时变参数PGM(1, 1)变形预测模型及其应用

在GM(1，1)模型的基础上，考虑参数随时间的变化，用多项式逼近模型参数，同时针对GM(1，1)模型背景值取值方法的不足，引入背景值最佳生成系数，建立了时变参数PGM(1，1)变形预测模型。多项式中的待定系数采用最小二乘法确定，背景值最佳生成系数采用搜索法确定。实例计算表明，时变参数PGM(1，1)变形预测模型具有较高的模拟精度和预测精度，适合用于变形体的变形预测。

Time-Varying Parameter PGM (1, 1) Deformation Prediction Model and Its Applications

In this paper, the parameters of GM (1, 1) model were considered to be time-varying. By using polynomial function to describe the time-varying parameters of GM (1, 1) model and introducing an optimal production coefficient of the background value into the model simultaneously, the time-varying parameter PGM (1, 1) deformation prediction model was developed. The coefficients of the polynomial were solved by the principle of least squares, and the optimal production coefficient of the background value was determined by searching algorithm. Then, the model was used to predict deformation. The case study showed that the time-varying parameter PGM (1, 1) deformation prediction model has high simulation precision and prediction precision. So it is very suitable to be applied to the deformation prediction of the deformation object.