Identification of parametric models with a priori knowledge of process properties

Krzysztof B. Janiszowski; Paweł Wnuk

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 4, page 767-776
  • ISSN: 1641-876X

Abstract

top
An approach to estimation of a parametric discrete-time model of a process in the case of some a priori knowledge of the investigated process properties is presented. The knowledge of plant properties is introduced in the form of linear bounds, which can be determined for the coefficient vector of the parametric model studied. The approach yields special biased estimation of model coefficients that preserves demanded properties. A formula for estimation of the model coefficients is derived and combined with a recursive scheme determined for minimization of the sum of absolute model errors. The estimation problem of a model with known static gains of inputs is discussed and proper formulas are derived. This approach can overcome the non-identifiability problem which has been observed during estimation based on measurements recorded in industrial closed-loop control systems. The application of the proposed approach to estimation of a model for an industrial plant (a water injector into the steam flow in a power plant) is presented and discussed.

How to cite

top

Krzysztof B. Janiszowski, and Paweł Wnuk. "Identification of parametric models with a priori knowledge of process properties." International Journal of Applied Mathematics and Computer Science 26.4 (2016): 767-776. <http://eudml.org/doc/287174>.

@article{KrzysztofB2016,
abstract = {An approach to estimation of a parametric discrete-time model of a process in the case of some a priori knowledge of the investigated process properties is presented. The knowledge of plant properties is introduced in the form of linear bounds, which can be determined for the coefficient vector of the parametric model studied. The approach yields special biased estimation of model coefficients that preserves demanded properties. A formula for estimation of the model coefficients is derived and combined with a recursive scheme determined for minimization of the sum of absolute model errors. The estimation problem of a model with known static gains of inputs is discussed and proper formulas are derived. This approach can overcome the non-identifiability problem which has been observed during estimation based on measurements recorded in industrial closed-loop control systems. The application of the proposed approach to estimation of a model for an industrial plant (a water injector into the steam flow in a power plant) is presented and discussed.},
author = {Krzysztof B. Janiszowski, Paweł Wnuk},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {absolute error measure; constrained parameters estimation; identification; parametric MISO models},
language = {eng},
number = {4},
pages = {767-776},
title = {Identification of parametric models with a priori knowledge of process properties},
url = {http://eudml.org/doc/287174},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Krzysztof B. Janiszowski
AU - Paweł Wnuk
TI - Identification of parametric models with a priori knowledge of process properties
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 4
SP - 767
EP - 776
AB - An approach to estimation of a parametric discrete-time model of a process in the case of some a priori knowledge of the investigated process properties is presented. The knowledge of plant properties is introduced in the form of linear bounds, which can be determined for the coefficient vector of the parametric model studied. The approach yields special biased estimation of model coefficients that preserves demanded properties. A formula for estimation of the model coefficients is derived and combined with a recursive scheme determined for minimization of the sum of absolute model errors. The estimation problem of a model with known static gains of inputs is discussed and proper formulas are derived. This approach can overcome the non-identifiability problem which has been observed during estimation based on measurements recorded in industrial closed-loop control systems. The application of the proposed approach to estimation of a model for an industrial plant (a water injector into the steam flow in a power plant) is presented and discussed.
LA - eng
KW - absolute error measure; constrained parameters estimation; identification; parametric MISO models
UR - http://eudml.org/doc/287174
ER -

References

top
  1. Aguire, L.A., Barroso, M.F.S., Saldanha R.R., and Mendes E.M.A.M. (2004). Imposing steady-state performance on identified nonlinear polynomial models by means of constrained parameter estimation, IEE Proceedings: Control Theory and Applications 151(2): 174-179. 
  2. Astrom, K.J. (1983). Theory and applications of adaptive control-a survey, Automatica 19(5): 471-486. 
  3. Bun, M.J.G. and Carree, M.A. (2000). Bias-corrected estimation in dynamic panel data models, Journal of Business and Economic Statistics 23(2): 200-210. Zbl1255.62340
  4. Draper, N.R. and Smith, H. (1998). Applied Regression Analysis, 3rd Edition, Wiley, Berlin. Zbl0895.62073
  5. Eykhoff, P. (1974). System Identification Parameter and State Estimation, John Wiley and Sons, London/New York, NY. Zbl0667.93102
  6. Ferretti, G., Maffezzoni, C. and Scattolini, R. (1991). Recursive estimation of time delay in sampled data systems, Automatica 27(4): 653-661. Zbl0850.93177
  7. Gautier, M. and Briot, S. (2011). New method for global identification of the joint drive gains of robots using a known payload mass, Proceedings of the IEEE Conference on Inteligent Robots and Systems, San Francisco, CA, USA, pp. 25-30. 
  8. Goodwin, C.G. and Welsh, J.S. (2002). Bias issues in closed loop identification with application to adaptive control, Communication in Information and Systems 2(4): 349-370. Zbl1136.93361
  9. Gourieroux, C., Phillips, P.C.B. and Yu, J. (2010). Indirect inference for dynamic panel models, Journal of Econometrics 157(1): 68-77. Zbl06608387
  10. Hayakawa, K. (2010). The effects of dynamic feedbacks of LS and MM estimator accuracy in panel data models; some additional results, Journal of Econometrics 159(1): 202-208. Zbl06609329
  11. Heath, W.P. (2001). Bias of indirect non-parametric transfer function for plants in closed loop, Automatica 37(10): 1529-1540. Zbl0983.93010
  12. Isermann, R. (1988). Identifikation dynamischer Systeme, Springer, Berlin. Zbl0637.93003
  13. Janiszowski, K. (1998). Towards least sum of absolute errors estimation, IFAC Symposium on Large Scale Systems, LSS'98, Patras, Greece, pp. 613-619. 
  14. Janiszowski, K.B. (2014). Approximation of linear dynamic process model using the frequency approach and a non-quadratic measure of the model error, International Journal of Applied Mathematics and Computer Science 24(1): 99-111, DOI: 10.2478/amcs-2014-0008. Zbl1292.93085
  15. Kiviet, J.F. (1995). On bias, inconsistency and efficiency of various estimators in dynamic panel data models, Journal of Econometrics 68(1): 53-78. Zbl0831.62096
  16. Kowalczuk, Z. and Kozłowski, E. (2000). Continuous-time approaches to identification of continuous-time systems, Automatica 36(8): 1229-1236. Zbl0953.93503
  17. Kozłowski, E. and Kowalczuk, Z. (2007). Robust to measurement faults parameter estimation algorithms in problems of systems diagnostics, in Z. Kowalczuk and B. Wiszniewski (Eds.), Intelligent Information Extraction for Diagnostic Purposes, PWNT, Gdańsk, pp. 221-240. 
  18. Ljung, L. (1999). System Identification-Theory for the User, Prentice Hall, Englewood Cliffs, NJ. Zbl0615.93004
  19. Ljung, L. and Foorsell, U. (1998). Bias, variance and optimal experiment design: Some comments on closed loop identification, in D. Norman-Cyrot (Ed.), Perspectives in Control, Springer-Verlag, Berlin, pp. 205-216. Zbl0971.93076
  20. Ljung, L. and Gunnarson, S. (1990). Adaptation and tracking in system identification-a survey, Automatica 26(1): 7-21. Zbl0714.93053
  21. Ninness, B.M., Hjalmarson, H. and Gustafsson, F. (1999). The fundamental role of general othonormal bases in system identification, IEEE Transactions on Automatic Control 44(7): 1384-1406. Zbl0963.93021
  22. Norton, J.P. (1980). An Introduction to Identification, Academic Press, London/ New York, NJ. Zbl0617.93064
  23. Phillips, P. and Sul, D. (2007). Bias in dynamic panel estimation with fixed effects, incidental trends and cross section dependence, Journal of Econometrics 137(1): 162-188. Zbl06576081
  24. Söderström, T., Fan, H., Carlsson, B. and Bigi, S. (1997). Least squares parameter estimation of continuous-time ARX models from discrete-time data, IEEE Transactions on Automatic Control 42(5): 659-673. Zbl0890.93085
  25. Söderström, T. and Stoica, P. (1989). System Identification, Prentice Hall, Hertfordshire. Zbl0695.93108

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.