Modeling and Estimation of Structural Damage [Hardcover]

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

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 SlÃ.