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

Xin Li, Shaopeng Li, Yan Jiang, Qingshan Yang, Liuliu Peng, Jianhan Yu and Min Lin

Reliability Engineering and System Safety, 2025, vol. 264, issue PB

Abstract: 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.

Keywords: Wind field simulation; Higher-order stochastic wave; Non-Gaussian stochastic process; Fast fourier transform (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:264:y:2025:i:pb:s0951832025006027

DOI: 10.1016/j.ress.2025.111402

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