加权灰色预测模型及其计算实现

鉴于GM（1，1）灰色预测模型中背景值取值方法的不足，引入背景值最佳生成系数，得到新的背景值计算式，从而将GM（1，1）预测模型扩展为加权灰色预测模型－－PGM（1，1）预测模型；并对PGM（1，1）预测模型中的最佳生成系数p及灰参数的估计计算进行了详细论述，应用迭代法来确定要应的数值。实例表明，此方法的拟合精度和预测效果均优于GM（1，1）模型。

Weighted Grey Prediction Model and Implement of Its Computation

The prior information is not known well because the deformation objects are very complex.Therefore,the deformation monitoring and prediction analysis of the deformation object is very important work in order to protect the life of the human being and the safety of the belongings.We know that the prediction model has been constructed using the background value in the ordinarly grey prediction model - GM(1,1) model.The effect of the background value is not represented in the model.The optimal production coefficient of the background value is put forward and the computation formula has been derived by the authors based on the shortages of the computation method of the background value in the GM(1,1) model - grey prediction model.And the weighted grey prediction model - PGM(1,1) model has been constructed.The computation of the optimal production coefficient of the background value and the grey parameters have been discussed using the iterative computation methodology in detail.In order to validate the correctness and rationality of this method,the numerical example has been calculated and analyzed.The results of the practice examples show that the PGM(1,1) model is better than the GM(1,1) in the collocation accuracy and the prediction efficiency.So the PGM(1,1) model is very suitable to be applied to the deformation analysis and prediction of the deformation object in case that the monitoring data is less.