User:Mv/Books/00 Draft Theory Manual

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Cossan-X: Theory Manual

0th Draft

Introduction
Introduction
Basic Concepts in Logic
Boolean Algebra
Basic Concepts in Linear Algebra
Eigenvalue, eigenvector and eigenspace
Basic Concepts in Probability and Statistics
Random variables
Random variable sets
Random process
Random fields
Standard Normal Space
Nataf transformation
Uncertainty Modeling
Karhunen-Loève Expansion
Spectral Representation Method
Discretization of Random Fields
Representation of Non-Gaussian Random Fields
Reliability Analysis
Reliability
Reliability Analysis
Availability
Mean Time Between Failures
Failure
Safety Margin
Uncertainty Analysis
Performance function definition
Approximate Reliability Methods
Approximate Reliability Analysis Methods
Design point identification
Reliability index
FORM
SORM
Simulation Methods for Reliability Analysis
Simulation methods
Monte Carlo simulation
Latin Hypercube Sampling
Markov Chains
Importance sampling
Line sampling
Subset simulation
Systems Reliability
System Reliability Analysis
Reliability Block Diagram
Fault Tree
Fault Tree Analysis
Cut Sets
Sensitivity Analysis
Sensitivity
Global Sensitivity
Sobol indices
Local Sensitivity
Gradient Estimation
Monte Carlo Gradient Estimation
Meta-models
Meta-Models
Response surface
Neural Network
Mode based Meta-model
Non-parametric model
Structural Dynamics
Dynamics
Time domain analysis
Frequency domain analysis
Stochastic Finite Elements
Stochastic Finite Element Methods
Perturbation Method
Neumann Expansion Method
Polynomial Chaos (P-C) Expansion Method
Deterministic Optimization
Optimization
COBYLA
Cross Entropy
Evolution Strategies
Genetic Algorithms
SQP
Simulated Annealing
Optimization considering Uncertainties
Reliability Based Optimization
RBO using Global Response Surface
RBO using Local Response Surface
Fatigue and Fracture
Fatigue and Fracture
Linear elastic fracture mechanics
Fatigue
Crack propagation models using fracture mechanics approach
High Performance Computing
Parallel computing
Distributed computing
Job Manager
GP-GPU