A robust Gaussian process regression-based model for the determination of static Young's modulus for sandstone rocks

Abstract

Static Young's modulus (Es) is one of the leading mechanical rock properties. The Es can be measured from experimental lab methods. However, these methods are costly, time-consuming, and challenging to collect samples. Thus, some researchers have proposed alternative techniques, such as empirical correlations, to determine the Es. However, the previous studies have limitations: lack of accuracy, the need for specific data, and improper validation to prove the proper relationships between the inputs and outputs to show the correct physical behavior. In addition, most previous models were based on the dynamic Young's modulus. Therefore, this study aims to use the Gaussian process regression (GPR) method for Es determination using 1853 real global datasets. The utilization of global data to develop the Es prediction model is unique. The GPR model was validated by applying trend analysis to show that the correct relationships between the inputs and output are attained. Furthermore, different statistical error analyses, namely an average absolute percentage relative error (AAPRE), were performed to assess the GPR accuracy compared to current methods. This study confirmed that the GPR model has robustly and accurately predicted the Es with AAPRE of 5.41%, surpassing all the existing studied models that have AAPRE of more than 10%. The trend analysis results indicated that the GPR model follows the proper physical behaviors for all input trends. The GPR model can accurately predict the Es at different ranges of inputs. 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.