Research on non-stationary blasting vibration prediction models and analysis of equal-interval delay for vibration reduction

To address challenges in predicting and controlling vibrations arising from the non-stationary stochastic characteristics of blasting vibrations, a decoupled modeling approach is employed. The blasting vibration signal is decomposed into a coupled process comprising a non-stationary intensity component (characterized by a Gamma function) and a stochastic frequency component (represented by filtered white noise), establishing a predictive model for single-hole blasting vibrations. A multi-hole blasting vibration prediction model is further developed using Anderson’s superposition theory. Model parameters are optimized through stochastic search algorithms based on a comprehensive waveform similarity index (Z). Field experiments at two geologically distinct open-pit mines (Jiangxi and Beijing) demonstrate accurate waveform predictions for both single-hole and multi-hole models, validating their correctness and effectiveness. Statistical analysis of simulated waveforms reveals vibration reduction patterns under varying conditions. Results indicate that the vibration reduction rate generally increases with extended inter-hole delay times but exhibits an inflection point where improvement transitions from rapid to gradual. Under identical delay conditions: (1) The vibration reduction rate increases with blast hole quantity, suggesting optimized hole numbers enhance vibration control in short-delay blasting; (2) Larger blast center distances reduce vibration reduction efficiency, indicating that inter-hole delay adjustments alone cannot ensure effective suppression in far-field regions; (3) Higher longitudinal wave velocities improve vibration reduction due to amplified superposition effects in high-wave-velocity geological media.