Soize, Christian. Uncertainty Quantification : An Accelerated Course with Advanced Applications in Computational Engineering / [electronic resource] : / by Christian Soize.. — 1st ed. 2017.. — XXII, 329 p. 110 illus., 86 illus. in color. : online resource. — (Interdisciplinary Applied Mathematics,) 47 0939-6047 ;. - Interdisciplinary Applied Mathematics, 47 .
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.
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Анотація: 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.
9783319543390
10.1007/978-3-319-54339-0 doi
Computer mathematics. Applied mathematics. Engineering mathematics. Probabilities. Computational Science and Engineering. Mathematical and Computational Engineering. Probability Theory and Stochastic Processes.