Developing Hybrid DMO-XGBoost and DMO-RF Models for Estimating the Elastic Modulus of Rock

Accurate estimation of the elastic modulus (E) of rock is critical for the design of geotechnical projects such as mining, slopes, and tunnels. However, the determination of rock mechanical parameters usually involves high budget and time requirements. To address this problem, numerous researchers have developed machine learning models to estimate the E of rock. In this study, two novel hybrid ensemble learning models were developed to estimate the E of rock by optimizing the extreme gradient boosting (XGBoost) and random forest (RF) algorithms through the dwarf mongoose optimization (DMO) approach. Firstly, 90 rock samples with porosity, dry density, P-wave velocity, slake durability, and water absorption as input indicators were collected. Subsequently, the hyperparameters of XGBoost and RF were tuned by DMO. Based on the optimal hyperparameters configuration, two novel hybrid ensemble learning models were constructed using the training set (80% of the data). Finally, the performance of the developed models was evaluated by the coefficient of determination (R² score), root mean squared error (RMSE), mean absolute error (MAE), and variance accounted for (VAF) on the test set (20% of the data). The results show that the DMO-RF model achieved the best comprehensive performance with an R² score of 0.967, RMSE of 0.541, MAE of 0.447, and VAF of 0.969 on the test set. The dry density and slake durability were more influential indicators than others. Moreover, the convergence curves suggested that the DMO-RF model can reduce the generalization error and avoid overfitting. The developed models can be regarded as viable and useful tools in estimating the E of rock.