A combined polynomial transformation and proper orthogonal decomposition approach for generation of non-Gaussian wind loads on large roof structures. (1st November 2015) - Li, Jing; Li, Lijuan; Wang, Xin
Highlights: A cubic polynomial model is derived for generating multivariate non-Gaussian processes. The relation for transform of the correlation functions is derived. A new approach combining the polynomial model with the POD technique is proposed. A procedure is proposed to verify the POD and B-spline surface interpolation techniques. Numerical results show that the proposed approach is valid, efficient, and memory saving. Abstract: 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.