Methodology

Abstract

This documentation is introducing the theoretical basics upon which the Uranie platform (based on Uranie v4.11.0), has been developed at CEA/DES. Since this platform is designed for uncertainty propagation, sensitivity analysis and surrogate model generation, the main methods which have been implemented are introduced and discussed. This document is however not made to give a complete overview of the methodology but more to open the scope of the reader by largely relying on a list of references, without getting to attached on the structure of the Uranie platform itself.

Commit:

61cebb3

Contents:

• 1. Glossary
• 2. Basic statistical elements
  • 2.1. Random variable modelisation
  • 2.2. Statistical treatments and operations
  • 2.3. Combining these aspects: performing PCA
• 3. The Sampler module
  • 3.1. Introduction
  • 3.2. The Stochastic methods
  • 3.3. QMC method
• 4. Generating Surrogate Models
  • 4.1. Introduction
  • 4.2. The Linear Regression
  • 4.3. Chaos polynomial expansion
  • 4.4. The kriging method
• 5. Sensitivity analysis
  • 5.1. Brief reminder of theoretical aspects
  • 5.2. The regression method
• 6. Dealing with optimisation issues
  • 6.1. Introduction
• 7. The Calibration module
  • 7.1. Brief reminder of theoretical aspects
  • 7.2. Using minimisation techniques
  • 7.3. Analytical linear Bayesian estimation
  • 7.4. Approximate Bayesian Computation techniques (ABC)
  • 7.5. Markov chain Monte Carlo approach
  • 7.6. CIRCE method
• 8. The Uncertainty modeler module
  • 8.1. Tests based on the Empirical Distribution Function (“EDF tests”)

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