Abstract
Karhunen-Loeve(KL) expansion of auto-covariance of input Gaussian random process is carried out using standard normal variables as the basis of KL expansion. Input random processes for many practicle problems have non-Gaussian random process description, so an algorithm is developed to find the basis random variables of KL expansion for non-Gaussian processes. The basis random variables of KL expansion are obtained via nonlinear transformation of marginal cumulative distribution function using standard deviation. Results are obtained for three known skewed distributions, Log-Normal, Beta, and Exponential. In all the cases, it is found that the proposed algorithm matches very well with the known solutions and can be applied to solve non-Gaussian process using Spectral Stochastic Finite Element Method.
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