| Summary: | This book introduces the fundamental concepts of probability and reliability, the classical methods of uncertainty modelling, time-dependent and time-independent reliability analysis methods, model verification and validation, two main categories of design optimization under uncertainty (DOUU) methods (e.g., reliability-based design optimization and robust design optimization), the state-of-the-art approaches of physics informed methods for DOUU, and a comprehensive survey of engineering applications of DOUU. Each chapter begins with the fundamental theories and methods in a lucid, is easy-to-follow treatment, then elaborates on the corresponding advanced approaches using detailed methodologies, mathematical models, numerical examples, tables, and graphs. References and exercises are presented at the end of chapters. The book is ideal for both educational and research needs for readers from undergraduate students, graduate students, and faculty to engineering designers. Offers both the fundamental and the state-of-the-art theories and methods of design optimization under uncertainty; Explains the in-depth theories of design optimization under uncertainty in a lucid with step-by-step derivation; Introduces the exercise problems using graphics, tables, and results that are all originally developed
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