle with low frequency (LF) limit, which will be shown in detail. Numerical results are shown in comparing extracted effective parameters and orientation angle with analytical results from low frequency limit. Good agreements are achieved to demonstrate the accuracy of our efficient model. [ABSTRACT FROM AUTHOR]

Probability of detection (POD) is widely used for measuring reliability of nondestructive testing (NDT) systems. Typically, POD is determined experimentally, while it can be enhanced by utilizing physics-based computational models in combination with model-assisted POD (MAPOD) methods. With the development of advanced physics-based methods, such as ultrasonic NDT testing, the empirical information, needed for POD methods, can be reduced. However, performing accurate numerical simulations can be prohibitively time-consuming, especially as part of stochastic analysis. In this work, stochastic surrogate models for computational physics-based measurement simulations are developed for cost savings of MAPOD methods while simultaneously ensuring sufficient accuracy. The stochastic surrogate is used to propagate the random input variables through the physics-based simulation model to obtain the joint probability distribution of the output. The POD curves are then generated based on those results. Here, the stochastic surrogates are constructed using non-intrusive polynomial chaos (NIPC) expansions. In particular, the NIPC methods used are the quadrature, ordinary least-squares (OLS), and least-angle regression sparse (LARS) techniques. The proposed approach is demonstrated on the ultrasonic testing simulation of a flat bottom hole flaw in an aluminum block. The results show that the stochastic surrogates have at least two orders of magnitude faster convergence on the statistics than direct Monte Carlo sampling (MCS). Moreover, the evaluation of the stochastic surrogate models is over three orders of magnitude faster than the underlying simulation model for this case, which is the UTSim2 model. [ABSTRACT FROM AUTHOR]

Full wave scattering models for ultrasonic waves are necessary for the accurate prediction of voltage signals received from complex defects/flaws in practical nondestructive evaluation (NDE) measurements. We propose the high-order Nyström method accelerated by the multilevel fast multipole algorithm (MLFMA) as an improvement to the state-of-the-art full-wave scattering models that are based on boundary integral equations. We present numerical results demonstrating improvements in simulation time and memory requirement. Particularly, we demonstrate the need for higher order geom-etry and field approximation in modeling NDE measurements. Also, we illustrate the importance of full-wave scattering models using experimental pulse-echo data from a spherical inclusion in a solid, which cannot be modeled accurately by approximation-based scattering models such as the Kirchhoff approximation. [ABSTRACT FROM AUTHOR]

In this paper, we simulate some of the benchmark problems proposed by the World Federation of Nondestructive Evaluation Centers (WFNDEC) using a full wave simulation model based on accurate solutions to the boundary integral equations for ultrasonic scattering. Much of the previous work on modeling these problems relied on the Kirch-hoff approximation to find the scattered fields from defects. Here we instead use a numerical method, called the Nyström method, for finding the scattered fields more accurately by solving the boundary integral equations of scattering. We compare our model's predictions with both measurements and Kirchhoff approximation based models. We expect the presented results to serve as a validation of our model as well as a comparison between the Kirchhoff approximation and the Nyström method. [ABSTRACT FROM AUTHOR]

Elastic waves in solids find important applications in ultrasonic non-destructive evaluation. The scattering of elastic waves has been treated using many approaches like the finite element method, boundary element method and Kirchhoff approximation. In this work, we propose a novel accurate and efficient high order Nystr?om method to solve the boundary integral equations for elastodynamic scattering problems. This approach employs high order geometry description for the element, and high order interpolation for fields inside each element. Compared with the boundary element method, this approach makes the choice of the nodes for interpolation based on the Gaussian quadrature, which renders matrix elements for far field interaction free from integration, and also greatly simplifies the process for singularity and near singularity treatment. The proposed approach employs a novel efficient near singularity treatment that makes the solver able to handle extreme geometries like very thin penny-shaped crack. Numerical results are presented to validate the approach. By using the frequency domain response and performing the inverse Fourier transform, we also report the time domain response of flaw scattering. [ABSTRACT FROM AUTHOR]

Previously, concentric coplanar capacitive sensors have been developed to quantitatively characterize the permittivity or thickness of one layer in multi-layered dielectrics. Electrostatic Green's functions due to a point source at the surface of one- to three-layered test-pieces were first derived in the spectral domain, under the Hankel transform. Green's functions in the spatial domain were then obtained by using the appropriate inverse transform. Utilizing the spatial domain Green's functions, the sensor surface charge density was calculated using the method of moments and the sensor capacitance was calculated from its surface charge. In the current work, the spectral domain Green's functions are used to derive directly the integral equation for the sensor surface charge density in the spectral domain, using Parseval's theorem. Then the integral equation is discretized to form matrix equations using the method of moments. It is shown that the spatial domain approach is more computationally efficient, whereas the Green's function derivation and numerical implementation are easier for the spectral domain approach. [ABSTRACT FROM AUTHOR]

Nondestructive evaluation (NDE) of airframe structures may involve finding eddy-current distributions in complicated geometrical features including cracks, fasteners, sharp corners/edges, multi-layered structures, complex ferrite-cored probes, etc. The eddy-current problem can be formulated in terms of boundary integral equations (BIE), which can be discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). The Fast Multipole Method (FMM) is a well-established and effective method for accelerating numerical solutions of the matrix equations. Accelerated by the FMM, the BIE method can now solve large-scale electromagnetic wave propagation and diffusion problems. The traditional BIE method requires O(N2) operations to compute the system of equations and another O(N3) operations to solve the system using direct solvers, with N being the number of unknowns; in contrast, the BIE method accelerated by the two-level FMM can potentially reduce the operations and memory requirement to O(N3/2). This paper introduces the procedure of the FMM accelerated BIE method, which is not only efficient in meshing complicated geometries, accurate for solving singular fields or fields in infinite domains, but also practical and often superior to other methods in solving large-scale problems. Computational tests of the numerical FMM solutions against the conventional BIE results are presented for the two-dimensional Helmholtz equation with a complex wave number. [ABSTRACT FROM AUTHOR]