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Author Soize, Christian
Title Stochastic Models of Uncertainties in Computational Mechanics
Imprint Reston : American Society of Civil Engineers, 2012
©2012
book jacket
Descript 1 online resource (134 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Lecture Notes in Mechanics Ser
Lecture Notes in Mechanics Ser
Note Cover -- Contents -- 1 Introduction -- 2 Short overview of probabilistic modeling of uncertainties and related topics -- 2.1 Uncertainty and variability -- 2.2 Types of approach for probabilistic modeling of uncertainties -- 2.3 Types of representation for the probabilistic modeling of uncertainties -- 2.4 Construction of prior probability models using the maximum entropy principle under the constraints defined by the available information -- 2.5 Random Matrix Theory -- 2.6 Propagation of uncertainties and methods to solve the stochastic dynamical equations -- 2.7 Identification of the prior and posterior probability models of uncertainties -- 2.8 Robust updating of computational models and robust design with uncertain computational models -- 3 Parametric probabilistic approach to uncertainties in computational structural dynamics -- 3.1 Introduction of the mean computational model in computational structural dynamics -- 3.2 Introduction of the reduced mean computational model -- 3.3 Methodology for the parametric probabilistic approach of modelparameter uncertainties -- 3.4 Construction of the prior probability model of model-parameter uncertainties -- 3.5 Estimation of the parameters of the prior probability model of the uncertain model parameter -- 3.6 Posterior probability model of uncertainties using output-predictionerror method and the Bayesian method -- 4 Nonparametric probabilistic approach to uncertainties in computational structural dynamics -- 4.1 Methodology to take into account both the model-parameter uncertainties and the model uncertainties (modeling errors) -- 4.2 Construction of the prior probability model of the random matrices -- 4.3 Estimation of the parameters of the prior probability model of uncertainties -- 4.4 Comments about the applications and the validation of the nonparametric probabilistic approach of uncertainties
5 Generalized probabilistic approach to uncertainties in computational structural dynamics -- 5.1 Methodology of the generalized probabilistic approach -- 5.2 Construction of the prior probability model of the random matrices -- 5.3 Estimation of the parameters of the prior probability model of uncertainties -- 5.4 Posterior probability model of uncertainties using the Bayesian method -- 6 Nonparametric probabilistic approach to uncertainties in structural-acoustic models for the low- and medium-frequency ranges -- 6.1 Reduced mean structural-acoustic model -- 6.2 Stochastic reduced-order model of the computational structuralacoustic model using the nonparametric probabilistic approach of uncertainties -- 6.3 Construction of the prior probability model of uncertainties -- 6.4 Model parameters, stochastic solver and convergence analysis -- 6.5 Estimation of the parameters of the prior probability model of uncertainties -- 6.6 Comments about the applications and the experimental validation of the nonparametric probabilistic approach of uncertainties in structural acoustics -- 7 Nonparametric probabilistic approach to uncertainties in computational nonlinear structural dynamics -- 7.1 Nonlinear equation for 3D geometrically nonlinear elasticity -- 7.2 Nonlinear reduced mean model -- 7.3 Algebraic properties of the nonlinear stiffnesses -- 7.4 Stochastic reduced-order model of the nonlinear dynamical system using the nonparametric probabilistic approach of uncertainties -- 7.5 Comments about the applications of the nonparametric probabilistic approach of uncertainties in computational nonlinear structural dynamics -- 8 Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data -- 8.1 Definition of the problemto be solved
8.2 Construction of a family of prior algebraic probability models (PAPM) for the tensor-valued random field in elasticity theory -- 8.3 Methodology for the identification of a high-dimension polynomial chaos expansion using partial and limited experimental data -- 8.4 Computational aspects for constructing realizations of polynomial chaos in high dimension -- 8.5 Prior probability model of the random VVC -- 8.6 Posterior probability model of the random VVC using the classical Bayesian approach -- 8.7 Posterior probability model of the random VVC using a new approach derived from the Bayesian approach -- 8.8 Comments about the applications concerning the identification of polynomial chaos expansions of random fields using experimental data -- 9 Conclusion -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V
LNMech 2 presents the main concepts, formulations, and recent advances in the use of a mathematical-mechanical modeling process to predict the responses of a real structural system in its environment
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Soize, Christian Stochastic Models of Uncertainties in Computational Mechanics Reston : American Society of Civil Engineers,c2012 9780784412237
Subject Stochastic models.;Uncertainty (Information theory);Mechanics, Applied -- Mathematical models
Electronic books
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