半参数改进灰色模型在滑坡变形预测中的应用
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摘要
滑坡灰色模型的模型误差主要来自降雨量、温度等外界影响因子,传统的半参数灰色模型没有考虑这些对滑坡变形影响较大的外界因子,而把相邻时刻的模型误差当作是不变的,预测精度较低。针对这一问题,该文提出了将这些影响因子当作非参数变量引入模型,通过改进正规矩阵来建立半参数改进灰色模型,可以得到更加准确的模型误差,并且能够将其补偿到观测序列中,使预测结果更加准确。计算结果表明,本文所述模型在观测序列的拟合和预测中均有较好的结果,能够充分地利用在滑坡中采集到的各种信息,并且达到更优的结果。
The model error of landslide gray model mainly comes from external influence factors such as rainfall,temperature and so on,the traditional semiparametric gray models didn't consider these influence factors,it regarded the model error of the adjacent time as constant,so the forecast accuracy was lower.In view of this problem,this paper tried to regard these influence factors as nonparametric variables,then introduced into the model,establishing a semiparametric improved gray model by improving the normal matrix,a more accurate model error could be obtained,and the model error could compensate to the observation sequence,then we could get more accurate prediction result.The calculation results showed that the model described in this paper had better results in the fitting and prediction of the observation sequence,the model described in this paper could make full use of all kinds of information collected in landslides and achieve better results.
The model error of landslide gray model mainly comes from external influence factors such as rainfall,temperature and so on,the traditional semiparametric gray models didn't consider these influence factors,it regarded the model error of the adjacent time as constant,so the forecast accuracy was lower.In view of this problem,this paper tried to regard these influence factors as nonparametric variables,then introduced into the model,establishing a semiparametric improved gray model by improving the normal matrix,a more accurate model error could be obtained,and the model error could compensate to the observation sequence,then we could get more accurate prediction result.The calculation results showed that the model described in this paper had better results in the fitting and prediction of the observation sequence,the model described in this paper could make full use of all kinds of information collected in landslides and achieve better results.
引文
[1] 彭振斌,张闯,彭文祥,等.GM(1,1)模型背景值构造的不同方法与应用[J].东北大学学报(自然科学版),2017,38(6):869-873.(PENG Zhenbin,ZHANG Chuang,PENG Wenxiang,et al.Different structure methods and application of background value in GM(1,1)model[J].Journal of Northeastern University(Natural Science),2017,38(6):869-873.)
[2] 梁永平,严丽萍.基于小波消噪的动态灰色桥墩沉降预测模型[J].测绘地理信息,2017,42(6):65-68.(LIANG Yongping,YAN Liping.Dynamic grey bridge pier subsidence prediction model based on wavelet de-noising[J].Journal of Geomatics,2017,42(6):65-68.)
[3] 张冬菊,黄声享.基于整体最小二乘的灰色模型在大坝变形分析中的应用[J].工程勘察,2017(12):55-59.(ZHANG Dongju,HUANG Shengxiang.A TLS-GM model based on total least squares and its application in dam deformation monitoring[J].Geotechnical Investigation &Surveying,2017(12):55-59.)
[4] 尹晖,周晓庆,张晓鸣.非等间距GM(1,1)建模方法对比分析及应用[J].测绘工程,2017,26(2):1-4.(YIN Hui,ZHOU Xiaoqing,ZHANG Xiaoming.Non-equidistant GM(1,1)modeling comparison and application[J].Engineering of Surveying and Mapping,2017,26(2):1-4.)
[5] 尹晖,周晓庆,张晓鸣.非等间距多点变形预测模型及其应用[J].测绘学报,2016,45(10):1140-1147.(YIN Hui,ZHOU Xiaoqing,ZHANG Xiaoming.Nonequidistant multi-point deformation prediction model and its application[J].Acta Geodaetica et Cartographica Sinica,2016,45(10):1140-1147.)
[6] 胡宏昌,孙海燕.正规矩阵R及平滑因子α的选取[J].测绘工程,2003,12(4):5-8.(HU Hongchang,SUN Haiyan.Choice of the regular matrix R and smoothing parameterα[J].Engineering of Surveying and Mapping,2003,12(4):5-8.)
[7] 孙海燕,吴云.半参数回归与模型精化[J].武汉大学学报(信息科学版),2002,27(2):172-175.(SUN Haiyan,WU Yun.Semiparametric regression and model refining[J].Geomatics and Information Science of Wuhan University,2002,27(2):172-175.)
[8] 丁士俊,朱留洋,姜卫平.一种计算补偿最小二乘正则化参数的最优化方法[J].大地测量与地球动力学,2015,35(1):115-117.(DING Shijun,ZHU Liuyang,JIANG Weiping.An optimization method for calculating regularized parameter of penalized least squares[J].Journal of Geodesy and Geodynamics,2015,35(1):115-117.)
[9] 潘申运.补偿最小二乘法改进灰色预测模型的应用分析[J].测绘科学,2014,39(11):104-107.(PAN Shenyun.Application of penalized least squares method in gray forecasting model[J].Science of Surveying and Mapping,2014,39(11):104-107.)
[10]周敏,周世健,王奉伟.正规矩阵选取半参数灰色模型改进的预测建模[J].测绘科学,2016,41(8):152-155.(ZHOU Min,ZHOU Shijian,WANG Fengwei.Improvement of regular matrix selection and its application in predicting and modeling of semiparame gray model[J].Science of Surveying and Mapping,2016,41(8):152-155.)
[11]周敏.半参数模型的若干问题探讨[D].南昌:东华理工大学,2017.(ZHOU Min.Discussion on some problems of semi-parametric model[D].Nanchang:East China University of Technology,2017.)
[12]高宁,崔希民,高彩云,等.变形平差系统模型误差的半参数补偿方法[J].大地测量与地球动力学,2012,32(1):114-117.(GAO Ning,CUI Ximin,GAO Caiyun,et al.Semiparametric compensation method for model error of deformation adjustment system[J].Journal of Geodesy and Geodynamics,2012,32(1):114-117.)
[13]陆付民,蒋廷耀.基于多因子即泰勒级数的滑坡变形预测模型研究[J].大地测量与地球动力学,2017,37(10):1029-1032.(LU Fumin,JIANG Tingyao.The deformation forecast model of landslides based on multiple factors and taylor series[J].Journal of Geodesy and Geodynamics,2017,37(10):1029-1032.)
[14]陆付民,李劲.基于时效降雨量即温度因子的滑坡变形预测模型研究[C]//水利水电测绘科技论文集.[出版地不详:出版者不详],2017:317-319.(LU Fumin,LI Jin.Research on landslide deformation prediction model based on aging rainfall and temperature factor[J].Water Conservancy and Hydropower Surveying and Mapping Science Proceedings.[S.l.:s.n.],2017:317-319.)
[15]张军,刘祖强,王红.顾及降水因子的卡尔曼滤波在滑坡变形数据处理中的应用[J].测绘科学,2012,37(6):58-61.(ZHANG Jun,LIU Zhuqiang,WANG Hong.Landslide deformation monitoring analysis and forcast using Kalman filtering considering rainfall[J].Science of Surveying and Mapping,2012,37(6):58-61.)
[2] 梁永平,严丽萍.基于小波消噪的动态灰色桥墩沉降预测模型[J].测绘地理信息,2017,42(6):65-68.(LIANG Yongping,YAN Liping.Dynamic grey bridge pier subsidence prediction model based on wavelet de-noising[J].Journal of Geomatics,2017,42(6):65-68.)
[3] 张冬菊,黄声享.基于整体最小二乘的灰色模型在大坝变形分析中的应用[J].工程勘察,2017(12):55-59.(ZHANG Dongju,HUANG Shengxiang.A TLS-GM model based on total least squares and its application in dam deformation monitoring[J].Geotechnical Investigation &Surveying,2017(12):55-59.)
[4] 尹晖,周晓庆,张晓鸣.非等间距GM(1,1)建模方法对比分析及应用[J].测绘工程,2017,26(2):1-4.(YIN Hui,ZHOU Xiaoqing,ZHANG Xiaoming.Non-equidistant GM(1,1)modeling comparison and application[J].Engineering of Surveying and Mapping,2017,26(2):1-4.)
[5] 尹晖,周晓庆,张晓鸣.非等间距多点变形预测模型及其应用[J].测绘学报,2016,45(10):1140-1147.(YIN Hui,ZHOU Xiaoqing,ZHANG Xiaoming.Nonequidistant multi-point deformation prediction model and its application[J].Acta Geodaetica et Cartographica Sinica,2016,45(10):1140-1147.)
[6] 胡宏昌,孙海燕.正规矩阵R及平滑因子α的选取[J].测绘工程,2003,12(4):5-8.(HU Hongchang,SUN Haiyan.Choice of the regular matrix R and smoothing parameterα[J].Engineering of Surveying and Mapping,2003,12(4):5-8.)
[7] 孙海燕,吴云.半参数回归与模型精化[J].武汉大学学报(信息科学版),2002,27(2):172-175.(SUN Haiyan,WU Yun.Semiparametric regression and model refining[J].Geomatics and Information Science of Wuhan University,2002,27(2):172-175.)
[8] 丁士俊,朱留洋,姜卫平.一种计算补偿最小二乘正则化参数的最优化方法[J].大地测量与地球动力学,2015,35(1):115-117.(DING Shijun,ZHU Liuyang,JIANG Weiping.An optimization method for calculating regularized parameter of penalized least squares[J].Journal of Geodesy and Geodynamics,2015,35(1):115-117.)
[9] 潘申运.补偿最小二乘法改进灰色预测模型的应用分析[J].测绘科学,2014,39(11):104-107.(PAN Shenyun.Application of penalized least squares method in gray forecasting model[J].Science of Surveying and Mapping,2014,39(11):104-107.)
[10]周敏,周世健,王奉伟.正规矩阵选取半参数灰色模型改进的预测建模[J].测绘科学,2016,41(8):152-155.(ZHOU Min,ZHOU Shijian,WANG Fengwei.Improvement of regular matrix selection and its application in predicting and modeling of semiparame gray model[J].Science of Surveying and Mapping,2016,41(8):152-155.)
[11]周敏.半参数模型的若干问题探讨[D].南昌:东华理工大学,2017.(ZHOU Min.Discussion on some problems of semi-parametric model[D].Nanchang:East China University of Technology,2017.)
[12]高宁,崔希民,高彩云,等.变形平差系统模型误差的半参数补偿方法[J].大地测量与地球动力学,2012,32(1):114-117.(GAO Ning,CUI Ximin,GAO Caiyun,et al.Semiparametric compensation method for model error of deformation adjustment system[J].Journal of Geodesy and Geodynamics,2012,32(1):114-117.)
[13]陆付民,蒋廷耀.基于多因子即泰勒级数的滑坡变形预测模型研究[J].大地测量与地球动力学,2017,37(10):1029-1032.(LU Fumin,JIANG Tingyao.The deformation forecast model of landslides based on multiple factors and taylor series[J].Journal of Geodesy and Geodynamics,2017,37(10):1029-1032.)
[14]陆付民,李劲.基于时效降雨量即温度因子的滑坡变形预测模型研究[C]//水利水电测绘科技论文集.[出版地不详:出版者不详],2017:317-319.(LU Fumin,LI Jin.Research on landslide deformation prediction model based on aging rainfall and temperature factor[J].Water Conservancy and Hydropower Surveying and Mapping Science Proceedings.[S.l.:s.n.],2017:317-319.)
[15]张军,刘祖强,王红.顾及降水因子的卡尔曼滤波在滑坡变形数据处理中的应用[J].测绘科学,2012,37(6):58-61.(ZHANG Jun,LIU Zhuqiang,WANG Hong.Landslide deformation monitoring analysis and forcast using Kalman filtering considering rainfall[J].Science of Surveying and Mapping,2012,37(6):58-61.)