结构函数与均方根分形表征效果的比较

为了比较结构函数与均方根两种测度方法的分形表征效果，模拟了具有不同理论分形维数的Weierstrass—Mandelbrot分形轮廓曲线；制备了车削、磨削和砂纸打磨的不同粗糙表面，并提取了它们的轮廓曲线；然后用结构函数和均方根两种方法对理论和实际的轮廓曲线进行了分形表征和分维计算．研究表明，两种测度方法对分形模拟轮廓曲线均具有较好的表征效果；对于机加工粗糙表面，均方根测度方法比结构函数测度方法的适应性强，无标度区间宽，表征效果好；另外，均方根测度方法还具有物理意义明确，分维计算简单和分形表征直观等优点．

Comparison of Fractal Characterization Effects of Structure Function and Mean Square Root

In order to compare the fractal characterization effects of the structure function method and the mean square root method different Weierstrass-Mandelbrot fractal profile curves were simulated with known fractal dimensions. Three rough surfaces were machined by turning, grinding and rubbing with emery papers, and their profile curves were collected with stylus measurement and A/D techniques. And then, fractal characterizations and dimension calculations were conducted in two kinds of profile curves with the methods of the structure function and the mean square root. The investigations showed that for the simulated fractal curves, good fractal characterization effects were obtained by two methods; for the machined rough surfaces, the mean square root method has good adaptability to different surfaces over the structure function method. In addition, the mean square root method possesses the advantages of definite physical meanings and simple fractal dimension calculations.