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

中图分类号: 

• TP18