考虑约束的贝叶斯概率反演方法  

Bayesian back analysis considering constraints

作　　者：陶袁钦 孙宏磊 蔡袁强[1,2] TAO Yuan-qin;SUN Hong-lei;CAI Yuan-qiang(College of Civil Engineering and Architecture,Zhejiang University,Hangzhou 310058,China;College of Civil Engineering,Zhejiang University of Technology,Hangzhou 310014,China)

机构地区：[1]浙江大学建筑工程学院,浙江杭州310058 [2]浙江工业大学土木工程学院,浙江杭州310014

出　　处：《岩土工程学报》2021年第10期1878-1886,共9页Chinese Journal of Geotechnical Engineering

基　　金：国家重点研发计划项目(2017YFE0119500,2016YFC0800200);国家自然科学基金项目(52078464,U2006225,51620105008)。

摘　　要：土体参数对岩土工程计算模型的预测效果至关重要。在土体参数识别问题中,基于MCMC抽样的贝叶斯方法是一种反演土体参数概率分布的常见方法。然而该方法通常仅考虑土体参数的先验分布、预测与观测间的差异,不考虑其他已知信息如土体参数间的经验性相互关系等,当采用数值模拟作为计算模型时,该方法计算负担大,限制了其运用。为此,提出了一种考虑附加约束信息的近似贝叶斯方法REn KF-MDA,并将其与无约束MCMC、考虑约束的MCMC、正则化集合卡尔曼滤波REnKF进行对比,采用简单多项式算例和地基沉降案例说明该方法的有效性。结果表明:融合附加约束信息有助于提高反演参数的合理性和可信度,约束强弱由约束协方差决定。以考虑约束的MCMC为参考,REnKF可准确估计均值但显著低估了参数后验分布的不确定性,REn KF-MDA可同时合理地估计均值和不确定性。Soil parameters significantly affect the prediction performance of geotechnical models.In the field of parameter identification,the MCMC-based Bayesian method is an effective way to infer the probability distribution of soil parameters.However,this method only considers the prior distribution of soil parameters and the difference between predictions and observations,without considering other additional information such as empirical correlations between soil parameters.In addition,the MCMC method leads to high computational cost if the numerical methods are used as the model,which limits its application.In this study,a new approximate Bayesian method considering the additional constraints is proposed,named REnKF-MDA.The proposed method is compared with the MCMC-based Bayesian method,MCMC-based Bayesian method with constraints,and REnKF.The effectiveness of the proposed REnKF-MDA method is illustrated by a simple polynomial case and a foundation settlement project.The results indicate that assimilating the additional constraint informations is helpful to improve the rationality and confidence of the inferred parameters.The confidence of the constraint is determined by the covariance of the constraint information.Taking the MCMC-based Bayesian method with constraints as a reference,the REnKF provides an accurate evaluation of the mean value,but significantly underestimates the uncertainty of the posterior distributions.In contrast,the REnKF-MDA estimates both the mean and uncertainty well.

关 键 词：贝叶斯方法 参数估计 集合卡尔曼滤波 约束信息 数据融合 

分 类 号：TU431[建筑科学—岩土工程]