Duct Modeling Using the Generalized RBF Neural Network for Active Cancellation of Variable Frequency Narrow Band Noise
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Research Article Duct Modeling Using the Generalized RBF Neural Network for Active Cancellation of Variable Frequency Narrow Band Noise Hadi Sadoghi Yazdi,1 Javad Haddadnia,1 and Mojtaba Lotfizad2 1 Engineering 2 Department
Department, Tarbiat Moallem University of Sabzevar, P.O. Box 397, Sabzevar, Iran of Electrical Engineering, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, Iran
Received 27 April 2005; Revised 1 February 2006; Accepted 30 April 2006 Recommended by Shoji Makino We have shown that duct modeling using the generalized RBF neural network (DM RBF), which has the capability of modeling the nonlinear behavior, can suppress a variable-frequency narrow band noise of a duct more efficiently than an FX-LMS algorithm. In our method (DM RBF), at first the duct is identified using a generalized RBF network, after that N stage of time delay of the input signal to the N generalized RBF network is applied, then a linear combiner at their outputs makes an online identification of the nonlinear system. The weights of linear combiner are updated by the normalized LMS algorithm. We have showed that the proposed method is more than three times faster in comparison with the FX-LMS algorithm with 30% lower error. Also the DM RBF method will converge in changing the input frequency, while it makes the FX-LMS cause divergence. Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
In the recent years, acoustic noise canceling by active methods, due to its numerous applications, has been in the focus of interest of many researches. Contrary to the passive method, it is possible using the active method to suppress or reduce the noise in a small space particularly in low frequencies (below 500 Hz) [1, 2]. Active noise control was introduced for the first time by Paul Lveg in 1936 for suppressing the noise in a duct [3]. In the active control method by producing a sound with the same amplitude but with opposite phase, the noise is removed. For this purpose, the amplitude and phase of a noise must be detected and inverted. The developed system must have the adaptive noise control capability [3]. In usual manner, an FIR filter is used in ANC whose weights are updated by a linear algorithm [4, 5]. Using the linear algorithm of LMS is not possible due to the nonlinear environment of the duct and the appearing of the secondary path transfer function H(z). Hence, the FX-LMS algorithm is presented in which the filtered input noise x (n) is used as an input to the algorithm [6, 7]. The notable points in ANC are as follows. (i) The duct length and the distance between the system elements are such that the system becomes causal [8].
(ii) Regarding the speaker response, no decrease will be obtained in frequencies below 200 Hz [2]. Also passive techniques for reducing the noise in frequencies below 500 Hz have not been successful [1, 2]. Therefore, the ANC systems are used in the range of 200 to 500 Hz and above 500 Hz. The existence of nonlinear effects in ANC complicates the use of the linear
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