Vol. 6(21), Jul. 2016, PP. 2987-2997 2987 Article History: IJMEC DOI: 649123/10215 Received Date: Oct. 23, 2015 Accepted Date: Mar. 19, 2016 Available Online: Jul. 08, 2016 Training Wavelet Neural Networks Using Hybrid Particle Swarm Optimization and Gravitational Search Algorithm for System Identification Navid Razmjooy * and Mehdi Ramezani Department of Electrical Engineering, University of Tafresh, Tafresh, Iran Phone Number: +98-914-4539067 *Corresponding Author's E-mail: navid.razmjooy@hotmail.com Abstract ystem identification is mainly the process of improving a mathematical modeling of a physical system using experimental data. In this paper, a new hybrid wavelet neural network is proposed for the system identification purposes. The Gravitational Search Algorithm (GSA) is a new evolutionary algorithm which recently introduced and has a good performance in different optimization problems. The GSA inspired by the law of gravity and mass interactions. The only disadvantage of GSA is that suffers from slow searching speed in the last iterations. In this paper the hybridization of the defined algorithms (GSAPSO) is proposed for constructing and training wavelet neural networks. The difference of the conventional neural network and wavelet neural network is that the activation function of the original WNN is based on wavelet transformation. This algorithm is based on the optimal selection of network weights dynamically during the training process. The suggested method determines the optimal value of the weights and solves the optimization problem of wavelet neural network structure. The problem of finding a good neural model is then discussed through solutions achieved by wavelet neural networks trained by PSO based and GSA based algorithms. Experimental results show that this method can improve the performance of the wavelet based neural network significantly. Keywords: Neural Network, Wavelet, Learning neural network, Gravitational search algorithm, Particle swarm optimization, System Identification, Nonlinear System. 1. Introduction The system physical representation and identification of linear and nonlinear dynamic systems by using the measured experimental data has become a problem of considerable importance in engineering. System identification, which is based on the method of least square fit to identify system parameters, may be classified into two categories: one in a deterministic manner and the other in a statistical manner. Recently, Artificial Neural Networks as the nonparametric identification method has become a popular technique for the purposes of identification. Neural networks due to its characteristics like: adaptability, massive parallelism, the inherent capability to handle nonlinear systems and robustness have been widely used in complex nonlinear function mapping [1-4]. The defined networks suffer from the lack of strong constructive technique. Since, they require describing the neuron’s parameters, as well as choosing network’s architecture. Multilayer perceptron networks (MLP) define a large variety of feed forward neural networks [5]. Conventional MLP is a static network with a forward direction of signal flow and wit no feedback loops, and is usually constructed with sigmoid neurons and trained with the back-propagation (BP) algorithm [6]. Due to multilayered structure of these kinds of networks and the greedy nature of the BP algorithm, the training process often stick in an incorrect local minimum of the error surface and converges too slowly. This process makes The MLP construction to be very time consuming since the optimal number of hidden neurons S