Simulation of highly skewed non-Gaussian stochastic processes

In this paper, a simulation methodology is proposed to generate sample func tions of a stationary, non-Gaussian stochastic process with prescribed spec tral density function and prescribed marginal probability distribution. The proposed methodology is a modified version of the Yamazaki and Shinozuka i terative algorithm that has certain difficulties matching the prescribed ma rginal probability distribution. Although these difficulties are usually su fficiently small when simulating non-Gaussian stochastic processes with sli ghtly skewed marginal probability distributions, they become more pronounce d for highly skewed probability distributions (especially at the tails of s uch distributions). Two major modifications are introduced in the original Yamazaki and Shinozuka iterative algorithm to ensure a practically perfect match of the prescribed marginal probability distribution regardless of the skewness of the distribution considered. First, since the underlying "Gaus sian" stochastic process from which the desired non-Gaussian process is obt ained as a translation process becomes non-Gaussian after the first iterati on, the empirical (non-Gaussian) marginal probability distribution of the u nderlying stochastic process is calculated at each iteration. This empirica l non-Gaussian distribution is then used instead of the Gaussian to perform the nonlinear mapping of the underlying stochastic process to the desired non-Gaussian process. This modification ensures that at the end of the iter ative scheme every generated non-Gaussian sample function will have the exa ct prescribed non-Gaussian marginal probability distribution. Second, befor e the start of the iterative scheme, a procedure named "spectral preconditi oning" is carried out to check the compatibility between the prescribed spe ctral density function and prescribed marginal probability distribution. If these two quantities are found to be incompatible, then the spectral densi ty function can be slightly modified to make it compatible with the prescri bed marginal probability distribution. Finally, numerical examples (includi ng a stochastic process with a highly skewed marginal probability distribut ion) are provided to demonstrate the capabilities of the proposed algorithm .