Uncertainty estimation of rock shear strength parameters based on gene expression programming—Bayesian inference

Aiming at the problem that the current estimation methods of rock shear strength parameters cannot reflect and quantify their uncertainty, an estimation method based on gene expression programming (GEP) and Bayesian inference (BI) is proposed to realize uncertainty prediction in the sense of probability. Based on the rock strength parameter dataset, GEP was used to establish the mapping relationship between rock shear strength parameters and uniaxial compressive strength (UCS), and tensile strength (UTS). Then, according to the function expression, prior information, and the likelihood function, the joint posterior probability distribution of the rock shear strength parameters was obtained by BI. The results showed that the GEP-BI method can effectively predict the shear strength parameters under the given UCS and UTS of rock experimental data, and can also give the probability distribution of the predicted results, which has strong interpretability and uncertainty analysis ability. According to the uncertainty degree and prediction effectiveness of the results, it was suggested to adopt the lognormal distribution as the likelihood function, which can effectively avoid the meaningless negative value. Compared with machine learning methods, the GEP-BI model has a better prediction effect, which proves the feasibility and effectiveness of the GEP-BI method.