薄膜涂层摩擦学性能分析的多变量灰色优化模型

The Grey Multi-variable Optimizing Model and Its Application to Analysis of the Tribological Behaviors of the Film

运用灰色系统理论,提出了离子镀(Ti,Cr)N、TiN、CrN薄层的摩擦学性能分析的多变量优化灰色MGM(1,n)模型。MGM(1,n)模型是GM(1,1)模型在多元变量情况下的推广,它通过联立求解建立的多个多元微分方程,使MGM模型中的参数能够反映多个变量间的相互影响、相互制约的关系,它以相对误差最小为目标函数,通过优化求解模型最佳参数。薄膜涂层摩擦学性能分析实例表明该模型精度高、简单实用,为薄膜涂层设计和工程实际使用提供了指导依据。

Based on the Grey system,a optimizing Grey model MGM(1,n)was put forward to analyze the tribological behaviors of(Ti,Cr)N,TiN and CrN films.The MGM(1,n)model builds multiple equations with multivariables,by simultaneous solution the obtained model parameters can reflect the restricted and affected multi-variables relation with one another.Taking the mean relative error as objective function,all optimum parameters of the optimizing MGM(1,n)were found by optimizing.The examples for the tribological behaviors ...