Modeling and simulating nonstationary thunderstorm winds based on multivariate AR-GARCH

Abstract Extreme winds such as thunderstorm winds typically exhibit nonstationary characteristics. When these winds act on the structure, the time domain analysis method is used considering the structural and/or aerodynamic nonlinearity in the wind-induced structural response analysis. Because the time domain analysis method needs a sufficient number of wind speed samples, the efficient simulation of nonstationary winds becomes a crucial task. The time series method is more suitable in generating the nonstationary process due to the high efficiency. As a typical time series model, the autoregressive-generalized autoregressive conditional heteroskedasticity (AR-GARCH) model could be a good candidate to characterize these samples. In this paper, the method based on the multivariate AR-GARCH model is proposed to model and simulate the multivariate nonstationary wind speed process. Specifically, Baba-Engle-Kraft-Kroner (BEKK) model is adopted since it can maintain the positive definiteness of conditional covariance matrix. The numerical simulations based on samples with different time-varying variances obtained by spectral representation method (SRM) are given to demonstrate the applicability of the proposed method. The measured thunderstorm wind speed is adopted to illustrate and validate the accuracy of the proposed method. The results show that the time-varying variance and cross correlation can be satisfactorily maintained.

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