低维混沌时序非线性动力系统的预测方法及其应用研究

马军海; 陈予恕

低维混沌时序非线性动力系统的预测方法及其应用研究

马军海¹,
陈予恕²

1.
天津大学管理学院, 天津 300072;
2.
天津大学力学系, 天津 300072

基金项目: 国家自然科学基金资助项目(19990510);国家重点基研础究专项经费资助项目(G1998020316)

详细信息

作者简介:
马军海(1965-),男,教授,二站博士后;陈予恕(1931-)山东肥城人,教授,博导,俄国科学院外籍院士.

中图分类号: O175.14;O241.1
计量
- 文章访问数: 2541
- HTML全文浏览量: 89
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- 被引次数: 0
出版历程
- 收稿日期: 2000-02-22
- 修回日期: 2001-01-08
- 刊出日期: 2001-05-15

Study on the Prediction Method of Low-Dimension Time Series That Arise From the Intrinsic Nonlinear Dynamics

MA Jun-hai¹,
CHEN Yu-shu²

1.
School of Management, Tianjin Univerity, Tianjin 300072, P R China;
2.
Department of Mechanics, Tianjin University, Tianjin 300072, P R China

摘要

摘要: 主要研究由低维混沌时序所确定的非线性动力系统的预测方法及其应用。在国外学者研究工作的基础上,应用一种非线性混沌模型在相空间内对时序进行重构工作,先通过改进的最小二乘方法来估计模型的参数,满足一定精度后,再采用最优化方法来估计模型的参数,并用所求得的混沌时序模型在其相空间内对时序的未来值进行预测。给出了非常有代表性的实例对文中模型和算法进行验证。结果发现采用该算法能较准确地求得模型的参数,在相空间中对混沌时序进行预测,将传统方法中的外推变成了相空间中的内插,及选取最佳的模型阶数等工作都能增加预测的准确程度,且混沌时序不可能进行长期的预测。
- 非线性 /
- 混沌模型 /
- 参数识别 /
- 时序预测
Abstract: The prediction methods and its applications of the nonlinear dynamic systems determined from chaotic time series of low dimension are discussed mainly.Based on the work of the foreign researchers,the chaotic time series in the phase space adopting one kind of nonlinear chaotic model were reconstructed.At first,the model parameters were estimated by using the improved least square method.Then as the precision was satisfied,the optimization method was used to estimate these parameters.At the end by using the obtained chaotic model,the future data of the chaotic time series in the phase space was predicted.Some representative experimental examples were analyzed to testify the models and the algorithms developed in this paper.The results show that if the algorithms developed here are adopted,the parameters of the corresponding chaotic model will be easily calculated well and true.Predictions of chaotic series in phase space make the traditional methods change from outer iteration to interpolations.And if the optimal model rank is chosen,the prediction precision will increase notably.Long term superior predictability of nonlinear chaotic models is proved to be irrational and unreasonable.
- nonlinear /
- chaotic model /
- parameter identification /
- time series prediction

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参考文献(19)

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