分形分析方法在电树枝结构研究中的应用

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摘要聚合物绝缘材料中电树枝结构复杂多样, 不同结构电树枝具有不同的分形维数。本文利用Matlab编程, 采用计盒维数法对不同结构形状电树枝图像的分形进行了分析计算。计算结果表明电树枝形状越复杂, 其计盒分形维数和局部分形维数越大。在二维平面上, 电树枝的计盒分形维数越小, 其发展空间越大, 发展速度越快。不同结构电树枝的稳定局部分形维数分布在一定的范围内, 因此可以从分形维数理论上对不同结构形状的电树枝进一步进行分类。本文基于所提出的方法, 分别对聚乙烯及聚乙烯/蒙脱土纳米复合材料中不同生长阶段和复杂结构的电树枝进行了分析计算。

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	张晓虹
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关键词 ：电树枝结构, 计盒分形维数, 局部分形维数, 电树枝分类

Abstract：The shapes of electrical trees in polymeric insulating materials are complex and diverse, and the different shapes of the electrical trees have different fractal dimensions. In the present paper, box-counting dimension method is used though Matlab programming, for analyzing and calculating the fractal images of different shapes of electrical trees. The results show that the more complex the shapes of electrical trees is, the greater its box-counting fractal dimension and the local fractal dimension are. In the two-dimensional plane, the smaller of the box-counting dimension of electrical trees is, its space of spreading is greater and rate of spreading is faster. The stable local fractal dimension of different shapes of electrical trees is in a certain range, so electrical trees can be classified base on the fractal theory. Electrical trees at different growth stages and in complex shapes in polyethylene and polyethylene/ montmorillonite nanocomposites are analyzed and calculated based on the proposed method.

Key words： Shapes of electrical trees box-counting dimension local fractal dimension classification of electrical trees

收稿日期: 2012-03-30 出版日期: 2013-11-27

PACS:

TM215

基金资助:国家自然科学基金（51077029）和高等学校博士学科点专项科研基金（20092303110003）资助项目。

作者简介: 张晓虹女,1958年生,博士,教授,博士生导师,主要从事工程电介质理论与应用技术方面的研究。迟晓红女,1987年生,博士研究生,主要从事高电压与绝缘技术方面的研究。

引用本文:

张晓虹, 迟晓红, 高俊国, 王伟. 分形分析方法在电树枝结构研究中的应用[J]. 电工技术学报, 2013, 28(1): 14-20. Zhang Xiaohong, Chi Xiaohong, Gao Junguo, Wang Wei. Application of Fractal Analysis on Researching Shapes of Electrical Trees. Transactions of China Electrotechnical Society, 2013, 28(1): 14-20.

链接本文:

http://dgjsxb.ces-transaction.com/CN/Y2013/V28/I1/14

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