| Description |
1 online resource (353 pages) |
| Series |
Scientific Computation |
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Scientific computation.
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| Contents |
Intro -- Preface -- Acknowledgments -- Contents -- Part I Voxel-Based Inversion Algorithms -- 1 A Bilinear Conjugate-Gradient Inversion Algorithm -- 1.1 Optimization via Nonlinear Least-Squares -- 1.2 A Bilinear Conjugate-Gradient Inversion Algorithm Using Volume-Integrals -- 1.3 The Algorithm -- 1.4 Example: Raster Scan at Three Frequencies -- 2 Voxel-Based Inversion Via Set-Theoretic Estimation -- 2.1 The Electromagnetic Model Equations -- 2.2 Set-Theoretic Estimation -- 2.3 Statistical Analysis of the Feasible Set -- 2.4 A Layer-Stripping Algorithm |
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2.5 Some Examples of the Inversion Algorithm -- 2.6 Application to Aircraft Structures -- Part II Materials Characterization -- 3 Modeling Composite Structures -- 3.1 Background -- 3.2 Constitutive Relations for Advanced Composites -- 3.3 Example Calculations Using VIC-3D® -- 3.4 A Coupled-Circuit Model of Maxwell's Equations -- 3.5 Eddy-Current Detection of Prepreg FAWT -- 3.6 An Anisotropic Inverse Problem for Measuring FAWT -- 3.6.1 Return to an Analysis of Fig. 3.10 -- 3.7 Further Results for Permittivity -- 3.8 Comments and Conclusions -- 3.9 Eigenmodes of Anisotropic Media |
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3.10 Computing a Green's Function for a Layered Workpiece -- 3.11 An Example of the Multilayer Model -- 3.12 A Bulk Model -- 4 Application of the Set-Theoretic Algorithm to CFRP's -- 4.1 Background -- 4.2 Statistical Analysis of the Feasible Set -- 4.3 An Anisotropic Inverse Problem for Measuring FAWT -- 4.3.1 First Set-Theoretic Result -- 4.3.2 Second Set-Theoretic Result -- 4.3.3 Comment -- 4.4 Modeling Microstructure Quantification Problems -- 4.4.1 Delaminations -- 4.4.2 Transverse Ply with Microcrack -- 4.5 Layer-Stripping for Anisotropic Flaws |
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4.6 Advanced Features for Set-Theoretic Microstructure Quantification -- 4.6.1 A Heuristic Iterative Scheme to Determine a Zero-Cutoff Threshold -- 4.7 Progress in Modeling Microstructure Quantification -- 4.8 Handling Rotations of Anisotropic Media -- 5 An Electromagnetic Model for Anisotropic Media: Green's Dyad for Plane-Layered Media -- 5.1 Theory -- 5.2 Applications -- 5.3 Some Inverse Problems with Random Anisotropies -- 5.4 Detectability of Flaws in Anisotropic Media: Application to Ti64 -- 6 Stochastic Inverse Problems: Models and Metrics -- 6.1 Introducing the Problem |
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6.2 NLSE: Nonlinear Least-Squares Parameter Estimation -- 6.3 Confidence Levels: Stochastic Global Optimization -- 6.4 Summary -- 7 Integration of Functionals, PCM and Stochastic IntegralEquations -- 7.1 Theoretical Background -- 7.2 Probability Densities and Numerical Procedures -- 7.3 Second-Order Random Functions -- 7.4 A One-Dimensional Random Surface -- 7.5 gPC and PCM -- 7.6 HDMR and ANOVA -- 7.7 Determining the ANOVA Anchor Point -- 7.8 Interpolation Theory Using Splines Based Upon Higher-Order Convolutions of the Unit Pulse -- 7.9 Two-Dimensional Functions |
| Summary |
This book expands on the subject matter of Computational Electromagnetics and Model-Based Inversion: A Modern Paradigm for Eddy-Current Nondestructive Evaluation. It includes (a) voxel-based inversion methods, which are generalizations of model-based algorithms; (b) a complete electromagnetic model of advanced composites (and other novel exotic materials), stressing the highly anisotropic nature of these materials, as well as giving a number of applications to nondestructive evaluation; and (c) an up-to-date discussion of stochastic integral equations and propagation-of-uncertainty models in nondestructive evaluation. As such, the book combines research started twenty-five years ago in advanced composites and voxel-based algorithms, but published in scattered journal articles, as well as recent research in stochastic integral equations. All of these areas are of considerable interest to the aerospace, nuclear power, civil infrastructure, materials characterization and biomedical industries. The book covers the topic of computational electromagnetics in eddy-current nondestructive evaluation (NDE) by emphasizing three distinct topics: (a) fundamental mathematical principles of volume-integral equations as a subset of computational electromagnetics, (b) mathematical algorithms applied to signal-processing and inverse scattering problems, and (c) applications of these two topics to problems in which real and model data are used. It is therefore more than an academic exercise and is valuable to users of eddy-current NDE technology in industries as varied as nuclear power, aerospace, materials characterization and biomedical imaging |
| Notes |
7.10 Probability of Detection and the Chebychev Inequality |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed April 5, 2021) |
| In |
Springer Nature eBook |
| Subject |
Nondestructive testing.
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Electromagnetic testing.
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Physics.
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Quality control.
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Physics
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Quality Control
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Occupational Health
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nondestructive testing.
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physics.
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quality control.
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Electromagnetic testing
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Nondestructive testing
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| Form |
Electronic book
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| Author |
Murphy, R. Kim
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Sabbagh, Elias H
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Zhou, Liming
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Wincheski, Russell
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| ISBN |
9783030679569 |
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303067956X |
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9783030679552 |
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3030679551 |
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