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
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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[10]

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

[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.  Google Scholar

[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.  Google Scholar

[13]

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

[14]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[18]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[10]

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

[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.  Google Scholar

[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.  Google Scholar

[13]

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

[14]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[18]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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%
[1]

Yunhai Xiao, Soon-Yi Wu, Bing-Sheng He. A proximal alternating direction method for $\ell_{2,1}$-norm least squares problem in multi-task feature learning. Journal of Industrial & Management Optimization, 2012, 8 (4) : 1057-1069. doi: 10.3934/jimo.2012.8.1057

[2]

Chengxiang Wang, Li Zeng, Wei Yu, Liwei Xu. Existence and convergence analysis of $\ell_{0}$ and $\ell_{2}$ regularizations for limited-angle CT reconstruction. Inverse Problems & Imaging, 2018, 12 (3) : 545-572. doi: 10.3934/ipi.2018024

[3]

Ying Lin, Rongrong Lin, Qi Ye. Sparse regularized learning in the reproducing kernel banach spaces with the $ \ell^1 $ norm. Mathematical Foundations of Computing, 2020, 3 (3) : 205-218. doi: 10.3934/mfc.2020020

[4]

Jun Wang, Xing Tao Wang. Sparse signal reconstruction via the approximations of $ \ell_{0} $ quasinorm. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1907-1925. doi: 10.3934/jimo.2019035

[5]

Pengbo Geng, Wengu Chen. Unconstrained $ \ell_1 $-$ \ell_2 $ minimization for sparse recovery via mutual coherence. Mathematical Foundations of Computing, 2020, 3 (2) : 65-79. doi: 10.3934/mfc.2020006

[6]

Pia Heins, Michael Moeller, Martin Burger. Locally sparse reconstruction using the $l^{1,\infty}$-norm. Inverse Problems & Imaging, 2015, 9 (4) : 1093-1137. doi: 10.3934/ipi.2015.9.1093

[7]

Qi Li, Hong Xue, Changxin Lu. Event-based fault detection for interval type-2 fuzzy systems with measurement outliers. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1301-1328. doi: 10.3934/dcdss.2020412

[8]

Martene L. Fair, Stephen L. Campbell. Active incipient fault detection in continuous time systems with multiple simultaneous faults. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 211-224. doi: 10.3934/naco.2011.1.211

[9]

David L. Russell. Coefficient identification and fault detection in linear elastic systems; one dimensional problems. Mathematical Control & Related Fields, 2011, 1 (3) : 391-411. doi: 10.3934/mcrf.2011.1.391

[10]

Zhanyou Ma, Pengcheng Wang, Wuyi Yue. Performance analysis and optimization of a pseudo-fault Geo/Geo/1 repairable queueing system with N-policy, setup time and multiple working vacations. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1467-1481. doi: 10.3934/jimo.2017002

[11]

Yuhong Dai, Nobuo Yamashita. Convergence analysis of sparse quasi-Newton updates with positive definite matrix completion for two-dimensional functions. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 61-69. doi: 10.3934/naco.2011.1.61

[12]

Shuhua Wang, Zhenlong Chen, Baohuai Sheng. Convergence of online pairwise regression learning with quadratic loss. Communications on Pure & Applied Analysis, 2020, 19 (8) : 4023-4054. doi: 10.3934/cpaa.2020178

[13]

Lianjun Zhang, Lingchen Kong, Yan Li, Shenglong Zhou. A smoothing iterative method for quantile regression with nonconvex $ \ell_p $ penalty. Journal of Industrial & Management Optimization, 2017, 13 (1) : 93-112. doi: 10.3934/jimo.2016006

[14]

Huining Qiu, Xiaoming Chen, Wanquan Liu, Guanglu Zhou, Yiju Wang, Jianhuang Lai. A fast $\ell_1$-solver and its applications to robust face recognition. Journal of Industrial & Management Optimization, 2012, 8 (1) : 163-178. doi: 10.3934/jimo.2012.8.163

[15]

Wei Li, Yun Teng. Enterprise inefficient investment behavior analysis based on regression analysis. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1015-1025. doi: 10.3934/dcdss.2019069

[16]

Braxton Osting, Jérôme Darbon, Stanley Osher. Statistical ranking using the $l^{1}$-norm on graphs. Inverse Problems & Imaging, 2013, 7 (3) : 907-926. doi: 10.3934/ipi.2013.7.907

[17]

Peili Li, Xiliang Lu, Yunhai Xiao. Smoothing Newton method for $ \ell^0 $-$ \ell^2 $ regularized linear inverse problem. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021044

[18]

Victor Meng Hwee Ong, David J. Nott, Taeryon Choi, Ajay Jasra. Flexible online multivariate regression with variational Bayes and the matrix-variate Dirichlet process. Foundations of Data Science, 2019, 1 (2) : 129-156. doi: 10.3934/fods.2019006

[19]

Jiang Xie, Junfu Xu, Celine Nie, Qing Nie. Machine learning of swimming data via wisdom of crowd and regression analysis. Mathematical Biosciences & Engineering, 2017, 14 (2) : 511-527. doi: 10.3934/mbe.2017031

[20]

Bingzheng Li, Zhengzhan Dai. Error analysis on regularized regression based on the Maximum correntropy criterion. Mathematical Foundations of Computing, 2020, 3 (1) : 25-40. doi: 10.3934/mfc.2020003

 Impact Factor: 

Metrics

  • PDF downloads (78)
  • HTML views (176)
  • Cited by (0)

Other articles
by authors

[Back to Top]