Blast-Induced Ground Vibration Prediction and Uncertainty Quantification in Granite Quarries Using Deep Ensembles Model

Abstract

Ground vibration is one of the most dangerous environmental problems associated with blasting operations in mining. Therefore, accurate prediction and controlling the blast-induced ground vibration are imperative for environmental protection and sustainable development. The empirical approaches give inaccurate results as obvious in the literature, hence, numerous researchers have started to use the fast-growing soft computing approaches with satisfying prediction performance. However, not only achieving the high-prediction performance but also detecting prediction uncertainty is very important for especially blasting operations which is a safety-critical system. This study aims to propose the deep ensembles model to predict the blast-induced ground vibration and quantify the prediction uncertainty, which is usually not addressed. The deep ensembles model includes training an ensemble of deep neural networks (DNN) on the same data, by initializing each network randomly, to yield multiple predictions on both the predicted value and the uncertainty value. In this study, 200 published data from ten granite quarry sites in Ibadan and Abeokuta areas, Nigeria were used. The input parameters were the distance from the blasting face and the weight of the charge per delay, while the targeted output was the peak particle velocity (PPV). For comparison, a single DNN model and an empirical equation (USBM equation) were applied. According to the coefficient of determination\({\text{R}}^{2}\), root mean squared error (RMSE), negative log-likelihood (NLL), mean prediction interval width (MPIW), and prediction interval coverage probability (PICP), the deep ensembles model gave both the most accurate predictions and the most reliable predictive uncertainty quantification.