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  • ISSN 1006-3080
  • CN 31-1691/TQ

基于稀疏D-vine Copula的建模方法及其在过程监测中的应用

邱穗庆 李绍军

邱穗庆, 李绍军. 基于稀疏D-vine Copula的建模方法及其在过程监测中的应用[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20211231001
引用本文: 邱穗庆, 李绍军. 基于稀疏D-vine Copula的建模方法及其在过程监测中的应用[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20211231001
QIU Suiqing, LI Shaojun. Sparse D-vine Copula-Based Modeling Approach and Its Application in Process Monitoring[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20211231001
Citation: QIU Suiqing, LI Shaojun. Sparse D-vine Copula-Based Modeling Approach and Its Application in Process Monitoring[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20211231001

基于稀疏D-vine Copula的建模方法及其在过程监测中的应用

doi: 10.14135/j.cnki.1006-3080.20211231001
基金项目: 国家自然科学基金项目(21676086)
详细信息
    作者简介:

    邱穗庆(1995—),男,江西赣州人,硕士生,主要研究方向为工业过程数据监控。 E-mail:1543921814@qq.com

    通讯作者:

    李绍军, E-mail:lishaojun@ecust.edu.cn

  • 中图分类号: TP277

Sparse D-vine Copula-Based Modeling Approach and Its Application in Process Monitoring

  • 摘要: 针对工业过程中高维数据的非线性非高斯性问题,提出了一种基于稀疏D-vine Copula (sparse D-vine Copula-based, SDVC)的过程监测方法。首先,针对传统的Vine Copula结构优化方法容易引起估计误差在Vine结构中累积,并且计算负担随着数据维数的增加急剧增长,修正了二元Copula的先验概率,使得高层次结构树中的二元Copula更倾向于优化为独立状态,实现了高层次树结构稀疏优化。其次,对Vine结构节点次序确定方法进行改进,根据节点间的相关性总和依次展开,使其更适用于水平结构的D-vine建模。最后,引入高密度区域(HDR)与密度分位数理论,构建适用于任意分布的广义局部概率(GLP)指标实现对工业过程的实时监测。通过田纳西-伊斯曼(TE)和醋酸脱水工业过程验证了所提出方法的优越性能。

     

  • 图  1  五元D-vine图解模型

    Figure  1.  Graphical model of five-dimension D-vine

    图  2  SDVC过程监控方法流程图

    Figure  2.  Algorithm flowchart of SDVC monitoring approach

    图  3  TE过程的稀疏D-vine和D-vine的结构信息矩阵

    Figure  3.  Structure information matrix of sparse D-vine and D-vine for TE process

    图  4  TE过程中故障13的过程监测图

    Figure  4.  Fault detection charts of TE process for Fault 13

    图  5  醋酸脱水过程监测图

    Figure  5.  Monitoring charts of acetic acid dehydration

    表  1  D-vine和SDVC方法的CPU耗时

    Table  1.   CPU time cost of D-vine and SDVC methods

    MethodD-vineSDVC
    Offline modeling4.645m3.573m
    Online monitoring0.104s0.087s
    下载: 导出CSV

    表  2  TE过程21个故障的检测率(CL=0.99)

    Table  2.   Fault detection rates for 21 faults of TE process (CL=0.99)

    Fault
    No.
    PCAKPCAD-vineSDVCFault
    No.
    PCAKPCAD-vineSDVC
    T2SPET2SPEGLPGLPT2SPET2SPEGLPGLP
    199.1399.7599.7599.7599.7599.631298.3883.8899.5099.1398.3899.25
    296.7598.5098.1398.2598.3898.501393.7594.6394.7594.6394.7595.00
    30.502.504.385.002.007.881485.8810099.8899.8899.88100
    40.631.502.002.250.885.75151.633.009.137.133.0015.88
    523.3813.7527.0027.0024.3829.501618.389.0032.3835.3831.0038.25
    61001001001001001001777.8895.3895.3894.6396.1394.50
    737.1322.1342.3842.6339.3844.631889.2590.0089.8889.8889.8890.00
    896.2594.7597.3897.7597.7598.131911.386.634.136.6323.0022.13
    92.132.133.384.881.507.252025.1337.7545.0050.6377.5078.75
    1032.2519.5045.0060.0075.7577.632142.0043.0044.6349.7547.8850.25
    118.5044.2534.5040.8837.3844.88/////
    下载: 导出CSV

    表  3  醋酸脱水过程的检测率和误报率(CL=0.98)

    Table  3.   FAR and FDR of the acetic acid dehydration process

    IndexPCAKPCAD-vineSDVC
    T2SPET2SPEGLPGLP
    FDR100100100100100100
    FAR4.001.005.501.502.000.50
    下载: 导出CSV
  • [1] 何雨旻, 侍洪波. 基于多块卷积变分信息瓶颈的多变量动态过程故障诊断[J]. 华东理工大学学报(自然科学版), 2021, 47(6): 716-725.
    [2] 邬东辉, 顾幸生. 基于自适应稀疏表示和保局投影的工业故障检测[J]. 华东理工大学学报(自然科学版), 2021, 47(4): 455-464.
    [3] 刘强, 卓洁, 郎自强, 等. 数据驱动的工业过程运行监控与自优化研究展望[J]. 自动化学报, 2018, 44(11): 1944-1956.
    [4] GE Z Q. Review on data-driven modeling and monitoring for plant-wide industrial processes[J]. Chemometrics and Intelligent Laboratory Systems, 2017, 171: 16-25. doi: 10.1016/j.chemolab.2017.09.021
    [5] WOLD S, ESBENSEN K, GELADI P. Principal component analysis[J]. Chemometrics and Intelligent Laboratory Systems, 1987, 2(1): 37-52.
    [6] GAUTHIER J L, MANOLESCU P, DUCHESNE C. The Sequential Multi-block PLS algorithm (SMB-PLS): Comparison of performance and interpretability[J]. Chemometrics and Intelligent Laboratory Systems, 2018, 180: 72-83. doi: 10.1016/j.chemolab.2018.07.005
    [7] CAI P P, DENG X G. Incipient fault detection for nonlinear processes based on dynamic multi-block probability related kernel principal component analysis[J]. ISA Transactions, 2020, 105: 210-220. doi: 10.1016/j.isatra.2020.05.029
    [8] ZHANG Y, HU Z. Multivariate process monitoring and analysis based on multi-scale KPLS[J]. Chemical Engineering Research and Design, 2011, 89(12): 2667-2678. doi: 10.1016/j.cherd.2011.05.005
    [9] KANO M, TANAKA S, HASEBE S, et al. Monitoring independent components for fault detection[J]. AIChE Journal, 2003, 49: 969-976. doi: 10.1002/aic.690490414
    [10] YU J, QIN S. Multimode process monitoring with Bayesian inference-based finite Gaussian mixture models[J]. AIChE Journal, 2008, 54(7): 1811-1829. doi: 10.1002/aic.11515
    [11] WEI Y, ZHANG S. Dependence analysis of finance markets: Copula-garch model and its application[J]. Systems Engineering, 2004, 4: 7-12.
    [12] MADADGAR S, MORADKHANI H. Drought analysis under climate change using copula[J]. Journal of Hydrologic Engineering, 2011, 18(7): 746-759.
    [13] GENEST C, FAVRE A C. Everything you always wanted to know about Copula modeling but were afraid to ask[J]. Journal of Hydrologic Engineering, 2007, 12(4): 347-368. doi: 10.1061/(ASCE)1084-0699(2007)12:4(347)
    [14] JOE H. Families of m-Variate distributions with given margins and m(m-1)/2 bivariate dependence parameters[J]. Distributions with Fixed Marginals & Related Topics Lecture Notesmonograph, 1996, 28: 120-141.
    [15] REN X, TIAN Y, LI S J. Vine copula-based dependence description for multivariate multimode process monitoring[J]. Industrial & Engineering Chemistry Research, 2015, 54(41): 10001-10019.
    [16] 周南, 李绍军. 基于核密度估计的R-Vine Copula选择及其在故障检测中的应用[J]. 高校化学工程学报, 2019, 33(2): 443-452. doi: 10.3969/j.issn.1003-9015.2019.02.024
    [17] 崔群, 李绍军. 基于伯恩斯坦多项式和D-vine copula的过程监控方法[J]. 高校化学工程学报, 2021, 35(1): 118-126. doi: 10.3969/j.issn.1003-9015.2021.01.014
    [18] NAGLER T, BUMANN C. Model selection in sparse high-dimensional vine copula models with an application to portfolio risk[J]. Journal of Multivariate Analysis, 2019, 172: 180-192. doi: 10.1016/j.jmva.2019.03.004
    [19] ZHOU Y, REN X, LI S J. Probabilistic weighted copula regression model with adaptive sample selection strategy for complex industrial processes[J]. IEEE Transactions on Industrial Informatics, 2020, 16(11): 6972-6981. doi: 10.1109/TII.2020.2972813
    [20] SKALR A. Fonctions dé repartition á n dimension et leurs marges[J]. Publications Del'Institut de Statistique de L'Université de Paris, 1959, 8: 229-231.
    [21] BEDFORD T, COOKE R M. Probability density decomposition for conditionally dependent random variables modeled by vines[J]. Annals of Mathematics and Artificial Intelligence, 2001, 32(1): 245-268.
    [22] KOVACS, E, SZANTAI, T. On the connection between cherry-tree copulas and truncated R-vine copulas [M]. Kybernetika, 2016, 53(3): 437-460.
    [23] AAS K, CZADO C. Pair-Copula constructions of multiple dependence[J]. Insurance Mathematics & Economics, 2009, 44(2): 182-198.
    [24] BOWMAN A W. An alternative method of cross-validation for the smoothing of density estimates[J]. Biometrika, 1984, 71(2): 353-360. doi: 10.1093/biomet/71.2.353
    [25] HYNDMAN R. Computing and graphing highest density regions[J]. Journal of the American Statistical Association, 1996, 50(2): 120-126.
    [26] BRECHMANN E, SCHEPSMEIER U. Modeling dependence with C-and D-vine copulas: The R package CDVine[J]. Journal of Statistical Software, 2013, 52(3): 1-27.
    [27] 曾根保, 李绍军, 钱锋. 醋酸脱水系统的动态模拟及其控制[J]. 计算机与应用化学, 2008, 25(5): 533-536. doi: 10.3969/j.issn.1001-4160.2008.05.005
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出版历程
  • 收稿日期:  2021-12-31
  • 网络出版日期:  2022-04-12

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