改进的卡尔曼灰色模型在隧道沉降预测中的应用
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摘要
为提高地表沉降预测精度,针对灰色预测模型(GM(1,1))易受随机干扰影响致使预测精度不高的问题,建立了基于卡尔曼滤波的灰色理论预测模型。考虑到沉降量受到温度和时间因素影响较大的特点,将地表的沉降看作时间、温度的相关函数来建立卡尔曼滤波模型,并利用迭代滤波理论和LevenbergMarquardt优化滤波,构建改进的卡尔曼滤波模型。改进的卡尔曼滤波模型与灰色模型相结合,应用于地表沉降预测中,并将改进的卡尔曼滤波灰色模型预测结果与卡尔曼滤波灰色模型的预测结果进行对比。实例计算表明,使用改进的卡尔曼滤波对消除检测数据扰动误差后的数据进行灰色模型预测的精度相比于单纯灰色预测的预测精度更高。
In order to improve the prediction accuracy of surface subsidence, and solve the problem that the gray prediction model(GM(1,1)) is easily affected by random interference, the gray theory prediction model based on kalman filter is established.Since the subsidence can be greatly affected by temperature, precipitation and time, the subsidence of land surface is regarded as the correlation function of these factors.The improved kalman filter model is constructed by using the iterative filtering theory and levenberg-marquardt optimization filter, which is combined with the gray model and applied to the prediction of surface subsidence.The result shows that the accuracy of the improved model is higher than that of the pure gray model.
In order to improve the prediction accuracy of surface subsidence, and solve the problem that the gray prediction model(GM(1,1)) is easily affected by random interference, the gray theory prediction model based on kalman filter is established.Since the subsidence can be greatly affected by temperature, precipitation and time, the subsidence of land surface is regarded as the correlation function of these factors.The improved kalman filter model is constructed by using the iterative filtering theory and levenberg-marquardt optimization filter, which is combined with the gray model and applied to the prediction of surface subsidence.The result shows that the accuracy of the improved model is higher than that of the pure gray model.
引文
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[15]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.
[2]韩亚坤,文鸿雁,郭雷.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(01):136-139.
[3]罗亦泳,张立亭,鲁铁定,等.露天矿边坡变形预测的协同进化多核相关向量机模型[J].中国安全科学学报, 2016(11):110-114.
[4]李秀珍,孔纪名,王成华.最优加权组合模型在滑坡变形预测中的应用[J].自然灾害学报, 2008, 17(2):53-57.
[5]周吕,文鸿雁,韩亚坤.灰色预测与Kalman滤波在建筑物沉降变形分析中的应用[J].测绘科学, 2014, 39(4):149-151.
[6]陈亮青,邹宗兴,苑谊,王艳昆.考虑诱发因素影响滞后性的库岸滑坡位移预测[J].人民长江,2018,49(10):60-65.
[7]付杰,牛瑞卿.三峡库区老蛇窝滑坡变形规律数据挖掘[J].人民长江,2012,43(23):31-35.
[8]陆付民,蒋廷耀.基于多因子及泰勒级数的滑坡变形预测模型研究[J].大地测量与地球动力学, 2017, 37(10):1029-1032.
[9]陆付民,李劲.顾及时间和开挖深度的卡尔曼滤波模型在建筑物变形分析中的应用[J].测绘通报,2012(02):59-61.
[10]崔凯,秦晓同,荆祥.季节性冻土区路基高边坡变形多因素时变预测模型[J/OL].哈尔滨工程大学学报,2019(06):1-7.
[11]文鸿雁,周吕,韩亚坤,等.基于卡尔曼滤波的GM(1,1)模型在高铁隧道沉降变形分析中的应用[J].大地测量与地球动力学, 2014, 34(1):88-91.
[12]崔希璋,於宗俦,陶本藻,等.广义测量平差[M].武汉:武汉大学出版杜, 2005.
[13]杨宏,李亚安,李国辉.一种改进扩展卡尔曼滤波新方法[J].计算机工程与应用, 2010, 46(19):18-20.
[14] Dennis J E J, Schnabel R B. Numerical methods for unconstrained optimization and nonlinear equations/[M]//Numerical methods for unconstrained optimization and nonlinear equations. Prentice-Hall, 1983:64-64.
[15]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.