基于相空间重构预测方法预测能力的评估

为了客观地评估基于相空间重构预测方法的预测能力,使用非线性局部Lyapunov指数来替代均方根误差。根据误差平均相对增长的饱和性质,可以确定预测方法的最大预测期限。通过计算得到重构Lorenz相空间和原始Lorenz相空间的最大预测期限分别是12,13s,k-近邻方法(k=1,2,3,4,5)的最大预测期限分别是12.0,9.8,9.7,9.2,8.8s,多变量预测方法的最大预测期限是12.8s,单变量预测方法的最大预测期限是12.0s。研究表明,重构的Lorenz系统的相空间可预报性与原始Lorenz相空间相当。此外,对于重构的Lorenz相空间,由于k-近邻方法集合了预测能力参差不齐的成员,导致其预测能力逊色于零级近似预测,多变量预测方法的预测能力与单变量预测方法几乎相当。

Evaluation of predictive abilities of nonlinear chaotic models based on reconstructed phase space

To evaluate the predictive ability of nonlinear chaotic models based on reconstructed phase space of Lorenz system more precisely, a new evaluation method was introduce based on the nonlinear local Lyapunov exponent, instead of Root-mean-square Error which may include much more uncertainty. In this paper, the predictive ability of nonlinear chaotic models was evaluated in light of their predictability which can be determined according to the saturation property of the mean relative growth of initial error. The results indicate that the predictability of the reconstructed Lorenz phase space is 12 s while the original phase space 13 s and k-Nearest Neighbors methods (when k equals 1,2,3,4,5) 12.0, 9.8, 9.7, 9.2, 8.8 s respectively. Besides, the predictability of univariate chaotic model and multivariate chaotic model is 12.0, and 12.8 s respectively. It is found that the predictability of the reconstructed Lorenz phase space is similar to the original Lorenz system, which testifies the feasibility of the prediction methods based on phase space reconstruction, to certain extent. Besides, for reconstructed Lorenz phase space k-Nearest Neighbors method is not superior to zeroth-order approximation for the poor performances of some members. In addition, compared with univariate chaotic model, multivariate chaotic model has almost parallel predictive ability.