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, implementation details, and practical exercises to reinforce the concepts outlined in the book. Sections start with a review of the history of probability theory and recent developments 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.
Table of Contents
1. Introduction to Uncertainty Quantification for Engineers2. Probability and Statistics in Uncertainty Quantification
3. Random Processes in Uncertainty Quantification
4. Sampling Methods in Uncertainty Quantification
5. Surrogate Modeling in Uncertainty Quantification
6. Model Selection, Calibration, and Validation in Uncertainty Quantification
7. Sensitivity Analysis in Uncertainty Quantification
8. Stochastic Expansion Methods in Uncertainty Quantification
9. Markov Models
10. Non-Probabilistic Methods in Uncertainty Quantification
11. Uncertainty propagation in Uncertainty Quantification
Authors
Yan Wang Professor of Mechanical Engineering, Georgia Institute of Technology, USA.. 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. Anh.V. Tran Research Staff Member, Department of Scientific Machine Learning, Sandia National Laboratories, USA.. 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 Georgia Institute of Technology,.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.
