A New Method for Structure Detection of Nonlinear ARX model:

Identification of nonlinear dynamic black box models involves structure detection of nonlinear system (i.e. selecting the regressors that have the most contribution to the output and the regressor function) and finally estimation of model parameters. As the NARX representation can describe many nonlinear dynamic models, it will be used here as the desired structure. It should be noted that when the order of the system increases, even for moderately complex systems the number of candidate terms becomes very large. So, structure detection is necessary in order to have an efficient description of the dynamic systems. In this paper, a new method for selecting regressors with the most contribution to the output and finding an efficient representation of nonlinear dynamic systems is presented. The purposed method, named ANOVA_BSD, is based on the combination of analysis of variance and suboptimal bootstrap algorithm. The anticipated structure takes the advantage of nonlinear ARX polynomial to model different nonlinearities of the system, such as sine and cosine functions. The proposed method is tested on two different systems and simulation results show that ANOVA_BSD effectively reduces model complexity without any noticeable loss in the accuracy.