Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure

Soize, Christian; Ghanem, Roger

doi:10.1137/s1064827503424505

Cited by 520 publications

(426 citation statements)

References 20 publications

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“…(ii.1) -The first one corresponds to the spectral methods such as the Polynomial Chaos representations (see [63,64] and also [65,66,67,68,69,70,71,72,73]) which can be applied in infinite dimension for stochastic processes and random fields, which allow the effective construction of mapping h to be carried out and which allow any random variable X in L 2 N , to be written as…”

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

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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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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

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“…Polynomial Chaos (PC) Method [8][9][10][11]: In this method, orthogonal polynomials are used to decompose the output over the entire random space. Arguments of these polynomials follow known probability density functions.…”

Section: Uncertainty Quantification: Deterministic and Stochasticmentioning

confidence: 99%

A 'Maximum Entropy'-Based Novel Numerical Methodology for Problems in Statistical Electromagnetics

Chatterjee¹

2014

PIER M

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Abstract-This paper presents the development of a novel 'maximum entropy'-based numerical methodology for the solution of electromagnetic problems, where the inputs and system parameters vary statistically. The application of this methodology to the problem of a plane wave impinging on an array of cylindrical conducting rods with stochastic variations in its parameters is then presented. To address this problem, a statistically significant number of replicas of this array of conductors are constructed. The current profiles in these coupled conductors are estimated by using the Method of Moments (MoM). Upon estimation of the current profiles on the conductors, the monostatic radar crosssection is estimated for each replica of the array. The probability density function is then constructed through the estimation of a finite number of moments from the available output data subject to the constraint of maximum entropy. The methodology is very general in its scope and its application to scatterers with other geometries such as spheres, spheroids and ellipsoids as well as to other application areas would form the basis of our future work.

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“…We denote by (Ξ, B Ξ , P ξ ) the m-dimensional probability space de ned by random vector ξ. Random vector X then admits a generalized chaos representation [23,24] writing:…”

Section: Polynomial Chaos Decompositionmentioning

confidence: 99%

“…(7) leads to a K-L decomposition of the random level-set in 12 terms and thus 12 (uncorrelated but dependent) random variables have to be identi ed in this case. The e ect of the value of tolerance ǫ KL on the reconstruction of the random level-set is quanti ed using iso-contour plots of the probability P in to be inside the hole, de ned in equation (24). In Figure 7, three contours are plotted (P in = 0.1, 0.5 and 0.9) for three di erent values of tolerance ǫ KL .…”

Section: Example 2: Circle With Random Position Of Center and Random mentioning

confidence: 99%

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

Stefanou

Nouy

Clément

2009

Numerical Meth Engineering

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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.

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Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure

Cited by 520 publications

References 20 publications

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

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

A 'Maximum Entropy'-Based Novel Numerical Methodology for Problems in Statistical Electromagnetics

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

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