Eigenanalysis of vector autoregressive model for optimal fitting of a predefined cross power spectral density matrix: Application to numeric generation of stationary homogeneous isotropic/anisotropic turbulent wind fields

Abstract

Turbulent wind fields representing realistic atmospheric conditions are required for wind turbine load calculations. For a statistically stationary situation, the wind loads on a wind turbine depend, among other wind characteristics, on the spectra and spatial coherences of the velocity field in the rotor plane (i.e. the cross-power spectral density matrix). In this study, a novel approach is proposed to optimally calibrate the parameters of a vector autoregressive model for reproducing a predefined target cross-power spectral density matrix to be used for the synthetic generation of turbulent wind fields. This approach is based on the eigenanalysis of the companion matrix of the vector autoregressive model. In this work, the cross-power spectral density matrix, for different turbulent wind conditions, is considered as targets. This approach is compared to the state-of-the-art approaches for calibration of parameters of vector autoregressive models. The discussion covers the implications derived from approaching the vector autoregressive model determination in the frequency domain or in the time domain.