Stochastic finite element: a non intrusive approach by regression

Berveiller, Marc; Sudret, Bruno; Lemaire, Maurice

doi:10.3166/remn.15.81-92

Cited by 338 publications

(258 citation statements)

References 2 publications

Supporting

Mentioning

249

Contrasting

Order By: Relevance

“…There are two distinct classes of techniques for the definition and computation of this approximation. The first class is composed by direct simulation methods [100,74,101,102,103,104]. These methods are often called non-intrusive since they offer the advantage of only requiring the availability of classical deterministic codes.…”

Section: Propagation Of Uncertainties or What Are The Methods To Solvmentioning

confidence: 99%

“…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%

See 1 more Smart Citation

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

Soize

2013

Journal of Sound and Vibration

139

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: Propagation Of Uncertainties or What Are The Methods To Solvmentioning

confidence: 99%

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

139

106

View full text Add to dashboard Cite

show abstract

“…From this sample, a postprocessor determines the approximation of the output. Collocation [32], regression [24] and projection methods belongs to this group of non-intrusive methods. Some stochastic methods, so-called intrusive methods, require to access to the heart of the deterministic model to be implemented like the Spectral Stochastic Finite Element Method.…”

Section: Approximation Methodsmentioning

confidence: 99%

Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

Clénet

2016

Scientific Computing in Electrical Engineering

View full text Add to dashboard Cite

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. To cite this version :Stephane CLÉNET -Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics -2016Any correspondence concerning this service should be sent to the repository Administrator : archiveouverte@ensam.eu Approximation Methods to solve Stochastic Problems in Computational ElectromagneticsStéphane ClénetAbstract To account for uncertainties on model parameters, the stochastic approach can be used. The model parameters as well as the outputs are then random fields or variables. Several methods are available in the literature to solve stochastic models like sampling methods, perturbation methods or approximation methods. In this paper, we propose an overview on the solution of stochastic problems in computational electromagnetics using approximation methods. Some applications will be presented in order to illustrate the possibilities offered by the approximation methods but also their current limitations due to the curse of dimensionality. Finally, recent numerical techniques proposed in the literature to face the curse of dimensionality are presented for non-intrusive and intrusive approaches.

show abstract

“…Often, the form of equations or code used to solve the deterministic equations is complex and it makes the implementation of the PC difficult, if not impossible. Therefore, non-intrusive methods have been proposed based on regression technique [30,31] or on projection method [19,20]. Instead of building prior expansions of uncertainty sources and of finding the coefficients by solving the corresponding equations, these approaches use interpolation methods and project a set of deterministic simulations, which are defined using samples of parameters chosen carefully, with a polynomial basis.…”

Section: Determination Of the Pc Coefficientsmentioning

confidence: 99%

Sensitivity study of dynamic systems using polynomial chaos

Sandoval

Anstett-Collin

Basset

2012

Reliability Engineering & System Safety

View full text Add to dashboard Cite

Global sensitivity has mainly been analyzed in static models, though most physical systems can be described by differential equations. Very few approaches have been proposed for the sensitivity of dynamic models and the only ones are local. Nevertheless, it would be of great interest to consider the entire uncertainty range of parameters since they can vary within large intervals depending on their meaning. Other advantage of global analysis is that the sensitivity indices of a given parameter are evaluated while all the other parameters can be varied. In this way, the relative variability of each parameter is taken into account, revealing any possible interactions. This paper presents the global sensitivity analysis for dynamic models with an original approach based on the polynomial chaos (PC) expansion of the output. The evaluation of the PC expansion of the output is less expensive compared to direct simulations. Moreover, at each time instant, the coefficients of the PC decomposition convey the parameter sensitivity and then a sensitivity function can be obtained. The PC coefficients are determined using non-intrusive methods. The proposed approach is illustrated with some well-known dynamic systems.

show abstract

Stochastic finite element: a non intrusive approach by regression

Cited by 338 publications

References 2 publications

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

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

Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

Sensitivity study of dynamic systems using polynomial chaos

Contact Info

Product

Resources

About