Preface ix
1 Introduction 1
1.1 Users Guide 1
1.2 Modeling & 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 & Scope 16
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 31
2.5 Expectations and Moments 38
2.6 Moment Generating Functions & Cumulants 42
3 Random Processes 51
3.1 Properties of a Random Process 54
3.2 Stationarity 58
3.3 Spectral Analysis 61
3.3.1 Spectral Representation of Deterministic Signals 62
3.3.2 Spectral Representation of Stochastic Signals 66
3.3.3 Power Spectral Density 68
3.3.4 Relationship to Correlation Functions 72
3.3.5 Higher-order Spectra 75
3.4 Markov Models 83
3.5 Information Theoretics 83
3.5.1 Mutual Information 87
3.5.2 Transfer Entropy 89
3.6 Random Process Models for Structural Response Data 93
4 Modeling in Structural Dynamics 99
4.1 Why Build Mathematical Models? 100
4.2 Good Versus Bad Models - An Example 101
4.3 Elements of Modeling 104
4.3.1 Newton’s Laws 104
4.3.2 Background to
OBNB doesn't sell books, but you may be able to find a copy at one of these websites:
Modeling and estimation of structural damage by Jonathan Michael Nichols. ISBN 9781118776971. Published by John Wiley & Sons in 2015. Publication and catalogue information, links to buy online and reader comments.
