基于补充改进集合经验模态分析法⁃多尺度排列熵分析桥梁振动信号优化滤波方法

doi:10.13229/j.cnki.jdxbgxb20190013

摘要/Abstract

摘要：

针对桥梁振动信号高度非平稳特征和含噪声成分严重的问题，提出了一种应用于桥梁健康监测领域的信号自适应分解与重构的优化滤波方法。该方法以自适应加噪的完备集合经验模态分解(CEEMDAN)为核心算法，将原始振动信号逐级分解为多个不同特征时间尺度相对平稳的固有模态函数(IMF)，采用端点对称延拓法抑制端点效应，引入多尺度排列熵(MPE)分析各IMF在不同尺度上的熵均值，检索随机程度较大的IMF分量，将含噪严重与由于加噪分解产生的伪分量剔除完成一次滤波，为了择优选取剩余IMF进行信号重构保证滤波具有较好的相似度与光滑度，建立了优化重构模型完成两次滤波。研究表明：本文方法在自适应分解阶段较常用的集合经验模态分解(EEMD)、补充集合经验模态分解(CEEMD)方法具有更好的完备性、正交性与计算效率，在一定程度上抑制了模态混叠现象，端点效应问题有所改善，并对IMF进行优化重构，经分析最终的滤波信号具有较高的信噪比，通过对真实桥梁振动信号分析再一次验证了本文方法的优势，该方法的滤波结果可以作为实现桥梁健康监测技术的可靠依据。

关键词: 桥梁工程, 桥梁健康监测, 分解与重构, 滤波, 补充集合经验模态分析

Abstract:

To solve the problem of bridge vibration signal with high degree of non-stationary feature, an optimization filtering method of adaptive decomposition and reconstruction is proposed for the bridge health monitoring. On the basis of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), the original signal is decomposed into multiple intrinsic mode functions (IMFs) with different feature time-scales. The endpoint mirroring method is used to suppress endpoint effect. In order to find the IMFs with high randomness, the multi-scale permutation entropy (MPE) is introduced to analyze the mean entropy value of each IMF at different scales. Then the noise component and abnormal component are respectively eliminated to complete the first filtering. In order to achieve better similarity and smoothness for the final filter, the optimized reconstruction model is established to complete the second filtering. The research shows that adaptive decomposition stage of the proposed method has better completeness, orthogonality and computational efficiency than traditional ensemble empirical mode decomposition (EEMD) and complementary ensemble empirical mode decomposition (CEEMD) methods. Meanwhile, the proposed method suppresses the mode mixing phenomenon to a certain extent, and the endpoint effect is improved. Through the optimized reconstruction, the final filter signal has high signal-to-noise ratio. Finally, the measured signal analysis once again proves the advantages of the proposed method, the filter result can be used as the basis of bridge health monitoring technology.

Key words: bridge engineering, bridge health monitoring, decomposition and reconstruction, filtering, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)

中图分类号:

U448.27

王伯昕,杨海涛,王清,高欣,陈小旭. 基于补充改进集合经验模态分析法⁃多尺度排列熵分析桥梁振动信号优化滤波方法[J]. 吉林大学学报(工学版), 2020, 50(1): 216-226.

Bo-xin WANG,Hai-tao YANG,Qing WANG,Xin GAO,Xiao-xu CHEN. Bridge vibration signal optimization filtering method based on improved CEEMD⁃multi⁃scale permutation entropy analysis[J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(1): 216-226.

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	s1	s2	s3
IMF1	-0.002 5	-0.001 5	0.003 7
IMF2	-0.001 3	0.000 2	0.002 7
IMF3	0.004 1	0.008 2	0.019 3
IMF4	0.005 5	0.106 9	0.896 3
IMF5	-0.058 4	0.397 7	0.894 7
IMF6	0.243 9	0.937 4	0.019 6
IMF7	0.983 0	0.023 4	0.015 6
IMF8	0.320 9	0.021 3	0.019 2
IMF9	0.054 9	0.028 1	0.019 5
RS	0.088 6	0.045 1	0.030 1

	s1	s2	s3
IMF1	-0.001 9	-0.001 9	0.003 4
IMF2	-0.001 2	-0.000 3	0.002 8
IMF3	0.006 0	0.011 0	0.018 3
IMF4	0.002 7	0.098 0	0.907 6
IMF5	-0.065 3	0.431 5	0.877 8
IMF6	0.287 2	0.921 9	0.018 8
IMF7	0.981 4	0.019 7	0.014 2
IMF8	0.311 1	0.023 3	0.019 8
RS	0.102 9	0.052 3	0.035 2

	s1	s2	s3
IMF1	0.069 7	0.473 6	0.861 3
IMF2	0.098 4	0.953 4	0.001 9
IMF3	0.972 5	0.027 3	0.024 1
IMF4	0.049 0	0.022 8	0.014 8
IMF5	0.032 5	0.016 0	0.010 6
IMF6	0.033 4	0.016 6	0.011 1
RS	0.032 4	0.016 2	0.010 8

方法	Mse	t/s	Ort
EEMD	0.003 3	324.5855	0.216 8
CEEMD	0.002 8	294.0562	0.222 4
本文	4.103 8×10^-5	50.1826	0.103 5

	相似度	光滑度	目标函数
LB ₁	0.419 2	0.007 0	0.997 3
LB ₂	0.350 3	0.007 0	0.917 1
LB ₃	0.190 3	0.007 1	0.727 0
LB ₄	0.189 3	0.007 1	0.725 8
LB ₅	0.187 2	0.007 1	0.723 3
LB ₆	0.187 3	0.007 1	0.723 4
LB ₇	0.185 8	0.007 1	0.721 7