Nonlinear model identification of an experimental ball-and-tube system using a genetic programming approach

Most processes in industry are characterized by nonlinear and time-varying behavior. The identification of mathematical models typically nonlinear systems is vital in many fields of engineering. The developed mathematical models can be used to study the behavior of the underlying system as well as for supervision, fault detection, prediction, estimation of unmeasurable variables, optimization and model-based control purposes. A variety of system identification techniques are applied to the modeling of process dynamics. Recently, the identification of nonlinear systems by genetic programming (GP) approaches has been successfully applied in many applications. GP is a paradigm of evolutionary computation field based on a structure description method that applies the principles of natural evolution to optimization problems and its nature is a generalized hierarchy computer program description. GP adopts a tree structure code to describe an identification problem. Unlike the traditional approximation methods where the structure of an approximate model is fixed, the structure of the GP tree itself is modified and optimized and, thus, there is a possibility that GP trees could be more appropriate or accurate approximate models. This paper focuses the GP method for structure selection in a system identification applications. The proposed GP method combines different techniques for tuning of crossover and mutation probabilities with an orthogonal least-squares (OLS) algorithm to estimate the contribution of the branches of the tree to the accuracy of the discrete polynomial Nonlinear AutoRegressive with eXogenous inputs (NARX) model. The nonlinear system identification procedure, based on a NARX representation and GP, is applied to empirical case study of an experimental ball-and-tube system. The results demonstrate that the GP with OLS is a promising technique for NARX modeling. (C) 2009 Elsevier Ltd. All rights reserved.