高阶常微分方程的演化建模用于时间序列的分析

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个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，

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

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.