Degree Type

Dissertation

Date of Award

2020

Degree Name

Doctor of Philosophy

Department

Electrical and Computer Engineering

Major

Electrical Engineering(Electromagnetics, Microwave,and Nondestructive Evaluation)

First Advisor

Jiming Song

Abstract

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.

DOI

https://doi.org/10.31274/etd-20200902-52

Copyright Owner

Praveen Gurrala

Language

en

File Format

application/pdf

File Size

290 pages

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