Polynomial chaos representation of spatio-temporal random fields from experimental measurements

Das, Sonjoy; Ghanem, Roger; Finette, Steven

doi:10.1016/j.jcp.2009.08.025

Cited by 82 publications

(50 citation statements)

References 39 publications

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“…While this approach is straightforward for scalar random fields, extending the method to higher dimensions is fraught with difficulties. Moreover, constructing the PC representation of the random fields directly from measurement data involves significantly more computations [21]. On the other hand, the OLE approach discussed in this paper is simpler to implement.…”

Section: Discussionmentioning

confidence: 99%

“…The left-hand side of the three-dimensional integrals in Eqs. (19)(20)(21) as well as the integrands consist of matrices/vectors. These expressions are to be interpreted to be the generic form for computing the elements of matrices/vectors in the left-hand side of these equations.…”

Section: Case 1: Random Spatial Variations In the Modulus Of Elasticitymentioning

confidence: 99%

“…As the shape functions {S k (x, y, z)} are available numerically, the evaluation of the three-dimensional integrals in Eqs. (19)(20)(21) is carried out numerically using Gauss' quadrature scheme. The damage trajectories with time are subsequently computed corresponding to each realization.…”

Section: Case 1: Random Spatial Variations In the Modulus Of Elasticitymentioning

confidence: 99%

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3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

Appalanaidu

Gupta

2017

Acta Mech

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A stochastic finite element-based methodology is developed for creep damage assessment in pipings carrying high-temperature fluids. The material properties are assumed to be spatially randomly inhomogeneous and are modelled as 3-D non-Gaussian fields. A spectral-based approach for random field discretization that preserves exactly the non-Gaussian characteristics is used in developing the stochastic finite element model. The meshing used in random field discretization is distinct from FE meshing, depends on the correlation characteristics of the random fields and is computationally efficient. The methodology enables estimating the failure probability and the most likely regions of failure in a section of a circular pipe.

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Section: Discussionmentioning

confidence: 99%

Section: Case 1: Random Spatial Variations In the Modulus Of Elasticitymentioning

confidence: 99%

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3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

Appalanaidu

Gupta

2017

Acta Mech

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“…Assuming that the integral f 2 ω X dx is finite, a natural approximation space to consider is Π N , using elements p n [ω X ] as basis elements: this simplifies computations and allows straightforward computation of probabilistic moments. Several extensions of this idea have been considered for vector-valued parameters [25], Karhunen-Loeve expansions [12], random fields [3], etc., and arise in applications to micro-channel fluid flow [28], electrochemical processes [4], and electromagnetic systems [20], to name a few.…”

Section: Non-polynomial Modificationsmentioning

confidence: 99%

Computation of connection coefficients and measure modifications for orthogonal polynomials

Narayan

Hesthaven

2011

Bit Numer Math

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We observe that polynomial measure modifications for families of univariate orthogonal polynomials imply sparse connection coefficient relations. We therefore propose connecting L 2 expansion coefficients between a polynomial family and a modified family by a sparse transformation. Accuracy and conditioning of the connection and its inverse are explored. The connection and recurrence coefficients can simultaneously be obtained as the Cholesky decomposition of a matrix polynomial involving the Jacobi matrix; this property extends to continuous, non-polynomial measure modifications on finite intervals. We conclude with an example of a useful application to families of Jacobi polynomials with parameters (γ, δ ) where the fast Fourier transform may be applied in order to obtain expansion coefficients whenever 2γ and 2δ are odd integers.

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“…The statistical inverse problem for identifying a non-Gaussian random field as a model parameter of a BVP, using polynomial chaos expansion has been initialized in [32,33], used in [34,35], and revisited in [36]. In [37], the construction of the probability model of the random coefficients of the polynomial chaos expansion is proposed by using the asymptotic sampling Gaussian distribution constructed with the Fisher information matrix, and used for model validation [38].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Representations and Statistical Inverse Identification for Uncertainty Quantification in Computational Mechanics

Soize¹,

Desceliers²,

Guilleminot³

et al. 2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Polynomial chaos representation of spatio-temporal random fields from experimental measurements

Cited by 82 publications

References 39 publications

3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

3-D stochastic finite elements for thermal creep analysis of piping structures with spatial material inhomogeneities

Computation of connection coefficients and measure modifications for orthogonal polynomials

Stochastic Representations and Statistical Inverse Identification for Uncertainty Quantification in Computational Mechanics

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