Process Monitoring Using Multiscale Methods

  • Chris Aldrich
  • Lidia Auret
Part of the Advances in Computer Vision and Pattern Recognition book series (ACVPR)


Principal component analysis is widely used in disturbance detection, isolation and diagnosis in industrial and chemical processes, and several extensions of the basic principal component methodology have been considered in previous chapters to handle features such as autocorrelation in data, time–frequency localization and nonlinearity. In this chapter, a statistical process control approach based on singular spectrum analysis is proposed. The method involves expressing a time series as the sum of identifiable components whose basis functions are obtained from measurements. Using decomposition by means of singular spectrum analysis, a multimodal representation is obtained that can be used together with existing statistical process control methods to construct a novel process monitoring scheme. It is observed that singular spectrum analysis can perform significantly better than other methods, particularly in detecting mean shift changes. However, the performance of the approach can degrade in the presence of parameter changes, as well as excessive autocorrelation of the variables.


Control Chart Exponentially Weighted Moving Average Statistical Process Control Multivariate Time Series Singular Spectrum Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abdi, H. (2007). Bonferroni and Šidàk corrections for multiple comparisons. In N. Salkind (Ed.), Encyclopedia of measurement and statistics (pp. 103–107). Thousand Oaks: Sage.Google Scholar
  2. Allen, M., & Smith, L. (1996). Monte Carlo SSA: Detecting irregular oscillations in the presence of coloured noise. Journal of Climate, 9, 3373–3404.CrossRefGoogle Scholar
  3. Aradhye, H., Bakshi, B. R., Strauss, R., & Davis, J. (2003). Multiscale SPC using wavelets: Theoretical analysis and properties. American Institution of Chemical Engineers Journal, 49(4), 939–958.CrossRefGoogle Scholar
  4. Bakshi, B. R. (1998). Multiscale PCA with applications to multivariate statistical process monitoring. AICHE Journal, 44(7), 1596–1610.CrossRefGoogle Scholar
  5. Bakshi, B. R. (1999). Multiscale analysis and modeling using wavelets. Journal of Chemometrics, 1999, 415–434.CrossRefGoogle Scholar
  6. Bersimis, S., Psarakis, S., & Panaretos, J. (2007). Multivariate statistical process control charts: An overview. Quality and Reliability Engineering International, 23, 517–543.CrossRefGoogle Scholar
  7. Broomhead, D., & King, G. (1986). Extracting qualitative dynamics from experimental data. Physica D, 20, 217–236.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Daubechies, I. (1992). Ten lectures on wavelets, Vol. 61 of CBMS-NSF series in Applied mathematics. Philadelphia: SIAM.Google Scholar
  9. Donoho, D., Johnstone, I., Kerkyacharian, G., & Picard, D. (1995). Wavelet shrinkage: Asymptopia? Journal of the Royal Statistical Society, Series B, 57, 301–369.MathSciNetzbMATHGoogle Scholar
  10. Dunia, R., & Qin, S. J. (1998). Joint diagnosis of process and sensor faults using principal control analysis. Control Engineering Practice, 6, 457–469.CrossRefGoogle Scholar
  11. Elsner, J., & Tsonis, A. (1996). Singular Spectrum Analysis – A new tool in time series analysis. New York: Plenum Press.CrossRefGoogle Scholar
  12. Fourie, S., & de Vaal, P. L. (2000). Advanced process monitoring using an online multiscale principal component analysis methodology. Computers and Chemical Engineering, 24, 755–760.CrossRefGoogle Scholar
  13. Ganesan, R., Das, T., & Venkataraman, V. (2004). Wavelet-based multiscale statistical process monitoring: A literature review. IIE Transactions, 36, 787–806.CrossRefGoogle Scholar
  14. Ghil, M., Allen, M., Dettinger, M., Ide, K., Kondrashov, D., Mann, M., Robertson, A., Saunders, A., Tian, Y., Varadi, F., & Yiou, P. (2002). Advanced spectral methods for climatic times series. Reviews of Geophysics, 40(1), 3.1–3.41.CrossRefGoogle Scholar
  15. Ghil, M., Yiou, P., Hallegatte, S., Malamud, B. D., Naveau, P., Soloviev, A., Friederichs, P., Keilis-Borok, V., Kondrashov, D., Kossobokov, V., Mestre, O., Nicolis, C., Rust, H. W., Shebalin, P., Vrac, M., Witt, A., & Zaliapin, I. (2011). Extreme events: Dynamics, statistics and prediction. Nonlinear Processes in Geophysics, 18(3), 295–350.
  16. Golyandina, N., Nekrutin, V., & Zhigljavsky, A. (2001). Analysis of time series structure: SSA and related techniques. Boca Raton: Chapman & Hall/CRC.CrossRefGoogle Scholar
  17. Harris, T., & Ross, W. (1991). Statistical process control procedures for correlated observations. Canadian Journal of Chemical Engineering, 69, 48–57.CrossRefGoogle Scholar
  18. Hassani, H., & Zhigljavksy, A. (2009). Singular spectrum analysis: Methodology and application to economics data. Journal of Systems Science and Complexity, 22, 372–394.MathSciNetCrossRefGoogle Scholar
  19. Huang, N., Shen, Z., Long, S., Wu, M., Shih, H., Zheng, Q., Yen, N. C., Tung, C., & Liu, H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London, Series A, 454, 903–995.MathSciNetzbMATHCrossRefGoogle Scholar
  20. Jackson, J. E. (1991). A user’s guide to principal components. New York: Wiley.zbMATHCrossRefGoogle Scholar
  21. Jemwa, G. T., & Aldrich, C. (2006). Classification of process dynamics with Monte Carlo singular spectrum analysis. Computers and Chemical Engineering, 30(5), 816–831.CrossRefGoogle Scholar
  22. Jolliffe, I. (2002). Principal component analysis (2nd ed.). New York: Springer.zbMATHGoogle Scholar
  23. Kano, M., Nagao, K., Hasebe, S., Hashimoto, I., Ohno, H., Strauss, R., & Bakshi, B. (2000). Comparison of statistical process monitoring methods: Application to the Eastman challenge problem. Computers and Chemical Engineering, 24, 175–181.CrossRefGoogle Scholar
  24. Kano, M., Nagao, K., Hasebe, S., Hashimoto, I., Ohno, H., Strauss, R., & Bakshi, B. (2002). Comparison of multivariate statistical process monitoring methods with applications to the Eastman challenge problem. Computers and Chemical Engineering, 26, 161–174.CrossRefGoogle Scholar
  25. Kantz, H., & Schreiber, T. (1997). Nonlinear time series analysis. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  26. Kautsky, J., & Turcajová, R. (1995). Adaptive wavelets for signal analysis. In Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns, CAIP’95 (pp.906–911). London: Springer.
  27. Kourti, T., & MacGregor, J. F. (1995). Process analysis, monitoring and diagnosis, using multivariate projection methods. Chemometrics and Intelligent Laboratory Systems, 28, 3–21.Google Scholar
  28. Kourti, T., Lee, J., & MacGregor, J. F. (1996). Experiences with industrial applications of projection methods for multivariate statistical process control. Computers and Chemical Engineering, 20, S745–S750.CrossRefGoogle Scholar
  29. Kresta, J., MacGregor, J. F., & Martile, T. (1991). Multivariate statistical monitoring of process operating performance. Canadian Journal of Chemical Engineering, 69, 35–47.CrossRefGoogle Scholar
  30. Ku, W., Storer, R. H., & Georgakis, C. (1995). Disturbance detection and isolation by dynamic principal component analysis. Chemometrics and Intelligent Laboratory Systems, 30, 179–196.CrossRefGoogle Scholar
  31. Lee, J. M., Yoo, C., Choi, S., Vanrolleghem, W., & Lee, I.-B. (2004). Nonlinear process monitoring using kernel principal component analysis. Chemical Engineering Science, 59, 223–234.CrossRefGoogle Scholar
  32. Lee, D., Park, J., & van Rolleghem, P. (2005). Adaptive multiscale principal analysis for online monitoring of a sequencing batch reactor. Journal of Biotechnology, 116, 195–210.CrossRefGoogle Scholar
  33. Lennox, J., & Rosen, C. (2002). Adaptive multiscale principal component analysis for online monitoring of wastewater treatment. Water Science and Technology, 45, 227–235.Google Scholar
  34. MacGregor, J. F., & Kourti, T. (1995). Statistical process control of multivariate processes. Control Engineering Practice, 3, 403–414.CrossRefGoogle Scholar
  35. Mallat, S. (1989). A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693.zbMATHCrossRefGoogle Scholar
  36. Mallat, S. (1999). A wavelet tour of signal processing (2nd ed.). San Diego: Academic.zbMATHGoogle Scholar
  37. Montgomery, D. C. (1996). Introduction to statistical quality control. New York: Wiley.Google Scholar
  38. Montgomery, D. C., & Mastrangelo, C. (1991). Some statistical process control methods for autocorrelated data. Journal of Quality Technology, 23, 179–193.Google Scholar
  39. Moskvina, V., & Zhigljavsky, A. (2003). An algorithm based on singular spectrum analysis for change-point detection. Communications in Statistics: Simulation and Computation, 32, 319–352.MathSciNetzbMATHCrossRefGoogle Scholar
  40. Nomikos, P., & MacGregor, J. F. (1995a). Multivariate SPC charts for monitoring batch processes. Technometrics, 37(1), 41–59.zbMATHCrossRefGoogle Scholar
  41. Nomikos, P., & MacGregor, J. F. (1995b). Multi-way part least squares in monitoring batch processes. Chemometrics and Intelligent Laboratory Systems, 30, 97–108.CrossRefGoogle Scholar
  42. Plaut, G., & Vautard, R. (1994). Spells of low-frequency oscillations and weather regimes in the Northern Hemisphere. Journal of the Atmospheric Sciences, 51, 210–236.MathSciNetCrossRefGoogle Scholar
  43. Reis, M., Saraiva, P., & Bakshi, B. R. (2008). Multiscale statistical process control using wavelet packets. AICHE Journal, 54(9), 2366–2378.CrossRefGoogle Scholar
  44. Runger, G. C., & Willemain, T. R. (1995). Model-based and model-free control of autocorrelated processes. Journal of Quality Technology, 27(4), 283–292.Google Scholar
  45. Saucier, A. (2005). Construction of data-adaptive orthogonal wavelet bases with an extension of principal component analysis. Applied Computer Harmonics Analysis, 18, 300–328.MathSciNetzbMATHCrossRefGoogle Scholar
  46. Sauer, T., Yorke, J. A., & Casdagli, M. (1991). Embedology. Journal of Statistical Physics, 65, 579–616.MathSciNetzbMATHCrossRefGoogle Scholar
  47. Shaffer, J. P. (1995). Multiple hypothesis testing. Annual Reviews in Psychology, 46, 561–584.CrossRefGoogle Scholar
  48. Strang, G. (2009). Introduction to linear algebra. Wellesley: Wellesley-Cambridge.Google Scholar
  49. Tiao, G., & Box, G. (1981). Modeling multiple time series with applications. Journal of the American Statistical Association, 76, 802–816.MathSciNetzbMATHGoogle Scholar
  50. Tjostheim, D., & Paulsen, J. (1982). Empirical identification of multiple time series. Journal of Time Series Analysis, 3, 265–282.MathSciNetzbMATHCrossRefGoogle Scholar
  51. Vautard, R., & Ghil, M. (1989). Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D, 35, 395–424.MathSciNetzbMATHCrossRefGoogle Scholar
  52. Vautard, R., Yiou, P., & Ghil, M. (1992). Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Physica D, 58, 95–126.CrossRefGoogle Scholar
  53. Westerhuis, J., Kourti, T., & MacGregor, J. F. (1998). Analysis of multiblock and hierarchical PCA and PLS models. Journal of Chemometrics, 12, 301–321.CrossRefGoogle Scholar
  54. Wierda, S. (1994). Multivariate statistical process control – Results and directions for future research. Statistica Neerlandica, 48, 147–168.MathSciNetzbMATHCrossRefGoogle Scholar
  55. Wilson, G. (1973). The estimation of parameters in multivariate time series models. Journal of the Royal Statistical Society, Series B, 35, 76–85.zbMATHGoogle Scholar
  56. Wise, B., & Gallagher, N. (1996). The process chemometrics approach to process monitoring and fault detection. Journal of Process Control, 6(6), 329–348.CrossRefGoogle Scholar
  57. Yiou, P., Sornette, D., & Ghil, M. (2000). Data-adaptive wavelets and multi-scale singular-spectrum analysis. Physica D, 142, 254–290.MathSciNetzbMATHCrossRefGoogle Scholar
  58. Yoon, S., & MacGregor, J. F. (2004). Principal component analysis of multiscale data for process monitoring and fault diagnosis. AICHE Journal, 50(11), 2891–2903.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Chris Aldrich
    • 1
    • 2
  • Lidia Auret
    • 2
  1. 1.Western Australian School of MinesCurtin UniversityPerthAustralia
  2. 2.Department of Process EngineeringUniversity of StellenboschStellenboschSouth Africa

Personalised recommendations