基于灰色-马尔科夫理论的加工误差预测

Machining Error Prediction Based on Grey-Markov Theory

为了预测加工误差,采用灰色系统理论GM(1,1)模型对高速加工中心连续钻削并铰孔的12个mm孔的相对误差进行了建模,求解得到时间响应序列模型及灰色预测值;采用马尔科夫概率转移矩阵对灰色系统理论的预测结果进行状态划分并修正,并建立预测结果的对比曲线图;采用方差比与小概率误差对预测精度进行检验。结果证明,采用灰色系统理论与马尔科夫概率矩阵修正方法相结合,对加工误差进行预测是可行的,为相关误差补偿技术的研究奠定了良好的基础。

In order to predict machining error, the model of relative error ot 12 holes, which were drilled and reamed with machining center and the diameter of each one is 12, was made with the GM （ 1, 1 ） model of grey system theory and the time response sequence of the model and grey prediction results were achieved. Using Markov probability transfer matrix, the classification of grey prediction results were stated and modified and the graph of comparison of prediction results was established. The accuracy was tested based on the variance ratio and small error probability. The results prove that the combination of the grey theory and Markov probability matrix correction method is feasible to the machining error prediction, laid a good foundation for error compensation.