Process Monitoring Using Multiscale Methods

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.

[1]  S. J. Wierda Multivariate statistical process control—recent results and directions for future research , 1994 .

[2]  Andrew L. Rukhin,et al.  Analysis of Time Series Structure SSA and Related Techniques , 2002, Technometrics.

[3]  Pedro M. Saraiva,et al.  Multiscale statistical process control using wavelet packets , 2008 .

[4]  A. Saucier Construction of data-adaptive orthogonal wavelet bases with an extension of principal component analysis , 2005 .

[5]  Theodora Kourti,et al.  Statistical Process Control of Multivariate Processes , 1994 .

[6]  John F. MacGregor,et al.  Multi-way partial least squares in monitoring batch processes , 1995 .

[7]  D. Tjøstheim,et al.  EMPIRICAL IDENTIFICATION OF MULTIPLE TIME SERIES , 1982 .

[8]  S. H. Fourie,et al.  Advanced process monitoring using an on-line non-linear multiscale principal component analysis methodology , 2000 .

[9]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Stelios Psarakis,et al.  Multivariate statistical process control charts: an overview , 2007, Qual. Reliab. Eng. Int..

[11]  Vladimir Kossobokov,et al.  Extreme events: dynamics, statistics and prediction , 2011 .

[12]  Manabu Kano,et al.  Comparison of multivariate statistical process monitoring methods with applications to the Eastman challenge problem , 2002 .

[13]  T. Harris,et al.  Statistical process control procedures for correlated observations , 1991 .

[14]  George C. Runger,et al.  Model-Based and Model-Free Control of Autocorrelated Processes , 1995 .

[15]  Jaroslav Kautsky,et al.  Adaptive Wavelets for Signal Analysis , 1995, CAIP.

[16]  J. Edward Jackson,et al.  A User's Guide to Principal Components: Jackson/User's Guide to Principal Components , 2004 .

[17]  Seongkyu Yoon,et al.  Principal‐component analysis of multiscale data for process monitoring and fault diagnosis , 2004 .

[18]  Bhavik R. Bakshi,et al.  Multiscale SPC using wavelets: Theoretical analysis and properties , 2003 .

[19]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[20]  G. C. Tiao,et al.  Modeling Multiple Time Series with Applications , 1981 .

[21]  Theodora Kourti,et al.  Process analysis, monitoring and diagnosis, using multivariate projection methods , 1995 .

[22]  Ignacio E. Grossmann,et al.  Computers and Chemical Engineering , 2014 .

[23]  I. Johnstone,et al.  Wavelet Shrinkage: Asymptopia? , 1995 .

[24]  R. Vautard,et al.  Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series , 1989 .

[25]  Michael Ghil,et al.  ADVANCED SPECTRAL METHODS FOR CLIMATIC TIME SERIES , 2002 .

[26]  R. Vautard,et al.  Singular-spectrum analysis: a toolkit for short, noisy chaotic signals , 1992 .

[27]  S. Mallat A wavelet tour of signal processing , 1998 .

[28]  Bhavik R. Bakshi,et al.  Multiscale analysis and modeling using wavelets , 1999 .

[29]  J. Macgregor,et al.  Experiences with industrial applications of projection methods for multivariate statistical process control , 1996 .

[30]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[31]  G. P. King,et al.  Extracting qualitative dynamics from experimental data , 1986 .

[32]  J. Macgregor,et al.  Analysis of multiblock and hierarchical PCA and PLS models , 1998 .

[33]  C. Rosen,et al.  Adaptive multiscale principal components analysis for online monitoring of wastewater treatment. , 2002, Water science and technology : a journal of the International Association on Water Pollution Research.

[34]  Leonard A. Smith,et al.  Monte Carlo SSA: Detecting irregular oscillations in the Presence of Colored Noise , 1996 .

[35]  Manabu Kano,et al.  Comparison of statistical process monitoring methods: application to the Eastman challenge problem , 2000 .

[36]  V. Moskvina,et al.  An Algorithm Based on Singular Spectrum Analysis for Change-Point Detection , 2003 .

[37]  J. Shaffer Multiple Hypothesis Testing , 1995 .

[38]  Thomas E. Marlin,et al.  Multivariate statistical monitoring of process operating performance , 1991 .

[39]  D. Sornette,et al.  Data-adaptive wavelets and multi-scale singular-spectrum analysis , 1998, chao-dyn/9810034.

[40]  Christos Georgakis,et al.  Disturbance detection and isolation by dynamic principal component analysis , 1995 .

[41]  S. Joe Qin,et al.  Joint diagnosis of process and sensor faults using principal component analysis , 1998 .

[42]  J. Elsner,et al.  Singular Spectrum Analysis: A New Tool in Time Series Analysis , 1996 .

[43]  Barry M. Wise,et al.  The process chemometrics approach to process monitoring and fault detection , 1995 .

[44]  Peter A Vanrolleghem,et al.  Adaptive multiscale principal component analysis for on-line monitoring of a sequencing batch reactor. , 2005, Journal of biotechnology.

[45]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[46]  I. Jolliffe Principal Component Analysis , 2002 .

[47]  Tapas K. Das,et al.  Wavelet-based multiscale statistical process monitoring: A literature review , 2004 .

[48]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[49]  B. Bakshi Multiscale PCA with application to multivariate statistical process monitoring , 1998 .

[50]  Anatoly A. Zhigljavsky,et al.  Singular spectrum analysis: methodology and application to economics data , 2009, J. Syst. Sci. Complex..

[51]  G. Strang Introduction to Linear Algebra , 1993 .

[52]  Neil Salkind Encyclopedia of Measurement and Statistics , 2006 .

[53]  G. Plaut,et al.  Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere. , 1994 .

[54]  Chris Aldrich,et al.  Classification of process dynamics with Monte Carlo singular spectrum analysis , 2003, Comput. Chem. Eng..

[55]  John F. MacGregor,et al.  Multivariate SPC charts for monitoring batch processes , 1995 .

[56]  G. T. Wilson The Estimation of Parameters in Multivariate Time Series Models , 1973 .

[57]  C. Yoo,et al.  Nonlinear process monitoring using kernel principal component analysis , 2004 .

[58]  J. E. Jackson A User's Guide to Principal Components , 1991 .

[59]  Douglas C. Montgomery,et al.  Some Statistical Process Control Methods for Autocorrelated Data , 1991 .