Trend term and noise removal method for blasting vibration signals based on Fourier decomposition

The trend term and noise in blasting vibration signals severely affect the accuracy of analysis. However, existing adaptive decomposition methods still have limitations in removing these trend and noise components. This study develops a Fourier decomposition-based (FDM) preprocessing approach for blasting vibration signals by optimizing key parameters, including the cross-correlation threshold, the ultra-low-frequency energy threshold, and the decomposition search path. A comparison between the High-to-Low Frequency Searching (HTL-FS) and Low-to-High Frequency Searching (LTH-FS) search paths indicates that LTH-FS achieves superior decomposition performance when applied to blasting vibration signals. The sensitivity of FDM to different ultra-low-frequency energy thresholds is systematically examined, and a criterion for identifying valid components is established. The results demonstrate that FDM can effectively separate low-frequency trend components, high-frequency noise, and meaningful signal information in blasting vibration records. Compared with Empirical Mode Decomposition (EMD), Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and Variational Mode Decomposition (VMD), the pure signal obtained via FDM exhibits the smoothest time-history curve, the highest signal-to-noise ratio (23.2406), and the lowest root-mean-square error (0.0246). At the same time, this paper further confirms the effectiveness of FDM as a high-precision preprocessing method for blasting signals by analyzing the blasting vibration signals in two actual cases: the Chongli Tunnel blasting project and the Caomao Mountain Tunnel blasting project.