基于最小截平方和估计的监测数据分析方法

发布时间：2018-05-26 04:04

本文选题：最小截平方和(LTS) + 离群点　；参考：《数理统计与管理》2017年04期

【摘要】：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。
[Abstract]:Outliers inevitably exist in the monitoring data of water engineering safety, but the most widely used least square method (LSs) is not capable of eliminating outliers, on the contrary, it is easier to absorb outliers, which makes the regression curve deviate seriously from reality. Aiming at the defects of LS in this respect, based on the theory of minimizing the sum of squared residuals, this paper presents a method of estimating least trimmed squared LTSs to construct a safety monitoring model for water engineering. According to the monitoring data of the actual engineering and the analysis and processing of the monitoring data, the optimal data group is obtained by eliminating the outliers. By solving the regression coefficient of the optimal data group, the fitting curve closest to the actual data is obtained. Compared with LS estimation, the results of LTS estimation are more reasonable, robust and can improve the prediction accuracy of the data significantly. Therefore, LTS estimation has a good application prospect in water engineering safety monitoring and other data analysis.
【作者单位】：西安理工大学西北旱区生态水利工程国家重点实验室培育基地;福州大学至诚学院;河海大学水文水资源与水利工程科学国家重点实验室;国电陕西水电开发有限公司;
【基金】：国家自然科学基金项目(41301597、51409205) 博士后自然科学基金项目(2015M572656XB) 陕西省重点科技创新团队(2013KCT-015) 水文水资源与水利工程科学国家重点实验室开放研究基金(2014491011) 陕西省博士后科研项目西安理工大学水利水电学院青年科技创新团队(2016ZZKT-14)
【分类号】：O212.1;TV698.1

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