Use of Genetic Programming in the Identification of Rational Model Structures

This paper demonstrates how genetic programming can be used for solving problems in the field of non-linear system identification of rational models. By using a two-tree structure rather than introducing the division operator in the function set, this genetic programming approach is able to determine the “true” model structure of the system under investigation. However, unlike use of the polynomial, which is linear in the parameters, use of rational model is non-linear in the parameters and thus noise terms cannot be estimated properly. By means of a second optimisation process (real-coded GA) which has the aim of tunning the coefficients to the “true” values, these parameters are then correctly computed. This approach is based upon the well-known NARMAX model representation, widely used in non-linear system identification.

[1]  S. Billings,et al.  Rational model identification using an extended least-squares algorithm , 1991 .

[2]  Peter J. Fleming,et al.  Multiobjective genetic programming for gas turbine engine model identification , 1998 .

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

[4]  Peter J. Fleming,et al.  An Evolutionary Approach to Non-Linear Polynomial System Identification , 1997 .

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

[6]  Zbigniew Michalewicz,et al.  Evolutionary Computation 1 , 2018 .

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

[8]  P. Fleming,et al.  Multi-objective genetic programming for nonlinear system identification , 1998 .

[9]  Kurt Dirk Bettenhausen,et al.  Signal path oriented approach for generation of dynamic process models , 1996 .

[10]  Michèle Sebag,et al.  Evolutionary identification of macro-mechanical models , 1996 .

[11]  P. Angeline.  An Investigation into the Sensitivity of Genetic Programming to the Frequency of Leaf Selection Duri , 1996 .

[12]  Heinz Mühlenbein,et al.  Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization , 1993, Evolutionary Computation.

[13]  William B. Langdon.  Evolving Data Structures with Genetic Programming , 1995, ICGA.

[14]  Hitoshi Iba,et al.  Genetic programming using a minimum description length principle , 1994 .

[15]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[16]  Eduardo Sontag.  Polynomial Response Maps , 1979 .

[17]  Hitoshi Iba,et al.  System Identification using Structured Genetic Algorithms , 1993, ICGA.

[18]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.