针对对原始数据进行不同形式的函数变换将引起灰色模型预测精度变化的问题,采用DGM(1,1)模型对其建模数据列进行对数函数变换。研究了数据列的光滑性、凹凸性与灰色预测精度之间的关系;通过对残差、后验差比和相对误差平均值的分析,比较了对数变换前后的精度变化。应用实例证明,函数变换后生成的新数据列较原始数据列具有更好的光滑性;提高光滑性,保持凹凸性,并不增大还原误差即可大幅提高预测精度,对沉降灾害的预报具有一定的指导意义和应用价值。 Aiming at the problem that different forms of function transformation on the original data will lead to the change of the prediction accuracy of the gray model, the logarithmic function transformation of the modeling data column is performed by the DGM (1,1) model. The relationship between the smoothness, concavity and convexity, and the gray prediction accuracy of the data series is studied. The variation of the precision before and after the logarithm transformation is compared by analyzing the residuals, the posterior difference ratios and the average relative errors. The application example proves that the new data sequence generated after the function transformation has a better smoothness than the original data sequence; the smoothness is improved, the concavo-convexity is maintained, the prediction accuracy can be greatly improved without increasing the reduction error, and the prediction of the settlement disaster has Certain guiding significance and application value.