【摘要】 镀层表面轮廓曲线具有分形结构,可以用分形维数(D)来定量表征。为了验证现有D值测算方法的准确性,利用W–M分形函数生成了具有不同D值的标准表面轮廓曲线,并用垂直截面法、尺码法、盒维数法、方差法、结构函数法、协方差加权法、功率谱法、均方根法共8种方法计算了其D值。研究表明,尺码法的相对误差范围在6.20%~22.77%之间,平均相对误差最大,为16.76%;其次是协方差加权法,其相对误差范围为2.17%~21.35%,平均相对误差为11.73%;盒维法、功率谱法和方差法的平均相对误差分别为8.61%、6.92%和5.25%;均方根法和垂直截面法的相对误差范围分别为0.51%~9.84%和0.19%~3.97%;结构函数法的最大相对误差仅为1.21%,最小相对误差低至0.01%,平均相对误差仅为0.45%。因此,结构函数法最准确,是计算分形维数的最佳方法。更多还原

【Abstract】 The surface profile curve of coating is fractal and can be quantitatively characterized by the fractal dimension(D). To verify the accuracy of the present methods for calculating the D value, the W-M fractal function was used to generate the standard surface profile curves with different fractal dimensions, and then the D values were calculated by eight methods including the vertical section method, yard stick method, box counting method, variation method, structure function method, weighted covariation method, power spectrum density method and root mean square method. The results indicated that the yard stick method has a maximum relative error ranging from 6.20% to 22.77% with a mean relative error of 16.76%, which is the largest among those of all the methods; the relative error of weighted covariation method is in a range between 2.17% and 21.35%, and 11.73% averagely; the mean relative errors of box dimension method, power spectrum density method, and variation method are 8.61%, 6.92% and 5.25%, respectively; the mean relative errors of mean square root method and vertical section method are 0.51%-9.84% and 0.19%-3.97%, respectively; and the structure function method has a relative error of 1.21% maximum, 0.01% minimum, and 0.45% averagely. Therefore, the structure function method has the highest accuracy and is most suitable for calculating the fractal dimension.更多还原