残差修正灰色模型及其在珩磨尺寸预报中的应用

Grey Model for Residual Modification and its Application in Honing Size Prediction

针对一阶一变量灰色模型(Grey model with first order and one variable,GM(1,1))预测精度低、稳健性差的问题,提出了一种改进的GM(1,1)模型。通过背景值优化和参数累积估计,重新推导了GM(1,1)模型的预测公式,并引入残差修正系数和加权马尔科夫链对预测值进行两次残差修正,以提高预测精度。对柱塞套内圆珩磨尺寸的预测结果表明,该模型在原始数据波动条件下的预测精度最高,能弥补其它GM(1,1)模型的不足并实现对珩磨尺寸的预报。

To improve the prediction accuracy and robustness of the grey model with first order and one variable(GM(1,1)),an improved GM(1,1)model is proposed.The prediction formula of the GM(1,1)model is rededuced with the background value optimization and parameter estimation,and the prediction values are modified two times by introducing the residual modification coefficients and the weighted Markov processes to improve the prediction accuracy.The prediction results of the plunger bushing internal honing size show that the model has the highest prediction accuracy under the original data fluctuation,it can cover the shortages of the other GM(1,1)models and predict the honing size.