基于总体最小二乘的改进GM(1,1)模型及其在建筑物沉降预测中的应用

摘要

介绍灰色系统理论及GM(1,1)模型,在GM(1,1)模型灰参数求解以建立微分方程时采用的最小二乘方法求未考虑模型中存在数据相关性的问题,引进总体最小二乘这种能够处理系数矩阵和观测矩阵同时存在偶然误差的平差方法,将总体最小二乘平差准则用于模型灰参数的解算,并且考虑系数矩阵和观测矩阵的权阵.分析这种改进的GM(1,1)模型的应用并以具体工程实例为背景讨论改进模型的优越性.%The theory of gray system with GM(1,1) model is introduced,because the least-squares method can not contain the data relativities in the model when solving the gray parameters of GM(1,1) model to establish differential equation.The total least squares method which can handle random errors both in coefficient matrix and observation matrix,applies adjustment criteria to solving the gray parameters,by considering the relative weight matrix.Analysis is made on the application of this improved GM(1,1)model and discussed the superiority of the improved method based on the specific example.