Feature Extraction Method for Blasting Vibration Signal Based on WOA-VMD and Hilbert Spectrum Analysis

Extracting the instantaneous time–frequency distribution and energy evolution of a blasting vibration signal is a critical approach for investigating rock mass structural stability and blast-induced seismic effects. This paper proposes a blasting vibration signal feature extraction method based on whale optimization algorithm–variational mode decomposition (WOA-VMD) and Hilbert spectrum analysis. First, WOA optimizes VMD parameters (decomposition layer K, penalty factor α) to yield the optimal parameter set, and the optimized VMD then decomposes vibration signals into intrinsic mode functions (IMFs). Second, a quantitative multiscale permutation entropy (MPE)-based criterion is introduced to discard noise-dominated invalid components, eliminating subjective judgment errors, while wavelet threshold denoising is applied to valid components for signal reconstruction. Finally, Hilbert spectrum analysis is performed on the reconstructed signals, so that denoising serves as an intermediate check and the outcome is the distance dependence of the time–frequency features and energy evolution. The method is applied to measured vibration signals from three single-hole coal mine blasting experiments. Results indicate that optimized VMD exhibits stronger adaptability in frequency-domain segmentation, significantly mitigating mode mixing. The MPE-based criterion, combined with wavelet denoising, accurately eliminates noise components, showing robust performance in energy retention, noise suppression, and signal smoothness. Within 700–1200 m from the blasting center, signal energy is predominantly concentrated in the 0.3–0.5 s interval and 0–60 Hz frequency band. As distance increases, both the energy peak and center frequency decay exponentially, while the peak arrival time increases linearly.