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Cascade modeling of nonlinear systems

Şenalp, Erdem Türker
Modeling of nonlinear systems based on special Hammerstein forms has been considered. In Hammerstein system modeling a static nonlinearity is connected to a dynamic linearity in cascade form. Fundamental contributions of this work are: 1) Introduction of Bezier curve nonlinearity representations; 2) Introduction of B-Spline curve nonlinearity representations instead of polynomials in cascade modeling. As a result, local control in nonlinear system modeling is achieved. Thus, unexpected variations of the output can be modeled more closely. As an important demonstration case, a model is developed and named as Middle East Technical University Neural Networks and Cascade Model (METU-NN-C). Application examples are chosen by considering the Near-Earth space processes, which are important for navigation, telecommunication and many other technical applications. It is demonstrated that the models developed based on the contributions of this work are especially more accurate under disturbed conditions, which are quantified by considering Space Weather parameters. Examples include forecasting of Total Electron Content (TEC), and mapping; estimation of joint angle of simple forced pendulum; estimation of joint angles of spring loaded inverted double pendulum with forced table; identification of Van der Pol oscillator; and identification of speakers. The operation performance results of the International Reference Ionosphere (IRI-2001), METU Neural Networks (METU-NN) and METU-NN-C models are compared qualitatively and quantitatively. As a numerical example, in forecasting the TEC by using the METU-NN-C having Bezier curves in nonlinearity representation, the average absolute error is 1.11 TECu. The new cascade models are shown to be promising for system designers and operators.