Engineering Mechanics

Proceedings Vol. 15 (2009)

ENGINEERING MECHANICS 2009

Copyright © 2009 Institute of Theoretical and Applied Mechanics, Academy of Sciences of the Czech Republic, v.v.i., Prague

 

M. Vořechovský
pages 1431 - 1443, full text

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 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 a 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.

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