变形监测缺失数据序列灰色建模方法探讨

在测量工作中，由于气候环境、观测方法、观测仪器以及观测人员自身因素等多方面的原因，可能造成观测数据的丢失或者不完全。文中针对这类数据的处理，采用加权平均法和三次样条插值法对缺失数据进行修复，建立GM （1，1）模型，并与非等间隔预测模型进行对比。通过两组仿真数据和两组实测数据验证发现：对于呈指数增长的序列和高增长序列修复之后建模预测精度更高；三次样条插值法数据修复后GM （1，1）建模预测精度较加权平均法预测精度更高；对于低增长序列，直接采用非等间隔建模预测精度更高。

The gray modeling method in missing data sequence of deformation monitoring

For the measurement w ork , because of the climatic environment , observation method , observation instrument and the factors of the observation ,the data can be lost or incomplete .This paper proposes to repair the missing data by using weighed averaging method and the spline interpolation method .Then the GM (1 ,1)model is established .Compared two methods with the non‐equal interval forecasting model ,the experimental results show that the models of repairing missing data have higher prediction accuracy for exponential growth and high growth sequence .But for the two methods ,the prediction accuracy of the spline model is higher than the weighted averaging method .For the low growth sequences ,the prediction accuracy of the non‐equal interval method is higher than the other .