最小一乘法 GM（1，1）在变形监测中的应用

摘要

在分析GM（1，1）建模过程和最小一乘法原理的基础上提出最小一乘法GM（1，1），解算最小一乘法GM（1，1）的线性规划问题，分析和比较了最小一乘法GM（1，1）和GM（1，1）在变形监测数据处理中的应用。结果表明：将变形系统看成灰色体系，采用最小一乘法GM（1，1）模型预报沉降变形监测结果是可行的和有效的，即使在较少的数据信息情况下，通过缩短外推时间，也可以达到较高的预测精度，具有实用和推广价值。%Based on analysis of progress of GM (1,1) modeling and principle of least absolute deviation , the article propose GM(1,1) model based on least absolute deviation and solute the linear programming problem in GM (1,1) mod-el based on least absolute deviation , analyze and compare GM (1,1) model based on least absolute deviation with GM (1,1) in application of deformation observation data processing .The results show that take The deformed system as gray system and adopt GM (1,1) model based on least absolute deviation to predict deformation monitoring results is feasible and effective , even in the case of less data , extrapolation by shortening the time , higher prediction accuracy can also be reached , so it has practical and promotional value .