Bayesian selection of the optimal composite kernels for probabilistic estimation of UCS with explicit consideration of measurement errors and the anisotropic characteristic of input features

Uniaxial compressive strength (UCS) of rocks is one of the most widely utilised parameters for design or analysis of tunnelling engineering. In engineering practice, complete and high-quality rock samples are often not available, especially for highly fragile rocks. In this case, it necessitates the use of indirect methods, such as a data-driven Gaussian process regression (GPR) method. Despite reasonable performance of conventional GPR method in predicting UCS, it does not explicitly consider the measurement uncertainty associated with UCS, nor quantify the reliability of the predicted UCS. Moreover, conventional GPR method does not extensively investigate the effect of anisotropic characteristics of input features on UCS prediction, despite their potential significance. To address these issues, this paper proposes a Bayesian Gaussian process regression (GPR) approach for probabilistic estimation of UCS, considering anisotropic characteristics of input features, and measurement errors associated with UCS in an explicit manner using composite kernels. Both real-life and numerical examples are adopted for illustration and validation. Results showed that both the accuracy and reliability of UCS prediction are improved significantly by considering anisotropic characteristics of input features and measurement errors associated with UCS: coefficient of determination (<i>R</i>²) increased about 150.9% compared to the model with isotropic kernels.