Higher-order stochastic wave: a novel algorithm for simulating 4th-order non-Gaussian wind fields

The simulation of non-Gaussian wind fields over large-span structures is crucial for assessing the dynamic reliability of structures under non-Gaussian loads. Traditionally, wind fields are modeled as discrete multivariate stochastic processes in space, characterized by cross-spectra and cross-trispectra matrices. However, increased spatial scales lead to a greater number of discrete points, causing potential computational instabilities in the Cholesky decomposition of these matrices. To address this, this study derives a new higher-order spectrum representation method (HOSRM) to represent and simulate fourth-order non-Gaussian stochastic waves. This method mainly expands the traditional second-order spectrum representation method (SRM) for simulating stochastic waves by introducing higher-order cumulant function tensors and trispectral tensors, thereby completing the modeling of fourth-order non-Gaussian stochastic waves (symmetric nonlinear stochastic waves) from a frequency domain perspective. In order to improve the simulation efficiency of this theoretical framework, the fast Fourier transform algorithm is cleverly integrated into the simulation. This approach facilitates a novel representation of the fourth-order non-Gaussian wind field via stochastic waves. Then, the ensemble properties of the non-Gaussian wind field across 1st-, 2nd-, and 4th-order within this refined modeling method are derived and validated. The reliability and accuracy of the proposed algorithm are demonstrated through simulations of a non-Gaussian wind field for a long-span cable-stayed bridge. Comparative analysis with traditional 2nd-order stochastic wave methods highlights the unique advantages and features of this innovative approach.