基于熵-盲数的贝叶斯渗流参数反演分析研究
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摘要
已有的贝叶斯参数反演方法仅考虑反演过程中的随机性,忽略了渗流参数的灰色和未确知等不确定性,本文提出一种基于熵-盲数理论的贝叶斯渗流参数反演方法。该方法在反演模型中引入熵-盲数理论,将待反演参数视为盲数,充分考虑反演过程中的不确定性,采用差分进化自适应Metropolis(DREAM)算法对渗流参数的后验分布进行推导,利用响应面模型替代渗流场数值模拟的正演模型,解决传统贝叶斯渗流参数反演方法需要大量调用正演模型进行运算才能达到收敛、计算效率较低的问题。通过算例分析及某碾压混凝土坝坝基的渗透系数反演,验证了该方法的有效性和准确性。
The existing parameter inversion methods based on Bayesian theory consider only the randomness in inversion process, neglecting the grey and unascertained uncertainties in seepage parameters. This paper presents an inversion method for estimating seepage parameters based on Bayesian theory and entropy-blind numbers. This new method introduces the entropy-blind number theory into the inversion model, taking the parameters to be inverted as blind numbers and fully considering the uncertainties in inversion process. We use a differential evolution adaptive metropolis(DREAM) algorithm to derive the posterior distribution of seepage parameters, and adopt a response surface model to replace the seepage simulation forward model, thereby avoiding a large number of forward model simulations in the traditional Bayesian seepage parameter inversion method. Our new method and its accuracy are validated through example analysis and a case study of permeability coefficient inversion for the foundation of a concrete gravity dam.
The existing parameter inversion methods based on Bayesian theory consider only the randomness in inversion process, neglecting the grey and unascertained uncertainties in seepage parameters. This paper presents an inversion method for estimating seepage parameters based on Bayesian theory and entropy-blind numbers. This new method introduces the entropy-blind number theory into the inversion model, taking the parameters to be inverted as blind numbers and fully considering the uncertainties in inversion process. We use a differential evolution adaptive metropolis(DREAM) algorithm to derive the posterior distribution of seepage parameters, and adopt a response surface model to replace the seepage simulation forward model, thereby avoiding a large number of forward model simulations in the traditional Bayesian seepage parameter inversion method. Our new method and its accuracy are validated through example analysis and a case study of permeability coefficient inversion for the foundation of a concrete gravity dam.
引文
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[14]钟登华,鄢玉玲,崔博,等.考虑压实质量影响的碾压混凝土坝层间结合质量动态评价研究[J].水利学报,2017,48(10):1135-1146.ZHONG Denghua,YAN Yuling,CUI Bo,et al.Dynamic evaluation of RCC dam Interlayer bonding quality considering the influence of compaction quality[J].Journal of Hydraulic Engineering,2017,48(10):1135-1146.(in Chinese)
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[17]VRUGT J A.Markov chain Monte Carlo simulation using the DREAM software package:Theory,concepts,and MATLAB implementation[J].Environmental Modelling and Software,2016,75:273-316.
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[19]杨运,吴吉春,骆乾坤,等.DREAM算法分析地下水数值模拟不确定性的影响因素[J].地质评论,2016,62(2):343-361.YANG Yun,WU Jichun,LUO Qiankun,et al.Analysis of the uncertainty of groundwater numerical simulation based on the DREAM algorithm[J].Geological Review,2016,62(2):343-361.(in Chinese)
[20]曹飞凤,尹祖宏.融合MCMC方法的差分进化算法在水文模型参数优选中的应用[J].南水北调与水利科技,2015,13(2):202-205.CAO Feifeng,YIN Zuhong.Application of differential evolution algorithm combined with Markow Chain Monte Carlo in parameter optimization of hydrologic model[J].South-to-North Water Transfers and Water Science and Technology,2015,13(2):202-205.(in Chinese)
[21]陈海涛,黄鑫,邱林,等.基于最大熵原理的区域农业干旱度概率分布模型[J].水利学报,2013,44(2):221-226.CHEN Haitao,HUANG Xin,QIU Lin,et al.Probability distribution model of regional agricultural drought degree based on the maximum entropy principle[J].Journal of Hydraulic Engineering,2013,44(2):221-226.(in Chinese)
[22]程正飞,王晓玲,吕鹏,等.基于VOF法的碾压混凝土坝自由渗流场数值模拟[J].水利学报,2015,46(5):558-566.CHENG Zhengfei,WANG Xiaoling,LV Peng,et al.Numerical simulation of free seepage field in RCC dams based on VOF method[J].Journal of Hydraulic Engineering,2015,46(5):558-566.(in Chinese)
[2]房殿利,强丽峰,孙强,等.柴河水库土坝渗透系数反演分析[J].人民黄河,2014,36(4):95-98.FANG Dianli,QIANG Lifeng,SUN Qiang,et al.Permeability coefficient inverse analysis for the earth dam in Chaihe Reservoir[J].Yellow River,2014,36(4):95-98.(in Chinese)
[3]刘武,陈益峰,胡冉,等.基于非稳定渗流过程的岩体渗透特性反演分析[J].岩石力学与工程学报,2015,34(2):362-373.LIU Wu,CHEN Yifeng,HU Ran,et al.Back analysis of rock permeability with consideration of transient flow process[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(2):362-373.(in Chinese)
[4]魏连伟,邵景力,张建立,等.模拟退火算法反演水文地质参数算例研究[J].吉林大学学报(地球科学版),2004,34(4):612-616.WEI Lianwei,SHAO Jingli,ZHANG Jianli,et al.Application of simulated annealing algorithm to hydrogeological parameter inversion[J].Journal of Jilin University(Earth Science Edition),2004,34(4):612-616.(in Chinese)
[5]张繁昌,肖张波,印兴耀.地震数据约束下的贝叶斯随机反演[J].石油地球物理勘探,2014,49(1):176-183.ZHANG Fanchang,XIAO Zhangbo,YIN Xingyao.Bayesian stochastic inversion constrained by seismic data[J].Oil Geophysical Prospecting,2014,49(1):176-183.(in Chinese)
[6]陆乐,吴吉春,陈景雅.基于贝叶斯方法的水文地质参数识别[J].水文地质工程地质,2008(5):58-63.LU Le,WU Jichun,CHEN Jingya.Identification of hydrogeological parameters based on the Bayesian method[J].Hydrogeology&Engineering Geology,2008(5):58-63.(in Chinese)
[7]殷建.基于贝叶斯理论的P-III分布参数估计与不确定性研究[D].杨凌:西北农林科技大学,2015.YIN Jian.Bayesian theory for estimating P-III distribution parameters and uncertainty[D].Yangling:Northwest A&F University,2015.(in Chinese)
[8]李朋涛.基于嵌套贝叶斯方法的水文地质参数反演[D].北京:中国矿业大学,2016.LI Pengtao.Inversion of hydrogeological parameters based on the nested Bayesian method[D].Beijing:China University of Mining and Technology,2016.(in Chinese)
[9]张江江.地下水污染源解析的贝叶斯监测设计与参数反演方法[D].杭州:浙江大学,2017.ZHANG Jiangjiang.Bayesian monitoring design and parameter inversion for groundwater contaminant source identification[D].Hangzhou:Zhejiang University,2017.(in Chinese)
[10]YUSTRES A,ASENSIO L,ALONSO J,et al.A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow[J].Computational Geosciences,2012,16(1):1-20.
[11]MOREIRA P H S,VAN GENUCHTEN M T,ORLANDEH R B,et al.Bayesian estimation of the hydraulic and solute transport properties of a small-scale unsaturated soil column[J].Journal of Hydrology and Hydromechanics,2016,64(1):30-44.
[12]刘开第,吴和琴,庞彦军.不确定性信息数学处理及应用[M].北京:科学出版社,1999.LIU Kaidi,WU Heqin,PANG Yanjun.Mathematical processing and application of uncertain information[M].Beijing:Science Press,1999.(in Chinese)
[13]陈训龙,龚文惠,邱金伟,等.基于盲数理论的边坡可靠度分析[J].岩石力学与工程学报,2016,35(6):1155-1160.CHEN Xunlong,GONG Wenhui,QIU Jinwei,et al.Reliability analysis of slopes based on blind data theory[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(6):1155-1160.(in Chinese)
[14]钟登华,鄢玉玲,崔博,等.考虑压实质量影响的碾压混凝土坝层间结合质量动态评价研究[J].水利学报,2017,48(10):1135-1146.ZHONG Denghua,YAN Yuling,CUI Bo,et al.Dynamic evaluation of RCC dam Interlayer bonding quality considering the influence of compaction quality[J].Journal of Hydraulic Engineering,2017,48(10):1135-1146.(in Chinese)
[15]SHI X Q,YE M,CURTIS G P,et al.Assessment of parametric uncertainty for groundwater reactive transport modeling[J].Water Resources Research,2014,50:4416-4439.
[16]VRUGT J A,TER BRAAK C J F,DIKS C G H,et al.Accelerating markov chain monte carlo simulation by differential evolution with self-adaptive randomized subspace sampling[J].International Journal of Nonlinear Sciences and Numerical Simulation,2009,10(3):273-290.
[17]VRUGT J A.Markov chain Monte Carlo simulation using the DREAM software package:Theory,concepts,and MATLAB implementation[J].Environmental Modelling and Software,2016,75:273-316.
[18]骆乾坤,吴剑锋,杨运,等.基于DREAM算法的含水层渗透系数空间变异特征识别[J].南京大学学报(自然科学),2016,52(3):448-455.LUO Qiankun,WU Jianfeng,YANG Yun,et al.Identification of the spatial variability of aquifer hydraulic conductivity[J].Journal of Nanjing University(Natural Sciences),2016,52(3):448-455.(in Chinese)
[19]杨运,吴吉春,骆乾坤,等.DREAM算法分析地下水数值模拟不确定性的影响因素[J].地质评论,2016,62(2):343-361.YANG Yun,WU Jichun,LUO Qiankun,et al.Analysis of the uncertainty of groundwater numerical simulation based on the DREAM algorithm[J].Geological Review,2016,62(2):343-361.(in Chinese)
[20]曹飞凤,尹祖宏.融合MCMC方法的差分进化算法在水文模型参数优选中的应用[J].南水北调与水利科技,2015,13(2):202-205.CAO Feifeng,YIN Zuhong.Application of differential evolution algorithm combined with Markow Chain Monte Carlo in parameter optimization of hydrologic model[J].South-to-North Water Transfers and Water Science and Technology,2015,13(2):202-205.(in Chinese)
[21]陈海涛,黄鑫,邱林,等.基于最大熵原理的区域农业干旱度概率分布模型[J].水利学报,2013,44(2):221-226.CHEN Haitao,HUANG Xin,QIU Lin,et al.Probability distribution model of regional agricultural drought degree based on the maximum entropy principle[J].Journal of Hydraulic Engineering,2013,44(2):221-226.(in Chinese)
[22]程正飞,王晓玲,吕鹏,等.基于VOF法的碾压混凝土坝自由渗流场数值模拟[J].水利学报,2015,46(5):558-566.CHENG Zhengfei,WANG Xiaoling,LV Peng,et al.Numerical simulation of free seepage field in RCC dams based on VOF method[J].Journal of Hydraulic Engineering,2015,46(5):558-566.(in Chinese)
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