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

Abstract New parameter estimation algorithms, based on an extended model set, a global data model and a threshold model formulation, are derived for identifying severely non-linear systems. It is shown that in each case an integrated structure determination and parameter estimation algorithm based on an orthogonal decomposition of the regression matrix can be derived to provide procedures for identifying parsimonious models of unknown systems with complex structure. Simulation studies are included to illustrate the techniques discussed.

[1]  Å. Björck.  Solving linear least squares problems by Gram-Schmidt orthogonalization , 1967 .

[2]  W. E. Gentleman.  Least Squares Computations by Givens Transformations Without Square Roots , 1973 .

[3]  T. Söderström.  On model structure testing in system identification , 1977 .

[4]  Torsten Bohlin,et al.  Maximum-power validation of models without higher-order fitting , 1978, Autom..

[5]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .

[6]  Tohru Ozaki.  Non-linear threshold autoregressive models for non-linear random vibrations , 1981 .

[7]  Dorothée Normand-Cyrot,et al.  Nonlinear state affine identification methods: Applications to electrical power plants , 1984, Autom..

[8]  C. Hsu,et al.  Domain of stability of synchronous generators by a cell mapping approach , 1985 .

[9]  S. Billings,et al.  Correlation based model validity tests for non-linear models , 1986 .

[10]  S. Billings,et al.  A prediction-error and stepwise-regression estimation algorithm for non-linear systems , 1986 .

[11]  I. J. Leontaritis,et al.  Model selection and validation methods for non-linear systems , 1987 .

[12]  M. Korenberg,et al.  The nonlinear identification of a heat exchanger , 1987, 26th IEEE Conference on Decision and Control.

[13]  S. Billings,et al.  Orthogonal parameter estimation algorithm for non-linear stochastic systems , 1988 .

[14]  Sheng Chen,et al.  Identification of non-linear output-affine systems using an orthogonal least-squares algorithm , 1988 .

[15]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[16]  Sheng Chen,et al.  Identification of non-linear rational systems using a prediction-error estimation algorithm , 1989 .

[17]  Sheng Chen,et al.  Representations of non-linear systems: the NARMAX model , 1989 .

[18]  S. A. Billings,et al.  The identification of linear and non-linear models of a turbocharged automotive diesel engine , 1989 .

[19]  Sheng Chen,et al.  Identification of MIMO non-linear systems using a forward-regression orthogonal estimator , 1989 .