Polynomial chaos expansion of a multimodal random vector

Adaptive sparse polynomial chaos expansion based on least angle regression

Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which makes the computational cost of classical solution schemes (may it be intrusive (i.e. of Galerkin typ...

Stochastic analysis of saturated–unsaturated flow in heterogeneous media by combining Karhunen-Loeve expansion and perturbation method

In this study, a stochastic model for transient saturated–unsaturated flow is developed based on the Karhunen-Loeve expansion of the input random soil properties combined with a perturbation method. The log-transformed saturated hydraulic conductivity f ðxÞ and the soil pore size distribution parameter aðxÞ are assumed to be normal random functions with known covariances. We decompose f ðxÞ and...

Identification of multi-modal random variables through mixtures of polynomial chaos expansions

A methodology is introduced for the identification of a multi-modal real-valued random variable from a collection of samples. The random variable is seen as a finite mixture of uni-modal random variables. A functional representation of the random variable is used, which can be interpreted as a mixture of polynomial chaos expansions. After a suitable separation of samples into sets of uni-modal ...

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

Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods

[1] An efficient method for uncertainty analysis of flow in random porous media is explored in this study, on the basis of combination of Karhunen-Loeve expansion and probabilistic collocation method (PCM). The random log transformed hydraulic conductivity field is represented by the Karhunen-Loeve expansion and the hydraulic head is expressed by the polynomial chaos expansion. Probabilistic co...