Mechanical Engineering in Uncertainties from Classical Approaches to Some Recent Developments

ISBN-13: 9781789450101 / Angielski / Twarda / 2021 / 352 str.

Christian Gogu

Spis treści

Foreword xiMaurice LEMAIREPreface xvChristian GOGUPart 1. Modeling, Propagation and Quantification of Uncertainties 1Chapter 1. Uncertainty Modeling 3Christian GOGU1.1. Introduction 31.2. The usefulness of separating epistemic uncertainty from aleatory uncertainty 61.3. Probability theory 101.3.1. Theoretical context 101.3.2. Probabilistic approach for modeling aleatory uncertainties 131.3.3. Probabilistic approach for modeling epistemic uncertainties 161.4. Probability box theory (p-boxes) 211.5. Interval analysis 241.6. Fuzzy set theory 251.7. Possibility theory 271.7.1. Theoretical context 271.7.2. Comparison between probability theory and possibility theory 301.7.3. Rules for combining possibility distributions 341.8. Evidence theory 351.8.1. Theoretical context 351.8.2. Rules for combining belief mass functions 381.9. Evaluation of epistemic uncertainty modeling 401.10. References 40Chapter 2. Microstructure Modeling and Characterization 43François WILLOT2.1. Introduction 432.2. Probabilistic characterization of microstructures 452.2.1. Random sets 452.2.2. Covariance 472.2.3. Granulometry 502.2.4. Minkowski functionals 512.2.5. Stereology 532.2.6. Linear erosion 532.2.7. Representative volume element 542.3. Point processes 552.3.1. Homogeneous Poisson point processes 562.3.2. Inhomogeneous Poisson point processes 582.4. Boolean models 592.4.1. Definition and Choquet capacity 592.4.2. Properties 612.4.3. Covariance 632.4.4. Other characteristics 632.5. RSA models 662.6. Random tessellations 672.6.1. Voronoi tessellation 682.6.2. Johnson-Mehl tessellation 692.6.3. Laguerre tessellation 692.6.4. Random Poisson tessellation 702.6.5. The dead-leaves model 712.6.6. Generalized random partition models 722.7. Gaussian fields 732.8. Conclusion 762.9. Acknowledgments 772.10. References 77Chapter 3. Uncertainty Propagation at the Scale of Aging Civil Engineering Structures 83David BOUHJITI, Julien BAROTH and Frédéric DUFOUR3.1. Introduction 833.2. Problem positioning 853.2.1. Probabilistic formulation 853.2.2. Thermo-hydro-mechanical-leakage transfer function 863.2.3. Resulting probabilistic THM-F problem 873.3. Random field-based modeling of material properties 883.3.1. Random fields 883.3.2. Generation methods for discretized random fields 883.3.3. Random fields and autocorrelations 913.3.4. Application: contribution to modeling the cracking of reinforced concrete works by self-correlated r.f 923.4. Modeling uncertainty propagation using response surface methods 983.4.1. Probabilistic coupling strategies 983.4.2. Polynomial chaos method 1013.5. Conclusion 1083.6. References 108Chapter 4. Reduction of Uncertainties in Multidisciplinary Analysis Based on a Polynomial Chaos Sensitivity Study 113Sylvain DUBREUIL, Nathalie BARTOLI, Christian GOGU and Thierry LEFEBVRE4.1. Introduction 1134.2. MDA with model uncertainty 1154.2.1. Formalism 1154.2.2. Solving the random MDA 1194.2.3. Approximation of the quantity of interest using sparse polynomial chaos 1224.3. Sensitivity analysis and uncertainty reduction 1244.3.1. Introduction 1244.3.2. Sobol' indices approximated by polynomial chaos 1264.4. Application to an aeroelastic test case 1284.4.1. Presentation 1284.4.2. Construction of disciplinary metamodels 1314.4.3. Sensitivity analysis and uncertainty reduction 1334.5. Conclusion 1404.6. References 140Part 2. Taking Uncertainties into Account: Reliability Analysis and Optimization under Uncertainties 143Chapter 5. Rare-event Probability Estimation 145Jean-Marc BOURINET5.1. Introduction 1455.1.1. Mapping to the multivariate standard normal space 1475.1.2. Copulas and correlation 1495.1.3. Isoprobabilistic transformations 1525.2. MPFP-based methods 1595.2.1. First-order reliability method 1595.2.2. Second-order reliability method 1635.3. Simulation methods 1665.3.1. Crude MC simulation 1675.3.2. Subset simulation 1685.3.3. IS and CE methods 1825.4. Sensitivity measures 1895.4.1. Introduction 1895.4.2. FORM 1915.4.3. Crude MC simulation and subset simulation 1955.5. References 198Chapter 6. Adaptive Kriging-based Methods for Failure Probability Evaluation: Focus on AK Methods 205Cécile MATTRAND, Pierre BEAUREPAIRE and Nicolas GAYTON6.1. Introduction 2056.2. Presentation of Kriging 2086.2.1. Principle 2086.2.2. Identification of Kriging hyperparameters 2096.2.3. Kriging-based prediction 2106.2.4. Illustration of Kriging-based prediction 2106.3. Employing Kriging to calculate failure probabilities 2116.3.1. The EFF function 2126.3.2. The U function 2126.3.3. The IMSET function 2136.3.4. The SUR function 2136.3.5. The H function 2146.3.6. The OBJ function 2146.3.7. The L function 2146.3.8. Discussion 2146.4. The AK-MCS method: presentation and generic principle 2156.4.1. Presentation of the AK-MCS method 2156.4.2. Illustration of the AK-MCS method 2176.4.3. Discussion 2196.5. The AK-IS method for estimating probabilities of rare events 2196.5.1. Presentation of the AK-IS method 2196.5.2. Illustration of the AK-IS method 2206.5.3. Discussion 2206.6. The AK-SYS method for system reliability problems 2226.6.1. Some generalities about system reliability analysis 2226.6.2. Presentation of the AK-SYS method 2236.6.3. Illustration of the AK-SYS method 2256.6.4. Alternatives to the AK-SYS method 2266.6.5. Application to problems indexed by a subset 2276.7. The AK-HDMR1 method for high-dimensional problems 2296.7.1. HDMR functional decomposition 2306.7.2. Presentation of the AK-HDMR1 method 2316.8. Conclusion 2336.9. References 234Chapter 7. Global Reliability-oriented Sensitivity Analysis under Distribution Parameter Uncertainty 237Vincent CHABRIDON, Mathieu BALESDENT, Guillaume PERRIN, Jérôme MORIO, Jean-Marc BOURINET and Nicolas GAYTON7.1. Introduction 2377.2. Theoretical framework and notations 2427.3. Global variance-based reliability-oriented sensitivity indices 2447.3.1. Introducing the Sobol' indices on the indicator function 2447.3.2. Rewriting Sobol' indices on the indicator function using Bayes' Theorem 2457.4. Sobol' indices on the indicator function adapted to the bi-level input uncertainty 2477.4.1. Reliability analysis under distribution parameter uncertainty 2477.4.2. Bi-level input uncertainty: aggregated versus disaggregated types of uncertainty 2497.4.3. Disaggregated random variables 2507.4.4. Extension to the bi-level input uncertainty and pick-freeze estimators 2517.5. Efficient estimation using subset sampling and KDE 2537.5.1. The problem of estimating the optimal distribution at failure 2537.5.2. Data-driven tensorized KDE 2577.5.3. Methodology based on subset sampling and data-driven tensorized G-KDE 2587.6. Application examples 2587.6.1. Example #1: a polynomial function toy-case 2617.6.2. Example #2: a truss structure 2647.6.3. Example #3: application to a launch vehicle stage fallback zone estimation 2677.6.4. Summary about numerical results and discussion 2747.7. Conclusion 2747.8. Acknowledgments 2757.9. References 275Chapter 8. Stochastic Multiobjective Optimization: A Descent Algorithm 279Quentin MERCIER and Fabrice POIRION8.1. Introduction 2798.2. Mathematical refresher 2818.2.1. Stochastic processes 2818.2.2. Convex analysis 2828.3. Multiobjective optimization and common descent vector 2888.3.1. Binary relations 2888.3.2. Multiobjective optimization, Pareto preorder 2908.3.3. Common descent vector 2968.4. Descent algorithm for multiobjective optimization and its extension to the stochastic framework 2988.4.1. Multiple gradient descent algorithm 2988.4.2. Stochastic multiple gradient descent algorithm 3008.5. Illustrations 3058.5.1. Performance of the SMGDA algorithm 3058.5.2. Multiobjective approach to RBDO problems 3098.5.3. Rewriting the probabilistic constraint 3108.6. References 316List of Authors 319Index 321

O autorze

Christian Gogu is Associate Professor at the University Toulouse III-Paul Sabatier, France. His research, which he carries out at the Clement Ader Institute, focuses, in particular, on taking into account uncertainties in the design and optimization of aeronautical systems.