Qualitative Validation and Generalization in Nonlinear System Identification

Cell to cell mapping for global analysis of nonlinear systems is adopted to enable the qualitative validation of identified nonlinear systems. The method provides a framework of the global analysis of a diverse range of nonlinear systems, including continuous and discrete time systems and nonlinear identified models. In the present study, the method is used to reveal the dynamic properties of a nonlinear system, including the fixed points, periodic, aperiodic solutions or chaotic behaviour and the corresponding stability properties. The orthogonal least squares algorithm (OLS) is then used to identify a parametric NARMAX model of the system. The resulting model is analysed using the same framework and the dynamic properties of the model are qualitatively compared with thos of the original system. Based on the results of the validation, a modified selection criterion for the OLS algorithm is proposed, which incorporates the nonlinear degree of the terms in the model complexity. The effectiveness of the new algorithm is demonstrated using examples.