Maximum likelihood estimation of stochastic chaos representations from experimental data

Desceliers, Christophe; Ghanem, Roger; Soize, Christian

doi:10.1002/nme.1576

Cited by 132 publications

(111 citation statements)

References 11 publications

Supporting

Mentioning

111

Contrasting

Order By: Relevance

“…Today, many applications of such an approach have been carried out for direct and inverse problems. We refer the reader to [65,74,75,76,77,78,79,80,81] and in particular, to Section 3.7 for a short overview concerning the identification and inverse stochastic problems related to the parametric and nonparametric probabilistic approaches of uncertainties.…”

Section: Types Of Representation For the Stochastic Modeling Of Uncermentioning

confidence: 99%

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

140

106

View full text Add to dashboard Cite

To cite this version:Christian Soize. Stochastic modeling of uncertainties in computational structural dynamics -Recent theoretical advances. Journal of Sound and Vibration, Elsevier, 2013, 332 (10) AbstractThis paper deals with a short overview on stochastic modeling of uncertainties. We introduce the types of uncertainties, the variability of real systems, the types of probabilistic approaches, the representations for the stochastic models of uncertainties, the construction of the stochastic models using the maximum entropy principle, the propagation of uncertainties, the methods to solve the stochastic dynamical equations, the identification of the prior and the posterior stochastic models, the robust updating of the computational models and the robust design with uncertain computational models. We present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties, and for their identification with experimental data. We also present the construction of the posterior stochastic model of uncertainties using the Bayesian method when experimental data are available.

show abstract

Section: Types Of Representation For the Stochastic Modeling Of Uncermentioning

confidence: 99%

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

140

106

View full text Add to dashboard Cite

show abstract

“…In this section, we don't make any further assumption and identify a random vector with arbitrary probability law. For this purpose and following [13], we use a polynomial chaos (PC) representation of X, identi ed with a maximum likelihood principle. This leads to the resolution of an optimization problem on a Stiefel manifold.…”

Section: Polynomial Chaos Representation Of Random Variablesmentioning

confidence: 99%

“…As in [13], we impose the second order moments of samples to be conserved after the probabilistic identi cation. Although a few samples are available in practice, one can be relatively con dent in those moments.…”

Section: Maximum Likelihood Estimation 421 Conservation Of Second mentioning

confidence: 99%

“…In practice, due to the prohibitive cost of the estimation of joint pdfs and also due to the small number of available samples, it was proposed in [13] to use a pseudo likelihood function:…”

Section: Maximum Likelihood Principlementioning

confidence: 99%

“…The problem of random geometry identi cation is thus equivalent to the identi cation of a random level-set function, which is a random eld. Some general techniques for the identi cation of random elds have been proposed in [13,14]. These techniques consist in the representation of the random eld on a polynomial chaos basis.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identification of random shapes from images through polynomial chaos expansion of random level set functions

Stefanou

Nouy

Clément

2009

Numerical Meth Engineering

View full text Add to dashboard Cite

To cite this version:G. Stefanou, Anthony Nouy, Alexandre Clement. Identification of random shapes from images through polynomial chaos expansion of random level-set functions. International Journal for Numerical Methods in Engineering, Wiley, 2009, 79 (2) SUMMARYIn this paper, an e cient method is proposed for the identi cation of random shapes in a form suitable for numerical simulation within the eXtended Stochastic Finite Element Method (X-SFEM).The method starts from a collection of images representing di erent outcomes of the random shape to identify. The key-point of the method is to represent the random geometry in an implicit manner using the level-set technique. In this context, the problem of random geometry identi cation is equivalent to the identi cation of a random level-set function, which is a random eld. This random eld is represented on a polynomial chaos basis and various e cient numerical strategies are proposed in order to identify the coe cients of its polynomial chaos decomposition. The performance of these strategies is evaluated through some "manufactured" problems and useful conclusions are provided. The propagation of geometrical uncertainties in structural analysis using the X-SFEM is nally examined.key words:Random geometry; Level-set method; Probabilistic identi cation; Polynomial chaos; Maximum likelihood; Extended stochastic nite element method.

show abstract

Stochastic representation for anisotropic permeability tensor random fields

Guilleminot

Soize

Ghanem

2011

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

International audienceIn this paper, we introduce a novel stochastic model for the permeability tensor associated with stationary random porous media. In the light of recent works on mesoscale modeling of permeability, we first discuss the physical interpretation of the permeability tensor randomness. Subsequently, we propose a nonparametric prior probabilistic model for non-Gaussian permeability tensor random fields, making use of the information theory and a maximum entropy procedure, and provide a physical interpretation of the model parameters. Finally, we demonstrate the capability of the considered class of random fields to generate higher levels of statistical fluctuations for selected stochastic principal permeabilities. This unique flexibility offered by the parameterization of the model opens up many new possibilities for both forward simulations (e.g. for uncertainty propagation in predictive simulations) and stochastic inverse problem solving

show abstract

Maximum likelihood estimation of stochastic chaos representations from experimental data

Cited by 132 publications

References 11 publications

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Identification of random shapes from images through polynomial chaos expansion of random level set functions

Stochastic representation for anisotropic permeability tensor random fields

Contact Info

Product

Resources

About