A Monte Carlo simulation model for stationary non-Gaussian processes

Translation vectors with non-identically distributed components

“…Exact expressions for the joint pdfs and cdfs of Z have been derived [6]. The underlying Gaussian vector Y has components that are standard Gaussian random variables, and correlation matrix r g ZE[YY T ] that is equal to the scaled covariance matrix x g Zr g .…”

“…A variety of techniques exist for generating realizations of non-Gaussian random variables, processes, and fields [1][2][3][4]. One of these techniques is the translation technique, in which non-Gaussian random quantities or functions are modelled as non-linear transformations of Gaussian random quantities [5,6]. The translation mapping has been successfully applied to random variables, vectors, and vector fields of arbitrary dimension.…”

A new approach for simulation of non-Gaussian processes

“…At present the static transforms (Gurley and Kareem, 1996) relating a nonGaussian process to its underlying Gaussian process have been the basis of a variety of non-Gaussian process simulation techniques. The static transform methods can be grouped into two types: for the first type an iterative procedure is used to match the desired target spectrum by updating the spectrum of the initial Gaussian process (Yamazaki and Shinozuka, 1988;Gurley and Kareem, 1998;Deodatis and Micaletti, 2001), while in the second type the iterative procedure is avoided because the method begins with the target spectrum or the correlation of the non-Gaussian process and transforms it to an underlying correlation of a Gaussian process (Gurley and Kareem, 1996;Gioffrè and Gusella, 2001b;Grigoriu et al, 2003). There are two approaches to the transformational relations: the first is to derive relation expressions of the two processes according to the prescribed probability distribution (Grigoriu et al, 2003;Holmes and Cochran, 2003); the second is to give relation expressions with parameters and determine the parameters according to the prescribed lower-order moments (e.g., mean, variance, skewness and kurtosis) (Kareem, 2008).…”