Skip to main content
SpringerLink
Log in

Non-linear process monitoring using kernel principal component analysis: A review of the basic and modified techniques with industrial applications

  • Review
  • Published:
Brazilian Journal of Chemical Engineering Aims and scope Submit manuscript

Abstract

Timely detection and diagnosis of process abnormality in industries is crucial for minimizing downtime and maximizing profit. Among various process monitoring and fault detection techniques, principal component analysis (PCA) and its different variants are probably the ones with maximum applications. Because of the linearity constraint of the conventional PCA, some non-linear variants of PCA have been proposed. Among different non-linear variants of PCA, the kernel PCA (KPCA) has gained maximum attention in the field of industrial fault detection. This article revisits the basic KPCA algorithm along with different limitations of KPCA and the crucial open issues in design of KPCA based monitoring system. Different modifications proposed by different researchers are reviewed. Strategies adopted by various researchers for optimal selection of kernel parameter and number of principal components are also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Alauddin M, Khan F, Imtiaz S, Ahmed S (2018) A bibliometric review and analysis of data-driven fault detection and diagnosis methods for process systems. Ind Eng Chem Res 57(32):10719–10735

    Article  CAS  Google Scholar 

  • Apsemidis A, Psarakis S, Moguerza JM (2020) A review of machine learning kernel methods in statistical process monitoring. Comput Ind Eng 142:106376

    Article  Google Scholar 

  • Bencheikh, F., Harkat, M. F., Kouadri, A., & Bensmail, A. (2020). New reduced kernel PCA for fault detection and diagnosis in cement rotary kiln. Chemometrics and Intelligent Laboratory Systems, 104091.

  • Cai. D (2014). Kernel PCA. http://www.cad.zju.edu.cn/home/dengcai/Data/code/KPCA.m

  • Cano E.L., Moguerza J.M., Corcoba M.P. (2015) Nonlinear Profiles with R. In: Quality Control with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-24046-6_10

  • Cao Y, Jan NM, Huang B, Fang M, Wang Y, Gui W (2021) Multimodal process monitoring based on variational Bayesian PCA and Kullback-Leibler divergence between mixture models. Chemometrics Intell Lab Syst 210:104230

    Article  CAS  Google Scholar 

  • Cheng CY, Hsu CC, Chen MC (2010) Adaptive kernel principal component analysis (KPCA) for monitoring small disturbances of nonlinear processes. Ind Eng Chem Res 49(5):2254–2262

    Article  CAS  Google Scholar 

  • Cheng, H., Wu, J., Huang, D., Liu, Y., & Wang, Q. (2021). Robust adaptive boosted canonical correlation analysis for quality-relevant process monitoring of wastewater treatment. ISA transactions.

  • Cho JH, Lee JM, Choi SW, Lee D, Lee IB (2005) Fault identification for process monitoring using kernel principal component analysis. Chem Eng Sci 60(1):279–288

    Article  CAS  Google Scholar 

  • Choi SW, Lee IB (2004) Nonlinear dynamic process monitoring based on dynamic kernel PCA. Chem Eng Sci 59(24):5897–5908

    Article  CAS  Google Scholar 

  • Choi SW, Lee C, Lee JM, Park JH, Lee IB (2005) Fault detection and identification of nonlinear processes based on kernel PCA. Chemom Intell Lab Syst 75(1):55–67

    Article  CAS  Google Scholar 

  • Cui P, Li J, Wang G (2008) Improved kernel principal component analysis for fault detection. Expert Syst Appl 34(2):1210–1219

    Article  Google Scholar 

  • Deng X, Cai P, Cao Y, Wang P (2020) Two-step localized kernel principal component analysis based incipient fault diagnosis for nonlinear industrial processes. Ind Eng Chem Res 59(13):5956–5968

    Article  CAS  Google Scholar 

  • Deng X, Tian X, Chen S (2013) Modified kernel principal component analysis based on local structure analysis and its application to nonlinear process fault diagnosis. Chemom Intell Lab Syst 127:195–209

    Article  CAS  Google Scholar 

  • Dong D, McAvoy TJ (1996) Nonlinear principal component analysis—based on principal curves and neural networks. Comput Chem Eng 20(1):65–78

    Article  CAS  Google Scholar 

  • Elaissi I, Jaffel I, Taouali O, Messaoud H (2013) Online prediction model based on the SVD–KPCA method. ISA Trans 52(1):96–104

    Article  PubMed  Google Scholar 

  • Fazai R, Taouali O, Harkat MF, Bouguila N (2016) A new fault detection method for nonlinear process monitoring. Int J Adv Manuf Technol 87(9–12):3425–3436

    Article  Google Scholar 

  • Fezai R, Mansouri M, Taouali O, Harkat MF, Bouguila N (2018) Online reduced kernel principal component analysis for process monitoring. J Process Control 61:1–11

    Article  CAS  Google Scholar 

  • Ge Z, Song Z, Ding SX, Huang B (2017) Data mining and analytics in the process industry: the role of machine learning. IEEE Access 5:20590–20616

    Article  Google Scholar 

  • Ge Z, Yang C, Song Z (2009) Improved kernel PCA-based monitoring approach for nonlinear processes. Chem Eng Sci 64(9):2245–2255

    Article  CAS  Google Scholar 

  • Geng Z, Zhu Q (2005) Multiscale nonlinear principal component analysis (NLPCA) and its application for chemical process monitoring. Ind Eng Chem Res 44(10):3585–3593

    Article  CAS  Google Scholar 

  • Guo L, Wu P, Gao J, Lou S (2019) Sparse kernel principal component analysis via sequential approach for nonlinear process monitoring. IEEE Access 7:47550–47563

    Article  Google Scholar 

  • Hamrouni I, Lahdhiri H, ben Abdellafou K, Taouali O (2020) Fault detection of uncertain nonlinear process using reduced interval kernel principal component analysis (RIKPCA). Int J Adv Manuf Technol 106(9):4567–4576

    Article  Google Scholar 

  • Harkat, M. F., Kouadri, A., Fezai, R., Mansouri, M., Nounou, H., & Nounou, M. (2020) Machine Learning-Based Reduced Kernel PCA Model for Nonlinear Chemical Process Monitoring. J Control Autom Electr Syst 1–14.

  • He Q, Kong F, Yan R (2007) Subspace-based gearbox condition monitoring by kernel principal component analysis. Mech Syst Signal Process 21(4):1755–1772

    Article  Google Scholar 

  • Hiden HG, Willis MJ, Tham MT, Montague GA (1999) Non-linear principal components analysis using genetic programming. Comput Chem Eng 23(3):413–425

    Article  CAS  Google Scholar 

  • Hoegaerts L, De Lathauwer L, Goethals I, Suykens JA, Vandewalle J, De Moor B (2007) Efficiently updating and tracking the dominant kernel principal components. Neural Netw 20(2):220–229

    Article  CAS  PubMed  Google Scholar 

  • Huang K, Wu Y, Wen H, Liu Y, Yang C, Gui W (2020) Distributed dictionary learning for high-dimensional process monitoring. Control Eng Pract 98:104386

    Article  Google Scholar 

  • Jaffel I, Taouali O, Harkat MF, Messaoud H (2016) Moving window KPCA with reduced complexity for nonlinear dynamic process monitoring. ISA Trans 64:184–192

    Article  PubMed  Google Scholar 

  • Jaffel I, Taouali O, Harkat MF, Messaoud H (2017) Kernel principal component analysis with reduced complexity for nonlinear dynamic process monitoring. Int J Adv Manuf Technol 88(9–12):3265–3279

    Article  Google Scholar 

  • Jia F, Martin EB, Morris AJ (2000) Non-linear principal components analysis with application to process fault detection. Int J Syst Sci 31(11):1473–1487

    Article  Google Scholar 

  • Jia M, Xu H, Liu X, Wang N (2012) The optimization of the kind and parameters of kernel function in KPCA for process monitoring. Comput Chem Eng 46:94–104

    Article  CAS  Google Scholar 

  • Jiang Q, Yan X (2018) Parallel PCA–KPCA for nonlinear process monitoring. Control Eng Pract 80:17–25

    Article  Google Scholar 

  • Joe Qin S (2003) Statistical process monitoring: basics and beyond. J Chemometrics J Chemometrics Soc 17(8–9):480–502

    Article  CAS  Google Scholar 

  • Khediri IB, Limam M, Weihs C (2011) Variable window adaptive kernel principal component analysis for nonlinear nonstationary process monitoring. Comput Ind Eng 61(3):437–446

    Article  Google Scholar 

  • Kim KI, Franz MO, Scholkopf B (2005) Iterative kernel principal component analysis for image modeling. IEEE Trans Pattern Anal Mach Intell 27(9):1351–1366

    Article  PubMed  Google Scholar 

  • Kitayama M. (2020). MATLAB-Kernel-PCA. GitHub; https://github.com/kitayama1234/MATLAB-Kernel-PCA.

  • Kramer MA (1991) Nonlinear principal component analysis using autoassociative neural networks. AIChE J 37(2):233–243

    Article  CAS  Google Scholar 

  • Kruger U, Antory D, Hahn J, Irwin GW, McCullough G (2005) Introduction of a nonlinearity measure for principal component models. Comput Chem Eng 29(11–12):2355–2362

    Article  CAS  Google Scholar 

  • Lahdhiri H, Elaissi I, Taouali O, Harakat MF, Messaoud H (2018) Nonlinear process monitoring based on new reduced Rank-KPCA method. Stoch Env Res Risk Assess 32(6):1833–1848

    Article  Google Scholar 

  • Lee S, Kwak M, Tsui KL, Kim SB (2019) Process monitoring using variational autoencoder for high-dimensional nonlinear processes. Eng Appl Artif Intell 83:13–27

    Article  Google Scholar 

  • Lee DS, Lee MW, Woo SH, Kim YJ, Park JM (2006) Multivariate online monitoring of a full-scale biological anaerobic filter process using kernel-based algorithms. Ind Eng Chem Res 45(12):4335–4344

    Article  CAS  Google Scholar 

  • Lee JM, Yoo C, Choi SW, Vanrolleghem PA, Lee IB (2004) Nonlinear process monitoring using kernel principal component analysis. Chem Eng Sci 59(1):223–234

    Article  CAS  Google Scholar 

  • Li N, Yang Y (2015) Ensemble kernel principal component analysis for improved nonlinear process monitoring. Ind Eng Chem Res 54(1):318–329

    Article  CAS  Google Scholar 

  • Liu J, Chen J, Wang D (2021) Linear and exponential fault-assistant feature extraction methods for process monitoring. Control Eng Pract 109:104732

    Article  Google Scholar 

  • Liu X, Kruger U, Littler T, Xie L, Wang S (2009) Moving window kernel PCA for adaptive monitoring of nonlinear processes. Chemom Intell Lab Syst 96(2):132–143

    Article  CAS  Google Scholar 

  • Ma, J., & Jiang, J. (2012). Detection and identification of faults in npp instruments using kernel principal component analysis. J Eng Gas Turbines Power, 134(3).

  • Mansouri M, Nounou M, Nounou H, Karim N (2016) Kernel PCA-based GLRT for nonlinear fault detection of chemical processes. J Loss Prev Process Ind 40:334–347

    Article  CAS  Google Scholar 

  • Mika, S., Schölkopf, B., Smola, A. J., Müller, K. R., Scholz, M., & Rätsch, G. (1999). Kernel PCA and de-noising in feature spaces. In Advances in neural information processing systems (pp. 536–542).

  • Muller KR, Mika S, Ratsch G, Tsuda K, Scholkopf B (2001) An introduction to kernel-based learning algorithms. IEEE Trans Neural Networks 12(2):181–201

    Article  CAS  PubMed  Google Scholar 

  • Navi M, Meskin N, Davoodi M (2018) Sensor fault detection and isolation of an industrial gas turbine using partial adaptive KPCA. J Process Control 64:37–48

    Article  CAS  Google Scholar 

  • Nguyen VH, Golinval JC (2010) Fault detection based on kernel principal component analysis. Eng Struct 32(11):3683–3691

    Article  Google Scholar 

  • Park CH, Park H (2005) Nonlinear discriminant analysis using kernel functions and the generalized singular value decomposition. SIAM J Matrix Anal Appl 27(1):87–102

    Article  Google Scholar 

  • Qin SJ (2003) Statistical process monitoring: basics and beyond. J Chemometrics J Chemometrics Soc 17(8–9):480–502

    Article  CAS  Google Scholar 

  • Qin SJ (2012) Survey on data-driven industrial process monitoring and diagnosis. Annu Rev Control 36(2):220–234

    Article  Google Scholar 

  • Qiu K. (2020). Kernel Principal Component Analysis (KPCA), MATLAB Code for non-linear dimensionality reduction, fault detection, and fault diagnosis through the use of kernels. https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA

  • Rathi, Y., Dambreville, S., & Tannenbaum, A. (2006, February). Statistical shape analysis using kernel PCA. In Image processing: algorithms and systems, neural networks, and machine learning (Vol. 6064, p. 60641B). International Society for Optics and Photonics.

  • Rosipal R, Girolami M (2001) An expectation-maximization approach to nonlinear component analysis. Neural Comput 13(3):505–510

    Article  Google Scholar 

  • Saegusa R, Sakano H, Hashimoto S (2004) Nonlinear principal component analysis to preserve the order of principal components. Neurocomputing 61:57–70

    Article  Google Scholar 

  • Samuel RT, Cao Y (2016) Nonlinear process fault detection and identification using kernel PCA and kernel density estimation. Syst Sci Control Eng 4(1):165–174

    Article  Google Scholar 

  • Schölkopf B, Smola A, Müller KR (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10(5):1299–1319

    Article  Google Scholar 

  • Smola, A., Schölkopf, B., 2006 {on-line}. KPCA code in Software section of Kernel machines site. http://www.kernel-machines.org/code/kpca_toy.m

  • Sumana C, Bhushan M, Venkateswarlu CH, Gudi RD (2011) Improved nonlinear process monitoring using KPCA with sample vector selection and combined index. Asia-Pac J Chem Eng 6(3):460–469

    Article  CAS  Google Scholar 

  • Sun R, Tsung F, Qu L (2007) Evolving kernel principal component analysis for fault diagnosis. Comput Ind Eng 53(2):361–371

    Article  Google Scholar 

  • Tan S, Mayrovouniotis ML (1995) Reducing data dimensionality through optimizing neural network inputs. AIChE J 41(6):1471–1480

    Article  CAS  Google Scholar 

  • Taouali O, Jaffel I, Lahdhiri H, Harkat MF, Messaoud H (2016) New fault detection method based on reduced kernel principal component analysis (RKPCA). Int J Adv Manuf Technol 85(5–8):1547–1552

    Article  Google Scholar 

  • Wang H, Yao M (2015) Fault detection of batch processes based on multivariate functional kernel principal component analysis. Chemom Intell Lab Syst 149:78–89

    Article  CAS  Google Scholar 

  • Wang, T., Qiao, M., Zhang, M., Yang, Y., & Snoussi, H. (2018). Data-driven prognostic method based on self-supervised learning approaches for fault detection. J Intell Manuf, 1–9.

  • Xu X, Ding J (2021) Decentralized dynamic process monitoring based on manifold regularized slow feature analysis. J Process Control 98:79–91

    Article  CAS  Google Scholar 

  • Yin S, Ding SX, Xie X, Luo H (2014) A review on basic data-driven approaches for industrial process monitoring. IEEE Trans Industr Electron 61(11):6418–6428

    Article  Google Scholar 

  • Yoo CK, Lee IB (2006) Nonlinear multivariate filtering and bioprocess monitoring for supervising nonlinear biological processes. Process Biochem 41(8):1854–1863

    Article  CAS  Google Scholar 

  • Zhang Y (2009) Enhanced statistical analysis of nonlinear processes using KPCA KICA and SVM. Chem Eng Sci 64(5):801–811

    Article  CAS  Google Scholar 

  • Zhang Y, Li S, Teng Y (2012) Dynamic processes monitoring using recursive kernel principal component analysis. Chem Eng Sci 72:78–86

    Article  CAS  Google Scholar 

  • Zhang Y, Ma C (2011) Fault diagnosis of nonlinear processes using multiscale KPCA and multiscale KPLS. Chem Eng Sci 66(1):64–72

    Article  CAS  Google Scholar 

  • Zhang Y, Qin SJ (2008) Improved nonlinear fault detection technique and statistical analysis. AIChE J 54(12):3207–3220

    Article  CAS  Google Scholar 

  • Zhang, Q., Li, P., Lang, X., & Miao, A. (2020). Improved dynamic kernel principal component analysis for fault detection. Measurement, 107738.

  • Zheng W, Zou C, Zhao L (2005) An improved algorithm for kernel principal component analysis. Neural Process Lett 22(1):49–56

    Article  Google Scholar 

  • Zhou Z, Du N, Xu J, Li Z, Wang P, Zhang J (2019) Randomized kernel principal component analysis for modeling and monitoring of nonlinear industrial processes with massive data. Ind Eng Chem Res 58(24):10410–10417

    Article  CAS  Google Scholar 

Download references

Funding

There is no funding received for this work.

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031, India

    Ajaya Kumar Pani

Authors
  1. Ajaya Kumar Pani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ajaya Kumar Pani.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pani, A.K. Non-linear process monitoring using kernel principal component analysis: A review of the basic and modified techniques with industrial applications. Braz. J. Chem. Eng. 39, 327–344 (2022). https://doi.org/10.1007/s43153-021-00125-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s43153-021-00125-2

Keywords

Search

Navigation