Probabilistic prediction of uniaxial compressive strength for rocks from sparse data using Bayesian Gaussian process regression with Synthetic Minority Oversampling Technique (SMOTE)

Uniaxial compressive strength (UCS) of rocks is one of key rock strength parameters. Generally speaking, UCS can be measured directly through uniaxial compression tests, which is often unfeasible, especially when intact rock samples are highly fragile. Alternatively, the UCS of rocks can be estimated indirectly from other easily available rock indices. Note that adequate measurement data is the prerequisite for the accurate estimation of UCS using indirect methods. This may be difficult to achieve due to the limitation of time and budget, especially for small- to medium-sized projects. In this case, it becomes a challenging issue on how to develop a robust and reliable model for UCS estimation using the sparse measurement data. A fully Bayesian Gaussian process regression (fB-GPR) approach with Synthetic Minority Oversampling Technique (SMOTE) is proposed in this paper to address this problem. A real-life example from Malaysia was used for illustration and validation of proposed method. Results showed that when the synthetic sample size in SMOTE reaches 30 (i.e., optimal synthetic sample size), the coefficient of determination (R2) increases by about 18.92%, and the accuracy of feature selection reaches 98%, compared with the scenario with only sparse measurement data used for fB-GPR model development.