【作者】 修妍；

【导师】 马军海；

【作者基本信息】 天津大学 ， 管理科学与工程， 2007， 博士

【摘要】 随着非线性混沌动力学的发展,人们对时间序列的复杂性有了更深刻的认识,尤其是混沌时间序列的分析已经成为一个非常重要的研究方向。混沌时间序列分析包括混沌特征参数判别和混沌时序预测等方面,由于混沌现象普遍地存在于自然界中,因此混沌时序的分析在各种动力系统的混沌检验及预测等方面显得尤为重要。本文对混沌时序的判别及预测进行了研究,主要成果如下:1.应用Takens’估计方法研究了经典混沌系统所生成时间序列的分形特征。并运用Takens’估计法研究了上海证券数据A股指数开盘价、收盘价、最高价、最低价的分形特征,发现其分形维数随着时间推移有进一步增加的趋势。结合最大Lyapunov指数的计算结果,表明上海证券数据总体表现为低自由度的弱混沌系统。2.基于K熵理论首先研究了混沌时间序列的最大可预测度问题。在此研究工作的基础上,提出了一种运用RBF神经网络在K熵限定的最大可预测度内对混沌系统进行直接多步预测的方法,并以Lorenz系统为例对其进行了相应的预测研究。研究结果表明:本文提出的在K熵限定的最大可预测度内进行直接多步预测具有比递推多步预测运行速度快,且预测精度更高的特点,便于对系统的实时预测和控制。3.利用遗传算法强全局随机搜索特点,结合DRNN神经网络对非线性数据具有鲁棒性和自学习能力的优点,通过将历年的农机总动力数据作为时间序列进行分析,建立DRNN神经网络预测模型对农机总量进行了预测。通过与校验用数据的比较证明本文建立的预测模型具有较高的精度。4.在加权一阶局域预测模型的理论基础上,提出运用径向基神经网络代替加权一阶局域预测模型构成了基于径向基神经网络的局域预测模型。通过对Logistic映射以及Lorenz系统的三个分量的混沌时间序列的预测仿真,表明该预测方法对混沌时间序列的预测具有较好的效果。更多还原

【Abstract】 With the development of nonlinear chaotic dynamic, there are more profound recognitions to the complexity of time series. Especially the analysis of time series is becoming an important research aspect. The analyses of chaotic time series include identification of chaotic characteristic parameter and prediction of chaotic time series, and so on. Because chaotic phenomenon widely exists in nature, the analysis of chaotic time series is more important in the field of chaotic identification and prediction on many dynamic systems.The identification and prediction of chaotic time series are researched in the paper. The main contents are as follows:1. The fractal dimension of time series of classical chaotic systems is firstly confirmed by Takens’estimator method. Then Takens’estimator method is compared with G-P method, it shows that Takens’estimator method inherits all virtues of G-P method and has better characteristics than G-P method such as low computation complexity and fast calculation speed. The fractal characteristics of opening quotation, closing quotation, maximum price and minimum price in Shanghai stock market are calculated by Takens’estimator method. The results demonstrate that the fractal dimension of Shanghai stock data has increasing trends with time. To further prove the chaotic behaviors of Shanghai stock data, the maximum Lyapunov exponent is calculated by the approach of small data sets. The results also indicate that Shanghai stock data are a feeble chaotic system that is in low degree of freedom.2. The maximum predictability time of chaotic time series is studied on the basis of Kolmogorov entropy theory. Then a method of direct multi-step prediction of chaotic time series is proposed, which is based on Kolmogorov entropy and radial basis functions neural networks. And the Lorenz system is predicted by the method. Simulation results for direct multi-step prediction method are compared with recurrence multi-step prediction method. The results indicate that the direct multi-step prediction is more accurate and rapid than the recurrence multi-step prediction within the maximum predictability time of chaotic time series. So, it is convenient to forecast and control with real time using the method of direct multi-step prediction. 3.Agricultural machine power is forecast by diagonal recurrent neural network (DRNN) forecasting model, which is combined the characteristic of global random search of genetic algorithm with the virtue of robust and self-study for nonlinear data of DRNN and agricultural machine power data in history is analyzed by time series. The forecasting results is compared with verify data, that prove the forecasting model in this paper has higher precision.4. A local-region linear prediction method based on radial basis function neural net is presented for chaotic time series prediction, which theory foundation is add-weighted one-rank local-region single-step method. The prediction method is built by using RBFNN substitute for add-weighted one-rank model. The Logistic map and the three axes of Lorenz system are applied to verify the method. Simulation results indicate that the method is effective for prediction of chaotic time series.更多还原