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分析得出原始GM(1,1)模型对应的灰微分方程仅是白化微分方程的梯形积分形式,因此以辛普生求积公式为基础建立了新的灰微分方程,而辛普生求积公式也是一种近似表达形式,因而对新的灰微分方程添加动态扰动项,以弥补灰微分方程与白化微分方程的差别,同时对初始值添加修正项,使其更加符合最小二乘法思想。将改进后的GM(1,1)模型应用到基坑变形预测中,实例应用结果显示,改进的GM(1,1)模型具有较高的预测精度。
It is concluded that the gray differential equation corresponding to the original GM (1,1) model is only the trapezoidal integral form of the albinism differential equation, so a new gray differential equation is established based on the Simplon quadrature formula, and the Simpson product of the quadrature Therefore, the dynamic perturbation term is added to the new gray differential equation to make up for the difference between the gray differential equation and the whitening differential equation. Meanwhile, the correction term is added to the initial value to make it more accord with the least square method. The improved GM (1,1) model is applied to the deformation prediction of foundation pit. The practical application results show that the improved GM (1,1) model has higher prediction accuracy.