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    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), 2023, 49(3): 391-400. 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), 2023, 49(3): 391-400. 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, 2023, 49(3): 391-400. 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, 2023, 49(3): 391-400. 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

    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的问题,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,以实现对工业过程的实时监测。通过田纳西-伊斯曼(Tennessee-Eastman, TE)和醋酸脱水工业过程验证了所提出方法的优越性能。

       

      Abstract: Process monitoring is a crucial part of ensuring the safety and quality of industrial production. A sparse D-vine Copula-based (SDVC) process monitoring method is proposed for the problem of nonlinearity and non-Gaussian properties of high-dimensional data in industrial processes. Firstly, considering that the traditional Vine Copula structure optimization method tends to cause estimation errors to accumulate in the Vine structure and the computational burden grows sharply with the increase of data dimensionality. The prior probability of bivariate Copula is modified so that the bivariate Copula in high-level structure tree is more inclined to be optimized to independent states, and the sparse optimization of the high-level tree structure is achieved. Secondly, the Vine structure node order determination method is improved. It is expanded sequentially according to the sum of correlations among nodes, making it more applicable to D-vine modeling of horizontal structure. Finally, the high density region (HDR) and density quantile theory are introduced to determine the control boundary and construct generalized local probability (GLP) index to realize real-time monitoring of industrial processes. The superior performance of the proposed method was verified through the Tennessee-Eastman (TE) and acetic acid dehydration industrial processes.

       

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