De-noising method of tunnel blasting signal based on CEEMDAN decomposition-wavelet packet analysis
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摘要: 针对隧道爆破施工中采集到的实测振动信号，引入一种基于总体平均经验模态分解方法（CEEMDAN分解）联合小波包分析的降噪方法。首先，通过CEEMDAN分解得到多个本征模态分量，利用相关系数筛选出包含噪声的模态分量，并通过模态分量的频谱图及方差贡献率进行校核。然后，利用小波包阈值降噪方法对含有噪声的模态分量进行处理。最后，将未经处理的模态分量与去噪完成的分量重构得到最终纯净的爆破振动信号。同时，通过小波包能量谱分析验证此降噪方法的可行性。本文引入的方法兼具CEEMDAN分解及小波包分析的优点，与现有方法相比，去噪效果较好，可以应用于类似隧道爆破信号的去噪处理中。Abstract: Aiming at the measured vibration signals collected during tunnel blasting construction, a noise reduction method based on the overall average empirical mode decomposition method (CEEMDAN decomposition) combined with wavelet packet analysis was in troduced. First, a series of multiple intrinsic modal components were obtained by CEEMDAN decomposition, and the modal components containing noise were selected using correlation coefficients, checked by the spectrogram and the variance contribution rate of the modal components. Then, the wavelet packet threshold noise reduction method was used to process the modal components containing noise. Finally, the unprocessed modal components and the de-noised components were reconstructed to obtain the final pure blasting vibration signal. At the same time, the feasibility of this noise reduction method has been verified by wavelet packet energy spectrum analysis. This method combines the advantages of CEEMDAN decomposition and wavelet packet analysis. Compared with existing methods, the de-noising effect is better, and it can be applied to the de-noising processing of similar tunnel blasting signals.
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图 8 小波包降噪处理前后的C15信号
Figure 8. signal (C15) before and after wavelet packet noise reduction
图 9 CEEMDAN-小波包阈值降噪后的信号
Figure 9. CEEMDAN-wavelet packet threshold signal after noise reduction
图 10 用于对比的几种方法的降噪效果
Figure 10. Noise reduction effect of several methods for comparison
图 11 小波包能量占有百分比
Figure 11. Signal energy distribution before and after noise reduction
表 1 本征模态分量（IMF）的相关系数
Table 1. Correlation coefficients of modal components (IMF)
模态分量 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 ri 0.129 0.103 0.097 0.063 0.051 0.687 0.760 0.562 0.260 0.139 0.023 0.003 0.007 0.001 
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表 2 模态分量（IMF）的方差贡献率
Table 2. Variance contribution rate of modal component (IMF)
方差贡献率 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 e(j) 1.65 0.07 0.41 0.29 0.23 13.42 38.31 34.98 8.71 1.59 0.28 0.24 0.04 0.01
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表 3 去噪效果对比
Table 3. Comparison of noise reduction effects
去噪方法 η σ 小波包阈值去噪 66.412 1.40×10−4 EMD-小波包联合去噪 84.9511 2.55×10−5 EEMD-小波包联合去噪 84.0313 2.43×10−5 新方法去噪 94.0802 2.40×10−5
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