Application of Proper Orthogonal Decomposition Method in Wind Field Simulation for Roof Structures

Abstract

The Weighted Amplitude Wave Superposition (WAWS) method and the Proper Orthogonal Decomposition (POD) technique are first introduced. Then the POD technique combined with a wind field reconstruction method for a flat roof is studied. And also, wind field extension using B-spline interpolation and the wind field reconstruction are verified. On this basis, a two-step simulation algorithm to generate wind field is presented for roof structures. Finally, an engineering example is selected in order to demonstrate the capabilities and efficiency of the proposed algorithm. The conclusions can be summarized as follows: (1) The modal values of the nodes on a roof can be obtained by using B-spline surface interpolation method based on the values of the control nodes. (2) There is similarity between the control POD interpolated mode and the integral POD mode, which indicates that the spatial distribution property of the integral wind field can be known through interpolation based on the POD analysis of the wind field of the control nodes. (3) The equation derived in this paper indicates that wind field reconstruction using the integral POD interpolated modes and the control POD interpolated modes respectively, will result in two identical wind velocity time histories of an interpolation node. Both are approximate to the original time history. And the degree of approximation is affected mainly by interpolation results of the modes. Steps are also suggested in order to improve and ensure the simulation precision for those roof structures with complex shape and large number of discrete points for simulation. (4) In the engineering example, wind field simulation of the roof of Foshan Century Lotus Stadium, the results show that the proposed algorithm is very efficient with sufficient precision. Therefore, the proposed algorithm is advantageous for wind resistance analysis of a large scale roof.