Simulating Wind Speed Time Series by Karhunen-Loève Expansion - Xiao, Qing; Wu, Lianghong; Chen, Chaoyang (International Journal of Industrial Engineering: Theory, Applications and Practice, 2024)
This paper aims to simulate non-Gaussian wind speed time series X(t) with a prescribed probability distribution and a given autocorrelation function (ACF). Given a set of historical observations of wind speed time series, the quantile function of X(t) is ﬁtted by the generalized lambda distribution (GLD), the ACF of wind speed time series is ﬁtted by a weighted sum of products of Gaussian function and cosine function. Then, the marginal transformation is applied to map X(t) to a standard normal space, where the Karhunen-Lo`eve (K-L) expansion method is employed to construct a Gaussian stochastic process Z(t) to match the ACF of X(t). The proposed method features the advantage that the spectral decomposition can be performed analytically, analytical formulae can be derived to calculate eigenvalues and eigenfunctions of the ACF of X(t), and Z(t) can be conveniently constructed by K-L expansion. Finally, case studies are performed to check the proposed method, the results indicate that the K-L expansion and GLD can accurately capture the ACF and distribution function of wind speed time series.