Uncertainty Analysis

Probability Theory

• Sample Space vs Event
• Random Variable
• Expected Value
• Normal Distribution and Lognormal Distribution
• Probability Density Function (PDF)
• Cumulative Distribution Function (CDF)
• Moment of a Random Variable
• Moment Generation Function
• Covariance
• Correlation
• Variance of a Uniform Distribution

Karhunen-Loève Expansion

• Multivariate Gaussian PDF
• Karhunen-Loève Expansion
  • Discrete KLE Example
  • Continuous KLE Example

First Order Second Moment Method

• FOSM
• FOSM Example

Quadrature

• Quadrature Example

Surrogate Modeling

• Definition of Surrogate Modeling
• Polynomial Chaos Expansion
• Expected Value and Variance Calculations using PCE
• Multi-Dimensional Polynomial Chaos Expansion
• non-Intrusive Surrogate Modeling

Sensitivity Analysis

• Sobol Indices
• Calculating Sobol Indices

Monte Carlo Methods