The Use of the Proper Orthogonal Decomposition for the Characterization of the Dynamic Response of Structures Due to Wind Loading

Abstract

This thesis presents a study of the wind load forces and their influence on the response of structures. The study is based on the capacity of the Proper Orthogonal Decomposition method (POD) to identify and extract organized patterns that are hidden or embedded inside a complex field. Technically this complex field is defined as a multi-variate random process, which in wind engineering is represented by unsteady pressure signals recorded on multiple points of the surface of a structure. The POD method thus transforms the multi-variate random pressure field into a sequence of load shapes that are uncorrelated with each other. The effect of each uncorrelated load shape on the structural response is relatively easy to evaluate and the individual contributions can be added linearly afterwards. Additionally, since each uncorrelated load shape is associated with a percentage of the total energy involved in the loading process, it is possible to neglect those load shapes with low energy content. Furthermore, the load shapes obtained with the POD often reveal physical flow structures, like vortex shedding, oscillations of shear layers, etc. This later property can be used in conjunction with classical results in fluid mechanics to theorize about the physical nature of different flow mechanics and their interactions. The POD method is well suited to be used in conjunction with the classical modal analysis, not only to calculate the structural response for a given pressure field but to observe the details of the wind-structure interaction. A detailed and complete application is presented here but the methodology is very general since it can be applied to any recorded pressure field and for any type of structure.