Table of Contents
1 Cover
4 Foreword
5 Preface
6 PART 1: Modeling, Propagation and Quantification of Uncertainties 1 Uncertainty Modeling 1.1. Introduction 1.2. The usefulness of separating epistemic uncertainty from aleatory uncertainty 1.3. Probability theory 1.4. Probability box theory (p-boxes) 1.5. Interval analysis 1.6. Fuzzy set theory 1.7. Possibility theory 1.8. Evidence theory 1.9. Evaluation of epistemic uncertainty modeling 1.10. References 2 Microstructure Modeling and Characterization 2.1. Introduction 2.2. Probabilistic characterization of microstructures 2.3. Point processes 2.4. Boolean models 2.5. RSA models 2.6. Random tessellations 2.7. Gaussian fields 2.8. Conclusion 2.9. Acknowledgments 2.10. References 3 Uncertainty Propagation at the Scale of Aging Civil Engineering Structures 3.1. Introduction 3.2. Problem positioning 3.3. Random field-based modeling of material properties 3.4. Modeling uncertainty propagation using response surface methods 3.5. Conclusion 3.6. References 4 Reduction of Uncertainties in Multidisciplinary Analysis Based on a Polynomial Chaos Sensitivity Study 4.1. Introduction 4.2. MDA with model uncertainty 4.3. Sensitivity analysis and uncertainty reduction 4.4. Application to an aeroelastic test case 4.5. Conclusion 4.6. References
7
PART 2: Taking Uncertainties into Account: Reliability Analysis and Optimization under Uncertainties
5 Rare-event Probability Estimation
5.1. Introduction
5.2. MPFP-based methods
5.3. Simulation methods
5.4. Sensitivity measures
5.5. References
6 Adaptive Kriging-based Methods for Failure Probability Evaluation: Focus on AK Methods
6.1. Introduction
6.2. Presentation of Kriging
6.3. Employing Kriging to calculate failure probabilities
6.4. The AK-MCS method: presentation and generic principle
6.5. The AK-IS method for estimating probabilities of rare events
6.6. The AK-SYS method for system reliability problems
6.7. The AK-HDMR1 method for high-dimensional problems
6.8. Conclusion
6.9. References
7 Global Reliability-oriented Sensitivity Analysis under Distribution Parameter Uncertainty
7.1. Introduction
7.2. Theoretical framework and notations
7.3. Global variance-based reliability-oriented sensitivity indices
7.4. Sobol’ indices on the indicator function adapted to the bi-level input uncertainty
7.5. Efficient estimation using subset sampling and KDE
7.6. Application examples
7.7. Conclusion
7.8. Acknowledgments
7.9. References
8 Stochastic Multiobjective Optimization: