Heuristic Order Reduction of NARX-OBF models Applied to Nonlinear System Identification

Abstract

Nonlinear system identification concerns the determination of the model

structure and its parameters. Although the designers often seek the best

model for each system, it can be tricky to determine, at the same time, the

best structure and the parameters which optimize the model performance.

This paper proposes the use of a Genetic Algorithm, GA, and the Leven

berg-Marquardt, LM, method to obtain the model parameters, as well as

perform the order reduction of the model. In order to validate the proposed

methodology, the identification of a magnetic levitator, operating in closed

loop, was performed. The class NARX-OBF, Nonlinear Auto Regressive

with eXogenous input-Orthonormal Basis Function, was used. The use of

OBF functions aims to reduce the number of terms in NARX models. Once

the model is found, the order reduction is performed using GA and LM, in

a hybrid application, capable of determining the model parameters and re

ducing the original model order, simultaneously. The results show, consid

ering the inherent trade-of between accuracy and computational effort, the

proposed methodology provided an implementation with good mean square

error, when compared with the full NARX-OBF model.