Issues in Spectral Source Separation Techniques for Plant-wide Oscillation Detection and Diagnosis
In the last few years, three multivariate spectral
analysis techniques namely, Principal Component Analysis (PCA),
Independent Component Analysis (ICA) and Non-negative Matrix
Factorization (NMF) have emerged as effective tools for oscillation
detection and isolation. While the first method is used in determining
the number of oscillatory sources, the latter two methods
are used to identify source signatures by formulating the detection
problem as a source identification problem in the spectral domain.
In this paper, we present a critical drawback of the underlying linear
(mixing) model which strongly limits the ability of the associated
source separation methods to determine the number of sources
and/or identify the physical source signatures. It is shown that the
assumed mixing model is only valid if each unit of the process gives
equal weighting (all-pass filter) to all oscillatory components in its
inputs. This is in contrast to the fact that each unit, in general, acts
as a filter with non-uniform frequency response. Thus, the model
can only facilitate correct identification of a source with a single
frequency component, which is again unrealistic. To overcome
this deficiency, an iterative post-processing algorithm that correctly
identifies the physical source(s) is developed. An additional issue
with the existing methods is that they lack a procedure to pre-screen
non-oscillatory/noisy measurements which obscure the identification
of oscillatory sources. In this regard, a pre-screening procedure
is prescribed based on the notion of sparseness index to eliminate
the noisy and non-oscillatory measurements from the data set used
for analysis.
[1] S.M. Kanbur, D. Iono, N.R. Tanvir and M.A. Hendry. On the use
of principal component analysis in analysing cepheid light curves.
Monthly Notices of the Royal Astronomical Society, 329(1):126-134,
2002.
[2] B.R. Bakshi. Multiscale PCA with application to multivariate statistical
process monitoring. AIChE, 44(7):1596-1610, 1998.
[3] D. Peter, W. Mitchell, and T. Lohnes. Maximum likelihood principal
component analysis with correlated measurement errors: theoritical
and practical considerations. Chemometrics and Intelligent Laboratory
Systems, 45(1):65-85, 1999.
[4] X. Li and X. Yao. Multiscale process monitoring in machining. IEEE
Transactions on Industrial Electronics, 52(3):924-925, 1998.
[5] D. Guillamet and J. Vitriz. A new iris recognition method using
independent component analysis. In Pattern Recognit. Lett.,24, 2003.
[6] N.F. Thornhill and A. Horch. Advances and new directions in plantwide
disturbance detection and diagnosis. Control Engineering Practice,
15(10):1196-1206, 2007.
[7] D.D. Lee and H.S. Seung. Learning the parts of object by nonnegative
matrix factorization. Nature, 401(3):788-791, 1999.
[8] A.K. Tangirala, J. Kanodia and S.L. Shah. Non negative matrix
factorization for detection and diagnosis of plantwide oscillations.
Industrial Engineering and Chemistry Research,46(3):801-817, 2007.
[9] N.F. Thornhill, S.L. Shah and B.Huang. Detection and diagnosis of
unit wide oscillations. Process Control and Instrumentation, 26, 2000.
[10] N.F. Thornhill, S.L. Shah, B.Huang and A.Vishnubhotla. Spectral
principal component analysis of dynamic process data. Control Engineering
Practice, 10833-846, 2002.
[11] Patrik O. Hoyer. Nonnegative matrix factorization with sparseness
constraints. Journal of Machine Learning Research, 514571469, 2004
[12] A.H. Rinen, J. Karhunen and E. Oja. Independent component analysis.
In Wiley, New York, 2001.
[1] S.M. Kanbur, D. Iono, N.R. Tanvir and M.A. Hendry. On the use
of principal component analysis in analysing cepheid light curves.
Monthly Notices of the Royal Astronomical Society, 329(1):126-134,
2002.
[2] B.R. Bakshi. Multiscale PCA with application to multivariate statistical
process monitoring. AIChE, 44(7):1596-1610, 1998.
[3] D. Peter, W. Mitchell, and T. Lohnes. Maximum likelihood principal
component analysis with correlated measurement errors: theoritical
and practical considerations. Chemometrics and Intelligent Laboratory
Systems, 45(1):65-85, 1999.
[4] X. Li and X. Yao. Multiscale process monitoring in machining. IEEE
Transactions on Industrial Electronics, 52(3):924-925, 1998.
[5] D. Guillamet and J. Vitriz. A new iris recognition method using
independent component analysis. In Pattern Recognit. Lett.,24, 2003.
[6] N.F. Thornhill and A. Horch. Advances and new directions in plantwide
disturbance detection and diagnosis. Control Engineering Practice,
15(10):1196-1206, 2007.
[7] D.D. Lee and H.S. Seung. Learning the parts of object by nonnegative
matrix factorization. Nature, 401(3):788-791, 1999.
[8] A.K. Tangirala, J. Kanodia and S.L. Shah. Non negative matrix
factorization for detection and diagnosis of plantwide oscillations.
Industrial Engineering and Chemistry Research,46(3):801-817, 2007.
[9] N.F. Thornhill, S.L. Shah and B.Huang. Detection and diagnosis of
unit wide oscillations. Process Control and Instrumentation, 26, 2000.
[10] N.F. Thornhill, S.L. Shah, B.Huang and A.Vishnubhotla. Spectral
principal component analysis of dynamic process data. Control Engineering
Practice, 10833-846, 2002.
[11] Patrik O. Hoyer. Nonnegative matrix factorization with sparseness
constraints. Journal of Machine Learning Research, 514571469, 2004
[12] A.H. Rinen, J. Karhunen and E. Oja. Independent component analysis.
In Wiley, New York, 2001.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:49184", author = "A.K. Tangirala and S. Babji", title = "Issues in Spectral Source Separation Techniques for Plant-wide Oscillation Detection and Diagnosis", abstract = "In the last few years, three multivariate spectral
analysis techniques namely, Principal Component Analysis (PCA),
Independent Component Analysis (ICA) and Non-negative Matrix
Factorization (NMF) have emerged as effective tools for oscillation
detection and isolation. While the first method is used in determining
the number of oscillatory sources, the latter two methods
are used to identify source signatures by formulating the detection
problem as a source identification problem in the spectral domain.
In this paper, we present a critical drawback of the underlying linear
(mixing) model which strongly limits the ability of the associated
source separation methods to determine the number of sources
and/or identify the physical source signatures. It is shown that the
assumed mixing model is only valid if each unit of the process gives
equal weighting (all-pass filter) to all oscillatory components in its
inputs. This is in contrast to the fact that each unit, in general, acts
as a filter with non-uniform frequency response. Thus, the model
can only facilitate correct identification of a source with a single
frequency component, which is again unrealistic. To overcome
this deficiency, an iterative post-processing algorithm that correctly
identifies the physical source(s) is developed. An additional issue
with the existing methods is that they lack a procedure to pre-screen
non-oscillatory/noisy measurements which obscure the identification
of oscillatory sources. In this regard, a pre-screening procedure
is prescribed based on the notion of sparseness index to eliminate
the noisy and non-oscillatory measurements from the data set used
for analysis.", keywords = "non-negative matrix factorization, PCA, source separation,
plant-wide diagnosis", volume = "2", number = "7", pages = "70-6", }