基于优化初始值的GM(1,1)模型及其在大坝监测中的应用

Optimized Initial Value-based GM(1,1) Model and Its Application to Dam Monitoring

传统的GM(1,1)模型通常以第1点作为初始值来确定积分常数C,缺少一定的理论依据。文中就GM(1,1)模型初始值的优化选取进行了深入的探讨,提出建模方差的概念。依据建模方差2δ最小的原则,对传统GM(1,1)模型的初始值进行改进,提出基于优化初始值的GM(1,1)模型。在大坝变形监测数据分析中应用优化的GM(1,1)模型,采用C++语言编程建立了相应的预测模型。大量的数据分析计算表明,优化的GM(1,1)模型预报精度优于传统的GM(1,1)模型和多项式拟合模型。

The traditional GM（1,1） model usually takes the first point as the initial value to determine the integral constant C, and this practice lacks a certain theoretical basis. For this reason, the optimization of the initial value of GM（1,1） model is discussed and the concept of modeling variance is proposed. Modeling variance is used to find the optimized initial values with the method of minimum modeling variation in GM（1,1） model. An improved GM （1,1） model based on optimized initial value is developed for the analysis of dam deformation monitoring data. And a corresponding forecast model is constructed with C＋＋. Data analysis shows that the prediction accuracy of the optimized GM（1,1） model is higher than that of traditional GM（1,1） model and polynomial fitting model.