Probabilistic estimation of variogram parameters of geotechnical properties with a trend based on Bayesian inference using Markov chain Monte Carlo simulation
Probabilistic estimation of variogram parameters of geotechnical properties with a trend based on Bayesian inference using Markov chain Monte Carlo simulation
复制标题
使用马尔可夫链蒙特卡罗模拟基于贝叶斯推理的岩土特性变差函数参数的趋势概率估计
DOI：
10.1080/17499518.2020.1757720
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通讯作者：
Chen Xiangyu
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作者：
Xu Jiabao;Zhang Lulu;Li Jinhui;Cao Zijun;Yang Haoqing;Chen Xiangyu
当岩土力学性质随空间坐标呈现趋势时，变异函数模型的估计是一项具有挑战性的任务。在以往的研究中，常用的是基于普通最小二乘法的趋势去除方法。然而，得到的变异图是有偏的，因为残差被假设为统计独立的。本研究以压锥贯入试验（CPTU）的贯入阻力（q c）数据为研究对象，探讨了利用马尔可夫链蒙特卡罗（MCMC）模拟贝叶斯推理方法估计岩土力学性能有趋势的变异函数的能力。结果表明，贝叶斯推理方法可以准确地估计变异函数参数和趋势函数系数。在后验变异函数模型的基础上，采用kriging和序贯高斯模拟（SGS）方法给出了预测不确定性和总不确定性边界。96%的验证点位于总不确定度的95%置信区间内，该不确定度基于NS31的200次q c测量。预测的SSD中位数和平均值分别为0.34和0.87，比趋势去除法更接近SSD标准。在NS31和NS12，随采样密度的增加，变异函数的模型不确定性、预测不确定性和预测总不确定性均减小。
ABSTRACT When geotechnical properties show a trend with spatial coordinates, estimation of a variogram model is a challenging task. In the previous studies, the trend-removal method based on ordinary least-squares approach has been commonly used. However, the obtained variogram is biased because the residuals are assumed to be statistically independent. In this study, the ability of Bayesian inference using Markov chain Monte Carlo (MCMC) simulation to estimate the variogram of geotechnical properties with a trend is explored using cone penetration resistance (q c) data of piezocone penetration tests (CPTU). The results show that the Bayesian inference method can estimate variogram parameters and the coefficients of trend function accurately. Based on the posterior variogram models, the predictive uncertainty and total uncertainty bounds are presented using kriging and sequential Gaussian simulation (SGS) methods. 96% validation points lie within the 95% confidence intervals of the total uncertainty based on 200 measurements of q c at NS31. The median and mean SSD of the prediction are 0.34 and 0.87, which is closer to the SSD criterion than the trend-removal method. The model uncertainty of the variograms, the predictive and total uncertainty of prediction all decrease as the sampling density increases at NS31 and NS12.