Fundamentals of Uncertainty Quantification for Engineers: Methods and Models - Softcover

Wang

Softcover

ISBN 10: 0443136610 ISBN 13: 9780443136610

Verlag: Elsevier, 2025

Inhaltsangabe

Fundamentals of Uncertainty Quantification for Engineers: Methods and Models provides a comprehensive introduction to uncertainty quantification (UQ) accompanied by a wide variety of applied examples and implementation details to reinforce the concepts outlined in the book. Sections start with an introduction to the history of probability theory and an overview of recent developments of UQ methods in the domains of applied mathematics and data science. Major concepts of copula, Monte Carlo sampling, Markov chain Monte Carlo, polynomial regression, Gaussian process regression, polynomial chaos expansion, stochastic collocation, Bayesian inference, modelform uncertainty, multi-fidelity modeling, model validation, local and global sensitivity analyses, linear and nonlinear dimensionality reduction are included. Advanced UQ methods are also introduced, including stochastic processes, stochastic differential equations, random fields, fractional stochastic differential equations, hidden Markov model, linear Gaussian state space model, as well as non-probabilistic methods such as robust Bayesian analysis, Dempster-Shafer theory, imprecise probability, and interval probability. The book also includes example applications in multiscale modeling, reliability, fatigue, materials design, machine learning, and decision making.

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Über die Autorinnen und Autoren

Dr. Yan Wang is a Professor of Mechanical Engineering at the Georgia Institute of Technology. He leads the Multiscale Systems Engineering Research Group at Georgia Tech. His research interests include probabilistic and non‐probabilistic approaches to quantify uncertainty in both physics‐based and data‐driven models for multiscale systems engineering for materials design. He has over 200 publications, including the first book on uncertainty quantification in multiscale materials modelling co‐edited with David McDowell.

Dr. Anh V. Tran is a research staff member at the Department of Scientific Machine Learning, Sandia National Laboratories. His research areas include uncertainty quantification, optimization, machine learning for multiscale computational materials science.

David L. McDowell Ph.D. is Regents’ Professor Emeritus at the Georgia Institute of Technology, having joined Georgia Tech as a faculty member in 1983. His research focuses on multiscale modelling of materials with emphasis on multiscale modeling of the inelastic behavior of metals, microstructure-sensitive computational fatigue analysis of microstructures, methods for materials design that are robust against uncertainty, and coarse-grained atomistic modelling methods.

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Fundamentals of Uncertainty Quantification for Engineers provides a comprehensive introduction to uncertainty quantification (UQ) accompanied by a wide variety of applied examples, implementation details, and practical exercises to reinforce the concepts outlined in the book. It starts with review of the history of probability theory and recent development of UQ methods in the domains of applied mathematics and data science. Major concepts of probability axioms, conditional probability, and Bayes’ rule are discussed and examples of probability distributions in parametric data analysis, reliability, risk analysis, and materials informatics are included. Random processes, sampling methods, and surrogate modeling techniques including multivariate polynomial regression, Gaussian process regression, multi-fidelity surrogate, support-vector machine, and decision tress are also covered. Methods for model selection, calibration, and validation are introduced next, followed by chapters on sensitivity analysis, stochastic expansion methods, Markov models, and non-probabilistic methods. The book concludes with a chapter describing the methods that can be used to predict UQ in systems, such as Monte Carlo, stochastic expansion, upscaling, Langevin dynamics, and inverse problems, with example applications in multiscale modeling, simulations, and materials design.

Details zur Ausgabe

• Verlag: Elsevier
• Erscheinungsdatum: 2025
• Sprache: Englisch
• ISBN 10: 0443136610
• ISBN 13: 9780443136610
• Einband: Tapa blanda
• Anzahl der Seiten: 434
• Kontakt zum Hersteller: ELSEVIER; https://www.elsevier.com/es-es; ; Mooswaldallee 6; Freiburg; 79108; Deutschland