Higher order dynamic mode decomposition of wind pressures on square buildings

Wind pressures on buildings with different aspect ratios were investigated via higher-order dynamic mode decomposition (HODMD) in this study. Taken's embedding theorem was used to augment the spatial dimensionality of the original snapshot matrix by introducing time delay coordinates. HODMD was applied to reveal the spatial-temporal evolution characteristics of fluctuating wind pressures on building surfaces. It was found that HODMD can successfully extract the modes and corresponding frequencies from the random pressure field. As the aspect ratio increases, the main mode is more dominant than other modes. Moreover, comparisons between HODMD and proper orthogonal decomposition (POD) suggests that the first-order mode shapes extracted by HODMD and POD are generally similar, and both can reflect the main characteristics of the fluctuating pressure field. However, the higher-order mode shapes extracted by HODMD and POD are different due to higher-order nonlinearities. The modes of HODMD oscillate at a fixed frequency while those of POD resemble random signals, indicating the physical meaning of HODMD is more evident. Furthermore, HODMD is proven to be superior to POD in reconstructing pressure fields with less root mean square errors, because HODMD reconstructs the pressure field directly while POD primarily aims to rebuild the energy field.