Engineering Safety-Oriented Blasting-Induced Seismic Wave Signal Processing: An EMD Endpoint Suppression Method Based on Multi-Scale Feature

Blasting-induced seismic waves are typically nonlinear and non-stationary signals. The EMD-Hilbert transform is commonly used for time-frequency analysis of such signals. However, during the empirical mode decomposition (EMD) processing of blasting-induced seismic waves, endpoint effects occur, resulting in varying degrees of divergence in the obtained intrinsic mode function (IMF) components at both ends. The further application of the Hilbert transform to these endpoint-divergent IMFs yield artificial time-frequency analysis results, adversely impacting the assessment of blasting-induced seismic wave hazards. This paper proposes an improved EMD endpoint effect suppression algorithm that considers local endpoint development trends, global time distribution, energy matching, and waveform matching. The method first analyzes global temporal characteristics and endpoint amplitude variations to obtain left and right endpoint extension signal fragment S(<i>t</i>)_L and S(<i>t</i>)_R. Using these as references, the original signal is divided into "b" equal segments S(<i>t</i>)₁, S(<i>t</i>)₂ … S(<i>t</i>)_b. Energy matching and waveform matching functions are then established to identify signal fragments S(<i>t</i>)_i and S(<i>t</i>)<i>_j</i> that match both the energy and waveform characteristics of S(<i>t</i>)_L and S(<i>t</i>)_R. Replacing S(<i>t</i>)_L and S(<i>t</i>)<i>_R</i> with S(<i>t</i>)_i and S(<i>t</i>)_j effectively suppresses the EMD endpoint effects. To verify the algorithm's effectiveness in suppressing EMD endpoint effects, comparative studies were conducted using simulated signals to compare the proposed method with mirror extension, polynomial fitting, and extreme value extension methods. Three evaluation metrics were utilized: error standard deviation, correlation coefficient, and computation time. The results demonstrate that the proposed algorithm effectively reduces the divergence at the endpoints of the IMFs and yields physically meaningful IMF components. Finally, the method was applied to the analysis of actual blasting seismic signals. It successfully suppressed the endpoint effects of EMD and improved the extraction of time-frequency characteristics from blasting-induced seismic waves. This has significant practical implications for safety assessments of existing structures in areas affected by blasting.