A hybrid RF–PSO–BiLSTM model for blast fragmentation prediction

Abstract

Blast fragmentation is a key indicator for evaluating blasting performance, but its accurate prediction remains challenging because of the nonlinear coupling among blasthole geometry, explosive energy input, and rock-mass properties. In this study, a hybrid RF–PSO–BiLSTM model was developed using 90 field blasting cases. The dataset was divided once into 72 development samples and 18 independent test samples. Five-fold cross-validation was performed exclusively within the development set for feature evaluation and PSO-based hyperparameter optimization, while the independent test set remained isolated throughout model development. Random forest (RF) feature screening excluded the burden-to-hole-diameter ratio B/D because of its relatively low additional predictive contribution, and six variables, S/B, H/B, T/B, Pf, XB, and E, were retained as model inputs. Particle swarm optimization (PSO) was then employed to optimize the BiLSTM hyperparameters. Under the same evaluation protocol, the proposed model outperformed SVM, BPNN, LSTM, XGBoost, RF–LSTM, and RF–PSO–LSTM, achieving R2 = 0.9412, RMSE = 0.0402, and MAE = 0.0375 on the independent test set. SHAP analysis further showed that the global feature importance followed E > XB > T/B > Pf > S/B > H/B. Higher XB, T/B, and S/B values generally increased the predicted X50, whereas increasing Pf tended to reduce it; the effect of E was the most prominent but exhibited a nonlinear pattern. Ten additional field blasting cases yielded a mean relative error of 2.69%, providing preliminary evidence of the engineering applicability of the model under conditions similar to those represented in the available data. The developed framework can also serve as a surrogate predictor for target-fragmentation-oriented blast-parameter design, although further cross-site and cross-geological validation is required before broader application.