### “Informative PLS score-loading plots for process understanding and monitoring”

**Authors:**Rolf Ergon,

**Affiliation:**Telemark University College

**Reference:**2005, Vol 26, No 1, pp. 23-37.

**Keywords:**PLS, score-loading correspondence, biplot, process understanding and monitoring

**Abstract:**Principal component regression (PCR) based on principal component analysis (PCA) and partial least squares regression (PLSR) are well known projection methods for analysis of multivariate data. They result in scores and loadings that may be visualized in a score-loading plot (biplot) and used for process monitoring. The difficulty with this is that often more than two principal or PLS components have to be used, resulting in a need to monitor more than one such plot. However, it has recently been shown that for a scalar response variable all PLSR/PCR models can be compressed into equivalent PLSR models with two components only. After a summary of the underlying theory, the. present paper shows how such two-component PLS (2PLS) models can be utilized in informative score-loading biplots for process understanding and monitoring. The possible utilization of known projection model monitoring statistics and variable contribution plots is also discussed, and a new method for visualization of contributions directly in the biplot is presented. An industrial data example is included.

PDF (1925 Kb) DOI: 10.4173/mic.2005.1.2

**DOI forward links to this article:**

[1] Min Wu, Qi Lei, Weihua Cao and Jinhua She (2011), doi:10.1016/j.conengprac.2011.06.001 |

**References:**

[1] CHIANG, L.H., RUSSEL, E.L. BRAATZ, R.D. (2001). Fault Detection and Diagnosis in Industrial Systems, Springer, London.

[2] ERGON, R. (2002). PLS score-loading correspondence and a bi-orthogonal factorization, Journal of Chemometrics, 16, pp. 368-373 doi:10.1002/cem.736

[3] ERGON, R. (2003). Compression into two-component PLS factorizations, Journal of Chemometrics, 17, pp. 303-312 doi:10.1002/cem.803

[4] HELLAND, I.S. (1988). On the structure of partial least squares regression, Communications in statistics, 17, 581-607.

[5] HODOUIN, D., MACGREGOR, J.F., HOU, M. FRANKLIN, M. (1993). Multivariate Statistical Analysis of Mineral Processing Plant Data, Can. Inst. Mining Bull. 86, No. 975, 23-34.

[6] HÖSKULDSSON, A. (1996). Prediction Methods in Science and Technology, Vol, 1 Basic Theory. Thor Publishing, Copenhagen.

[7] JOHNSON, R.A. WICHERN, D.W. (1992). Applied Multivariate Statistical Analysis, Prentice-Hall, New Jersey.

[8] KOURTI, T. MacGregor, J.F. (1996). Multivariate SPC Methods for Process and Product Monitoring, Journal of Quality Technology, 28, pp. 409-428.

[9] MACGREGOR, J.F. KOURTI, T. (1995). Statistical Process Control of Multivariate Processes, Control Eng. Practice 3, pp. 403-414 doi:10.1016/0967-0661(95)00014-L

[10] MARTENS, H. NÆS, T. (1989). Multivariate Calibration, Wiley, New York.

[11] SKAGERBERG, B. SUNDIN, L. (1993). Multidimensional monitoring of complex industrial processes, ABB Review 4, pp. 31-38.

**BibTeX:**

@article{MIC-2005-1-2,

title={{Informative PLS score-loading plots for process understanding and monitoring}},

author={Ergon, Rolf},

journal={Modeling, Identification and Control},

volume={26},

number={1},

pages={23--37},

year={2005},

doi={10.4173/mic.2005.1.2},

publisher={Norwegian Society of Automatic Control}

};