Quantifying Uncertainty
Sakamoto, S and Ghanem, R.G.. "Polynomial chaos decomposition for the simulation of non-Gaussian nonstationary stochastic processes" Journal of Engineering Mechanics-ASCE. 128
(2).
FEB 2002.
pp. 190--201.
A method is developed for representing and synthesizing random processes that have been specified by their two-point correlation function and their nonstationary marginal probability density functions. The target process is represented as a polynomial transformation of an appropriate Gaussian process. The target correlation structure is decomposed according to the Karhunen-Loeve expansion of the underlying Gaussian process. A sequence of polynomial transformations in this process is then used to match the one-point marginal probability density functions. The method results in a representation of a stochastic process that is particularly well suited for implementation with the spectral stochastic finite element method as well as for general purpose simulation of realizations of these processes.