Computational Inverse Techniques in Nondestructive Evaluation

Ill-posedness. Regularization. Stability. Uniqueness. To many engineers, the language of inverse analysis projects a mysterious and frightening image, an image made even more intimidating by the highly mathematical nature of most texts on the subject. But the truth is that given a sound experimental strategy, most inverse engineering problems can be well-posed and not difficult to deal with. Computational Inverse Techniques in Nondestructive Evaluation sets forth in clear, easy-to-understand terms the principles, computational methods, and algorithms of inverse analyses based on elastic waves or the dynamic responses of solids and structures. After describing the features of inverse problems, the authors discuss the regularization methods useful in handling ill-posed problems. The book also presents practical optimization algorithms, including some developed and successfully tested by his research group. Inverse analyses are fast becoming one of the engineer's most powerful tools in nondestructive evaluation and testing. With straightforward examples, a wealth of specific applications, and clear exposition written by engineers for engineers, this book offers an outstanding opportunity to overcome any trepidation and begin using inverse analysis in practice.

Table of Contents:
INTRODUCTION Forward and Inverse Problems Encountered in Structural Systems General Procedures to Solve Inverse Problems Outline of the Book FUNDAMENTALS OF INVERSE PROBLEMS A Simple Example: A Single-Bar A Slightly Complex Problem: A Composite Bar Type III Ill-Posedness Types of Ill-Posed Inverse Problems Explicit Matrix Systems Inverse Solution for Systems with Matrix Form General Inversion by Singular Value Decomposition (SVD) Systems in Functional Forms: Solution by Optimization Choice of the Outputs or Effects Simulated Measurement Examination of Ill-Posedness REGULARIZATION FOR ILL-POSED PROBLEMS Tikhonov Regularization Regularization by SVD Iterative Regularization Method Regularization by Discretization (Projection) Regularization by Filtering CONVENTIONAL OPTIMIZATION TECHNIQUES1 The Role of Optimization in Inverse Problems Optimization Formulations Direct Search Gradient-Based Methods Nonlinear Least Squares Method Some References for Optimization Methods GENETIC ALGORITHMS Introduction Basic Concept of GAs Micro-GAs Intergeneration Project Genetic Algorithm (IP-GA) Improved IP-GA IP-GA with Three Parameters (IP3-GA) GAs with Search Space Reduction (SR-GA) GA Combined with the Gradient-Based Method Other Minor Tricks in the Implementation of GAs for Inverse Problems Some References for GA NEURAL NETWORKS General Concepts of Neural Networks Role of Neural Networks in Solving Inverse Problems Multilayer Perceptrons Performance of MLP A Progressive Learning Neural Network A Simple Application of NN References on Neural Networks INVERSE IDENTIFICATION OF IMPACT LOADS Introduction Displacement as System Effects Identification of Impact Loads on the Surface of Beams Line Loads on the Surface of Composite Laminates Point Loads on the Surface of Composite Laminates Ill-Posedness Analysis INVERSE IDENTIFICATION OF MATERIAL CONSTANTS OF COMPOSITES Introduction Statement of the Problem Using the Uniform mGA Using the Real mGA Using the Combined Optimization Method Using the Progressive NN for Identifying Elastic Constants INVERSE IDENTIFICATION OF MATERIAL PROPERTY OF FUNCTIONALLY GRADED MATERIALS Introduction Statement of the Problem Rule-of-Mixture Use of Gradient-Based Optimization Methods Use of Uniform mGA Use of Combined Optimization Method Use of Progressive NN Model INVERSE DETECTION OF CRACKS IN BEAMS USING FLEXURAL WAVES Introduction Beams with a Horizontal Delamination Beam Model of Flexural Wave Beam Model of for Transient Response to an Impact Load Extensive Experimental Study Inverse Crack Detection Using Uniform mGA Inverse Crack Detection Using Progressive NN INVERSE DETECTION OF DELAMINATIONS IN COMPOSITE LAMINATES Introduction Statement of the Problem Delamination Detection Using Uniform mGA Delamination Detection Using the IP-GA Delamination Detection Using the Improved IP-GA Delamination Detection Using the Combined Optimization Method Delamination Detection Using the Progressive NN INVERSE DETECTION OF FLAWS IN STRUCTURES Introduction Inverse Identification Formulation Use of Uniform mGA Use of Newton's Root Finding Method Use of Levenberg -Marquardt Method OTHER APPLICATIONS Coefficients Identification for Electronic Cooling System Identification of the Material Parameters of a PCB Identification of Material Property of Thin Films Crack Detection Using Integral Strain Measured by Optic Fibers Flaw Detection in Truss Structure Protein Structure Prediction Fitting of Interatomic Potentials Parameter Identification in Valve-Less Micropumps TOTAL SOLUTION FOR ENGINEERING SYSTEMS: A NEW CONCEPT Introduction Approach Towards a Total Solution Inverse Algorithms Numerical Examples