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

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 WienerKhintchine 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.

Automated summary

This paper proposes a novel simulation method for the reliability evaluation of long span structures, considering the spatial variation and non-Gaussianity of input excitations. The method is based on the wavenumber-frequency spectrum and unified Hermite polynomial model, and it transforms the non-Gaussian data into underlying Gaussian data within an applicable range, while providing corresponding remedies for incompatibility issues.