Doctor of Philosophy
Civil and Environmental Engineering
The time series of the wind speed from hurricane and downburst events can exhibit nonstationary non-Gaussian characteristics. Moreover, the time series of the wind pressure for a stationary wind may not be Gaussian. This thesis is focused on analyzing, characterizing, and simulating nonstationary/stationary Gaussian/non-Gaussian of wind speed and wind pressure coefficients by using time-frequency transform techniques such as the S-transform (ST) and discrete orthonormal S-transform (DOST). It is shown that by removing the mean of downburst winds, the multivariate nonstationary downburst wind speed processes can be efficiently decomposed and simulated by applying ST and DOST. It was also found that the hurricane wind speed could be treated as stationary (constant mean) and non-Gaussian or nonstationary (time-varying mean) Gaussian. The implication of using the two approaches to treat the hurricane wind, in terms of simulation, gust factor, and turbulence intensity, is presented and discussed.
An aspect of characterizing the multivariate stochastic processes from their samples (e.g., wind pressures at multiple taps on a low building model from wind tunnel tests) is to estimate their power spectral density (PSD) and coherence functions. To obtain unbiased estimates of the PSD and coherence function, a new multi-taper ST is proposed and it is shown by simulation results that these functions for samples of multivariate stationary processes can be effectively estimated by averaging the time-frequency decomposition results from the proposed multi-taper ST or form ST but at the high-frequency range.
Since in practice, one is faced with simulating multivariate wind speed or pressure time series conditioned on the observed samples or segment of samples, a new framework is proposed for such a need for multivariate nonstationary non-Gaussian processes. The use of the proposed algorithm is illustrated by numerical examples, including sampling a segment of hurricane wind conditional on a segment of observed hurricane winds.
Summary for Lay Audience
The samples of the downburst wind speed, hurricane wind speed, and wind pressure on the building can be used to evaluate their stochastic characteristics such as the power spectral density function and coherence function. Knowing these characteristics, samples of the time series of the wind speed and wind pressure can be generated through numerical algorithms; the samples can be used for analyzing the responses of structures.
This thesis is focused on the characterization of stochastic processes such as wind speed and wind pressure. The topics of characterization and simulation of univariate and multivariate processes are not new but are difficult, especially if the processes are nonstationary (i.e., with time-varying characteristics) and the non-Gaussian (i.e., the marginal probability distribution is not Gaussian). New techniques to characterize the process through time-frequency decomposition are proposed. Also, new algorithms are developed to carry out unconditional and conditional simulations of univariate and multivariate nonstationary and non-Gaussian processes. These algorithms are shown by numerical examples and validated with the prescribed conditions for the simulation.
Xiao, Minyu, "Modelling and Simulation of Nonstationary Non-Gaussian Wind Speed and Wind Pressure Coefficients" (2022). Electronic Thesis and Dissertation Repository. 8813.
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