基于径向基函数神经网络的混沌时间序列相空间重构双参数联合估计

鉴于径向基函数(RBF)神经网络模型在非线性预测方面的优良性能, 提出了利用该预测模型对混沌时间序列相空间重构的两个关键参数——延迟时间和嵌入维数进行联合估计的方法, 并以客观的评价指标为依据给出其最优估计值. 以Lorenz系统为例进行数值分析, 得到RBF单步及多步预测模型中嵌入维数和延迟时间的最佳参数估计值, 并在原模型中对估计值进行校验. 结果表明, 该方法可以有效地估计出嵌入维数和延迟时间, 从而显著提高预测精度.

Parameter joint estimation of phase space reconstruction in chaotic time series based on radial basis function neural networks

In this paper, we propose a joint estimation method of two parameters for phase space reconstruction in chaotic time series, based on radial basis function (RBF) neural networks. And we obtain the best estimation values, according to some objective standards. Furthermore, The single-step and multi-step RBF prediction model is used to estimate the best embedding dimension and delay time, and Lorenz system is selected as an example. Finally, the estimation values are tested in the original model. The simulations show that we can obtain the best estimation values through the method, and the prediction accuracy is significantly improved.