Incipient fault detection method for chemical process based on ensemble learning transfer entropy

doi:10.11949/0438-1157.20230287

Abstract

Abstract:

Traditional multivariate statistical analysis methods directly perform fault analysis on the mean and variance of process data. But as long as the monitoring statistics remain within the normal region surrounded by control limits, changes in the data distribution cannot be detected. To solve this problem, a method based on ensemble learning transfer entropy is proposed to obtain monitoring statistics and control limits based on this data set. Firstly, the transfer entropy is used to measure the information transfer between variables, and then the transfer entropy dataset is obtained through a sliding window, and the monitoring statistics and control limits are derived from this dataset. Then, the constructed indicators are ranked and binned using the rank sum ratio method, and the probability density parameters of the transfer entropy and the corresponding monitoring statistics of the part with good binning results are screened. Finally, the monitoring results are fused using an algorithm combining ensemble learning and Bayesian inference strategies to detect process faults in real-time. The method is used for fault detection of numerical examples and continuously stirred tank reactor processes and is compared with kernel principal component analysis, kernel independent component analysis, weighted statistical local kernel principal component analysis and weighted statistical feature kernel independent component analysis to verify that the proposed the method has good performance in detecting minor faults.

Key words: incipient fault, principal component analysis, transfer entropy, rank sum ratio method, ensemble learning

摘要：

传统的多元统计分析方法直接对过程数据的均值和方差进行故障分析，但只要监测统计量保持在控制极限所包围的正态区域内，就不能检测出数据分布的变化。针对这一问题，提出一种基于集成学习传递熵的微小故障检测方法。该方法首先利用传递熵提取变量间的信息传递，通过滑动窗口获取传递熵数据集，并根据此数据集求取监测统计量和控制限。然后，利用秩和比法对构建的评价指标进行排序分档，筛选出分档结果良好的传递熵数据集对应的监测统计量。最后，利用集成学习与贝叶斯推理策略相结合的算法对监测结果进行融合，实时检测过程故障。将该方法用于数值例子和连续搅拌反应釜过程的故障检测，并与核主元分析、核独立元分析、加权统计局部核主元分析和加权统计特征核独立元分析进行对比，验证了所提方法具有良好的微小故障检测性能。

关键词: 微小故障, 主元分析, 传递熵, 秩和比法, 集成学习

CLC Number:

TP 277

Guang WANG, Fashun SHAN, Yucheng QIAN, Jianfang JIAO. Incipient fault detection method for chemical process based on ensemble learning transfer entropy[J]. CIESC Journal, 2023, 74(7): 2967-2978.

王光, 单发顺, 钱禹丞, 焦建芳. 基于集成学习传递熵的化工过程微小故障检测方法[J]. 化工学报, 2023, 74(7): 2967-2978.

Figures/Tables 13

Fig.1 Flow chart of ETEn-based fault monitoring

Table 1 Pairwise comparison matrix and weights of evaluation index

指标	ACC	TPR	FPR	TNR	FNR	Precision	F	权值
ACC	1	5	5	5	5	5	3	0.412
TPR	1/5	1	1	1	1	1	1/3	0.076
FPR	1/5	1	1	1	1	1	1/3	0.076
TNR	1/5	1	1	1	1	1	1/3	0.076
FNR	1/5	1	1	1	1	1	1/3	0.076
Precision	1/5	1	1	1	1	1	1/3	0.076
F	1/3	3	3	3	3	3	1	0.211

Table 2 RSR binning results for parameter B in the numerical example

分档	概率单位Z	WRSR	分档结果^②
$R S R_{u p}$ ^①	>6	>0.721	39、34、29、35
$R S R_{u p}$ ^①	>6	>0.724	35、40、31、33
$R S R_{m i d}$	4~6	0.273~0.721	28、21、25、27、30、26、32、38、40、36、31、33、20、37
$R S R_{m i d}$	4~6	0.274~0.724	39、34、24、32、30、37、29、20、36、38、27、23、26、22
$R S R_{d o w n}$	<4	<0.273	22、24、23
$R S R_{d o w n}$	<4	<0.274	28、25、21

Table 2 RSR binning results for parameter B in the numerical example

分档	概率单位Z	WRSR	分档结果^②
$R S R_{u p}$ ^①	>6	>0.721	39、34、29、35
$R S R_{u p}$ ^①	>6	>0.724	35、40、31、33
$R S R_{m i d}$	4~6	0.273~0.721	28、21、25、27、30、26、32、38、40、36、31、33、20、37
$R S R_{m i d}$	4~6	0.274~0.724	39、34、24、32、30、37、29、20、36、38、27、23、26、22
$R S R_{d o w n}$	<4	<0.273	22、24、23
$R S R_{d o w n}$	<4	<0.274	28、25、21

Fig.2 The fault alarm rate corresponding to different transfer entropy window parameters

Fig.3 Fault 1 monitoring diagrams of the numerical examples

Table 3 The detection performance of the five methods for numerical examples

故障		KPCA		KICA		WSLKPCA		WSFKICA		ETEn
故障		$T^{2}$	$S P E$	$I^{2}$	$S P E$	$T^{2}$	$S P E$	$T^{2}$	$S P E$	$E T^{2}$	$E S P E$
1	故障检测率	54.0%	0	5.4%	81.8%	30.9%	97.0%	68.9%	82.9%	93.0%	99.0%
	误报率	0.6%	0	0.7%	0.9%	9.1%	4.2%	3.8%	2.4%	0	0
	DD/min	57	ND	ND	6	150	10	38	54	9	9
2	故障检测率	60.8%	0	13.8%	66.4%	84.4%	68.3%	69.9%	76.0%	76.7%	80.6%
	误报率	2.0%	0	0.6%	0.7%	0.8%	5.1%	4.2%	1.6%	0	0
	DD/min	233	ND	ND	219	9	93	37	28	63	45
平均故障检测率		57.4%	0	9.6%	74.1%	57.7%	82.7%	69.4%	79.5%	84.9%	89.8%

Table 3 The detection performance of the five methods for numerical examples

故障		KPCA		KICA		WSLKPCA		WSFKICA		ETEn
故障		$T^{2}$	$S P E$	$I^{2}$	$S P E$	$T^{2}$	$S P E$	$T^{2}$	$S P E$	$E T^{2}$	$E S P E$
1	故障检测率	54.0%	0	5.4%	81.8%	30.9%	97.0%	68.9%	82.9%	93.0%	99.0%
	误报率	0.6%	0	0.7%	0.9%	9.1%	4.2%	3.8%	2.4%	0	0
	DD/min	57	ND	ND	6	150	10	38	54	9	9
2	故障检测率	60.8%	0	13.8%	66.4%	84.4%	68.3%	69.9%	76.0%	76.7%	80.6%
	误报率	2.0%	0	0.6%	0.7%	0.8%	5.1%	4.2%	1.6%	0	0
	DD/min	233	ND	ND	219	9	93	37	28	63	45
平均故障检测率		57.4%	0	9.6%	74.1%	57.7%	82.7%	69.4%	79.5%	84.9%	89.8%

Fig.4 Schematic diagram of the closed-loop CSTR model

Table 4 Description of the variables in the closed-loop CSTR model

索引	变量	说明
1	$C_{i}$	进料浓度
2	$T_{i}$	进料温度
3	$C$	反应物浓度
4	$T$	反应物温度
5	$Q_{c}$	冷却剂流速
6	$T_{c i}$	入口冷却剂温度
7	$T_{c}$	冷却剂温度

Table 4 Description of the variables in the closed-loop CSTR model

索引	变量	说明
1	$C_{i}$	进料浓度
2	$T_{i}$	进料温度
3	$C$	反应物浓度
4	$T$	反应物温度
5	$Q_{c}$	冷却剂流速
6	$T_{c i}$	入口冷却剂温度
7	$T_{c}$	冷却剂温度

Table 5 CSTR system fault

故障	说明	$σ$
1	$C_{i} = C_{i, 0} + σ$	0.06
2	$T_{i} = T_{i, 0} + (k - 1000) σ$ ^①	1/3000
3	$T_{i} = T_{i, 0} + σ ξ$ ^②	0.1

Table 5 CSTR system fault

故障	说明	$σ$
1	$C_{i} = C_{i, 0} + σ$	0.06
2	$T_{i} = T_{i, 0} + (k - 1000) σ$ ^①	1/3000
3	$T_{i} = T_{i, 0} + σ ξ$ ^②	0.1

Table 6 RSR binning results for parameter B in the CSTR system

分档	概率单位 $Z$	WRSR	分档结果
$R S R_{u p}$	>6	>0.670	22、26、25、24
		>0.681	29、38、35、34
		>0.685	40、22、39、31
$R S R_{m i d}$	4~6	0.319~0.670	32、31、27、37、34、36、33、28、23、29、35、39、20、38
		0.322~0.681	33、25、27、32、28、23、22、21、39、40、30、36、24、37
		0.323~0.685	25、29、20、38、30、33、27、34、37、36、26、24、28、21
$R S R_{d o w n}$	<4	<0.319	21、40、30
		<0.322	31、20、26
		<0.323	32、35、23

Table 6 RSR binning results for parameter B in the CSTR system

分档	概率单位 $Z$	WRSR	分档结果
$R S R_{u p}$	>6	>0.670	22、26、25、24
		>0.681	29、38、35、34
		>0.685	40、22、39、31
$R S R_{m i d}$	4~6	0.319~0.670	32、31、27、37、34、36、33、28、23、29、35、39、20、38
		0.322~0.681	33、25、27、32、28、23、22、21、39、40、30、36、24、37
		0.323~0.685	25、29、20、38、30、33、27、34、37、36、26、24、28、21
$R S R_{d o w n}$	<4	<0.319	21、40、30
		<0.322	31、20、26
		<0.323	32、35、23

Fig.5 Fault 1 monitoring diagram of the CSTR system

Fig.6 Fault 3 monitoring diagram of the CSTR system

Table 7 The detection performance of the five methods for the CSTR system

故障		KPCA		KICA		WSLKPCA		WSFKICA		ETEn
故障		$T^{2}$	SPE	$I^{2}$	SPE	$T^{2}$	SPE	$T^{2}$	SPE	$E T^{2}$	ESPE
1	故障检测率/%	57.6	0	45.8	39.0	93.4	76.1	84.2	93.6	99.4	99.0
	误报率/%	4.6	0	1.2	0.7	7.9	4.4	4.7	4.4	0	0
	DD/min	65	ND	42	46	38	113	0	0	8	10
2	故障检测率/%	48.4	0	10.6	36.4	68.9	72.7	28.9	76.1	99.4	86.6
	误报率/%	0.6	0	0.6	0.8	2.4	0.8	0	3.4	0.4	0
	DD/min	338	ND	447	294	161	142	80	8	10	74
3	故障检测率/%	38.2	0	18.6	20.6	83.4	76.1	69.3	63.5	99.6	99.2
	误报率/%	1	0	3.3	1.9	0	3.6	4.7	4.4	0.2	0
	DD/min	101	ND	93	ND	61	36	0	0	7	9
平均故障检测率/%		48.1	0	25.0	32.0	81.9	75.0	60.8	77.7	99.5	94.9

Table 7 The detection performance of the five methods for the CSTR system

故障		KPCA		KICA		WSLKPCA		WSFKICA		ETEn
故障		$T^{2}$	SPE	$I^{2}$	SPE	$T^{2}$	SPE	$T^{2}$	SPE	$E T^{2}$	ESPE
1	故障检测率/%	57.6	0	45.8	39.0	93.4	76.1	84.2	93.6	99.4	99.0
	误报率/%	4.6	0	1.2	0.7	7.9	4.4	4.7	4.4	0	0
	DD/min	65	ND	42	46	38	113	0	0	8	10
2	故障检测率/%	48.4	0	10.6	36.4	68.9	72.7	28.9	76.1	99.4	86.6
	误报率/%	0.6	0	0.6	0.8	2.4	0.8	0	3.4	0.4	0
	DD/min	338	ND	447	294	161	142	80	8	10	74
3	故障检测率/%	38.2	0	18.6	20.6	83.4	76.1	69.3	63.5	99.6	99.2
	误报率/%	1	0	3.3	1.9	0	3.6	4.7	4.4	0.2	0
	DD/min	101	ND	93	ND	61	36	0	0	7	9
平均故障检测率/%		48.1	0	25.0	32.0	81.9	75.0	60.8	77.7	99.5	94.9

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