Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Observations on non-Gaussian Karhunen-Loève expansions

L.B. Li*, S.T. Quek, K.K. Phoon
National University of Singapore, Civil Engineering Department, Singapore, 117576

  Full Text
The non-Gaussian Karhunen-Loève (K-L) expansion has been used to generate a non-Gaussian process using an iterative scheme. Numerical results show that different non-Gaussian processes can be generated satisfying the same prescribed covariance function and marginal distribution by changing the assumed starting distribution of the K-L random variables. Non-Gaussian K-L processes produced by assuming an initial Gaussian distribution for the K-L random variables appear to be translation processes. When the K-L random variables were assigned a lognormal distribution before the iteration procedure, the resulting process is clearly non-translation. Hence, it would appear that translation processes form a subset of K-L processes. In other words, the class of non-Gaussian K-L processes is larger and potentially capable of providing better fit to observed data.

Keywords:  Karhunen-Loève expansion; Modified Latin hypercube orthogonalization; Translation process; Multivariate Gaussianity; Up-crossing rate; Rank correlation

* Corresponding author. Tel.: +65 68746347; E-mail: