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    The GM model based grey prediction method is presented to predict the cutter's life. The model building method for the GM model is introduced, and the feasibility and prediction accuracy of this grey prediction method are verified and analyzed by an example of predicting the cutter's life during cutting the easy to cutting steel.
    提出采用基于数 (GM)模型的色预测方法预测刀具耐用度 ,介绍了GM模型的色建模方法 ,并通过切削易切钢的刀具耐用度预测实例分析验证了该方法的可行性及预测精度
    In this paper, GM (1,1) model was converted to an optimization model, which doesn't need to identify the parameters of grey differential equation, using the average relative error between restored value of the model and real value as objective function. The model was called Improve GM (1,1) model, IGM (1,1) for short.
    本文以模型还原值与实际值平均相对误差最小化为目标函数将 GM( 1 ,1 )模型转化成一个不用进行微分方程参数辨识的优化模型 ,称之为改进的 GM( 1 ,1 )模型 ,简称 IGM( 1 ,1 ) .
    IGM (1,1) avoids the problem how to rationally select background values in parameter identification of grey differential equation and realize the direct modeling of GM (1,1).
    IGM( 1 ,1 )避开了微分方程参数辨识时的合理选取背景值的问题 ,实现 GM( 1 ,1 )模型的直接建模 .
    Apply two kind of numerical solution method of differential equation to estimate the parameter a and u in the GM(1,1) model,established the time response expression of grey differential equation,and improvement was done on the model′s boundary condition,the application domain and the prediction precision of the consequent established GM(1,1) model are discussed.
    应用微分方程的两种数值解法估计GM(1,1)模型中的待辩参数a、u,并对模型的边界条件做了改进,建立了微分方程的时间响应表达式,讨论了由此建立的GM(1,1)模型的适用范围和预测精度.
 

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