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基于$ \pmb k $近邻主元得分差分的故障检测策略

张成 高宪文 李元

张成, 高宪文, 李元.基于k近邻主元得分差分的故障检测策略.自动化学报, 2020, 46(10): 2229-2238 doi: 10.16383/j.aas.c180163
引用本文: 张成, 高宪文, 李元.基于k近邻主元得分差分的故障检测策略.自动化学报, 2020, 46(10): 2229-2238 doi: 10.16383/j.aas.c180163
Zhang Cheng, Gao Xian-Wen, Li Yuan. Fault detection strategy based on principal component score difference of k nearest neighbors. Acta Automatica Sinica, 2020, 46(10): 2229-2238 doi: 10.16383/j.aas.c180163
Citation: Zhang Cheng, Gao Xian-Wen, Li Yuan. Fault detection strategy based on principal component score difference of k nearest neighbors. Acta Automatica Sinica, 2020, 46(10): 2229-2238 doi: 10.16383/j.aas.c180163

基于$ \pmb k $近邻主元得分差分的故障检测策略

doi: 10.16383/j.aas.c180163
基金项目: 

国家自然科学基金 61490701

国家自然科学基金 61573088

国家自然科学基金 61673279

辽宁省自然科学基金 2015020164

详细信息
    作者简介:

    张成   沈阳化工大学副教授, 东北大学博士研究生.主要研究方向为复杂工业过程故障诊断.
    E-mail: zhangcheng@syuct.edu.cn

    李元   沈阳化工大学教授. 2004年获得东北大学博士学位.主要研究方向为系统识别, 故障检测, 复杂过程故障诊断.
    E-mail: liyuan@mail.tsinghua.edu.cn

    通讯作者:

    高宪文   东北大学教授. 1998年获得东北大学博士学位.主要研究方向为工业过程监视和故障诊断, 数据分析, 模式识别.本文通信作者.
    E-mail: gaoxianwen@ise.neu.edu.cn

Fault Detection Strategy Based on Principal Component Score Difference of $ \pmb k $ Nearest Neighbors

Funds: 

National Natural Science Foundation of China 61490701

National Natural Science Foundation of China 61573088

National Natural Science Foundation of China 61673279

National Natural Science Foundation of Liaoning Province 2015020164

More Information
    Author Bio:

    ZHANG Cheng    Associate professor at Shenyang University of Chemical Technology, Ph.D. candidate at Northeastern University. His main research interest is fault diagnosis of processes

    LI Yuan    Professor at Shenyang University of Chemical Technology. She received her Ph.D. degree from Northeastern University in 2004. Her research interest covers system identification, fault detection and classification, and data-driven complex process fault diagnosis

    Corresponding author: GAO Xian-Wen    Professor at Northeastern University. He received his Ph.D. degree from Northeastern University in 1998. His research interest covers industrial process monitoring and fault diagnosis, process data analysis, and pattern recognition. Corresponding author of this paper
  • 摘要: 针对具有非线性和多模态特征过程的故障检测问题, 本文提出一种基于k近邻主元得分差分的故障检测策略.首先, 通过主元分析(Principal component analysis, PCA)方法计算样本的真实得分.然后, 应用样本的k近邻均值计算样本估计得分.接下来, 通过上述两种得分计算样本的得分差分矩阵和残差矩阵, 其中残差矩阵由样本的估计得分计算得到,这区别于传统方法.最后, 在差分子空间和残差子空间中分别建立新的统计指标进行故障检测.值得注意的是本文的得分差分方法能够消除数据结构对过程故障检测的影响, 同时, 新的统计量能够提高过程的故障检测率.将本文方法在两个模拟例子和Tennessee Eastman (TE)过程中进行测试, 并与传统方法如PCA、KPCA、DPCA和~FD-kNN等进行对比分析, 测试结果证明了本文方法的有效性.
    Recommended by Associate Editor LIU Yun-Gang
    1)  本文责任编委 刘允刚
  • 图  1  非线性例子:样本散点图

    Fig.  1  Nonlinear case: scatter plots of samples

    图  2  PCA检测结果

    Fig.  2  Detection results using PCA

    图  3  KPCA检测结果

    Fig.  3  Detection results using KPCA

    图  4  KPCA前4个主元等高线

    Fig.  4  Contourlines of the first four PCs in KPCA

    图  5  FD-kNN检测结果

    Fig.  5  Detection results using FD-kNN

    图  6  kDiff-PCA检测结果

    Fig.  6  Results using kDiff-PCA

    图  7  多模态例子:样本散点图

    Fig.  7  Multimodal case: scatter plots of samples

    图  8  PCA检测结果

    Fig.  8  Detection results using PCA

    图  9  多模态例子:得分散点图

    Fig.  9  Multimodal case: scatter plots of scores

    图  10  PC-kNN检测结果

    Fig.  10  Detection results using PC-kNN

    图  11  kDiff-PCA检测结果

    Fig.  11  Results using kDiff-PCA

    图  12  样本得分差分散点图

    Fig.  12  Scatter plots of score difference of samples

    图  13  TE过程

    Fig.  13  Layout of TE process

    图  14  F1kDiff-PCA检测结果

    Fig.  14  Detection results using kDiff-PCA of F1

    图  15  F2kDiff-PCA检测结果

    Fig.  15  Detection results using kDiff-PCA of F2

    图  16  F3kDiff-PCA检测结果

    Fig.  16  Detection results using kDiff-PCA of F3

    图  17  F4kDiff-PCA检测结果

    Fig.  17  Detection results using kDiff-PCA of F4

    图  18  F5kDiff-PCA检测结果

    Fig.  18  Detection results using kDiff-PCA of F5

    表  1  参数设置, 故障检测率和误报率

    Table  1  Setting of parameters, FDR and FAR

    方法 PCs k FDR FAR
    PCA 2 - 0 0
    PC-kNN 2 3 85 0
    本文方法 2 5 100 0
    下载: 导出CSV

    表  2  各种方法的故障检测率

    Table  2  FDRs using different methods

    方法 F1 F2 F3 F4 F5
    PCA-T2 54.6 0.1 89.4 67.8 3.4
    PCA-SPE 79.8 0.6 98.8 76.5 1.4
    KPCA-T2 69.6 1.4 6.1 67.6 0.5
    KPCA-SPE 83.5 1.4 65.5 83.5 2
    DPCA-T2 84.1 0 93.5 75.9 4.5
    DPCA-SPE 65.8 0.1 88.1 76.6 1.5
    Tdiff2 87.3 1.5 92.5 72.5 4.8
    qdiff 92.5 90.3 100 92.5 95.1
    下载: 导出CSV

    表  3  各种方法的故障误报率

    Table  3  FARs using different methods

    方法 F1 F2 F3 F4 F5
    PCA-T2 0 0 1.5 1.5 1.5
    PCA-SPE 0 0 2.5 2.5 2.5
    KPCA-T2 0.5 0.5 2 2 2
    KPCA-SPE 0 0 2.5 2.5 2.5
    DPCA-T2 0 0 3 3 3
    DPCA-SPE 0 0 2.5 2.5 2.5
    Tdiff2 0 0 0.5 0.5 0.5
    qdiff 0 0 1 1 1
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-03-22
  • 录用日期:  2018-07-05
  • 刊出日期:  2020-10-29

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