补偿最小二乘法改进灰色预测模型的应用分析

Application of penalized least squares method in gray forecasting model

文章讨论了灰色预测模型和半参数模型,针对经典最小二乘在解算GM(1,1)模型待识别向量时存在的模型误差,采用将模型误差当作非参数信号的补偿最小二乘法进行数据处理。根据矿区变形观测特点,简要说明了正规矩阵R和平滑因子α的选取,并结合淮南市朱集矿地表移动观测站的实测数据对改正模型进行检验分析,结果表明:该方法可有效地削弱模型系统误差影响,提高预测模型精度。

In the paper, grey forecasting model model errors of classical least squares in calculating and semi-parametric model were discussed, as to the the recognized vector of GM （1, 1） Model, penalized least squares method that regards the model error as non-parametric information was used to process da- ta. According to the characteristics of mining deformation monitoring, the selection of regularizer R and smoothing parameter a were described briefly, and the corrected model was tested and analyzed with ob- served data of the surface displacement observation station of Zhuji Mine in Huainan City. The result showed that the method could weaken the influence of systematic errors of the model effectively and im- prove the accuracy of the forecasting model.