Modeling strongly non-Gaussian non-stationary stochastic processes using the Iterative Translation Approximation Method and Karhunen–Loève expansion

• A new model for non-stationary and non-Gaussian stochastic processes is presented.
• The model improves the ITAM by upgrading directly the autocorrelation function.
• KL-ITAM improves the accuracy/efficiency of non-Gaussian stochastic process modeling.
• Utilizes the K–L expansion for simulation of general non-Gaussian random processes.

A method is proposed for modeling non-Gaussian and non-stationary random processes using the Karhunen–Loève expansion and translation process theory that builds upon an existing family of procedures called the Iterative Translation Approximation Method (ITAM). The new method improves the ITAM by iterating directly on the non-stationary autocorrelation function. The existing ITAM requires estimation of the evolutionary spectrum from the autocorrelation function for which no unique relation exists. Consequently, computationally expensive estimates or simplifying assumptions/approximations reduced the ITAM performance for non-stationary processes. The proposed method improves the accuracy of the resulting process while maintaining computational efficiency. Several examples are provided.