On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview

Panayirci, H. Murat; Schuëller, G.I.

doi:10.1007/s11831-011-9058-5

Cited by 26 publications

(14 citation statements)

References 85 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, it should be noticed for completeness that chaos representations could have been used for modeling the mesoscale random tensor random field as well (that is, without being coupled with a prior algebraic representation). Such functional models have received a considerable attention during the past two decades, due to the developments of stochastic solvers associated with the now popular stochastic finite element method; see [12] and the recent survey [37]. Although they have been shown to be very useful for uncertainty propagation (through Galerkin-type projections for instance), their identification typically requires a very large amount of experimental data which is seldom (if ever) available in practice.…”

Section: ∀X ∈ ω [C(x)] = [Q][c(x)][q]mentioning

confidence: 99%

Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media

Guilleminot¹,

Soize²

2013

Multiscale Model. Simul.

View full text Add to dashboard Cite

Abstract. This paper is concerned with the construction of a new class of generalized nonparametric probabilistic models for matrix-valued non-Gaussian random fields. More specifically, we consider the case where the random field may take its values in some subset of the set of real symmetric positive-definite matrices presenting sparsity and invariance with respect to given orthogonal transformations. Within the context of linear elasticity, this situation is typically faced in the multiscale analysis of heterogeneous microstructures, where the constitutive elasticity matrices may exhibit some material symmetry properties and may then belong to a given subset M sym n (R) of the set of symmetric positive-definite real matrices. First of all, we present an overall methodology relying on the framework of information theory and define a particular algebraic form for the random field. The representation involves two independent sources of uncertainties, namely one preserving almost surely the topological structure in M sym n (R) and the other one acting as a fully anisotropic stochastic germ. Such a parametrization does offer some flexibility for forward simulations and inverse identification by uncoupling the level of statistical fluctuations of the random field and the level of fluctuations associated with a stochastic measure of anisotropy. A novel numerical strategy for random generation is subsequently proposed and consists in solving a family of Itô stochastic differential equations. The algorithm turns out to be very efficient when the stochastic dimension increases and allows for the preservation of the statistical dependence between the components of the simulated random variables. A Störmer-Verlet algorithm is used for the discretization of the stochastic differential equation. The approach is finally exemplified by considering the class of almost isotropic random tensors.

show abstract

Section: ∀X ∈ ω [C(x)] = [Q][c(x)][q]mentioning

confidence: 99%

Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media

Guilleminot¹,

Soize²

2013

Multiscale Model. Simul.

View full text Add to dashboard Cite

show abstract

“…Finally, there exist other well-established methods in the literature, based on alternative expansions, which involve a basis of known random functions with deterministic coefficients, namely, polynomial chaos expansion. The latest methodological developments of polynomial chaos expansion can be found in the works of Panayirci and Schuëller 29 and Yu et al, 30 whereas recent applications can be found in different fields, eg, hydrology, 31 piezoelectric materials, 32 and dosimetry to study human exposure to magnetic fields. 33 Resuming PCA, it is widely used in statistics to look at the covariance structure of multivariate and complex data.…”

Section: Dimensionality Reduction In Feamentioning

confidence: 99%

Applying functional principal components to structural topology optimization

Alaimo

Auricchio

Bianchini

et al. 2018

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary Structural topology optimization aims to enhance the mechanical performance of a structure while satisfying some functional constraints. Nearly all approaches proposed in the literature are iterative, and the optimal solution is found by repeatedly solving a finite element analysis (FEA). It is thus clear that the bottleneck is the high computational effort, as these approaches require solving the FEA a large number of times. In this work, we address the need for reducing the computational time by proposing a reduced basis method that relies on functional principal component analysis (FPCA). The methodology has been validated considering a simulated annealing approach for compliance minimization in 2 classical variable thickness problems. Results show the capability of FPCA to provide good results while reducing the computational times, ie, the computational time for an FEA is about one order of magnitude lower in the reduced FPCA space.

show abstract

“…For latest methodological developments on PCE, see for instance [22,34]. Recently, PCE has been applied in different areas, ranging from hydrology [28], properties of piezoelectric materials [31], and the study of stochastic dosimetry to assess the variability of human exposure to magnetic fields [19].…”

Section: Literature Reviewmentioning

confidence: 99%

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

et al. 2015

View full text Add to dashboard Cite

The great influence of uncertainties on the behavior of physical systems has always drawn attention to the importance of a stochastic approach to engineering problems. Accordingly, in this paper, we address the problem of solving a Finite Element analysis in the presence of uncertain parameters. We consider an approach in which several solutions of the problem are obtained in correspondence of parameters samples, and propose a novel non-intrusive method, which exploits the functional principal component analysis, to get acceptable computational efforts. Indeed, the proposed approach allows constructing an optimal basis of the solutions space and projecting the full Finite Element problem into a smaller space spanned by this basis. Even if solving the problem in this reduced space is computationally convenient, very good approximations are obtained by upper bounding the error between the full Finite Element solution and the reduced one. Finally, we assess the applicability of the proposed approach through different test cases, obtaining satisfactory results

show abstract

On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview

Cited by 26 publications

References 85 publications

Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media

Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media

Applying functional principal components to structural topology optimization

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

Contact Info

Product

Resources

About