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基于DPCA残差互异度的故障检测与诊断方法

张成 戴絮年 李元

张成, 戴絮年, 李元. 基于DPCA残差互异度的故障检测与诊断方法. 自动化学报, 2020, 46(x): 1−10 doi: 10.16383/j.aas.c190884
引用本文: 张成, 戴絮年, 李元. 基于DPCA残差互异度的故障检测与诊断方法. 自动化学报, 2020, 46(x): 1−10 doi: 10.16383/j.aas.c190884
Zhang Cheng, Dai Xu-Nian, Li Yuan. Fault detection and diagnosis based on residual dissimilarity in dynamic principal component analysis. Acta Automatica Sinica, 2020, 46(x): 1−10 doi: 10.16383/j.aas.c190884
Citation: Zhang Cheng, Dai Xu-Nian, Li Yuan. Fault detection and diagnosis based on residual dissimilarity in dynamic principal component analysis. Acta Automatica Sinica, 2020, 46(x): 1−10 doi: 10.16383/j.aas.c190884

基于DPCA残差互异度的故障检测与诊断方法

doi: 10.16383/j.aas.c190884
基金项目: 国家自然科学基金项目(61490701, 61673279), 辽宁省自然基金项目(2019-MS-262), 辽宁省教育厅基金项目(LJ2019013)
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

    戴絮年:沈阳化工大学研究生. 沈阳化工大学信息工程学院硕士研究生. 主要研究方向为基于数据驱动的多工况过程故障检测. E-mail: daixunian1996@163.com

    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, 故障检测和复杂过程故障诊断. 本文通信作者. E-mail: li-yuan@mail.tsinghua.edu.cn

Fault Detection and Diagnosis based on Residual Dissimilarity in Dynamic Principal Component Analysis

Funds: Supported by National Natural Science Foundation of China (61490701, 61673279), Liaoning Natural Science Fund Project(2019-MS- 262), Liaoning Provincial Department of Education Fund Project(LJ2019013)
  • 摘要: 针对动态主元分析方法中残差自相关性降低过程故障检测率问题, 提出基于动态主元分析残差互异度的故障检测与诊断方法. 首先, 应用动态主元分析(Dynamic principal component analysis, DPCA)计算动态过程数据的残差得分; 接下来, 应用滑动窗口技术并结合互异度指标(Dissimilarity)来监控过程残差得分状态; 最后, 利用基于变量贡献图的方法进行过程故障诊断分析. 本文方法通过DPCA捕获过程的动态特征, 同时互异度指标区别于传统的平方预测误差(Square prediction error, SPE), 它可以有效地对具有自相关性的残差得分进行过程状态监控. 通过一个数值例子和Tennessee Eastman(TE)过程的仿真实验并与传统方法对比分析, 仿真结果进一步证实了本文方法的有效性.
  • 图  1  主元累计方差贡献率

    Fig.  1  Cumulative percent variance of principal component

    图  2  DPCA残差得分自相关性

    Fig.  2  Autocorrelation of residual score in DPCA

    图  3  PCA-SPE故障检测结果

    Fig.  3  Fault detection results using PCA-SPE

    图  4  DPCA-SPE故障检测结果

    Fig.  4  Fault detection results using DPCA-SPE

    图  5  DPCA残差得分自相关性

    Fig.  5  Autocorrelation of residual score in DPCA

    图  6  DPCA-Diss故障检测结果

    Fig.  6  Fault detection results using DPCA-Diss

    图  7  监控变量贡献图

    Fig.  7  Contribution charts of the monitored variables

    图  8  输入变量u

    Fig.  8  Input variable u

    图  9  TE过程

    Fig.  9  Layout of TE process

    图  10  故障5检测结果

    Fig.  10  Detection results of Fault5

    图  11  故障19检测结果

    Fig.  11  Detection results of Fault19

    图  12  故障5贡献图

    Fig.  12  Contribution chart of Fault5

    图  13  故障10贡献图

    Fig.  13  Contribution chart of Fault10

    图  14  变量33

    Fig.  14  Variable 33

    图  15  变量18

    Fig.  15  Variable 18

    表  1  各种方法故障检测率

    Table  1  Fault detection rates using different methods

    检测方法 FDR(%)
    PCA-SPE 4.4
    DPCA-SPE 16.6
    DPCA-Diss 95.1
    下载: 导出CSV

    表  2  各种方法故障检测率(%)

    Table  2  Fault detection rates using different methods(%)

    故障号 PCA-SPE KPCA-SPE DPCA-SPE Diss DPCA-Diss
    1 99.75 93.75 98.88 34.25 96.13
    2 91.88 94.50 91.75 8.88 93.63
    4 99.88 53.88 4.25 9.75 21.63
    5 64.25 7.50 100.00 14.13 99.38
    6 100.00 63.38 100.00 96.38 99.88
    7 34.25 98.63 20.00 30.25 48.75
    8 79.38 40.25 65.25 70.25 96.75
    10 56.50 3.63 90.13 30.88 96.63
    11 67.38 53.00 7.75 76.75 91.00
    12 87.00 57.75 97.75 98.88 99.75
    13 94.50 62.00 93.13 65.75 93.50
    14 89.13 88.13 7.75 62.00 94.38
    15 3.25 3.13 2.50 2.50 77.50
    16 56.63 2.88 89.63 54.25 98.38
    17 94.88 74.00 71.88 88.50 96.63
    18 90.38 85.75 89.50 87.00 89.00
    19 51.88 6.00 46.25 73.13 97.13
    20 60.13 21.63 87.38 71.00 90.00
    21 37.00 5.25 16.75 22.50 33.88
    下载: 导出CSV

    表  3  各种方法平均故障误报率(%)

    Table  3  Mean fault alarm rate of methods(%)

    PCA-SPE KPCA-SPE DPCA-SPE Diss DPCA-Diss
    FDR(%) 1.68 2.27 1.69 0.26 1.68
    下载: 导出CSV
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  • 收稿日期:  2019-12-24
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