×

zbMATH — the first resource for mathematics

Geometric properties of partial least squares for process monitoring. (English) Zbl 1233.62208
Summary: Projection to latent structures or partial least squares (PLS) produces output-supervised decomposition on input X, while principal component analysis (PCA) produces unsupervised decomposition of input X. The effect of output Y on the X-space decomposition in PLS is analyzed and geometric properties of the PLS structure are revealed. Several PLS algorithms are compared in a geometric way for the purpose of process monitoring. A numerical example and a case study are given to illustrate the analysis results.

MSC:
62P30 Applications of statistics in engineering and industry; control charts
62H25 Factor analysis and principal components; correspondence analysis
65C60 Computational problems in statistics (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alcala, C.; Qin, S., Reconstruction-based contribution for process monitoring, Automatica, 45, 7, 1593-1600, (2009) · Zbl 1188.90074
[2] Chiang, L.H.; Russell, E.; Braatz, R.D., Fault detection and diagnosis in industrial systems, (2001), Springer London · Zbl 0982.93005
[3] Choi, S.W.; Lee, I.B., Multiblock PLS-based localized process diagnosis, Journal of process control, 15, 3, 295-306, (2005)
[4] Dayal, B.S.; MacGregor, J.F., Improved PLS algorithms, Journal of chemometrics, 11, 1, 73-85, (1997)
[5] De Jong, S., SIMPLS: an alternative approach to partial least squares regression, Chemometrics and intelligent laboratory systems, 18, 3, 251-263, (1993)
[6] Di Ruscio, D., A weighted view on the partial least-squares algorithm, Automatica, 36, 6, 831-850, (2000) · Zbl 0953.93078
[7] Downs, J.J.; Vogel, E.F., A plant-wide industrial process control problem, Computers & chemical engineering, 17, 3, 245-255, (1993)
[8] Dunia, R.; Qin, S.J., Subspace approach to multidimensional fault identification and reconstruction, Aiche journal, 44, 8, 1813-1831, (1998)
[9] Helland, I.S., On the structure of partial least squares regression, Communications in statistics-simulation and computation, 17, 2, 581-607, (1988) · Zbl 0695.62167
[10] Hóskuldsson, A., PLS regression methods, Journal of chemometrics, 2, 211-228, (1988)
[11] Kresta, J.V.; MacGregor, J.F.; Marlin, T.E., Multivariate statistical monitoring of process operating performance, Canadian journal of chemical engineering, 69, 1, 35-47, (1991)
[12] Lee, G.; Han, C.H.; Yoon, E.S., Multiple-fault diagnosis of the tennessee eastman process based on system decomposition and dynamic PLS, Industrial and engineering chemistry research, 43, 25, 8037-8048, (2004)
[13] Lu, N.; Gao, F.; Wang, F., Sub-PCA modeling and on-line monitoring strategy for batch processes, Aiche journal, 50, 1, 255-259, (2004)
[14] MacGregor, J.F.; Jaeckle, C.; Kiparissides, C.; Koutoudi, M., Process monitoring and diagnosis by multiblock PLS methods, Aiche journal, 40, 5, 826-838, (1994)
[15] Qin, S.J., Recursive PLS algorithms for adaptive data modeling, Computers and chemical engineering, 22, 4-5, 503-514, (1998)
[16] Qin, S.J., Statistical process monitoring: basics and beyond, Journal of chemometrics, 17, 8-9, 480-502, (2003)
[17] Ter Braak, C.J.F.; De Jong, S., The objective function of partial least squares regression, Journal of chemometrics, 12, 1, 41-54, (1998)
[18] Westerhuis, J.A.; Gurden, S.P.; Smilde, A.K., Generalized contribution plots in multivariate statistical process monitoring, Chemometrics and intelligent laboratory systems, 51, 1, 95-114, (2000)
[19] Wise, B.M.; Gallagher, N.B., The process chemometrics approach to process monitoring and fault detection, Journal of process control, 6, 329-348, (1996)
[20] Xia, C.; Howell, J.; Thornhill, N., Detecting and isolating multiple plant-wide oscillations via spectral independent component analysis, Automatica, 41, 12, 2067-2075, (2005) · Zbl 1100.93518
[21] Zhang, X.D., Matrix analysis and applications, (2004), Tsinghua University Press Beijing
[22] Zhou, D.H., Li, G., & Qin, S.J. (2009). Total projection to latent structures for process monitoring, AIChE Journal, published online, doi:10.1002/aic.11977
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.