Structure identification of nonlinear dynamic systems - A survey on input/output approaches

Abstract In the past several methods have been elaborated for the identification of nonlinear dynamic systems. Most of the methods assume that the structure of the system is given a priori. Therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation. However in nonlinear system theory several methods are known to determine the structure of a system. In this paper structure identification of block-oriented (especially cascade) models, of semi-linear dynamic models with signal-dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered. Different structure selection methods are summarized based on step and impulse tests, frequency response measurements, correlation analysis, repeated reproducible tests and normal operating data.

[1]  A. Gardiner.  Identification of processes containing single-valued non-linearities† , 1973 .

[2]  M. Schetzen.  Measurement of the Kernels of a Non-linear System of Finite Order† , 1965 .

[3]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[4]  M. Korenberg.  Identifying Noisy Cascades of Linear and Static Nonlinear Systems , 1985 .

[5]  Alan A. Desrochers.  On an improved model reduction technique for nonlinear systems , 1981, Autom..

[6]  H. Akaike.  Statistical predictor identification , 1970 .

[7]  H. Unbehauen,et al.  Two Algorithms for Model Structure Determination of Nonlinear Dynamic Systems with Applications to Industrial Processes , 1988 .

[8]  A. G. Ivakhnenko,et al.  Polynomial Theory of Complex Systems , 1971, IEEE Trans. Syst. Man Cybern..

[9]  Stephen A. Billings,et al.  Identification of systems containing linear dynamic and static nonlinear elements , 1982, Autom..

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

[11]  R. Kashyap.  A Bayesian comparison of different classes of dynamic models using empirical data , 1977 .

[12]  R. Bhansali,et al.  Some properties of the order of an autoregressive model selected by a generalization of Akaike∘s EPF criterion , 1977 .

[13]  W. L. Yuen.  Pseudorandom signals as separable processes , 1973 .

[14]  W. Rugh,et al.  Complete identification of a class of nonlinear systems from steady-state frequency response , 1975 .

[15]  A. B. Gardiner.  Determination of the linear output signal of a process containing single-valued nonlinearities , 1968 .

[16]  Toshio Yoshimura,et al.  Prediction of the peak flood using revised GMDH alogrithms , 1982 .

[17]  Stephen A. Billings,et al.  Identi cation of a class of nonlinear systems using correlation analysis , 1978 .

[18]  Torsten Söderström,et al.  Model-structure selection by cross-validation , 1986 .

[19]  K. Naka,et al.  Identification of multi-input biological systems. , 1974, IEEE transactions on bio-medical engineering.

[20]  A. B. Gardiner.  Elimination of the effect of nonlinearities on process crosscorrelations , 1966 .

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

[22]  I. J. Leontaritis,et al.  Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .

[23]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[24]  Toshio Yoshimura,et al.  Track/vehicle system identification by a revised group method of data handling (GMDH) , 1985 .

[25]  R. Haber.  Structural identification of quadratic block-oriented models based on estimated Volterra kernels , 1989 .

[26]  S. A. Billings,et al.  Structure Detection and Model Validity Tests in the Identification of Nonlinear Systems , 1983 .

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

[28]  S. Billings,et al.  Theory of separable processes with applications to the identification of nonlinear systems , 1978 .

[29]  Y. Bard,et al.  Nonlinear System Identification , 1970 .

[30]  George N. Saridis,et al.  Identification of Nonlinear Nondynamic Systems with Application to a Hot Steel Rolling Mill , 1978 .

[31]  Mark A. Franklin,et al.  A Learning Identification Algorithm and Its Application to an Environmental System , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[32]  George N. Saridis,et al.  A model reduction technique for nonlinear systems , 1980, Autom..

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

[34]  A. Ivakhnenko.  Heuristic self-organization in problems of engineering cybernetics , 1970 .

[35]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[36]  R. Haber.  Nonlinearity Tests for Dynamic Processes , 1985 .

[37]  Robert Haber,et al.  Identification of ‘linear’ systems having signal-dependent parameters † , 1985 .

[38]  Anil Mital.  Prediction of human static and dynamic strengths by modified basic GMDH algorithm , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[39]  Saburo Ikeda,et al.  Sequential GMDH Algorithm and Its Application to River Flow Prediction , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[40]  A. Desrochers,et al.  On determining the structure of a non-linear system , 1984 .