基于多块信息提取的PCA故障诊断方法

doi:10.11949/j.issn.0438-1157.20180842

摘要/Abstract

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

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

中图分类号:

TP277

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.

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

图/表 15

图1 传统多块建模方法与多块信息建模方法对比

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

表1 子块划分结果

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	$X D$	$x t e s t D$

表1 子块划分结果

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	$X D$	$x t e s t D$

图2 基于MBI-PCA的故障监测流程

Fig.2 Fault monitoring flowchart based on MBI-PCA

图3 故障1监测结果

Fig.3 Monitoring result of fault 1

图4 故障1诊断结果

Fig.4 Isolation result of fault 1

图5 故障2监测结果

Fig.5 Monitoring result of fault 2

图6 故障2诊断结果

Fig.6 Isolation result of fault 2

表2 TE过程各故障漏报率

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

图7 故障5监测结果

Fig.7 Monitoring result of fault 5

图8 故障5诊断结果及相关变量特性

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

图9 故障11监测结果

Fig.9 Monitoring result of fault 11

图10 故障11诊断结果及相关变量特性

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

图11 故障21 PCA与MBI-PCA方法监测结果对比

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

图12 故障0的监测结果

Fig.12 Monitoring results of fault 0

表3 几种现有的多块监测方法性能比较

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

表3 几种现有的多块监测方法性能比较

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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