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Article(id=1228805364246836162, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228805359561802007, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2025.06.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1718899200000, receivedDateStr=2024-06-21, revisedDate=1727366400000, revisedDateStr=2024-09-27, acceptedDate=null, acceptedDateStr=null, onlineDate=1770899628936, onlineDateStr=2026-02-12, pubDate=1749484800000, pubDateStr=2025-06-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770899628936, onlineIssueDateStr=2026-02-12, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770899628936, creator=13701087609, updateTime=1770899628936, updator=13701087609, issue=Issue{id=1228805359561802007, tenantId=1146029695717560320, journalId=1225147924628267009, year='2025', volume='38', issue='6', pageStart='1133', pageEnd='1362', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770899627819, creator=13701087609, updateTime=1770901542852, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228813391846896476, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228805359561802007, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228813391846896477, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228805359561802007, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1242, endPage=1251, ext={EN=ArticleExt(id=1228805364540437454, articleId=1228805364246836162, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=A spectral ensemble sparse representation classification model-driven super-robust intelligent diagnostic method, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Under the background of industrial big data and intelligent manufacturing, data-driven intelligent fault diagnosis technology has become a crucial enabling technology. It ensures the safe and reliable operation of high-end equipment, facilitates equipment health management, and supports intelligent operation and maintenance. Existing intelligent fault diagnosis models often fail to simultaneously achieve superior diagnostic accuracy, strong noise immunity, high computational efficiency, and robust hyperparameter performance. To address these limitations, this paper proposes a novel spectral ensemble sparse representation classification model-driven super-robust intelligent diagnostic method. The proposed method designs a vibration data augmentation strategy based on cascade segmentation operators, aiming to enhance both the quantity and quality of vibration data samples. It utilizes the spectral features of vibration signals for dictionary atom design and constructs a spectral ensemble dictionary design strategy that incorporates spectral feature fusion. This improves the reconstruction capability of the spectral sparse representation dictionary. The method develops an intelligent recognition strategy based on the spectral sparse approximation error minimization criterion to achieve intelligent diagnosis of test samples health status. The proposed method is validated on a planetary gear transmission fault dataset. Results demonstrate that the intelligent diagnosis method can integrate the advantages of superior diagnostic accuracy, strong noise immunity, high computational efficiency, and robust hyperparameter selection. Its diagnosis results surpass existing advanced methods, showcasing significant application for data-driven intelligent fault diagnosis of industrial equipment.

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在工业大数据与智能制造背景下，数据驱动的智能故障诊断技术已被视为保障高端装备安全可靠服役、实现装备健康管理与智能运维的关键赋能技术。针对现有智能故障诊断模型无法兼顾诊断精度优越性、强抗噪鲁棒性、高效计算效率与强超参数稳健性的问题，提出一种谱集成稀疏识别模型驱动的超鲁棒智能诊断方法。所提方法设计了基于级联分割算子的振动数据增强策略，以提升振动数据样本的数量与质量；利用振动信号的频谱特征实现字典原子设计，并构建了考虑谱特征融合的谱集成字典设计策略，提升谱稀疏表示字典的重构功能；构建了基于谱稀疏近似误差最小准则的智能识别策略，实现测试样本健康状态的智能诊断。运用所提方法在行星齿轮传动系统故障数据集上开展了试验验证，结果表明，所提智能诊断方法可以实现优越的诊断精度、强抗噪鲁棒性、高效计算效率以及强超参数选择稳健性的优势集成，诊断结果优于现有方法，在数据驱动的工业设备智能故障诊断方面展现出重要应用前景。

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孔运（1993—），男，博士，副教授。E-mail：
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2.北京理工大学唐山研究院，河北 唐山 063015
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label=Fig. 9, caption=Robustness analysis of different diagnosis methods with parameters selection of window length and overlap rate, figureFileSmall=UxjS/B45nS+XofCSydMrbw==, figureFileBig=G9L3yC6Vg8dXzhMfrBKdIA==, tableContent=null), ArticleFig(id=1228805371825943018, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805364246836162, language=CN, label=图9, caption=不同诊断方法对窗长与重叠率参数选择的稳健性分析, figureFileSmall=UxjS/B45nS+XofCSydMrbw==, figureFileBig=G9L3yC6Vg8dXzhMfrBKdIA==, tableContent=null), ArticleFig(id=1228805371934994926, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805364246836162, language=EN, label=Tab.1, caption=

Diagnostic algorithm process of proposed method

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算法： 基于谱稀疏近似误差最小准则的谱稀疏智能识别策略
输入: 健康状态属性数目NH, 分割窗长L与重叠率δ, 训练数据集{xh}h=1NH, 稀疏阈值 T, 测试信号z
子程序1: 振动数据增强
1: For h = 1,2,⋯,NH, do
2: 　　根据式(2)与(3)生成训练样本并增强训练数据集{xh}h=1NH
3: End For
输出: 增强的振动训练数据集{Xh}h=1NH
子程序2: 谱集成字典设计
4: For h = 1,2,⋯,NH, do
5: 　　根据式(4)~(6)设计健康状态属性特定的谱字典矩阵{Xh}h=1NH
6: End For
7: 根据式(7)设计谱集成字典DSE
输出: 谱集成字典DSE
子程序3: 谱稀疏智能识别
8: 根据式(2)与(3)利用测试信号z生成测试样本{zk}k=1K
9: 根据式(8)~(10)获取谱特征向量{Z˜k}k=1K
10:For k = 1,2,⋯,K, do
11: 　　根据式(11)计算谱稀疏编码向量Ak∗
12: 　　根据式(12)与(13)计算分解Ak∗并谱-次稀疏编码向量{Ak,h*}h=1NH
13: 　　 For h = 1,2,⋯,NH, do
14: 　　　　根据式(14)计算谱稀疏近似误差Ek,hSSA
15: 　　 End For
16:根据式(15)诊断测试样本zk的健康状态属性label(zk)
17: End For
输出: 测试样本的健康状态属性{label(zk)}k=1K
), ArticleFig(id=1228805372035658234, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805364246836162, language=CN, label=表1, caption=

所提方法的诊断算法流程

, figureFileSmall=null, figureFileBig=null, tableContent=
算法： 基于谱稀疏近似误差最小准则的谱稀疏智能识别策略
输入: 健康状态属性数目NH, 分割窗长L与重叠率δ, 训练数据集{xh}h=1NH, 稀疏阈值 T, 测试信号z
子程序1: 振动数据增强
1: For h = 1,2,⋯,NH, do
2: 　　根据式(2)与(3)生成训练样本并增强训练数据集{xh}h=1NH
3: End For
输出: 增强的振动训练数据集{Xh}h=1NH
子程序2: 谱集成字典设计
4: For h = 1,2,⋯,NH, do
5: 　　根据式(4)~(6)设计健康状态属性特定的谱字典矩阵{Xh}h=1NH
6: End For
7: 根据式(7)设计谱集成字典DSE
输出: 谱集成字典DSE
子程序3: 谱稀疏智能识别
8: 根据式(2)与(3)利用测试信号z生成测试样本{zk}k=1K
9: 根据式(8)~(10)获取谱特征向量{Z˜k}k=1K
10:For k = 1,2,⋯,K, do
11: 　　根据式(11)计算谱稀疏编码向量Ak∗
12: 　　根据式(12)与(13)计算分解Ak∗并谱-次稀疏编码向量{Ak,h*}h=1NH
13: 　　 For h = 1,2,⋯,NH, do
14: 　　　　根据式(14)计算谱稀疏近似误差Ek,hSSA
15: 　　 End For
16:根据式(15)诊断测试样本zk的健康状态属性label(zk)
17: End For
输出: 测试样本的健康状态属性{label(zk)}k=1K
), ArticleFig(id=1228805372132127232, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805364246836162, language=EN, label=Tab.2, caption=

Transmission parameters of planetary gearbox

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行星齿轮齿数轴承类型宽度/mm内径/mm外径/mm滚子类型
行星架—行星轮：NJ204144720圆柱滚子
太阳轮16
齿圈143输入端：6208188040球
行星轮63 (3)
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行星齿轮箱的传动参数

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行星齿轮齿数轴承类型宽度/mm内径/mm外径/mm滚子类型
行星架—行星轮：NJ204144720圆柱滚子
太阳轮16
齿圈143输入端：6208188040球
行星轮63 (3)
), ArticleFig(id=1228805372362813965, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805364246836162, language=EN, label=Tab.3, caption=

Diagnosis accuracy results of different methods

, figureFileSmall=null, figureFileBig=null, tableContent=
健康状
态类标		诊断精度/%
S-ESRCESRIRDL-SRCDCNN
NS10099.1997.2397.32
ORF10010010099.86
IRF10098.7010089.85
REF10099.9810096.21
RGF100100100100
SGF10099.9899.7297.06
PGF10099.1293.0898.29
PBF10099.6299.8194.76
平均值10099.5798.7396.67
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不同方法的诊断精度结果

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健康状
态类标		诊断精度/%
S-ESRCESRIRDL-SRCDCNN
NS10099.1997.2397.32
ORF10010010099.86
IRF10098.7010089.85
REF10099.9810096.21
RGF100100100100
SGF10099.9899.7297.06
PGF10099.1293.0898.29
PBF10099.6299.8194.76
平均值10099.5798.7396.67
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Anti-noise performance results of different methods

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SNR /dB整体平均识别精度/%
S-ESRCESRIRDL-SRCDCNN
−573.88±0.3221.52±0.2522.76±0.1940.75±1.68
094.92±0.1249.61±0.5348.19±0.5369.62±1.40
599.55±0.0293.75±0.1588.69±0.1886.84±0.78
1099.97±0.0199.19±0.0798.22±0.1091.25±0.97
1599.99±0.0099.50±0.0298.63±0.0994.12±1.19
20100.0±0.0099.53±0.0498.74±0.0494.42±0.90
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不同方法的抗噪性能结果

, figureFileSmall=null, figureFileBig=null, tableContent=
SNR /dB整体平均识别精度/%
S-ESRCESRIRDL-SRCDCNN
−573.88±0.3221.52±0.2522.76±0.1940.75±1.68
094.92±0.1249.61±0.5348.19±0.5369.62±1.40
599.55±0.0293.75±0.1588.69±0.1886.84±0.78
1099.97±0.0199.19±0.0798.22±0.1091.25±0.97
1599.99±0.0099.50±0.0298.63±0.0994.12±1.19
20100.0±0.0099.53±0.0498.74±0.0494.42±0.90
), ArticleFig(id=1228805372723524134, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805364246836162, language=EN, label=Tab.5, caption=

Robustness analysis results of different methods under different sparse threshold

, figureFileSmall=null, figureFileBig=null, tableContent=
稀疏阈值T整体平均识别精度/%
DL-SRCESRIRS-ESRC
698.7799.3399.99
1098.7399.57100.0
1498.7499.62100.0
1898.6999.69100.0
2298.8199.68100.0
2698.8699.67100.0
3098.8499.70100.0
3498.9499.69100.0
3899.0699.69100.0
4099.1499.69100.0
平均值98.86±0.1499.63±0.11100.0±0.00
), ArticleFig(id=1228805372832576044, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805364246836162, language=CN, label=表5, caption=

不同方法在不同稀疏阈值下的稳健性分析结果

, figureFileSmall=null, figureFileBig=null, tableContent=
稀疏阈值T整体平均识别精度/%
DL-SRCESRIRS-ESRC
698.7799.3399.99
1098.7399.57100.0
1498.7499.62100.0
1898.6999.69100.0
2298.8199.68100.0
2698.8699.67100.0
3098.8499.70100.0
3498.9499.69100.0
3899.0699.69100.0
4099.1499.69100.0
平均值98.86±0.1499.63±0.11100.0±0.00
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谱集成稀疏识别模型驱动的超鲁棒智能诊断方法
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孔运 1, 2, 3 , 黄国昱 1 , 董明明 1 , 陈科 1, 5 , 刘辉 1 , 褚福磊 4
振动工程学报 | 2025,38(6): 1242-1251
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振动工程学报 | 2025, 38(6): 1242-1251
谱集成稀疏识别模型驱动的超鲁棒智能诊断方法
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孔运1, 2, 3 , 黄国昱1, 董明明1, 陈科1, 5, 刘辉1, 褚福磊4
作者信息
  • 1.北京理工大学机械与车辆学院，北京 100081
  • 2.北京理工大学唐山研究院，河北 唐山 063015
  • 3.重庆大学高端装备机械传动全国重点实验室，重庆 400044
  • 4.清华大学机械工程系，北京 100084
  • 5.内蒙古第一机械集团股份有限公司，内蒙古 包头 014032

通讯作者:

孔运（1993—），男，博士，副教授。E-mail：
A spectral ensemble sparse representation classification model-driven super-robust intelligent diagnostic method
Yun KONG1, 2, 3 , Guoyu HUANG1, Mingming DONG1, Ke CHEN1, 5, Hui LIU1, Fulei CHU4
Affiliations
  • 1.School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
  • 2.Tangshan Research Institute，Beijing Institute of Technology，Tangshan 063015，China
  • 3.State Key Laboratory of Mechanical Transmission for Advanced Equipment，Chongqing University，Chongqing 400044，China
  • 4.Department of Mechanical Engineering，Tsinghua University，Beijing 100084，China
  • 5.Inner Mongolia First Machinery Group Co., Ltd., Baotou 014032, China
出版时间: 2025-06-10 doi: 10.16385/j.cnki.issn.1004-4523.2025.06.012
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摘要
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在工业大数据与智能制造背景下，数据驱动的智能故障诊断技术已被视为保障高端装备安全可靠服役、实现装备健康管理与智能运维的关键赋能技术。针对现有智能故障诊断模型无法兼顾诊断精度优越性、强抗噪鲁棒性、高效计算效率与强超参数稳健性的问题，提出一种谱集成稀疏识别模型驱动的超鲁棒智能诊断方法。所提方法设计了基于级联分割算子的振动数据增强策略，以提升振动数据样本的数量与质量；利用振动信号的频谱特征实现字典原子设计，并构建了考虑谱特征融合的谱集成字典设计策略，提升谱稀疏表示字典的重构功能；构建了基于谱稀疏近似误差最小准则的智能识别策略，实现测试样本健康状态的智能诊断。运用所提方法在行星齿轮传动系统故障数据集上开展了试验验证，结果表明，所提智能诊断方法可以实现优越的诊断精度、强抗噪鲁棒性、高效计算效率以及强超参数选择稳健性的优势集成，诊断结果优于现有方法，在数据驱动的工业设备智能故障诊断方面展现出重要应用前景。

故障诊断  /  数据驱动  /  稀疏表示  /  谱集成字典

Under the background of industrial big data and intelligent manufacturing, data-driven intelligent fault diagnosis technology has become a crucial enabling technology. It ensures the safe and reliable operation of high-end equipment, facilitates equipment health management, and supports intelligent operation and maintenance. Existing intelligent fault diagnosis models often fail to simultaneously achieve superior diagnostic accuracy, strong noise immunity, high computational efficiency, and robust hyperparameter performance. To address these limitations, this paper proposes a novel spectral ensemble sparse representation classification model-driven super-robust intelligent diagnostic method. The proposed method designs a vibration data augmentation strategy based on cascade segmentation operators, aiming to enhance both the quantity and quality of vibration data samples. It utilizes the spectral features of vibration signals for dictionary atom design and constructs a spectral ensemble dictionary design strategy that incorporates spectral feature fusion. This improves the reconstruction capability of the spectral sparse representation dictionary. The method develops an intelligent recognition strategy based on the spectral sparse approximation error minimization criterion to achieve intelligent diagnosis of test samples health status. The proposed method is validated on a planetary gear transmission fault dataset. Results demonstrate that the intelligent diagnosis method can integrate the advantages of superior diagnostic accuracy, strong noise immunity, high computational efficiency, and robust hyperparameter selection. Its diagnosis results surpass existing advanced methods, showcasing significant application for data-driven intelligent fault diagnosis of industrial equipment.

fault diagnosis  /  data-driven  /  sparse representation  /  spectral ensemble dictionary
孔运, 黄国昱, 董明明, 陈科, 刘辉, 褚福磊. 谱集成稀疏识别模型驱动的超鲁棒智能诊断方法. 振动工程学报, 2025 , 38 (6) : 1242 -1251 . DOI: 10.16385/j.cnki.issn.1004-4523.2025.06.012
Yun KONG, Guoyu HUANG, Mingming DONG, Ke CHEN, Hui LIU, Fulei CHU. A spectral ensemble sparse representation classification model-driven super-robust intelligent diagnostic method[J]. Journal of Vibration Engineering, 2025 , 38 (6) : 1242 -1251 . DOI: 10.16385/j.cnki.issn.1004-4523.2025.06.012
正文
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高端装备是能源电力、交通运输、航空航天等制造业领域的基石，机械故障轻则造成装备系统功能失效，重则造成人员与经济的重大损失[1-2]。数据驱动的智能故障诊断技术是保障高端装备安全可靠服役的关键利器，亦是高端装备实现数字化与智能化转型升级的关键赋能技术，被视为高端装备智能化与信息化技术水平的重要标志[3]。
数据驱动的智能机械故障诊断方法的核心思想为利用丰富的历史状态数据学习判别性抽象特征以实现健康状态的智能识别与故障诊断，其可以粗略划分为基于传统机器学习的故障诊断方法和基于表示学习的故障诊断方法。YOON等[4]从原始信号和频谱信号与谱平均信号中提取统计状态指标，输入K-近邻分类器实现了行星齿轮箱的健康状态识别。然而，基于传统机器学习的故障诊断方法存在依赖专家经验知识、适用性与泛化性不足等局限。
近年来，以表示学习为核心的数据驱动故障诊断方法迅速成为智能机械故障诊断领域的前沿技术，其中最具代表性的方法为基于深度学习的智能故障诊断方法。雷亚国等[5]采用振动信号的频谱特征作为堆叠降噪自编码器的输入特征，实现了对行星齿轮箱的故障诊断。ZHAO等[6]利用振动时频图像作为卷积神经网络模型的输入特征，实现了行星轮轴承智能诊断。LUO等[7]提出一种基于弹性原型网络的元学习模型，并实现了平稳转速至时变转速的跨域小样本轴承故障诊断。上述研究体现了深度学习方法在智能故障诊断精度方面的优越性能，但在深层网络架构设计、强噪声干扰下的鲁棒性、超参数稳健性以及特征可解释性方面的研究仍有待进一步深入[1]。
稀疏表示理论具有突出的信号自适应表征优势，一直是信号处理与模式识别领域的研究热点[8-9]。基于信号稀疏表示的故障诊断方法可以实现故障冲击特征的解耦分离与增强辨识。WANG等[10]提出了基于广义极小极大凹惩罚的稀疏正则化模型，并将其用于轴承故障冲击特征辨识。张成等[11]提出了自适应学习字典的稀疏表示方法，并将其用于轴承诊断。
基于稀疏表示的模式识别方法则同样具备强大的特征学习与智能识别功能，且相比深度学习，无须复杂深层网络架构设计和海量超参数调优，其在数据驱动的智能故障诊断方面亦体现出重要前景。基于稀疏表示的模式识别方法可以粗略分为基于重构误差的稀疏表示分类方法和基于分类器训练的稀疏表示分类方法[12]。WRIGHT等[13]提出了基于稀疏重构误差分类的人脸识别方法。MEI等[14]采用基于重构误差的稀疏表示分类方法，实现了视觉跟踪与汽车分类。KONG等[15]提出基于数据增强的结构化稀疏表示识别方法，实现了行星轴承智能故障诊断。基于分类器的稀疏表示分类方法则利用稀疏编码作为分类器模型的输入特征实现智能识别。JIANG等[16]提出了类标一致性K-SVD方法用于人脸识别。ZHAO等[17]提出了基于字典学习的稀疏表示分类方法，实现了行星轴承的智能故障诊断。KONG等[18]建立了考虑稀疏表示字典与分类器模型协同学习的优化目标，提出了判别字典学习驱动的稀疏智能诊断方法，实现了旋转机械智能故障诊断。尽管上述基于稀疏表示的智能诊断方法取得了较好的诊断精度，但尚无法兼顾“诊断精度优越性、抗噪鲁棒性、高效计算效率、超参数选择稳健性”优势。
为此，本文提出一种谱集成稀疏识别（spectral ensemble sparse representation classification，S-ESRC）模型驱动的超鲁棒智能诊断方法。该方法设计了基于级联分割算子的振动数据增强策略，提出了谱特征融合与谱集成字典设计方法，构建了基于谱稀疏近似误差最小准则的智能诊断策略，以解决现有智能诊断模型无法实现“优越诊断精度、强抗噪鲁棒性、高计算效率及强超参数稳健性”的优势集成难题。经试验验证，所提方法可实现行星齿轮传动系统的超鲁棒智能诊断，同时具备优越诊断精度、强抗噪鲁棒性、高计算效率以及强超参数稳健性。
1　谱集成稀疏识别模型
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本节介绍所提谱集成稀疏识别模型驱动的超鲁棒智能诊断方法，包括振动数据增强、谱集成字典设计和谱稀疏智能识别过程，前两者实现振动信号的谱特征融合与谱集成字典设计，后者实现测试信号健康状态的智能故障诊断。
1.1　振动数据增强
一般而言，旋转机械状态监测采集的原始振动数据需进行适当预处理，以提升信号样本的数量与质量。受文献[15]启发，考虑旋转机械信号的预测-时移不变特征，本文提出了基于级联分割算子的振动数据增强策略，实现一维振动信号至二维健康状态矩阵的变换，以提升振动数据集的样本数量与质量。所提振动数据增强策略如图1所示，图中c表示稀疏编码。
所谓旋转机械信号的预测-时移不变特征是指：所监测机械设备健康状态不发生短时突变，在短时范围内任意两个局部数据块虽然因对应时间跨度不同有所差异，但局部数据块的预测健康状态类标属性应一致，如图1(a)所示。因此，短时范围内任意两个局部数据块的预测健康状态属性应满足短时预测-时移不变特征，公式如下：
label⁡(xm;f)=label⁡(xn;f),xm=Rmx,xn=Rnx
式中，分割算子Rm∈ℝL×N用于实现起始索引值为m且分割窗长为L的局部数据块提取，其中N为总样本数量；xm和xn分别表示利用分割算子Rm和Rn从振动信号x∈ℝN中提取的两个局部数据块；label(xm; f )和label(xn; f )分别表示智能诊断模型f对于局部数据块xm和xn的预测健康状态属性。分割算子Rk的基本原理如图1(b)所示。通过增加相邻局部数据块之间的重叠比例并充分利用振动信号的短时预测-时移不变特征，以生成高质量数据样本并增强智能故障诊断模型的泛化能力。
为实现上述目的，本文提出基于级联分割算子的振动数据增强策略，如图1(c)所示。分割算子R根据如下公式实现振动数据样本增强：
X=R(x;L,δ)=[R1,R2,⋯,RK]⏟R(x;L,δ)=[R1x,R2x,⋯,RKx]=[x1,x2,⋯,xK]
式中，R = [R1, R2, ⋯, RK]表示级联分割算子，R(x; L, δ)用于实现一维振动信号x∈ℝN至二维样本矩阵X∈ℝL×K的转换。如图1(c)所示，级联分割算子R主要涉及两个超参数，即分割窗长L与重叠率δ。二维样本矩阵X中的每个局部数据块xk (k = 1, 2, ⋯, K)表示一个信号样本，使用级联分割算子R(x; L, δ)获取振动信号x∈ℝN的样本数量K，公式如下：
K=⌊N−round(δ×L)L−round(δ×L)⌋
式中，round(·)和⌊⋅⌋分别表示圆整运算符和向下圆整运算符。
1.2　谱集成字典设计策略
本节提出谱集成字典设计策略，增强振动信号的谱稀疏表示与重构功能，以提高谱集成稀疏识别模型实现数据驱动的机械故障诊断时对随机噪声工况与算法超参数设置的稳健性。假定Xh = [xh,1, xh,2, ⋯, xh,K−1, xh,K] ∈ ℝL×K表示与健康状态属性h相关联的增广训练样本矩阵，其中h = 1, 2, ⋯, NH（NH为所考虑的健康状态属性数目）。具体地，所提谱集成字典设计策略采用离散傅里叶变换（DFT）算子与L2范数归一化操作，设计与样本矩阵Xh相关联的健康状态属性特定的谱字典Xh∈ℝ(L/2)×K，公式如下：
yh,k[m]=∑l=0L−1xh,k[l]e−j(2π/L)ml；m=0,1,⋯,L−1；k=1,⋯,K
y~h,k[m]=2L|yh,k[m]|;m=0,1,⋯,L2−1;k=1,⋯,K
Xh=[y~h,1‖y~h,1‖2,y~h,2‖y~h,2‖2,⋯,y~h,K−1‖y~h,K−1‖2,y~h,K‖y~h,K‖2]∈ℝ(L/2)×K;h=1,2,⋯,NH
式中，yh,k表示与健康状态属性h关联的训练样本矩阵Xh中第k个样本xh,k的DFT结果；y~h,k表示样本xh,k在奈奎斯特频率范围内的截断幅值谱。
如式(6)所示，与健康状态h（h = 1, 2,⋯, NH）相关联的健康状态属性特定谱字典Xh∈ℝ(L/2)×K由K个L2范数归一化截断幅值谱向量构成。因此，健康状态属性特定的谱字典Xh可以很好地揭示与旋转机械设备特定健康状态属性相关联的振动信号频谱特征。
进而，考虑多种健康状态属性的谱特征融合，设计谱集成字典，不仅可以充分利用特定健康状态属性的类内频谱特征，还可以利用多种健康状态属性之间的振动频谱特征，进而增强谱集成字典的谱稀疏重构功能。为实现上述目的，假设{Xh}（h = 1, 2,⋯, NH）表示来自NH个不同健康状态的训练振动数据集，采用式(4)~(6)，则可获得NH个健康状态属性特定的谱字典{Xh}h=1NH，最终通过矩阵级联操作综合考虑多个健康状态属性特定的谱字典{Xh}h=1NH，获得谱集成字典DSE如下式所示：
DSE=[X1,X2,⋯,Xh,⋯,XNH−1,XNH]∈ℝ(L/2)×K×NH
1.3　谱稀疏智能识别策略
本节构建基于谱稀疏近似误差最小判别准则的谱稀疏智能识别策略，实现对测试样本的超鲁棒健康诊断，其有效性体现在：（1）相同健康状态属性的振动信号样本具有相似度较高的频谱特征，而且测试样本的谱特征稀疏编码系数倾向于映射在与真实健康状态属性相关联的谱字典；（2）未知属性的测试信号样本倾向于在使用真实健康状态属性特定的谱字典进行稀疏重构时获得最小的谱稀疏近似误差。基于谱稀疏近似误差最小准则的谱稀疏智能识别策略的基本原理如图2所示。假设z∈ℝN为健康状态未知的振动测试信号，采用所提谱稀疏智能识别策略实现测试样本健康状态诊断的步骤如下：
步骤1：测试样本的谱特征向量设计。针对健康状态属性未知的测试信号z∈ℝN，首先采用式(2)和(3)所示的振动数据增强策略，获取测试样本矩阵Z = [z1, z2, ⋯, zK]∈ℝL×K，并利用DFT算子与截断幅值谱设计测试样本的谱特征空间Y∈ℝ(L/2)×K，公式如下：
Zk[n]=∑l=0L−1zk[l]e−j(2π/L)nl;n=0,1,⋯,L−1;k=1,⋯,K
Z~k[n]=2L|Zk[n]|;n=0,1,⋯,L2−1;k=1,⋯,K
Y=[Z~1,Z~2,⋯,Z~K−1,Z~K]∈ℝ(L/2)×K
式中，Zk和Z~k分别表示测试样本zk的DFT结果和截断谱特征向量。
步骤2：测试样本的谱稀疏编码计算。计算测试样本zk的谱特征向量Z~k关于谱集成字典DSE∈ℝ(L/2)×K×NH的谱稀疏编码Ak∗，公式如下：
Ak∗=argminA‖Z~k−DSEA‖22,s.t.‖A‖0⩽T
式中，Ak∗∈ℝ(K×NH)×1；T为稀疏阈值。
步骤3：谱稀疏编码向量分解。式(11)所得谱稀疏编码向量Ak∗包含与不同健康状态属性特定谱字典{Xh}相关联的谱稀疏编码。因此，进一步将谱稀疏编码向量Ak∗根据其关于不同健康状态属性特定的谱字典的分布情况分解为NH个谱-次稀疏编码{Ak,1∗, Ak,2∗, ⋯, Ak,NH∗}，公式如下：
Ak∗=∑h=1NHAk,h∗=∑h=1NHShAk∗
式中，算子Sh∈ℝ(K×NH)×(K×NH)用于实现从谱稀疏编码向量Ak∗中显式提取与健康状态属性h相关联的谱-次稀疏编码Ak,h∗。
步骤4：谱稀疏重构误差计算。根据步骤3中获得的谱-次稀疏编码{Ak,1∗, Ak,2∗, ⋯, Ak,NH∗}，计算测试样本zk关于谱集成字典DSE的谱稀疏近似的重构误差{Ek,1SSA, Ek,2SSA, ⋯, Ek,NHSSA}，如下式所示：
Ek,hSSA(zk;DSE,Ak,h∗)=‖Z~k−DSEAk,h∗‖22;h=1,2,⋯,NH
步骤5：基于谱稀疏近似误差最小准则的健康诊断。利用谱集成字典的强大谱稀疏重构功能，根据谱稀疏近似误差最小判别准则，建立鲁棒健康诊断模型f (zk; DSE, Ak*)，实现测试样本zk健康状态属性label(zk)的诊断预测，公式如下：
label(zk)=f(zk;DSE,Ak∗)：≜argminh=1,2,⋯,NHEk,hSSA(zk;DSE,Ak,h∗)
1.4　算法流程
所提的基于谱集成稀疏识别模型的超鲁棒智能诊断算法程序，主要由振动数据增强子程序、谱集成字典设计子程序、谱稀疏智能识别子程序构成。诊断算法流程如表1所示。
2　行星齿轮传动系统故障诊断
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为验证所提谱集成稀疏识别模型驱动的超鲁棒智能诊断S-ESRC框架实现数据驱动的智能机械故障诊断的有效性，本节将分析行星齿轮传动系统故障数据集，并对比所提方法与前沿方法的诊断精度、抗噪性能、计算效率及超参数选择稳健性。
2.1　振动数据集
开展振动测试与故障数据集采集的行星齿轮传动系统故障模拟装置如图3所示，主要由驱动电机、转速/转矩传感器、行星齿轮箱、磁粉制动器及数据采集系统等组成。其中，数据采集系统包括加速度传感器（安装于行星齿轮箱箱体顶部）、转速/转矩传感器、电流传感器、数据采集卡、笔记本电脑与附属电缆等。通过电火花加工技术在行星齿轮传动的部件表面加工局部缺陷故障。表2为行星齿轮箱的传动参数。图3显示了行星齿轮传动系统的7种故障状态及损伤位置。图4显示了行星齿轮传动系统在正常状态以及7种故障状态下的加速度信号时域波形及频谱。
试验过程中，分别采集行星齿轮传动系统在8种不同健康状态的振动加速度数据。相关试验参数设置为：电机驱动太阳轮转频为25 Hz，磁粉制动器施加的载荷为7.8 N·m，信号采样频率为25.6 kHz，训练与测试信号的采样时间均为60 s。
2.2　所提方法的智能诊断结果
利用所提谱集成稀疏识别模型驱动的超鲁棒智能诊断S-ESRC方法进行验证试验时，算法参数设置如下：（1）分割窗长L和重叠率δ分别为900和0.98；（2）稀疏阈值T为10。此时，行星齿轮传动系统每一健康状态对应的训练样本和测试样本数目均为4218，谱集成字典DSE的尺寸为33744，且相邻4218个连续字典原子分别构成对应的健康状态属性特定的谱字典。
图5展示了不同健康状态下代表性测试样本的谱稀疏编码分布情况。结果表明，相同健康状态属性的振动信号样本具有更相似的频谱特征，而且测试样本的谱特征稀疏编码系数倾向于映射在与真实健康状态属性相关联的谱字典，从而验证了所提方法的正确性。图6为不同健康状态下测试样本关于不同属性特定谱字典的谱稀疏近似误差分布情况。结果表明，未知健康状态属性的测试样本倾向于使用真实类标所对应的属性特定谱字典稀疏重构并获得最小谱稀疏近似误差，因此验证了所提方法的假设合理性与正确性。所提谱集成稀疏识别模型驱动的超鲁棒智能诊断方法的诊断结果如图7所示，结果表明，所提方法具有优越的行星齿轮传动系统诊断性能，8类健康状态的诊断精度均为100%。
2.3　对比方法的智能诊断结果
本节将从诊断精度、抗噪鲁棒性、计算效率和超参数选择稳健性4个方面，对比了所提方法与基于数据增强的结构化稀疏表示智能诊断ESRIR[15]、基于字典学习的稀疏表示分类DL-SRC[17]和深度卷积神经网络DCNN[6]这3种前沿方法的试验结果，以综合验证所提谱集成稀疏识别模型驱动的超鲁棒智能诊断方法S-ESRC的优越性。
表3为不同方法的诊断精度结果。表3的结果表明，所提S-ESRC方法的整体平均识别精度为100%，全面优于3种前沿对比方法。进一步，通过对训练数据集与测试数据集添加高斯随机白噪声，对比分析所提方法与对比方法的抗噪性能，结果如表4所示。所提S-ESRC方法在信噪比SNR为−5、0、5、10和20 dB时的整体平均识别精度分别为73.88%、94.92%、99.55%、99.97%、99.99%和100%，均优于3种对比方法，从而验证了所提S-ESRC方法在随机噪声工况下的优异抗噪声鲁棒性能。
为综合对比不同诊断方法的计算效率，在计算机配置为2.2 GHz Intel Xeon CPU E5与64 GB RAM Windows 7操作系统下采用MATLAB 2021a编程环境，统计不同方法的计算时间，结果如图8所示。结果表明，所提方法通过实现计算复杂度低的谱集成字典设计，并充分利用谱集成字典的强大重构功能，在保证优越诊断精度的同时，训练时间为2.38 s，且训练与测试总计算时间成本为最低，验证了所提S-ESRC方法的计算高效率。
最后，对比验证所提S-ESRC方法与前沿稀疏模式识别对比方法ESRIR和DL-SRC对算法模型超参数选择的稳健性。此处，采用交叉验证策略优选算法模型的最优超参数，并对比分析算法超参数分割窗长L、重叠率δ和稀疏阈值T对不同诊断方法整体平均识别精度的影响。
不同诊断方法对窗长与重叠率参数选择的稳健性分析的结果如图9所示。图9中亮黄色区域表明相应的超参数设置可以获得优异的诊断精度；因此，亮黄色区域越大则表明该方法对超参数窗长与重叠率选择的稳健性越强。本文所考虑的超参数窗长L与重叠率δ的范围分别为[600, 8000]和{0.25, 0.5, 0.75, 0.9: 0.02: 0.98}。由图9(a)和(b)可知，所提超鲁棒智能诊断S-ESRC方法的最低平均诊断精度仍高达96%，且对应最低平均诊断精度的超参数区域面积非常小。此外，所提方法最优诊断精度100%对应的亮黄色超参数区域面积占比超过70%。相比之下，图9(c)和(e)结果表明：对比方法ESRIR和DL-SRC在所考虑的超参数选择范围内可获得的最低平均诊断精度分别仅为45%和50%，远远低于所提方法；对比方法ESRIR和DL-SRC的最高平均诊断精度分别约为99%和98%，而且与最高平均诊断精度对应的超参数选择区域占比较小，远小于所提S-ESRC方法。上述结果验证了所提超鲁棒智能诊断S-ESRC方法的识别精度对算法超参数窗长L与重叠率δ的选择具有超强的稳健性，并且优于前沿的稀疏模式识别对比方法。
本文分析的稀疏阈值T的取值范围为[6:4:40]，以诊断精度为定量分析依据，不同方法对超参数稀疏阈值T选择的稳健性分析结果如表5所示。结果表明，所提超鲁棒智能诊断S-ESRC方法对比前沿方法ESRIR和DL-SRC具有更强的鲁棒性，在分析范围内的任意稀疏阈值T都可以取得优于99.99%的识别精度。相比之下，对比方法对稀疏阈值T的选择更加敏感，在所分析的稀疏阈值范围内的识别精度均不如所提超鲁棒智能诊断S-ESRC方法。上述不同方法对稀疏阈值T的稳健性分析结果进一步验证了所提方法对超参数稀疏阈值的强稳健性。
上述算法超参数稳健性的分析结果表明，所提超鲁棒智能诊断S-ESRC方法对比前沿方法ESRIR和DL-SRC在超参数选择稳健性方面性能更优。
3　结论
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本文从稀疏模式识别理论出发，提出了谱集成稀疏识别模型驱动的超鲁棒智能诊断方法，以实现数据驱动的智能机械故障诊断。通过开展行星齿轮传动系统故障诊断试验，对比分析了所提方法与对比方法的诊断精度、抗噪性能、计算效率和超参数选择稳健性，从而验证了所提方法的优越性。主要结论如下：
（1）所提超鲁棒智能诊断S-ESRC方法可以实现8种行星齿轮传动系统的健康状态故障诊断，取得的最优诊断精度为100%，从而验证了所提方法实现数据驱动的智能机械故障诊断的可行性。
（2）所提超鲁棒智能诊断S-ESRC方法与对比方法分析行星齿轮传动系统故障诊断数据集的试验结果表明，相比基于数据增强的结构化稀疏表示智能诊断ESRIR、基于字典学习的稀疏表示分类DL-SRC和深度卷积神经网络DCNN这3种前沿方法，所提方法可以获得更高的诊断精度、抗噪鲁棒性能、计算效率和超参数选择稳健性，综合诊断性能最优。
基金
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  • 北京市自然科学基金资助项目(3252008)
  • 国家自然科学基金资助项目(52105108)
  • 中国科协青年人才托举工程资助项目(2023QNRC001)
  • 北京市科协青年人才托举工程资助项目(BYESS2024294)
  • 高端装备机械传动全国重点实验室开放基金资助项目(SKLMT-MSKFKT-202304)
  • 河北省自然科学基金面上项目(E2023105039)
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2025年第38卷第6期
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文章信息
doi: 10.16385/j.cnki.issn.1004-4523.2025.06.012
  • 接收时间：2024-06-21
  • 首发时间：2026-02-12
  • 出版时间：2025-06-10
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出版历史
  • 收稿日期：2024-06-21
  • 修回日期：2024-09-27
基金
北京市自然科学基金资助项目(3252008)
国家自然科学基金资助项目(52105108)
中国科协青年人才托举工程资助项目(2023QNRC001)
北京市科协青年人才托举工程资助项目(BYESS2024294)
高端装备机械传动全国重点实验室开放基金资助项目(SKLMT-MSKFKT-202304)
河北省自然科学基金面上项目(E2023105039)
作者信息
    1.北京理工大学机械与车辆学院，北京 100081
    2.北京理工大学唐山研究院，河北 唐山 063015
    3.重庆大学高端装备机械传动全国重点实验室，重庆 400044
    4.清华大学机械工程系，北京 100084
    5.内蒙古第一机械集团股份有限公司，内蒙古 包头 014032

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孔运（1993—），男，博士，副教授。E-mail：
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2种不同金属材料的力学参数
科
Family		 属数
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
Percentage of total
species (%)
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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