Proceeding of the 5 th International Symposium on Mechatronics and its Applications (ISMA08), Amman, Jordan, May 27-29,2008 IMPROVEMENT OF LEARNING RATE FOR RBF NEURAL NETWORKS IN A HELICOPTER SOUND IDENTIFICATION SYSTEM INTRODUCING TWO-PHASE OSD LEARNING METHOD Gh. A. Montazer Tarbiat Modares University School of Engineering P.O. Box: 14115-179 - Tehran, Iran rnontazer@modares.ac.ir Reza Sabzevari Islamic Azad University of Qazvin School of Engineering Member of Young Researchers' Club eYRC) sabzevari@gmail.com Fatemeh Ghorbani Tarbiat Modares University School of Basic Sciences f_ghorbani200S@yahoo.com ABSTRACT This paper presents a novel approach in learning algorithms commonly used for training radial basis function neural networks. This approach could be used in applications which need real-time capabilities for retraining RBF neural networks. Proposed method is a Two-Phase Learning Algorithm which optimizes the functionality of Optimum Steepest Decent (OSD) learning method. This methodology speeds to attain better performance by initial calculation of centre and width of RBF units. This method has been tested in an audio processing application, a system for identifying helicopters using their sound of rotors. Comparing results obtained by employing different learning strategies shows interesting outcomes as have come in this paper. 1. INTRODUCTION Radial basis function (REF) networks were introduced into the neural network literature by Broomhead and Lowe in 1988 [1]. These networks have been extensively used for interpolation regression and classification due to their universal approximation properties and simple parameters estimation [2]. The theoretical basis of the RBF approach lies in the field of interpolation of multivariate functions. According to this viewpoint, the learning process could be deemed as finding a surface in a multidimensional space fitted on train data. The criterion to find the "best fitted surface" uses some statistical computations. According to different applications of RBF Neural Networks, there are a wide variety of learning strategies that have been proposed in literatures for changing the parameters of a RBF network. These strategies are of two main categories. The first category contains strategies in which centers and variances of the network are changed, including: 1) Fixed centers selected at random [3] 2) Self-organized selection of centers, containing [4]: a) K-Mean clustering procedure, b) The self-organizing feature map clustering procedure, 978-1-4244-2034-6/08/$25.00 ©2008 IEEE. 3) Supervised selection of centers [3], 4) Supervised selection of centers and variances [5]. The second category includes strategies in which the weights of the network are changed, containing: 1) The pseudo-inverse (minimum-norm) method [6] 2) The Least-Mean-Square (LMS) method [7] 3) The Steepest Decent (SD) method [8] 4) The Quick Propagation (QP) method [9] 5) Optimized version of previous methods [9]: including General Optimum Steepest Decent (GOSD), Optimum Steepest Decent (OSD) and Optimum Quick Propagation (OQP). In our previous work [9], we have presented a set of modified learning methods improving the classical ones. In this paper, we introduce a two-phase learning strategy benefiting one of modified methods, Optimum Steepest Decent (OSD), for RBF networks. In other words, this method is a hybridization of OSD learning method and the classical two-phase learning of the REF network. The organization of this paper is as follows: employing OSD method in two-phase learning is described in section two. Section three presents the implementation of proposed method on several benchmark data sets. Also discussions on the performance of this method in comparison with previous ones are come in this section. And finally in section four, conclusion of this work is presented. 2. TWO-PHASE LEARNING FOR RBF NETWORKS In this approach the learning process is divided in two consequent steps. The first step consists of determining centers of hidden units and the center widths. The second step is a supervised learning. The only parameters to be set are the weights between hidden and output layers representing coefficients of linear combinations of RBF unit outputs. The objective is to minimize the overall error function with respect to these weights. Assume <P ij = rp j (x i) as the outcome of j-th radial basis function with i-th element of X, as input vector, and Yij as the j-th