A Novel Identification Algorithm for Fractal Scaling Regionof Wear Particles

Abstract

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

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

CLC Number:

TH117.1

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.

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.

References

[1]Podsiadlo P，Stachowiak G W. Scale-invariant Analysis of Wear Particle Surface Morphology: II. Fractal Dimension[J]. Wear，2000，242(1/2)：180-188.
[2]Yuan C Q，Li J，Yan X P，et al. The Use of the Fractal Description to Characterize Engineering Surfaces and Wear Particles[J]. Wear，2003，255(1/6)：315-326.
[3]郭中领，符素华，张学会,等. 土壤粒径重量分布分形特征的无标度区间[J]. 土壤通报，2010，41(3)：537-541.
Guo Zhongling，Fu Suhua，Zhang Xuehui，et al. Scale-free Domain of Fractal Characteristic of the Soil Particle-size Distribution[J]. Chinese Journal of Soil Science，2010，41(3)：537-541.
[4]Tang G J，Du B Q，Wang S L. Scaleless Band Automatic Identification for Fractal Fault Diagnosis of Rotor System[J]. J. Power Eng.，2009，29：440-444.
[5]秦海勤，徐可君，江龙平. 分形理论应用中无标度区自动识别方法[J]. 机械工程学报，2006，42(12)：106-109.
Qin Haiqin，Xu Kejun，Jiang Longping. Fractal Scaleless Band Automatic Identification for Fractal Theory Application[J]. Chinese Journal of Mechanical Engineering，2006，42(12)：106-109
[6]Fang Zhijun，Zhou Yuanhua，Zou Daowen，et al. Efficient Scheme for Determining Fractal Scaleless Range[J]. Journal of Infrared and Millimeter Waves，2004，23(5)：321-324.
[7]党建武，施怡，黄建国. 分形研究中无标度区的计算机识别[J]. 计算机工程与应用，2003，39(12)：25-27.
Dang Jianwu，Shi Yi，Huang Jianguo. The Identification of Fractal Scaleless Band in the Study of Fractal with Computers[J]. Computer Engineering And Applications，2003，39(12)：25-27.
[8]巫兆聪. 分形分析中的无标度区确定问题[J]. 测绘学报，2002，31(3)：240-244.
Wu Zhaochong. Determination of Fractal Scaleless Range[J]. Acta Geodaetica Et Cartographica Sinica，2002，31(3)：240-244.
[9]庞茂，吴瑞明，谢明祥. 关联维数快速算法及其在机械故障诊断中的应用[J]. 振动与冲击，2010，29(12)：106-109.
Pang Mao，Wu Ruiming，Xie Jingxiang. Improved Correlation Dimension Algorithm with Its Application to Mechanical Fault Diagnosis[J]. Journal of Vibration and Shock，2010，29(12)：106-109.
[10]栾海军，汪小钦.多源遥感影像分形特征分析[J].遥感信息，2010，3:7-12.
Luan Haijun，Wang Xiaoqin. Fractal Features Analysis of Multi-source Remote Sensing Images[J].Remote Sensing Information，2010，3:7-12.
[11]蔡金华，龙毅，毋河海,等. 基于反S数学模型的地图目标分形无标度区自动确定[J]. 武汉大学学报(信息科学版)，2004，29(3)：249-253.
Cai Jinhua，Long Yi，Wu Hehai，et al. Automatic Determination of Fractal Non-scale Interval of Map Objects Based on Inverse ‘S’ Mathematical Model[J]. Geomatics and Information Science of Wuhan University，2004，29(3)：249-253.
[12]Yang H Y，Ye H,Wang G Z. Identification of Scaling Regime in Chaotic Correlation Dimension Calculation[C]//3rd IEEE Conferenceon Industrial Electronics and Applications.ICIEA，2008:1383-1387.
[13]Ji C C，Zhu H，Jiang W. A Novel Method to Identify the Scaling Region for Chaotic Time Series Correlation Dimension Calculation[J]. Chinese Science Bull， 2011，56： 925-932.
[14]王成栋，凌丹，苗强. 分形无标度区的一种自动识别方法[J]. 计算机工程与应用，2012，48(6):9-12，27.
Wang Chengdong，Ling Dan，Miao Qiang. Automatic Identification Method of Fractal Scaling Region[J]. Computer Engineering and Applications，2012，48(6):9-12，27.
[15]Ajay K B，Jibitesh M.On Calculation of Fractaldimension of Images[J].Pattern Recognition Letters，2001，22(6)：631-637.
[16]Kalyani S，Swarup K S. Particle Swarm Optimization Based K-means Clustering Approach for Security Assessment in Power Systems[J]. Expert Systems with Applications，2011，38(9)：10839-10846.
[17]Vasan A，Raju K S. Comparative Analysis of Simulated Annealing, Simulated Quenching and Genetic Algorithms for Optimal Reservoir Operation[J]. Applied Soft Computing，2009，9(1)： 274-281.
[18]金元生. 铁谱技术及在磨损研究中的应用[M]. 北京：机械工业出版社，1991.