利用卡尔曼滤波综合算法构建开采沉陷预测模型
|
摘要
为提高矿区地表沉陷预测精度,提出了基于自回归综合移动平均模型(Autoregressive Integrated Moving Average,ARIMA)的卡尔曼滤波模型与Elman神经网络相结合的综合预测模型。首先,针对沉陷监测序列的非平稳性与复杂性特点,ARIMA模型能够将原始数列平稳化,构建地表下沉预测模型,并作为卡尔曼滤波的状态方程;然后将Elman神经网络的沉陷预测结果作为观测值引入卡尔曼滤波观测方程中,建立综合预测模型;最后针对噪声方差Q与R选取的问题,统计出ARIMA模型与Elman神经网络模型的误差特性,从而计算出噪声Q与R的取值。分别将综合预测模型与BP神经网络模型、Elman神经网络模型以及卡尔曼滤波模型进行了预测精度对比,4种模型预测值与实测值的均方根误差分别为2.06、5.857 8、2.926 9、3.688 9 mm,相对误差分别为1.170 4%、3.0502%、1.432 6%、1.908 4%,绝对误差平均值分别为1.886 7、10.703 9、2.329 4、2.807 6 mm。研究表明:综合预测模型能够有效减小单一预测机制造成的同一性质误差累积,其预测精度明显优于其余3种模型,对于大幅提升矿区地表沉陷的预测精度有一定的参考价值。
In order to improve the prediction accuracy of mining subsidence in mining area,a integrated prediction model with the combination of the Kalman filter model and Elman neural network is proposed based on the autoregressive integrated moving average model(ARIMA).Firstly,in view of the non-stationarity and complexity characteristics of the subsidence mining monitoring sequence,ARIMA model is able to stabilize the original sequence,so as to construct the prediction model of surface subsidence and serve as the equation of state of Kalman filter;then,the results of Elman neural network subsidence prediction is introduced as the measured value into the Kalman filter measurement equation to establish the integrated prediction model;finally,for the selection of noise variance Q and R,the error characteristics of ARIMA model and Elman network model are calculated,so as to calculate the value of noise Q and R.Comparison of the prediction accuracy of the integrated prediction model proposed in this paper and BP neural network model,Elman neural network model,Kalman filter model.The results show that the root-mean-square-error(RMSE)of the prediction values and actual measured data of the four models are 2.06,5.857 8,2.926 9,3.688 9 mm respectively,the relative error of the four models are 1.170 4%、3.050 2%、1.432 6% and 1.908 4%,mean absolute errors of them are 1.886 7,10.703 9,2.329 4,2.807 6 mm.The study results indicated that the integrated prediction model can effectively reduce the accumulation of errors of the same nature caused by a single prediction mechanism,the prediction accuracy of the integrated model is superior to the ones of other three models,it is help for improving the prediction accuracy of mining subsidence in mining area.
In order to improve the prediction accuracy of mining subsidence in mining area,a integrated prediction model with the combination of the Kalman filter model and Elman neural network is proposed based on the autoregressive integrated moving average model(ARIMA).Firstly,in view of the non-stationarity and complexity characteristics of the subsidence mining monitoring sequence,ARIMA model is able to stabilize the original sequence,so as to construct the prediction model of surface subsidence and serve as the equation of state of Kalman filter;then,the results of Elman neural network subsidence prediction is introduced as the measured value into the Kalman filter measurement equation to establish the integrated prediction model;finally,for the selection of noise variance Q and R,the error characteristics of ARIMA model and Elman network model are calculated,so as to calculate the value of noise Q and R.Comparison of the prediction accuracy of the integrated prediction model proposed in this paper and BP neural network model,Elman neural network model,Kalman filter model.The results show that the root-mean-square-error(RMSE)of the prediction values and actual measured data of the four models are 2.06,5.857 8,2.926 9,3.688 9 mm respectively,the relative error of the four models are 1.170 4%、3.050 2%、1.432 6% and 1.908 4%,mean absolute errors of them are 1.886 7,10.703 9,2.329 4,2.807 6 mm.The study results indicated that the integrated prediction model can effectively reduce the accumulation of errors of the same nature caused by a single prediction mechanism,the prediction accuracy of the integrated model is superior to the ones of other three models,it is help for improving the prediction accuracy of mining subsidence in mining area.
引文
[1]黄声享.变形监测数据处理[M].武汉:武汉大学出版社,2010.Huang Shengxiang.Data Processing of Deformation Monitoring[M].Wuhan:Wuhan University Press,2010.
[2]李磊.采空区地表沉降监测数据分析与预测研究[D].西安:西安建筑科技大学,2012.Li Lei.Research of Monitoring Data Analysis and Prediction on the Settlement of Goaf Surface[D].Xi'an:Xi'an University of Architecture and Technology,2012.
[3]孟磊,于庆锋,宋永超.人工神经网络方法(BP)在变形监测中的应用[J].测绘与空间地理信息,2018,41(7):215-218.Meng Lei,Yu Qingfeng,Song Yongchao.Application of artificial neural network method(BP)in deformation monitoring[J].Geomatics Spatial Information Technology,2018,41(7):215-218.
[4]黄文杰,傅砾,肖盛.采用改进模糊层次分析法的风速预测模型[J].电网技术,2010,34(7):164-168.Huang Wenjie,Fu Li,Xiao Sheng.A predictive model of wind speed based on improved fuzzy analytical hierarchy process[J].Power System Technology,2010,34(7):164-168.
[5]朱军桃,熊东旭,李亚威.基于卡尔曼滤波的灰色马尔科夫组合模型在基坑变形监测中的应用[J].桂林理工大学学报,2017,37(4):653-657.Zhu Juntao,Xiong Dongxu,Li Yawei.Application of gray Markov combined modelbased on Kalman filter in foundation pit deformation monitoring[J].Journal of Guilin University of Technology,2017,37(4):653-657.
[6]容静,刘立龙,文鸿雁,等.基于卡尔曼滤波的GM(1,1)-AR预测模型在变形预测中的应用[J].桂林理工大学学报,2018,38(2):301-305.Rong Jing,Liu Lilong,Wen Hongyan,et al.Application of GM(1,1)-AR forecasting model based on Kalman filter in deformation forecast[J].Journal of Guilin University of Technology,2018,38(2):301-305.
[7]罗亦泳,姚宜斌,赵庆志,等.利用优化的组合核相关向量机算法构建地表下沉预测模型[J].武汉大学学报:信息科学版,2018,43(9):1295-1301.Luo Yiyong,Yao Yibin,Zhao Qingzhi,et al.Prediction of Surface Subsidence of underground mining based on HIOA and MK-RVM[J].Geomatics and Information Science of Wuhan University,2018,43(9):1295-1301.
[8]霍玉华.隧道围岩变形量预测的灰色模型应用比较研究[J].北京交通大学学报,2006,30(4):42-45.Huo Yuhua.Study on the gray model and its application in forecasting deformation of tunnel surrounding rock[J].Journal of Beijing Jiaotong University,2006,30(4):42-45.
[9]刘福臻,耿波涛,刘丹.矿区地表沉陷预测的KPCA-LSSVM模型[J].金属矿山,2018(5):130-134.Liu Fuzhen,Geng Botao,Liu Dan.Mine surface mining subsidence prediction based on KPCA-LSSVM mode[lJ].Metal Mine,2018(5):130-134.
[10]陈晨,魏冠军,寇瑞雄,等.基于Kalman滤波的GM(1,1)-AR模型在高层建筑物沉降变形分析中的应用[J].测绘工程,2018,27(10):64-67.Chen Chen,Wei Guanjun,Kou Ruixiong,et al.Application of GM(1,1)-AR model based on Kalman filter to settlement deformation analysis of high-rise buildings[J].Engineering of Surveying and Mapping,2018,27(10):64-67.
[11]修春波,任晓,李艳晴,等.基于卡尔曼滤波的风速序列短期预测方法[J].电工技术学报,2014,29(2):253-259.Xiu Chunbo,Ren Xiao,Li Yanqing,et al.Short-term prediction method of wind speed series based on Kalman filtering fusion[J].Transactions of China Electrotechnical Society,2014,29(2):253-258.
[12]李艳晴,修春波,张欣.基于卡尔曼滤波的迟滞神经网络风速序列预测[J].北京科技大学学报,2014,36(8):1108-1114.Li Yanqing,Xiu Chunbo,Zhang Xin.Wind speed forecasting by a hysteretic neural network based on Kalman filtering[J].Journal of University of Science and Technology Beijing,2014,36(8):1108-1114.
[13]Liu H,Tian H Q,Li Y F.Comparison of two new ARIMA-ANN and ARIMA-Kalman hybrid methods for wind speed prediction[J].Applied Energy,2012,98(1):415-424.
[14]韩亚坤,文鸿雁,郭雷,等.基于神经网络的新息自适应卡尔曼滤波在高速公路变形监测中的应用[J].桂林理工大学学报,2017,37(1):136-139.Han Yakun,Wen Hongyan,Guo Lei,et al.Application of innovation adaptive Kalman filter based on BP neural network in expressway deformation monitoring[J].Journal of Guilin University of Technology,2017,37(1):136-139.
[15]王利,李亚红,刘万林.卡尔曼滤波在大坝动态变形监测数据处理中的应用[J].西安科技大学学报,2006,26(3):353-357.Wang Li,Li Yalin,Liu Wanlin.Application of Kalman filtering in data processing of dam dynamicdeformation monitoring[J].Journal of Xi'an University of Science and Technology,2006,26(3):353-357.
[16]司守奎,孙兆亮.数学建模算法与应用[M].北京:国防工业出版社,2011.Si Shoukui,Sun Zhaoliang.Mathematical Modeling[M].Beijing:National Defence Industry Press,2011.
[17]潘迪夫,刘辉,李燕飞.基于时间序列分析和卡尔曼滤波算法的风电场风速预测优化模型[J].电网技术,2008,32(7):82-86.Pan Difu,Liu Hui,Li Yanfei.A wind speed forecasting optimization model for wind farms based on time series analysis and Kalman filter algorithm[J].Power System Technology,2008,32(7):82-86.
[18]谢荣晖,郑东健.卡尔曼滤波-AR模型在大坝变形预测中的应用[J].人民黄河,2017,39(2):133-135.Xie Ronghui,Zheng Dongjian.Application of Kalman filtering-ARmodel in dam deformation monitoring[J].Yellow River,2017,39(2):133-135.
[19]王新岩.PSO-Elman神经网络在尾矿坝位移预测中的应用[J].有色金属:矿山部分,2018,70(5):18-21.Wang Xinyan.Application of PSO-Elman neural network in displacement prediction of tailings dam[J].Nonferrous Metals:Mining Section,2018,70(5):18-21.
[20]王祖顺,韩吉德,王春青.回归-Elman网络在矿坝变形预测中的应用[J].测绘工程,2016,25(1):39-42.Wang Zushun,Han Jide,Wang Chunqing.Application of regressionElman network model to the dam deformation forcasting[J].Engineering of Surveying and Mapping,2016,25(1):39-42.
[21]李寻昌,叶君文,李葛,等.基于滑坡监测数据的Elman神经网络动态预测[J].煤田地质与勘探,2018,46(3):113-120.Li Xunchang,Ye Junwen,Li Ge,et al.Elman neural network dynamic prediction based on landslide monitoring data[J].Coal Geology&Exploration,2018,46(3):113-120.
[22]易云飞,盛康.基于时间序列分析的水位短期预测模型仿真[J].计算机工程与设计,2016(5):1331-1334.Yi Yunfei,Sheng Kang.Time series analysis based short-term forecasting model simulation of water level[J].Computer Engineering and Design,2016(5):1331-1334.
[2]李磊.采空区地表沉降监测数据分析与预测研究[D].西安:西安建筑科技大学,2012.Li Lei.Research of Monitoring Data Analysis and Prediction on the Settlement of Goaf Surface[D].Xi'an:Xi'an University of Architecture and Technology,2012.
[3]孟磊,于庆锋,宋永超.人工神经网络方法(BP)在变形监测中的应用[J].测绘与空间地理信息,2018,41(7):215-218.Meng Lei,Yu Qingfeng,Song Yongchao.Application of artificial neural network method(BP)in deformation monitoring[J].Geomatics Spatial Information Technology,2018,41(7):215-218.
[4]黄文杰,傅砾,肖盛.采用改进模糊层次分析法的风速预测模型[J].电网技术,2010,34(7):164-168.Huang Wenjie,Fu Li,Xiao Sheng.A predictive model of wind speed based on improved fuzzy analytical hierarchy process[J].Power System Technology,2010,34(7):164-168.
[5]朱军桃,熊东旭,李亚威.基于卡尔曼滤波的灰色马尔科夫组合模型在基坑变形监测中的应用[J].桂林理工大学学报,2017,37(4):653-657.Zhu Juntao,Xiong Dongxu,Li Yawei.Application of gray Markov combined modelbased on Kalman filter in foundation pit deformation monitoring[J].Journal of Guilin University of Technology,2017,37(4):653-657.
[6]容静,刘立龙,文鸿雁,等.基于卡尔曼滤波的GM(1,1)-AR预测模型在变形预测中的应用[J].桂林理工大学学报,2018,38(2):301-305.Rong Jing,Liu Lilong,Wen Hongyan,et al.Application of GM(1,1)-AR forecasting model based on Kalman filter in deformation forecast[J].Journal of Guilin University of Technology,2018,38(2):301-305.
[7]罗亦泳,姚宜斌,赵庆志,等.利用优化的组合核相关向量机算法构建地表下沉预测模型[J].武汉大学学报:信息科学版,2018,43(9):1295-1301.Luo Yiyong,Yao Yibin,Zhao Qingzhi,et al.Prediction of Surface Subsidence of underground mining based on HIOA and MK-RVM[J].Geomatics and Information Science of Wuhan University,2018,43(9):1295-1301.
[8]霍玉华.隧道围岩变形量预测的灰色模型应用比较研究[J].北京交通大学学报,2006,30(4):42-45.Huo Yuhua.Study on the gray model and its application in forecasting deformation of tunnel surrounding rock[J].Journal of Beijing Jiaotong University,2006,30(4):42-45.
[9]刘福臻,耿波涛,刘丹.矿区地表沉陷预测的KPCA-LSSVM模型[J].金属矿山,2018(5):130-134.Liu Fuzhen,Geng Botao,Liu Dan.Mine surface mining subsidence prediction based on KPCA-LSSVM mode[lJ].Metal Mine,2018(5):130-134.
[10]陈晨,魏冠军,寇瑞雄,等.基于Kalman滤波的GM(1,1)-AR模型在高层建筑物沉降变形分析中的应用[J].测绘工程,2018,27(10):64-67.Chen Chen,Wei Guanjun,Kou Ruixiong,et al.Application of GM(1,1)-AR model based on Kalman filter to settlement deformation analysis of high-rise buildings[J].Engineering of Surveying and Mapping,2018,27(10):64-67.
[11]修春波,任晓,李艳晴,等.基于卡尔曼滤波的风速序列短期预测方法[J].电工技术学报,2014,29(2):253-259.Xiu Chunbo,Ren Xiao,Li Yanqing,et al.Short-term prediction method of wind speed series based on Kalman filtering fusion[J].Transactions of China Electrotechnical Society,2014,29(2):253-258.
[12]李艳晴,修春波,张欣.基于卡尔曼滤波的迟滞神经网络风速序列预测[J].北京科技大学学报,2014,36(8):1108-1114.Li Yanqing,Xiu Chunbo,Zhang Xin.Wind speed forecasting by a hysteretic neural network based on Kalman filtering[J].Journal of University of Science and Technology Beijing,2014,36(8):1108-1114.
[13]Liu H,Tian H Q,Li Y F.Comparison of two new ARIMA-ANN and ARIMA-Kalman hybrid methods for wind speed prediction[J].Applied Energy,2012,98(1):415-424.
[14]韩亚坤,文鸿雁,郭雷,等.基于神经网络的新息自适应卡尔曼滤波在高速公路变形监测中的应用[J].桂林理工大学学报,2017,37(1):136-139.Han Yakun,Wen Hongyan,Guo Lei,et al.Application of innovation adaptive Kalman filter based on BP neural network in expressway deformation monitoring[J].Journal of Guilin University of Technology,2017,37(1):136-139.
[15]王利,李亚红,刘万林.卡尔曼滤波在大坝动态变形监测数据处理中的应用[J].西安科技大学学报,2006,26(3):353-357.Wang Li,Li Yalin,Liu Wanlin.Application of Kalman filtering in data processing of dam dynamicdeformation monitoring[J].Journal of Xi'an University of Science and Technology,2006,26(3):353-357.
[16]司守奎,孙兆亮.数学建模算法与应用[M].北京:国防工业出版社,2011.Si Shoukui,Sun Zhaoliang.Mathematical Modeling[M].Beijing:National Defence Industry Press,2011.
[17]潘迪夫,刘辉,李燕飞.基于时间序列分析和卡尔曼滤波算法的风电场风速预测优化模型[J].电网技术,2008,32(7):82-86.Pan Difu,Liu Hui,Li Yanfei.A wind speed forecasting optimization model for wind farms based on time series analysis and Kalman filter algorithm[J].Power System Technology,2008,32(7):82-86.
[18]谢荣晖,郑东健.卡尔曼滤波-AR模型在大坝变形预测中的应用[J].人民黄河,2017,39(2):133-135.Xie Ronghui,Zheng Dongjian.Application of Kalman filtering-ARmodel in dam deformation monitoring[J].Yellow River,2017,39(2):133-135.
[19]王新岩.PSO-Elman神经网络在尾矿坝位移预测中的应用[J].有色金属:矿山部分,2018,70(5):18-21.Wang Xinyan.Application of PSO-Elman neural network in displacement prediction of tailings dam[J].Nonferrous Metals:Mining Section,2018,70(5):18-21.
[20]王祖顺,韩吉德,王春青.回归-Elman网络在矿坝变形预测中的应用[J].测绘工程,2016,25(1):39-42.Wang Zushun,Han Jide,Wang Chunqing.Application of regressionElman network model to the dam deformation forcasting[J].Engineering of Surveying and Mapping,2016,25(1):39-42.
[21]李寻昌,叶君文,李葛,等.基于滑坡监测数据的Elman神经网络动态预测[J].煤田地质与勘探,2018,46(3):113-120.Li Xunchang,Ye Junwen,Li Ge,et al.Elman neural network dynamic prediction based on landslide monitoring data[J].Coal Geology&Exploration,2018,46(3):113-120.
[22]易云飞,盛康.基于时间序列分析的水位短期预测模型仿真[J].计算机工程与设计,2016(5):1331-1334.Yi Yunfei,Sheng Kang.Time series analysis based short-term forecasting model simulation of water level[J].Computer Engineering and Design,2016(5):1331-1334.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |