改进三次埃尔米特的高铁桥墩沉降数据插值法  

Improved cubic Hermite interpolation method for settlement data in high-speed railway bridge pier

作　　者：梁琦 龚循强[1,2] 鲁铁定[1,2] 游为[3] 汪宏宇 LIANG Qi;GONG Xunqiang;LU Tieding;YOU Wei;WANG Hongyu(School of Surveying and Geoinformation Engineering,East China University of Technology,Nanchang 330013,China;Key Laboratory of Mine Environmental Monitoring and Improving around Poyang Lake of Ministry of Natural Resources,East China University of Technology,Nanchang 330013,China;State-Province Joint Engineering Laboratory of Spatial Information Technology for High-speed Railway Safety,Southwest Jiaotong University,Chengdu,611756,China)

机构地区：[1]东华理工大学测绘与空间信息工程学院,南昌330013 [2]东华理工大学自然资源部环鄱阳湖区域矿山环境监测与治理重点实验室,南昌330013 [3]西南交通大学高速铁路安全运营空间信息技术国家地方联合工程实验室,成都611756

出　　处：《测绘科学》2024年第7期29-36,共8页Science of Surveying and Mapping

基　　金：国家自然科学基金项目(42101457);自然资源部环鄱阳湖区域矿山环境监测与治理重点实验室开放基金重点项目资助(MEMI-2023-01)。

摘　　要：针对高铁桥墩沉降观测量不等时距的问题,提出一种改进三次埃尔米特(Hermite)的插值方法,利用加权最小二乘所求的三次拟合多项式求导计算斜率代替原本三次Hermite使用斜率推算方法,考虑观测量整体的变化趋势,实现方法性能的提升。结合模拟数据和高铁桥墩沉降工程实例数据,将改进三次Hermite插值方法与其他5种传统方法进行比较,实验结果表明,本文所提方法的平均绝对误差(MAE)、均方根误差(RMSE)和平均绝对百分比误差(MAPE)在工程实例实验中比其他5种方法中最优的线性插值法平均提升了8.802%、11.456%、6.972%,说明本方法插值结果更为准确。To address the issue of Non-Equal Interval time settlement observations of high-speed railway bridge pier,this paper proposes an Improved cubic Hermite.Instead of using the conventional slope estimation method,this approach utilizes derivatives calculated from a weighted least squares fit of a third-degree polynomial to compute slopes,thereby considering the overall trend of observations and improving method performance.By comparing the Improved cubic Hermite with five traditional methods using both simulated and real-world settlement data from high-speed railway bridge pier,experimental results show that our proposed method uprates the average absolute error(MAE),root mean square error(RMSE),and mean absolute percentage error(MAPE)by an average of 8.802%,11.456%,and 6.972%across experiments of engineering examples compared to the best-performing linear interpolation method among the other five methods,indicating that our method yields more accurate interpolation results.

关 键 词：数据插值 高铁桥墩 改进三次Hermite 加权最小二乘 插值方法 

分 类 号：P207[天文地球—测绘科学与技术]