Regressor and structure selection in NARX models using a structured ANOVA approach

Automatica

Volumn 44, Issue 2, 2008, Pages 383-395

  Lind, Ingela ^a   Ljung, Lennart ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Analysis of variance; Nonlinear system identification; Structure identification

Indexed keywords

ANALYSIS OF VARIANCE (ANOVA); MATHEMATICAL MODELS; NONLINEAR SYSTEMS;

NONLINEAR AUTOREGRESSIVE MODELS; REGRESSOR SELECTION; STRUCTURE IDENTIFICATION;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 37849012165     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2007.06.010     Document Type: Article

References (26)

1. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (1974) 716-723
2. Autin, M., Biey, M., & Hasler, M. (1992). Order of discrete time nonlinear systems determined from input-output signals. In IEEE international symposium on circuits and systems, ISCAS '92 (Vol. 1, pp. 296-299).
3. Barnett W., and Lewis T. Outliers in statistical data (1978), Wiley, New York
4. Breiman L. Better subset regression using the nonnegative garrote. Technometrics 37 4 (1995) 373-384
5. Chen R., Liu J.S., and Tsay R.S. Additivity tests for nonlinear autoregression. Biometrika 82 (1995) 369-383
6. Friedman J.H. Multivariate adaptive regression splines. Annals of Statistics 19 1 (1991) 1-67
7. Gunn S.R., and Kandola J.S. Structural modeling with sparse kernels. Machine Learning 48 (2002) 137-163
8. Haber R., and Unbehauen H. Structure identification of nonlinear dynamic systems-a survey on input/output approaches. Automatica 26 (1990) 651-677
9. Korenberg M., Billings S.A., Liu Y.P., and McIlroy P.J. Orthogonal parameter estimation algorithm for nonlinear stochastic systems. International Journal of Control 48 1 (1988) 193-210
10. Lind, I. (2000). Model order selection of N-FIR models by the analysis of variance method. In Proceedings of the 12th IFAC symposium on system identification (pp. 367-372). Santa Barbara, June 2000.
11. Lind, I. (2006). Regressor and structure selection: Uses of ANOVA in system identification. Ph.D. thesis, Linköpings universitet, Linköping, Sweden, May 2006.
12. Lind I., and Ljung L. Regressor selection with the analysis of variance method. Automatica 41 4 (2005) 693-700
13. Ljung, L., Zhang, Q., Lindskog, P., & Juditsky, A. (2004). Modeling a non-linear electric circuit with black box and grey box models. In Proceedings of NOLCOS 2004-IFAC symposium on nonlinear control systems (pp. 543-548). Stuttgart, Germany, September 2004.
14. Mannale, R. (2006). Comparison of regressor selection methods in system identification. Technical report LiTH-ISY-R-2730, Department of Electrical Engineering, Linköping University, February 2006.
15. Miller Jr. R.G. Beyond ANOVA (1997), Chapman & Hall, London
16. Montgomery D.C. Design and analysis of experiments. (3rd ed) (1991), Wiley, New York
17. NOLCOS (2004). Special session on identification of nonlinear systems: The silver box study. In Proceedings of the 6th IFAC-symposium on nonlinear control systems. Stuttgart, Germany, September 01-03, 2004.
18. Pintelon R., and Schoukens J. System identification-a frequency domain approach (2001), IEEE Press, New York
19. Piroddi L., and Spinelli W. An identification algorithm for polynomial NARX models based on simulation error minimization. International Journal of Control 76 (2003) 1767-1781
20. Rhodes C., and Morari M. Determining the model order of nonlinear input/output systems. American Institute of Chemical Engineers Journal 44 1 (1998) 151-163
21. Rissanen J. Modelling by shortest data description. Automatica 14 (1978) 465-471
22. Rissanen J. Prediction minimum description length principles. Annals of Statistics 14 (1986) 1080-1100
23. Roll, J., Lind, I., & Ljung, L. (2006). Connections between optimisation-based regressor selection and analysis of variance. In The 45th IEEE conference on decision and control (pp. 4907-4914). San Diego, CA, December 2006.
24. Spinelli,W., Piroddi, L., & Lovera, M. (2006). A two-stage algorithm for structure identification of polynomial NARX models. In Proceedings of the American control conference (pp. 2387-2392). Minneapolis, MN, USA, June 2006.
25. Tibshirani R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 58 (1996) 267-288
26. Yuan M., and Lin Y. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society Series B-Statistical Methodology 68 1 (2006) 49-67