Soize C. Uncertainty Quantification: An Accelerated Course with Advanced Applications in Computational Engineering

Springer International Publishing AG, 2017. — 344 p. — (Interdisciplinary Applied Mathematics 47) — ISBN: 978-3-319-54338-3.This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials.
Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available.
This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.Fundamental Notions in Stochastic Modeling of Uncertainties and Their Propagation in Computational Models
Elements of Probability Theory
Markov Process and Stochastic Differential Equation
MCMC Methods for Generating Realizations and for Estimating the Mathematical Expectation of Nonlinear Mappings of Random Vectors
Fundamental Probabilistic Tools for Stochastic Modeling of Uncertainties
Brief Overview of Stochastic Solvers for the Propagation of Uncertainties
Fundamental Tools for Statistical Inverse Problems
Uncertainty Quantification in Computational Structural Dynamics and Vibroacoustics
Robust Analysis with Respect to the Uncertainties for Analysis, Updating, Optimization, and Design
Random Fields and Uncertainty Quantification in Solid Mechanics of Continuum Media