Non-destructive test-based assessment of uniaxial compressive strength and elasticity modulus of intact carbonate rocks using stacking ensemble models

The uniaxial compressive strength (UCS) and elasticity modulus (E) of intact rock are two fundamental requirements in engineering applications. These parameters can be measured either directly from the uniaxial compressive strength test or indirectly by using soft computing predictive models. In the present research, the UCS and E of intact carbonate rocks have been predicted by introducing two stacking ensemble learning models from non-destructive simple laboratory test results. For this purpose, dry unit weight, porosity, P-wave velocity, Brinell surface harnesses, UCS, and static E were measured for 70 carbonate rock samples. Then, two stacking ensemble learning models were developed for estimating the UCS and E of the rocks. The applied stacking ensemble learning method integrates the advantages of two base models in the first level, where base models are multi-layer perceptron (MLP) and random forest (RF) for predicting UCS, and support vector regressor (SVR) and extreme gradient boosting (XGBoost) for predicting E. Grid search integrating k-fold cross validation is applied to tune the parameters of both base models and meta-learner. The results demonstrate the generalization ability of the stacking ensemble method in the comparison of base models in the terms of common performance measures. The values of coefficient of determination (R2) obtained from the stacking ensemble are 0.909 and 0.831 for predicting UCS and E, respectively. Similarly, the stacking ensemble yielded Root Mean Squared Error (RMSE) values of 1.967 and 0.621 for the prediction of UCS and E, respectively. Accordingly, the proposed models have superiority in the comparison of SVR and MLP as single models and RF and XGBoost as two representative ensemble models. Furthermore, sensitivity analysis is carried out to investigate the impact of input parameters.