WAVELET TRANSFORM METHOD EVALUATE THE

FRACTAL CHARACTERIZATION OF PROFILES

Wang Anliang

(Institute of Mechanics, Chinese Academy of Sciences)

Yang Chunxin

(Beijing University of Aeronautics and Astronautics)

Abstract: Based on the Kiesswetter curve and fractal Brown motion functions with known fractal dimension, wavelet transform method can present accurately the fractal dimension. Furthermore, covering a wide fractal dimension, it is indicated that wavelet transform method is better for calculating the fractal dimensions of the fractal profiles than other 7 methods, which are the box dimension method, the yard stick method, the co-variation method, the structure function method, the variation method, the power spectrum method and the rescaled range analysis method. Wavelet transform method can be applied to distinguish the determinacy, fractal and stochastic process, and to evaluate the fractal characterization of surface profiles.

Key words: Wavelet transform  Fractal Brown motion  Kiesswetter curve  Fractal dimension

CLC No: TH161.14

国家自然科学基金(50176003)和中科院力学所非线性力学国家重点实验室资助项目. Received 20001218, received in revised form 20011020