Fault diagnosis based on PCA method with multi-block information extraction

doi:10.11949/j.issn.0438-1157.20180842

Abstract

Abstract:

Traditional monitoring methods only use sensor observation information to perform process fault monitoring, while ignoring other valid information contained in the original data. Aiming to this problem, a PCA fault monitoring algorithm based on multi-block information extraction is proposed. Firstly, two kinds of information of the cumulative error and the change rate of process variables are defined, so that new feature information can be extracted from the data. The process is divided into three sub-blocks based on each feature, and each sub-block is processed by the PCA method. Modeling and monitoring are carried out, and monitoring results are integrated by Bayesian method. Finally, a fault diagnosis method with weighted contribution graph is proposed to find the source variable which causes the fault. The validity and feasibility of the proposed method are demonstrated by numerical examples and the application of Tennessee-Eastman (TE) process monitoring.

Key words: principal component analysis, algorithm, model, fault diagnosis, information extraction, multi-block modelling

摘要：

传统的监控方法往往只利用传感器观测值信息进行过程的故障监测，而忽略了原始数据中包含的其他有效信息。为此，提出一种基于多块信息提取的PCA故障监测算法。首先，对过程变量的累计误差和变化率信息进行定义，从而能够从数据中提取新的特征信息，并基于每种特征将过程划分为3个子块；然后，利用PCA方法对每个子块进行建模与监测，通过贝叶斯方法对监测结果进行融合；最后，提出一种基于加权贡献图的故障诊断方法，分离出引发故障的源变量。通过数值例子与田纳西-伊斯曼（TE）过程监控中的应用证明了所提方法的有效性与可行性。

关键词: 主元分析, 算法, 模型, 故障诊断, 信息提取, 多块建模

CLC Number:

TP277

Bingbin GU, Weili XIONG. Fault diagnosis based on PCA method with multi-block information extraction[J]. CIESC Journal, 2019, 70(2): 736-749.

顾炳斌, 熊伟丽. 基于多块信息提取的PCA故障诊断方法[J]. 化工学报, 2019, 70(2): 736-749.

Figures/Tables 15

Fig.1 Comparison between traditional multi-block modeling method and multi-block information modeling method

Table 1 Sub-block division results

子块编号	训练数据集	测试样本
1	$X$	$x t e s t$
2	$X I$	$x t e s t I$
3	$X D$	$x t e s t D$

Table 1 Sub-block division results

子块编号	训练数据集	测试样本
1	$X$	$x t e s t$
2	$X I$	$x t e s t I$
3	$X D$	$x t e s t D$

Fig.2 Fault monitoring flowchart based on MBI-PCA

Fig.3 Monitoring result of fault 1

Fig.4 Isolation result of fault 1

Fig.5 Monitoring result of fault 2

Fig.6 Isolation result of fault 2

Table 2 Missing alarm rates of TE process/%

故障编号	子块1		子块2		子块3		BIC
故障编号	T²	SPE	T²	SPE	T²	SPE	T²	SPE
1	0.88	0.13	1.25	0.38	89.74	83.23	0.88	0.25
2	1.63	4.26	1.63	2	97.87	97.37	1.4	2.38
3	99.12	97.37	97.75	96.25	98.25	96.62	99.25	96.25
4	79.1	0	22.4	0	98.5	97.87	36.67	0
5	75.72	79.1	66.46	0.13	91.86	87.98	70.46	0
6	0.88	0	1.13	0.13	97.12	84.61	1	0
7	0	0	0.13	0.13	79.6	76.97	0	0
8	3.13	16.4	3.38	2.13	59.95	34.67	3.38	1.38
9	98.25	98.25	98.12	93.99	97.62	96.5	99.12	94.99
10	70.09	74.22	59.2	62.33	92.37	84.73	62.33	60.08
11	59.32	25.16	33.54	4.38	93.49	93.37	31.66	3.49
12	1.63	10.51	2.38	0.88	26.78	20.65	1.13	1
13	6.38	4.76	5.88	4.63	45.56	28.29	5.88	4.41
14	0.75	0	74.47	10.76	0.13	1.38	0	0
15	98.62	97	96.37	96.37	98.37	97	98.25	95.12
16	86.61	72.59	79.72	62.33	88.36	84.61	78.6	60.45
17	23.53	4.63	11.39	2.63	89.11	57.57	12.39	2.33
18	10.76	9.89	10.51	9.51	83.73	78.35	11.01	9.41
19	88.99	87.61	88.86	88.11	74.72	45.06	75.34	44.18
20	68.34	50.31	66.96	32.79	86.98	89.61	64.58	36.47
21	60.83	52.82	54.69	31.16	98.62	98.75	58.32	34.67
平均故障漏报率	44.50	37.38	41.72	28.26	80.42	73.10	38.65	26.12
平均故障误报率	0.52	1.32	0.8	3.35	1.38	2.67	0.37	3.07

Fig.7 Monitoring result of fault 5

Fig.8 Isolation result and related variable curves of fault 5

Fig.9 Monitoring result of fault 11

Fig.10 Isolation result and related variable curves of fault 11

Fig.11 Comparison between PCA and MBI-PCA of fault 21

Fig.12 Monitoring results of fault 0

Table 3 Comparison of some state of multi-block monitoring methods

故障编号	PCA	DPCA	MSMBPCA	FBPCA	MBI-PCA
故障编号	T²or SPE	$B I C T 2$ or SPE	$B I C T 2$ or SPE	$B I C T 2$ or SPE	$B I C T 2$ or SPE
0	0.022	0.026	0.0214	0.06	0.0144
1	0	0	0	0	0
2	0.02	0.02	0.01	0.01	0.01
3	0.97	0.94	—	0.88	0.96
4	0	0	0	0	0
5	0.75	0	0	0	0
6	0	0	0	0	0
7	0	0	0	0	0
8	0.03	0.02	0.03	0.01	0.01
9	0.98	0.93	—	0.91	0.95
10	0.7	0.44	0.18	0.11	0.6
11	0.25	0.22	0.3	0.19	0.03
12	0.02	0.01	0.02	0.01	0.01
13	0.05	0.05	0.05	0.05	0.05
14	0	0	0	0	0
15	0.97	0.93	—	0.78	0.95
16	0.73	0.52	0.15	0.1	0.30
17	0.05	0.03	0.13	0.03	0.03
18	0.10	0.09	0.1	0.1	0.09
19	0.88	0.8	0.48	0.3	0.44
20	0.50	0.27	0.33	0.1	0.36
21	0.53	0.44	0.46	0.33	0.35

Table 3 Comparison of some state of multi-block monitoring methods

故障编号	PCA	DPCA	MSMBPCA	FBPCA	MBI-PCA
故障编号	T²or SPE	$B I C T 2$ or SPE	$B I C T 2$ or SPE	$B I C T 2$ or SPE	$B I C T 2$ or SPE
0	0.022	0.026	0.0214	0.06	0.0144
1	0	0	0	0	0
2	0.02	0.02	0.01	0.01	0.01
3	0.97	0.94	—	0.88	0.96
4	0	0	0	0	0
5	0.75	0	0	0	0
6	0	0	0	0	0
7	0	0	0	0	0
8	0.03	0.02	0.03	0.01	0.01
9	0.98	0.93	—	0.91	0.95
10	0.7	0.44	0.18	0.11	0.6
11	0.25	0.22	0.3	0.19	0.03
12	0.02	0.01	0.02	0.01	0.01
13	0.05	0.05	0.05	0.05	0.05
14	0	0	0	0	0
15	0.97	0.93	—	0.78	0.95
16	0.73	0.52	0.15	0.1	0.30
17	0.05	0.03	0.13	0.03	0.03
18	0.10	0.09	0.1	0.1	0.09
19	0.88	0.8	0.48	0.3	0.44
20	0.50	0.27	0.33	0.1	0.36
21	0.53	0.44	0.46	0.33	0.35

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