Vector time-varying autoregressive (TVAR) models and their application to downburst wind speeds



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Texas Tech University


The extreme winds that can cause severe damage to buildings and infrastructures and also human casualties are commonly nonstationary. They generally have time-varying means as well as nonstationary fluctuating speeds; moreover, their velocity profiles differ significantly from the conventional log or power law profiles. These aspects are of great importance for wind loading on structures. Thunderstorm downbursts, one type of thunderstorm wind, dominate the extreme wind climate in many parts of the world and cause much damage. Analysis of such wind climates serve to produce the design wind speeds used in many codes and standards. These standards assume boundary layer wind profiles whereas the flow field in a thunderstorm is very complex and could not be more different. This area has been largely neglected in wind engineering to date. Partly due to the extraordinary complexity of this wind phenomena and the lack of full-scale data, wind loading on structures is still viewed as being generated by stationary boundary layer winds and the reliability of such gross assumptions needs to be evaluated. This dissertation aims to introduce into wind engineering the time-varying autoregressive (TVAR) model as a tool for nonstationary winds and develop a new model to characterize and simulate nonstationary wind fields; these techniques will be applied to two sets of representative downburst wind speed data. TVAR models are comprehensively presented in a unique manner with new insights and an improved identification approach. An uncertainty principle for TVAR models is formed heuristically. The so-called state space method using the Kalman filter that was commonly utilized for scalar TVAR models is reformed for vector/multivariate TVAR models; and a refined searching stage is introduced to adapt to the different smoothness classes of TVAR coefficients. This study is accompanied by many simulation studies, which reveal some important insights into the theory and identification of TVAR models. A nonparametric deterministic-stochastic hybrid (NDESH) model is proposed for nonstationary wind fields; this model has the capability to both characterize and simulate nonstationary wind fields. Most importantly, this model has rich physical meaning and is suitable for structural analyses under nonstationary winds. For the NDESH model, a specific identification methodology is proposed with the proper orthogonal decomposition (POD), wavelet shrinkage, state space method and TVAR models. By successfully applying the ideas and techniques presented in this dissertation to two sets of full-scale downburst data, it is discovered that downburst wind speeds indeed have consistent and yet different properties, namely, one set of data is stationary and the other is nonstationary in the smallest scale, and both fluctuating wind speeds can be characterized by TVAR(2) models. Many perspectives for future research are drawn oriented to the NDESH model.