水文时间序列的混沌性分析及预测研究（毕业设计）

目 录

摘 要： .............................................................................................................................. 2 第一章 绪论 ...................................................................................................................... 1

1.1研究背景 ............................................................................................................. 1 1.2水文时间序列研究现状 ..................................................................................... 2 1.3混沌理论 ............................................................................................................. 3 1.4本文研究内容和方法 ......................................................................................... 4 第二章 重构水文系统相空 .............................................................................................. 7

2.1重构相空间理论 ................................................................................................. 7 2.2水文系统重构延迟时间的确定 ......................................................................... 7 2.3水文系统重构嵌入维数的确定 ....................................................................... 11 第三章 水文时间序列的混沌性识别 ............................................................................ 13

3.1功率谱方法 ....................................................................................................... 13 3.2主分量分析法 ................................................................................................... 15 3.3庞加莱截面法 ................................................................................................... 16 3.4李雅普诺夫指数法 ........................................................................................... 16 第四章 水文混沌时间序列的Volterra预测 ............................................................ 18

4.1 Volterra泛函级数 ......................................................................................... 18 4.2水文混沌时间序列Volterra自适应模型 ..................................................... 18 4.3 Volterra滤波器自适应算法 ......................................................................... 19 4.4水文混沌时间序列Volterra自适应模型算法及实现 ................................. 20 4.5水文混沌时间序列Volterra自适应预测 ..................................................... 21 第五章 水文混沌时间序列的RBF预测 ........................................................................ 23

5.1RBF神经网络结构模型 ..................................................................................... 23 5.2RBF神经网络的学习算法 ................................................................................. 23 5.3水文时间序列的RBF预测 ................................................................................ 24 第六章 总结与展望 ........................................................................................................ 26

6.1 总结 .................................................................................................................. 26 6.2展望 ................................................................................................................... 26 参考文献 .......................................................................................................................... 27 附录： .............................................................................................................................. 29 致谢 .................................................................................................................................. 43

水文时间序列的混沌特性及预测研究

作者：侯琪武 专业班级：热动101 指导教师：王斌

摘 要：作为现代水文预测领域的一个重要分支，水文非线性时间序列的预测受到国内外专家的

青睐。为了丰富水文非线性系统的分析方法和理论，本文首先提出了两种水文预测模型，一种是Volterra滤波器自适应预测模型，另一种是径向基函数神经网络预测模型。利用这两种模型进行水文预测首先需要重构相空间，并进行混沌性识别，通过理论推导和数值模拟相结合的方法，得到了lorenz系统重构相空间的两个重要参数，其中延迟时间为10，嵌入维数为4。并利用庞加莱截面法和李雅普诺夫指数法等方法对lorenz系统进行了混沌性识别，证明了该系统是混沌系统。利用Volterra滤波器自适应模型和径向基函数神经网络模型对lorenz系统进行了预测和仿真，取得了良好的效果，预测误差都在允许的范围之内，证明前面所选的参数是合理的。在刚开始的时候预测误差较小，越到后面误差就逐渐增大了，这也印证了混沌系统的特点-对初始条件的敏感依赖性，只能对其进行短期的预测，和理论推导完全吻合。

关键词：水文预测；Volterra；径向基函数；lorenz

Hydrological characteristics of chaotic time series and forecasting

Author: Qi-Wu Hou Supervisor: Bin Wang

Abstract: As the field of modern hydrological forecasting is an important branch of nonlinear time

series forecasting hydrological favored by domestic and foreign experts. In order to enrich the hydrological nonlinear system analysis methods and theories, this paper proposes two hydrological forecasting model, a prediction model is adaptive Volterra filter, the other is a radial basis function neural network prediction model. Both models make use of hydrological forecasting first need reconstruction phase space and chaotic recognition, through theoretical analysis and numerical simulation methods have been two important parameters lorenz system reconstruction phase space, in which the delay time is 10, embedding dimension is 4. And use the Poincare section method and other methods for Lyapunov exponent lorenz chaotic system of identification to prove that the system is chaotic system. Volterra adaptive filter model and the use of radial basis function neural network model to predict lorenz system and simulation, and achieved good results, prediction errors are within the allowable range, pr …… 此处隐藏：4831字，全部文档内容请下载后查看。喜欢就下载吧 ……