A combined polynomial transformation and proper orthogonal decomposition approach for generation of non-Gaussian wind loads on large roof structures

The accurate simulation of stochastic wind loads acting on roof structures is necessary for time-domain response analysis of the structures. Recent experiments have revealed the non-Gaussian feature of wind pressures on roof structures. Considering such practical feature of wind pressure, a four-parameter cubic polynomial model is derived based on the properties of Gaussian stochastic vector and the correlation-distortion technique. The model is suitable for generating the multiple correlated wind pressure time histories with the prescribed power spectral density matrix and the prescribed lower-order moments-the mean, variance, skewness, and kurtosis. Further, in order to improve the computational efficiency and reduce the memory demand, a new approach that combines the polynomial model, the proper orthogonal decomposition (POD) technique, and the B-spline surface interpolation technique, is proposed for generating the non-Gaussian wind pressure fluctuations on large-span roof structures. Also, a six-step procedure is proposed for validation of the POD and B-spline surface interpolation techniques. Then, an engineering example is provided illustrating the proposed approach and demonstrating the capabilities of the methodology for a large-scale simulation purpose that is characterized by a large number of discrete points of the roof and a long time duration. It is shown that the wind pressure time histories are fast generated which coincide with the target auto-/cross-correlation functions and the prescribed non-Gaussian properties. Moreover, the computational efficiency of the proposed combined approach is compared with those of two algorithms-the single cubic polynomial model and the previous four-parameter exponential model, and the advantages are analyzed that contribute to the high efficiency and low memory demand of the proposed approach.