Computational aspects of electromagnetic NDE phenomena

The development of theoretical models that characterize various physical phenomena is extremely crucial in all engineering disciplines. In nondestructive evaluation (NDE), theoretical models are used extensively to understand the physics of material/energy interaction, optimize experimental design parameters and solve the inverse problem of defect characterization. This dissertation describes methods for developing computational models for electromagnetic NDE applications. Two broad classes of issues that are addressed in this dissertation are related to (i) problem formulation and (ii) implementation of computers;The two main approaches for solving physical problems in NDE are the differential and integral equations. The relative advantages and disadvantages of the two approaches are illustrated and models are developed to simulate electromagnetic scattering from objects or inhomogeneities embedded in multilayered media which is applicable in many NDE problems. The low storage advantage of the differential approach and the finite solution domain feature of the integral approach are exploited. Hybrid techniques and other efficient modeling techniques are presented to minimize the storage requirements for both approaches;The second issue of computational models is the computational resources required for implementation. Implementations on conventional sequential computers, parallel architecture machines and more recent neural computers are presented. An example which requires the use of massive parallel computing is given where a probability of detection model is built for eddy current testing of 3D objects. The POD model based on the finite element formulation is implemented on an NCUBE parallel computer. The linear system of equations is solved using direct and iterative methods. The implementations are designed to minimize the interprocessor communication and optimize the number of simultaneous model runs to obtain a maximum effective speedup;Another form of parallel computing is the more recent neurocomputer which depends on building an artificial neural network composed of numerous simple neurons. Two classes of neural networks have been used to solve electromagnetic NDE inverse problems. The first approach depends on a direct solution of the governing integral equation and is done using a Hopfield type neural network. Design of the network structure and parameters is presented. The second approach depends on developing a mathematical transform between the input and output space of the problem. A multilayered perceptron type neural network is invoked for this implementation. The network is augmented to build an incremental learning network which is motivated by the dynamic and modular features of the human brain

Finite element and boundary element analysis of electromagnetic NDE phenomena

The endeavor to produce quality products coupled with a drive to minimize failure in major industries such as aerospace, power and transportation is the driving force behind studies of electromagnetic nondestructive evaluation (NDE) methods. Popular domain and integral methods used for the purpose of modeling electromagnetic NDE phenomena include the finite element and boundary element methods. However no single numerical modeling technique has emerged as the optimal choice for all electromagnetic NDE processes. In a computer aided design environment, where the choice of an optimum modeling technique is critical, an evaluation of the various aspects of different numerical approaches is extremely helpful;In this dissertation, a comparison is made of the relative advantages and disadvantages of the finite element (FE) and boundary element (BE) methods as applied to the DC and AC Potential drop (DCPD and ACPD) methods for characterizing fatigue cracks. The comparison covers aspects of robustness, computer resource requirements and ease of numerically implementing the methods. Two dimensional FE and BE models are used to model an infinitely thin fatigue crack using the ACPD method, and a two and three dimensional FE and BE model is used to study the compact tension and single edge notch specimen using the DCPD method. Calibration curves and field plots in the specimen are compared to experimental and analytical data. The FE and BE methods are complementary numerical techniques and are combined to exploit their individual merits in the latter part of this dissertation. A three dimensional hybrid formulation to model eddy current NDE is then developed which discretizes the interior with finite elements and the exterior with boundary elements. The three dimensional model is applied to an absolute eddy current coil over a finite block. A feasibility study to confirm the validity of the formulation is undertaken by comparing the numerical results for probe lift-off and coil impedance measurements with published data;This comparative study outlined above indicates that when the solution is required at discrete points, as in the potential drop methods, or the model needs to handle infinite boundaries, as in eddy current NDE, the boundary element model is more suitable. Since it is based 011 the Green\u27s function, the BE method is limited to linear problems. Finite element analysis gives full field solutions, making it ideal for studying energy/defect interactions. The hybrid FE/BE formulation handles non-linearity and infinite boundaries naturally, thus utilizing the best of both worlds

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Hybrid-dual-fourier tomographic algorithm for a fast three-dimensionial optical image reconstruction in turbid media

A reconstruction technique for reducing computation burden in the 3D image processes, wherein the reconstruction procedure comprises an inverse and a forward model. The inverse model uses a hybrid dual Fourier algorithm that combines a 2D Fourier inversion with a 1D matrix inversion to thereby provide high-speed inverse computations. The inverse algorithm uses a hybrid transfer to provide fast Fourier inversion for data of multiple sources and multiple detectors. The forward model is based on an analytical cumulant solution of a radiative transfer equation. The accurate analytical form of the solution to the radiative transfer equation provides an efficient formalism for fast computation of the forward model

Electromagnetic Scattering from Semi-Infinite Planar Arrays

A hybrid method of moments (MM) based numerical model for the electromagnetic scattering from large finite by infinite planar slot arrays is developed. The method incorporates the novel concept of a physical basis function (PBF) to dramatically reduce the number of required unknowns. The model can represent a finite number of slot columns with slots oriented along the infinite axis, surrounded by an arbitrary number of coplanar dielectric slabs. Each slot column can be loaded with a complex impedance, allowing one to tailor the edge currents to provide a desired echo width pattern. The surface equivalence theorem is used to convert the original slotted ground plane geometry to an equivalent unbroken ground plane with magnetic surface currents. An integral equation based on these magnetic scattering currents is solved via the MM. The magnetic currents are approximated by a set of basis functions composed of periodic basis functions representing the edge slot columns and a single PBF representing the interior slot columns. In particular, the PBF captures the behavior of the central portion of the array where the perturbations from the edges have become negligible. Based on Floquet\u27s theorem, the PBF is able to represent an arbitrarily large number of slot columns with just one unknown. The array scanning method (ASM) provides the contributions from the individual edge columns. Finally, a newly developed one sided Poisson sum formulation provides an efficient means to account for the stratified dielectric media via a spectral domain conversion. The hybrid method is validated using both MM reference codes and measured data. The results clearly demonstrate the method\u27s accuracy as well as its ability to handle array problems too large for traditional MM solutions

Extended Seismic Source Characterisation using Linear Programming Inversion in a Dual Formulation

A linear programming (LP) inversion method in a dual formulation was applied to reconstruct the kinematics of finite seismic ruptures. In a general setting, this approach can yield results from several data sets: strong ground motion, teleseismic waveforms or/and geodesic data (static deformation). The dual formulation involves the transformation of a normal solution space into an equivalent but reduced space: the dual space. The practical result of this transformation is a simpler inversion problem that is therefore faster to resolve, more stable and more robust. The developed algorithm includes a forward problem that calculates Green’s functions using a finite differences method with a 3D structure model. To evaluate the performance of this algorithm, we applied it to the reconstitution of a realistic slip distribution model from a data set synthesised using this model, i.e., the solution of the forward problem. Several other standard inversion approaches were applied to the same synthetic data for comparison

Advanced Integral Equation and Hybrid Methods for the Efficient Analysis of General Waveguide and Antenna Structures

Three new numerical methods for the calculation of passive waveguide and antenna structures are presented in this work. They are designed to be used within a comprehensive hybrid CAD tool for the efficient analysis of those building blocks for which the fast mode-matching/2-D finite element technique cannot be applied. The advanced algorithms introduced here are doubly higher order, that is higher order basis functions are considered for current/field modeling whereas geometry discretization is performed with triangular/tetrahedral elements of higher polynomial degree

A Theory of Networks for Appxoimation and Learning

Learning an input-output mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multi-dimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. This paper considers the problems of an exact representation and, in more detail, of the approximation of linear and nolinear mappings in terms of simpler functions of fewer variables. Kolmogorov's theorem concerning the representation of functions of several variables in terms of functions of one variable turns out to be almost irrelevant in the context of networks for learning. We develop a theoretical framework for approximation based on regularization techniques that leads to a class of three-layer networks that we call Generalized Radial Basis Functions (GRBF), since they are mathematically related to the well-known Radial Basis Functions, mainly used for strict interpolation tasks. GRBF networks are not only equivalent to generalized splines, but are also closely related to pattern recognition methods such as Parzen windows and potential functions and to several neural network algorithms, such as Kanerva's associative memory, backpropagation and Kohonen's topology preserving map. They also have an interesting interpretation in terms of prototypes that are synthesized and optimally combined during the learning stage. The paper introduces several extensions and applications of the technique and discusses intriguing analogies with neurobiological data

Modeling of Electromagnetic NDE of Civil Structures

The inspection of civil structures, such as bridge decks, roadways and masonry is becoming an increasingly important area for the application of NDE methodologies. A variety of methods have been used for detecting flaws, cracks and voids as well as locating structural features such as reinforcing bars and tensioning cables. The large size of civil structures necessitates the use of an NDE technique that is capable of rapid inspection of large areas with good penetration. A candidate approach for such inspection is the microwave NDT method. Microwave energy penetrates dielectric materials such as those encountered in civil structures and consequently inspection can be accomplished using noncontact devices mounted on a fast scanning mechanism. The paper presents a numerical model for simulating electromagnetic scattering from two and three dimensional objects embedded in large structures. Such models are useful in the design and development of systems required for microwave imaging of civil structures.</p