分形分析方法在电树枝结构研究中的应用  

Application of Fractal Analysis on Researching Shapes of Electrical Trees

作　　者：张晓虹[1] 迟晓红[1] 高俊国[1] 王伟[1] 

机构地区：[1]哈尔滨理工大学工程电介质及其应用教育部重点实验室,哈尔滨150080

出　　处：《电工技术学报》2013年第1期14-20,共7页Transactions of China Electrotechnical Society

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

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。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.

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 

分 类 号：TM215[一般工业技术—材料科学与工程]