Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability

By Seung-Kyum Choi, Ramana V. Grandhi, R. Canfield, Chris L. Pettit. 2003

220 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3d3f2391e45bfcd40c631ddeb21fff81e4f73c71

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In Civil and Structural Engineering

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Adaptive sparse polynomial chaos expansion based on least angle regression (2011, methodology): “Two approaches based on a PC representation of the response are usually distinguished: – the projection approach: each PC coefficient is recast as a multidimensional integral [7, 8] which can be computed either by simulation or quadrature; – the regression approach [9, 10, 11, 12]: the PC coefficien”
Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions (2017, methodology): “From various non-intrusive methods, the regression method in Berveiller et al. (2006), Choi et al. (2004), Sudret (2008) is exploited in this study.”
Design of Composite Wings Including Uncertainties : A Probabilistic Approach (2009, methodology): “PCE is a method that has been used to explore the variability of response in control [23,24], computational fluid dynamics [25,26], and buckling problems [27].”
Polynomial-Chaos-based Kriging (2015, unknown): “Least-square minimization techniques have been introduced by Choi et al. (2004); Berveiller et al. (2006b); Sudret (2008).”
Least squares polynomial chaos expansion: A review of sampling strategies (2017, background): “Among the early work on sampling techniques for PCE via LSA, we mention [17] in which Latin hypercube (LH) sampling is used instead of the standard MC sampling.”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “Regression Regression methods [15, 27, 28 , 123 ]r ely on the same principles as classical response surface methods [62].”
Global sensitivity analysis using polynomial chaos expansions (2008, methodology): “Alternatively, non intrusive methods have been recently proposed (Field, 2002; Ghiocel and Ghanem, 2002; Choi et al., 2004; Berveiller et al., 2006).”
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2010, methodology): “Two approaches based on a PC representation of the response are usually distinguished: – the projection approach: each PC coefficient is recast as a multidimensional integral [6, 7] which can be computed either by simulation or quadrature; – the regression approach [8, 9, 10, 11]: the PC coefficient”
Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method (2014, methodology): “…= {ξck, ξϕk }, ξck = {ξc,1k ,ξc,2k , ⋯,ξc,nk}T, ξϕk = {ξϕ,1k , ξϕ,2k , ⋯,ξϕ,nk }T, can be performed using two sets of independent standard normal probabilistic collocation points (e.g., Li and Zhang, 2007; Li et al., 2013a) or Latin hypercube sampling points (Choi et al., 2004; Vořechovský, 2008).”