基于潜变量自回归算法的化工过程动态监测方法

doi:10.11949/j.issn.0438-1157.20181180

摘要/Abstract

摘要：

从建立潜变量自回归（AR）模型的角度出发，提出了一种基于潜变量自回归（LVAR）算法的化工过程动态建模与监测方法，旨在提取动态潜变量的同时给出各潜变量的AR模型。LVAR算法在最小化潜变量的AR模型残差的约束下，通过同时搜寻投影变换向量与AR系数向量，实现了对动态潜变量的特征提取及其AR模型的建立。此外，LVAR算法通过先提取动态潜变量后提取静态成分信息的方式，有效地区分了采样数据中的自相关性与交叉相关性。在对比实验中，通过比较分析LVAR方法与其他三种典型的动态过程监测方法在经典化工过程对象上的故障监测结果，验证了LVAR方法在动态过程监测上的优越性与可靠性。

关键词: 主成分分析, 故障检测, 缺失数据, 过程系统

Abstract:

From the viewpoint of constructing auto-regressive (AR) models for latent variables, the current paper proposed a dynamic modeling and monitoring approach for chemical processes based on latent variable auto-regressive (LVAR) algorithm. With respect to the requirement of minimizing AR model residual, the LVAR algorithm simultaneously searches for projecting vectors and AR coefficient vectors, so as to extracting dynamic latent variables and their corresponding AR models. In addition, the LVAR algorithm can efficiently distinguish the auto-correlated and cross-correlated relations inherited in the sampled data, by extracting the dynamic latent variables first and then the static component information. In the comparisons, the superiority and validity of the LVAR method are demonstrated by comparing the fault monitoring results in a classical chemical plant with other three counterparts.

Key words: principal component analysis, fault detection, missing data, process systems

中图分类号:

TP 277

唐俊苗, 俞海珍, 史旭华, 童楚东. 基于潜变量自回归算法的化工过程动态监测方法[J]. 化工学报, 2019, 70(3): 987-994.

Junmiao TANG, Haizhen YU, Xuhua SHI, Chudong TONG. Dynamic monitoring of chemical processes based on latent variable auto-regressive algorithm[J]. CIESC Journal, 2019, 70(3): 987-994.

图/表 5

图1 动态潜变量的自相关性示意图

Fig.1 Auto-correlation plots of dynamic latent variable

图2 残差矩阵FD+1中各列向量的自相关性示意图

Fig.2 Auto-correlation plots of column vectors in residual matrix FD+1

图3 平均故障漏报率对比

Fig.3 Comparison of average missing alarm rates

表1 TE过程监测上的故障误报率与故障漏报率

Table 1 False alarm rates and missing alarm rates achieved in TE process

No.	DPCA		DLV			DiPCA			LVAR
No.	$T 2$	$Q$	$T a 2$	$T s 2$	$Q s$	$T a 2$	$T s 2$	$Q s$	$T a 2$	$T s 2$
1	0.75	0.13	0	0	0.63	0.25	0.88	0.63	0	0.88
2	1.50	2.75	1.00	2.25	9.63	1.63	1.88	3.50	1.63	4.13
4	94.00	0	95.85	0	87.13	0	77.25	0	0.13	0
5	76.00	55.00	89.95	81.75	0.13	76.69	93.63	79.38	0	0
6	1.13	0	0.25	1.00	0	0.50	1.63	0	0	0
7	0	0	82.28	0	69.75	0	0	0	58.50	0
8	2.63	3.00	12.19	6.38	30.50	5.14	16.88	19.50	1.88	25.63
10	75.13	48.88	94.22	90.50	37.50	83.33	97.25	71.13	19.63	39.25
11	72.88	6.00	89.32	19.00	88.50	14.79	58.25	12.63	23.50	39.88
12	0.88	3.63	19.72	9.00	17.38	8.15	21.00	9.88	0.25	3.13
13	5.75	4.63	29.27	4.88	11.00	6.52	26.63	7.75	4.50	7.63
14	0.13	0	0	0	11.25	0	12.75	0	0	24.13
16	90.38	48.00	91.08	90.63	36.63	81.70	98.38	69.50	27.38	16.88
17	22.75	2.25	31.28	5.13	6.25	11.53	33.13	3.25	2.25	12.75
18	11.13	9.38	11.43	10.00	9.63	9.52	10.88	9.50	9.88	9.63
19	77.25	33.38	90.58	81.13	37.00	60.53	82.25	72.63	41.88	11.63
20	61.13	36.38	73.12	60.63	35.13	50.63	78.75	47.38	47.63	25.13
21	54.25	49.50	92.46	49.25	83.13	73.56	78.13	74.63	71.38	68.5
Ave.	35.98	16.83	50.22	28.42	31.73	26.92	43.86	26.74	16.54	15.28

表1 TE过程监测上的故障误报率与故障漏报率

Table 1 False alarm rates and missing alarm rates achieved in TE process

No.	DPCA		DLV			DiPCA			LVAR
No.	$T 2$	$Q$	$T a 2$	$T s 2$	$Q s$	$T a 2$	$T s 2$	$Q s$	$T a 2$	$T s 2$
1	0.75	0.13	0	0	0.63	0.25	0.88	0.63	0	0.88
2	1.50	2.75	1.00	2.25	9.63	1.63	1.88	3.50	1.63	4.13
4	94.00	0	95.85	0	87.13	0	77.25	0	0.13	0
5	76.00	55.00	89.95	81.75	0.13	76.69	93.63	79.38	0	0
6	1.13	0	0.25	1.00	0	0.50	1.63	0	0	0
7	0	0	82.28	0	69.75	0	0	0	58.50	0
8	2.63	3.00	12.19	6.38	30.50	5.14	16.88	19.50	1.88	25.63
10	75.13	48.88	94.22	90.50	37.50	83.33	97.25	71.13	19.63	39.25
11	72.88	6.00	89.32	19.00	88.50	14.79	58.25	12.63	23.50	39.88
12	0.88	3.63	19.72	9.00	17.38	8.15	21.00	9.88	0.25	3.13
13	5.75	4.63	29.27	4.88	11.00	6.52	26.63	7.75	4.50	7.63
14	0.13	0	0	0	11.25	0	12.75	0	0	24.13
16	90.38	48.00	91.08	90.63	36.63	81.70	98.38	69.50	27.38	16.88
17	22.75	2.25	31.28	5.13	6.25	11.53	33.13	3.25	2.25	12.75
18	11.13	9.38	11.43	10.00	9.63	9.52	10.88	9.50	9.88	9.63
19	77.25	33.38	90.58	81.13	37.00	60.53	82.25	72.63	41.88	11.63
20	61.13	36.38	73.12	60.63	35.13	50.63	78.75	47.38	47.63	25.13
21	54.25	49.50	92.46	49.25	83.13	73.56	78.13	74.63	71.38	68.5
Ave.	35.98	16.83	50.22	28.42	31.73	26.92	43.86	26.74	16.54	15.28

图4 故障10的过程监测结果

Fig.4 Monitoring charts of fault 10

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