基于最小截平方和估计的监测数据分析方法

Analysis Method of a Water Engineering Safety Monitoring Data Based on the Least Trimmed Square Estimation

水工程安全监测数据中不可避免地存在离群点,而应用最为广泛的最小二乘法(least square,LS)不具备剔除离群点的能力,反而更易吸收离群点,使回归曲线严重偏离实际。针对LS在此方面的缺陷,本文在最小化残差平方和理论的基础上,提出采用最小截平方和估计(least trimmed squares,LTS)方法来构建水工程安全监控模型。根据实际工程的监测资料并对监测资料分析处理,剔除离群点得到最优数据群。通过求解最优数据群的回归系数,进而得到最接近实际数据的拟合曲线。相比于LS估计,LTS估计所得结果更具有合理性、稳健性,且能够显著提高数据的预测精度。因此,LTS估计在水工程安全监测等数据分析中具有良好的应用前景。

The water engineering safety monitoring data inevitably existed outliers, but the most widely used least squares method （LS） had no ability to remove the outliers. And the LS was more easily disturbed by the outliers to mistake the actual regression curves. Aiming at the defects of LS, the least trimmed squares （LTS） was introduced, based on the least minimizing residual sum of squares, to construct the water engineering safety monitoring model. According to and analyzing monitoring data of actual project, the optimal data groups were obtained by removing the outliers. And then the m ost practical fitting curve was obtained by getting the regression coefficient of the optimal data groups. Compared with the least square method, the LTS results were more reasonable and robust. Meanwhile,the prediction accuracy of the data was significantly improved. Therefore, the LTS was great prospect for the water engineering safety monitoring data analysis.