分形维数在洪水分期的应用

分数阶积分是分形理论的一个重要分支，应用分数阶积分进行时间序列维数估计，其精度比box维数、量规法等方法高。在此方法的基础上，以金沙江上游石鼓站42年的流量数据为研究对象，对流量散点序列进行了分形分析，在初步证明洪峰散点序列是一种分形的前提下，将分数阶积分应用到洪水分期上，通过估算的维数确定洪水分期原则并定量划分了洪水的分期时间，论证了洪水分期的合理性，并将分数阶积分估算维数法与容量维数法进行比较。对比传统洪水分期方法，分形维数分期结果较为客观，受经验和人为影响较小，但是容量维数方法需要选择大量的洪峰点，分析计算的工作量很大，而分数阶积分具有运算方便、结果准确等优点，而且建立的分形函数关系方便进一步分析研究。〖

APPLICATION OF FRACTIONAL DIMENSION IN CLASSIFICATION OF SEASONAL FLOOD PERIODS

Fractional integral is an essential branch of fractal theory.In this paper,the authors adopted frac- tional integral in the evaluation of time series dimension,which has a higher accuracy than other methods such as box dimension,gauge method and so on.The characteristics of flood event series were then analyzed by using fractal theory.It is shown that the flood events have the character of self-similarity.The authors applied fractional integral in the classification of seasonal flood periods,and compared with the method of capacity dimension by taking the discharge data of Shigu station in the upriver of Jinshajiang as the major objective of research.The classification results using fractional dimension method turned out to be more ob- jective for less subjected to experiences and anthropogenic influence.However,due to the large demand of flood peak points,the workload of analysis and calculation is enormous.Fractional integral is conveniently operated with the production of accurate results;in addition,the established fractal function relationship provides convenience for further analysis.