Determination of nonlinear delay elements within NARMA models using dispersion functions

In nonlinear system identification of discrete-time models, it is critical to determine the nonlinear delay elements within models. This paper proposed the use of dispersion functions to pre-determine the significant delay elements which appear in nonlinear form within an unknown nonlinear autoregressive, moving-average (NARMA) model. The methodology is based on orthogonal projection, the use of dispersion functions, and hence meets the criterion of mean-squared error. According to the properties of dispersion functions, rules can be made to determine the possible delay elements by giving the observed input and output data. Furthermore, the rules of the determination are independent of the degree-of-nonlinearity of the model. Finally, computer simulations were performed and showed coinciding results.