Simulation of Multivariate Nonstationary Ground Motions Based on New Formulation of Cholesky Decomposition

Spectral representation method based on the direct decomposition of the power spectral density (PSD) or evolutionary power spectral density (EPSD) matrix through Cholesky decomposition usually results in large computational time and storage memory. In this study, a new formulation of the Cholesky decomposition for the EPSD matrix and corresponding simulation scheme are presented. The central idea of this approach is to separate the phase from the complex EPSD matrix. The derived real modulus matrix evidently expedites decomposition compared to the direct Cholesky decomposition of the complex EPSD matrix. In the proposed simulation scheme, the separated phase can be easily assembled. The modulus of EPSD matrix could be further decomposed into the lagged coherence matrix, which is independence of time and thus remarkably improves the Cholesky decomposition efficiency. The application of the proposed schemes to the spatially varying ground motion simulation is presented. Also the proposed approach facilitates the application