NARMAX Model Identification Using Multi-Objective Optimization Differential Evolution

Abstract

Multi-objective optimization differential evolution (MOODE) algorithm has demonstrated to be an effective algorithm for selecting the structure of nonlinear auto-regressive with exogeneous input (NARX) model in dynamic system modeling. This paper presents the expansion of the MOODE algorithm to obtain an adequate and parsimonious nonlinear auto-regressive moving average with exogenous input (NARMAX) model. A simple methodology for developing the MOODE-NARMAX model is proposed. Two objective functions were considered in the algorithm for optimization; minimizing the number of term of a model structure and minimizing the mean square error between actual and predicted outputs. Two simulated systems and two real systems data were considered for testing the effectiveness of the algorithm. Model validity tests were applied to the set of solutions called the Pareto-optimal set that was generated from the MOODE algorithm in order to select an optimal model. The results show that the MOODE-NARMAX algorithm is able to correctly identify the simulated examples and adequately model real data structures.