稳健动态GM(1,1)模型及其在变形预报中的应用

Robust dynamic GM(1,1) model and its application in deformation forecasting

常规GM(1,1)模型基于最小二乘原理,当建模数据中含有粗差时,将对整个模型的估值产生较大影响。为此,将稳健估计引入灰色模型建模,提出了稳健动态GM(1,1)模型的建模方法。通过对静态GM、动态GM及稳健动态GM进行建模,利用MATLAB编程对实测数据进行了验证计算分析。结果表明,当监测序列含有粗差时,稳健动态GM(1,1)模型相对其他模型能有效抵抗粗差的影响,预报精度也有较明显的提高。

The conventional GM （1, 1 ） model is based on the least squares principle. When gross error exists in the data, great effects will be made in the estimation of the model parameters. In this paper, the robust estimation is introduced into the grey model, and a robust dynamic GM （1, 1 ） model is put forward. Modeling of the static GM, dynamic GM and robust dynamic GM model is formulated, and is calculated, validated and analyzed with MATLAB using the measured data. Results indicate that when the monitoring data contains a gross error, the robust dynamic model can effectively resist the effects of gross errors than other GM models, and significantly improve forecast accuracy.