Simulation of second-order processes using Karhunen–Loeve expansion

A unified and practical framework is developed for generating second-order stationary and non-stationary, Gaussian and non-Gaussian processes with a specified marginal distribution function and covariance function. It utilizes the Karhunen–Loeve expansion for simulation and an iterative mapping scheme to fit the target marginal distribution function. The proposed method has three main advantages: (a) processes with Gaussian-like marginal distribution can be generated almost directly without iteration, (b) distributions that deviate significantly from the Gaussian case can be handled efficiently and (c) non-stationary processes can be generated within the same unified framework. Four numerical examples are used to demonstrate the validity and convergence characteristics of the proposed algorithm. Based on these examples, it was shown that the proposed algorithm is more robust and general than the commonly used spectral representation method.