Simulation of strongly non-Gaussian non-stationary stochastic processes utilizing Karhunen-Loeve expansion
Hwanpyo Kim, Michael D. Shields · cIRcle (University of British Columbia) · 2015
The simulation of non-stationary and non-Gaussian stochastic processes is a challenging problem of considerable practical interest. Recently, Shields et al. have developed a class of conceptually simple and efficient methods for simulation of non-Gaussian processes using translation process theory (collectively referred to as the Iterative Translation Approximation Method - ITAM) that iteratively upgrades the underlying Gaussian power spectral density function for simulation using the spectral representation method. However, the currently existing ITAM method for generation of non-stationary and non-Gaussian processes requires additional approximations in the estimation of the evolutionary spectrum. An extension of the ITAM is proposed that utilizes the K-L expansion. The developed method iteratively upgrades the covariance function directly and, in so doing, avoids the complex and non-unique inverse problem of estimating the evolutionary spectrum from the non-stationary autocorrelation. The application of the method for a strongly non-Gaussian and non-stationary process with a prescribed target non-Gaussian correlation function is demonstrated.