Extended model set, global data and threshold model identification of severely non-linear systems

References

• Billings , S. A. , and Chen , S. , 1989 , Identification of non-linear rational systems using a prediction-error estimation algorithm. International Journal of Systems Science , 20 , 467 – 494 .
   Web of Science ®Google Scholar
• Billings , S. A. , Chen , S. , and Backhouse , R, J. , 1989 a, The identification of linear and nonlinear models of a turbocharged automotive diesel engine. Mechanical Systems and Signal Processing , 3 , 123 – 142 .
   Web of Science ®Google Scholar
• Billings , S. A. , Chen , S. , and Korenberg , M. J. , 1989 b, Identification of MIMO non-linear systems using a forward-regression orthogonal estimator. International Journal of Control , 49 , 2157 – 2189 .
   Web of Science ®Google Scholar
• Billings , S. A. , Korenberg , M. J. , and Chen , S. , 1988 , Identification of non-linear output-affine systems using an orthogonal least-squares algorithm. International Journal of Systems Science , 19 , 1559 – 1568 .
   Web of Science ®Google Scholar
• Billings , S. A. , and Leontaritis , I. J. , 1981 , Identification of nonlinear systems using parameter estimation techniques. Proceedings of the I.E.E. Conference on Control and its Applications , Warwick , England, pp. 83 – 187 .
   Google Scholar
• Billings , S. A. , and Voon , W. S. F. , 1986 , Correlation based model validity tests for non-linear models. International Journal of Control , 44 , 235 – 244 ; 1987 , Piecewise linear identification of non-linear systems. Ibid. , 46 , 215 – 235 .
   Web of Science ®Google Scholar
• Björck , A. , 1967 , Solving linear least squares problems by Gram-Schmidt orthogonalization. Nordisk Tidskr Informations-Bechandling , 7 , 1 – 21 .
   Google Scholar
• Bohlin , T. , 1978 , Maximum-power validation of models without higher-order fitting. Automatica , 14 , 137 – 146 .
   Web of Science ®Google Scholar
• Bozdogan , H. , 1988 , ICOMP: a new model-selection criterion. Classification and Related Methods of Data Analysis , edited by H. H. Bock , ( Amsterdam : Elsevier ) , pp. 599 – 608 .
   Google Scholar
• Chen , S. , and Billings , S. A. , 1989 , Representations of non-linear systems: the NARMAX model. International Journal of Control , 49 , 1013 – 1032 .
   Web of Science ®Google Scholar
• Chen , S. , Billings , S. A. , and Luo , W. , 1989 , Orthogonal least-squares methods and their application to non-linear system identification. International Journal of Control , 50 , 1873 – 1896 .
   Web of Science ®Google Scholar
• Dang Van Mien , H. , and Normand-Cyrot , D. , 1984 , Nonlinear state affine identification methods: applications to electrical power plants. Automatics , 20 , 175 – 188 .
   Web of Science ®Google Scholar
• Gentleman , W. M. , 1973 , Least squares computations by Givens transformations without square roots. Journal of the Institute of Mathematics and its Applications , 12 , 329 – 336 .
   Google Scholar
• Golub , G. , 1965 , Numerical methods Tor solving linear least squares problems. Numerische Mathematik , 7 , 206 – 216 .
   Google Scholar
• Korenberg , M. J. , Billings , S. A. , Liu , Y. P. , and McIlroy , P. J. , 1988 , Orthogonal parameter estimation algorithm for non-linear stochastic systems. International Journal of Control , 48 , 193 – 210 .
   Web of Science ®Google Scholar
• Lai , H. Y. , and Hsieh Su-Hua , 1988 , Threshold modelling of nonlinear dynamic systems. 6th International Conference on Modal Analysis , Hyatt Orlando , U.S.A. , pp. 89 – 95 .
   Google Scholar
• Leontaritis , I. J. , and Billings , S. A. , 1985 , Input-output parameter models for non-linear systems. Part 1: Deterministic non-linear systems. Part 2: Stochastic non-linear systems. International Journal of Control , 41 , 303 – 344 ; 1987a, Model selection and validation methods for non-linear systems. Ibid. , 45 , 311 – 341 ; 1987 b, Experimental design and idcntifiability for non-linear systems. International Journal of Systems Science , 18 , 189 – 202 .
   Google Scholar
• Liu , Y. P. , Korenberg , M. J. , Billings , S. A. , and Fadzil , M. B. , 1987 , The nonlinear identification of a heat exchanger. Presented at the 26th l.E.E.E. Conference on Decision and Control , Los Angeles , California , U.S.A.
   Google Scholar
• Ozaki , T. , 1981 , Non-linear threshold autoregressive models for non-linear random vibrations. Journal of Applied Probability , 18 , 443 – 451 ; 1985 , Non-linear time series models and dynamical systems. Handbook of Statistics 5: Time Series in the Time Domain , ( edited by E. J. Hannan , P. R. Krishnaiah , and M. M , Rao , ) ( Amsterdam : North-Holland ), pp. 25 – 83 .
   Google Scholar
• Polchai , A. , and Hsu , C. S. , 1985 , Domain of stability of synchronous generators by a cell mapping approach. International Journal of Control , 41 , 1253 – 1271 .
   Web of Science ®Google Scholar
• Söderström , T. , 1977 , On model structure testing in system identification. International Journal of Control , 26 , 1 – 18 .
   Web of Science ®Google Scholar
• Tong , H. , and Lim , K. S. , 1980 , Threshold autoregression, limit cycles and cyclical data. Journal of the Royal Statistical Society , Pt B, 42 , 245 – 292 .
   Google Scholar