Article(id=1241409508887556140, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241409507583127593, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2024.04.019, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1690905600000, receivedDateStr=2023-08-02, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773904691191, onlineDateStr=2026-03-19, pubDate=1732982400000, pubDateStr=2024-12-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773904691191, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773904691191, creator=13701087609, updateTime=1773904691191, updator=13701087609, issue=Issue{id=1241409507583127593, tenantId=1146029695717560320, journalId=1240670690148397066, year='2024', volume='41', issue='4', pageStart='1', pageEnd='204', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773904690881, creator=13701087609, updateTime=1773904736091, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241409697262137710, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241409507583127593, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241409697262137711, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241409507583127593, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=150, endPage=155, ext={EN=ArticleExt(id=1241409511592882242, articleId=1241409508887556140, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Time-frequency Analysis of Non-Stationary Vibration Signals based on EP-CEEMDAN Algorithm, columnId=1240702076553065119, journalTitle=Blasting, columnName=BLASTING SAFETY, runingTitle=null, highlight=null, articleAbstract=

The intrinsic mode confusion of empirical mode decomposition (EMD) and the ensemble empirical mode decomposition (EEMD) can only suppress mode confusion to a limited extent, as the white noise added by EEMD cannot be fully neutralized, which compromises the completeness of the original signal. Additionally, both methods fail to avoid interference from endpoint effects. Modal confusion and endpoint effects lead to distortions in the time-frequency analysis results obtained from the Hilbert transforms of EMD and EEMD. A complete ensemble empirical mode decomposition with adaptive noise and endpoint processing (EP-CEEMDAN) is proposed to address these issues. Simulation experiments were conducted to compare EMD, EEMD, and EP-CEEMDAN decomposition results on simulated vibration signals. Through multiscale permutation entropy detection and marginal spectral analysis, it was verified that EP-CEEMDAN has better control over endpoint effects and mode confusion, proving that EP-CEEMDAN is a more effective adaptive algorithm than EMD and EEMD. Finally, EP-CEEMDAN was applied to the processing of measured non-stationary vibration signals, where adaptive white noise was added at the endpoints of the vibration signals during each stage of decomposition. The method successfully generated various intrinsic mode functions (IMF) by calculating a unique residual signal. The EP-CEEMDAN algorithm effectively suppresses IMF endpoint divergence and modal confusion, while the time-frequency spectrum obtained through the Hilbert transform offers high resolution in both time and frequency domains. This result can be used for vibration feature recognition in non-stationary vibration signals.

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QU Ling (1983-), female, born in Qufu, Shandong Province, Ph. D, engineer, mainly engaged in ocean, engineering, and other data processing algorithms, (E-mail) .
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针对经验模态分解(Empirical Mode Decomposition,EMD)固有的模态混淆及集合经验模态分解(Ensemble Empirical Mode Decomposition,EEMD)能在一定程度上抑制模态混淆但由于添加的白噪声无法完全中和,原始信号的完备性无法保证。同时二者均无法免除端点效应的干扰,模态混淆和端点效应导致EMD和EEMD希尔伯特变换得到的时频分析结果失真。提出添加端点处理程序的自适应补充集合经验模态分解算法(Endpoint Processing-Complete Ensemble Empirical Mode Decomposition with Adaptive Noise,EP-CEEMDAN),实施仿真实验对比EMD、EEMD、EP-CEEMDAN对仿真含噪非平稳振动信号的分解结果,并通过多尺度排列熵检测和边际谱分析验证EP-CEEMDAN对端点效应和模态混淆均具有良好的控制效果,从而证明相比EMD和EEMD,EP-CEEMDAN是一种更优良的自适应算法。最后将EP-CEEMDAN应用于实测非平稳振动信号处理中,发现其通过对端点处理后的振动信号在分解的每一阶段添加自适应白噪声,再通过计算唯一的余项信号获得各个固有模态函数(Intrinsic Mode Function,IMF)。EP-CEEMDAN算法得到的IMF端点发散和模态混淆都得到了有效抑制,经希尔伯特变换得到的时频谱在时域和频域均具有较高的分辨率。该结果可用于非平稳振动信号振动特征识别,对进一步分析工程振动危害提供依据。

, correspAuthors=null, authorNote=null, correspAuthorsNote=
屈玲(1983-),女,山东省曲阜市,博士、工程师,从事海洋、工程等数据处理算法研究,(E-mail)
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孙苗(1993-),女,湖北省武汉市,博士、讲师,从事水下钻孔爆破理论研究,(E-mail)

SUN Miao (1993-), female, born in Wuhan, Hubei Province, Ph. D, lecturer, mainly engaged in underwater drilling and blasting, (E-mail) .

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孙苗(1993-),女,湖北省武汉市,博士、讲师,从事水下钻孔爆破理论研究,(E-mail)

SUN Miao (1993-), female, born in Wuhan, Hubei Province, Ph. D, lecturer, mainly engaged in underwater drilling and blasting, (E-mail) .

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孙苗(1993-),女,湖北省武汉市,博士、讲师,从事水下钻孔爆破理论研究,(E-mail)

SUN Miao (1993-), female, born in Wuhan, Hubei Province, Ph. D, lecturer, mainly engaged in underwater drilling and blasting, (E-mail) .

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Physica A: Statistical Mechanics and its Applications, 2019, 515: 217-231., articleTitle=Multivariate multiscale fractional order weighted permutation entropy of nonlinear time series, refAbstract=null), Reference(id=1241409540068012948, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241409508887556140, doi=null, pmid=null, pmcid=null, year=2015, volume=19, issue=8, pageStart=71, pageEnd=79, url=null, language=null, rfNumber=[16], rfOrder=26, authorNames=李军, 李青, journalName=电机与控制学报, refType=null, unstructuredReference=李军, 李青. 基于CEEMDAN-排列熵和泄漏积分ESN的中期电力负荷预测研究[J]. 电机与控制学报, 2015, 19(8): 71-79., articleTitle=基于CEEMDAN-排列熵和泄漏积分ESN的中期电力负荷预测研究, refAbstract=null), Reference(id=1241409540214813597, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241409508887556140, doi=null, pmid=null, pmcid=null, year=2015, volume=19, issue=8, pageStart=71, pageEnd=79, url=null, language=null, rfNumber=[16], rfOrder=27, authorNames=LI Jun, LI Qing, journalName=Electric Machines and Control, refType=null, unstructuredReference=LI Jun, LI Qing. 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Geotechnical and Geological Engineering, 2022, 40: 1363-1372., articleTitle=Analysis and research on blasting network delay of deep-buried diversion tunnel crossing fault zone based on EP-CEEMDAN-INHT, refAbstract=null), Reference(id=1241409541892535205, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241409508887556140, doi=null, pmid=null, pmcid=null, year=2021, volume=18, issue=12, pageStart=3337, pageEnd=3346, url=null, language=null, rfNumber=[18], rfOrder=29, authorNames=冯云智, 唐彬峰, 赵宁, journalName=铁道科学与工程学报, refType=null, unstructuredReference=冯云智, 唐彬峰, 赵宁. 改进多尺度排列熵及模糊算法的JTC状态检测[J]. 铁道科学与工程学报, 2021, 18(12): 3337-3346., articleTitle=改进多尺度排列熵及模糊算法的JTC状态检测, refAbstract=null), Reference(id=1241409542009975725, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241409508887556140, doi=null, pmid=null, pmcid=null, year=2021, volume=18, issue=12, pageStart=3337, pageEnd=3346, url=null, language=null, rfNumber=[18], rfOrder=30, authorNames=FENG Yun-zhi, TANG Bin-feng, ZHAO Ning, journalName=Journal of Railway Science and Engineering, refType=null, unstructuredReference=FENG Yun-zhi, TANG Bin-feng, ZHAO Ning. 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MPE of each component

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IMFMPE
EMDEEMDEP-CEEMDAN
10.88240.71450.4015
20.80170.62130.3226
30.65470.60240.2149
40.48120.4757 
50.32360.3659 
6 0.3321 
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各分量多尺度排列熵值大小

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IMFMPE
EMDEEMDEP-CEEMDAN
10.88240.71450.4015
20.80170.62130.3226
30.65470.60240.2149
40.48120.4757 
50.32360.3659 
6 0.3321 
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基于EP-CEEMDAN算法的非平稳振动信号时频分析
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孙苗 1, 2, 3 , 屈玲 4 , 袁立平 1 , 吴静 2, 3, 5 , 沈玉光 1
爆破 | 安全与管理 2024,41(4): 150-155
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爆破 | 安全与管理 2024, 41(4): 150-155
基于EP-CEEMDAN算法的非平稳振动信号时频分析
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孙苗1, 2, 3 , 屈玲4 , 袁立平1, 吴静2, 3, 5, 沈玉光1
作者信息
  • 1.湖北国土资源职业学院 环境与工程学院,武汉 430090
  • 2.中国地质大学(武汉) 岩土钻掘与防护教育部工程研究中心,武汉 430074
  • 3.湖北小城镇发展研究中心,孝感 432000
  • 4.湖北省地质局地球物理勘探大队,武汉 430056
  • 5.湖北工程学院 土木工程学院,孝感 432000
  • 孙苗(1993-),女,湖北省武汉市,博士、讲师,从事水下钻孔爆破理论研究,(E-mail)

    SUN Miao (1993-), female, born in Wuhan, Hubei Province, Ph. D, lecturer, mainly engaged in underwater drilling and blasting, (E-mail) .

通讯作者:

屈玲(1983-),女,山东省曲阜市,博士、工程师,从事海洋、工程等数据处理算法研究,(E-mail)
Time-frequency Analysis of Non-Stationary Vibration Signals based on EP-CEEMDAN Algorithm
Miao SUN1, 2, 3 , Ling QU4 , Li-ping YUAN1, Jing WU2, 3, 5, Yu-guang SHEN1
Affiliations
  • 1.College of Environment and Engineering, Hubei Land Resources Vocational College, Wuhan 430090, China
  • 2.Engineering Research Center of Rock-soil Drilling & Excavation and Protection, Ministry of Education of China University of Geosciences, Wuhan 430074, China
  • 3.Hubei Small Town Development Research Center, Xiaogan 432000, China
  • 4.Geophysical Exploration Brigade of Hubei Geological Bureau, Wuhan 430056, China
  • 5.Faculty of Civil Engineering, Hubei Engineering University, Xiaogan 432000, China
出版时间: 2024-12-01 doi: 10.3963/j.issn.1001-487X.2024.04.019
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针对经验模态分解(Empirical Mode Decomposition,EMD)固有的模态混淆及集合经验模态分解(Ensemble Empirical Mode Decomposition,EEMD)能在一定程度上抑制模态混淆但由于添加的白噪声无法完全中和,原始信号的完备性无法保证。同时二者均无法免除端点效应的干扰,模态混淆和端点效应导致EMD和EEMD希尔伯特变换得到的时频分析结果失真。提出添加端点处理程序的自适应补充集合经验模态分解算法(Endpoint Processing-Complete Ensemble Empirical Mode Decomposition with Adaptive Noise,EP-CEEMDAN),实施仿真实验对比EMD、EEMD、EP-CEEMDAN对仿真含噪非平稳振动信号的分解结果,并通过多尺度排列熵检测和边际谱分析验证EP-CEEMDAN对端点效应和模态混淆均具有良好的控制效果,从而证明相比EMD和EEMD,EP-CEEMDAN是一种更优良的自适应算法。最后将EP-CEEMDAN应用于实测非平稳振动信号处理中,发现其通过对端点处理后的振动信号在分解的每一阶段添加自适应白噪声,再通过计算唯一的余项信号获得各个固有模态函数(Intrinsic Mode Function,IMF)。EP-CEEMDAN算法得到的IMF端点发散和模态混淆都得到了有效抑制,经希尔伯特变换得到的时频谱在时域和频域均具有较高的分辨率。该结果可用于非平稳振动信号振动特征识别,对进一步分析工程振动危害提供依据。

经验模态分解  /  自适应补充集合经验模态分解  /  模态混淆  /  端点效应  /  希尔伯特变换

The intrinsic mode confusion of empirical mode decomposition (EMD) and the ensemble empirical mode decomposition (EEMD) can only suppress mode confusion to a limited extent, as the white noise added by EEMD cannot be fully neutralized, which compromises the completeness of the original signal. Additionally, both methods fail to avoid interference from endpoint effects. Modal confusion and endpoint effects lead to distortions in the time-frequency analysis results obtained from the Hilbert transforms of EMD and EEMD. A complete ensemble empirical mode decomposition with adaptive noise and endpoint processing (EP-CEEMDAN) is proposed to address these issues. Simulation experiments were conducted to compare EMD, EEMD, and EP-CEEMDAN decomposition results on simulated vibration signals. Through multiscale permutation entropy detection and marginal spectral analysis, it was verified that EP-CEEMDAN has better control over endpoint effects and mode confusion, proving that EP-CEEMDAN is a more effective adaptive algorithm than EMD and EEMD. Finally, EP-CEEMDAN was applied to the processing of measured non-stationary vibration signals, where adaptive white noise was added at the endpoints of the vibration signals during each stage of decomposition. The method successfully generated various intrinsic mode functions (IMF) by calculating a unique residual signal. The EP-CEEMDAN algorithm effectively suppresses IMF endpoint divergence and modal confusion, while the time-frequency spectrum obtained through the Hilbert transform offers high resolution in both time and frequency domains. This result can be used for vibration feature recognition in non-stationary vibration signals.

empirical mode decomposition  /  complete ensemble empirical mode decomposition with adaptive noise  /  mode mixing  /  endpoint effect  /  Hilbert transform
孙苗, 屈玲, 袁立平, 吴静, 沈玉光. 基于EP-CEEMDAN算法的非平稳振动信号时频分析. 爆破, 2024 , 41 (4) : 150 -155 . DOI: 10.3963/j.issn.1001-487X.2024.04.019
Miao SUN, Ling QU, Li-ping YUAN, Jing WU, Yu-guang SHEN. Time-frequency Analysis of Non-Stationary Vibration Signals based on EP-CEEMDAN Algorithm[J]. Blasting, 2024 , 41 (4) : 150 -155 . DOI: 10.3963/j.issn.1001-487X.2024.04.019
非平稳振动信号伴有瞬时、突变和振荡特征[1,2],在分析提取特征信息时存在较大难度,时频分析已成为处理这类信号的重要手段[3,4]。常用的时频分析方法有短时傅里叶变换(Short-time Fourier Transform,STFT)、连续小波变换(Continuous Wavelet Transform,CWT)、离散小波变换(Discrete Wavelet Transform,DWT)和希尔伯特-黄变换(Hilbert-Huang Transform,HHT)等[5-8]。上述方法除HHT外,多以傅里叶变换为理论依据,在时频分析过程中不可避免会受到傅里叶变换分析非平稳信号所带来的缺陷,如出现虚假频率和多余信号分量等[9,10]
HHT依据数据本身的时间尺度来进行模态分解,分解的过程保留了数据的特有属性。但由于非平稳振动信号具有强背景噪声及易突变等特性,导致HHT在振动信号处理中存在如下亟待解决的问题:模态混淆,噪声信号的混杂会使经验模态分解(Empirical Mode Decomposition,EMD)和集合经验模态分解(Ensemble Empirical Mode Decomposition,EEMD)的结果产生严重的模态混淆[11-14];端点效应,其几乎是所有时频分析方法都无法避免的存在。
为了解决上述问题,提出一种有针对性抑制端点效应和模态混淆的算法。该算法首先对待分析非平稳振动信号进行端点处理(Endpoint Processing,EP)[15],排除端点发散的干扰;再对端点处理后的信号进行自适应补充集合经验模态分解(Complete Ensemble Empirical Mode Decomposition with Adaptive Noise,CEEMDAN),其在EMD的每个阶段添加有限次的自适应白噪声[16,17],通过自适应白噪声抵消监测中混入的噪声。通过上述两步,可达到同时抑制端点效应和模态混淆的目的,从而有效克服传统HHT时频分析失真现象。最后通过仿真实验和实际非平稳振动信号分解验证EP-CEEMDAN是一种更优良的自适应算法。
对待分析原始信号St)进行端点处理,其本质是通过信号在端点处的变化趋势延拓出新的端点。找到St)中所有极大值点和极小值点对应的坐标,设左端点需要延拓的极大值点和极小值点时刻分别为tmax atmin a,其计算分以下2种情况。
情况1:tmax(a+1)<tmin(a+1)tmin atmax a求解见式(1)。
情况2:tmax(a+1)>tmin(a+1)tmax atmin a求解见式(2)。
设需要延拓的极大值点和极小值点发生时刻对应的幅值分别为xmaxaxmina,对所有极大值点坐标进行多项式拟合,代入tmaxa,可计算出xmaxaxmina计算同xmaxa。右端点延拓同左端点,经过上述步骤可得到端点处理后的St)。
对端点处理后的St)进行模态混淆抑制处理,是通过对端点处理后的信号进行CEEMDAN实现的。
CEEMDAN在EMD的每个阶段添加有限次的自适应白噪声[16,17],能实现在较少的平均次数下,其重构误差几乎为零。通过自适应白噪声抵消监测中混入的噪声是CEEMDAN最显著的优势,是EEMD的改进。具体步骤如下:
步骤一:在端点处理后的St)中添加自适应性白噪声Bit),i为加噪声的次数,一般取10~50,本文i=30。则第i次的信号可表示为St)=St)+αiBit)(i=1,2,3,…,30),其中αiBit)的标准差。可计算CEEMDAN的一阶IMF分量,见式(3)。
步骤二:得到一阶分量后的余项R1t)=St)-IMF1,构造新的待分解信号St)=R1t)+αiBit),重复步骤一。直到得到CEEMDAN的二阶IMF分量,此时余项为R2t)=St)-IMF2
步骤三:重复步骤一和步骤二,直到程序终止,共产生了k个IMF,St)最终分解式见式(4)。程序运行结束得到的余项为Rt)。
为增加论文可读性,对1.1节提出的EP算法和1.2节提出的CEEMDAN算法,进行汇总分析,并绘制算法运行流程图,EP-CEEMDAN算法运算流程图如图1所示。
排列熵(Permutation Entropy,PE)是一种检测时间序列随机性的方法[15],具有概念简单,计算速度快,抗干扰能力强等优点,特别适用于非线性数据。多尺度排列熵(Multiscale Permutation Entropy,MPE)在EP的基础上对检测信号进行粗粒化处理[18],得到的结果精度更高。实现步骤如下:
步骤一:对EP-CEEMDAN得到的任意IMF进行粗粒化处理,令任意IMF为xi),得到多尺度时间序列,如式(5)所示。
步骤二:对进行空间重构,得到m维空间的重构向量,记每种排列出现的概率为Pi(0<Pi≤1,im!)。
步骤三:根据式(6)计算的PE值,并对结果进行标准化处理,当Pi=1/m!时,有PEmax=log10m!,标准化后的排列熵为PE*=PE/PEmax
显然PE*的取值范围是[0,1],PE*越大信号越随机,反之越规则。根据文献[141518]当PE*大于0.6,被认为是异常信号(噪声、间歇、脉冲信号等),否则近似认为是平稳信号。对于爆破地震波信号,被剔除的异常分量是噪声分量,而噪声分量是导致EMD结果出现模态混淆的主要原因,剔除了噪声分量可实现EMD模态混淆抑制。
为验证EP-CEEMDAN是一种更优良的自适应算法,可实现非平稳振动信号细节特征信息提取,构建含有噪声信号的仿真信号用于模态分解。构建仿真信号St)=x1t)+x2t)+x3t),其中x1t)是功率为0.5的高斯白噪声;x2t)是频率为50的非高频正弦稳态信号;x3t)是频率为300的高频正弦稳态信号,如图2所示。计算x1t)、x2t)和x3t)的MPE值,计算结果为0.9239,0.1954和0.2017。不难发现,白噪声熵值远大于稳态信号且大于0.6。正弦稳态信号序列规则,信号稳定,对应熵值小。
首先对St)进行采用EMD、EEMD和EP-CEEMDAN进行分解,得到如图3所示的结果,并计算各种分解方法得到的IMF的MPE值,计算结果见表1
观察表1图3,可得下列结论。
(1)端点处理对信号细节信息提取至关重要,EMD和EEMD得到的IMF2IMF4右端点均存在发散,偏离真实发展趋势。
(2)白噪声的存在对EMD造成严重的模态混淆,如IMF2IMF3模态混淆严重,仅可将IMF5近似认为是稳态的信号,也就是原始信号的精细特征部分。
(3)EEMD得到IMF的熵值较EMD小,说明EEMD具有一定的降噪能力,模态混淆现象相比EMD分解有一定的缓解。
(4)EP-CEEMDAN能够抑制噪声的存在造成的IMF模态混淆和端点效应,分解结果可实现原始信号精细特征细节提取。
爆破地震波监测信号是典型的非平稳振动信号,以此信号分析为例,检验EP-CEEMDAN算法对实际含噪非平稳振动信号分解过程中遇到的端点效应和模态混淆的具有良好的抑制效果。以重庆市李家沱大桥下炸礁工程为研究对象,该桥是连接九龙坡区和巴南区的过江通道,是重要的交通枢纽。爆破施工时需密切关注其动态,保护其不受损坏,图4是爆破施工环境图。
在爆破施工时,对李家沱大桥进行实时动态监测。选取一条典型的爆破地震波监测信号进行分析,信号波形图如图5所示。按照仿真实验分析思路,首先对图5信号进行端点处理,再对端点处理后的信号进行CEEMDAN,完成上述两步,即可实现端点效应和模态混淆双重抑制,得到反映真实信号特征的数据信息。为对比原始信号和EP-CEEMDAN得到IMF,将EP-CEEMDAN得到IMF也放入图5中。
观察图5,可发现信号的特征时间是0~0.8 s,后面0.8~1.2 s信号逐渐平稳。实测信号被分解为9个IMF和唯一一个余项R。EP-CEEMDAN是按时间尺度自适应分解的,也就是按相邻两个明显的波峰之间的距离的大小顺序进行的分解,分解得到的各个分量的频率是按从高到低的顺序依次排列的,各分量包含了信号中不同分辨率和不同的时间尺度的特征。
可以发现:IMF1IMF9频率逐渐降低,说明地震波传播过程中高频衰减,IMF1~IMF5包含了振动信号的大部分能量,为优势频带,水下钻孔爆破危害效应主要由这些分量构成,是我们研究的重点频带。IMF6~IMF9为低频分量,频率开始明显地降低。
计算EP-CEEMDAN得到IMF的排列熵:PH*1=0.5017、PH*2=0.4843、PH*3=0.4047、PH*4=0.3385、PH*5=0.3065、PH*6=0.2741、PH*7=0.2537、PH*8=0.2373、PH*9=0.2265;根据图5和熵值大小可以发现:(1)9个IMF均属于稳态信号,信号序列规则,其中IMF1可以近似认为是稳态高频分量,IMF2IMF3可以认为是稳态中频分量,IMF4~IMF9可以认为是稳态低频分量;(2)IMF2IMF3分量依旧含有一定的模态混淆现象,根据分解结果和熵值大小可以发现模态混淆现象不严重;(3)未见明显的端点发散。
可认为EP-CEEMDAN得到的稳态IMF即为非稳态振动信号的特征部分,得到的IMF即为实际工程中需要进一步分析的精细细节特征信息。
对EP-CEEMDAN得到的稳态IMF进行Hilbert变换,不考虑余项,可得单个IMF的边际谱图,边际谱如图6所示。观察图6可发现,IMF边际谱物理意义十分明显,可从侧面反映EP-CEEMDAN得到IMF分量的正确性。其中IMF1频带最宽为20~80 Hz但是携带能量很少;IMF2情况与IMF1相同;能量绝大部分蕴含在IMF3~IMF6,该区域信号频率在0~15 Hz以内;IMF7~IMF9蕴含能量较少,频率在0~3 Hz左右,综上可发现接近90%的能量在0~15 Hz以内。
进一步分析信号时频能量分布,得到如图7所示的三维时频能量图,不难发现信号在频域和时域均具有较高分辨率,该图得到的分析结果和边际谱分析一致,信号主要能量集中在低频,特别是20 Hz以下的部分。实际工程应重点分析此范围时频能量信息,关注是否会引起爆区周围既有建(构)筑物破坏或产生共振作用。
通过IMF排列熵检测和边际谱物理意义解读以及三维时频能量图分析,可发现经EP-CEEMDAN信号分解算法得到的IMF可同时排除端点效应和模态混淆的干扰,得到物理意义更明确的分量。对此IMF分量进行Hilbert变换,得到的边际谱和时频能量谱在时域和频域均具有较高的分辨率,同时频能量信息具有对应性,侧面也反映出EP-CEEMDAN得到的IMF具有稳定性,不易突变,保证进一步Hilbert变换得到时频能量信息的稳定性。该结果可用于非平稳振动信号振动特征识别,对进一步分析工程振动危害提供依据。
(1)EP-CEEMDAN针对EMD固有的模态混淆和端点效应进行逐一改进,得到排除端点效应和模态混淆干扰的算法,相比传统EMD和EEMD得到的IMF稳定性和真实性更高。
(2)计算EP-CEEMDAN得到IMF的多尺度排列熵值,可判断IMF分量是否处于稳定状态;生成IMF边际谱图和时频能量三维图,可获取IMF分量蕴含的时-频-能量信息。分析结果的对应性反映出EP-CEEMDAN算法分解得到的IMF具有稳定不易突变性,实际物理意义更明显。
  • 湖北省自然科学基金计划项目(2022CFB334; 2022CFB948)
  • 岩土钻掘与教育部工程研究中心(202404; 202409)
  • 湖北省教育厅科学研究计划指导性项目(B2022602)
  • 湖北小城镇发展研究中心基金(2024A004)
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2024年第41卷第4期
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doi: 10.3963/j.issn.1001-487X.2024.04.019
  • 接收时间:2023-08-02
  • 首发时间:2026-03-19
  • 出版时间:2024-12-01
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  • 收稿日期:2023-08-02
基金
Hubei Provincial Natural Science Foundation of China(2022CFB334; 2022CFB948)
湖北省自然科学基金计划项目(2022CFB334; 2022CFB948)
Engineering Research Center of Rock-soil Drilling & Excavation and Protection, Ministry of Education(202404; 202409)
岩土钻掘与教育部工程研究中心(202404; 202409)
Hubei Provincial Department of Education Scientific Research Program Guidance Project(B2022602)
湖北省教育厅科学研究计划指导性项目(B2022602)
Hubei Small Town Development Research Center Fund(2024A004)
湖北小城镇发展研究中心基金(2024A004)
作者信息
    1.湖北国土资源职业学院 环境与工程学院,武汉 430090
    2.中国地质大学(武汉) 岩土钻掘与防护教育部工程研究中心,武汉 430074
    3.湖北小城镇发展研究中心,孝感 432000
    4.湖北省地质局地球物理勘探大队,武汉 430056
    5.湖北工程学院 土木工程学院,孝感 432000

通讯作者:

屈玲(1983-),女,山东省曲阜市,博士、工程师,从事海洋、工程等数据处理算法研究,(E-mail)
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
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红菇属 Russula 17 8.13
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