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.