灰色模型参数估计改进及其在变形预报中应用

Building Deformation Prediction Based on Weight Grey Model

经典的灰色模型在建模过程中,参数估计是依据最小二乘准则得到的。当观测数据中存在着较大随机波动时,导致系数矩阵中存在较大误差,这种估计方法可能影响参数的可靠性,进而影响该模型应用。针对这一问题,本文提出运用整体最小二乘法改进估计参数,该方法在解算法方程时,顾及了系数阵和观测向量同时存在的误差,因而可以改善参数的估计精度,提高模型预报精度。最后,结合矿山测量工程实际,证实了这种参数估计方法能提高老采空区残余沉降的预测精度。

Parameter estimation of classic grey model （GM ） is based on the least squares methods .When there are big random fluctuations in coefficient matrix causing by the observation data ,this criterion may affect the reliability of the parameter .Then its application is affected .In order to solve this problem ,total least squares （TLS） is used to estimate GM parameters .The error of the coefficient matrix and the error of observation vector are considered in modified GM .Thus ,the accuracy of the parameter is improved ,and the prediction precision of the model is improved too .Finally ,an example from mining surveying practice‐old goaf residual subsidence is discussed to compare the classic GM and modified GM ,and the results show that this method can improve prediction accuracy .