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采用传统GM(1,1)方法对建筑物的沉降进行预测时,仅考虑了观测向量中的误差。但系数矩阵中的元素是由观测量组成的,不可避免地含有误差。建立GM(1,1)联合模型,采用总体最小二乘拟合推估法求解灰参数及沉降预测值,即顾及了观测值与系数矩阵中含有的误差,同时考虑到系数矩阵中常数项元素以及其它各元素间的相关性,将灰参数与沉降预测的解算同时进行,有效地提高预测精度。
When using the traditional GM (1,1) method to predict the settlement of a building, only the errors in the observed vector are taken into account. However, the elements in the coefficient matrix are composed of observations and inevitably contain errors. The GM (1,1) joint model is established, and the total least square fitting estimate method is used to solve the gray parameter and settlement prediction value, which takes into account the error contained in the observation and coefficient matrix. At the same time, As well as the correlation among other elements, the gray parameter and the solution of settlement prediction are carried out at the same time, which effectively improves the prediction accuracy.