Prediction of ground vibration intensity in mine blasting using the novel hybrid MARS–PSO–MLP model

The present paper's primary goal is to propose a novel hybrid model with high reliability to predict peak particle velocity (PPV)—a ground vibration evaluation unit in mine blasting. This model is based on the coupling of the multivariate adaptive regression splines (MARS), particle swarm optimization (PSO), and multi-layer perceptron neural networks (MLP). To this end, a strategy of stacking the MARS models was applied. Multiple MARS models were developed first with different hyper-parameters. Subsequently, the outcome predictions from these MARS models were merged as a new data set. The MLP model was then developed based on the newly generated data set, called the MARS–MLP model. To improve the accuracy and reduction of the MARS–MLP model's error, the PSO algorithm was applied in terms of optimization of the MARS–MLP's weights, called the MARS–PSO–MLP model. The proposed MARS–PSO–MLP model was then compared with the stand-alone MARS, MLP, empirical models, and the hybrid PSO–MLP model (without stacking MARS models) using the same data set. The results revealed that the proposed strategies could significantly boost the MARS and MLP models' performance with the PSO algorithm's effective help. The proposed MARS–PSO–MLP model yielded the highest accuracy and reliability with a root-mean-squared error (RMSE) of 1.569, mean absolute error (MAE) of 1.017, and squared-correlation ( R 2 ) of 0.902. In comparison, the stand-alone models (i.e., MARS and MLP) and the hybrid model of PSO–MLP provided lower performances with an RMSE of 1.582 to 1.704, MAE of 0.941 to 1.427, and R 2 of 0.871 to 0.891. In contrast, poor performance with an RMSE of 5.059, MAE of 3.860, and R 2 of 0.127 was found for the empirical model, and it is not a reliable method to predict PPV in this study. This work's findings also indicated that explosive charge per delay, monitoring distance, spacing, powder factor, and burden have significant effects on PPV, the incredibly explosive charge per delay, and monitoring distance. Remarkable, the stemming variable has a minimal impact on PPV, and its role in the modeling of PPV is not exact.