一种无偏模型在变形监测中的应用
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摘要
针对变形发展趋势多样性的特点,将无偏NGM(1,1,k)模型应用于变形监测数据的分析预测中,说明无偏NGM(1,1,k)模型可分别用于拟合近似线性-指数增长趋势变形序列、近似非齐次指数变形序列和近似齐次指数变形序列。根据监测数据的发展特点可选择适合的建模方法。实例分析结果显示,无偏NGM(1,1,k)模型具有良好的拟合和预测精度,可用于滑坡位移的分析预测中。
According to the characteristics of diversity of the deformation development trend,the unbiased NGM(1,1,k)model is applied to analysis and prediction of deformation monitoring data.It is pointed out that unbiased NGM(1,1,k)model can be used to fit the approximate linear-exponential growth trend deformation sequence,the approximate nonhomogeneous deformation sequences and the approximate homogeneous exponential deformation sequence.The choice of modeling method should be made based on the development of the monitoring data.The example analysis results show that the unbiased NGM(1,1,k)model has good fitting and prediction accuracy,and can be applied in analysis and prediction of landslide displacement.
According to the characteristics of diversity of the deformation development trend,the unbiased NGM(1,1,k)model is applied to analysis and prediction of deformation monitoring data.It is pointed out that unbiased NGM(1,1,k)model can be used to fit the approximate linear-exponential growth trend deformation sequence,the approximate nonhomogeneous deformation sequences and the approximate homogeneous exponential deformation sequence.The choice of modeling method should be made based on the development of the monitoring data.The example analysis results show that the unbiased NGM(1,1,k)model has good fitting and prediction accuracy,and can be applied in analysis and prediction of landslide displacement.
引文
[1]陈鹏宇.地面沉降模拟计算的灰色离散GM(1,1)模型[J].地质灾害与环境保护,2009,20(4):101-105.(CHEN Pengyu.Discrete GM(1,1)for ground subsidence simulation[J].Journal of Geological Hazards and Environment Preservation,2009,20(4):101-105.)
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[3]李莉,陈鹏宇,段新胜.基坑变形预测的灰色二次优化模型[J].辽宁工程技术大学学报(自然科学版),2010,29(5):926-929.(LI Li,CHEN Pengyu,DUAN Xinsheng.Re-optimization grey model for forecast on deformation of foundation pit[J].Journal of Liaoning Technical University(Natural Science),2010,29(5):926-929.)
[4]CHEN P Y,YU H M,XIE K.GM(1,1)model based on optimum parameters of whitenization differential equation and its application on displacement forecasting of foundation pit[J].Journal of Grey System,2013,25(1):54-62.
[5]郭锴,陈伟清,文鸿雁,等.非等时距灰色线性组合模型在变形监测中的应用[J].测绘科学,2014,39(7):131-135.(GUO Kai,CHEN Weiqing,WEN Hongyan,et al.A comparative study of non-equal interval gray linear combination model in deformation monitoring[J].Science of Surveying and Mapping,2014,39(7):131-135.)
[6]陈威,唐德燕,张届.利用三点法-灰色组合模型预测铁路路基沉降[J].测绘科学,2015,40(7):37-40.(CHEN Wei,TANG Deyan,ZHANG Jie.Application of three-point-method-gray GM(1,1)combination model in settlement prediction for a railway line[J].Science of Surveying and Mapping,2015,40(7):37-40.)
[7]李克昭,李志伟,孟福军,等.基于综合优化GM(1,1)的形变预测模型[J].大地测量与地球动力学,2016,36(2):120-123.(LI Kezhao,LI Zhiwei,MENG Fujun,et al.Deformation forecasting model based on synthetic and optimized GM(1,1)[J].Journal of Geodesy and Geodynamics,2016,36(2):120-123.)
[8]陈鹏宇,段新胜.近似非齐次指数序列的离散GM(1,1)模型的建立及其优化[J].西华大学学报(自然科学版),2010,29(1):89-92.(CHEN Pengyu,DUAN Xinsheng.Creation of non-homogenous discrete GM(1,1)model and its optimization[J].Journal of Xihua University(Natural Science Edition),2010,29(1):89-92.)
[9]肖云,周春梅,虞珏,等.大冶铁矿滑坡预测模型研究[J].武汉工程大学学报,2010,32(1):9-11.(XIAO Yun,ZHOU Chunmei,YU Jue,et al.Study on prediction model in Hubei Daye iron mine slope[J].Journal of Wuhan Institute of Technology,2010,32(1):9-11.)
[10]彭正明,王腾军,曹冬冬,等.GM(1,1)模型的改进及其在变形预测中的应用[J].地球科学与环境学报,2012,34(4):102-106.(PENG Zhengming,WANG Tengjun,CAO Dongdong,et al.Improvement of GM(1,1)model and its application on deformation prediction[J].Journal of Earth Sciences and Environment,2012,34(4):102-106.)
[11]曾鼎文,吴浩中.优化的非等时距灰色模型在湖南高速公路路基沉降预测中的应用[J].公路工程,2013,38(4):269-272.(ZENG Dingwen,WU Haozhong.Application of optimization unequal time-interval gray model in forecast of subsidence of embankment settlement of expressway[J].Highway Engineering,2013,38(4):269-272.)
[12]陈鹏宇,段新胜.无偏直接PGM(1,1)模型及其优化[J].三峡大学学报(自然科学版),2009,31(5):66-68.(CHEN Pengyu,DUAN Xinsheng.Unbiased direct PGM(1,1)and its optimization[J].Journal of China Three Gorges University(Natural Sciences),2009,31(5):66-68.)
[13]郭峥英,陈鹏宇.建筑地基沉降预测的灰色模型与Asaoka法[J].工程勘察,2012(6):67-70.(GUO Zhengying,CHEN Pengyu.Grey model and Asaoka method in the forecast of architecture groundsill settlement[J].Geotechnical Investigation&Surveying,2012(6):67-70.)
[14]陈鹏宇,段新胜,项翔.优化白化方程参数的新NGM(1,1,k)模型及其应用[C]//第19届灰色系统全国会议论文集.北京:[出版者未知],2010:299-304.(CHEN Pengyu,DUAN Xinsheng,XIANG Xiang.New NGM(1,1,k)model with optimization parameters of whitenization differential equation and its application[C]∥Proceedings of the 19th National Conference on Grey System.Beijing:[s.n.],2010:299-304.)
[15]崔杰,党耀国,刘思峰.一种新的灰色预测模型及其建模机理[J].控制与决策,2009,24(11):1702-1706.(CUI Jie,DANG Yaoguo,LIU Sifeng.Novel grey forecasting model and its modeling mechanism[J].Control and Decision,2009,24(11):1702-1706.)
[16]战立青,施化吉.近似非齐次指数数据的灰色建模方法与模型[J].系统工程理论与实践,2013,33(3):689-694.(ZHAN Liqing,SHI Huaji.Methods and model of grey modeling for approximation non-homogenous exponential data[J].Systems Engineering-Theory&Practice,2013,33(3):689-694.)
[17]刘思峰,党耀国,方志耕,等.灰色系统理论及其应用[M].北京:科学出版社,2010.(LIU Sifeng,DANG Yaoguo,FANG Zhigeng,et al.Grey system theory and its application[M].Beijing:Science Press,2010.)
[18]崔伟杰,包腾飞,张学峰,等.改进的灰色线性回归组合模型在大坝变形监测中的应用[J].水电能源科学,2013,31(6):103-105.(CUI Weijie,BAO Tengfei,ZHANG Xuefeng,et al.Application of improved grey linear regression combination model in dam deformation monitoring[J].Water Resources and Power,2013,31(6):103-105.)
[19]李秀珍,孔纪名,王成华.灰色GM(1,1)残差修正模型在滑坡预测中的对比应用[J].山地学报,2007,25(6):741-746.(LI Xiuzhen,KONG Jiming,WANG Chenghua.Comparison and application of grey GM(1,1)modified residual error models in landslide predicting[J].Journal of Mountain Science,2007,25(6):741-746.)
[20]吴银亮,刘艳敏,祝艳波.动态灰色模型的滑坡位移时间预测方法研究[J].铁道建筑,2011(7):88-90.(WU Yinliang,LIU Yanmin,ZHU Yanbo.Study of time prediction method for landslide displacement based on dynamic grey model[J].Railway Engineering,2011(7):88-90.)
[21]徐峻龄,廖小平,李荷生.黄茨大型滑坡的预报及其理论和方法[J].铁道工程学报,1996(2):197-205.(XU Junling,LIAO Xiaoping,LI Hesheng.Prediction for Huangci landslide and its theory and method[J].Journal of Railway Engineering Society,1996(2):197-205.)
[2]陈鹏宇,段新胜.建筑物沉降的非等间隔GM(1,1)模型的建立与改进[J].工程勘察,2010(3):77-80.(CHEN Pengyu,DUAN Xinsheng.Establishment and improvement of non-equal interval GM(1,1)model of building subsidence[J].Geotechnical Investigation&Surveying,2010(3):77-80.)
[3]李莉,陈鹏宇,段新胜.基坑变形预测的灰色二次优化模型[J].辽宁工程技术大学学报(自然科学版),2010,29(5):926-929.(LI Li,CHEN Pengyu,DUAN Xinsheng.Re-optimization grey model for forecast on deformation of foundation pit[J].Journal of Liaoning Technical University(Natural Science),2010,29(5):926-929.)
[4]CHEN P Y,YU H M,XIE K.GM(1,1)model based on optimum parameters of whitenization differential equation and its application on displacement forecasting of foundation pit[J].Journal of Grey System,2013,25(1):54-62.
[5]郭锴,陈伟清,文鸿雁,等.非等时距灰色线性组合模型在变形监测中的应用[J].测绘科学,2014,39(7):131-135.(GUO Kai,CHEN Weiqing,WEN Hongyan,et al.A comparative study of non-equal interval gray linear combination model in deformation monitoring[J].Science of Surveying and Mapping,2014,39(7):131-135.)
[6]陈威,唐德燕,张届.利用三点法-灰色组合模型预测铁路路基沉降[J].测绘科学,2015,40(7):37-40.(CHEN Wei,TANG Deyan,ZHANG Jie.Application of three-point-method-gray GM(1,1)combination model in settlement prediction for a railway line[J].Science of Surveying and Mapping,2015,40(7):37-40.)
[7]李克昭,李志伟,孟福军,等.基于综合优化GM(1,1)的形变预测模型[J].大地测量与地球动力学,2016,36(2):120-123.(LI Kezhao,LI Zhiwei,MENG Fujun,et al.Deformation forecasting model based on synthetic and optimized GM(1,1)[J].Journal of Geodesy and Geodynamics,2016,36(2):120-123.)
[8]陈鹏宇,段新胜.近似非齐次指数序列的离散GM(1,1)模型的建立及其优化[J].西华大学学报(自然科学版),2010,29(1):89-92.(CHEN Pengyu,DUAN Xinsheng.Creation of non-homogenous discrete GM(1,1)model and its optimization[J].Journal of Xihua University(Natural Science Edition),2010,29(1):89-92.)
[9]肖云,周春梅,虞珏,等.大冶铁矿滑坡预测模型研究[J].武汉工程大学学报,2010,32(1):9-11.(XIAO Yun,ZHOU Chunmei,YU Jue,et al.Study on prediction model in Hubei Daye iron mine slope[J].Journal of Wuhan Institute of Technology,2010,32(1):9-11.)
[10]彭正明,王腾军,曹冬冬,等.GM(1,1)模型的改进及其在变形预测中的应用[J].地球科学与环境学报,2012,34(4):102-106.(PENG Zhengming,WANG Tengjun,CAO Dongdong,et al.Improvement of GM(1,1)model and its application on deformation prediction[J].Journal of Earth Sciences and Environment,2012,34(4):102-106.)
[11]曾鼎文,吴浩中.优化的非等时距灰色模型在湖南高速公路路基沉降预测中的应用[J].公路工程,2013,38(4):269-272.(ZENG Dingwen,WU Haozhong.Application of optimization unequal time-interval gray model in forecast of subsidence of embankment settlement of expressway[J].Highway Engineering,2013,38(4):269-272.)
[12]陈鹏宇,段新胜.无偏直接PGM(1,1)模型及其优化[J].三峡大学学报(自然科学版),2009,31(5):66-68.(CHEN Pengyu,DUAN Xinsheng.Unbiased direct PGM(1,1)and its optimization[J].Journal of China Three Gorges University(Natural Sciences),2009,31(5):66-68.)
[13]郭峥英,陈鹏宇.建筑地基沉降预测的灰色模型与Asaoka法[J].工程勘察,2012(6):67-70.(GUO Zhengying,CHEN Pengyu.Grey model and Asaoka method in the forecast of architecture groundsill settlement[J].Geotechnical Investigation&Surveying,2012(6):67-70.)
[14]陈鹏宇,段新胜,项翔.优化白化方程参数的新NGM(1,1,k)模型及其应用[C]//第19届灰色系统全国会议论文集.北京:[出版者未知],2010:299-304.(CHEN Pengyu,DUAN Xinsheng,XIANG Xiang.New NGM(1,1,k)model with optimization parameters of whitenization differential equation and its application[C]∥Proceedings of the 19th National Conference on Grey System.Beijing:[s.n.],2010:299-304.)
[15]崔杰,党耀国,刘思峰.一种新的灰色预测模型及其建模机理[J].控制与决策,2009,24(11):1702-1706.(CUI Jie,DANG Yaoguo,LIU Sifeng.Novel grey forecasting model and its modeling mechanism[J].Control and Decision,2009,24(11):1702-1706.)
[16]战立青,施化吉.近似非齐次指数数据的灰色建模方法与模型[J].系统工程理论与实践,2013,33(3):689-694.(ZHAN Liqing,SHI Huaji.Methods and model of grey modeling for approximation non-homogenous exponential data[J].Systems Engineering-Theory&Practice,2013,33(3):689-694.)
[17]刘思峰,党耀国,方志耕,等.灰色系统理论及其应用[M].北京:科学出版社,2010.(LIU Sifeng,DANG Yaoguo,FANG Zhigeng,et al.Grey system theory and its application[M].Beijing:Science Press,2010.)
[18]崔伟杰,包腾飞,张学峰,等.改进的灰色线性回归组合模型在大坝变形监测中的应用[J].水电能源科学,2013,31(6):103-105.(CUI Weijie,BAO Tengfei,ZHANG Xuefeng,et al.Application of improved grey linear regression combination model in dam deformation monitoring[J].Water Resources and Power,2013,31(6):103-105.)
[19]李秀珍,孔纪名,王成华.灰色GM(1,1)残差修正模型在滑坡预测中的对比应用[J].山地学报,2007,25(6):741-746.(LI Xiuzhen,KONG Jiming,WANG Chenghua.Comparison and application of grey GM(1,1)modified residual error models in landslide predicting[J].Journal of Mountain Science,2007,25(6):741-746.)
[20]吴银亮,刘艳敏,祝艳波.动态灰色模型的滑坡位移时间预测方法研究[J].铁道建筑,2011(7):88-90.(WU Yinliang,LIU Yanmin,ZHU Yanbo.Study of time prediction method for landslide displacement based on dynamic grey model[J].Railway Engineering,2011(7):88-90.)
[21]徐峻龄,廖小平,李荷生.黄茨大型滑坡的预报及其理论和方法[J].铁道工程学报,1996(2):197-205.(XU Junling,LIAO Xiaoping,LI Hesheng.Prediction for Huangci landslide and its theory and method[J].Journal of Railway Engineering Society,1996(2):197-205.)