A Novel Combination of Whale Optimization Algorithm and Support Vector Machine with Different Kernel Functions for Prediction of Blasting-Induced Fly-Rock in Quarry Mines

Abstract

This study proposed a novel data-driven model for estimating distance of fly-rock in bench blasting in open-pit mines using a robust combination of the whale optimization algorithm (WOA), support vector machine (SVM) and kernel functions. Four kernel functions were investigated for embedding in the SVM model, including linear (L), radius basis function (RBF), polynomial (P), and hyperbolic tangent (HT) functions. Then, the WOA was applied to optimize the kernel-based SVM models, namely WOA–SVM–L, WOA–SVM–P, WOA–SVM–RBF, and WOA–SVM–HT. A variety of conventional data-driven models were also developed for predicting fly-rock distance, including adaptive neuro-fuzzy inference system (ANFIS), gradient boosting machine (GBM), random forest (RF), classification and regression tree (CART), and artificial neural network (ANN). The blasting parameters and maximum fly-rock distance, as well as their relationship, were carefully investigated for this aim. The predictive results of the models were evaluated through two performance indices: root-mean-squared error (RMSE) and correlation coefficient (R2). These indices indicated that the linear function-based WOA–SVM model (i.e., WOA–SVM–L) seems to be not fit for predicting fly-rock with the largest error (i.e., RMSE = 9.080 and R2 = 0.937). In contrast, the WOA–SVM–RBF model yielded the highest accuracy in predicting the distance of fly-rock (i.e., RMSE = 5.241, R2 = 0.977). Meanwhile, the WOA–SVM–P and WOA–SVM–HT models provided lower performances than those of the WOA–SVM–RBF model, but they are acceptable. The conventional models (i.e., ANFIS, GBM, RF, CART, and ANN) are pretty well (i.e., RMSE in the range of 5.804 to 6.567; R2 in the range of 0.965 to 0.973); however, their performance is lower than those of the WOA–SVM–RBF model as well. Based on these results, the WOA–SVM model was proposed as a useful data-driven model for predicting fly-rock with high reliability in practical engineering.