Chapter 1 Introduction

1.1 Engineering background

1.2 Engineering uncertainties

1.2.1 Unpredictable loading conditions

1.2.2 Randomness of material properties

1.2.3 Major developments in stochastic finite element methods

1.3 The aim and layout of book

1.3.1 The aim

1.3.2 Book layout

Chapter 2 Mathematical background

2.1 Probability theory

2.1.1 The development of probability theory

2.1.2 Probability space

2.1.3 Distribution

2.1.4 Characteristic function

2.1.5 Moments

2.1.6 Cumulants

2.1.7 Covariance matrix

2.1.8 Entropy

2.1.9 Stochastic convergences

2.1.10 Basic limit theorems and inequities

2.2 Stochastic field

2.2.1 Second-order random field

2.2.2 Mercer’s theorem

2.2.3 Stationary random fields

2.2.4 Spectral expansion of stationary random fields

2.2.5 Ergodicity

2.2.6 Gaussian random fields

2.3 Stochastic Analysis

2.3.1 Brownian motion

2.3.2 Stochastic differential equations

2.4 Statistics

2.4.1 Estimation

2.4.2 Preliminary nonparametric statistics

Chapter 3 Representation of random fields

3.1 Constitutive laws

3.2 Stochastic constitutive laws

3.2.1 The spectral representation method

3.2.2 Karhunen-Loève expansion method

3.2.3 Other representation methods

3.3 Representation of Non-Gaussian fields

Chapter 4 Solvers of stochastic linear equations

4.1 The discretization of the stochastic fields

4.2 Monte Carlo method

4.3 Perturbation method

4.4 The neumann expansion method

4.5 The polynomial chaos expansion method

4.6 Thejoint diagonalization strategy

Chapter 5 Aircraft engineering applications

5.1 Aircraft structural health monitoring with uncertainties

5.2 Aircraft composite materials

5.3 Analysis of typical aircraft structures

5.3.1 Aircraft composite material modeling with random properties

5.3.2 Stochastic modeling of commercial aircraft rudder

5.3.3 Stochastic modeling of reinforced composite floor under fire conditions

Chapter 6 Reliability analysis

6.1 Introduction of engineering reliability analysis

6.2 Codes of practice

6.3 Airworthiness regulations

6.4 Reliability analysis for a single structural element

6.4.1 Random properties of loading and resistance only

6.4.2 Single structural member with multi random variables

6.4.3 Reliability index for linear failure functions

6.4.4 Reliability index for nonlinear failure functions

6.5 Application to reliability analysis

6.5.1 Reliability analysis of simply supported beam

6.5.2 Reliability analysis of structural glass

Chapter 7 Uncertainties in aircraft big data and de-noising technologies

7 1 Uncertainties in aircraft big data

7.1.1 The“Cocktail party affect”

7.1.2 System model

7.1.3 Literature review

7.2 Blind source separation algorithm Ⅰ

7.2.1 Cost function

7.2.2 Minimizing the cost function via numerical procedures

7.2.3 Parameterization of A

7.2.4 The explicit form of matrix J

7.2.5 Numerical methods

7.2.6 Numerical simulation

7 3 Blind source separation algorithm Ⅱ

7.3.1 Cost function

7.3.2 Numerical simulations

Chapter 8 Future directions

Index Ⅰ General convention

Index Ⅱ Abbreviation

Index Ⅲ Symbolic notation