Mathematical explanation on the POD applications for wind pressure fields with or without mean value components

The influence mechanism of mean value components, noted as P0, on POD applications for complete random fields PC(t) and fluctuating random fields PF(t) are illustrated mathematically. The critical philosophy of the illustration is introduction of a new matrix, defined as the correlation function matrix of P0, which connect the correlation function matrix of PC(t) and PF(t), and their POD results. Then, POD analyses for several different wind pressure fields were presented comparatively as validation. It\'s inevitable mathematically that the first eigenmode of PC(t) resembles the distribution of P0 and the first eigenvalue of PC(t) is close to the energy of P0, due to similarity of the correlation function matrixs of PC(t) and P0. However, the viewpoint is not rigorous mathematically that the first mode represents the mean pressure and the following modes represent the fluctuating pressure when PC(t) are employed in POD application. When PC(t) are employed, POD results of all modes would be distorted by the mean value components, and it\'s impossible to identify P0 and PF(t) separately. Consequently, characteristics of the fluctuating component, which is always the primary concern in wind pressure field analysis, can only be precisely identified with P0 excluded in POD.