Estimation of uniaxial compressive strength of rock using optimized support vector and kernel-based extreme learning machine models

Abstract

Uniaxial compressive strength (UCS) is a vital parameter that reflects the fundamental mechanical properties of rocks, playing an indispensable role in rock mass classification and the establishment of rock mass failure criteria. Currently, two methods, namely the direct and indirect methods, are employed to determine the UCS. The direct method, however, is high-priced and time-consuming. Consequently, the development of a stable and efficient indirect method holds great significance. In this study, kernel extreme learning machine (KELM) and support vector regression (SVR) are utilized to construct prediction models. Additionally, five metaheuristic optimization algorithms are introduced to strengthen the performance of the prediction models. Ten ensemble models are developed to predict the UCS. Using six input variables, an optimal prediction model is established based on four performance indicators. To address the stochasticity of model outputs, each model is run 100 times to obtain 100 output results. Furthermore, score analysis, uncertainty analysis and Wilcoxon test are employed to evaluate the superiority or inferiority of prediction models more precisely, respectively. The results imply that the HOA-KELM model receives the highest values for R² (0.9168), VAF (95.5308%), WI (0.9784) and PI (−11.4660), while achieving the lowest RMSE (13.3381), with a total score of 20 using KELM-based ensemble models, and the PSO-SVR model receives the highest values for R² (0.9440), VAF (96.9933%), WI (0.9733), and PI (−9.02626) while achieving the lowest RMSE (10.9402) and MAE (8.1081), with a total score of 20 using SVR-based ensemble models. Compared with the HOA-KELM model, the PSO-SVR model has been proven to have higher prediction accuracy by drawing the Taylor diagram. Therefore, the PSO-SVR model surpasses alternative models, establishing it as the preferred option for predicting the UCS of rocks.