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Article(id=1241777704824016931, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241777699996368955, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2024.02.018, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1686672000000, receivedDateStr=2023-06-14, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773992475943, onlineDateStr=2026-03-20, pubDate=1717171200000, pubDateStr=2024-06-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773992475943, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773992475943, creator=13701087609, updateTime=1773992475943, updator=13701087609, issue=Issue{id=1241777699996368955, tenantId=1146029695717560320, journalId=1240670690148397066, year='2024', volume='41', issue='2', pageStart='1', pageEnd='252', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773992474792, creator=13701087609, updateTime=1773992784144, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241778997575619516, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241777699996368955, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241778997575619517, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241777699996368955, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=143, endPage=150, ext={EN=ArticleExt(id=1241777705058897963, articleId=1241777704824016931, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=A Noise Reduction Smooth Model of Vibration Signal of Open-pit Deep-hole Blasting based on CEEMD, columnId=1240702072862069231, journalTitle=Blasting, columnName=BLASTING IN ORE AND ROCK, runingTitle=null, highlight=null, articleAbstract=

Due to the complex terrain and geological conditions in the blasting area, as well as errors in monitoring instruments, reflections of vibration propagation medium, and interference from magnetic fields, a significant amount of noise is often present in the original blasting vibration signals collected. To address this issue, a signal noise reduction smooth model based on complementary ensemble empirical mode decomposition (CEEMD) is proposed. Firstly, the measured blasting vibration signal is decomposed using CEEMD and an algorithm for low-pass filtering is established based on the obtained intrinsic mode function (IMF) component from the decomposition. Additionally, an objective function is constructed to calculate the optimal solution according to similarity and smoothness criteria for filtering algorithms. The resulting filtering algorithm model represents an optimal denoising smooth model for blasting vibration signals. To verify our noise reduction smooth model, a simulation signal is constructed and applied to actual open-pit deep-hole blasting vibration signal research. Finally, the noise reduction effects of empirical mode decomposition (EMD) method, wavelet threshold method, CEEMD-wavelet threshold method, and filter algorithm model BP3 are quantified and compared using two indexes: signal-to-noise ratio and root-mean-square error. It has been confirmed that the proposed noise reduction smooth model effectively reduces noise in open-pit blasting vibration signals. The findings demonstrate that our CEEMD-based noise reduction smooth model for open-pit deep-hole blasting vibrations possesses excellent denoising capabilities while preserving essential characteristic information from the original signals. Furthermore, the denoising effect of the proposed model surpasses that of EMD method, wavelet threshold method, and CEEMD-wavelet threshold method.

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ZHANG Yun-peng (1963-), male, professor, doctor, doctoral supervisor, mainly engaged in research in blasting field, (E-mail) .
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由于爆破区域地形地质条件的复杂、监测仪器的误差、振动传播介质的反射以及磁场的干扰等原因，采集的原始爆破振动信号常常会掺杂大量的噪声，针对此问题提出了基于互补集合经验模态分解（CEEMD）的信号降噪光滑模型。此模型将爆破振动信号进行CEEMD，基于分解所得到的IMF分量建立低通滤波算法。根据滤波算法的相似度与光滑度，构造目标函数并计算最优解，其对应的滤波算法模型即为爆破振动信号的最优降噪光滑模型。通过构造仿真信号验证了降噪光滑模型算法的可行性，并将模型应用了实际露天深孔爆破振动信号的研究。采用信噪比和均方根误差两种指标对比经验模态分解（EMD）方法、小波阈值法、CEEMD-小波阈值法与滤波算法模型BP3的降噪效果，验证了降噪光滑模型在对露天矿山爆破振动信号降噪方面的有效性，并通过频谱分析进一步验证了降噪光滑模型较CEEMD-小波阈值法的优越性。结果表明：基于CEEMD的露天深孔爆破振动信号降噪光滑模型具有良好的降噪能力，能够在保留原始爆破振动信号真实特征信息的前提下对信号进行降噪，且降噪效果优于EMD方法、小波阈值法和CEEMD-小波阈值法。

, correspAuthors=null, authorNote=null, correspAuthorsNote=
张云鹏（1963-），男，教授、博士、博导，主要从事爆破领域研究，（E-mail）。
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田婕（1998-），女，硕士研究生，主要从事爆破领域研究，（E-mail）。

TIAN Jie (1998-), female, postgraduate, mainly engaged in research in blasting field, (E-mail) .

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田婕（1998-），女，硕士研究生，主要从事爆破领域研究，（E-mail）。

TIAN Jie (1998-), female, postgraduate, mainly engaged in research in blasting field, (E-mail) .

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田婕（1998-），女，硕士研究生，主要从事爆破领域研究，（E-mail）。

TIAN Jie (1998-), female, postgraduate, mainly engaged in research in blasting field, (E-mail) .

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Correlation coefficients of the filtering algorithm model and the unnoised simulation signal

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滤波算法模型 BP1 BP2 BP3 BP4 BP5 BP6 BP7
相关系数0.92240.93520.06140.05650.05970.05480.0310
), ArticleFig(id=1241777725099282577, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777704824016931, language=CN, label=表1, caption=

滤波算法模型与未加噪仿真信号的相关系数

, figureFileSmall=null, figureFileBig=null, tableContent=
滤波算法模型 BP1 BP2 BP3 BP4 BP5 BP6 BP7
相关系数0.92240.93520.06140.05650.05970.05480.0310
), ArticleFig(id=1241777725178974361, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777704824016931, language=EN, label=Table 2, caption=

Blasting parameters

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 项目参数
爆区概况孔数64
炮孔直径/mm150
孔深/m16
超深/m2
孔距/m4
排距/m3
段高/m15
填塞高度/m4
单段最大药量/kg240
总爆破量/wt3.5
布孔方式菱形
装药结构连续装药
), ArticleFig(id=1241777726659563680, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777704824016931, language=CN, label=表2, caption=

爆破参数

, figureFileSmall=null, figureFileBig=null, tableContent=
 项目参数
爆区概况孔数64
炮孔直径/mm150
孔深/m16
超深/m2
孔距/m4
排距/m3
段高/m15
填塞高度/m4
单段最大药量/kg240
总爆破量/wt3.5
布孔方式菱形
装药结构连续装药
), ArticleFig(id=1241777726777004198, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777704824016931, language=EN, label=Table 3, caption=

Denoising effect evalution index

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降噪方法信噪比/dB均方根误差/×10-2
EMD16.95340.3872
小波阈值法21.04600.2416
CEEMD-小波阈值法21.05400.2414
滤波算法模型BP321.39980.2317
), ArticleFig(id=1241777726877667498, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241777704824016931, language=CN, label=表3, caption=

降噪效果评价指标

, figureFileSmall=null, figureFileBig=null, tableContent=
降噪方法信噪比/dB均方根误差/×10-2
EMD16.95340.3872
小波阈值法21.04600.2416
CEEMD-小波阈值法21.05400.2414
滤波算法模型BP321.39980.2317
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基于CEEMD的露天深孔爆破振动信号降噪光滑模型
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田婕 1 , 张云鹏 1, 2 , 闫鹏 1 , 孙文诚 3 , 杨曦 1, 2
爆破 | 矿岩爆破 2024,41(2): 143-150
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爆破 | 矿岩爆破 2024, 41(2): 143-150
基于CEEMD的露天深孔爆破振动信号降噪光滑模型
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田婕1 , 张云鹏1, 2 , 闫鹏1, 孙文诚3, 杨曦1, 2
作者信息
  • 1.华北理工大学　矿业工程学院，唐山　063210
  • 2.河北省矿业开发与安全技术重点实验室，唐山　063210
  • 3.承德广兴矿业有限责任公司，承德　067103

    • 田婕（1998-），女，硕士研究生，主要从事爆破领域研究，（E-mail）。

    TIAN Jie (1998-), female, postgraduate, mainly engaged in research in blasting field, (E-mail) .

通讯作者:

张云鹏（1963-），男，教授、博士、博导，主要从事爆破领域研究，（E-mail）。
A Noise Reduction Smooth Model of Vibration Signal of Open-pit Deep-hole Blasting based on CEEMD
Jie TIAN1 , Yun-peng ZHANG1, 2 , Peng YAN1, Wen-cheng SUN3, Xi YANG1, 2
Affiliations
  • 1.College of Mining Engineering, North China University of Science and Technology, Tangshan 063210, China
  • 2.Hebei Provincial Key Laboratory of Mine Development and Safety Technology, Tangshan 063210, China
  • 3.Chengde Guangxing Mining Co., Ltd., Chengde 067103, China
出版时间: 2024-06-01 doi: 10.3963/j.issn.1001-487X.2024.02.018
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摘要
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由于爆破区域地形地质条件的复杂、监测仪器的误差、振动传播介质的反射以及磁场的干扰等原因，采集的原始爆破振动信号常常会掺杂大量的噪声，针对此问题提出了基于互补集合经验模态分解（CEEMD）的信号降噪光滑模型。此模型将爆破振动信号进行CEEMD，基于分解所得到的IMF分量建立低通滤波算法。根据滤波算法的相似度与光滑度，构造目标函数并计算最优解，其对应的滤波算法模型即为爆破振动信号的最优降噪光滑模型。通过构造仿真信号验证了降噪光滑模型算法的可行性，并将模型应用了实际露天深孔爆破振动信号的研究。采用信噪比和均方根误差两种指标对比经验模态分解（EMD）方法、小波阈值法、CEEMD-小波阈值法与滤波算法模型BP3的降噪效果，验证了降噪光滑模型在对露天矿山爆破振动信号降噪方面的有效性，并通过频谱分析进一步验证了降噪光滑模型较CEEMD-小波阈值法的优越性。结果表明：基于CEEMD的露天深孔爆破振动信号降噪光滑模型具有良好的降噪能力，能够在保留原始爆破振动信号真实特征信息的前提下对信号进行降噪，且降噪效果优于EMD方法、小波阈值法和CEEMD-小波阈值法。

露天深孔爆破  /  振动信号  /  CEEMD  /  低通滤波  /  降噪光滑模型

Due to the complex terrain and geological conditions in the blasting area, as well as errors in monitoring instruments, reflections of vibration propagation medium, and interference from magnetic fields, a significant amount of noise is often present in the original blasting vibration signals collected. To address this issue, a signal noise reduction smooth model based on complementary ensemble empirical mode decomposition (CEEMD) is proposed. Firstly, the measured blasting vibration signal is decomposed using CEEMD and an algorithm for low-pass filtering is established based on the obtained intrinsic mode function (IMF) component from the decomposition. Additionally, an objective function is constructed to calculate the optimal solution according to similarity and smoothness criteria for filtering algorithms. The resulting filtering algorithm model represents an optimal denoising smooth model for blasting vibration signals. To verify our noise reduction smooth model, a simulation signal is constructed and applied to actual open-pit deep-hole blasting vibration signal research. Finally, the noise reduction effects of empirical mode decomposition (EMD) method, wavelet threshold method, CEEMD-wavelet threshold method, and filter algorithm model BP3 are quantified and compared using two indexes: signal-to-noise ratio and root-mean-square error. It has been confirmed that the proposed noise reduction smooth model effectively reduces noise in open-pit blasting vibration signals. The findings demonstrate that our CEEMD-based noise reduction smooth model for open-pit deep-hole blasting vibrations possesses excellent denoising capabilities while preserving essential characteristic information from the original signals. Furthermore, the denoising effect of the proposed model surpasses that of EMD method, wavelet threshold method, and CEEMD-wavelet threshold method.

open-pit deep-hole blasting  /  vibration signal  /  CEEMD  /  low-pass filtering  /  noise reduction smooth model
田婕, 张云鹏, 闫鹏, 孙文诚, 杨曦. 基于CEEMD的露天深孔爆破振动信号降噪光滑模型. 爆破, 2024 , 41 (2) : 143 -150 . DOI: 10.3963/j.issn.1001-487X.2024.02.018
Jie TIAN, Yun-peng ZHANG, Peng YAN, Wen-cheng SUN, Xi YANG. A Noise Reduction Smooth Model of Vibration Signal of Open-pit Deep-hole Blasting based on CEEMD[J]. Blasting, 2024 , 41 (2) : 143 -150 . DOI: 10.3963/j.issn.1001-487X.2024.02.018
正文
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爆破振动信号分析是矿业、岩土等工程领域用以研究爆破地震效应的有效手段。在爆破振动信号的现场采集过程中，由于爆破区域地形地质条件的复杂、监测仪器的误差、振动传播介质的反射以及磁场的干扰等原因，采集的原始爆破振动信号常常会掺杂大量的噪声，从而导致信号失真，对爆破振动信号的进一步分析产生一定的负面作用[1-3]。因此，进行爆破振动信号识别与降噪处理十分必要。
小波阈值去噪方法对不同的频率成分提供不同的分析分辨率，同时在时频域的局部化性质中有明显优势，是处理非平稳信号一种常用的方法，但小波基函数的选择、小波分解层数的确定、阈值函数及阈值估计方法的选取都会对最终的信号去噪效果产生影响且难以进行最佳的选择[4,5]，此外单一小波基处理信号还可能会使信号产生失真现象[6]。希尔伯特-黄变换（Hilbert-Huang transform，HHT）是非线性非平稳信号分析技术中的一项重要突破，可以利用经验模态分解（Empirical mode decompo-sition，EMD）把信号分解成具有不同特征尺度、自适应性良好的固有模态函数（Intrinsic mode function，IMF），并对其能量特征进行分析[7,8]。近几年的一些研究表明，EMD分解得到的IMF分量之间存在模态混叠现象，容易造成降噪后的信号失真[9-11]。集成经验模态分解（Ensemble empirical mode decomposition，EEMD）通过在信号中多次加入不同的辅助白噪声，分别对其进行EMD分解，将所得到的IMF分量做平均运算得到最终的实际分量[12]。EEMD方法能有效地消除EMD方法中存在的模态混叠现象，但需要较高的迭代次数以减少重构信号中残留的辅助噪声，导致计算效率低下[13]。互补集合经验模态分解（Complementary ensemble empirical mode decomposition，CEEMD）是在EEMD分解的基础上，用正负成对的白噪声代替加入的辅助白噪声，这样就能在减少模态混叠现象的同时，消除重构信号中的残余辅助噪声，提高计算效率[14]。
CEEMD虽然有效解决了EMD分解中的模态混叠问题，但其分解得到的IMF分量并非全部都是具有实际物理意义的有用分量[15]，基于不同IMF分量组合重构的降噪信号，不一定都能保留原始爆破振动信号的形态特征信息。为此建立基于CEEMD的爆破振动信号滤波算法，考虑相似度、光滑度构建降噪光滑模型。通过仿真信号分析验证降噪光滑模型的可行性，并将模型用于实际露天深孔爆破振动信号的研究，通过信噪比、均方根误差两种指标对比分析工程领域中常用的降噪方法EMD方法、小波阈值法、CEEMD-小波阈值法与本文方法的降噪效果[16]，最后通过频谱进一步验证本文方法较核心算法同为CEEMD的CEEMD-小波阈值法的优越性。
1　基于CEEMD的降噪光滑模型
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原始爆破振动信号经CEEMD分解后，得到n个IMF分量及1个残余分量res。重构信号s（t）可表示为
噪声成分主要存在于高频部分，因此从重构信号s（t）中由高频向低频去除分量，即构建低通滤波算法，获得多个低通信号[17]，构建的低通滤波算法可表示为
1.1　相似度
余弦相似度可以表示经滤波算法得到的降噪信号和原始爆破振动信号的相似程度。如式（3）所示，余弦相似度越大，表示降噪信号曲线越接近原始爆破振动信号，即两个曲线的相似程度越高[18]。
式中：表示滤波算法模型；xj（t）表示原始爆破振动信号；N为采样点数。
以0~1之间的任意实数为底数a，Cs值为指数，定义相似度公式Sm如式（4）所示
此时，余弦相似度越大，Sm的值越小，曲线相似度越高。
1.2　光滑度
光滑度指的是曲线的曲折程度。若曲线f（x）在区间[a，b]内具有一阶连续导数，且切线随着切点的移动连续转动即曲率相等，则该曲线为光滑曲线[19]。
曲线连续，则有
切线连续，则一阶导数相等
曲率相等，则有
推理可得
将二阶导数按离散公式展开，则有
将式（9）、（10）代入式（8）可得
对于任意一条曲线f（x），该曲线在任意点x0处的光滑度可表示为
式中：h为采样间隔；M的值越接近于0；则曲线f（x）在除左右两个端点之外的x0邻域内越光滑。
1.3　目标函数
基于原始爆破振动信号经CEEMD得到的IMF分量及残余分量，考虑滤波算法模型的相似度Sm以及光滑度M，建立目标函数
式中，μ、1-μ为相似度、光滑度的影响因子。μ越大，信号的相似度越高，光滑度越差；μ越小，信号的相似度越低，光滑度越好。根据1.2节的分析可知，当目标函数F取得最小值时得到目标函数的最优解，最优解对应的滤波算法模型即为爆破振动信号的最优降噪光滑模型。见图1。
2　仿真信号分析
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2.1　最优降噪光滑模型的选取
构造仿真信号y（t），通过仿真信号分析验证上述降噪光滑模型算法的可行性。仿真信号表达式如式（14）所示，露天深孔爆破产生的振动主频主要分布在10~60 Hz之间，其中[20]，y1（t）表示频率为50 Hz的低频正弦信号，y2（t）表示频率为150 Hz的高频噪声信号，y3（t）表示均值为0、标准差为3的高斯白噪声。
对仿真信号进行CEEMD，得到7个IMF分量及1个残余分量，如图2所示。基于所得到的7个IMF分量及1个残余分量，构建7个滤波算法模型BP1~BP7，分别计算各滤波算法所得降噪信号的余弦相似度Cs、光滑度M。
由式（4）、式（13）可知，a的取值影响Sm值的大小，进而影响目标函数F值的大小，由于a可取0~1之间的任意实数，以0.1为间隔对a取值，计算a值取0.1~0.9时Sm的值并绘制成对照图。由图3可以看出，随着a值增大，各滤波算法模型的Sm值均有不同程度的增大；a值越接近0各滤波算法模型Sm值之间差距越大，表示Sm值受a值影响越大，a值越接近1各滤波算法模型之间Sm值差距越小，表示Sm值受a值影响越小。a取中间值0.5时不会致使滤波算法的Sm值之间落差过大或差异过小，故本文选取0.5作为底数a的值。
先将目标函数中μ的值固定为0.5，依据式（13）确定目标函数值，绘制各滤波算法模型Cs、M、F之间的关系图。由图4可知，随着滤波算法模型编号增大，余弦相似度Cs的值逐渐减小，表示由各滤波算法得到的降噪信号与仿真信号的相似程度逐渐减小，其中相似度最大的滤波算法模型为BP1；光滑度M的值逐渐减小，表示各降噪信号愈发光滑，其中最光滑的滤波算法模型为BP7；目标函数F的值呈现先减小后增大最后趋于平稳的趋势，其中F值最小的滤波算法模型为BP2。
仿真信号y（t）与滤波算法模型BP1、BP2、BP7的对照图如图5所示，由于BP1仅考虑信号的相似度，曲线极不平滑，含有大量噪声毛刺，降噪效果较差；BP7仅考虑曲线的光滑度，过度降噪导致信号失真，已经脱离了原始仿真信号形态；BP2波形光滑，峰值处毛刺减少，且保留了原始仿真信号形态特征。由此可见当滤波算法模型仅考虑单一因素的影响时，降噪效果并不好，需要综合考虑相似度、光滑度对滤波算法模型的影响。
由式（13）可知，目标函数F值的大小受相似度影响因子、光滑度影响因子，即μ取值大小的影响。图6为μ值取0.1~0.9时，各滤波算法模型所对应的目标函数F的值。由图6可以看出：7个滤波算法模型中，BP2的平均目标函数F值最小，而且当μ值取0.3~0.9时，目标函数值最小的模型均为BP2。
2.2　结果验证
为了验证最优降噪光滑模型选取的准确性，利用式（15）计算各滤波算法模型与未加噪的仿真信号的相关系数，相关系数越接近1，表示信号的相关程度越大[21]，计算结果见表1。
式中：表示滤波算法模型；y1（t）表示未加噪仿真信号。
由表1可知，7个滤波算法模型中，BP2与未加噪仿真信号的相关系数最大，达到了0.9352，表示滤波算法模型BP2与未加噪仿真信号的相关程度最大。用仿真信号减去BP2滤波算法模型，与仿真信号的噪声部分进行对比，由图7可以看出，二者具有相似的形态特征，且相关系数高达0.9081，表明该模型降噪效果较好。
3　工程实例分析
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3.1　工程概况
以某露天铁矿山生产爆破为例，爆破方式采用深孔爆破，孔内微差时间42 ms，采用数码电子雷管逐孔起爆，爆破参数见表2，装药结构见图8。采用TC-4850N测振仪采集生产爆破振动信号，采样频率为5000 Hz，采样时间为2 s，共计10000个采样点，采集原始爆破振动信号如图9所示。
3.2　降噪光滑模型在实测信号中的应用
对实测原始爆破振动信号进行CEEMD，得到12个IMF分量及1个残余分量。从图10可以看出，IMF1~IMF3分量毛刺现象严重，混有大量噪声，IMF4~IMF6分量具有和原始爆破振动信号波形相似的形态特征，随着IMF7~IMF12分量频率的降低，噪声对IMF分量的影响也逐渐减小。
基于所得到的12个IMF分量及1个残余分量，构建12个滤波算法模型BP1~BP12，分别计算各滤波算法模型所得降噪信号的余弦相似度、光滑度。考虑到相似度、光滑度对滤波算法模型的影响相当，即滤波算法模型中相似度影响因子和光滑度影响因子都取0.5[15]，此时计算出各滤波算法模型的目标函数值，并将计算结果绘制成关系图如图11所示。
由图11可知，当μ值取0.5时，随着原始爆破振动信号各滤波算法模型编号的增大，Cs、M的值逐渐减小，目标函数F的值先减小后增大最后趋于平稳，其走势与仿真信号分析结果一致。滤波算法模型BP3的目标函数F值最小，即模型BP3的降噪效果最好。
绘制出原始爆破振动信号及滤波算法模型BP3的对照图。由图12（a）、图12（b）可以看出，原始爆破振动信号在峰值点处的曲线不平滑，有较大的噪声干扰，滤波算法模型BP3得到的降噪信号峰值时的噪声毛刺明显减少，曲线变得平滑；由图12整体可以看出，滤波算法模型BP3得到的降噪信号形态特征保留完整，降噪效果较为理想。
利用工程领域中常用的降噪方法：EMD方法、小波阈值法和CEEMD-小波阈值法，分别对原始爆破振动信号进行降噪，采用信噪比（Signal-to-Noise Ratio，SNR）和均方根误差（Root Mean Square Error，RMSE）两种指标对这三种方法与滤波算法模型BP3的降噪效果量化并进行对比[21]，验证该降噪光滑模型在对露天矿山爆破振动信号降噪方面的有效性。
信噪比SNR是有用信号功率与噪声信号功率的比值，SNR越大表明降噪效果越好。计算公式为
均方根误差RMSE，其数值越小表明降噪效果越好。计算公式为
式中：表示经滤波算法模型得到的降噪信号；xj（t）表示原始爆破振动信号；N为采样点数。
由表3可以看出，EMD方法、小波阈值法、CEEMD-小波阈值法的信噪比均低于滤波算法模型BP3，相较于信噪比最低的EMD方法，滤波算法模型BP3的信噪比提高了26.23%，且滤波算法模型BP3的均方根误差最小，表明相对于EMD方法、小波阈值法和CEEMD-小波阈值法，本文建立的降噪光滑模型在对露天矿山爆破振动信号降噪方面，有着较好的降噪效果。
为进一步验证该降噪光滑模型较核心算法同为CEEMD的CEEMD-小波阈值法的优越性，将两种方法降噪前后信号频谱图进行对比。如图13所示，滤波算法模型BP3及CEEMD-小波阈值法在0~200 Hz频段相较于原始爆破振动信号均无较大的变化，表明两种方法在降噪过程中没有破坏信号的真实信息；由图13（a）可以看出，峰值处滤波算法模型BP3幅值高于CEEMD-小波阈值法，表明滤波算法模型BP3保留了更多优势主频能量；由图13（b）可以看出，在200 Hz以上频段，随着频率增大，CEEMD-小波阈值法处理后的信号、滤波算法模型BP3的能量均逐渐降低，滤波算法模型BP3显著低于CEEMD-小波阈值法处理后的信号及原始爆破振动信号的能量，说明滤波算法模型BP3相较于CEEMD-小波阈值法更好地去除了高频噪声污染[4]。
4　结论
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以某露天矿所测得的原始爆破振动信号为例，基于CEEMD分解信号所得IMF分量，考虑降噪信号曲线的相似度、光滑度，构造目标函数，计算该目标函数最优解，找到对应的滤波算法，即为露天矿山爆破振动信号的最优降噪光滑模型：
（1）通过最优降噪光滑模型BP3得到的降噪信号曲线更加平滑，噪声毛刺减少，且形态特征保留完整，整体波形与原始爆破振动信号具有较高的相似性，说明滤波算法模型BP3在保留原始爆破振动信号真实信息的前提下去除了高频噪声污染，验证了该模型良好的降噪能力。
（2）与EMD方法、小波阈值法、CEEMD-小波阈值法相比，最优降噪光滑模型BP3信噪比最大，均方根误差最小，表明在对实测爆破振动信号降噪的过程中能够更大程度保留有用信号，有利于爆破振动响应中的信号降噪研究。
（3）滤波算法模型BP3及CEEMD-小波阈值法在0~200 Hz频段相较于原始爆破振动信号均无较大的变化，峰值处滤波算法模型BP3幅值高于CEEMD-小波阈值法，在200 Hz以上频段滤波算法模型BP3显著低于CEEMD-小波阈值法处理后的信号及原始爆破振动信号的能量，说明滤波算法模型BP3相较于CEEMD-小波阈值法更好地去除了高频噪声污染。
基金
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  • 河北省教育厅在读研究生创新能力培养资助项目(CXZZBS2023124)
  • 河北省高等学校科学技术研究项目(QN2023166)
  • 河北省自然科学基金(E2016209388)
文献
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2024年第41卷第2期
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doi: 10.3963/j.issn.1001-487X.2024.02.018
  • 接收时间：2023-06-14
  • 首发时间：2026-03-20
  • 出版时间：2024-06-01
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  • 收稿日期：2023-06-14
基金
Innovative Ability Training for Postgraduates in Hebei Provincial Department of Education(CXZZBS2023124)
河北省教育厅在读研究生创新能力培养资助项目(CXZZBS2023124)
Science and Technology Research Project of Colleges and Universities in Hebei Province(QN2023166)
河北省高等学校科学技术研究项目(QN2023166)
Natural Science Foundation of Hebei Province(E2016209388)
河北省自然科学基金(E2016209388)
作者信息
    1.华北理工大学　矿业工程学院，唐山　063210
    2.河北省矿业开发与安全技术重点实验室，唐山　063210
    3.承德广兴矿业有限责任公司，承德　067103

通讯作者:

张云鹏（1963-），男，教授、博士、博导，主要从事爆破领域研究，（E-mail）。
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2种不同金属材料的力学参数
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Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
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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
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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