一种辨识磨粒群分形无标度区的新算法

摘要/Abstract

摘要：

针对磨粒群分形维数计算精度偏低，且无标度区辨识过程中容易出现局部最优的问题，提出了一种辨识无标度区的新算法。首先利用模拟退火K-means算法对磨粒群r～N(r)(尺度~测度)双对数曲线的一阶局部导数聚类，剔除一阶导数为0及波动很大的区间，然后利用模拟退火K-means算法对曲线的二阶局部导数聚类，识别出精确的无标度区间。应用新算法对典型的分形图形进行了分形维数计算，计算结果与理论值吻合度较高;同时应用新算法对磨粒群的分形无标度区进行了辨识。研究表明：磨粒群的分形无标度区较宽，新算法对磨粒群等多孔图形的无标度区辨识效果较好，能显著提高磨粒群分形维数的计算精度。

关键词: 无标度区, 磨粒群, 分形维数, 模拟退火

Abstract:

To improve the calculation accuracy of the fractal dimension of wear particles and overcome the local optimum problem in identification of scaling region, a novel method of identifying scaling region was developed. First, the first partial derivative of the wear particles' scale r~measure N(r) double logarithmic curve were clustered using the simulated annealing K-means algorithm and regions of which first derivative was 0 or changed widely were removed based on the clustering result. Then the simulated annealing K-means algorithm was used again for the second partial derivative to identify the precise scaling region.Calculation results and the theoretical value are very close in application of the method to fractal dimension calculation of typical fractal images. Then the method was applied to identify the scaling region of wear particles. Results show that the scaling region of wear particles is wide; the new method is effective to distinguish the scaling region of porous graphics like wear particle sand can significantly improve the calculation accuracy of the fractal dimension of wear particles.

Key words: scaling region, wear particle, fractal dimension, simulated annealing

中图分类号:

TH117.1

张怀亮, 邹佰文, 肖雷. 一种辨识磨粒群分形无标度区的新算法[J]. 中国机械工程, 2014, 25(3): 371-376.

Zhang Huailiang, Zou Baiwen, Xiao Lei. A Novel Identification Algorithm for Fractal Scaling Regionof Wear Particles[J]. China Mechanical Engineering, 2014, 25(3): 371-376.

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