ABSTRACT

This paper sets out to simulate non-Gaussian wind speed time series. Given a set of historical wind speed observations, if the cumulative distribution function is not explicitly known, a probability distribution based on Fourier series is developed to recover the analytical expression of the cumulative distribution function. The marginal transformation is then applied to map wind speed observations to the standard normal space, where the autocorrelation function is represented by a weighted sum of Chebyshev polynomials. Finally, an explicit formula is derived to generate samples of wind speed time series. Testing on three sets of historical wind speed observations, it shows that the proposed method can well match the cumulative distribution function and autocorrelation function of wind speed time series, the absolute errors between the fitted cumulative distribution function and empirical cumulative distribution function are less than $0.015$; the autocorrelation function of generated wind speed time series is in a good agreement with that of historical wind speed observations, the differences are less than $0.15$.

摘要

本文着手模拟非高斯风速时间序列。给定一组历史风速观测值，如果累积分布函数不是明确知道的，则开发基于傅立叶级数的概率分布来恢复累积分布函数的解析表达式。然后应用边际变换将风速观测值映射到标准正态空间，其中自相关函数由切比雪夫多项式的加权和表示。最后，推导出一个显式公式来生成风速时间序列的样本。对三组历史风速观测值进行测试，表明该方法能够很好地匹配风速时间序列的累积分布函数和自相关函数，$0.015$; 生成的风速时间序列的自相关函数与历史风速观测值吻合较好，差异小于$0.15$.