International Journal of Computer Applications (0975 – 8887) International Conference on Communication, Circuits and Systems “iC3S-2012” 1 Nonlinear System Identification using Evolutionary Computing based Training Schemes Swati Swayamsiddha School of Electronics Engineering KIIT University, Bhubaneswar, India H.Pal Thethi School of Electronics Engineering KIIT University, Bhubaneswar, India ABSTRACT The present work deals with application of recently developed evolutionary computing based training methods for non-linear system identification problem. Generally, most of the systems are nonlinear in nature. The conventionally used standard derivative based identification scheme does not work satisfactorily for nonlinear systems, which is due to premature settling of the model parameters. To prevent the premature settling of the weights, evolutionary computing based update algorithms have been proposed. In this paper we have compared three popular derivative free evolutionary computing based update algorithms namely Genetic Algorithm (GA), Differential Evolution (DE) and Particle Swarm Optimization (PSO) for identification of nonlinear systems, in terms of convergence graph of cost function over number of iterations. It has been demonstrated that the derivative free population based schemes provided excellent performance for identification of nonlinear systems and they are not trapped in problem of local minima as well. Keywords Nonlinear System Identification, Particle Swarm Optimization, Genetic Algorithm, Differential Evolution. 1. INTRODUCTION The system identification problem can be considered as an optimization task where the idea is to estimate the parameters of the model and minimize the error between the output of known plant and the output of adaptive model [8],[9]. This error is minimized iteratively over a period of time by using update algorithm. Conventionally, derivative based adaptive algorithms such as normalized Least Mean Square (nLMS) and Recursive Least Squares (RLS) have been used to minimize this error signal. But in derivative based algorithms there are chances of error being trapped into local minima. This paper intends to use evolutionary approach for nonlinear system identification and attempts to show how Genetic Algorithm (GA), Differential Evolution (DE) and Particle Swarm Optimization (PSO) can be formulated in minimizing the error signal [1],[2],[3],[4],[5]. The performance analysis of these evolutionary based techniques is also carried out to show the effectiveness of the proposed methodology. 2. MODEL OF NONLINEAR SYSTEM IDENTIFICATION In system identification a mathematical model of a known plant is created. Earlier system identification has been used in modern communication and control [7],[8],[9]. Generally the system identification problem involves the following considerations: the structure realization and a method of updating the weights of the model. Fig.1 shows the schematic representation of an adaptive system identification process. A random signal x(k) is applied as input of the nonlinear system, the output of this block is y(k). To mimic an ideal system, noise of known strength is added. The output of this block is y n (k), which is considered to be the output of known plant. Same random input x(k) is also applied to the adaptive system model, thereby producing the output of model ŷ (k).The prediction error is then calculated which is mathematically given as e(k)=y n (k)-ŷ (k). This error signal is then used to calculate the mean square error(MSE) function, which serves as the cost function for the evolutionary based update algorithm. () noise y n (k) ()  + x(k) _ e( k) Fig. 1: Adaptive Nonlinear System Identification Scheme Nonlinear system EC based update algorithm Model Σ Σ