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Informationen zum Autor Jonathan M. Nichols received the B.Sc. degree from the University of Delaware in 1997 and the M. Sc. and Ph.D. degrees from Duke University in 1999 and 2002 respectively, all in Mechanical Engineering.?He is currently the Associate Superintendent for the Naval Research Laboratory Optical Sciences Division in Washington, D.C. His research interests include damage identification in structures, modelling and analysis of infrared imaging devices, signal and image processing, and parameter estimation. Kevin D. Murphy received the B.Sc. (Mechanical Engineering) and M. Sc. (Applied Mechanics) degrees from the University of Michigan in 1988 and 1990 respectively.?He received his Ph.D. from Duke University in 1994 in Mechanical Engineering.?He is currently a Professor and Mechanical Engineering Department Chair at the University of Louisville. His research focuses on the nonlinear mechanics, vibrations, and stability of structures for a broad variety of applications. Specific applications areas include: vibrations of damaged structures, adhesion/sticking contact in MEMS devices, and vibrations in manufacturing problems. Klappentext Modelling and Estimation of Damage in Structures is a comprehensiveguide to solving the type of modelling and estimation problems associated with the physics of structural damage.* Provides a model-based approach to damage identification* Presents an in-depth treatment of probability theory and random processes* Covers both theory and algorithms for implementing maximum likelihood and Bayesian estimation approaches* Includes experimental examples of all detection and identification approaches* Provides a clear means by which acquired data can be used to make decisions regarding maintenance and usage of a structure Zusammenfassung Modelling and Estimation of Damage in Structures is a comprehensiveguide to solving the type of modelling and estimation problems associated with the physics of structural damage. Inhaltsverzeichnis Preface xi 1 Introduction 1 1.1 Users' Guide 1 1.2 Modeling and Estimation Overview 2 1.3 Motivation 4 1.4 Structural Health Monitoring 7 1.4.1 Data-Driven Approaches 10 1.4.2 Physics-Based Approach 14 1.5 Organization and Scope 17 2 Probability 21 2.1 Probability Basics 23 2.2 Probability Distributions 25 2.3 Multivariate Distributions, Conditional Probability, and Independence 28 2.4 Functions of Random Variables 32 2.5 Expectations and Moments 39 2.6 Moment-Generating Functions and Cumulants 43 3 Random Processes 51 3.1 Properties of a Random Process 54 3.2 Stationarity 57 3.3 Spectral Analysis 61 3.3.1 Spectral Representation of Deterministic Signals 62 3.3.2 Spectral Representation of Stochastic Signals 65 3.3.3 Power Spectral Density 67 3.3.4 Relationship to Correlation Functions 71 3.3.5 Higher Order Spectra 74 3.4 Markov Models 81 3.5 Information Theoretics 82 3.5.1 Mutual Information 85 3.5.2 Transfer Entropy 87 3.6 Random Process Models for Structural Response Data 91 4 Modeling in Structural Dynamics 95 4.1 Why Build Mathematical Models? 96 4.2 Good Versus Bad Models - An Example 97 4.3 Elements of Modeling 99 4.3.1 Newton's Laws 101 4.3.2 Background to Variational Methods 101 4.3.3 Variational Mechanics 103 4.3.4 Lagrange's Equations 105 4.3.5 Hamilton's Principle 108 4.4 Common Challenges 114 4.4.1 Impact Problems 114 4.4.2 Stress Singularities and Cracking 117 4.5 Solution Techniques 119 4.5.1 Analytical Techniques I - Ordinary Differential Equations 119 4.5.2 Analytical Techniques II - Partial Differential Equations 128 4.5.3 Local Discretizations 131 4.5...
