Stochastic analysis of wind data
Smith, Douglas A.
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Autoregressive Moving Average (ARMA) models are used to investigate wind speed and longitudinal component wind speed data. Field data obtained at Texas Tech University's Wind Engineering Research Field Laboratory is used for this investigation. Autoregressive models of order 3, AR(3) models, are shown to adequately describe the 15-minute records collected at the field site. ARMA models provide insight into mechanically generated turbulence observed in the wind field not easily seen in the frequency domain. The AR(3) model parameters exhibit a constant linear correlation. Thus a single model parameter can be used to specify the model. This implies that the mechanically generated turbulence in the wind is a constant process. The underlying processes generating stationary and nonstationary wind records is investigated using the AR(3) models. As used here, the 15-minute records are classified as stationary or nonstationary based on the nonparametric run and reverse arrangements tests. Statistical testing indicates there is not a significant difference between the stationary records and the nonstationary records. The AR(3) model parameters and the white noise variance are shown to be linearly related to roughness length, shear velocity, and height above ground. Thus an AR(3) model is established from physical parameters. This allows extension of these results to other terrains. Using the log law to describe the mean flow in conjunction with the AR(3) model to describe the turbulence provides an simple way to simulate time domain wind data. Simulations using this combination of models are shown to adequately describe field data and to match the spectral results published in the literature. The procedures developed in this dissertation appear to be extendable to wind-induced pressures. When ARMA models are developed for pressures, the two models can be combined to produce transfer function models. After a state space model is developed to describe the 3-dimensional wind field and a similar model developed for wind induced pressures on the building surface, a new economical computational technique will be available to the engineer to compute wind loads on structures. The procedures and results presented in this dissertation are useful to wind tunnel modelers, computational wind engineers and structural analysts solving nonlinear structural dynamics problems. Wind tunnel modelers can use the AR(3) models to verify that their approach flow matches the field conditions. These models may be useful to numerical modelers as an input boundary conditions or to verify the accuracy of their numerical models. The structural analysts can easily generate simulations of wind time histories using these procedures which can then be combined with drag coefficients to generate loads for their structures.