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Article(id=1244336747207836505, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, articleNumber=null, orderNo=null, doi=10.16450/j.cnki.issn.1004-6801.2025.05.016, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1682438400000, receivedDateStr=2023-04-26, revisedDate=1694102400000, revisedDateStr=2023-09-08, acceptedDate=null, acceptedDateStr=null, onlineDate=1774602599192, onlineDateStr=2026-03-27, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774602599192, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774602599192, creator=13701087609, updateTime=1774602599192, updator=13701087609, issue=Issue{id=1244336743298740932, tenantId=1146029695717560320, journalId=1244311425741537314, year='2025', volume='45', issue='5', pageStart='855', pageEnd='1056', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774602598261, creator=13701087609, updateTime=1774603435030, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244340253042000577, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244340253042000578, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=976, endPage=984, ext={EN=ArticleExt(id=1244336747442717540, articleId=1244336747207836505, tenantId=1146029695717560320, journalId=1244311425741537314, language=EN, title=Research on Noise Reduction of Inertial Navigation Heterogeneous Signals Based on Noise‑Sensitive Prior and Improved VMD, columnId=1244336744728998604, journalTitle=Journal of Vibration,Measurement and Diagnosis, columnName=PAPER, runingTitle=null, highlight=null, articleAbstract=

Aiming at the multi-source noise of inertial navigation in the attitude estimation of coal mine bolting jumbo，a noise reduction method of inertial navigation heterogeneous signal is proposed based on noise sensitive prior and improved variational mode decomposition（VMD），which avoids the over-decomposition and under-decomposition problems caused by the parameter fixation. Firstly，the noise sensitivity difference of the heterogeneous signals （acceleration and angular velocity） of coal mine bolting jumbo is investigated by using the variation of the signal characteristics in the time and frequency domains. Secondly，according to the noise-sensitive characteristics，the dual decomposition layer and energy fluctuation model are constructed，so that the decomposition parameters have the ability of adaptive optimization and the synchronous optimal decomposition of the inertial-guide heterogeneous signals is realized. Based on the Pearson correlation coefficient （PCC），the modal component screening parameter，correlation coefficient P，is designed to consider the noise sensitivity difference，to achieve screening practical modal components and simultaneous noise reduction of heterogeneous signals. Finally，the proposed method is compared with the noise reduction results of complementary ensemble empirical mode decomposition （CEEMD） and improved complete ensemble empirical mode decomposition with adaptive noise （ICEEMDAN）. The results show that the method proposed in this paper considers the noise sensitivity differences of heterogeneous signals，thereby improving the signal-to-noise ratio of inertial measurement and enhancing the attitude initialization accuracy of bolting jumbo. The pitch error is reduced by 81.818 %，and the yaw error is reduced by 87.958 %，which lays a good foundation for accurate roadway support.

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针对煤矿锚杆钻车姿态估计中惯性导航的多源噪声，提出一种基于噪声敏感先验的改进变分模态分解（variational mode decomposition，简称VMD）惯导异构信号降噪方法。首先，利用加速度和角速度时频域参数特性变化，探究捷联惯导异构信号的噪声敏感差异和多源噪声作用规律；其次，根据异构信号噪声敏感先验和最大峭度变化趋势，构建双分解层，并通过能量波动模型监测在不同分解层下模态分量的能量变化，避免参数固定造成的过分解和欠分解问题，实现对惯导异构信号同步VMD分解；然后，根据皮尔逊相关系数（Pearson correlation coefficient，简称PCC）拟合兼顾噪声敏感差异的模态筛选参数——联合相关系数P，筛选有效模态分量，实现惯导异构信号同步降噪；最后，将所提方法与惯性信号降噪基准方法，即互补集合经验模态分解（complementary ensemble empirical mode decomposition，简称CEEMD）和改进的自适应噪声完备集合经验模态分解（improved complete ensemble empirical mode decomposition with adaptive noise，简称 ICEEMDAN）进行降噪结果对比。结果表明：所提方法兼顾异构信号噪声敏感差异，实现了异构信号同步分解与重构，提升了惯性测量信噪比，改善了矿用锚杆钻车姿态初始化精度，俯仰角误差减少81.818%，航向角误差减少87.958%，消除了横滚角误差，为精准支护奠定了良好基础。

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陈龙，男，1990年12月生，博士、讲师。主要研究方向为煤机装备智能化、车辆系统动力学与控制。 E-mail：
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刘宇，男，1993年9月生，博士。主要研究方向为煤机装备多传感器融合定位。曾发表《RRR-MF： time-domain feature reconstruction of road roughness in front of anchor machine via multimodal fusion》（《Measurement》 2022，Vol.199）等论文。 E-mail：

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刘宇，男，1993年9月生，博士。主要研究方向为煤机装备多传感器融合定位。曾发表《RRR-MF： time-domain feature reconstruction of road roughness in front of anchor machine via multimodal fusion》（《Measurement》 2022，Vol.199）等论文。 E-mail：

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刘宇，男，1993年9月生，博士。主要研究方向为煤机装备多传感器融合定位。曾发表《RRR-MF： time-domain feature reconstruction of road roughness in front of anchor machine via multimodal fusion》（《Measurement》 2022，Vol.199）等论文。 E-mail：

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figureFileBig=C8VOwLZejcC+f0CCMlJFzg==, tableContent=null), ArticleFig(id=1244351838280073979, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=CN, label=图12, caption=降噪结果时域对比, figureFileSmall=q42qPnetQk3n4Z1/OfCgLQ==, figureFileBig=C8VOwLZejcC+f0CCMlJFzg==, tableContent=null), ArticleFig(id=1244351838372348671, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=EN, label=Tab.1, caption=

Center frequency variation of inertial measurement

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静态加速度实际加速度静态角速度实际角速度
164.49196.9524.302177.94
), ArticleFig(id=1244351838485594881, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=CN, label=表1, caption=

惯性测量中心频率变化

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静态加速度实际加速度静态角速度实际角速度
164.49196.9524.302177.94
), ArticleFig(id=1244351838586258182, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=EN, label=Tab.2, caption=

Variation of time‑domain parameters of inertial measurement

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参数静态加速度/g实际加速度/g静态角速度/(rad·s-1)实际角速度/(rad·s-1)
均值-0.021 80.052 20.000 10.000 7
方差0.006 90.095 97.1×10-60.015 4
最大值0.089 50.758 90.005 50.271 1
最小值-0.091 2-0.416 5-0.005 6-0.276 8
), ArticleFig(id=1244351838682727180, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=CN, label=表2, caption=

惯性测量时域参数变化

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参数静态加速度/g实际加速度/g静态角速度/(rad·s-1)实际角速度/(rad·s-1)
均值-0.021 80.052 20.000 10.000 7
方差0.006 90.095 97.1×10-60.015 4
最大值0.089 50.758 90.005 50.271 1
最小值-0.091 2-0.416 5-0.005 6-0.276 8
), ArticleFig(id=1244351838787584784, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=EN, label=Tab.3, caption=

Parameters of acceleration screening results

, figureFileSmall=null, figureFileBig=null, tableContent=
筛选方法筛选结果
CEEMD‑PCCIMF1
CEEMD联合相关系数IMF1
ICEEMDAN‑PCCIMF1
ICEEMDAN联合相关系数IMF1
改进VMD‑PCCIMF1
改进VMD联合相关系数IMF4
), ArticleFig(id=1244351838879859475, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=CN, label=表3, caption=

加速度筛选结果参数

, figureFileSmall=null, figureFileBig=null, tableContent=
筛选方法筛选结果
CEEMD‑PCCIMF1
CEEMD联合相关系数IMF1
ICEEMDAN‑PCCIMF1
ICEEMDAN联合相关系数IMF1
改进VMD‑PCCIMF1
改进VMD联合相关系数IMF4
), ArticleFig(id=1244351838972134171, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=EN, label=Tab.4, caption=

Parameters of acceleration screening results

, figureFileSmall=null, figureFileBig=null, tableContent=
筛选方法筛选结果
CEEMD‑PCCIMF1
CEEMD联合相关系数IMF3
ICEEMDAN‑PCCIMF1
ICEEMDAN联合相关系数IMF3
改进VMD‑PCCIMF1
改进VMD联合相关系数IMF41
), ArticleFig(id=1244351839039243044, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=CN, label=表4, caption=

角速度筛选结果参数

, figureFileSmall=null, figureFileBig=null, tableContent=
筛选方法筛选结果
CEEMD‑PCCIMF1
CEEMD联合相关系数IMF3
ICEEMDAN‑PCCIMF1
ICEEMDAN联合相关系数IMF3
改进VMD‑PCCIMF1
改进VMD联合相关系数IMF41
), ArticleFig(id=1244351839198626600, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=EN, label=Tab.5, caption=

Acceleration SNR before and after denoising

, figureFileSmall=null, figureFileBig=null, tableContent=
方法
实际测量-11.78-5.40-19.31
CEEMD‑PCC-10.32-5.13-19.07
CEEMD联合相关系数-10.32-5.13-19.07
ICEEMDAN‑PCC-10.13-4.73-19.02
ICEEMDAN联合相关系数-10.13-4.73-19.02
改进VMD‑PCC-2.71-2.36-9.81
改进VMD联合相关系数-1.52-0.78-2.45
), ArticleFig(id=1244351839311872815, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=CN, label=表5, caption=

降噪前后的加速度信噪比

, figureFileSmall=null, figureFileBig=null, tableContent=
方法
实际测量-11.78-5.40-19.31
CEEMD‑PCC-10.32-5.13-19.07
CEEMD联合相关系数-10.32-5.13-19.07
ICEEMDAN‑PCC-10.13-4.73-19.02
ICEEMDAN联合相关系数-10.13-4.73-19.02
改进VMD‑PCC-2.71-2.36-9.81
改进VMD联合相关系数-1.52-0.78-2.45
), ArticleFig(id=1244351839391564599, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=EN, label=Tab.6, caption=

Angular velocity SNR before and after denoising

, figureFileSmall=null, figureFileBig=null, tableContent=
方法
实际测量-33.99-39.11-30.18
CEEMD‑PCC-32.32-38.94-29.34
CEEMD联合相关系数-22.34-17.38-20.73
ICEEMDAN‑PCC-31.92-38.94-29.34
ICEEMDAN联合相关系数-21.13-17.38-20.73
改进VMD‑PCC-6.46-11.26-7.10
改进VMD联合相关系数-2.82-5.06-3.86
), ArticleFig(id=1244351839467062075, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=CN, label=表6, caption=

降噪前后的角速度信噪比

, figureFileSmall=null, figureFileBig=null, tableContent=
方法
实际测量-33.99-39.11-30.18
CEEMD‑PCC-32.32-38.94-29.34
CEEMD联合相关系数-22.34-17.38-20.73
ICEEMDAN‑PCC-31.92-38.94-29.34
ICEEMDAN联合相关系数-21.13-17.38-20.73
改进VMD‑PCC-6.46-11.26-7.10
改进VMD联合相关系数-2.82-5.06-3.86
), ArticleFig(id=1244351839542559550, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=EN, label=Tab.7, caption=

Comparison of the attitude initialization results of the bolting jumbo before and after denoising

, figureFileSmall=null, figureFileBig=null, tableContent=
测量方法初始姿态
横滚角俯仰角航向角
静态测量0.0120.313177.674
实际测量0.0110.346177.292
本研究方法0.0120.319177.628
), ArticleFig(id=1244351839639028545, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336747207836505, language=CN, label=表7, caption=

降噪前后锚杆钻车姿态初始化结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
测量方法初始姿态
横滚角俯仰角航向角
静态测量0.0120.313177.674
实际测量0.0110.346177.292
本研究方法0.0120.319177.628
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基于噪声敏感先验的改进VMD惯导异构信号降噪
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刘宇 1, 2 , 陈龙 1 , 陶磊 2 , 王宏伟 1, 2 , 黄庆学 1, 2
振动、测试与诊断 | 论文 2025,45(5): 976-984
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振动、测试与诊断 | 论文 2025, 45(5): 976-984
基于噪声敏感先验的改进VMD惯导异构信号降噪
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刘宇1, 2 , 陈龙1 , 陶磊2, 王宏伟1, 2, 黄庆学1, 2
作者信息
  • 1太原理工大学机械工程学院　太原，030024
  • 2智能采矿装备技术全国重点实验室　太原，030032

    • 刘宇，男，1993年9月生，博士。主要研究方向为煤机装备多传感器融合定位。曾发表《RRR-MF： time-domain feature reconstruction of road roughness in front of anchor machine via multimodal fusion》（《Measurement》 2022，Vol.199）等论文。 E-mail：

通讯作者:

陈龙，男，1990年12月生，博士、讲师。主要研究方向为煤机装备智能化、车辆系统动力学与控制。 E-mail：
Research on Noise Reduction of Inertial Navigation Heterogeneous Signals Based on Noise‑Sensitive Prior and Improved VMD
Yu LIU1, 2 , Long CHEN1 , Lei TAO2, Hongwei WANG1, 2, Qingxue HUANG1, 2
Affiliations
  • 1.College of Mechanical Engineering，Taiyuan University of Technology　Taiyuan，030024，China
  • 2.State Key Laboratory of Intelligent Mining Equipment Technology　Taiyuan，030032，China
出版时间: 2025-10-01 doi: 10.16450/j.cnki.issn.1004-6801.2025.05.016
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摘要
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针对煤矿锚杆钻车姿态估计中惯性导航的多源噪声，提出一种基于噪声敏感先验的改进变分模态分解（variational mode decomposition，简称VMD）惯导异构信号降噪方法。首先，利用加速度和角速度时频域参数特性变化，探究捷联惯导异构信号的噪声敏感差异和多源噪声作用规律；其次，根据异构信号噪声敏感先验和最大峭度变化趋势，构建双分解层，并通过能量波动模型监测在不同分解层下模态分量的能量变化，避免参数固定造成的过分解和欠分解问题，实现对惯导异构信号同步VMD分解；然后，根据皮尔逊相关系数（Pearson correlation coefficient，简称PCC）拟合兼顾噪声敏感差异的模态筛选参数——联合相关系数P，筛选有效模态分量，实现惯导异构信号同步降噪；最后，将所提方法与惯性信号降噪基准方法，即互补集合经验模态分解（complementary ensemble empirical mode decomposition，简称CEEMD）和改进的自适应噪声完备集合经验模态分解（improved complete ensemble empirical mode decomposition with adaptive noise，简称 ICEEMDAN）进行降噪结果对比。结果表明：所提方法兼顾异构信号噪声敏感差异，实现了异构信号同步分解与重构，提升了惯性测量信噪比，改善了矿用锚杆钻车姿态初始化精度，俯仰角误差减少81.818%，航向角误差减少87.958%，消除了横滚角误差，为精准支护奠定了良好基础。

变分模态分解  /  降噪  /  惯导异构信号  /  锚杆钻车

Aiming at the multi-source noise of inertial navigation in the attitude estimation of coal mine bolting jumbo，a noise reduction method of inertial navigation heterogeneous signal is proposed based on noise sensitive prior and improved variational mode decomposition（VMD），which avoids the over-decomposition and under-decomposition problems caused by the parameter fixation. Firstly，the noise sensitivity difference of the heterogeneous signals （acceleration and angular velocity） of coal mine bolting jumbo is investigated by using the variation of the signal characteristics in the time and frequency domains. Secondly，according to the noise-sensitive characteristics，the dual decomposition layer and energy fluctuation model are constructed，so that the decomposition parameters have the ability of adaptive optimization and the synchronous optimal decomposition of the inertial-guide heterogeneous signals is realized. Based on the Pearson correlation coefficient （PCC），the modal component screening parameter，correlation coefficient P，is designed to consider the noise sensitivity difference，to achieve screening practical modal components and simultaneous noise reduction of heterogeneous signals. Finally，the proposed method is compared with the noise reduction results of complementary ensemble empirical mode decomposition （CEEMD） and improved complete ensemble empirical mode decomposition with adaptive noise （ICEEMDAN）. The results show that the method proposed in this paper considers the noise sensitivity differences of heterogeneous signals，thereby improving the signal-to-noise ratio of inertial measurement and enhancing the attitude initialization accuracy of bolting jumbo. The pitch error is reduced by 81.818 %，and the yaw error is reduced by 87.958 %，which lays a good foundation for accurate roadway support.

variational mode decomposition  /  noise reduction  /  inertial navigation heterogeneous signal  /  bolting jumbo
刘宇, 陈龙, 陶磊, 王宏伟, 黄庆学. 基于噪声敏感先验的改进VMD惯导异构信号降噪. 振动、测试与诊断, 2025 , 45 (5) : 976 -984 . DOI: 10.16450/j.cnki.issn.1004-6801.2025.05.016
Yu LIU, Long CHEN, Lei TAO, Hongwei WANG, Qingxue HUANG. Research on Noise Reduction of Inertial Navigation Heterogeneous Signals Based on Noise‑Sensitive Prior and Improved VMD[J]. Journal of Vibration,Measurement and Diagnosis, 2025 , 45 (5) : 976 -984 . DOI: 10.16450/j.cnki.issn.1004-6801.2025.05.016
正文
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引言
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采掘失衡阻碍煤炭绿色智能采掘装备的发展［1］，落后的巷道锚护水平是掘进工作亟待解决的问题。其中，锚杆钻车车体姿态估计是锚护智能化的基础。不依赖环境特征且具有独立位姿解算能力的惯性导航技术被广泛应用于井下定位系统［2⁃3］。然而，传统的锚杆钻车惯性定位技术面临诸多问题。如：煤矿锚杆钻车油泵振动、变频器辐射和电源工频传导等外界多源噪声引起惯性器件的测量误差；惯性器件自身测量误差与多源噪声耦合［4］，进一步降低了惯性测量的信噪比。因此，有必要研究惯导异构信号（加速度和角速度）同步降噪方法，以提高锚杆钻车姿态估计的准确性。
惯导降噪方法主要包括小波分析［5⁃6］、经验模态分解和变分模态分解。以小波分析为基础的降噪方法针对陀螺仪的随机漂移问题取得较好的效果，但是处理多源噪声干扰下的惯性信号具有参数局限性。EMD是一种自适应的时频域信号分解方法，能有效减弱惯性信号噪声［7⁃8］。张明等［9］通过向原始信号加入正负对高斯白噪声，改善了EMD的模态混叠效应，并提出基于CEEMD的陀螺降噪方法。文献［10⁃11］采用自适应噪声完备集合经验模态分解消除CEEMD中由附加噪声产生的误差，但本征模态函数（intrinsic mode function，简称IMF）存在虚假分量。然而，以EMD为基础的降噪方法没有从根本上解决模态混叠和边界效应等问题。
VMD［12⁃13］是一种非递归模式的信号时频分析方法，其将非平稳信号分解为多个带限本征模态函数（band‑limited intrinsic mode function，简称BLIMFs），频率分辨率高，分解易收敛，不存在模态混叠现象。芦竹茂等［14］提出基于VMD的组合广义形态滤波器陀螺降噪方法。目前，VMD降噪算法主要针对单一传感器信号。陈龙等［15］利用VMD对加速度和角速度同步进行降噪。异构信号同步降噪对VMD的分解参数和筛选参数的鲁棒性要求较高。分解参数k是影响VMD信噪分离有效性的关键参数，现有方法通过模态中心频率［15］、峭度［16］和合成谱峭度［17］来确定k值。然而，现有k值调节水平不能满足惯导异构信号的多样性和时变性的要求。另一方面，PCC［15］或谱峭度［18］作为模态筛选参数，能精准重构单一惯性信号，但无法兼顾异构信号噪声敏感差异，且不利于低信噪比信号重构。
针对上述问题，笔者提出一种基于噪声敏感先验的改进VMD惯导异构信号降噪方法，探究惯导信号敏感差异及干扰噪声作用规律，将其应用于分解参数和模态筛选参数优化过程中，以实现惯导异构信号同步降噪。
1　惯导信号敏感分析及噪声作用规律
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1.1　异构信号敏感性差异
陀螺仪和加速度计的不同测量原理造成噪声敏感差异。静态条件下，陀螺仪容易受到低频噪声的影响，加速度计通常更加敏感于高频噪声［19］。在实验室条件下静态测量数据用表示，对采样时间为1 s的加速度和角速度进行分析。加速度中心频率约为150 Hz，角速度中心频率小于50 Hz。不同频率上的能量分布差异都体现出异构信号的噪声敏感差异，因此惯导降噪算法需要兼顾异构信号静态噪声敏感差异。惯性测量频域变化和中心频率变化分别如图1和表1所示。
1.2　干扰噪声作用规律
煤矿井下多源噪声对惯导信号的作用规律是稳定的，惯性信号首先受到中低频段电磁干扰的影响［20‑21］。捷联惯导通过电路连接锚杆钻车电机，电磁干扰沿着电路传输至敏感器件。现有研究将电源工频50 、100及150 Hz谐波作为惯性器件低频噪声的主要来源［22］。此外，捷联惯导系统的测量精度受到车体振动影响。锚杆钻车轴向柱塞泵产生的机械振动和流体振动通过壳体向整个车体传播，车体不同位置的频率特性不同，特征频率范围约为40~2 500 Hz［23］。结合惯导工作频段，40~250 Hz范围的振动噪声是造成惯性测量高频噪声的主要因素。
实验室条件下，锚杆钻车油泵电机开启后的实际数据用表示。笔者根据时频域参数特征变化，研究煤矿井下多源噪声对惯导异构信号的作用规律。频谱图中，电磁耦合和油泵振动干扰在20~230 Hz范围内响应，异构信号不同频率的能量分布变化与现有研究结论基本一致。同时，惯导异构实测信号的功率谱能量向高频区移动，中心频率均大于160 Hz。时域中，实际加速度的平均值为静态测量的2.39倍，方差为13.87倍。实际角速度的平均值为静态测量的5倍，方差为2 169倍。惯性测量时域变化和时域参数变化分别如图2和表2所示。实验室条件下的多源噪声对陀螺仪的影响远大于对加速度计的影响。
2　改进VMD惯导异构信号降噪方法
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在传统VMD降噪基础上，本研究基于噪声敏感先验的改进VMD惯导降噪方法实现了惯导异构信号同步降噪，通过异构信号敏感先验优化了分解参数和模态筛选参数。首先，不再采用传统VMD的单分解层，根据异构信号噪声敏感先验和最大峭度变化趋势，构造了惯导异构信号同步预分解的双分解层初始值kacc和kgyro，为进一步增强模态分解的鲁棒性，构建能量波动模型，在初值基础上实现异构信号最佳同步分解；其次，兼顾惯导异构信号噪声敏感差异，提出新模态分量筛选参数——联合相关系数P，实现异构信号同步重构。改进VMD惯导降噪流程如图3所示。
2.1　变分模态分解原理
VMD方法将非平稳异构信号的局部特征附加到瞬时频率上，分解为预设的k个调幅调频分量信号。引入一个二次罚函数项和拉格朗日乘子项求解最优化问题。即
其中：为瞬时幅值；，为瞬时频率；为中心频率；为函数对时间t的偏导数；为脉冲函数；为原始信号。
2.2　双分解层与参数优化
峭度可描述信号的冲击特性，可以捕捉静态惯性测量的时变噪声。本研究通过异构信号噪声敏感先验和最大峭度变化趋势［16］确定双分解层kacc和kgyro。双分解层初值确定流程如图4所示。
根据噪声敏感先验，增加角速度的分解层数，以提升分解分辨率。其中，无量纲峭度Q定义为
其中：μ为样本均值；σ为样本标准差；E为期望。
以加速度和角速度为例，峭度变化曲线如图5所示。由图可知：加速度kacc=20时峭度最大，设分解层数初值为20；角速度kgyro=43时峭度最大，则分解层数初值为43。双分解层的初值充分考虑了异构信号的噪声敏感差异，避免异构信号使用同一分解参数，造成欠分解或过分解。
由于惯性敏感器件受到外界时变噪声影响，双分解层初值存在优化空间。为增强双分解层对噪声的抗干扰能力，本研究在信号能量计算公式［18］基础上构建能量波动模型，即
其中：为第j个模态能量；为趋势项能量；为实际信号能量；N为采样个数。
双分解层参数优化过程伴随着信号能量波动，经实验检验，当能量残差趋于0时（-0.01≤γ≤0.012），对应分解层k即为最佳分解层数，分解参数优化流程如图6所示。
2.3　模态筛选参数优化
噪声分量和有效模态分量的筛选依赖合理的参数设置。皮尔逊相关系数［15］是多信号模态筛选的主要参数，将实际测量作为唯一筛选因素，度量每个模态分量与之间的线性相关程度。将视为离散型随机变量，PCC模型为
然而，对于信噪比很低的静态惯性测量，最大PCC无法准确甄别噪声对有效信号的影响程度，且不能对噪声敏感差异的惯导异构信号进行同步重构。因此，本研究对模态筛选参数进行优化，在PCC基础上构建联合相关系数P，即
其中：为第k个模态分量的信号序列；m为采样个数。
联合相关系数P引入具有噪声敏感先验的静态测量，与共同作为筛选因素，同步分析高频振动和低频电磁干扰对各模态分量的影响程度。联合相关系数P兼顾惯导异构信号噪声敏感差异，P越大噪声影响程度越小，P越小则噪声影响程度越大。
综上所述，本研究以剥离油泵高频振动和提高低频模态分量的分辨率为目标，充分发挥惯导异构信号噪声敏感差异在分解参数与筛选参数优化过程中的指导作用，实现惯导异构信号同步最佳分解，并利用联合相关系数P进行同步重构。
3　实验验证
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实验平台包括CMM1‑10煤矿用液压锚杆钻车、FOSN Ⅱ光纤捷联惯性导航系统和英伟达 Jetson Xavier NX 边缘计算平台，测试系统见图7。
3.1　3种模态分解结果对比与分析
FOSN Ⅱ 系统的采样频率为450 Hz，将采样时间为1 s的实际惯导异构信号作为测试数据，对比本研究分解方法、CEEMD和ICEEMDAN的分解结果。
分解结果揭示出加速度和角速度在不同频率上的能量分布差异，以及不同分解方法在提取频谱信息方面的差异。加速度的3种模态分解结果如图8所示。由图可知：CEEMD将加速度分解成7个IMF，主频率大于100 Hz的IMF有1个；ICEEMDAN将加速度分解为8个IMF，主频率大于100 Hz的IMF有1个，上述分解结果的低频分辨率远高于高频分辨率。根据加速度噪声敏感先验分析，高频振动是加速度计的主要干扰源，CEEMD和ICEEMDAN的分解结果存在模态混叠。本研究分解方法通过设置双分解层，将高频IMF（大于100 Hz）的占比提升了78.95%，主频率大于100 Hz的IMF有15个，其中增加信号分解的高频分辨率是剥离高频油泵振动噪声的关键。
根据角速度噪声敏感先验可知，陀螺仪对低频振动敏感，CEEMD和ICEEMDAN在捕捉低频振动噪声时存在局限性。角速度的3种模态分解结果如图9所示。由图可知：CEEMD将角速度分解为7个IMF，主频率在10~25 Hz区间的IMF有1个；ICEEMDAN将角速度分解为8个IMF，主频率在10~25 Hz区间的IMF有1个。本研究分解方法通过kgyro和能量波动模型提高了10~25 Hz区间信号的分解水平，IMF的个数由1变为4，其中提高信号分解的低频分辨率是重构角速度的关键。
3.2　2种模态筛选结果对比与分析
本研究将联合相关系数P作为有效模态筛选参数，并与PCC进行对比。3种模态分解方法下，加速度筛选结果及参数分别如图10和表3所示。角速度筛选结果和参数分别如图11和表4所示。
以筛选加速度为例，使用本研究提出的VMD分解方法，联合相关系数P选取IMF4，PCC选取IMF1；ICEEMDAN和CEEMD分解，联合相关系数P和 PCC均选取最高中心频率的模态分量IMF1。由图8和表3可知，联合相关系数P和PCC筛选加速度的高频模态分量，本研究筛选结果IMF4的频率域特性与静态加速度测量最相近；其余方法筛选结果的频率能量分布集中在大于200 Hz的高频域，说明对锚杆钻车振动噪声抑制效果不佳。
以筛选角速度为例，使用本研究提出的VMD分解方法，联合相关系数P选取IMF41，PCC选取IMF1，二者频率能量分布情况截然相反；ICEEMDAN和CEEMD分解，联合相关系数P均选取IMF3，PCC均选取IMF1。由图9和表4可知，本研究筛选结果IMF41的频谱特性与静态角速度测量最相近，其余方法都无法筛选出有效的模态分量。根据3种模态分解结果对比与分析可知，ICEEMDAN和CEEMD对的分解结果，若仅调整筛选参数，不论是联合相关系数P还是PCC，都无法消除电源工频噪声混叠效应。本研究分解方法匹配PCC筛选出IMF1，其频率能量分布集中在高频域，这是车体振动主导的噪声模态分量。
综上所述，根据惯导信号敏感分析及噪声作用规律，采用联合相关系数P筛选的加速度和角速度均与静态测量的时频特性相似度最高，验证了联合相关系数P对惯导异构信号同步筛选的有效性。
3.3　惯导降噪结果对比与分析
本研究对比不同模态分解算法和不同筛选参数的降噪结果，降噪结果时域对比如图12所示。由图可知，基于噪声敏感先验的改进VMD惯导异构信号降噪结果与静态测量的时域平均差值最小。
本研究采用信噪比（signal noise ratio，简称 SNR）作为降噪的评价指标。降噪前后加速度和角速度的信噪比分别如表5和表6所示。与实际加速度测量相比，本研究方法信噪比总体提高了86.655%，三轴分别高了87.097%、85.556%和87.312%；与实际角速度测量相比，本研究方法信噪比总体提高了88.692%，3个方向分别提高了91.703%、87.062%和87.210%。可见，所提降噪方法提升了静态惯导异构信号测量的准确性。
综上所述，基于噪声敏感先验的改进VMD惯导降噪方法对异构信号同步分解能力优于CEEMD和ICEEMDAN。相较于最大PCC筛选，联合相关系数P能更好地兼顾加速度和角速度的噪声敏感特性，实现异构信号同步重构，提升了静态惯性测量的信噪比。
3.4　锚杆钻车姿态初始化结果对比
通过锚杆钻车静态姿态初始化结果，进一步验证了所提降噪方法的有效性。降噪前后锚杆钻车姿态初始化结果对比由表7所示。由表可知，本研究所提降噪方法将俯仰角误差从0.033°降到0.006°，减少了81.818%；航向角误差从0.382°降到0.046°，减少了87.958%。此外，横滚角对噪声的抗干扰能力较强，误差约0.001°，降噪后横滚角误差被消除。
4　结论
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1） 为提升惯性测量准确性和惯性初始化的可靠性，提出一种基于噪声敏感先验的改进VMD惯导异构信号降噪模型，探究了捷联式惯导异构信号的噪声敏感差异性和多源噪声作用规律，为异构信号同步降噪提供新思路。
2） 根据异构信号噪声敏感先验和最大峭度变化，构建惯导信号双分解层和能量波动模型，自适应完成异构信号的同步最佳分解。与分解基准方法CEEMD和ICEEMDAN相比，提高了噪声干扰频段的分解分辨率。同时，本研究拟合模态筛选参数——联合相关系数P，兼顾加速度计和陀螺仪噪声敏感差异，实现了异构信号的同步重构。
3） 搭建惯导异构信号降噪测试平台，对比测量信号信噪比和姿态初始化结果。实验结果表明，与实际惯性测量相比，降噪后的角速度和加速度的信噪比均提升86%以上。此外，增强了煤矿用锚杆钻车姿态初始化的抗干扰能力，俯仰角误差减少了81.818%，航向角误差减少了87.958%，并消除了横滚角误差。
基金
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  • 国家重点研发计划资助项目(2020YFB1314000)
  • 中央引导地方科技发展资金资助项目(YDZJSX2022A015)
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2025年第45卷第5期
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doi: 10.16450/j.cnki.issn.1004-6801.2025.05.016
  • 接收时间：2023-04-26
  • 首发时间：2026-03-27
  • 出版时间：2025-10-01
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  • 收稿日期：2023-04-26
  • 修回日期：2023-09-08
基金
国家重点研发计划资助项目(2020YFB1314000)
中央引导地方科技发展资金资助项目(YDZJSX2022A015)
作者信息
    1太原理工大学机械工程学院　太原，030024
    2智能采矿装备技术全国重点实验室　太原，030032

通讯作者:

陈龙，男，1990年12月生，博士、讲师。主要研究方向为煤机装备智能化、车辆系统动力学与控制。 E-mail：
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