回归分析与抗差卡尔曼滤波协同下大型边坡短期变形的预测方法
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摘要
由于边坡滑移影响因素众多,无法建立精确的动力学模型,因此利用传统抗差卡尔曼滤波模型进行边坡短期变形预测十分困难,无法满足大型边坡高精度的预警需求。建立回归分析与抗差卡尔曼滤波协同下大型边坡短期变形预测模型,利用拟合值代替含粗差数据进行滤波预测运算,解决了卡尔曼滤波缺乏对粗差的抗干扰性问题。利用金堆城露天钼矿大型边坡监测数据开展工程案例研究,结果表明2种预测模型都是有效的,但回归分析与抗差卡尔曼滤波协同下大型边坡短期变形预测模型精度和抗差性2个指标都优于传统抗差卡尔曼滤波模型。
Due to many factors affecting the landslide,it is difficult to create an accurate kinetic model,and also it is hard to predict the short-term deformation of large-scale slope by using the traditional dynamic model to meet the demand for high-precision early warning of large-scale slopes. The short-term deformation prediction model for large-scale slope was established under the cooperation of regression analysis and robust Kalman filter. Fitting value was adopted to replace the data containing gross errors for filtering and prediction operation,which solves the problem of Kalman filter lacking for anti-interference to gross errors. The engineering case based on monitoring data of large-scale slope in Jinduicheng Open-pit Molybdenum Mine showed that both of the prediction models are effective,but the precision and robustness of the short-term deformation prediction model of large-scale slope under the cooperation of regression analysis and robust Kalman filter are better than the traditional robust Kalman filter model.
Due to many factors affecting the landslide,it is difficult to create an accurate kinetic model,and also it is hard to predict the short-term deformation of large-scale slope by using the traditional dynamic model to meet the demand for high-precision early warning of large-scale slopes. The short-term deformation prediction model for large-scale slope was established under the cooperation of regression analysis and robust Kalman filter. Fitting value was adopted to replace the data containing gross errors for filtering and prediction operation,which solves the problem of Kalman filter lacking for anti-interference to gross errors. The engineering case based on monitoring data of large-scale slope in Jinduicheng Open-pit Molybdenum Mine showed that both of the prediction models are effective,but the precision and robustness of the short-term deformation prediction model of large-scale slope under the cooperation of regression analysis and robust Kalman filter are better than the traditional robust Kalman filter model.
引文
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[15]赵选民.数理统计[M].北京:科学出版社,2002.Zhao Xuanmin.Mathematical Statistics[M].Beijing:Science Press,2002.
[2]冯勤生.边坡岩体变形灰色预测研究[J].内蒙古科技大学学报,2011,30(3):196-198.Feng Qinsheng.Study of grey forecasting in slope rock mass deformation[J].Journal of Inner Mongolia University of Science and Technology,2011,30(3):196-198.
[3]齐公玉.基于均方误差最小的卡尔曼滤波实用算法[J].测绘通报,2009(7):9-11.Qi Gongyu.Kalman Filter applied algorithm based on mean square error minimum[J].Bulletin of Surveying and Mapping,2009(7):9-11.
[4]李希峰.抗差卡尔曼滤波在桥梁塔索中的变形监测中的应用[D].南京:河海大学,2006.Li Xifeng.The Application of Robust Kalman Filtering in Bridge Cable Tower Deformation Monitor[D].Nanjing:Hehai University,2006.
[5]高宁.抗野值自适应卡尔曼滤波方法的研究[J].中国惯性技术学报.2003,11(3):25-28.Gao Ning.The research of adaptively robust Kalman filtering[J].Journal of Chinese Inertial Technology,2003,11(3):25-28.
[6]杨元喜.动态系统的抗差kalman滤波[J].测绘科学技术学报,1997,14(2):79-84.Yang Yuanxi.Robust Kalman filtering of dynamical system[J].Journal of Geomatics Science and Technology,1997,14(2):79-84.
[7]高广为.基于当前加速度模型的抗差自适应Kalman滤波[J].测绘学报,2006,35(1):15-18.Gao Guangwei.Adaptive robust Kalman filtering based on the current statistical model[J].Acta Geodaetica et Cartographica Sinica,2006,35(1):15-18.
[8]Mostafa E.Investigation of adaptive robust Kalman filtering algorithms for GPS/DR navigation system filters[J].IOP Conference Series-Materials Science and Engineering,2017,187(1):12-19
[9]Mahmoud M S.Robust Kalman filtering for continuous time-lag systems with Markovian jump parameter[J].Engineering,Electrical&Electronic,2003,50(1):98-105
[10]周江文.经典误差理论与抗差估计[J].测绘学报,1989,18(2):115-120.Zhou Jiangwen.The classical error theory and robust estimation[J].Acta Geodaetica et Cartographica Sinica,1989,18(2):115-120.
[11]程明飞.抗差自适应Kalman滤波及其在GNSS测姿系统中的应用[D].上海:华东师范大学,2016.Cheng Mingfei.Robust Adaptive Kalman Filtering and Its Application in GNSS Attitude Determination[D].Shanghai:East China Normal University,2016.
[12]刘伟诚.基于自适应卡尔曼滤波的沉降变形监测数据估计[J].水利与建筑工程学报,2012,10(5):26-29.Liu Weicheng.Estimation for deformation monitoring data based on adaptive Kalman filtering method[J].Journal of Water Resources and Architectural Engineering,2012,10(5):26-29.
[13]杨元喜.抗差估计理论及其应用[M].北京:解放军出版社,1993.Yang Yuanxi.Robust Estimation Theory and Its Application[M].Beijing:People's Liberation Army Press,1993.
[14]张小红.一种改进的抗差Kalman滤波方法在精密单点定位中的应用[J].武汉大学学报:信息科学版,2015,40(7):858-864.Zhang Xiaohong.An improved robust Kalman filtering and its application in PPP[J].Geomatics and Information Science of Wuhan University,2015,40(7):858-864.
[15]赵选民.数理统计[M].北京:科学出版社,2002.Zhao Xuanmin.Mathematical Statistics[M].Beijing:Science Press,2002.