甘祥前,任超,刘林波,刘中流

• 1:桂林理工大学测绘地理信息学院
• 2:广西空间信息与测绘重点实验室

摘要(Abstract)：

针对非等间距单点灰色预测模型在处理多点变形预测时,没有考虑点与点之间的关联性和它们之间的相互影响,而且容易受建模数据随机扰动性影响这一问题,该文提出了一种基于马尔可夫的非等间距多点灰色预测模型。首先,结合某基坑的变形实测数据,建立非等间距多点灰色预测模型和非等间距单点灰色预测模型,通过两种模型预测结果对比验证非等间距多点灰色预测模型在处理多点变形预测问题上的优越性;然后运用马尔可夫模型建立状态转移概率矩阵对预测结果进行修正;最后建立基于马尔可夫的非等间距多点灰色预测模型。结果表明,基于马尔可夫的非等间距多点灰色预测模型的拟合及预测精度更高,适应性更强,更符合实际变形情况,具有实际参考价值。

关键词(KeyWords)： 非等间距多点灰色预测模型;非等间距单点灰色预测模型;马尔可夫模型;变形监测

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金地区科学基金项目(41461089);; 广西科技厅自然科学基金项目(2014GXNSFAA118288);; 广西空间信息与测绘重点实验室项目(16-380-25-22)

作者(Author): 甘祥前,任超,刘林波,刘中流

DOI: 10.16251/j.cnki.1009-2307.2018.11.002

参考文献(References)：

• [1]邓聚龙.灰色理论基础[M].武汉:华中科技大学出版社,2002.(DENG Julong.Gray theoretical basis[M].Wuhan:Huazhong University of Science and Technology Press,2002.)
• [2]岳仁宾,腾德贵,胡波,等.灰色模型在深基坑变形监测中的应用研究[J].测绘通报,2014(S1):85-87.(YUE Renbin,TENG Degui,HU Bo,et al.Application of gray model in deformation monitoring of deep foundation[J].Bulletin of Surveying and Mapping,2014(S1):85-87.)
• [3]周英.基于改进后灰色模型的某深基坑变形预测[D].成都:成都理工大学,2015.(ZHOU Ying.Prediction of deformation in deep foundation pit based on the improved grey model[D].Chengdu:Chengdu University of Technology,2015.)
• [4]明祖涛,刘军,夏力,等.改进的灰色模型在高铁沉降预测中的应用[J].测绘科学,2015,40(4):137-140.(MING Zutao,LIU Jun,XIA Li,et al.Study of the implementation of improved grey model in high-speed railway settlement prediction[J].Science of Surveying and Mapping,2015,40(4):137-140.)
• [5]袁德宝,崔希民,高宁.同时利用x(1)(1)和x(1)(n)为GM(1,1)建模初始条件的预测方法研究[J].大地测量与地球动力学,2013,33(3):79-82.(YUAN Debao,CUI Ximin,GAO Ning.A forecast method combining x(1)(1)with x(1)(n)as initial value of GM(1,1)model[J].Journal of Geodesy and Geodynamics,2013,33(3):79-82.)
• [6]高宁,崔希民,高彩云.高层建筑物沉降变形的灰线性预测[J].测绘科学,2012,37(3):96-98.(GAO Ning,CUI Ximin,GAO Caiyun.Application of GM(1,1)and line regression for predicting subsidence and deformation of high building[J].Science of Surveying and Mapping,2012,37(3):96-98.)
• [7]吴开岩,张献州,马龙,等.基于多元整体最小二乘优化的多点灰色动态变形分析模型[J].大地测量与地球动力学,2016,36(8):682-685.(WU Kaiyan,ZHANG Xianzhou,MA Long,et al.A multivariable grey deformation analysis model based on multivariate total least-squares optimization[J].Journal of Geodesy and Geodynamics,2016,36(8):682-685.)
• [8]石世云.多变量灰色模型MGM(1,n)在变形预测中的应用[J].测绘学报,1998,27(10):9-12.(SHI Shiyun.Application of multivariable gray model in deformation prediction[J].Acta Geodaetica et Cartographica Sinica,1998,27(10):9-12.)
• [9]吴海清.基于非等间距模型的建筑物沉降预测方法研究[J].测绘科学,2008,33(3):59-61,86.(WU Haiqing.Study on the application of non-equidistant data sequent model in construction subsidence forecasting[J].Science of Surveying and Mapping,2008,33(3):59-61,86.)
• [10]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.Non-equidistant multi-point deformation prediction model and its application[J].Acta Geodaetica et Cartographica Sinica,2016,45(10):1140-1147.)
• [11]徐茂林,郭兆鹏,李海铭.多变量非等时距灰色预测模型在露天矿边坡灾害预警中的应用[J].测绘科学,2014,39(9):83-86.(XU Maolin,GUO Zhaopeng,LI Haiming.Application of multivariate non-equidistance gray forecast model in open-pit slope disaster warning[J].Science of Surveying and Mapping,2014,39(9):83-86.)
• [12]李克昭,李志伟,赵磊杰.马尔可夫理论的优化灰色模型预测建模[J].测绘科学,2016,41(8):1-5.(LI Kezhao,LI Zhiwei,ZHAO Leijie.An optimized gray model deformation forecasting modeling based on Markov theory[J].Science of Surveying and Mapping,2016,41(8):1-5.)
• [13]曾祥艳.灰色预测GM(1,1)模型的几种拓展模型研究[D].成都:电子科技大学,2016.(ZENG Xiangyan.Study on several kinds of developed models of GM(1,1)[D].Chengdu:University of Electronic Science and Technology of China,2016.)
• [14]WANG Q J,WANG C C,XIE R A,et al.An improved SCGM(1,m)model for multi-point deformation analysis[J].Geosciences Journal,2014,18(4):477-484.
• [15]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 Rongqi,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.)