GM(1,1)正弦模型修补气温监测缺失数据的探讨

Exploration of Repairing Temperature Monitoring Patch Missing Data with GM(1,1)Sinusoidal Model

目的建立预测精度较好的大气温度监测缺失数据修补的方法和模型。方法采用正弦函数对GM(1,1)标准模型进行修正,建立分段的GM(1,1)正弦修正模型对缺失数据进行修补。以万宁试验站某天监测的温度日记时值数据为试验数据,同时建立GM(1,1)标准模型、GM(1,1)时序修正模型和GM(1,1)正弦修正模型,对比分析各模型的修补误差,确立较好的修补模型。结果从模型的拟合效果分析,GM(1,1)标准模型和GM(1,1)正弦修正模型的拟合性最好,GM(1,1)时序修正模型的拟合性相对较差一些;从预测精度上分析,GM(1,1)标准模型和GM(1,1)时序修正模型预测修补效果差,平均相对误差分别达到22.54%和17.70%,而GM(1,1)正弦修正模型预测修补的平均误差仅为3.14%,得到了较大的改进,预测效果好。结论正弦修正模型能很好地修补缺失数据,其修补效果比时序修正模型和标准模型都要好。

Objective To e ：stablishing a method and model with better prediction accuracy for repairing atmospheric temperature monitoring missing data. Methods GM（1,1） standard model was modified by sine function,and the missing data was repaired by the segmented GM（1,1）sinusoidal model established. Using the temperature diary time value data monitored one day in Wanning station as the test data,the GM（1,1） standard model,GM（1,1）timing corrected model and GM（1,1）sinusoidal model were established at the same time. Missing data repairing by the three models were comparatively analyzed,and the relatively better repair model was determined.Results From the analysis of the model fitting results,the fitting of the GM（1,1）standard model and GM（1,1）sinusoidal model was the best,while fitting of the GM（1,1）timing corrected model was relatively poor. From the prediction accuracy of the analysis,GM（1,1）standard model and GM（1,1）timing corrected model showed poor results in repairing prediction,with the average relative errors of 22.54% and 17.70%,respectively. Whereas the average prediction error of GM（1,1）sinusoidal model was only 3.14%,which showed great improvement,and had a good prediction result. Conclusion GM（1,1）sinusoidal model could well repair the missing data,and its result was better than those of GM（1,1）standard model and GM（1,1）timing corrected model.