优化背景值的时变参数GM(1,1)在铁路沉降中的应用  

Application of time-varying parametre GM(1,1) model with optimized background value in railway settlement analysis

作　　者：张振超 张军[3] 袁德宝[1] 杨恒 马生昀[3] ZHANG Zhenchao;ZHANG Jun;YUAN Debao;YANG Heng;MA Shengyun(College of Geoscience and Surveying Engineering,China University of Mining and Technology(Beijing),Beijing 100083,China;Water Conservancy and Civil Engineering College,Inner Mongolia Agricultural University,Hohhot 010018,China;College of Science,Inner Mongolia Agricultural University,Hohhot 010018,China;College of Earth Science and Engineering,Hohai University,Nanjing 211100,China)

机构地区：[1]中国矿业大学(北京)地球科学与测绘工程学院,北京100083 [2]内蒙古农业大学水利与土木建筑工程学院,呼和浩特010018 [3]内蒙古农业大学理学院,呼和浩特010018 [4]河海大学地球科学与工程学院,南京211100

出　　处：《测绘科学》2020年第3期39-45,共7页Science of Surveying and Mapping

基　　金：国家自然科学基金项目(71661027);内蒙古自治区自然科学基金项目(2018MS03047);内蒙古农业大学教育教学改革研究重点项目(JGZD201815)。

摘　　要：针对传统的GM(1,1)模型在建筑(构筑)物形变和沉降预测中的灰色作用量恒定和背景值构造有偏差的缺陷,该文通过引入线性时间项的灰色作用量和广义加权构造最优背景值相结合的方法构建了优化背景值的时变参数GM(1,1)模型。以实际铁路沉降监测点的累计沉降监测数据为例,分别采用传统的GM(1,1)模型、时变参数GM(1,1)模型和优化背景值的时变参数GM(1,1)模型对观测数据进行了拟合和预测。结果表明,优化背景值的时变参数GM(1,1)模型的拟合和预测精度相比传统GM(1,1)模型和时变参数GM(1,1)模型有很大提高,适合于铁路沉降数据的监控和分析。研究结果可为铁路的沉降预测提供一定的参考价值。Taking the consideration of the deficiency of traditional GM(1,1) model which have constant grey action and the deviation in background value construction.A time-varying parameter GM(1,1) which have optimal background value is provided by incorporating the grey action of linear time term and the generalized weighting method of constructing the optimal background value.Taking the accumulated settlement monitoring data of actual railway settlement monitoring point as an example,the traditional GM(1,1) model,time-varying parameter GM(1,1) model and time-varying parameter GM(1,1) model with optimized background values are built to fit and predict the observed data.The results show that the fitting and prediction accuracy of the time-varying parameter GM(1,1) model with optimized background values proposed in this paper has the very high simulation and prediction precision,which is suitable for the monitoring and analyzing Railway Settlement data.The research results can provide some references for railway settlement prediction.

关 键 词：沉降监测 背景值 时变参数 GM(1 1)模型 

分 类 号：P258[天文地球—测绘科学与技术]