Mechanics and Uncertainty

Maurice Lemaire is Emeritus Professor at the French Institute for Advanced Mechanics in Clermont-Ferrand, France and Scientific Advisor of Phimeca Engineering S.A.

• Foreword viiPreface xiIntroduction xvChapter 1. Understanding Uncertainty 11.1. Uncertainty and reality 11.1.1. Awareness of uncertainty 11.1.2. Territories of uncertainty 41.1.3. Conclusion 81.2. Robustness and reliability 91.2.1. Robustness 91.2.2. Reliability 131.2.3. Relationship between robustness and reliability 161.2.4. Optimizing robustness and reliability 191.2.5. Conclusion 211.3. Designing for robust production 221.3.1. Robustness and lifecycles 221.3.2. Description of the V cycle 231.3.3. Uncertainty in the V cycle 251.3.4. Uncertainty linked to a step in the V cycle 291.3.5. Robustness and uncertainty 331.3.6. Conclusion 38Chapter 2. Modeling Uncertainty 412.1. Random uncertainty 412.1.1. Modeling uncertainty 412.1.2. Exploration of Mediocristan 422.1.3. From statistics to probabilities 472.1.4. Polynomial chaos 502.1.5. Exploration of Extremistan 522.1.6. Conclusion 552.2. Uncertainty in behavior models 552.2.1. Uncertainty and input data 562.2.2. Uncertainty in behavior models 612.3. Uncertainty propagation 702.3.1. The problem of uncertainty propagation 702.3.2. Analyzing sensitivity to uncertainty 712.3.3. Reliability analysis – classification methods 822.3.4. Model reductions 922.3.5. Quantifying uncertainty 982.3.6. Conclusion 100Chapter 3. Decision Support under Uncertainty 1013.1. Decision support in design 1013.1.1. Decision support 1013.1.2. Modeling decision support 1033.1.3. Multi-criteria decision analysis (MCDA) 1063.1.4. Conclusion 1093.2. Summary and conclusion 1103.2.1. Three perspectives 1103.2.2. Challenges in engineering science 1193.2.3. Industrial issues 123Bibliography 125Index 145