基于集合卡尔曼滤波的岩土力学参数动态估计
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摘要
针对非确定性过程,引入集合卡尔曼滤波(EnKF)理论,视岩土变形体为一个随机动态系统,将位移观测值作为系统的输出,用集合卡尔曼滤波模型来描述系统的状态;进一步耦合数值分析方法实现岩土力学参数的随机动态估计,在有效地获得待估参数的同时还给出估计值的不确定性。通过数值算例表明,集合卡尔曼滤波可以有效地对含噪声的量测数据进行处理,能够跟踪岩土力学行为的动态变化。对比于常用最优化算法,集合卡尔曼滤波同时给出反演结果和先验知识的后验分布,显示出更好的实时性和可靠性。
With respect to the uncertainty process,the ensemble Kalman filter(EnKF) is introduced,the geomechanical deformation is treated as a dynamic stochastic system,and the displacement observation is looked as the output to describe the state of system with ensemble Kalmen filter. Furthermore,it is coupled with numerical modeling to cope with the uncertainty. Thus,the dynamical estimation of geomechanical parameters is performed,the parameter and its uncertainty are simultaneously obtained. The numerical examples show that the can effectively deal with the measured data polluted by noise,and can dynamically tract with the mechanical response of rock/soil mass. Compared with the conventional optimization algorithm,the EnKF shows the better character of real time and reliability because it can provide the inversion results and the posteriori distribution of the priori information together.
With respect to the uncertainty process,the ensemble Kalman filter(EnKF) is introduced,the geomechanical deformation is treated as a dynamic stochastic system,and the displacement observation is looked as the output to describe the state of system with ensemble Kalmen filter. Furthermore,it is coupled with numerical modeling to cope with the uncertainty. Thus,the dynamical estimation of geomechanical parameters is performed,the parameter and its uncertainty are simultaneously obtained. The numerical examples show that the can effectively deal with the measured data polluted by noise,and can dynamically tract with the mechanical response of rock/soil mass. Compared with the conventional optimization algorithm,the EnKF shows the better character of real time and reliability because it can provide the inversion results and the posteriori distribution of the priori information together.
引文
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[19]秦军,阎广建,刘绍民.集合卡尔曼滤波在遥感反演地表参数中的应用——以核驱动模型反演BRDF为例[J].中国科学(D辑)地球科学,2005,35(8):790798.(QIN Jun,YAN Guangjian,LIU Shaomin.Application of ensemble Kalman filter to geophysical parameters retrieval in remote sensing:a case study of kernel-driven BRDF model inversion[J].Sciences in China(Series D Earth Sciences),2005,35(8):790798.(in Chinese))
[20]Itasca Consulting Group,Inc.FLAC3D(fast Lagrangian analysis of continua)user manual,version2.1[R].Minneapolis,Minnesota:Itasca Consulting Group,Inc.,2002.
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[2]王芝银,杨志法,王思敬,等.岩石力学位移反演分析回顾及进展[J].力学进展,1998,28(4):488493.(WANG Zhiyin,YANG Zhifa,WANG Sijing,et al.A review on inverse analysis of displacements in rock mechanics[J].Advances in Mechanics,1998,28(4):488493.(in Chinese))
[3]王芝银,李云鹏.地下工程位移反分析及程序[M].西安:陕西科学技术出版社,1993.(WANG Zhiyin,LI Yunpeng.Methods and programs of back analysis of displacements in underground engineering[M].Xi′an:Shaanxi Science and Technology Press,1993.(in Chinese))
[4]周保生,朱维申.巷道围岩参数的人工神经网络预测[J].岩土力学,1999,20(1):2226.(ZHOU Baoshen,ZHU Weishen.Study on forecasting the parameters of roadway surrounding rock based byartificial neural networks[J].Rock and Soil Mechanics,1999,20(1):2226.(in Chinese)).
[5]冯夏庭.智能岩石力学导论[M].北京:科学出版社,2000.(FENG Xiating.Introduction to intelligent rock mechanics[M].Beijing:Science Press,2000.(in Chinese))
[6]孙钧.岩土力学反演问题的随机理论与方法[M].汕头:汕头大学出版社,1996.(SUN Jun.The stochastic theory and method of back analysis problems in rock and soil mechanics[M].Shantou:The Shantou University Press,1996.(in Chinese))
[7]BOLZON G,FEDELE R,MAIER G.Parameter identification of a cohesive crack model by Kalman filter[J].Computer Methods in Applied Mechanics and Engineering,2002,191(25/26):28472871.
[8]TANAKA M,MATSUMOTO T,YAMAMURA H.Application of BEM with extended Kalman filter to parameter identification of an elastic plate under dynamic loading[J].Engineering Analysis with Boundary Elements,2004,28(3):213219.
[9]蒋树屏.扩张卡尔曼滤波器有限元法耦合算法及其隧道工程应用[J].岩土工程学报,1996,18(4):1119.(JIANG Shuping.Coupling algorithm of extended Kalman filter-FEM and its application in tunnel engineering[J].Chinese Journal of Geotechnical Engineering,1996,18(4):1119.(in Chinese))
[10]蒋树屏,赵阳.复杂地质条件夏公路隧道围岩监测量测与非确定性反分析研究[J].岩石力学与工程学报,2004,23(20):43603464.(JIANG Shuping,ZHAO Yang.Study on monitoring and back analysis for road tunnel with complex geology[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(20):43603464.(in Chinese))
[11]王元淳,刘玉敏.正交各向异性平面弹性问题物性值v12和G12的反分析[J].力学与实践,2001,23(1):3840.(WANG Yuanchun,LIU Yumin.Inverse analysis of material parameters v12and G12of orthotropic plane elastic problem[J].Mechanics and Engineering,2001,23(1):3840.(in Chinese))
[12]费剑锋,韩月琪.集合卡尔曼滤波数据同化在一维波动方程中的应用[J].气象科技,2005,3(2):109114.(FEI Jianfeng,HAN Yueqi.Application of ensemble Kalman filter assimilation in one-dimensional wave equation[J].Meteorological Science and Technology,2005,3(2):109114.(in Chinese))
[13]EVENSEN G.The ensemble Kalman filter:theoretical formulation and practical implementation[J].Ocean Dynamics,2003,53(4):343367.
[14]EVENSEN G.Sequential Data assimilation with nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics[J].J.Geophys.Res.,1994,99(C5):1014310162.(in Chinese))
[15]刘成思,薛纪善.关于集合卡尔曼滤波的理论和方法的发展[J].热带气象学报,2005,21(6):828633.(LIU Chengsi,XUE Jishan.The ensemble Kalman filer theory and method development[J].Journal of Tropical Meteorology,2005,21(6):828633.(in Chinese))
[16]高山红,吴增茂,谢红琴.Kalman滤波在气象数据同化中的发展和应用[J].地球科学进展,2000,15(5):571575.(GAO Shanhong,WU Zengmao,XIE Hongqin.The developments and applications of Kalman filter in meteorological data assimilation[J].Advance in Earth Science,2000,15(5):571575.(in Chinese))
[17]高拴柱.集合卡尔曼滤波资料同化技术及研究现状[J].气象,2005,31(6):38.(GAO Shuanzhu.Review on ensemble Kalman filter data assimilation[J].Meteorology,2005,31(6):38.(in Chinese))
[18]朱江,汪萍.集合卡尔曼平滑和集合卡尔曼滤波在污染源反演中的应用[J].大气科学,2006,30(5):871882.(ZHU Jiang,WANG Ping.Ensemble Kalman smoother and ensemble Kalman filter approaches to the joint air quality state and emission estimation problem[J].Chinese Journal of Atmospheric Sciences,2006,30(5):871882.(in Chinese))
[19]秦军,阎广建,刘绍民.集合卡尔曼滤波在遥感反演地表参数中的应用——以核驱动模型反演BRDF为例[J].中国科学(D辑)地球科学,2005,35(8):790798.(QIN Jun,YAN Guangjian,LIU Shaomin.Application of ensemble Kalman filter to geophysical parameters retrieval in remote sensing:a case study of kernel-driven BRDF model inversion[J].Sciences in China(Series D Earth Sciences),2005,35(8):790798.(in Chinese))
[20]Itasca Consulting Group,Inc.FLAC3D(fast Lagrangian analysis of continua)user manual,version2.1[R].Minneapolis,Minnesota:Itasca Consulting Group,Inc.,2002.
[21]刘波,韩彦辉.FLAC原理、实例与应用指南[M].北京:人民交通出版社,2005.(LIU Bo,HAN Yanhui.FLAC′s theory,example and application guide[M].Beijing:China Communications Press,2005.(in Chinese))
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