August  2021, 4(3): 167-184. doi: 10.3934/mfc.2021010

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

Received  June 2021 Revised  July 2021 Published  August 2021 Early access  July 2021

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

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.

Citation: Nana Xu, Jun Sun, Jingjing Liu, Xianchao Xiu. A novel scheme for multivariate statistical fault detection with application to the Tennessee Eastman process. Mathematical Foundations of Computing, 2021, 4 (3) : 167-184. doi: 10.3934/mfc.2021010
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[20]

Y. LiuB. LiuX. Zhao and M. Xie, A mixture of variational canonical correlation analysis for nonlinear and quality-relevant process monitoring, IEEE Trans. Industrial Electron., 65 (2018), 6478-6486.  doi: 10.1109/TIE.2017.2786253.

[21]

Y. LiuJ. ZengL. XieS. Luo and H. Su, Structured joint sparse principal component analysis for fault detection and isolation, IEEE Trans. Ind. Inform., 15 (2019), 2721-2731.  doi: 10.1109/TII.2018.2868364.

[22]

K. PengK. ZhangB. YouJ. Dong and Z. Wang, A quality-based nonlinear fault diagnosis framework focusing on industrial multimode batch processes, IEEE Trans. Industrial Electron., 63 (2016), 2615-2624.  doi: 10.1109/TIE.2016.2520906.

[23]

Y. SiY. Wang and D. Zhou, Key-performance-indicator-related process monitoring based on improved kernel partial least squares, IEEE Trans. Industrial Electron., 68 (2021), 2626-2636.  doi: 10.1109/TIE.2020.2972472.

[24]

Y. TaoH. ShiB. Song and S. Tan, A novel dynamic weight principal component analysis method and hierarchical monitoring strategy for process fault detection and diagnosis, IEEE Trans. Industrial Electron., 67 (2020), 7994-8004.  doi: 10.1109/TIE.2019.2942560.

[25]

X. XiuY. YangL. Kong and W. Liu, Data-driven process monitoring using structured joint sparse canonical correlation analysis, IEEE Trans. Circuits-II, 68 (2021), 361-365.  doi: 10.1109/TCSII.2020.2988054.

[26]

X. XiuY. YangL. Kong and W. Liu, Laplacian regularized robust principal component analysis for process monitoring, J. Process Contr., 92 (2020), 212-219.  doi: 10.1016/j.jprocont.2020.06.011.

[27]

X. XiuY. YangW. LiuL. Kong and M. Shang, An improved total variation regularized RPCA for moving object detection with dynamic background, J. Ind. Manag. Optim., 16 (2020), 1685-1698.  doi: 10.3934/jimo.2019024.

[28]

Y. YangS. X. Ding and L. Li, Parameterization of nonlinear observer-based fault detection systems, IEEE Trans. Automat. Control, 61 (2016), 3687-3692.  doi: 10.1109/TAC.2016.2532381.

[29]

S. YinS. X. DingA. HaghaniH. Hao and P. Zhang, A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process, J. Process Contr., 22 (2012), 1567-1581.  doi: 10.1016/j.jprocont.2012.06.009.

[30]

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show all references

References:
[1]

H. Akaike, Stochastic theory of minimal realization. System identification and time-series analysis, IEEE Trans. Automatic Control, AC-19 (1974), 667-674.  doi: 10.1109/tac.1974.1100707.

[2]

S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Now Foundations and Trends, 2011. doi: 10.1561/2200000016.

[3]

C. ChenB. HeY. Ye and X. Yuan, The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent, Math. Program., 155 (2016), 57-79.  doi: 10.1007/s10107-014-0826-5.

[4]

L. ChenD. Sun and K.-C. Toh, An efficient inexact symmetric Gauss-Sediel based majorized ADMM for high-dimensonal convex composite conic programming, Math. Program., 161 (2017), 237-270.  doi: 10.1007/s10107-016-1007-5.

[5]

Z. ChenS. X. DingT. PengC. Yang and W. Gui, Fault detection for non-Gaussian processes using generalized canonical correlation analysis and randomized algorithms, IEEE Trans. Industrial Electron., 65 (2018), 1559-1567.  doi: 10.1109/TIE.2017.2733501.

[6]

Z. ChenS. X. DingK. ZhangZ. Li and Z. Hu, Canonical correlation analysis-based fault detection methods with application to alumina evaporation process, Control Engrg. Pract., 46 (2016), 51-58.  doi: 10.1016/j.conengprac.2015.10.006.

[7]

Z. ChenK. ZhangS. X. DingY. A. W. Shardt and Z. Hu, Improved canonical correlation analysis-based fault detection methods for industrial processes, J. Process Contr., 41 (2016), 26-34.  doi: 10.1016/j.jprocont.2016.02.006.

[8]

L. H. Chiang, E. L. Russell and R. D. Braatz, Fault Detection and Diagnosis in Industrial Systems, Advanced Textbooks in Control and Signal Processing, Springer-Verlag, London, 2001. doi: 10.1007/978-1-4471-0347-9.

[9]

S. X. Ding, Data-Driven Design of Fault Diagnosis and Fault-Tolerant Control Systems, Advances in Industrial Control, Springer-Verlag, London, 2014. doi: 10.1007/978-1-4471-6410-4.

[10]

S. X. Ding, Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools, Springer Science & Business Media, 2008.

[11]

J. J. Downs and E. F. Vogel, A plant-wide industrial process control problem, Comput. Chem. Engrg., 17 (1993), 245-255.  doi: 10.1016/0098-1354(93)80018-I.

[12]

Z. GaoC. Cecati and S. X. Ding, A survey of fault diagnosis and fault-tolerant techniques-Part I: Fault diagnosis with model-based and signal-based approaches, IEEE Trans. Industrial Electron., 62 (2015), 3757-3767.  doi: 10.1109/TIE.2015.2417501.

[13]

S. M. Gross and R. Tibshirani, Collaborative regression, Biostatistics, 16 (2015), 326-338.  doi: 10.1093/biostatistics/kxu047.

[14]

H. Hotelling, Relations between two sets of variates, Biometrika, 28 (1936), 321-377.  doi: 10.1093/biomet/28.3-4.321.

[15]

W. HuB. CaiA. ZhangV. D. Calhoun and Y.-P. Wang, Deep collaborative learning with application to the study of multimodal brain development, IEEE Trans. Biomed. Engrg., 66 (2019), 3346-3359.  doi: 10.1109/TBME.2019.2904301.

[16]

Q. JiangS. X. DingY. Wang and X. Yan, Data-driven distributed local fault detection for large-scale processes based on the GA-regularized canonical correlation analysis, IEEE Trans. Industrial Electron., 64 (2017), 8148-8157.  doi: 10.1109/TIE.2017.2698422.

[17]

Q. Jiang and X. Yan, Multimode process monitoring using variational Bayesian inference and canonical correlation analysis, IEEE Trans. Automat. Sci. Engrg., 16 (2019), 1814-1824.  doi: 10.1109/TASE.2019.2897477.

[18]

J. Liu, S. Ji and J. Ye, Multi-task feature learning via efficient $\ell_{2, 1}$-norm minimization, preprint, arXiv: 1205.2631.

[19]

R. LiuY. YangL. Li and S. X. Ding, Key performance indicators based fault detection and isolation using data-driven approaches, IEEE Trans. Circuits-II, 68 (2021), 291-295.  doi: 10.1109/TCSII.2020.2993306.

[20]

Y. LiuB. LiuX. Zhao and M. Xie, A mixture of variational canonical correlation analysis for nonlinear and quality-relevant process monitoring, IEEE Trans. Industrial Electron., 65 (2018), 6478-6486.  doi: 10.1109/TIE.2017.2786253.

[21]

Y. LiuJ. ZengL. XieS. Luo and H. Su, Structured joint sparse principal component analysis for fault detection and isolation, IEEE Trans. Ind. Inform., 15 (2019), 2721-2731.  doi: 10.1109/TII.2018.2868364.

[22]

K. PengK. ZhangB. YouJ. Dong and Z. Wang, A quality-based nonlinear fault diagnosis framework focusing on industrial multimode batch processes, IEEE Trans. Industrial Electron., 63 (2016), 2615-2624.  doi: 10.1109/TIE.2016.2520906.

[23]

Y. SiY. Wang and D. Zhou, Key-performance-indicator-related process monitoring based on improved kernel partial least squares, IEEE Trans. Industrial Electron., 68 (2021), 2626-2636.  doi: 10.1109/TIE.2020.2972472.

[24]

Y. TaoH. ShiB. Song and S. Tan, A novel dynamic weight principal component analysis method and hierarchical monitoring strategy for process fault detection and diagnosis, IEEE Trans. Industrial Electron., 67 (2020), 7994-8004.  doi: 10.1109/TIE.2019.2942560.

[25]

X. XiuY. YangL. Kong and W. Liu, Data-driven process monitoring using structured joint sparse canonical correlation analysis, IEEE Trans. Circuits-II, 68 (2021), 361-365.  doi: 10.1109/TCSII.2020.2988054.

[26]

X. XiuY. YangL. Kong and W. Liu, Laplacian regularized robust principal component analysis for process monitoring, J. Process Contr., 92 (2020), 212-219.  doi: 10.1016/j.jprocont.2020.06.011.

[27]

X. XiuY. YangW. LiuL. Kong and M. Shang, An improved total variation regularized RPCA for moving object detection with dynamic background, J. Ind. Manag. Optim., 16 (2020), 1685-1698.  doi: 10.3934/jimo.2019024.

[28]

Y. YangS. X. Ding and L. Li, Parameterization of nonlinear observer-based fault detection systems, IEEE Trans. Automat. Control, 61 (2016), 3687-3692.  doi: 10.1109/TAC.2016.2532381.

[29]

S. YinS. X. DingA. HaghaniH. Hao and P. Zhang, A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process, J. Process Contr., 22 (2012), 1567-1581.  doi: 10.1016/j.jprocont.2012.06.009.

[30]

R. Y. ZhongX. XuE. Klotz and S. T. Newman, Intelligent manufacturing in the context of industry 4.0: A review, Engineering, 3 (2017), 616-630.  doi: 10.1016/J.ENG.2017.05.015.

Figure 1.  Comparison of CCA and the proposed SCR
Figure 2.  Detection strategy
Figure 3.  Illustration of detection indices
Figure 4.  Detection results for Type I
Figure 5.  Detection results for Type II
Figure 6.  Flowchart of the TE process
Figure 7.  Detection results for IDV(2) in the TE process
Figure 8.  Detection results for IDV(10) in the TE process
Figure 9.  Detection results for IDV(18) in the TE process
Figure 10.  Detection results for IDV(15) in the TE process
Figure 11.  Relative differences
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
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
Table 2.  Detection results in term of FDR and FAR
Fault No. CCA-r1 CCA-r2 SCR
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%
Fault No. CCA-r1 CCA-r2 SCR
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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