无偏灰色模型和Origin拟合函数在变形监测预报中的对比应用

摘要

According to the inherent defects of grey model,three kinds of grey model are improved to obtain the unbiased forecast through parameter transformation between the whitenization equation and the grey differential equation.Three case studies are used to compare the application of unbiased grey model and Origin fitting functions on deformation monitoring data processing.The results show that under the condition of a ‘small sample’,the two methods achieve about the same fitting and prediction accuracy.When modeling data is large,the unbiased grey model is not as good as the Origin fitting functions.Considering the application effect and modeling requirements,it is pointed out that the unbiased grey model has a simple modeling principle and can be used to deal with small sample deformation monitoring data.However,from a practical perspective,Origin fitting functions does not need to consider the amount of data and time interval of deformation monitoring.It is recommended to apply Origin fitting in deformation monitoring data processing.%针对灰色模型的固有缺陷,通过白化方程与灰微分方程之间的参数变换实现了三类灰色模型的无偏性.通过3个实例对比分析了无偏灰色模型和Origin拟合函数在变形监测预报中的应用效果,结果表明,在“少数据建模”情况下,无偏灰色模型拟合预测精度与Origin拟合函数相当;当建模数据较多时,则不及Origin拟合函数.无偏灰色模型建模原理简单,可用于处理小样本变形监测数据.Origin拟合函数不需要考虑数据量和变形监测时间间隔,可用于处理变形监测数据.