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.
• Introduces all major topics of uncertainty quantification with engineering examples and implementation details1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Biography - p. xi 7. Preface - p. xiii 8. Part One: Fundamentals of uncertainty quantification - p. xiv 9. Chapter One: Uncertainty quantification for engineering decision making - p. 3 10. Chapter Two: Probability and statistics in uncertainty quantification - p. 37 11. Chapter Three: Sampling methods in uncertainty quantification - p. 85 12. Chapter Four: Surrogate modeling in uncertainty quantification - p. 109 13. Chapter Five: Stochastic expansion methods in uncertainty quantification - p. 143 14. Chapter Six: Bayesian inference in uncertainty quantification - p. 177 15. Chapter Seven: Sensitivity analysis in uncertainty quantification - p. 207 16. Chapter Eight: Linear and nonlinear dimensionality reduction techniques in uncertainty quantification - p. 235 17. Chapter Nine: Applications of uncertainty quantification in engineering - p. 265 18. Part Two: Advanced topics of uncertainty quantification - p. 305 19. Chapter Ten: Stochastic processes in uncertainty quantification - p. 309 20. Chapter Eleven: Markov models in uncertainty quantification - p. 347 21. Chapter Twelve: Nonprobabilistic methods in uncertainty quantification - p. 371 22. Index - p. 411
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.
• Introduces all major topics of uncertainty quantification with engineering examples and implementation details1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Biography - p. xi 7. Preface - p. xiii 8. Part One: Fundamentals of uncertainty quantification - p. xiv 9. Chapter One: Uncertainty quantification for engineering decision making - p. 3 10. Chapter Two: Probability and statistics in uncertainty quantification - p. 37 11. Chapter Three: Sampling methods in uncertainty quantification - p. 85 12. Chapter Four: Surrogate modeling in uncertainty quantification - p. 109 13. Chapter Five: Stochastic expansion methods in uncertainty quantification - p. 143 14. Chapter Six: Bayesian inference in uncertainty quantification - p. 177 15. Chapter Seven: Sensitivity analysis in uncertainty quantification - p. 207 16. Chapter Eight: Linear and nonlinear dimensionality reduction techniques in uncertainty quantification - p. 235 17. Chapter Nine: Applications of uncertainty quantification in engineering - p. 265 18. Part Two: Advanced topics of uncertainty quantification - p. 305 19. Chapter Ten: Stochastic processes in uncertainty quantification - p. 309 20. Chapter Eleven: Markov models in uncertainty quantification - p. 347 21. Chapter Twelve: Nonprobabilistic methods in uncertainty quantification - p. 371 22. Index - p. 411
