小波变换方法评价曲线的分形特征

WAVELET TRANSFORM METHOD EVALUATE THE FRACTAL CHARACTERIZATION OF PROFILES

应用小波变换对Kiesswetter曲线和3种方法生成的分数维布朗运动（FBm）进行了分析,验证了该方法计算分形维数具有较高的精度。在宽广的分形维数范围内,与其他7种计算方法比较表明,小波变换方法的精确性和一致性都最好。小波变换为进一步分辨确定性信号、分形特征的信号或完全随机性的信号提供了一种有效工具,为评价粗糙表面形貌的分形特征提供了前提条件。

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.