Fault detection method based on kernel entropy independent component analysis

doi:10.11949/0438-1157.20220269

Abstract

Abstract:

Traditional kernel independent component analysis (KICA) reduces the dimension according to the size of eigenvalues, but large eigenvalues do not necessarily obtain the largest contribution of information entropy. To solve this problem, a fault detection method based on kernel entropy independent component analysis (KEICA) is proposed. The training data set is projected into the high-dimensional kernel space. The kernel principal component is selected by the contribution to the information entropy of data, and the independent component analysis (ICA) model is established. The $I 2$ and $S P E$ statistics are obtained for the training sample, and the control limits of the statistics are calculated by using kernel density estimation. The kernel matrix of the test data to the training data is calculated, and projected on the ICA model. The statistics of the test samples are calculated. The samples whose statistics exceed the control limit can be identified as fault samples. This method is used for fault detection of a nonlinear numerical example and the Tennessee Eastman (TE) process, and compared with the traditional kernel principal component analysis (KPCA), kernel entropy component analysis (KECA) and KICA methods. The monitoring effect of KEICA is compared, and it's better than the other three methods.

Key words: fault detection, information entopy, kernel density estimation, kernel entropy component analysis, kernel independent component analysis

摘要：

传统核独立成分分析（KICA）依据特征值的大小进行降维，但是特征值大并不一定取得的信息熵贡献度也是最大的。针对这个问题，提出一种基于核熵独立成分分析（KEICA）的故障检测方法。将训练数据集投影在高维核空间，通过对数据信息熵的贡献大小选取核主成分，并建立独立成分分析（ICA）模型。对训练样本求 $I 2$ 和 $S P E$ 统计量，并利用核密度估计计算统计量的控制限。计算测试数据对训练数据的核矩阵，将其投影在ICA模型上并计算测试样本的统计量，统计量超出控制限的样本即可被识别为故障样本。将该方法用于非线性数值例子和Tennessee Eastman（TE）过程的故障检测，并与传统的核主成分分析（KPCA）、核熵成分分析（KECA）和KICA方法进行对比，表明KEICA的监测效果优于其他三种方法。

关键词: 故障检测, 信息熵, 核密度估计, 核熵成分分析, 核独立成分分析

CLC Number:

TP 277

Jinyu GUO, Zhe WANG, Yuan LI. Fault detection method based on kernel entropy independent component analysis[J]. CIESC Journal, 2022, 73(8): 3647-3658.

郭金玉, 王哲, 李元. 基于核熵独立成分分析的故障检测方法[J]. 化工学报, 2022, 73(8): 3647-3658.

Figures/Tables 8

References 10

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Item	KPCA		KECA			KICA		KEICA
Item	SPE	T²	SPE	T²	CS	SPE	I²	SPE	I²
FDR/%	70.25	8.00	7.50	64.38	20.31	77.00	90.25	100	100
FAR/%	1.25	1.25	1.25	1.88	1.25	1.88	1.88	0	0.63

Item	KPCA		KECA			KICA		KEICA
Item	SPE	T²	SPE	T²	CS	SPE	I²	SPE	I²
FDR/%	70.25	8.00	7.50	64.38	20.31	77.00	90.25	100	100
FAR/%	1.25	1.25	1.25	1.88	1.25	1.88	1.88	0	0.63

故障序号	FDR/%
	KPCA		KECA			KICA		KEICA
	SPE	T²	SPE	T²	CS	SPE	I²	SPE	I²
1	99.50	99.25	99.37	99.13	99.69	99.25	99.25	100	99.63
2	98.60	98.25	98.54	98.63	98.85	96.50	98.00	99.25	98.63
4	88.00	14.00	25.60	40.25	90.63	57.50	64.63	100	85.25
7	100	97.00	67.80	99.63	100	99.38	92.75	100	100
11	65.38	37.75	58.88	63.38	76.56	70.75	68.50	83.63	68.00
12	96.87	98.60	96.35	96.00	99.69	87.88	97.63	99.63	99.50
13	95.87	94.10	95.31	93.63	96.35	95.50	95.25	96.25	95.63
17	86.88	79.00	85.25	83.38	92.70	87.13	82.75	97.25	90.88
20	45.25	38.60	50.10	38.63	70.83	59.38	63.00	77.75	63.13

故障序号	FDR/%
	KPCA		KECA			KICA		KEICA
	SPE	T²	SPE	T²	CS	SPE	I²	SPE	I²
1	99.50	99.25	99.37	99.13	99.69	99.25	99.25	100	99.63
2	98.60	98.25	98.54	98.63	98.85	96.50	98.00	99.25	98.63
4	88.00	14.00	25.60	40.25	90.63	57.50	64.63	100	85.25
7	100	97.00	67.80	99.63	100	99.38	92.75	100	100
11	65.38	37.75	58.88	63.38	76.56	70.75	68.50	83.63	68.00
12	96.87	98.60	96.35	96.00	99.69	87.88	97.63	99.63	99.50
13	95.87	94.10	95.31	93.63	96.35	95.50	95.25	96.25	95.63
17	86.88	79.00	85.25	83.38	92.70	87.13	82.75	97.25	90.88
20	45.25	38.60	50.10	38.63	70.83	59.38	63.00	77.75	63.13

故障序号	FAR/%
	KPCA		KECA			KICA		KEICA
	SPE	T²	SPE	T²	CS	SPE	I²	SPE	I²
1	5.60	0	0	2.50	1.25	1.25	0.63	3.13	0.63
2	3.70	1.25	0	3.13	0.63	0	0.63	3.75	0
4	8.00	0.60	0	4.38	1.25	1.88	1.88	5.00	0.63
7	1.80	0	0	2.50	0.63	3.13	3.75	1.88	1.25
11	5.63	1.25	2.50	3.75	3.75	4.38	2.50	4.38	2.50
12	4.37	1.25	2.50	3.75	19.38	1.88	1.88	1.25	22.50
13	1.87	0	0	0.63	2.50	1.88	2.50	3.13	1.88
17	5.63	0.63	1.25	6.88	1.88	4.38	3.13	5.00	1.25
20	1.87	0	0.63	1.88	0	0	0	3.13	0.63