Narrow Results

In this paper, a novel learning algorithm of wavelet networks based on the Fast Wavelet Transform (FWT) is proposed. It has many advantages compared to other algorithms, in which we solve the problem in previous works, when the weights of the hidden layer to the output layer are determined by applying the back propagation algorithm or by direct solution which requires to compute the matrix inversion, this may cause intensive computation when the learning data is too large. However, the new algorithm is realized by iterative application of FWT to compute the connection weights. Furthermore, we have extended the novel learning algorithm by using Levenberg–Marquardt method to optimize the learning functions. The experimental results have demonstrated that our model is remarkably more refreshing than some of the previously established models in terms of both speed and efficiency.

In this paper, we extend the wavelet networks for identification and H_∞ control of a class of nonlinear dynamical systems. The technique of feedback linearization, supervisory control and H_∞ control are used to design an adaptive control law and also the parameter adaptation laws of the wavelet network are developed using a Lyapunov-based design. By some theorems, it will be proved that even in the presence of modeling errors, named network error, the stability of the overall closed-loop system and convergence of the network parameters and the boundedness of the state errors are guaranteed. The applicability of the proposed method is illustrated on a nonlinear plant by computer simulation.

This paper presents an application of wavelet networks (WNs) in identification and control design for a class of structures equipped with a type of semiactive actuators, which are called magnetorheological (MR) dampers. The nonlinear model is identified based on a WN framework. Based on the technique of feedback linearization, supervisory control and H_∞ control, an adaptive control strategy is developed to compensate for the nonlinearity in the structure so as to enhance the response of the system to earthquake type inputs. Furthermore, the parameter adaptive laws of the WN are developed. In particular, it is shown that the proposed control strategy offers a reasonably effective approach to semiactive control of structures. The applicability of the proposed method is illustrated on a building structure by computer simulation.

Taking advantage of both the scaling property of wavelets and the high learning ability of neural networks, wavelet networks have recently emerged as a powerful tool in many applications in the field of signal processing such as data compression, function approximation as well as image recognition and classification. A novel wavelet network-based method for image classification is presented in this paper. The method combines the Orthogonal Least Squares algorithm (OLS) with the Pyramidal Beta Wavelet Network architecture (PBWN). First, the structure of the Pyramidal Beta Wavelet Network is proposed and the OLS method is used to design it by presetting the widths of the hidden units in PBWN. Then, to enhance the performance of the obtained PBWN, a novel learning algorithm based on orthogonal least squares and frames theory is proposed, in which we use OLS to select the hidden nodes. In the simulation part, the proposed method is employed to classify colour images. Comparisons with some typical wavelet networks are presented and discussed. Simulations also show that the PBWN-orthogonal least squares (PBWN-OLS) algorithm, which combines PBWN with the OLS algorithm, results in better performance for colour image classification.

In this paper, a Wavelet Neuro-Fuzzy model has been proposed. The proposed work caters an application of wavelet network used in fuzzy systems for forecasting of dynamic systems. A wavelet network approximates the consequent part of each fuzzy rule. The wavelet network is a feed-forward neural network with one hidden layer that uses a combination of Wavelet and Sigmoid Activation Function. A hybrid learning method composed of genetic algorithm and gradient descent is proposed to tune the learning parameters of the proposed Wavelet Neuro-Fuzzy model. Further, an analysis regarding the convergence and stability of gradient descent learning is presented for the proposed Wavelet Neuro-Fuzzy model. To evaluate the effectiveness of proposed model and learning strategy, three different classes of benchmark problems have been considered.

This paper presents a new approach of face recognition based on wavelet network using 2D fast wavelet transform and multiresolution analysis. This approach is divided in two stages: the training stage and the recognition stage. The first consists to approximate every training face image by a wavelet network. The second consists in recognition of a new test image by comparing it to all the training faces, the distances between this test face and all images from the training set are calculated in order to identify the searched person. The usual training algorithms presents some disadvantages when the weights of the wavelet network are computed by applying the back-propagation algorithm or by direct solution which requires computing an inversion of matrix, this computation may be intensive when the learning data is too large. We present in this paper our solutions to overcome these limitations. We propose a novel learning algorithm based on the 2D Fast Wavelet Transform. Furthermore, we have increased the performances of our algorithm by introducing the Levenberg–Marquardt method to optimize the learning functions and using the Beta wavelet which has at both an analytical expression and wavelet filter bank. Extensive empirical experiments are performed to compare the proposed method with other approaches as PCA, LDA, EBGM and RBF neural network using the ORL and FERET benchmarks.

In recent years, the field of speech enhancement has greatly benefited from the rapid development of neural networks. However, the requirement for large amounts of noisy and clean speech pairs for training limits the widespread use of these models. Wavelet network-based speech enhancement typically relies on clean speech signals as a training target. This paper presents a new method that combines a neural network with the wavelet theory for speech enhancement without the need for clean speech signals as targets in training mode. Five wide evaluation criteria, namely short-time objective intelligibility (STOI), signal-to-noise ratio (SNR), segmental signal-to-noise ratio (SNRseg), weighted spectral slope (WSS) and logarithmic spectral distance (LSD), have been used to confirm the effectiveness of the proposed method. The results show that the proposed method performs similar to a wavelet neural network (WNN) trained with clean signals, or even superior to those obtained from the clean target-based strategies.