含噪混沌时间序列相空间重构参数估计-计算机应用技术专业论文.docxVIP

重庆大学硕士学位 重庆大学硕士学位论文 英文摘要 PAGE PAGE IV whose dimension is equal to phase space’s in algebraic geometry. In order to estimate the optimal delay time of chaotic system, the method finds the first local minimum value of nonlinear multiple autocorrelation function as delay time. The numerical results show that, the result of low dimension system by this method is equal to the best delay time when the noise level is up to 80%; the result of high dimension system is appropriate when the noise level is up to 60%. In addition, the result of 100 data points is equal to 2000 data points’ for low dimension system; the results are same when noise level being below 20% and very close to each other when noise level being above 20% for high-dimensional chaotic systems. The time complexity of nonlinear multiple autocorrelation function is low. Experimental results show that as the embedding dimension increases, delay time estimated by the function owns supremum and infimum. Based on this point, this paper also presents a new method to estimate delay time and embedding dimension. This method calculates the optimal delay time for every embedding dimension, and then selects the value corresponding to the first point of the curve tending to be stable as parameters. The numerical results show that delay time and embedding dimension by the method are appropriate. Keywords：Chaotic Time Series, Phase Space Reconstruction, Delay Time, Embedding Dimension, Noise Level 重庆大学硕士学位 重庆大学硕士学位论文 目录 目 录 中文摘要I 英文摘要 II 1 绪 论 1 1.1 课题产生背景和研究意义 1 1.2 国内外研究现状 2 1.3 研究目标 4 1.4 研究内容 4 1.5 论文组织结构 4 2 混沌理论 6 2.1 混沌相关概念 6 2.1.1 混沌定义 6 2.1.2 相空间 7 2.1.3 吸引子 7 2.1.4 初值敏感性 8 2.1.5 分形 9 2.2 混沌识别 9 2.2.1 Lyapunov 指数 10 2.2.2 关联维数 11 2.2.3 功率谱 12 2.3 相空间重构 14 2.4 本章小结 16 3 相空间重构参数估计现有方法分析 17 3.1 时间延迟估计现有方法分析 17 3.1.1 复自相关法分析 18 3.1.2 平均位移法分析 20 3.1.3 互信息法分析 23 3.1.4 C-C 法分析 25 3.2 嵌入维数估计现有方法分析 27 3.2.1 G-P 方法分析 27 3.2.2 伪近邻法分析 28 3.2.3 Cao 法分析 28 3.3 本章小结 31 4 相空间重构参数估计新方法 33 4.1 混沌系统的非