Stochastic Finite-Element Analysis of Seismic Soil-Structure Interaction

By D. Ghiocel, Roger G. Ghanem. 2002

203 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e407223ff6e6c00ab4ca1df497b763499d222487

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In Civil and Structural Engineering

In Statistics and Probability

Citations in the corpus

Collocation-based stochastic finite element analysis for random field problems (2007, methodology): “Although a new implementation of SSFEM [5], which is theoretically equivalent to the original SSFEM, has been developed for the purpose of utilizing commonly available FEM codes as a black box, this novel implementation of SSFEM (mentioned in this paper as black-box SSFEM) uses random sampling of th”
Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2005, methodology): “We borrow the termnon-intrusivefrom [23] for this way of evaluating the PCexpansion.”
Uncertainty quantification in chemical systems (2009, methodology): “Investigations have employed both samplingbased ‘non-intrusive’ collocation methods [17, 23, 24] where relevant Galerkin projections are computed numerically, and ‘intrusive’ methods involving Galerkin projection reformulation of governing equations [13].”
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”
Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems (2010, methodology): “Several methods have been proposed for the definition and computation of the approximate solution: L2 projection [19, 21], interpolation [3, 14, 49, 51, 54], regression [6] or Galerkin projections [2, 16, 18, 35].”
The generalization of Latin hypercube sampling (2015, methodology): “Meanwhile, LHS has been applied to nearly every type of probabilistic analysis one can imagine, ranging from the estimation of reliability (probability of failure) [19] to coefficient estimation for polynomial chaos, neural network, and other types of surrogate models [20, 21].”
Quasi-random numbers in stochastic finite element analysis (2007, methodology): “1 Non-intrusive projection scheme The PCE coefficients can be computed using a projection approach (Ghiocel and Ghanem, 2002; Le Maître et al., 2002), which exploits the orthogonality of the PCE basis.”
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2010, methodology): “Projection approach The PC coefficients can be computed using a projection approach [6, 7], which exploits the orthonormality of the PC basis.”
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).”
Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations (2015, background): “Non-intrusive methods may be classified as projection methods (Ghiocel and Ghanem, 2002; Le Maitre et al., 2002), stochastic or probabilistic collocation methods (Xiu and Hesthaven, 2005), gradient-based methods also known as collocation methods coupled with sensitivity derivatives (Perez, 2008),…”
A stochastic finite element procedure for moment and reliability analysis (2006, methodology): “Again within the framework of polynomial chaos expansion ofthe response, alternative methods for computing the response coefficients may be considered in the future: thenon intrusive methodused by (Ghiocel and Ghanem, 2002, Choiet al., 2004a;2004b) or theregression method(Berveilleret al.,2006).”
Polynomial-Chaos-based Kriging (2015, unknown): “So-called projections methods were developed by Ghiocel and Ghanem (2002); Le Maˆıtre et al. (2002); Keese and Matthies (2005); Xiu and Hes-thaven (2005), see a review in Xiu (2009).”