Intelligent prediction of rock mass deformation modulus through three optimized cascaded forward neural network models

Rock mass deformation modulus (E_m) is a key parameter that is needed to be determined when designing surface or underground rock engineering constructions. It is not easy to determine the deformability level of jointed rock mass at the laboratory; thus, researchers have suggested different in-situ test methods. Today, they are the best methods; though, they have their own problems: they are too costly and time-consuming. Addressing such difficulties, the present study offers three advanced and efficient machine-learning methods for the prediction of E_m. The proposed models were based on three optimized cascaded forward neural network (CFNN) using the Levenberg–Marquardt algorithm (LMA), Bayesian regularization (BR), and scaled conjugate gradient (SCG). The performance of the proposed models was evaluated through statistical criteria including coefficient of determination (R²) and root mean square error (RMSE). The computational results showed that the developed CFNN-LMA model produced better results than other CFNN-SCG and CFNN-BR models in predicting the E_m. In this regard, the R² and RMSE values obtained from CFNN-LMA, CFNN-SCG, and CFNN-BR models were equal to (0.984 and 1.927), (0.945 and 2.717), and (0.904 and 3.635), respectively. In addition, a sensitivity analysis was performed through the relevancy factor and according to its results, the uniaxial compressive strength (UCS) was the most impacting parameters on E_m.