A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic vector process by a translation process with applications in wind velocity simulation

Abstract

Several methodologies utilize translation vector process theory for simulation of non-Gaussian stochastic vector processes and fields. However, translation theory imposes certain compatibility conditions on the non-Gaussian cross-spectral density matrix (CSDM) and the non-Gaussian marginal probability density functions (PDFs). For many practical applications such as simulation of wind velocity time histories, the non-Gaussian CSDM and PDFs are assigned arbitrarily. As a result, they are often incompatible. The generally accepted approach to addressing this incompatibility is to approximate the incompatible pair of CSDM/PDFs with a compatible pair that closely matches the incompatible pair. A limited number of techniques are available to do so and these methodologies are usually complicated and time consuming. In this paper, a novel iterative methodology is presented that simply and efficiently estimates a non-Gaussian CSDM that: (a) is compatible with the prescribed non-Gaussian PDFs and (b) closely approximates the prescribed incompatible non-Gaussian CSDM. The corresponding underlying Gaussian CSDM is also determined and used for simulation purposes. Numerical examples are provided demonstrating the capabilities of the methodology for both general non-Gaussian stochastic vector processes and a non-Gaussian vector wind velocity process.