This book is designed as a brief guide
for engineers, researchers and senior
students who deal with the analysis and
modeling of structures with stochastic
nature, from large engineering projects such
as aircraft structures, through to small
engineered components like soil and civil
structures.
Stochastic Finite Element Methods and
Its Applications to Aircraft Engineering
provides a formidable resource covering
theories and applications of SFEMs,
including the fundamentals and research
frontiers of SFEMs, its applications to
advanced material modeling and stochastic
computational engineering analysis and
engineering reliability analysis.
這是汪峰編著的這本《隨機有限單元法及其在航
空工程中的應用(英文版)》的英文簡介。

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-Loeve 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 The joint 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 Generaiconvention
Index II Abbreviation
Index III Symbolic notation