Uncertainty Quantification

An Accelerated Course with Advanced Applications in Computational Engineering
Softcover Nachdruck of the original 1. Auflage 2017
ISBN: 978-3-319-85372-7
Verlag: Springer International Publishing

Buch, Englisch, Band 47, 329 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 5329 g

Reihe: Interdisciplinary Applied Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Soize, Christian

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

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.

Über Autor(innen)

Christian Soize is professor at Universite Paris-Est Marne-la-Valee. His research interests include stochastic modeling of uncertainties in computational mechanics, their propagation and their quantification.