Simulation of simply cross correlated random fields by series expansion methods

By Miroslav Vorechovský. 2008

145 citations recorded by the source corpus.

A practical framework for generating cross correlated fields with a specified marginal distribution function, an autocorrelation function and cross correlation coefficients is presented in the paper. The contribution promotes a recent journal paper [1]. The approach relies on well known series expansion methods for simulation of a Gaussian random field. The proposed method requires all cross correlated fields over the domain to share an identical autocorrelation function and the cross correlation structure between each pair of simulated fields to be simply defined by a cross correlation coefficient. Such relations result in specific properties of eigenvectors of covariance matrices of discretized field over the domain. These properties are used to decompose the eigenproblem which must normally be solved in computing the series expansion into two smaller eigenproblems. Such decomposition represents a significant reduction of computational effort. Non-Gaussian components of a multivariate random field are proposed to be simulated via memoryless transformation of underlying Gaussian random fields for which the Nataf model is employed to modify the correlation structure. In this method, the autocorrelation structure of each field is fulfilled exactly while the cross correlation is only approximated. The associated errors can be computed before performing simulations and it is shown that the errors happen especially in the cross correlation between distant points and that they are negligibly small in practical situations.

Subfields: Ocean Engineering, Safety, Risk, Reliability and Quality, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/332c0fe1b7ddd73ab70019136ee9e201647819d3

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Citations in the corpus

Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method (2014, background): “It is known to converge in the mean square sense for any distribution of Hi(x, y) (e.g., Vořechovský, 2008).”
Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion (2011, methodology): “The Expansion Optimal Linear Estimation method (EOLE) (proposed by Li and Der kiureghian [20] for the case of uncorrelated Gaussian random fields) and its extension by Vořechovsky [19] to cover the case of cross-correlated non-Gaussian random fields are used herein to discretize the two random field”
Karhunen-Loève expansion for multi-correlated stochastic processes (2013, methodology): “A related approach has been recently introduced by Vořechovský [34].”
Response surface methods for slope reliability analysis: Review and comparison (2016, methodology): “…ξ when spatial variability of soil properties is considered, Np realizations of independent or cross-correlated random fields are generated using the Karhunen–Loève expansion technique (e.g., Ghiocel and Ghanem, 2002; Phoon et al., 2002; Ghanem and Spanos, 2003; Vořechovský, 2008; Cho, 2010).”
Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme (2014, background): “cross-correlated sample functions have for example been proposed in (Popescu et al. 1998; Field and Grigoriu 2012; Vořechovský 2008; Cho et al. 2013).”