Wavelet networks for nonlinear system modeling

Abstract

This study presents a nonlinear systems and function learning by using wavelet network. Wavelet networks are as neural network for training and structural approach. But, training algorithms of wavelet networks is required a smaller number of iterations when the compared with neural networks. Gaussianbased mother wavelet function is used as an activation function. Wavelet networks have three main parameters; dilation, translation, and connection parameters (weights). Initial values of these parameters are randomly selected. They are optimized during training (learning) phase. Because of random selection of all initial values, it may not be suitable for process modeling. Because wavelet functions are rapidly vanishing functions. For this reason heuristic procedure has been used. In this study serial-parallel identification model has been applied to system modeling. This structure does not utilize feedback. Real system outputs have been exercised for prediction of the future system outputs. So that stability and approximation of the network is guaranteed. Gradient methods have been applied for parameters updating with momentum term. Quadratic cost function is used for error minimization. Three example problems have been examined in the simulation. They are static nonlinear functions and discrete dynamic nonlinear system.

Quasi-ARX wavelet network for SVR based nonlinear system identification

“…However, most of the wavelet basis are redundant and should be eliminated, thus Orthogonal Least Square (OLS) algorithm [21] is introduced to select the most important ones, and the size of basis could be determined by some well known approaches such as AIC and FPE [4]. This method has been successfully applied in researches on WN [6,7,22].…”

“…Recently, nonlinear system identification by wavelet networks is attracting a growing interest [4][5][6], not only due to the universal approximation ability of WNs, but also for the efficient constructive methods, both for determining the parameters and for choosing network structure [7]. However, similar with NNs, most of WNs are used as black-box methods, which emphasize on the input-output representation ability and neglect some properties of the highly successful linear black-box modeling, such as the linear structure and simplicity [8].…”

Model Identification in Wavelet Neural Networks Framework

“…A wavelet is a waveform of effectively limited duration that has an average value of zero and localized properties hence a random initialization may lead to wavelons with a value of zero. Also random initialization affects the speed of training and may lead to a local minimum of the loss function, [16]. In [2] the wavelons are initialized at the center of the input dimension of each input vector x i .…”

Wavelet Neural Networks: A Practical Guide

“…J. Yao, Song, Zhang, & Cheng, 2000), in time series prediction, (Cao, et al, 1995;Chen, Yang, & Dong, 2006;Cristea, Tuduce, & Cristea, 2000), signal classification and compression, (Kadambe & Srinivasan, 2006;Pittner, Kamarthi, & Gao, 1998;Subasi, Alkan, Koklukaya, & Kiymik, 2005), signal denoising, (Z. Zhang, 2007), static, dynamic (Allingham, West, & Mees, 1998;Oussar & Dreyfus, 2000;Oussar, Rivals, Presonnaz, & Dreyfus, 1998;Pati & Krishnaprasad, 1993;Postalcioglu & Becerikli, 2007; Q. Zhang & Benveniste, 1992), and nonlinear modeling, (Billings & Wei, 2005), nonlinear static function approximation, (Jiao, Pan, & Fang, 2001;Szu, Telfer, & Kadambe, 1992;Wong & Leung, 1998), to mention the most important.…”