A novel scheme for multivariate statistical fault detection with application to the Tennessee Eastman process

Nana Xu; Jun Sun; Jingjing Liu; Xianchao Xiu

doi:10.3934/mfc.2021010

Article Contents

2021, Volume 4, Issue 3: 167-184. Doi: 10.3934/mfc.2021010

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A novel scheme for multivariate statistical fault detection with application to the Tennessee Eastman process

1.
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China
2.
Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, China
3.
State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 200433, China

^* Corresponding author: Xianchao Xiu
^* Corresponding author: Xianchao Xiu

Received: May 31, 2021

Revised: June 30, 2021

Early access: July 2021

Published: August 2021

This work was supported in part by the National Natural Science Foundation of China under Grant 12001019

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Abstract

Canonical correlation analysis (CCA) has gained great success for fault detection (FD) in recent years. However, it cannot preserve the prior information of the underlying process. To cope with these difficulties, this paper proposes an improved CCA-based FD scheme using a novel multivariate statistical technique, called sparse collaborative regression (SCR). The core of the proposed method is to take the prior information as a supervisor, and then integrate it with CCA. Further, the $ \ell_{2,1} $-norm is employed to reduce redundancy and avoid overfitting, which facilitates its interpretability. In order to solve the proposed SCR, an efficient alternating optimization algorithm is developed with convergence analysis. Finally, some experimental studies on a simulated example and the benchmark Tennessee Eastman process are conducted to demonstrate the superiority over the classical CCA in terms of the false alarm rate and fault detection rate. The detection results indicate that the proposed method is promising.

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Mathematics Subject Classification: Primary: 93C83, 90C25; Secondary: 62P30, 65K05.

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Figure 1. Comparison of CCA and the proposed SCR

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Figure 2. Detection strategy

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Figure 3. Illustration of detection indices

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Figure 4. Detection results for Type I

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Figure 5. Detection results for Type II

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Figure 6. Flowchart of the TE process

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Figure 7. Detection results for IDV(2) in the TE process

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Figure 8. Detection results for IDV(10) in the TE process

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Figure 9. Detection results for IDV(18) in the TE process

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Figure 10. Detection results for IDV(15) in the TE process

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Figure 11. Relative differences

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Table 1. The selected faults in TE process

Fault No.	Description	Type
IDV(1)	A/C feed ratio	step change
IDV(2)	component B	step change
IDV(3)	feed D temperature	step change
IDV(4)	RCW inlet temperature	step change
IDV(5)	CCW inlet temperature	step change
IDV(6)	feed A loss	step change
IDV(7)	C header pressure loss	step change
IDV(8)	feed A-C components	random variation
IDV(9)	feed D temperature	random variation
IDV(10)	feed C temperature	random variation
IDV(11)	RCW inlet temperature	random variation
IDV(12)	CCW inlet temperature	random variation
IDV(13)	reaction kinetics	slow drift
IDV(14)	RCW valve	sticking
IDV(15)	CCW valve	sticking
IDV(16)	unknown fault	unknown
IDV(17)	unknown fault	unknown
IDV(18)	unknown fault	unknown
IDV(19)	unknown fault	unknown
IDV(20)	unknown fault	unknown
IDV(21)	unknown fault	constant

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Table 2. Detection results in term of FDR and FAR

Fault No.	CCA-r1		CCA-r2		SCR
Fault No.	FDR	FAR	FDR	FAR	FDR	FAR
IDV(1)	99.75%	0.63%	99.88%	0.63%	99.88%	0.00%
IDV(2)	96.50%	0.63%	97.50%	0.00%	99.50%	0.00%
IDV(3)	11.13%	3.25%	13.00%	2.50%	32.75%	1.75%
IDV(4)	100%	1.88%	99.88%	1.25%	100%	1.25%
IDV(5)	100%	4.38%	100%	3.75%	100%	2.50%
IDV(6)	100%	2.50%	100%	2.50%	100%	1.75%
IDV(7)	100%	3.75%	96.88%	2.50%	100%	0.63%
IDV(8)	96.50%	1.88%	97.50%	0.63%	99.75%	0.00%
IDV(9)	8.75%	2.50%	9.75%	2.50%	12.63%	1.63%
IDV(10)	86.88%	1.25%	89.50%	0.63%	96.75%	0.00%
IDV(11)	76.50%	0.63%	76.88%	0.63%	85.13%	0.00%
IDV(12)	99.13%	1.25%	99.75%	0.00%	100%	0.00%
IDV(13)	95.75%	0.63%	95.13%	0.63%	99.75%	0.00%
IDV(14)	100%	1.88%	99.88%	0.63%	100%	0.63%
IDV(15)	13.13%	4.38%	16.88%	4.38%	48.50%	1.75%
IDV(16)	93.00%	7.50%	94.38%	1.25%	97.38%	0.63%
IDV(17)	94.13%	3.13%	97.63%	2.50%	98.25%	1.25%
IDV(18)	90.88%	1.88%	92.50%	0.00%	95.75%	0.00%
IDV(19)	92.00%	1.25%	92.50%	1.25%	92.50%	0.63%
IDV(20)	86.88%	0.63%	87.13%	0.63%	92.13%	0.00%
IDV(21)	44.63%	4.38%	61.50%	0.63%	72.38%	0.00%

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