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针对GM(1,1)建模过程存在背景值、时间因素和初始条件3方面的不足,该文提出三重加权TPGM(1,1)预测模型。通过对背景值进行加权生成新的背景值,建立PGM(1,1)模型;在PGM(1,1)基础上考虑到时间因素,在求解灰参数时进行第2次加权建立DPGM(1,1)模型;最后考虑到初始条件对预测模型的影响,在DPGM(1,1)基础上进行第3次加权,建立TPGM(1,1)模型。通过实例分析,比较GM(1,1)、PGM(1,1)、DPGM(1,1)、TPGM(1,1)4种模型在变形监测数据处理中的拟合和预测结果,表明三重加权TPGM(1,1)模型拟合效果更好、预测精度更高;该模型具有前3种模型的优点,同时弥补了传统GM(1,1)存在的不足。
Aiming at the deficiency of background value, time factor and initial condition of GM (1,1) modeling process, a triple weighted TPGM (1,1) prediction model is proposed. The PGM (1, 1) model is established by weighting the background values to generate a new background value. Taking PGM (1,1) time into consideration, the second weighted DPGM (1, 1) model. Finally, considering the influence of the initial conditions on the prediction model, the third weighting based on DPGM (1,1) is used to establish the TPGM (1,1) model. Through case analysis, the fitting and forecasting results of deformation monitoring data were compared among the four models of GM (1,1), PGM (1,1), DPGM (1,1) and TPGM (1,1) The weighted TPGM (1,1) model has better fitting effect and higher prediction accuracy. The model has the advantages of the first three models and at the same time makes up for the shortcomings of the traditional GM (1,1).