摘 要：针对时间序列风速确定性与随机性相结合的复杂非线性特征，基于相空间重构理论和最大Lyapunov指数对其进行混沌与分形特征分析。首先，以经典Lorenz混沌系统及非混沌完全随机白噪声时间序列为验证算例，通过相空间重构和最大Lyapunov指数法判断以上2种非线性时间序列的混沌特征，分别从定性和定量的角度验证了所提方法的可行性；其次，对美国风能研究中心实测风速数据进行相空间重构，计算其最大Lyapunov指数并估算其可预测时间，最后采用G-P算法分析了实测风速时间序列的饱和关联维数。结果表明：相空间重构理论及最大Lyapunov指数法均可作为判断混沌特征的重要方法，时间序列风速具有明显的混沌分形特征及短期可预测性。

Abstract:In view of wind speed time series showing the complex nonlinear characteristics of the combination of determinacy and randomness,the chaotic and fractal characteristics are analyzed based on phase space reconstruction theory and maximum Lyapunov exponent. First of all, based on the classical Lorenz chaotic system and non-chaotic completely random white noise time series, the chaotic characteristics of the above two kinds of nonlinear time series are studied and determined by the phase space reconstruction and maximum Lyapunov exponent methods. Then, the phase space of the measured wind speed data of the US wind energy center is reconstructed and the maximum Lyapunov exponent is calculated and the predictable time is estimated. Finally, the G-P algorithm is used to analyze the saturation correlation dimension of measured wind speed time series. The results indicate that the phase space reconstruction theory and the maximum Lyapunov exponent method can be used as effective methods to judge chaos characteristics.Time series wind speed has clear chaos and fractal characteristics and shortterm predictability.

TK83

国家自然科学基金（51676131，51176129）