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 modelparameter 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 outputpredictionerror method and the Bayesian method  4 Nonparametric probabilistic approach to uncertainties in computational structural dynamics  4.1 Methodology to take into account both the modelparameter 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 structuralacoustic models for the low and mediumfrequency ranges  6.1 Reduced mean structuralacoustic model  6.2 Stochastic reducedorder 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 reducedorder 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 highdimension polynomial chaos expansions with random coefficients for nonGaussian tensorvalued 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 tensorvalued random field in elasticity theory  8.3 Methodology for the identification of a highdimension 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 mathematicalmechanical modeling process to predict the responses of a real structural system in its environment 

Description based on publisher supplied metadata and other sources 

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

