Uncertainty Quantification : An Accelerated Course with Advanced Applications in Computational Engineering /
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 wi...
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Main Authors: | |
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Corporate Authors: | |
Published: |
Springer International Publishing : Imprint: Springer,
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Publisher Address: | Cham : |
Publication Dates: | 2017. |
Literature type: | eBook |
Language: | English |
Series: |
Interdisciplinary Applied Mathematics,
47 |
Subjects: | |
Online Access: |
http://dx.doi.org/10.1007/978-3-319-54339-0 |
Summary: |
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. |
Carrier Form: | 1 online resource (XXII, 329 pages): illustrations. |
ISBN: | 9783319543390 |
Index Number: | QA71 |
CLC: | TP3 |
Contents: | 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. |