A Study On Applications Of Proper Orthogonal Decomposition To Wind Load And Wind-induced Response Of Buildings

Wind pressures acting on buildings are complicated functions of both time and space. Earlier studies have applied the proper orthogonal decornposition(POD) technique to such random wind pressure fields to identify hidden deterministic structures. In this paper, the POD technique is applied to analysis of wind-induce response on a large-scale roof and a tall building.The POD provides mathematical tools to simplify the stochastic process. POD expresses a multi-dimensional random process through a series of fully coherent components uncorrelated in some statistical sense. Likewise for the classic modal analysis of structures, a limited number of modes is usually enough to approximate the actual process.In particular, POD has been applied to defining a wave superimposition based procedure for the digital simulation of multi-variate random processes and correlated time series.In the paper, firstly, present the formulation and application of proper orthogonal decomposition of covariance and cross-power spectral density matrices are presented in the analysis of wind load effects on structures. Then the dynamic response of linear structures subjected to random loads is analyzed by a technique called Double Modal Transformation (DMT) that is expressed through a double series whose terms depend on structural and loading modes. Detailed discussion on the truncation of higher wind loading modes in the modeling and associated analysis of wind effects are discussed.From the paper it is found that this technique of proper orthogonal decomposition not only enhances our understanding of the underlying physics of wind loads and their effects on structures, but also provides efficient means to estimate structural response under multi-correlated excitations. The technique is potentially useful in specifying the fluctuating surface pressure field around structures.