周昀琦,王奉伟,周世健,罗亦泳,周清

• 1:Environmental and Geomatics Engineering Department
• 2:University College London
• 3:同济大学测绘与地理信息学院
• 4:南昌航空大学

摘要(Abstract)：

针对传统的变形监测建模方法一般针对单一监测点的变形预测模型,未考虑到监测点间相互作用的变形特点,该文分析了变形监测点间的相互关联性,通过相关系数法对监测点进行分类,并将邻近监测点的观测序列值作为和时间因素等同的影响因子应用到建模过程中,利用高斯过程算法进行训练,建立预测模型。为提高高斯过程算法的模型预测精度,应选择适合工程案例最优协方差函数。通过实例分析,比较GM(1,1)、多点灰色预测模型和顾及邻近点变形因素的高斯过程等3种模型在基坑围岩、滑坡等变形监测数据处理中的预测精度,表明该文算法考虑到监测点间的变形关联性,充分利用高斯过程在针对小样本、非线性数据建模时的高自适应性等优点,具有较高的预测精度。

关键词(KeyWords)： 多点灰色预测;高斯过程;相关性分析;变形预测

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(41374007);; 江西省自然科学基金项目(20151BAB213031)

作者(Author): 周昀琦,王奉伟,周世健,罗亦泳,周清

DOI: 10.16251/j.cnki.1009-2307.2018.04.019

参考文献(References)：

• [1]周世健,罗亦泳,鲁铁定.局部均值分解(LMD)方法在多尺度变形分析中的应用分析探讨[J].江西科学,2014,32(4):461-466.(ZHOU Shijian,LUO Yiyong,LU Tieding.Discussion for the local mend decomposition in analysis of multi-scale deformation[J].Jiangxi Science,2014,32(4):461-466.)
• [2]黄润秋,许强,戚国庆.降雨及水库诱发滑坡的评价与预测[M].北京:科学出版社,2007.(HUANG Runqiu,XU Qiang,QI Guoqing.Evaluation and prediction of rainfall and resevoir induced landslides[M].Beijing:Science Press,2007.)
• [3]卢书强,易庆林,易武,等.三峡库区卧沙溪滑坡变形失稳机制分析[J].中国地质灾害与防治学报,2013,24(2):21-25.(LU Shuqiang,YI Qinglin,YI Wu,et al.Analysis on deformation and failure mechanism of Woshaxi landslide in the Three Gorges Reservoir area[J].The Chinese Journal of Geological Hazard and Control,2013,24(2):21-25.)
• [4]李志伟,贺跃光,朱建军.边坡多点监测资料的联合分析模型及其修正[J].矿冶工程,2005,25(3):11-13.(LI Zhiwei,HE Yueguang,ZHU Jianjun.Cojoint analysis model of multi-point slope monitoring data and its revision[J].Mining and Metallurgical Engineering,2005,25(3):11-13.)
• [5]尹晖,陈永奇,张琰.贫信息条件下的多点变形预测模型及其应用[J].测绘学报,1997,26(4):365-372.(YIN Hui,CHEN Yongqi,ZHANG Yan.Multi-point deformation prediction model with poor data information and its application[J].Acta Geodaetica et Cartographica Sinica,1997,26(4):365-372.)
• [6]王穗辉,潘国荣.基于MATLAB多变量灰色模型及其在变形预测中的应用[J].土木工程学报,2005,38(5):24-27.(WANG Suihui,PAN Guorong.A Matlab-based multi-point grey model and its application in deformation prediction[J].China Civil Engineering Journal,2005,38(5):24-27.)
• [7]冯志,李兆平,李祎.多变量灰色系统预测模型在深基坑维护结构变形预测中的应用[J].岩石力学与工程学报,2007,26(S2):4319-4324.(FENG Zhi,LI Zhaoping,LI Yi.Application of a multi-point grey model to deformation prediction of supporting structure for deep pit[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(S2):4319-4324.)
• [8]赵洪波.支持向量机在隧道围岩变形预测中的应用[J].岩石力学与工程学报,2005,24(4):649-653.(ZHAO Hongbo.Predicting the surrounding deformations of tunnel using support vector machine[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(4):649-653.)
• [9]范千,王新洲,许承权.大坝变形预测的支持向量机模型[J].测绘工程,2007,16(6):1-4.(FAN Qian,WANG Xinzhou,XU Chengquan.Support vector machine model for dam deformation prediction[J].Engineering of Surveying and Mapping,2007,16(6):1-4.)
• [10]宋志宇,李俊杰.最小二乘支持向量机在大坝变形预测中的应用[J].水电能源科学,2006,24(6):49-52,115-116.(SONG Zhiyu,LI Junjie.Research on dam displacement forecasting model based on least squares support vector machine[J].Water Resources and Power,2006,24(6):49-52,115-116.)
• [11]罗亦泳,姚宜斌,张立亭,等.基于高斯过程的GPS高程转换模型[J].测绘通报,2015(11):11-14,59.(LUO Yiyong,YAO Yibin,ZHANG Liting,et al.GPS height transformation model based on Gaussian process[J].Bulletin of Surveying and Mapping,2015(11):11-14,59.)
• [12]曲轶松.基于高斯过程的数据处理的研究[D].北京:北京交通大学,2014:1-84.(QU Yisong.Research on data processing based on Gaussian process[D].Beijing:Beijing Jiaotong University,2014:1-84.)
• [13]RASMUSSEN C E,WILLIAM C K I.Gaussian processes for machine learning[M].Massachusetts:The MIT Press,2006.
• [14]何习平,华锡生,何秀凤.加权多点灰色模型在高边坡变形预测中的应用[J].岩土力学,2007,28(6):1187-1191.(HE Xiping,HUA Xisheng,HE Xiufeng.Weighted multi-point grey model and its application to high rock slope deformation forecast[J].Rock and Soil Mechanics,2007,28(6):1187-1191.)
• [15]SEEGER M.Gaussian processes for machine learning[J].International Journal of Neural System,2004,14(2):69-106.
• [16]苏国韶.基于高斯过程机器学习的冲击地压危险性预测[J].辽宁工程技术大学学报(自然科学报),2009,28(5):762-765.(SU Guoshao.Forecast of rock burst intensity based on Gaussian process machine learning[J].Journal of Liaoning Technical University(Natural Science),2009,28(5):762-765.)
• [17]孙斌,姚海涛,刘婷.基于高斯过程回归的短期风速预测[J].中国电机工程学报,2012,32(29):104-109.(SUN Bin,YAO Haitao,LIU Ting.Short-term wind speed forecasting based on Gaussian process regression model[J]//Proceedings of the CSEE,2012,32(29):104-109.)
• [18]徐冲,刘保国,刘开云,等.基于粒子群-高斯过程回归耦合算法的滑坡位移时序分析预测智能模型[J].岩土力学,2011,32(6):1669-1675.(XU Chong,LIU Baoguo,LIU Kaiyun,et al.Intelligent analysis model of landslide displacement time series based on coupling PSO-GPR[J].Rock and Soil Mechanics,2011,32(6):1669-1675.)
• [19]雷鸣.基于高斯过程的变形预测算法研究[D].抚州:东华理工大学,2013:1-62.(LEI Ming.Gaussian process of deformation based algorithm[D].Fuzhou:East China University of Technology,2013:1-62.)
• [20]VAPNIK V.The nature of statistical learning theory[M].2nd ed.New York:Springer-Verlag,1998:360-374.
• [21]李世贵,易庆林,吴娟娟,等.背景值优化的多点灰色模型在滑坡变形预测中的应用[J].中国地质灾害与防治学报,2015,26(2):3-9.(LI Shigui,YI Qinglin,WU Juanjuan,et al.A multi-point model for background value optimization and its application to landslide deformation prediction[J].The Chinese Journal of Geological Hazard and Control,2015,26(2):3-9.)
• [22]张智星.MATLAB程序设计与应用[M].北京:清华大学出版社,2002.(ZHANG Zhixing.Application and design of MATLAB programming[M].Beijing:Tsinghua University Press,2002.)