Application of Time-Frequency Interpolation and Proper Orthogonal Decomposition in Nonstationary Wind-Field Simulation

Abstract

The spectral representation method is widely used to generate nonstationary processeses. However, the operations of Cholesky decomposition in two directions and double summations are fairly time consuming. Moreover, the effectiveness of only frequency interpolation schemes is limited, and existing proper orthogonal decomposition (POD) schemes have their own limitations. An efficient approach to decomposition for a time-varying coherence matrix based on time-frequency interpolation has been proposed to accelerate Cholesky decomposition. The key idea is that the decomposition of a coherence matrix is continuous in both time and frequency directions and changes slowly, which is suitable for interpolation approximation. Naturally, conducting interpolation in both directions can greatly reduce the operations of a Cholesky decomposition. Then a diagonal POD strategy is taken into account to further factorize the diagonal elements of interpolated decomposition results, combined with accurate evolutionary spectra. Furthermore, each group of time functions is fully utilized to take into account the dissimilar spectra in different component processes. The efficiency and accuracy of the proposed method are evaluated in a numerical example. The results show that the simulation is very efficient, and both time-frequency interpolation approximation and POD reconstruction–based results agree well with target curves.