Full-wave modeling of ultrasonic scattering for non-destructive evaluation

The physical modeling and simulation of nondestructive evaluation (NDE) measurements has a major role in the advancement of NDE and structural health monitoring (SHM). In ultrasonic NDE (UNDE) simulations, evaluating the scattering of ultrasound by defects is a computationally-intensive process. Many UNDE system models treat the scattering process using exact analytical methods or high-frequency approximations such as the Kirchhoff approximation (KA) to make the simulation effort tractable. These methods naturally have a limited scope. This thesis aims to supplement the existing scattering models with fast and memory-efficient full-wave models that are based on the boundary element method (BEM). For computational efficiency, such full-wave models should be applied only to those problems wherein the existing approximation methods are not suitable. Therefore, the adequacy of different scattering models for representing various test scenarios has to be studied. Although analyzing scattering models by themselves is helpful, their true adequacy is revealed only when they are combined with models of other elements of the NDE system, and the resulting predictions are evaluated against measurements. Very few comprehensive studies of this nature exist, particularly for full-wave scattering models. To fill this gap, two different scattering models-- the KA and a boundary-element method-- are integrated into a UNDE system model in this work, and their predictions for standard measurement outputs are compared with experimental data for various benchmark problems. This quantitative comparison serves as a guideline for selecting between the KA and full-wave scattering models for performing UNDE simulations. In accordance with theoretical expectations, the KA is shown to be inappropriate for modeling penetrable (inclusion-type) defects and non-specular scattering, such as diffraction from thin cracks above certain angles of incidence. A key challenge to the use of full-wave scattering methods in UNDE system models is the high computational cost incurred during simulations. Whereas the development of fast finite element methods (FEM) has inspired various applications of the FEM for ultrasound modeling in 3D heterogeneous and anisotropic media, very few applications of the BEM exist despite the progress in accelerated BEMs for elastodynamics. The BEM is highly efficient for modeling scattering from arbitrary shaped 3D defects in homogeneous isotropic media due to a reduction in the dimensionality of the scattering problem, and this potential has not been exploited for UNDE. Therefore, building on recent developments, this work proposes a fast and memory-efficient implementation of the BEM for elastic-wave scattering in UNDE applications. This method features three crucial elements that provide robustness and fast convergence. They include the use of (1) high-order discretization methods for fast convergence, (2) the combined-field integral equation (CFIE) formulation for overcoming the fictitious eigenfrequency problem, and (3) the multi-level fast-multipole algorithm (MLFMA) for reducing the computational time and memory resource complexity. Although numerical implementations based on a subset of these three elements are reported in the literature, the implementation presented in this thesis is the first to combine all three. Some numerical examples are presented to demonstrate the importance of these elements in making the BEM viable for practical applications in UNDE. This thesis contains the first implementation of the diagonal-form MLFMA for solving the CFIE formulation for elastic wave scattering without using any global regularization techniques that reduce hypersingular integrals into less singular ones

Full Wave Modeling of Ultrasonic Scattering Using Nystrom Method for NDE Applications

Approximate methods for ultrasonic scattering like the Kirchhoff approximation and the geometrical theory of diffraction (GTD) can deliver fast solutions with relatively small computational resources compared to accurate numerical methods. However, these models are prone to inaccuracies in predicting scattered fields from defects that are not very large compared to wavelength. Furthermore, they do not take into account physical phenomena like multiple scattering and surface wave generation on defects. Numerical methods like the finite element method (FEM) and the boundary element method (BEM) can overcome these limitations of approximate models. Commercial softwares such as Abaqus FEA and PZFlex use FEM, while CIVA has a 2D FEM solver [1-3]. In this work, we study the performance of the Nyström method (NM) [4,5], an alternative boundary integral equation solver to the BEM, in modeling ultrasonic scattering from defects. To handle larger problems, the Nyström method is accelerated by the multilevel fast multipole algorithm (MLFMA). We apply the NM to benchmark problems and compare its predictions with those of exact and approximate analytical models as well as with experimental results from the World Federation of NDE Centers (WFNDEC). Several examples will be presented to demonstrate the prediction of creeping waves by the NM while also illustrating its improved accuracy over the Kirchhoff approximation. We will conclude with a discussion on the validity and limitations of the NM in modelling practical NDE problems

Fast Uncertainty Propagation of Ultrasonic Testing Simulations for MAPOD and Sensitivity Analysis

Model-assisted probability of detection (MAPOD) and sensitivity analysis (SA) are widelyused for measuring the reliability of nondestructive testing (NDT) systems., such as ultrasonictesting (UT), and understanding the effects of uncertainty parameters. In this work, a stochastic expansion-based metamodel is used in lieu of the physics-based NDT simulation model for efficient uncertainty propagation while keeping satisfactory accuracy. The proposed stochasticmetamodeling approach is demonstrated for MAPOD and SA on a benchmark case for UT simulations on a fused quartz block with a spherically-void defect. The proposed approach is compared with direct Monte Carlo sampling (MCS), and MCS with Kriging metamodels. The results indicate that around one order of magnitude reduction in the number of model evaluations required for MAPOD analysis can be obtained. Moreover, the results indicate around two orders of magnitude reduction of the number of model evaluations for the convergence of the statistical moments and obtaining the problem sensitivities

Full-wave modeling of ultrasonic scattering for non-destructive evaluation

The physical modeling and simulation of nondestructive evaluation (NDE) measurements has a major role in the advancement of NDE and structural health monitoring (SHM). In ultrasonic NDE (UNDE) simulations, evaluating the scattering of ultrasound by defects is a computationally-intensive process. Many UNDE system models treat the scattering process using exact analytical methods or high-frequency approximations such as the Kirchhoff approximation (KA) to make the simulation effort tractable. These methods naturally have a limited scope. This thesis aims to supplement the existing scattering models with fast and memory-efficient full-wave models that are based on the boundary element method (BEM). For computational efficiency, such full-wave models should be applied only to those problems wherein the existing approximation methods are not suitable. Therefore, the adequacy of different scattering models for representing various test scenarios has to be studied. Although analyzing scattering models by themselves is helpful, their true adequacy is revealed only when they are combined with models of other elements of the NDE system, and the resulting predictions are evaluated against measurements. Very few comprehensive studies of this nature exist, particularly for full-wave scattering models. To fill this gap, two different scattering models-- the KA and a boundary-element method-- are integrated into a UNDE system model in this work, and their predictions for standard measurement outputs are compared with experimental data for various benchmark problems. This quantitative comparison serves as a guideline for selecting between the KA and full-wave scattering models for performing UNDE simulations. In accordance with theoretical expectations, the KA is shown to be inappropriate for modeling penetrable (inclusion-type) defects and non-specular scattering, such as diffraction from thin cracks above certain angles of incidence. A key challenge to the use of full-wave scattering methods in UNDE system models is the high computational cost incurred during simulations. Whereas the development of fast finite element methods (FEM) has inspired various applications of the FEM for ultrasound modeling in 3D heterogeneous and anisotropic media, very few applications of the BEM exist despite the progress in accelerated BEMs for elastodynamics. The BEM is highly efficient for modeling scattering from arbitrary shaped 3D defects in homogeneous isotropic media due to a reduction in the dimensionality of the scattering problem, and this potential has not been exploited for UNDE. Therefore, building on recent developments, this work proposes a fast and memory-efficient implementation of the BEM for elastic-wave scattering in UNDE applications. This method features three crucial elements that provide robustness and fast convergence. They include the use of (1) high-order discretization methods for fast convergence, (2) the combined-field integral equation (CFIE) formulation for overcoming the fictitious eigenfrequency problem, and (3) the multi-level fast-multipole algorithm (MLFMA) for reducing the computational time and memory resource complexity. Although numerical implementations based on a subset of these three elements are reported in the literature, the implementation presented in this thesis is the first to combine all three. Some numerical examples are presented to demonstrate the importance of these elements in making the BEM viable for practical applications in UNDE. This thesis contains the first implementation of the diagonal-form MLFMA for solving the CFIE formulation for elastic wave scattering without using any global regularization techniques that reduce hypersingular integrals into less singular ones.</p

Functional reconstruction of lateral oral tongue defects using K's technique: Technical note

Tongue plays an important role in speech and deglutition. It is important to restore the anatomical form to achieve optimum function and aesthetics after ablative cancer resection of tongue lesions. Ideal reconstruction of these defects should be done with a flap that provides adequate bulk and pliable tissue [1]. Usually smaller defects are left to granulate without any reconstruction these may produce unaesthetic anatomical form and speech deformity [2,3]. We describe a technique of primary closure which will restore the anatomical form of the tongue and result in optimal speech

Full Wave Modeling of Ultrasonic Scattering Using Nystrom Method for NDE Applications

Approximate methods for ultrasonic scattering like the Kirchhoff approximation and the geometrical theory of diffraction (GTD) can deliver fast solutions with relatively small computational resources compared to accurate numerical methods. However, these models are prone to inaccuracies in predicting scattered fields from defects that are not very large compared to wavelength. Furthermore, they do not take into account physical phenomena like multiple scattering and surface wave generation on defects. Numerical methods like the finite element method (FEM) and the boundary element method (BEM) can overcome these limitations of approximate models. Commercial softwares such as Abaqus FEA and PZFlex use FEM, while CIVA has a 2D FEM solver [1-3]. In this work, we study the performance of the Nyström method (NM) [4,5], an alternative boundary integral equation solver to the BEM, in modeling ultrasonic scattering from defects. To handle larger problems, the Nyström method is accelerated by the multilevel fast multipole algorithm (MLFMA). We apply the NM to benchmark problems and compare its predictions with those of exact and approximate analytical models as well as with experimental results from the World Federation of NDE Centers (WFNDEC). Several examples will be presented to demonstrate the prediction of creeping waves by the NM while also illustrating its improved accuracy over the Kirchhoff approximation. We will conclude with a discussion on the validity and limitations of the NM in modelling practical NDE problems.</p

Efficient Model-Assisted Probability of Detection and Sensitivity Analysis for Ultrasonic Testing Simulations using Stochastic Metamodeling

Model-assisted probability of detection (MAPOD) and sensitivity analysis (SA) are important for quantifying the inspection capability of nondestructive testing (NDT) systems. To improve the computational efficiency, this work proposes the use of polynomial chaos expansions (PCEs), integrated with least-angle regression (LARS), a basis-adaptive technique, and a hyperbolic truncation scheme, in lieu of the direct use of the physics-based measurement model in the MAPOD and SA calculations. The proposed method is demonstrated on three ultrasonic testing cases and compared with Monte Carlo sampling (MCS) of the physics model, MCS-based kriging, and the ordinary least-squares (OLS)-based PCE method. The results show that the probability of detection (POD) metrics of interests can be controlled within 1% accuracy relative to using the physics model directly. Comparison with metamodels shows that the LARS-based PCE method can provide up to an order of magnitude improvement in the computational efficiency