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Article(id=1241355805648277672, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241355799189058005, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2023.04.023, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1669046400000, receivedDateStr=2022-11-22, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773891887341, onlineDateStr=2026-03-19, pubDate=1701360000000, pubDateStr=2023-12-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773891887341, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773891887341, creator=13701087609, updateTime=1773891887341, updator=13701087609, issue=Issue{id=1241355799189058005, tenantId=1146029695717560320, journalId=1240670690148397066, year='2023', volume='40', issue='4', pageStart='1', pageEnd='229', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773891885801, creator=13701087609, updateTime=1773898068569, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241381731652129441, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241355799189058005, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241381731652129442, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241355799189058005, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=174, endPage=182, ext={EN=ArticleExt(id=1241355807225336002, articleId=1241355805648277672, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Noise Reduction Analysis of Loosening Blasting Vibration Signal based on LMD-MFE-SVD, columnId=1240702076553065119, journalTitle=Blasting, columnName=BLASTING SAFETY, runingTitle=null, highlight=null, articleAbstract=

In order to improve the analysis accuracy of loosening blasting vibration signals, a hybrid denoising method based on local mean decomposition (LMD), multiscale fuzzy entropy (MFE), and singular value filtering (SVD) was established. Firstly, the vibration signal was decomposed by LMD method to obtain a series of product components (PF). Then, the blasting vibration signal was preliminarily denoised by calculating MFE and correlation coefficients. Finally, the real signal components were denoised and extracted by SVD filtering on the residual noise of the main PF components. The results show that the proposed LMD-MFE-SVD denoising method can effectively deal with the noisy PF components. For the simulated signal with multiple components with noise, the LMD algorithm is more efficient than the EMD algorithm. Furthermore, the signal-to-noise ratio (SNR), root mean square error (RMSE) and percentage of distortion (PRD) of the proposed LMD-MFE-SVD method are significantly improved by 11.73%, 22.07% and 9.25%, respectively, compared with the LMD algorithm, which indicates that the noise reduction efficiency is considerable. According to the waveform and spectrum comparison of the measured loosening blasting vibration signal after denoising by the proposed LMD-MFE-SVD method, the denoised signal waveform is more concentrated with most of the signal information retained. The frequency spectrum is clearer, and the signal frequency peaks are effectively displayed.

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ZHANG Xian-tang (1973-), male, born in Jingxing, Hebei Province, professor, doctoral supervisor, mainly engaged in research on rock and soil structure dynamics and blasting engineering, (E-mail) .
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为提高松动爆破振动信号分析精度，在局部均值分解（LMD）的基础上，建立一种基于局部均值分解（LMD）-多尺度模糊熵（MFE）-奇异值滤波（SVD）的混合去噪方法。使用LMD方法对松动爆破振动信号进行分解，获得一系列乘积分量（PF）；通过计算MFE和相关系数，对爆破振动信号进行初步降噪；针对主要PF分量的残留噪声，使用SVD滤波进行降噪处理，提取真实信号成分。通过上述处理，最终实现松动爆破信号降噪。结果表明：提出的LMD-MFE-SVD降噪方法具有可行性和应用价值，能够对含噪的PF分量进行有效处理；对于含多信号成分、多噪声的仿真信号，LMD类算法相较EMD类改进算法降噪效率更高，信噪比（SNR）、均根方误差（RMSE）和失真百分比（PRD）指标表现显著提升，而相较LMD算法，提出的LMD-MFE-SVD算法降噪效率进一步提高，依次提升11.73%、22.07%和9.25%，降噪效率显著；根据实测松动爆破振动信号去噪后的波形和频谱对比，提出的LMD-MFE-SVD降噪后的信号波形更为集中，能保留多数信号信息，信号频谱图更为清晰，有效显示信号频率波峰，更利于松动爆破振动信号的特征分析。

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张宪堂（1973-），男，河北井陉人，教授、博士生导师，主要从事岩土结构动力学和爆破工程研究，（E-mail）。
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周红敏（1975-），女，河北新乐人，副教授、硕士生导师，主要从事工程防灾减灾控制研究，（E-mail）。

ZHOU Hong-min (1975-), female, born in Xinle, Hebei Province, associate professor, master's supervisor, mainly engaged in engineering disaster prevention and mitigation control research, (E-mail) .

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周红敏（1975-），女，河北新乐人，副教授、硕士生导师，主要从事工程防灾减灾控制研究，（E-mail）。

ZHOU Hong-min (1975-), female, born in Xinle, Hebei Province, associate professor, master's supervisor, mainly engaged in engineering disaster prevention and mitigation control research, (E-mail) .

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周红敏（1975-），女，河北新乐人，副教授、硕士生导师，主要从事工程防灾减灾控制研究，（E-mail）。

ZHOU Hong-min (1975-), female, born in Xinle, Hebei Province, associate professor, master's supervisor, mainly engaged in engineering disaster prevention and mitigation control research, (E-mail) .

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reduction, figureFileSmall=nr4TVfBpDYUmfoSnX3b+YQ==, figureFileBig=0Q8w4OCwBN8etvfmzUv9NA==, tableContent=null), ArticleFig(id=1241355822064783380, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355805648277672, language=CN, label=图9, caption=SVD降噪后信号频谱图, figureFileSmall=nr4TVfBpDYUmfoSnX3b+YQ==, figureFileBig=0Q8w4OCwBN8etvfmzUv9NA==, tableContent=null), ArticleFig(id=1241355822186418204, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355805648277672, language=EN, label=Table 1, caption=

Fuzzy entropy of PF

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 PF1PF2PF3PF4PF5PF6
FuzzyEn10.72960.35400.28610.05340.01130.0053
FuzzyEn20.50220.38640.44520.10940.02300.0106
FuzzyEn30.38090.44590.51030.16270.03480.0160
FuzzyEn40.31360.49430.55740.21040.04700.0214
), ArticleFig(id=1241355822282887200, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355805648277672, language=CN, label=表1, caption=

PF分量模糊熵

, figureFileSmall=null, figureFileBig=null, tableContent=
 PF1PF2PF3PF4PF5PF6
FuzzyEn10.72960.35400.28610.05340.01130.0053
FuzzyEn20.50220.38640.44520.10940.02300.0106
FuzzyEn30.38090.44590.51030.16270.03480.0160
FuzzyEn40.31360.49430.55740.21040.04700.0214
), ArticleFig(id=1241355822387744806, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355805648277672, language=EN, label=Table 2, caption=

Noise reduction index table

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 EEMDCEEMDMEEMDLMDLMD-MFE-SVD
SNR5.11216.87547.065110.295911.5031
RMSE1.41291.27231.24350.89040.6939
PRD/%44.975440.499140.665128.344425.7226
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降噪指标表

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 EEMDCEEMDMEEMDLMDLMD-MFE-SVD
SNR5.11216.87547.065110.295911.5031
RMSE1.41291.27231.24350.89040.6939
PRD/%44.975440.499140.665128.344425.7226
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Parameter table during the LMD-MFE-SVD decomposition process

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信号段PF分量相关系数FuzzyEn1信号段PF分量相关系数FuzzyEn1
0.4~1.2 sPF10.95770.01232.7~4.1 sPF10.57410.0067
PF20.27610.0774PF20.54580.0063
PF30.21600.0823PF30.29090.0077
PF40.05230.1137PF40.01740.0044
PF50.02300.0601PF50.01420.0029
   PF60.01150.0039
), ArticleFig(id=1241355822748454969, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241355805648277672, language=CN, label=表3, caption=

LMD-MFE-SVD分解过程参数表

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信号段PF分量相关系数FuzzyEn1信号段PF分量相关系数FuzzyEn1
0.4~1.2 sPF10.95770.01232.7~4.1 sPF10.57410.0067
PF20.27610.0774PF20.54580.0063
PF30.21600.0823PF30.29090.0077
PF40.05230.1137PF40.01740.0044
PF50.02300.0601PF50.01420.0029
   PF60.01150.0039
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基于LMD-MFE-SVD的松动爆破降噪分析
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周红敏 1 , 赵事成 1 , 王慧珍 1 , 余辉 1, 2 , 李文豪 1 , 张宪堂 1, 2
爆破 | 安全与管理 2023,40(4): 174-182
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爆破 | 安全与管理 2023, 40(4): 174-182
基于LMD-MFE-SVD的松动爆破降噪分析
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周红敏1 , 赵事成1, 王慧珍1, 余辉1, 2, 李文豪1, 张宪堂1, 2
作者信息
  • 1.山东科技大学　山东省土木工程防灾减灾重点实验室，青岛　266590
  • 2.安徽理工大学　矿山地下工程教育部工程研究中心，淮南　232001

    • 周红敏（1975-），女，河北新乐人，副教授、硕士生导师，主要从事工程防灾减灾控制研究，（E-mail）。

    ZHOU Hong-min (1975-), female, born in Xinle, Hebei Province, associate professor, master's supervisor, mainly engaged in engineering disaster prevention and mitigation control research, (E-mail) .

通讯作者:

张宪堂（1973-），男，河北井陉人，教授、博士生导师，主要从事岩土结构动力学和爆破工程研究，（E-mail）。
Noise Reduction Analysis of Loosening Blasting Vibration Signal based on LMD-MFE-SVD
Hong-min ZHOU1 , Shi-cheng ZHAO1, Hui-zhen WANG1, Hui YU1, 2, Wen-hao LI1, Xian-tang ZHANG1, 2
Affiliations
  • 1.Shandong Key Laboratory of Disaster Prevention and Mitigation of Civil Engineering, Shandong University of Science and Technology, Qingdao 266590, China
  • 2.Engineering Research Center of Underground Mine Construction, Ministry of Education, Anhui University of Science and Technology, Huainan 232001, China
出版时间: 2023-12-01 doi: 10.3963/j.issn.1001-487X.2023.04.023
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摘要
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为提高松动爆破振动信号分析精度，在局部均值分解（LMD）的基础上，建立一种基于局部均值分解（LMD）-多尺度模糊熵（MFE）-奇异值滤波（SVD）的混合去噪方法。使用LMD方法对松动爆破振动信号进行分解，获得一系列乘积分量（PF）；通过计算MFE和相关系数，对爆破振动信号进行初步降噪；针对主要PF分量的残留噪声，使用SVD滤波进行降噪处理，提取真实信号成分。通过上述处理，最终实现松动爆破信号降噪。结果表明：提出的LMD-MFE-SVD降噪方法具有可行性和应用价值，能够对含噪的PF分量进行有效处理；对于含多信号成分、多噪声的仿真信号，LMD类算法相较EMD类改进算法降噪效率更高，信噪比（SNR）、均根方误差（RMSE）和失真百分比（PRD）指标表现显著提升，而相较LMD算法，提出的LMD-MFE-SVD算法降噪效率进一步提高，依次提升11.73%、22.07%和9.25%，降噪效率显著；根据实测松动爆破振动信号去噪后的波形和频谱对比，提出的LMD-MFE-SVD降噪后的信号波形更为集中，能保留多数信号信息，信号频谱图更为清晰，有效显示信号频率波峰，更利于松动爆破振动信号的特征分析。

松动爆破  /  振动降噪  /  局部均值分解  /  多尺度模糊熵  /  奇异值滤波

In order to improve the analysis accuracy of loosening blasting vibration signals, a hybrid denoising method based on local mean decomposition (LMD), multiscale fuzzy entropy (MFE), and singular value filtering (SVD) was established. Firstly, the vibration signal was decomposed by LMD method to obtain a series of product components (PF). Then, the blasting vibration signal was preliminarily denoised by calculating MFE and correlation coefficients. Finally, the real signal components were denoised and extracted by SVD filtering on the residual noise of the main PF components. The results show that the proposed LMD-MFE-SVD denoising method can effectively deal with the noisy PF components. For the simulated signal with multiple components with noise, the LMD algorithm is more efficient than the EMD algorithm. Furthermore, the signal-to-noise ratio (SNR), root mean square error (RMSE) and percentage of distortion (PRD) of the proposed LMD-MFE-SVD method are significantly improved by 11.73%, 22.07% and 9.25%, respectively, compared with the LMD algorithm, which indicates that the noise reduction efficiency is considerable. According to the waveform and spectrum comparison of the measured loosening blasting vibration signal after denoising by the proposed LMD-MFE-SVD method, the denoised signal waveform is more concentrated with most of the signal information retained. The frequency spectrum is clearer, and the signal frequency peaks are effectively displayed.

loosening blasting  /  denoising of vibration signal  /  LMD  /  MFE  /  SVD
周红敏, 赵事成, 王慧珍, 余辉, 李文豪, 张宪堂. 基于LMD-MFE-SVD的松动爆破降噪分析. 爆破, 2023 , 40 (4) : 174 -182 . DOI: 10.3963/j.issn.1001-487X.2023.04.023
Hong-min ZHOU, Shi-cheng ZHAO, Hui-zhen WANG, Hui YU, Wen-hao LI, Xian-tang ZHANG. Noise Reduction Analysis of Loosening Blasting Vibration Signal based on LMD-MFE-SVD[J]. Blasting, 2023 , 40 (4) : 174 -182 . DOI: 10.3963/j.issn.1001-487X.2023.04.023
正文
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松动爆破作为相对成熟的爆破技术，多用于矿山开采和基坑开挖。在进行松动爆破振动监测时，周边环境间断噪声多、噪声类型复杂，且松动爆破的段别间隔时间长，更易受到噪声的干扰，对信号降噪模型的性能和效果提出更高要求。经验模态分解（empirical mode decomposition，EMD）作为主要的信号消噪方法，因其在处理非线性、非平稳信号时降噪效率稳定，在爆破振动信号分析领域中得到广泛应用[1]。然而EMD在处理间断噪声时会出现明显的模态混叠现象，对分解精度产生不利影响。为了解决该问题，学界相继提出了集合经验模态分解（ensemble empirical mode decomposition，EEMD）[2]、互补集合经验模态分解（complementary ensemble empirical mode decomposition，CEEMD）[3]和改进的经验模态分解方法（modified ensemble empirical mode decompostion，MEEMD）[4]等一系列改进算法，在爆破振动和故障检测领域进行应用，取得了较好的去噪效果。而为处理模态分解类算法的端点问题，学界又陆续提出极点对称分解算法（extreme-point symmetric mode decomposition，ESMD）[5]和基于模态分解类的熵值筛选算法，有效解决了固有模态分量（（intrinsic mode function，IMF）筛选过程的端点问题。
IMF分量本质为调频信号，重构信号准确度更多取决于对IMF分量的人为界定，降噪效果波动较大[6]。为处理上述问题，Smith在进行脑电感知数据处理时提出局部均值分解（local mean decomposition，LMD）方法[7]。程军圣等建立仿真信号用于LMD方法降噪效果验证[8]，表现出良好的信号处理能力。后续李伟将LMD方法应用于矿山微震信号提取[9]，取得了可观的分类准确率。然而LMD方法仍存在缺陷：其一，LMD方法更多应用于机械故障检测、脑电信号提取领域，其他领域的拓展较少；其二，在使用LMD方法对信号进行分解，需要有效判断噪声分量与真实分量的界限，而界限判断的难易多取决于信号的复杂程度。
基坑开挖时周边环境嘈杂，工程机械施工噪声大，振动信号成分复杂，对降噪精度要求更高。基于上述问题，本文建立一种基于LMD-MFE-SVD的爆破振动信号降噪模型，对松动爆破振动信号进行LMD分解，得到乘积分量（product function，PF）；结合相关系数和多尺度模糊熵（multiscale fuzzy entropy，MFE）进行PF分量筛选，对含噪分量进行SVD滤波得到更准确的爆破振动信号，为后续信号分析提供依据。
1　模型理论基础
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1.1　LMD原理
LMD方法是一种新的自适应非平稳信号的分析处理方法，从原信号分解出若干PF分量，每个PF分量都是单个包络信号和对应调频信号的乘积，其分解过程如下[10]：
（1）确定原信号x（t）的局部极值点，计算相邻两个极值点的平均值ui和包络估计值vi。
（2）将全部相邻的局部均值ui和局部包络估计值vi分别用折线连接，采用滑动平均方法对其进行平滑处理，得到局部均值函数u11（t）和局部包络估计函数v11（t），从原始信号中剔除u11（t）得到零均值函数h11（t）。
（3）对h11（t）进行解调，得到解调信号l11（t）
（4）将l11（t）作为原始信号，计算包络估计值v12（t），若v12≠1，重复步骤（1）、（2），迭代n次后得到的l1n（t）为纯调幅调频信号，则迭代停止，可得到下式
考虑到l1n为纯调幅调频信号为理想情况，实际中为使v1n（t）更快收敛，可进行简化处理。设置增减量为δ，使，则计算对应的包络信号如下
（5）将纯调幅调频信号l1n（t）与包络信号v1（t）相乘得到乘积函数PF1
式中，v1（t）为乘积函数PF1的瞬时幅值。
（6）从原信号x（t）中分离出乘积函数PF1，得到新的函数w1（t），重复步骤（1）~（5），直至残差分量wj（t）为常值或单调函数，可得到下式
原始信号x（t）可分解为j个PF分量和一个残差分量的wj（t）和，则原始信号x（t）重构为
1.2　MFE原理
熵是时间序列复杂性的度量，多尺度模糊熵可代替一般熵中的硬阈值准则，用以衡量时间序列于不同尺度因子下的复杂性和自相似性，统计结果稳定性更好[11]，其计算步骤如下：
（1）将原始时间序列粗粒化
对长度为N的原始序列Xi={x1，x2，…，xN}，预先设定嵌入维数m和相似容限r，建立粗粒向量yi（τ）
式中：τ为尺度因子，τ=1；yj（1）为原序列。对于非零τ原始序列Xi可分为τ个每段长为N/τ的粗粒序列yj（τ）。
（2）计算多尺度模糊熵
对全部粗粒序列计算模糊熵，可认为其为尺度因子的函数，即多尺度模糊熵。通常认为熵值越小，序列的自相似性越高；熵值越大，序列越复杂。
1.3　SVD滤波原理
SVD是线性矩阵理论中的重要工具，目前已经广泛应用于工程降噪领域。一般认为，SVD值越大则对应能量较大或者能量集中信号，SVD值越小对应能量较小或者能量分散的信号[12]。
（1）构造Hankel矩阵
对于一维序列Xi={x1，x2，…，xN}构造Hankel矩阵。
（2）对矩阵H进行SVD滤波
式中：U1、W1、V1为较大奇异值；上标H表示共轭转置。
（3）重构滤波后信号
对信号矩阵斜对角线上元素求平均值，可得到滤波后信号序列
式中：为滤波后信号矩阵；m=max（1，k-p+1）；n=min（q，k）。
1.4　LMD-MFE-SVD混合去噪方法
针对松动爆破信号的特点，建立一种基于LMD-MFE-SVD的混合去噪方法，算法步骤见图1。
2　仿真信号分析
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2.1　建立仿真信号
为充分检验改进算法的可行性，有效计算信号熵值，合成由真实信号和噪声信号组成的仿真信号。真实信号包括低幅值低频余弦信号x1（t）、低幅值高频余弦信号x2（t）、调幅调频信号x3（t）和多频信号x4（t）、x5（t），噪声信号包括间接噪声x6（t）和高斯噪声x7（t）。
仿真信号表达式如下
2.2　仿真信号分析
对仿真信号进行LMD分解，可得到6个PF分量，如图2所示，各分量的相关系数依次为0.5178、0.6097、0.2560、0.2233、0.3907和0.1249，多尺度模糊熵值见表1。考虑到仿真信号由7类信号构成，分解得到的PF分量相关系数普遍较小，故本文相关系数阈值取0.2[13]。通过表1可知，PF1分量的多尺度模糊熵最大，且随着维度的增加而减少，与其余分量呈相反变换规律。参考相关系数，PF1分量为含噪乘积分量，PF2~PF5为真实乘积分量，而PF6为无用分量。
对PF1进行SVD滤波去噪，具体去噪效果见图3。通过观察图3（a）可知，SVD滤波对噪声分量进行了有效提取，得到了部分的信号特征；观察图3（b）可知，SVD滤波降噪后的信号更为集中，噪声分量得到了有效的剔除，具备一定的降噪效果。
2.3　算法优劣对比
为更好比较改进算法的优劣，引入EEMD、CEEMD、MEEMD和LMD对仿真信号进行分解。采用信噪比（SNR）[14]、均根方误差（RMSE）、失真百分比（PRD）对消噪质量进行量化分析。输入仿真信号进行分解，EEMD、CEEMD和MEEMD等5类算法得到的分量相关系数见图4，降噪指标数据见表2。通过图4可知，对于成分复杂、具有多类噪声的复杂信号，LMD类方法能够以更少的模态分解次数完成信号的整体分解，PF分量相关系数整体呈递减趋势，表现出良好的分解稳定性，仅IMF5分量作为折线凸点出现，与第二段的间接噪声有关。而EEMD类分解方法中的IMF6~IMF8整体作为凸点出现，可认为EEMD类方法难以有效处理间接噪声的出现，即对于间接出现的高频噪声，EEMD分解类算法处理的稳定性低于LMD类算法。参考表2可知，LMD类算法整体指标表现依次提升了71.62%、39.51%和35.71%。而提出的LMD-MFE-SVD算法相较LMD算法的性能略有提升，依次提升了11.73%、22.07%和9.25%，处理复杂信号的降噪效率和精确度更高。
3　实测信号分析
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3.1　爆破振动监测
工程监测地点位于青岛市平度市旧店镇金山路1号，处于青岛金星矿业现有矿山1#风井工业场地内，主要构筑物包括工业厂房、缓冲池、混凝反应池、高效斜板沉淀池、污泥浓缩池等，多为钢砼结构。施工位置处于厂区地磅房西南方向，邻近缓冲池和主要厂房。工程采用浅孔松动爆破技术，YT28凿岩机进行钻孔，炮孔孔深2.2~2.3 m，炮孔直径40 mm，共布设6个炮孔，炮孔间孔距、排距依次为1.5 m、1.5 m，最大单段药量为2.4 kg，单次爆破总药量为7.2 kg。采用2号岩石乳化炸药进行连续不耦合装药，对所开挖的基坑石方进行多段松动爆破，产生的爆破振动可能对厂区内既有的衬砌结构产生不利影响[15]。监测场地周围共布设4个爆破监测点，对土石方松动爆破进行监测，具体测点布设位置可见图5。
为充分考虑松动爆破对相邻建筑物的影响[16]，取监测点A测振数据作为实测信号，采样频率为8000 Hz，其振动信号如图6所示。通过振动信号可知，本次松动爆破共进行了6个段别的起爆，第5~6段起爆间隔时间较短，依次为0.4 s、1.0 s、0.4 s、0.85 s和0.15 s，考虑到松动爆破的各段间隔时间均大于0.1 s，可基本认为各段起爆之间的相互影响较小。松动爆破中Z向振速最高，最高振速为1.37 cm/s，单段爆破持续时间约为0.6 s。
3.2　实测信号分析
为充分检验LMD-MFE-SVD算法对实测松动爆破振动信号的适用度和降噪性能，选取0.4~1.2 s、2.7~4.1 s两段Z方向的振动信号进行分解，其中0.4~1.2 s为较完整的松动爆破信号，而2.7~4.1 s为信号中的高振速高频信号段，可能对监测点附近的厂房造成振动损害[17]，分解得到表3。通过分析表3可知，0.4~1.2 s信号段分解得到的PF分量中，PF2、PF3两分量为含噪分量，而PF4、PF5为无用分量；2.7~4.1 s信号段中，PF4、PF5和PF6分量为无用分量，PF3为含噪分量。
将0.4~1.2 s和2.7~4.1 s的松动爆破信号进行重构，对0.4~1.2 s信号中的PF2、PF3分量和2.7~4.1 s信号中的PF3分量进行SVD滤波降噪，得到的信号波形及频谱图如图7、图8和图9所示。观察图7可知，提出的LMD-MFE-SVD降噪方法能较好处理松动爆破信号，受限于整体信号段划分的影响，受到邻近波段干扰，信号起始部分有部分过度滤波的情况，但整体的降噪效果良好，波形更为集中，且有效消减了0.7~1.2 s和3.2~4.1 s信号段的模态混叠现象。观察图8、9可知，去噪后的频谱图更为清晰集中，能够明显标示出信号的高频波峰，更有利于对信号的频谱分析。
4　结论
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（1）文中提出的LMD-MFE-SVD降噪方法具备一定的可行性和应用价值，通过计算MFE和进行SVD滤波能够对含噪的PF分量进行有效处理，提高整体的降噪效果。
（2）对于多信号成分、多种类噪声的仿真信号，LMD类算法相较EEMD、CEEMD、MEEMD算法降噪效率更高，SNR、RMSE和PRD的指标表现依次提升了71.62%、39.51%和35.71%，而相较LMD算法的降噪效率，提出的LMD-MFE-SVD算法也有明显改进，依次提升了11.73%、22.07%和9.25%，具备可观的信号降噪效率。
（3）根据实测松动爆破振动信号去噪后的波形和频谱对比，提出的LMD-MFE-SVD降噪后的信号波形更为集中，信号频谱图更为集中清晰，可以在消除噪声分量的同时保留原始信号的能量特征信息，对松动爆破振动信号降噪和松动爆破效应分析具有指导意义。
基金
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  • 国家自然科学基金项目(51874189)
  • 2021年度矿山地下工程教育部工程研究中心开放基金资助项目(JYBGCZX2021102)
文献
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2023年第40卷第4期
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doi: 10.3963/j.issn.1001-487X.2023.04.023
  • 接收时间：2022-11-22
  • 首发时间：2026-03-19
  • 出版时间：2023-12-01
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  • 收稿日期：2022-11-22
基金
National Natural Science Foundation of China(51874189)
国家自然科学基金项目(51874189)
Project Supported by the Open Fund of the Engineering Research Center of Underground Mine Construction, Ministry of Education (Anhui University of Science and Technology) the Ministry of Education for Mining Underground Engineering in 2021(JYBGCZX2021102)
2021年度矿山地下工程教育部工程研究中心开放基金资助项目(JYBGCZX2021102)
作者信息
    1.山东科技大学　山东省土木工程防灾减灾重点实验室，青岛　266590
    2.安徽理工大学　矿山地下工程教育部工程研究中心，淮南　232001

通讯作者:

张宪堂（1973-），男，河北井陉人，教授、博士生导师，主要从事岩土结构动力学和爆破工程研究，（E-mail）。
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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