Error Assessment for Spectral Representation Method in Wind Velocity Field Simulation

Stochastic wind velocity fields are usually simulated as $N$ -variate stationary Gaussian processes by using the spectral representation method (SRM). However, the temporal statistics estimated from one SRM-simulated sample wind process cannot coincide with the target characteristics; the disagreements can be described by the bias and stochastic errors. For controlling the errors efficiently, this paper assesses the errors produced by both the Cholesky decomposition-based SRM (CSRM) and the eigendecomposition-based SRM (ESRM). The SRM is revisited first, followed by computing the temporal mean value, correlation function, power spectral density (PSD), and standard deviation of the SRM-simulated wind process. It is shown that the temporal correlation function and standard deviation are Gaussian, while the temporal PSD is non-Gaussian. Further, as mathematical expectations and standard deviations of the corresponding temporal estimations, the bias errors and stochastic errors of all the first- and second-order statistics are obtained in closed form for both the CSRM and the ESRM; the closed-form solutions are then verified in the numerical example. More importantly, this example is employed for taking a clear look at and making a comparison between the stochastic errors produced by the CSRM and by the ESRM; observations suggest that (1) in sum, the ESRM produces smaller stochastic errors than the CSRM and (2) if the ESRM is employed, stochastic errors will be distributed to each component of the wind process in a more uniform pattern. Moreover, some practical approaches are proposed to control the stochastic errors.