A comparative study on the development of hybrid SSA-RF and PSO-RF models for predicting the uniaxial compressive strength of rocks

In the field of rock engineering, uniaxial compressive strength (UCS) is a crucial mechanical parameter that cannot be ignored. Due to the difficulty in obtaining high-quality rock core samples in some projects, it is essential to develop a reliable UCS prediction method. In this study, the prediction of UCS was accomplished by employing random forest (RF) models, and two optimizers were used for hyperparameter optimization. A total of 126 cases were collected, which included four input indicators: density, p-wave velocity, Schmidt hammer rebound number, and point load index. In addition, five traditional models, including RF, multiple regression analysis (MR), back propagation neural network (BPNN), extreme learning machine (ELM), and support vector regression (SVR), were introduced for comparison. In order to improve the performance of the models, a five-fold cross-validation method was considered. To evaluate the comprehensive performance of the models, the technique for order preference by similarity to an ideal solution (TOPSIS) method was used, providing an effective approach for model selection. The results showed that the proposed hybrid models can predict the UCS of rocks well. Overall, the SSA-RF model was determined to be the best model for the prediction of the UCS, with values of coefficient of determination (R2), mean absolute error (MAE), mean absolute percentage error (MAPE), root-mean-square error (RMSE), value accounted for (VAF), Nash-Sutcliffe efficiency coefficient (NSC), and Theil's U-value of 0.9587, 7.0681, 11.8988%, 9.4234, 95.9747, − 2.0781, and 0.0129, respectively. The Gini index indicated that the UCS was more sensitive to the Schmidt hammer rebound number than other indicators. Finally, the UCS prediction models were ranked as follows: SSA-RF, PSO-RF, SVR, RF, MR, BPNN, and ELM. These findings provide valuable insights into the development of accurate and reliable UCS prediction models, which are critical in the engineering practice.