“Dynamic system multivariate calibration based on multirate sampling data”

Authors: Rolf Ergon and Maths Halstensen,
Affiliation: Telemark University College
Reference: 2001, Vol 22, No 2, pp. 73-88.

Keywords: Dynamic system, latent variables, multirate sampling

Abstract: The statistical principal component regression (PCR) and chemometric partial least squares regression (PLSR) algorithms based on latent variables (LV) modeling are effective tools for handling ill-conditioned regression data. In many process related cases the data form time series, and it may then be possible to improve the prediction/estimation results by utilizing the autocorrelation in the observations. This can be done by use of estimators found from experimental data by use of a combination of statistical/chemometric and system identification methods. In important industrial cases, the response variables arc product qualities which also in the experimental data are sampled at a low and possibly irregular rate, while the regressor variables are sampled at a higher rate. After a discussion of the options available, the paper shows how the autocorrelation of the regressor variables in such multirate sampling cases may be utilized by identification of latent variables based output error (LV + OE) estimators. An example using acoustic power spectrum regressor data is finally presented.

PDF PDF (1654 Kb)        DOI: 10.4173/mic.2001.2.2

DOI forward links to this article:
[1] Bernt Lie, David Di Ruscio, Rolf Ergon, Bjørn Glemmestad, Maths Halstensen, Finn Haugen, Saba Mylvaganam, Nils-Olav Skeie and Dietmar Winkler (2009), doi:10.4173/mic.2009.3.4
[2] Satu-Pia Reinikainen and Agnar H skuldsson (2003), doi:10.1002/cem.770
[1] BELSLEY, A.D. (1991). Conditioning Diagnosis: Collinearity and Weak Data in Regression, John Wiley and Sons.
[2] DI RUSCIO, D. (1997). A method for identification of combined deterministic-stochastic systems, Applications of Computer Aided Time Series Modeling, M. Aoki and A.M. Havenner, Eds., Springer-Verlag, New York.
[3] ERGON, R. (1998). Dynamic system calibration: The low primary output sampling rate case, Modeling, Identification and Control, 19:99-107 doi:10.4173/mic.1998.2.3
[4] ERGON, R. (1999). On primary output estimation by use of secondary measurements as input signals in system identification, IEEE Trans. Autom. Control, 44:821-825 doi:10.1109/9.754826
[5] ERGON, R. (1999). Dynamic System Multivariate Calibration for Optimal Primary Output Estimation, PhD thesis at the Norwegian University of Science and Technology, Trondheim, Norway.
[6] ERGON, R. HALSTENSEN, M. (2000). Dynamic system multivariate calibration with low sampling-rate y data, Journal of Chemometrics, 14:617-628.
[7] ERGON, R. ESBENSEN, K. (2001). A didactically motivated PLS prediction algorithm, Submitted to Modeling, Identification and Control, Jan. 2001 doi:10.4173/mic.2001.3.1
[8] ESBENSEN, K., HOPE, B., LIED, T.T., HALSTENSEN, M., GRAVERMOEN, T. SIMMER°, K. (1999). Acoustic chemometrics for fluid flow quantifications-II: A small constriction will go a long way, Journal of Chemometrics, 13:209-236.
[9] ESBENSEN, K. (2000). Multivariate Data Analysis - in practice, Camo ASA, Trondheim, Norway.
[10] GREWAL, M.S. ANDREWS, A. P. (1993). Kalman Filtering: Theory and Practice, Prentice Hall: New Jersey.
[11] HELLAND, I.S. (1988). On the structure of partial least squares regression, Communications in Statistics, 17:581-607.
[12] LJUNG, L. (1999). System Identification: Theory for the user, Prentice Hall: New Jersey.
[13] LJUNG, L. (1995). System Identification Toolbox for use with Matlab, The MathWorks Inc., Mass.
[14] MARTENS, H. NÆS, T. (1989). Multivariate Calibration, Wiley: Chichester, UK.
[15] MEJDELL, T. SKOGESTAD, S. (1989). Estimate of process output from multiple secondary measurements, Proc. American Control Conference, 2112-2121.
[16] NORRIS, K.H. (1993). Extracting information from spectrophotometric curves, Predicting chemical composition from visible and near-infrared spectra. Proc. IUFost Symp. Food Research and Data Analysis, Sept. 1982, Oslo, Norway.Martens and Russworm, eds., Applied Science Publ., 95-113.
[17] SÖDERSTRÖM, T. STOICA, P. (1989). System Identification, Prentice Hall: Cambridge, UK.

  title={{Dynamic system multivariate calibration based on multirate sampling data}},
  author={Ergon, Rolf and Halstensen, Maths},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}