Box and Jenkins non linear system Modelization using RBF Neural Network designed by NSGAII

The modeling process is to find a parametric model whose dynamic behavior close to that process. This model will be used to make predictions of the process output, or to simulate the process in a control system...etc. In this work we used RBF neural networks for modeling nonlinear systems. Generally the problem in neural networks is often to find a better structure. We propose in this work a method based on No Sorting Genetic Algorithm II (NSGA II) to determine the best parameters of a RBF NN. The NSGAII should provide the best connection weights between the hidden layer and output layer, find the parameters of the radial function of neurons in the hidden layer and the optimal number of neurons in the hidden layers and thus ensure learning necessary. Two functions are optimized by NSGAII: the number of neuron in the hidden layer of the RBF NN, and the error which is the difference between desired input and the output of the RBF NN. This method is applied to modeling Box and Jenkins system that is widely used. The obtained results are very satisfactory.