The Non-Linear Chaotic Model Reconstruction for the Exerimental Data Obtained From Different Dynamic System
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摘要: 动力系统实测非线性混沌数据的模型重构技术是相空间重构的重要内容。在判定了实测数据的非线性混沌特征,计算了实测数据的分维数,Lyapunov指数,并对其进行了本征值分解和噪声去除及确定其模型阶数以后,提出了一个动力系统实测数据的非线性混沌模型,给出了相应的模型参数辨识方法,并用其确立的混沌模型进行了预测工作,计算结果表明:模型参数辨识方法能迅速地将参数估计值带到多峰目标函数的全局最少值附近,然后再采用优化理论能较准确地求出模型的参数,用得到的混沌模型对系统进行预测工作其预测效果良好,且混沌时序不可能作长期预测。
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关键词:
- 非线性 /
- 混沌时序 /
- Lyapunov指数 /
- 混沌模型 /
- 参数辨识
Abstract: The non-linear chaotic model reconstruction is the major important quantitative index for describing accurate experimental data obtained in dynamic analysis. A lot of work has been done to distinguish chaos from randomness, to calulate fractral dimension and Lyapunov exponent, to reconstruct the state space and to fix the rank of model. In this paper, a new improved EAR method is presented in modelling and predicting chaotic timeseries, and a successful approach to fast estimation algorithms is proposed. Some illustrative experimental data examples from known chaotic systems are presented, emphasising the increase in predicting error with time. The calculating results tell us that the parameter identification method in this paper can effectively adjust the initial value towards the global limit value of the single peak target function nearby. Then the model paremeter can immediately be obtained by using the improved optimization method rapidly, and non-linear chaotic models can not provide long period superior predictions. Applications of this method are listed to real data from widely different areas.-
Key words:
- non-linear /
- chaotic timeseries /
- Lyapunov exponent /
- chaotic model /
- parameter identification
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[1] Wu Ya,Yang Shuzi.Application of several timeseries models in prediction[A].In:Applied Time Series Analysis[M].Beijing:World Scientific Publishing,1989. [2] Chen C H.Applied Timeseries Analysis[M].Beijing:World Scientific Publishing Cor,1989. [3] Yang Shuzi,Wu Ya.Applied Timeseries Analysis in Engineering[M].Beijing:World Scientific Publishing Cor,1992. [4] 马军海,陈予恕,刘曾荣.动力系统实测数据的非线性混沌特性的判定[J].应用数学和力学,1998,19(6):481～488. [5] Nerenberg M A H.Correlation dimension and systematic geometric effects[J].Phys Rev A,1990,42(6):7065～7674. [6] Alan Wolf,et al.Determining Lyapunov exponent from a timeseries[J].Phys D,1985,16(9):285～317. [7] Mess A I,et al.Singular-value decomposition and embedding dimension[J].Phys Rev A,1987,36(1):340～347. [8] Ma Junhai.The Non-Linear Dynamic System Reconstruction of the Chaotic Timeseries,A Thesis for Degree of Engineering[D].Tianjin:Tianjin University,1997,5. [9] Zhang Qinghua.Wavelet networks[J].IEE Transections on Neural Networks,1992,6(11):889～898. [10] Liang Yuecao.Predicting chaotic timeseries with wavelet networks[J].Phys.D,1995,85(8):225～238. [11] Dean Prichard.Generating surogate date for time series with several simultaneously measured variables[J].Phys Rev Lett,1994,191(7):230～245. [12] Davies M E.Reconstructing attractions from filtered time series[J].Phys D,1997,101:195～206. [13] Alexet Potapov.Distortions of reconstruction for chaotic attractors[J].Phys D,1997,101(5):207～226. -
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