Sun Miao, Wu Jing, Lu Yani, Yu Fangda, Zhou Hang
School of Civil Engineering & Research Center of Hubei Small Town Development, Hubei Engineering University, Xiaogan 432000, China.
Engineering Research Center of Rock-Soil Drilling & Excavation and Protection, Ministry of Education, China University of Geosciences, Wuhan 430074, China.
Sensors (Basel). 2025 Jul 5;25(13):4194. doi: 10.3390/s25134194.
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() and S(). Using these as references, the original signal is divided into "b" equal segments S(), S() … S(). Energy matching and waveform matching functions are then established to identify signal fragments S() and S() that match both the energy and waveform characteristics of S() and S(). Replacing S() and S() with S() and S() 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.
爆破引起的地震波通常是非线性和非平稳信号。经验模态分解（EMD）-希尔伯特变换常用于此类信号的时频分析。然而，在对爆破引起的地震波进行经验模态分解（EMD）处理过程中，会出现端点效应，导致所获得的本征模态函数（IMF）分量在两端出现不同程度的发散。将希尔伯特变换进一步应用于这些端点发散的IMF会产生人为的时频分析结果，对爆破引起的地震波危害评估产生不利影响。本文提出了一种改进的EMD端点效应抑制算法，该算法考虑了局部端点发展趋势、全局时间分布、能量匹配和波形匹配。该方法首先分析全局时间特征和端点幅度变化，以获得左右端点扩展信号片段S( )和S( )。以此为参考，将原始信号划分为“b”个等长段S( )、S( )…S( )。然后建立能量匹配和波形匹配函数，以识别与S( )和S( )的能量和波形特征都匹配的信号片段S( )和S( )。用S( )和S( )替换S( )和S( )可有效抑制EMD端点效应。为验证该算法在抑制EMD端点效应方面的有效性，使用模拟信号进行了对比研究，并将该方法与镜像扩展、多项式拟合和极值扩展方法进行比较。采用了三个评估指标：误差标准差、相关系数和计算时间。结果表明，所提出的算法有效降低了IMF端点处的发散，并产生了具有物理意义的IMF分量。最后，将该方法应用于实际爆破地震信号的分析。它成功抑制了EMD的端点效应，改善了爆破引起的地震波时频特征的提取。这对爆破影响区域内现有结构的安全评估具有重要的实际意义。
