基于MCMC法的混凝土坝坝体坝基变形模量随机反演

Stochastic inversion of deformation moduli of concrete dam body and foundation based on Markov chain Monte Carlo method

针对混凝土坝材料力学参数反演中存在大量不确定性问题,提出了混凝土重力坝坝体弹性模量与坝基变形模量的MCMC随机反演法。将坝体及坝基变形模量参数视为随机变量,基于Bayesian理论,利用无似然函数的马尔可夫链蒙特卡罗方法(Markov chain Monte Carlo(MCMC)without likelihoods)进行随机参数后验分布抽样。通过平稳后的马尔可夫链得到参数后验分布的随机样本,进而得到对应的期望值和标准差。以龙滩高混凝土重力坝为例,结合典型断面的二维平面有限元模型,采用无似然函数的MCMC算法对坝体、坝基变形模量进行了随机反演,得出所需反演参数(坝体弹性模量、坝基变形模量)的分布;分析了坝体、坝基变形模量分布的统计特性与观测值波动之间的关系,得出后验分布变异性与观测值离散性呈正相关关系。

In view of the large number of uncertainties in the inversion of mechanical parameters of concrete dam materials,the Markov chain Monte Carlo(MCMC)stochastic inversion method for elastic modulus of the dam body and deformation modulus of the dam foundation of the high concrete gravity dam is proposed.The deformation moduli of the dam body and dam foundation are considered as random variables.Based on the Bayesian theory,the Markov chain Monte Carlo without likelihoods method is used to sample the posterior distribution of the random parameters.The stationary Markov chain is used to obtain the random samples of the posterior distribution of parameters,and then the corresponding expected values and standard deviation are obtained.Taking the Longtan high concrete gravity dam as an example,based on the two-dimensional plane model for typical dam section,the deformation moduli of the dam body and foundation are inversed by the proposed method,and the distribution of the required inversion parameters(elastic modulus of the dam body and deformation modulus of the dam foundation)is obtained.The relationships between the statistical characteristics of the deformation modulus distribution of the dam body and foundation and the fluctuation of the observed values are analyzed.It is concluded that the variability of the posterior distribution is positively correlated with the discreteness of the observed values.