Calculating the fractal dimension from 3d images of electrical trees

Summary

Electrical treeing phenomenon is considered the main way to electrical breakdown of polymers, and therefore, a precursor of power equipment failure. One method for studying electrical trees is analysing their shape and geometrical structure. Fractal dimension, estimated through the box-counting method, has become a standard quantifier for the characterisation of the shape of an electrical tree. Fractal dimension has typically been calculated using two-dimensional (2D) images of a tree; however, the fractal dimension of 2D projected patterns differ from those of the complete three-dimensional (3D) pattern, due to 2D projection overlapping. The authors have previously shown that electrical trees can be 3D imaged and the tree structure extensively characterised. This paper presents a comparison between the estimated box-counting fractal dimension from 2D and 3D images of electrical trees. Electrical trees in epoxy resin were conventionally grown in laboratory and 3D imaged using X-ray computed tomography (XCT). The fractal dimensions from the 3D image and 2D projections of each tree were compared. For the cases analysed, the fractal dimension of 2D projections of the tree was not affected by the observation angle, and its value was lower than the dimension from the complete 3D model. The results emphasise the importance of 3D analysis for improved and accurate measurement of parameters that characterise the structure of electrical trees.

Additional informations

Authors

Khamlichi, NIRGUDE, DEVENDRANATH, Mehanna, LV

Keywords

Electrical trees, fractal dimension, 3D, box-counting