A stochastic model for purlin response
Time series models can provide an economical computational technique for an engineer for modeling wind speed, wind-induced pressures, and the response of a structure (or one of its components) to wind loads. Time series models are compact; yet contain almost all of the information that is in the original data. When combined with functional relationships that link the model parameters to physical parameters, a general description of the process is provided.
Autoregressive (AR) models are used in this thesis to characterize wind speed, wind-induced pressure, and associated wind-induced purlin displacement response data. The data used for the characterization was collected at the Texas Tech University's Wind Engineering Research Field Laboratory (WERFL). Autoregressive models of order 3 characterize the wind speed, wind-induced pressure, and purlin response adequately.
The AR model parameters exhibit linear correlation of varying degree depending on the data type (e.g. wind speed, wind-induced pressure, or purlin response). This implies that by establishing a single model parameter, the complete model is specified. The relationships of the model parameters to physical parameters are explored. This investigation shows that the AR (3) model parameters for wind speed are closely related to the variance of the wind speed. Although not fully developed in this work, there appears to be a functional relationship between the models for wind speed, windinduced pressure, and the associated structural response of a member. Preliminary investigation indicates that this relationship is likely to be independent of the angle of attack. Further, the residuals of autoregressive models on both wind speed and purlin response can be reasonably characterized using the log-logistic distribution.