Fast Hilbert–Wavelet Simulation of Nonstationary Wind Field Using Noniterative Simultaneous Matrix Diagonalization

Abstract

The frequency content and spatial correlation of nonstationary wind fields during extreme events typically present time-variant characteristics. Several effective schemes [e.g., using evolutionary power spectral density (EPSD) or Hilbert spectrum] have been highly developed and extensively used for analysis and the synthesis of time-dependent frequency distributions, whereas, until very recently, little attention has been paid to the accurate and efficient simulation of time-varying spatial correlations. The Hilbert transform together with the wavelet technique (Hilbert–wavelet scheme) holds great promise in accomplishing this task since a nonlinear, statistical relationship between the instantaneous phase difference and time-variant spatial correlation has recently been established. However, its engineering application is limited by the need to simultaneously solve a large number of nonlinear equations. To address this issue, the simultaneous matrix diagonalization (SMD) technique is introduced here to accelerate the Hilbert–wavelet simulation of nonstationary wind fields. Specifically, the SMD effectively obtains the target spatial correlation by the linear combination of uncorrelated wavelet subcomponents of the multivariate wind process. In addition, memory usage in the simulation of time-variant spatial correlation is greatly reduced using SMD. The SMD technique is usually implemented with iterative algorithms. To further improve the simulation efficiency, two-dimensional singular value decomposition (2dSVD) is employed to achieve a noniterative SMD. The high simulation fidelity and efficiency of the proposed Hilbert-wavelet-SMD approach are demonstrated by numerical examples. The simulation time consumption is compared with the state-of-the-art EPSD-based approach, and the proposed Hilbert-wavelet-SMD scheme shows superior efficiency.