Nonlinear Hammerstein model identification using genetic algorithm

In this paper, a new approach to nonlinear system identification using evolutionary LMS algorithm is proposed. The system in our method consists of a static nonlinear function in series with a dynamic linear transfer function, which the literature refers to them as Hammerstein models. The identified nonlinear function can be one of the hyperbolic functions or a general format of (ax+b) or a combination of them. The genetic algorithm is responsible for finding the correct structure and parameters of the nonlinear function, and the number of zeros and poles of the linear transfer function as well. In order to speed up the convergence process, we use a kind of dynamic mutation rate that increases with respect to the generation passed while the fitness remains unchanged. For the linear identification algorithm we prefer to parameterize the problem as ARMA and apply the traditional LMS algorithm. AIC is the fitness function evaluator of the GA chromosomes, using both the total error and estimated order of the linear section. Two different simulations show the effectiveness of our method. In the simulation two hard nonlinear functions, saturation and dead-zone, were used and show that despite of the small amount of information, which is limited to input-output signals, our approach can considerably identify the systems.