A Weighted EFOR Algorithm for Dynamic Parametrical Model Identification of the Nonlinear System

In this paper, the Nonlinear Auto-Regressive with exogenous inputs (NARX) model with parameters of interest for design (NARX-M-for-D), where the design parameter of the system is connected to the coefficients of the NARX model by a predefined polynomial function is studied. For the NARX-M-for-D of nonlinear systems, in practice, to predict the output by design parameter values are often difficult due to the uncertain relationship between the design parameter and the coefficients of the NARX model. To solve this issue and conduct the analysis and design, an improved algorithm, defined as the Weighted Extended Forward Orthogonal Regression (WEFOR), is proposed. Firstly, the initial NARX-M-for-D is obtained through the traditional Extended Forward Orthogonal Regression (EFOR) algorithm. Then a weight matrix is introduced to modify the polynomial functions with respect to the design parameter, and then an improved model, which is referred to as the final NARX-M-for-D is established. The genetic algorithm (GA) is used for deriving the weight matrix by minimizing the normalized mean square error (NMSE) over the data sets corresponding to the design parameter values used for modeling and first prediction. Finally, both the numerical and experimental studies are conducted to demonstrate the application of the WEFOR algorithm. The results indicate that the final NARX-M-for-D can accurately predict the system output of a nonlinear system. The new algorithm is expected to provide a reliable model for dynamic analysis and design of the nonlinear system.