Skip to main content

Comparison of linear and nonlinear dimension reduction techniques for automated process monitoring of a decentralized wastewater treatment facility

Abstract

Multivariate statistical methods for online process monitoring have been widely applied to chemical, biological, and engineered systems. While methods based on principal component analysis (PCA) are popular, more recently kernel PCA (KPCA) and locally linear embedding (LLE) have been utilized to better model nonlinear process data. Additionally, various forms of dynamic and adaptive monitoring schemes have been proposed to address time-varying features in these processes. In this analysis, we extend a common simulation study in order to account for autocorrelation and nonstationarity in process data and comprehensively compare the monitoring performances of static, dynamic, adaptive, and adaptive–dynamic versions of PCA, KPCA, and LLE. Furthermore, we evaluate a nonparametric method to set thresholds for monitoring statistics and compare results with the standard parametric approaches. We then apply these methods to real-world data collected from a decentralized wastewater treatment system during normal and abnormal operations. From the simulation study, adaptive–dynamic versions of all three methods generally improve results when the process is autocorrelated and nonstationary. In the case study, adaptive–dynamic versions of PCA, KPCA, and LLE all flag a strong system fault, but nonparametric thresholds considerably reduce the number of false alarms for all three methods under normal operating conditions.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  1. Banadda N, Nhapi I, Kimwaga R (2011) A review of modeling approaches in activated sludge systems. Afr J Environ Sci Technol 5:397–408

    CAS  Google Scholar 

  2. Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15:1373–1396

    Article  Google Scholar 

  3. Chen Q, Wynne RJ, Goulding P, Sandoz D (2000) The application of principal component analysis and kernel density estimation to enhance process monitoring. Control Eng Pract 8:531–543

    Article  Google Scholar 

  4. Cheng C, Chiu MS (2005) Nonlinear process monitoring using JITL-PCA. Chemom Intell Lab Syst 76:1–13

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  6. Chetouani Y (2008) A neural network approach for the real-time detection of faults. Stoch Environ Res Risk Assess 22:339–349

    Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  9. 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 75:55–67

    CAS  Article  Google Scholar 

  10. Chouaib C, Mohamed-Faouzi H, Messaoud D (2013) Adaptive kernel principal component analysis for nonlinear dynamic process monitoring. In: 2013 9th Asian Control Conference (ASCC). IEEE, Istanbul, Turkey

  11. Dong D, McAvoy TJ (1996) Batch tracking via nonlinear principal component analysis. AIChE J 42:2199–2208

    CAS  Article  Google Scholar 

  12. Downs JJ, Vogel EF (1993) A plant-wide industrial process control problem. Comput Chem Eng 17:245–255

    CAS  Article  Google Scholar 

  13. García-Díaz CJ (2011) Monitoring and forecasting nitrate concentration in the groundwater using statistical process control and time series analysis: a case study. Stoch Environ Res Risk Assess 25:331–339

    Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  15. Gikas P, Tchobanoglous G (2009) The role of satellite and decentralized strategies in water resources management. J Environ Manag 90:144–152

    CAS  Article  Google Scholar 

  16. Ham J, Lee DD, Mika S, Sch\(\ddot{\text{o}}\)lkopf B (2004) A kernel view of the dimensionality reduction of manifolds. In: Proceedings of the Twenty-First International Conference on Machine Learning. ACM, New York, USA, p 47

  17. Hart JD (1996) Some automated methods of smoothing time-dependent data. J Nonparametr Stat 6:115–142

    Article  Google Scholar 

  18. Haykin S (1999) Neural Networks. Prentice-Hall, Englewood Cliffs

    Google Scholar 

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

    CAS  Article  Google Scholar 

  20. Jackson JE, Mudholkar GS (1979) Control procedures for residuals associated with principal component analysis. Technometrics 21:341–349

    Article  Google Scholar 

  21. Jones MC, Marron JS, Sheather SJ (1996) A brief survey of bandwidth selection for density estimation. J Am Stat Assoc 91:401–407

    Article  Google Scholar 

  22. Kayo O (2006) Locally linear embedding algorithm: extensions and applications. Universitatis Ouluensis, Oulu. http://herkules.oulu.fi/isbn9514280415/isbn9514280415.pdf. Accessed 18 March 2014

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

    Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  25. Kruger U, Zhou Y, Irwin GW (2004) Improved principal component monitoring of large-scale processes. J Process Control 14:879–888

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  27. Ku W, Storer RH, Georgakis C (1995) Disturbance detection and isolation by dynamic principal component analysis. Chemom Intell Lab Syst 30:179–196

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  29. Lee JM, Yoo CK, Lee IB (2004b) Statistical process monitoring with independent component analysis. J Process Control 14:467–485

    CAS  Article  Google Scholar 

  30. Leverenz HL, Asano A (2011) Wastewater reclamation and reuse system. Treatise Water Sci 4:63–71

    CAS  Article  Google Scholar 

  31. 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 96:132–143

    Article  Google Scholar 

  32. Maulud A, Wang D, Romagnoli JA (2006) A multi-scale orthogonal nonlinear strategy for multivariate statistical process monitoring. J Process Control 16:671–683

    CAS  Article  Google Scholar 

  33. Miao A, Song Z, Ge Z, Zhou L, Wen Q (2013) Nonlinear fault detection based on locally linear embedding. J Control Theory Appl 11:615–622

    Article  Google Scholar 

  34. Mina J, Verde C (2007) Fault detection for large scale systems using Dynamic Principal Components Analysis with adaptation. Int J Comput Commun Control 2:185–194

    Article  Google Scholar 

  35. Mjalli FS, Al-Asheh S, Alfadala HE (2007) Use of artificial neural network black-box modeling for the prediction of wastewater treatment plants performance. J Environ Manag 83:329–338

    CAS  Article  Google Scholar 

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

    Article  Google Scholar 

  37. Parneet P (2013) Comparing and contrasting traditional membrane bioreactor models with novel ones based on time series analysis. Membranes 3:16–23

    Article  Google Scholar 

  38. Rato T, Reis M (2013) Defining the structure of DPCA models and its impact on process monitoring and prediction activities. Chemom Intell Lab Syst 125:74–86

    CAS  Article  Google Scholar 

  39. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323–2326

    CAS  Article  Google Scholar 

  40. Russell EL, Chiang LH, Braatz RD (2000) Fault detection in industrial processes using canonical variate analysis and dynamic principal component analysis. Chemom Intell Lab Syst 51:81–93

    CAS  Article  Google Scholar 

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

    Article  Google Scholar 

  42. Sheather SJ (2009) A modern approach to regression with R, vol 58. Springer, New York

    Book  Google Scholar 

  43. Sheather SJ, Jones MC (1991) A reliable data-based bandwidth selection method for kernel density estimation. J R Stat Soc B 53:683–690

    Google Scholar 

  44. Sköld M (2001) A bias correction for cross-validation bandwidth selection when a kernel estimate is based on dependent data. J Time Ser Anal 22:493–503

    Article  Google Scholar 

  45. Tenenbaum JB, De Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290:2319–2323

    CAS  Article  Google Scholar 

  46. van Sprang ENM, Ramaker HJ, Westerhuis JA, Gurden SP, Smilde AK (2002) Critical evaluation of approaches for on-line batch process monitoring. Chem Eng Sci 57:3979–3991

    Article  Google Scholar 

  47. Vuono D, Henkel J, Benecke J, Cath TY, Reid T, Johnson L, Drewes JE (2013) Flexible hybrid membrane treatment systems for tailored nutrient management: a new paradigm in urban wastewater treatment. J Membr Sci 446:34–41

    CAS  Article  Google Scholar 

  48. Westerhuis JA, Gurden SP, Smilde AK (2000) Generalized contribution plots in multivariate statistical process monitoring. Chemom Intell Lab Syst 51:95–114

    CAS  Article  Google Scholar 

  49. Wold S, Esbensen K, Geladi P (1987) Principal component analysis. Chemom Intell Lab Syst 2:37–52

    CAS  Article  Google Scholar 

  50. Woodall WH, Montgomery DC (2014) Some current directions in the theory and application of statistical process monitoring. J Qual Technol 46:78–94

    Google Scholar 

  51. Zeng Y, Zhang Z, Kusiak A, Tang F, Wei X (2016) Optimizing wastewater pumping system with data-driven models and a greedy electromagnetism-like algorithm. Stoch Environ Res Risk Assess 30:1263–1275

    Article  Google Scholar 

  52. Zhang W, Liu X, Qi R, Jiang Y (2013) Improved locally linear embedding based method for nonlinear system fault detection. Int J Adv Comput Technol 5:515–523

    Google Scholar 

  53. Zhao S, Xu Y (2005) Multivariate statistical process monitoring using robust nonlinear principal component analysis. Tsinghua Sci Technol 10:582–586

    CAS  Article  Google Scholar 

  54. Zheng Y, Zhang L (2013) Fault diagnosis of wet flue gas desulphurization system based on KPCA. In: The 19th International Conference on Industrial Engineering and Engineering Management. Springer, Berlin

Download references

Acknowledgments

This work was partially supported by the National Science Foundation under Cooperative Agreement EEC-1028969 (ERC/ReNUWIt) and by the State of Colorado through the Higher Education Competitive Research Authority. The authors would like to thank two anonymous referees whose comments and suggestions have improved the content and presentation of this work.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Karen Kazor.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 102 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kazor, K., Holloway, R.W., Cath, T.Y. et al. Comparison of linear and nonlinear dimension reduction techniques for automated process monitoring of a decentralized wastewater treatment facility. Stoch Environ Res Risk Assess 30, 1527–1544 (2016). https://doi.org/10.1007/s00477-016-1246-2

Download citation

Keywords

  • Multivariate statistical process control
  • Nonlinear time-varying process
  • Principle component analysis
  • Kernel principal component analysis
  • Locally linear embedding