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

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

邱穗庆,
李绍军^,

华东理工大学能源化工过程智能制造教育部重点实验室, 上海 200237

基金项目: 国家自然科学基金(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
计量
- 文章访问数: 133
- HTML全文浏览量: 74
- PDF下载量: 14
- 被引次数: 0
出版历程
- 收稿日期: 2021-12-31
- 网络出版日期: 2022-04-12

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

QIU Suiqing,
LI Shaojun^,

Key Laboratory of Smart Manufacturing in Energy Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China

摘要

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。
- 过程监测 /
- 相关性建模 /
- 非线性非高斯 /
- 稀疏D-vine Copula /
- 高密度区域
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.
- process monitoring /
- correlation modeling /
- nonlinearity and non-Gaussian /
- sparse D-vine Copula /
- high density region

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图 1 五元D-vine图解模型

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

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图 2 SDVC过程监控方法算法流程图

Figure 2. Algorithm flowchart of SDVC monitoring approach

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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

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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

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图 5 醋酸脱水过程监测图

Figure 5. Monitoring charts of acetic acid dehydration

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表 1 D-vine和SDVC方法的CPU耗时

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

Method	Time-consuming/s
Method	Offline modeling	Online monitoring
D-vine	278.700	0.104
SDVC	214.380	0.087

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.	Detection rate/%
	T²		SPE		GLP
	PCA	KPCA	PCA	KPCA	D-vine	SDVC
1	99.13	99.75	99.75	99.75	99.75	99.63
2	96.75	98.13	98.50	98.25	98.38	98.50
3	0.50	4.38	2.50	5.00	2.00	7.88
4	0.63	2.00	1.50	2.25	0.88	5.75
5	23.38	27.00	13.75	27.00	24.38	29.50
6	100.00	100.00	100.00	100.00	100.00	100.00
7	37.13	42.38	22.13	42.63	39.38	44.63
8	96.25	97.38	94.75	97.75	97.75	98.13
9	2.13	3.38	2.13	4.88	1.50	7.25
10	32.25	45.00	19.50	60.00	75.75	77.63
11	8.50	34.50	44.25	40.88	37.38	44.88
12	98.38	99.50	83.88	99.13	98.38	99.25
13	93.75	94.75	94.63	94.63	94.75	95.00
14	85.88	99.88	100.00	99.88	99.88	100.00
15	1.63	9.13	3.00	7.13	3.00	15.88
16	18.38	32.38	9.00	35.38	31.00	38.25
17	77.88	95.38	95.38	94.63	96.13	94.50
18	89.25	89.88	90.00	89.88	89.88	90.00
19	11.38	4.13	6.63	6.63	23.00	22.13
20	25.13	45.00	37.75	50.63	77.50	78.75
21	42.00	44.63	43.00	49.75	47.88	50.25

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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 (CL=0.98)

Method	FDR/%			FAR/%
Method	T²	SPE	GLP	T²	SPE	GLP
PCA	100	100	—	4.00	1.00	—
KPCA	100	100	—	5.50	1.50	—
D-Vine	—	—	100	—	—	2.00
SDVC	—	—	100	—	—	0.50

下载: 导出CSV

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