基于贝叶斯理论及MCMC-MH算法推演地基土材料阻尼比的概率分布模型

Inversion of a probability distribution model of soil damping ratio based on the Bayesian theory and the MCMC-MH algorithm

浅层土壤的材料阻尼比参数分布可以通过多通道表面波(MASW)分析法提取的表面波衰减曲线来反演识别,但是衰减曲线对于较大深度和小空间尺度土壤性质的变化不敏感,反演的土壤材料阻尼比分布是非唯一的和不确定的。基于该研究建立了土体材料阻尼比随深度变化的先验概率分布模型,利用Nataf变换和Karhunen-Loeve将其分解为标准高斯变量与特征值及特征向量的乘积和;随后依据贝叶斯理论,以TLM-PML模型结合频率波数域-半功率带宽法对衰减曲线进行正演,并与试验数据联合构建似然函数,使用蒙特卡洛马尔科夫链(MCMC)-Metropolis(MH)算法得到土体材料阻尼比的后验概率分布模型;对马尔科夫链的收敛性和独立性进行检验获得了多组相互独立的后验样本数据;用独立的后验样本计算出自由场振动响应,利用核密度估计得到具有一定置信度的置信区间,并与试验数据进行比较,验证了该研究提出的土体阻尼比非确定性概率模型的合理性和可靠性。

The parameter distribution of the material damping ratio of shallow soil can be identified by inversion through the surface wave attenuation curve extracted by the multi-channel surface wave analysis method(MASW).However,the attenuation curves of surface waves are insensitive to the property changes of soil with larger depths and small spatial scales,and the damping ratio distribution of subsoil material is non-unique and uncertain.Therefore,in this paper,the variation of the damping ratio with depth is expressed by a non-Gaussian prior probability distribution model,and then is decomposed into the sum of standard Gaussian variables and also eigenvalues and eigenvectors by using the Nataf transformation and the Karhunen-Loeve decomposition.Moreover,on the basis of the Bayesian theory,the TLM-PML theory was combined with a half-power bandwidth method in the frequency-wavenumber domain to simulate the attenuation curves,which is compared with the experimental data to construct the likelihood function.The Monte Carlo Markov chain(MCMC)-Metropolis(MH)algorithm was used to obtain the posterior probability distribution model of soil damping ratio from the posterior sample data,and the convergence and independence of the Markov chain were validated so that multiple sets of independent posterior sample data were obtained.Finally,the independent posterior samples were used to calculate the vibration responses of the free field.The confidence interval with a certain degree of confidence was obtained using the kernel density estimation and thus was compared with the experimental data,which validates the rationality and reliability of the non-deterministic probability model of soil damping ratio proposed in this paper.