混沌时间序列的局域高阶Volterra滤波器多步预测模型

依据相空间邻近轨道演化相似性特点建立训练模式，提出了基于自适应高阶非线性Volterra滤波器（HONFIR）的混沌时间序列多步预测模型（MSP-HONFIR）；通过定义距离相似度、趋势相似度来衡量轨道演化相似度，提出了混沌吸引子邻近轨道判别的新方法；从模型训练充分性角度出发探讨了MSP-HONFIR滤波器模型训练集规模控制的依据.数值研究表明MSP-HONFIR滤波器模型的多步预测性能优于原有HONFIR滤波器模型. 关键词： 混沌 非线性自适应预测 Volterra滤波器模型 训练模式

Local higher-order Volterra filter multi-step prediction model of chaotic time series

In general, the prediction modeling of chaotic time series is conducted by Volterra filters through constructing nonlinear fitting functions according to the methodology of pattern training. Since the proposed approach is consistent with the nonlinear characteristics of chaotic systems, the corresponding model turns to be more effective than conventional models. However, something abnormal is likely to occur, such as inadequate trainingor, over training, and the training data set size is not easy to choose, because the existing Volterra filters are trained point by point along the chaotic orbit. Based on the similarity of the evolving tendency of neighbor orbits in phase space, the chaotic time series multi-step-prediction model （MSP-HONFIR） employing the adaptive higher-order nonlinear Volterra filter （HONFIR） is constructed in this paper. A new method of choosing neighbor orbits in phase space is presented by considering the Euclidean distance and the evolving tendency. In addition, the criterion for the choice of the training data set size is discussed. Numerical experiments demonstrate that the performances of multi-step-prediction are improved compared to the original HONFIR method.