计算机工程 ›› 2010, Vol. 36 ›› Issue (2): 18-20.doi: 10.3969/j.issn.1000-3428.2010.02.007

• 博士论文 • 上一篇    下一篇

基于小波变换的气温趋势和分形特征分析

毛军军1,2,朱良燕1,2,张学友1,2,吴 涛1,2,3   

  1. (1. 安徽大学数学科学学院,合肥 230039; 2. 安徽大学智能计算与信号处理教育部重点实验室,合肥 230039; 3. 南京大学计算机软件新技术国家重点实验室,南京 210093)
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2010-01-20 发布日期:2010-01-20

Analysis of Temperature Trend and Fractal Feature Based on Wavelet Transform

MAO Jun-jun1,2, ZHU Liang-yan1,2, ZHANG Xue-you1,2, WU-tao1,2,3   

  1. (1. School of Mathematical Sciences, Anhui University, Hefei 230039; 2. Key Laboratory of Intelligent Computing & Signal Processing of Ministry of Education, Anhui University, Hefei 230039; 3. State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093)
  • Received:1900-01-01 Revised:1900-01-01 Online:2010-01-20 Published:2010-01-20

摘要: 将小波变换、多重分形和R/S分析法相结合,选择db4小波函数进行小波变换,利用分解与重构算法,从分形维数、非周期循环长度、奇异性指数、多重分形谱等方面探讨合肥市近54年来气温系统的动力学分形特性和演化规律,分析合肥市气温趋势的持续性、长期记忆性、统计自相似性和多重分形性。分析结果表明,合肥市气温变化过程是一个层次分明的过程,具有多标度结构且1月、8月、11月的分形维数较高,气温不规则程度高,复杂性高。

关键词: 小波变换, 分形特征, Hurst指数, 多重分形

Abstract: This paper analyses the dynamic characteristics and evolutionary principle of Hefei’s temperature over the past fifty-four years, it combine R/S analysis with wavelet transform, choosing db4 wavelet function, deconstruct and reconstruct the original data. It analyses the temperature based on multi-fractal analysis, discusses the stability, long-term memory, statistical self-similarity and multi-fractal of the temperature trend in Hefei from fractal dimension, non-periodic length of circulation, singular index, and multi-fractal spectrum. Analysis results show that the temperature change in Hefei whose level is clear has a multiple-scale structure, the fractal dimension of Janmary, August, November shows that the irregular degrees and the complexities of temperatures are higher than the others.

Key words: wavelet transform, fractal feature, Hurst exponent, multi-fractal

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