Proceedings Vol. 15 (2009)
ENGINEERING MECHANICS 2009
May 11 – 14, 2009, Svratka, Czech Republic
Copyright © 2009 Institute of Theoretical and Applied Mechanics, Academy of Sciences of the Czech Republic, v.v.i., Prague
ISSN 1805-8248 (printed)
ISSN 1805-8256 (electronic)
list of papers scientific commitee
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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