高阶常微分方程的演化建模用于时间序列的分析  

THE EVOLUTIONARY MODELING OF HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS FOR TIME SERIES ANALYSIS

作　　者：曹宏庆[1] 康立山[1] 陈毓屏[1] 

机构地区：[1]武汉大学软件工程国家重点实验室,武汉430072

出　　处：《小型微型计算机系统》2000年第4期344-349,共6页Journal of Chinese Computer Systems

基　　金：国家自然科学基金!(编号 :6963 5 0 3 0 );国家 863高技术项目基金;湖北省重大科技项目资助

摘　　要：本文提出采用高阶常微分方程模型代替传统的时序分析中所用的 ARMA模型来实现一维动态系统的建模 ,并针对传统方法建模过程中所遇到的困难 ,设计了将遗传程序设计与遗传算法相嵌套的混合演化建模算法 ,以遗传程序设计优化模型结构 ,以遗传算法优化模型参数 ,首次成功地实现了动态系统的高阶微分方程建模过程自动化 .对三个典型时间序列实例的实验结果表明 :采用此算法可由计算机自动发现适合描述该动态系统的高阶常微分方程模型 ,这些模型不仅具有较好的拟合和预测效果并且形式上也较传统的 ARMA模型更为灵活 .这表明本算法的研究可为时间序列的分析提供一个崭新而有力的工具 .This paper proposes a new way of modeling one dimentional dynamical systems by higher order ordinary differential equations (HODEs) instead of by the ARMA models used in the traditional analysis of time series. To overcome the drawbacks in traditional modeling methods, a hybrid evolutionary modeling algorithm (HEMA) is proposed to approach the modeling of dynamic systems whose main idea is to embed genetic algorithm (GA) in genetic programming (GP) where GP is employed to optimize the structure of a model, while a GA is employed to optimize the parameters of a model. It has taken a first step towards automating the modeling process of HODEs for dynamic systems successfully. The experimental results of three typical practical examples of time series indicate that, by running the HEMA, the computer can discover the HODEs models automatically which are appropriate to describe the system. Those models can not only fit the observed data but also give good predictions. Furthermore, their structures are more flexible than traditional ARMA models. This shows that the HEMA has great potential to provide a new and powerful tool for the analysis of time series.

关 键 词：时间序列 高阶常微分方程 建模 遗传程序设计 

分 类 号：O211.61[理学—概率论与数理统计] TP311[理学—数学]