基于贝叶斯高斯过程回归与模型选择的岩石单轴抗压强度估计方法

Estimation of uniaxial compressive strength based on fully Bayesian Gaussian process regression and model selection

为构建间接估计岩石单轴抗压强度(UCS)的最优模型并实现UCS的合理估计,提出了贝叶斯高斯过程回归(f B-GPR)方法。fB-GPR综合了高斯过程回归、贝叶斯理论与马尔科夫链蒙特卡洛模拟。所提方法与其它模型选择方法进行了对比,如赤池信息准则、贝叶斯信息准则、偏差信息准则、Kullback信息准则等。研究结果表明:基于fB-GPR的最优模型选择结果更为准确,预测结果与实际情况吻合度更高;100次随机试验中,fB-GPR方法将M-7选为最优模型的概率达到100%,最优模型选择的准确率远远高于其他模型选择方法;fB-GPR方法在误差值达到UCS标准差的50%时,仍可准确地进行模型选择,说明fB-GPR的准确性和鲁棒性更好,受UCS测量误差影响相对较小。研究成果可为构建岩土工程中关键参数预测的最优模型并实现合理预测提供借鉴与参考。

In order to establish an optimal model for estimating the uniaxial compressive strength(UCS)of rocks as well as its reasonable estimation,a fully Bayesian Gaussian process regression method(fB-GPR)is proposed by combining the Gaussian process regression(GPR),Bayesian framework and Markov Chain Monte Carlo(MCMC)simulation.The proposed fB-GPR approach is compared with different model selection methods,such as the Akaike information criterion(AIC),Bayesian information criterion(BIC),deviation information criterion(DIC),Kullback information criterion(KIC),etc.The results show that the proposed fB-GPR method performs better than other methods.In 100 random trials,the probability of M-7 being selected as the optimal model by fB-GPR method reaches 100%,and the accuracy of selecting the optimal model is far higher than other model selection methods.When the measurement noise reaches 50%of UCS standard deviation,the proposed fB-GPR can still achieve model selection accurately,which shows that the fB-GPR approach is robust and accurate,and is less affected by the measurement noise associated with UCS,comparing with other model selection methods.The proposed fB-GPR therefore provides a new way for establishing the optimal estimation model as well as reasonable estimation for the key geotechnical parameters in practice.