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

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.