Global sensitivity analysis

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Table of contents

Résumé étendu 
0.1 Limitation n°1 : gérer le temps de calcul
0.2 Limitation n°2 : gérer des paramètres variant dans l’espace et le temps
0.3 Limite n°3 : gérer lemanque de connaissance
0.4 En résumé…
1 Introduction 
1.1 Hazard, Risk, uncertainty and decision-making
1.2 Aleatory and Epistemic uncertainty
1.3 Epistemic uncertainty of type « parameter »
1.4 A real-case example
1.5 Objectives and structure of the manuscript
2 A probabilistic tool : variance-based global sensitivity analysis 
2.1 Global sensivity analysis
2.2 Variance-based global sensivity analysis
2.3 Application to slope stability analysis
2.3.1 Local sensitivity analysis
2.3.2 Global sensitivity analysis
2.4 Limitations and links with the subsequent chapters
3 Handling long-running simulators 
3.1 A motivating real case: the numerical model of the La Frasse landslide
3.1.1 Description of the model
3.1.2 Objective of the sensitivity analysis
3.2 A meta-model-based strategy
3.2.1 Principles
3.2.2 Step 1: setting the training data
3.2.3 Step 2: construction of the meta-model
3.2.4 Step 3: validation of themeta-model
3.3 A flexible meta-model: the krigingmodel
3.4 An additional source of uncertainty
3.5 Application to an analytical case
3.6 Application to the La Frasse case
3.7 Concluding remarks of Chapter 3
4 Handling functional variables 
4.1 Problem definition for functional outputs
4.2 Reducing the dimension
4.2.1 Principles
4.2.2 Principal Component Analysis
4.2.3 Interpreting the basis set expansion
4.3 Strategy description
4.3.1 Step 1: selecting the training samples
4.3.2 Step 2: reducing themodel output dimensionality
4.3.3 Step 3: constructing the meta-model
4.3.4 Step 4: validating the meta-model
4.4 Application to the La Frasse case
4.4.1 Construction of themeta-model
4.4.2 Computation and analysis of the main effects
4.5 Towards dealing with functional inputs
4.5.1 Strategy description
4.5.2 Case study
4.5.3 Discussion
4.6 Concluding remarks of Chapter 4
5 A more flexible tool to represent epistemic uncertainties 
5.1 On the limitations of the systematic use of probabilities
5.2 Handling vagueness
5.2.1 A motivating real-case: hazard related to abandoned underground structures
5.2.2 Membership function
5.2.3 Application
5.3 Reasoning with vagueness
5.3.1 Amotivating real-case: the inventory of assets at risk
5.3.2 Application of Fuzzy Logic
5.4 Handling imprecision
5.4.1 Possibility theory
5.4.2 A practical definition
5.4.3 Illustrative real-case application
5.5 Handling probabilistic laws with imprecise parameters
5.5.1 Amotivating example: the Risk-UE (level 1) model
5.5.2 Problem definition
5.5.3 Use for an informed decision
5.6 Concluding remarks of Chapter 5
6 Sensitivity analysis adapted to a mixture of epistemic and aleatory uncertainty 
6.1 State of the art of sensitivity analysis accounting for hybrid uncertainty representations
6.2 A graphical-based approach
6.2.1 Motivation
6.2.2 Joint propagation of randomness and imprecision
6.2.3 Contribution to probability of failure sample plot
6.2.4 Adaptation to possibilistic information
6.3 Case studies
6.3.1 Simple example
6.3.2 Case study n°1: stability analysis of steep slopes
6.3.3 Case study n°2: stability analysis in post-mining
6.3.4 Case study n°3: numerical simulation for stability analysis in post-mining
6.4 Concluding remarks for Chapter 6
7 Conclusions 
7.1 Achieved results
7.2 Open questions and Future developments
7.2.1 Model uncertainty
7.2.2 Use of new uncertainty theories for practical decision-making
A Functional decomposition of the variance: the Sobol´ indices 
B Universal kriging equations 
C Key ingredients of a bayesian treatment of kriging-based meta-modelling 
C.1 Principles of BayesianModel Averaging
C.2 Monte-Carlo-based procedures
C.3 Bayesian kriging
C.4 Deriving a full posterior distribution for the sensitivity indices
D Brief introduction to the main uncertainty theories 
D.1 Probability
D.2 Imprecise probability
D.3 Evidence theory
D.4 Probability bound analysis
D.5 Possibility theory
E Fuzzy RandomVariable 
Bibliography