镀层表面轮廓曲线分形维数计算方法的评价

发布时间：2018-05-19 07:33

本文选题：镀层 + 表面轮廓曲线　；参考：《电镀与涂饰》2017年08期

【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。
[Abstract]:The surface profile curve of the coating has fractal structure, which can be quantitatively characterized by fractal dimension (D). In order to verify the accuracy of the existing D value calculation methods, the standard surface contour curves with different D values are generated by using W M fractal function, and the vertical section method, the size method, the box dimension method, the variance method, the structure function method are used. The D value is calculated by eight methods, namely, covariance weighting method, power spectrum method and root mean square method. The results show that the relative error range of the size method is between 6.20% and 22.77%, and the average relative error is 16.76%. The second is the covariance weighting method, the relative error range is 2.17 and 21.35, and the average relative error is 11.73. The average relative errors of power spectrum method and variance method are 8.61% and 5.25%, respectively; the relative error range of root mean square method and vertical section method are 0.510.84% and 0.193.97, respectively; the maximum relative error of structural function method is only 1.21, the minimum relative error is as low as 0.01 and the average relative error is only 0.45. Therefore, the structural function method is the most accurate and the best method to calculate fractal dimension.
【作者单位】：广州民航职业技术学院飞机维修工程学院;华南理工大学机械与汽车工程学院;广州白云国际机场地勤服务有限公司机务工程部;
【基金】：中国民用航空局2015年民航科技创新引导资金广东省二类品牌专业建设项目广州民航职业技术学院校级科研项目
【分类号】：TQ153

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