基于蒙特卡罗方法的摩擦材料表面形貌分形插值模拟  

Fractal Interpolation Simulation of Surface Topography of Friction Material Based on the Monte-Carlo Method

作　　者：马润波[1,2] 杜建华[3] 董丽虹[2] 夏静[1] 许世蒙[1] 

机构地区：[1]装甲兵工程学院数学室,北京100072 [2]装甲兵工程学院装备再制造技术国防科技重点实验室,北京100072 [3]装甲兵工程学院科研部,北京100072

出　　处：《数学的实践与认识》2016年第11期162-170,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(51535011;11301542)

摘　　要：通过对铜基复合材料表面形貌的分析和研究,利用分形统计方法,对表征微凸体的特征参数进行分布规律讨论,结合蒙特卡罗方法和分形理论建立了表征微凸体大小的特征参数的数学模型,讨论了分形插值理论中迭代函数系统(IFS)的构造,提出了易于计算机实现的摩擦材料表面形貌模拟算法.同时,对表征微凸体特征的模拟数据进行非参数假设检验,检验结果表明这种模拟摩擦材料表面形貌的方法是可行的.Through analysis and research on the surface topography of reinforced copper matrix composite materials,taking advantage of fractal statistical method to discuss distribution law about characteristics parameter which symbolizes the asperity,combining Monte-Carlo method with fractal theory to set up mathematics model of characteristics parameter which symbolizes size of asperity,talking about the construction of iterated function system in fractal interpolated theory a easy realizable friction materials surface topography simulation algorithm was put forward At the same time,by nonparameter hypothesis test to check the simulation data of symbol asperity characteristics,the inspection results indicate the simulation method,which was used on the surface topography of friction material is feasible and effective And on the basis,more precise threedimensional simulation of friction materials surface topography can be get by using of fractal interpolated theory.

关 键 词：复合材料 分形插值 MONTE-CARLO方法 微凸体 非参数假设检验 

分 类 号：O212.7[理学—概率论与数理统计]