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Artificial neural networks and adaptive neuro-fuzzy inference systems for parameter identification of dynamic systems

There would always be some unknown geometric, inertial or any other kinds of parameters in governing differential equations of dynamic systems. These parameters are needed to be numerically specified in order to make these dynamic equations usable for dynamic and control analysis. In this study, two powerful techniques in the field of Artificial Intelligence (AI), namely Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) are utilized to explain how unknown parameters in differential equations of dynamic systems can be identified. The data required for training and testing the ANN and the ANFIS are obtained by solving the direct problem i.e. solving the dynamic equations with different known parameters and input stimulations. The governing ordinary differential equations of the system is numerically solved and the output values in different time steps are obtained. The output values of the system and their derivatives, the time and the inputs are given to the ANN and the ANFIS as their inputs and the unknown parameters in the dynamic equations are estimated as the outputs. Finally, the performances of the ANN and the ANFIS for identifying parameters of the system are compared based on the test data Percent Root Mean Square Error (% RMSE) values.