Nonlinear Hammerstein model identification using Genetic Algorithm

In this paper, a new approach to nonlinear system identification using evolutionary LMS Algorithm has been proposed. System in our method consists of a static nonlinear function in series with a dynamic linear transfer function, which literature refers to them as Hammerstein models. Identified nonlinear function can be one of the hyperbolic function or a general format of (ax+b) or a combination of them. Genetic Algorithm is responsible for finding the correct structure and parameters of the nonlinear function, and 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 increase with respect to the generation passed while the fitness remains unchanged. As the linear identification algorithm we prefer to parameterize the problem as ARMA and use the traditional LMS algorithm. AIC is the fitness function evaluator of the GA chromosomes, using both 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 deadzone, has been used and show that despite of small amount of information which is limited to input-output signals, our approach can considerably identify the systems.