Simulating multivariate stationary non-Gaussian process based on wavenumber–frequency spectrum and unified Hermite polynomial model

Abstract

It is of importance to model the input excitations considering the spatial variation and non-Gaussianity for the reliability evaluation of long span structures. The existing multivariate stationary non-Gaussian simulation methods are mainly based on the target marginal distribution and cross-spectrum matrix. Due to the Cholesky decomposition of cross-spectrum matrix, the computational cost of these methods increases rapidly with the increase of spatial points. Therefore, this paper develops a novel simulation method based on the wavenumber–frequency spectrum and unified Hermite polynomial model (UHPM). Firstly, UHPM is extended to the homogenous and stationary non-Gaussian field. Then, a complete transformation model from homogenous and stationary non-Gaussian auto-correlation function (ACF) into underlying Gaussian ACF with its applicable range is proposed. Furthermore, two types of incompatibility between the first four marginal moments and wavenumber–frequency spectrum are discussed, and the corresponding remedies are provided. To facilitate the calculation, the 2D-Fast Fourier Transform (FFT) technique is embedded in the Wiener–Khintchine transformation and spectral representation method (SRM). Finally, a unified simulation framework for multivariate stationary non-Gaussian process based on its relationship to the homogenous and stationary non-Gaussian field is presented. Two numerical examples, involving the simulations of non-Gaussian wind velocities and ground motion accelerations, are investigated to verify the capabilities of the proposed method.