基于故障判别增强KECA算法的故障检测

doi:10.11949/0438-1157.20190893

摘要/Abstract

摘要：

基于核熵主成分分析方法的统计模型仅利用正常工况下数据进行建模，而忽略了监控系统数据库中一些已知类别的先前故障数据。为了利用先前故障数据中包含的故障信息来增强故障检测性能，提出了一种故障判别增强KECA（fault discriminant enhanced kernel entropy component analysis, FDKECA）算法。该法通过采用无监督学习和监督学习方法建立模型，同时监测非线性核熵主成分（kernel entropy component, KEC）和故障判别成分（fault discriminant component, FDC）两类数据特征。此外，利用贝叶斯推理将相应的监视统计信息转换为故障概率，并通过加权两个子模型的结果来构建基于总体概率的监视统计量。通过数值仿真和田纳西伊斯曼（Tennessee Eastman, TE）过程仿真实验，证明和传统KECA相比，FDKECA算法能够有效利用故障数据提高故障检测率。

关键词: 过程控制, 过程系统, 故障检测, 核熵成分分析, 混合模型

Abstract:

The statistical model based on the kernel entropy principal component analysis method only uses the data under normal operating conditions for modeling, and ignores some known categories of previous failure data in the monitoring system database. This paper proposed a fault discriminant enhanced the kernel entropy component analysis algorithm by using fault information contained in the previous fault data to enhance the fault detection performance. The model adopted unsupervised learning and supervised learning methods to monitor two types of data features: nonlinear kernel entropy component and fault discriminant component. In addition, the proposed algorithm employed Bayesian inference to convert the corresponding monitoring statistics into failure probability. The weighted probability of the two sub-models generated the monitoring statistics of the overall probability. Through numerical simulation and Tennessee Eastman process simulation experiments, the FDKECA algorithm is more effective than the traditional KECA since the improvement of the fault detection rate.

Key words: process control, process systems, fault detection, kernel entropy component analysis, mixing model

中图分类号:

TP 277

韩宇, 李俊芳, 高强, 田宇, 禹国刚. 基于故障判别增强KECA算法的故障检测[J]. 化工学报, 2020, 71(3): 1254-1263.

Yu HAN, Junfang LI, Qiang GAO, Yu TIAN, Guogang YU. Fault detection based on fault discrimination enhanced kernel entropy component analysis algorithm[J]. CIESC Journal, 2020, 71(3): 1254-1263.

图/表 12

图1 FDKECA算法结构

Fig.1 Fault discriminant enhanced kernel entropy component analysis algorithmic structure

表1 数值仿真故障设置

Table 1 Numerical simulation fault setting

故障	故障描述	故障程度
故障	故障描述	训练集	测试集
D1	变量 $x_{2}$ 阶跃变化	-0.40	-0.38
D2	变量 $x_{1}$ 线性增加	0.01×（k-100）	0.011×（k-100）

表1 数值仿真故障设置

Table 1 Numerical simulation fault setting

故障	故障描述	故障程度
故障	故障描述	训练集	测试集
D1	变量 $x_{2}$ 阶跃变化	-0.40	-0.38
D2	变量 $x_{1}$ 线性增加	0.01×（k-100）	0.011×（k-100）

图2 KECA故障D1监控结果

Fig.2 Fault D1 monitoring results of KECA

图3 情况1训练下，FDKECA故障D1监控结果

Fig.3 FDKECA fault D1 monitoring results of case 1 training

图4 故障D1测试集投影

Fig.4 Fault D1 test projection

图5 KLNPDA故障D1监控结果

Fig.5 Fault D1 monitoring results of KLNPDA

图6 情况1下故障D1故障概率加权因子

Fig.6 Weighting factor of fault D1 for fault probability in case 1

图7 KECA故障D2监控结果

Fig.7 Fault D2 monitoring results of KECA

图8 情况1下FDKECA对故障D2监控结果

Fig.8 FDKECA fault D1 monitoring results of case 1 training

表2 三种情况下的检测率

Table 2 Fault detection rate in three cases/%

故障	KECA		FDKECA
	T²	Q	情况1		情况2		情况3
	T²	Q	PT	PQ	PT	PQ	PT	PQ
D1	15	5.5	84	7.5	45	10	85	10
D2	41	11	54.5	8.5	81.5	9	82.5	9

表3 TE过程故障检测率测试结果

Table 3 Test results of TE process fault detection rate/%

故障	KPCA		KECA		KLNPDA		FDKECA
故障	T²	Q	T²	Q	T²	Q	PT	PQ
1	99.8	99.0	99.8	99.5	99.7	99.2	100	100
2	98.4	2.6	98.4	98.8	98.6	98.5	99.8	100
3	3.2	2.8	6.4	12.6	46.2	45.5	65.2	61.8
4	98.9	84.0	95.3	93.5	96.2	91.2	99.3	98.8
5	30.8	17.0	36.5	94.3	42.7	43.7	43.6	94.3
6	99.6	50.0	99.8	100	100	99.3	100	100
7	100	77.8	100	99.9	100	99.8	100	100
8	99.0	31.4	97.6	97.7	99.5	97.6	99.3	99.0
9	3.7	3.8	17.5	19.1	64.2	45.6	89.6	52.7
10	47.8	60.8	66.7	60.8	63.7	59.6	74.0	72.5
11	69.1	66.2	57.1	67.7	74.3	67.6	75.1	72.5
12	99.0	34.8	97.5	99.2	99.7	96.5	99.7	99.7
13	95.0	12.8	92.8	95.5	95.7	95.1	95.7	95.8
14	99.9	37.1	100	99.7	100	100	100	100
15	8.9	1.1	7.1	13.1	66.2	38.7	85.1	47.3
16	31.1	54.1	58.5	51.0	62.7	40.8	74.5	63.3
17	93.5	33.2	75.1	80.1	90.1	89.5	98.6	93.8
18	90.0	2.3	91.1	92.1	91.8	92.0	93.0	93.3
19	6.0	13.4	17.6	19.8	20.0	14.6	28.3	28.8
20	58.4	47.6	59.1	58.6	63.5	69.0	68.0	73.2
21	40.0	43.5	48.0	45.3	57.0	51.6	57.7	54.2
Avg	65.3	36.9	67.6	71.3	77.7	73.1	83.1	81.0

图9 故障3监控结果

Fig.9 Monitoring results of fault 3

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