变形预测的一种最优线性组合模型

An Optimal Linear Combined Model of Deformation Prediction

介绍了灰色GM(1,1)、时间序列和非线性组合模型的基本概念,讨论了最优线性组合模型的定义及其权系数的求解方法。结合某大坝变形监测数据,建立了基于灰色与时间序列的非线性组合模型和最优线性组合模型,以及基于灰色、时间序列与非线性组合的最优线性组合模型,并把这3种组合模型的预测结果与GM(1,1)、时间序列模型进行比较。结果表明,融合GM(1,1)、时间序列与非线性灰色时间序列组合的最优线性组合模型的预测效果明显好于另两种模型,其预测误差小于1 mm。

Firstly the basic concepts of GM（ 1, 1）, time series model, nonlinear combined model were introduced. Then the definition of op-timal linear combination model and the calculation method of its weight were discussed in detail. After^-ards the nonlinear combined model and optimal linear combined model based on GM （ 1, 1） and time series, an optimal linear combined model based on GM （ 1, 1） , time series and nonlinear combined model were established and applied to defor^mation prediction by using a dam5 s defor^mation monitoring data. The pre-diction results of these 3 kinds of combined models were compared with those of single GM （ 1, 1） and time series model. The results show that the forecast effect of optimal linear combined model based on GM（ 1, 1）, time series and nonlinear combined model is obviously better than other models and its prediction error is less than 1 mm.