Nonlinear system identification concerns the determination of the model structure and its parameters.Although the designers often seek the best model for each system,it can be tricky to determine,at the same time,the ...Nonlinear system identification concerns the determination of the model structure and its parameters.Although the designers often seek the best model for each system,it can be tricky to determine,at the same time,the best structure and the parameters which optimize the model performance.This paper proposes the use of a Genetic Algorithm,GA,and the Levenberg-Marquardt,LM,method to obtain the model parameters,as well as perform the order reduction of the model.In order to validate the proposed methodology,the identification of a magnetic levitator,operating in closed loop,was performed.The class NARX-OBF,Nonlinear Auto Regressive with eXogenous input-Orthonormal Basis Function,was used.The use of OBF functions aims to reduce the number of terms in NARX models.Once the model is found,the order reduction is performed using GA and LM,in a hybrid application,capable of determining the model parameters and reducing the original model order,simultaneously.The results show,considering the inherent trade-of between accuracy and computational effort,the proposed methodology provided an implementation with good mean square error,when compared with the full NARX-OBF model.展开更多
In this paper,nonlinear vibration of electrostatically actuated microbeam is analyzed using differential transformation method.The high level of accuracy of the analytical solutions of the method was established throu...In this paper,nonlinear vibration of electrostatically actuated microbeam is analyzed using differential transformation method.The high level of accuracy of the analytical solutions of the method was established through comparison of the results of the solutions of exact analytical method,variational approach,homotopy analysis method and energy balance methods.Also,with the aid of the present analytical solution,the time response,velocity variation and the phase plots of the system are presented graphically.It is hope that the method will be widely applied to more nonlinear problems of systems in various fields of study.展开更多
文摘Nonlinear system identification concerns the determination of the model structure and its parameters.Although the designers often seek the best model for each system,it can be tricky to determine,at the same time,the best structure and the parameters which optimize the model performance.This paper proposes the use of a Genetic Algorithm,GA,and the Levenberg-Marquardt,LM,method to obtain the model parameters,as well as perform the order reduction of the model.In order to validate the proposed methodology,the identification of a magnetic levitator,operating in closed loop,was performed.The class NARX-OBF,Nonlinear Auto Regressive with eXogenous input-Orthonormal Basis Function,was used.The use of OBF functions aims to reduce the number of terms in NARX models.Once the model is found,the order reduction is performed using GA and LM,in a hybrid application,capable of determining the model parameters and reducing the original model order,simultaneously.The results show,considering the inherent trade-of between accuracy and computational effort,the proposed methodology provided an implementation with good mean square error,when compared with the full NARX-OBF model.
文摘In this paper,nonlinear vibration of electrostatically actuated microbeam is analyzed using differential transformation method.The high level of accuracy of the analytical solutions of the method was established through comparison of the results of the solutions of exact analytical method,variational approach,homotopy analysis method and energy balance methods.Also,with the aid of the present analytical solution,the time response,velocity variation and the phase plots of the system are presented graphically.It is hope that the method will be widely applied to more nonlinear problems of systems in various fields of study.
