An analytical formula for Gaussian to non-Gaussian correlation relationship by moment-based piecewise Hermite polynomial model with application in wind engineering

The Gaussian to non-Gaussian correlation relationship is often needed in wind engineering, e.g., simulation of stationary non-Gaussian wind pressure coefficient processes and characterizing the dependence of two non-Gaussian wind pressure coefficients. When the translation function between non-Gaussian and its underlying Gaussian variable is modelled by moment-based Hermite polynomial model (HPM), the closed-form equation of Gaussian to non-Gaussian correlation relationship has been established in literature. Recently, an improved translation function by moment-based piecewise Hermite polynomial model (PHPM) was proposed by some authors of this paper, which does not suffer from the monotonic limit. Nevertheless, the Gaussian to non-Gaussian correlation relationship by moment-based PHPM has not been derived. This study proposes an analytical formula for Gaussian to non-Gaussian correlation relationship by moment-based PHPM based on characteristics of truncated bivariate Gaussian distribution. Numerical investigations are then carried out to demonstrate the performance of the proposed analytical formula. Finally, it is applied to simulate the non-Gaussian wind pressure coefficient processes and establish the joint probability density function of two non-Gaussian wind pressure coefficients. Results show that the proposed analytical formula is effective. The possible limitation of using this analytical formula is also pointed out at last.