| 引用本文: | 张雨,任成龙.确定重构相空间维数的方法.[J].国防科技大学学报,2005,27(6):101-105.[点击复制] |
| ZHANG Yu,REN Chenglong.The Methods to Confirm the Dimension of Re-constructed Phase Space[J].Journal of National University of Defense Technology,2005,27(6):101-105[点击复制] |
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| 确定重构相空间维数的方法 |
| 张雨1,2, 任成龙1 |
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(1.长沙理工大学 载运工具研究所,湖南 长沙 410076;2.南京工程学院 机械工程系,江苏 南京 210013)
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| 摘要: |
| 计算混沌统计特征量前必须先获得重构相空间的维数，因此给出了最大特征值不变法、几何不变量法、虚假邻点法、预测误差最小法、最小Shannon熵法、经验赋值法六种确定方法，得出了应用最大特征值不变法和最小Shannon熵法的工程案例计算结果。 |
| 关键词: 混沌动力学 重构相空间 最小嵌入维 符号序列分析 Shannon熵 |
| DOI： |
| 投稿日期：2005-06-18 |
| 基金项目:湖南省自然科学基金(03JJY3006);江苏省高校自然科学研究计划(04KJB580037) |
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| The Methods to Confirm the Dimension of Re-constructed Phase Space |
| ZHANG Yu1,2, REN Chenglong1 |
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(1.Institute of Vehicle Operation Engineering, Changsha Univ. of Science and Technology, Changsha 410076, China;2.Department of Mechanism, Nanjing Institute of Technology, Nanjing 210013, China)
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| Abstract: |
| It is necessary to get the dimension of re-constructed phase space before calculating the chaotic statistical. characteristics. Six methods are offered which are the measurement of the on unaltered maximal characteristic value, the measurement of changeless geometry mete, the measurement of false nearest neighbors, the measurement of minimum prediction error, the measurement of minimal Shannon entropy, and the measurement of the experience evaluation. An engineering case is given to explain the application of the measurements of the unaltered maximal characteristic value and minimal Shannon entropy. |
| Keywords: chaos dynamics re-constructed phase space minimum embedding dimension symbolic series analysis Shannon entropy |
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