Stochastic model reduction for chaos representations

Doostan, Alireza; Ghanem, Roger; Red-Horse, John

doi:10.1016/j.cma.2006.10.047

Cited by 180 publications

(136 citation statements)

References 37 publications

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“…From a mathematical point of view, SFEM is a powerful tool for the solution of stochastic partial differential equations (PDEs) and it has been treated as such in numerous publications where convergence and error estimation issues are examined in detail e.g. [10][11][12]30,41,58,113,124]. SFEM has been successfully applied in a wide variety of problems (e.g.…”

Section: The Stochastic Finite Element Methods (Sfem)mentioning

confidence: 99%

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The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

869

407

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a b s t r a c tA powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). SFEM is an extension of the classical deterministic FE approach to the stochastic framework i.e. to the solution of static and dynamic problems with stochastic mechanical, geometric and/or loading properties. The considerable attention that SFEM received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large-scale problems. This article aims at providing a state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future.

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Section: The Stochastic Finite Element Methods (Sfem)mentioning

confidence: 99%

“…This approach is usually combined in the literature with the polynomial chaos (PC) approximation for the calculation of the response variability of uncertain finite element systems e.g. [1][2][3]19,22,28,29,41,66,67,94,108,113,187,189]. The combination is called the spectral stochastic finite element method (SSFEM).…”

Section: The Spectral Representation Methodsmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

869

407

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“…They consist in representing the solution on optimal reduced bases of deterministic functions and stochastic functions (scalar-valued random variables). Several strategies have been proposed for the extraction of reduced bases from approximate Karhunen-Loeve expansions (or classical spectral decompositions) of the solution [113,103]. Another method, called Generalized Spectral Decomposition method, has been recently proposed for the construction of such representations without knowing a priori the solution nor an approximation of it [69,114,70].…”

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

confidence: 99%

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

Soize

2013

Journal of Sound and Vibration

140

106

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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.

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“…To address such difficulties, a non intrusive method that builds a sparse PC expansion was introduced [37]. Another work proposes a model reduction technique for chaos representations that mitigates the computational cost without reducing the accuracy of the results [38].…”

Section: Spectral Stochastic Finite Element Methodsmentioning

confidence: 99%

Uncertainties in structural dynamics: overview and comparative analysis of methods

Daouk

Louf

Dorival

et al. 2015

Mechanics & Industry

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-When studying mechanical systems, engineers usually consider that mathematical models and structural parameters are deterministic. However, experimental results show that these elements are uncertain in most cases, due to natural variability or lack of knowledge. Therefore, engineers are becoming more and more interested in uncertainty quantification. In order to improve the predictability and robustness of numerical models, a variety of methods and techniques have been developed. In this work we propose to review the main probabilistic approaches used to model and propagate uncertainties in structural mechanics. Then we present the Lack-Of-Knowledge theory that was recently developed to take into account all sources of uncertainties. Finally, a comparative analysis of different parametric probabilistic methods and the Lack-Of-Knowledge theory in terms of accuracy and computation time provides useful information on modeling and propagating uncertainties in structural dynamics.

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Stochastic model reduction for chaos representations

Cited by 180 publications

References 37 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

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

Uncertainties in structural dynamics: overview and comparative analysis of methods

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