A bi-weighted-POD and its application on wind pressure field

Proper Orthogonal Decomposition (POD) is a reduced order modeling (ROM) method based on 2nd-order statics, which simplifies the investigated wind-pressure field in a new coordinate system formed by a set of orthonormal basis. This paper suggests a method of bi-weighted POD (which weights POD by area and at the same time by root-mean-square), and applies this method to the modal reduction of pressure field around buildings. Firstly, we introduce the POD expansion in a mean-square method, which demonstrates that POD is the optimal choice of ROM in the mean-square sense. Furthermore, we modify the original POD by the bi-weighting-method to improve its capacity of identifying coherent structures with lower energy in pressure field. For the last part, the validity of bi-weighted POD is roughly examined by a case study which applies the method to the pressure field of a 5∶1 rectangular cylinder. It turns out that the modified POD method improves the ROM accuracy at the area associated with lower energy in a significant way. In the meantime, a wind-pressure field ROM constructed by bi-weighted POD captures vital information provided by the original wind-pressure field and is spatially accuracy-consistent.