Proper Orthogonal Decomposition-Based Modeling, Analysis, and Simulation of Dynamic Wind Load Effects on Structures

Multicorrelated stationary random processes/fields can be decomposed into a set of subprocesses by diagonalizing their covariance or cross power spectral density (XPSD) matrices through the eigenvector/modal decomposition. This proper orthogonal decomposition (POD) technique offers physically meaningful insight into the process as each eigenmode may be characterized on the basis of its spatial distribution. It also facilitates characterization and compression of a large number of multicorrelated random processes by ignoring some of the higher eigenmodes associated with smaller eigenvalues. In this paper, the theoretical background of the POD technique based on the decomposition of the covariance and XPSD matrices is presented. A physically meaningful linkage between the wind loads and the attendant background and resonant response of structures in the POD framework is established. This helps in better understanding how structures respond to the spatiotemporally varying dynamic loads. Utilizing the POD-based modal representation, schemes for simulation and state-space modeling of random fields are presented. Finally, the accuracy and effectiveness of the reduced-order modeling in representing local and global wind loads and their effects on a wind-excited building are investigated.