Approximation to NLAR(p) with Wavelet Neural Networks

Recently, wavelet neural networks have become a popular tool for non-linear functional approximation. Wavelet neural networks, which basis functions are orthonormal scalling functions, are more suitable in approximating to function. Based on it, approximating to NLAR(p) with wavelet neural networks is studied.

Face Recognition Based on Wavelet Packet Coefficients and Radial Basis Function Neural Networks

An efficient face recognition system with face image representation using averaged wavelet packet coefficients, compact and meaningful feature vectors dimensional reduction and recognition using radial basis function (RBF) neural network is presented. The face images are decomposed by 2-level two-dimensional (2-D) wavelet packet transformation. The wavelet packet coefficients obtained from the wavelet packet transformation are averaged using two different proposed methods. In the first method, wavelet packet coefficients of individual samples of a class are averaged then decomposed. The wavelet packet coefficients of all the samples of a class are averaged in the second method. The averaged wavelet packet coefficients are recognized by a RBF network. The proposed work tested on three face databases such as Olivetti-Oracle Research Lab (ORL), Japanese Female Facial Expression (JAFFE) and Essexface database. The proposed methods result in dimensionality reduction, low computational complexity and provide better recognition rates. The computational complexity is low as the dimensionality of the input pattern is reduced.

Discussion of stability in a class of models on recurrent wavelet neural networks

Based on wavelet neural networks （WNNs） and recurrent neural networks （RNNs）, a class of models on recurrent wavelet neural networks （RWNNs） is proposed. The new networks possess the advantages of WNNs and RNNs. In this paper, asymptotic stability of RWNNs is researched.according to the Lyapunov theorem, and some theorems and formulae are given. The simulation results show the excellent performance of the networks in nonlinear dynamic system recognition.

APPROXIMATION ANALYSES FOR FUZZY VALUED FUNCTIONS IN L_1(μ)-NORM BY REGULAR FUZZY NEURAL NETWORKS

By defining fuzzy valued simple functions and giving L1(μ) approximations of fuzzy valued integrably bounded functions by such simple functions, the paper analyses by L1(μ)-norm the approximation capability of four-layer feedforward regular fuzzy neural networks to the fuzzy valued integrably bounded function F : Rn → FcO(R). That is, if the transfer functionσ: R→R is non-polynomial and integrable function on each finite interval, F may be innorm approximated by fuzzy valued functions defined as to anydegree of accuracy. Finally some real examples demonstrate the conclusions.

Wear State Recognition of Drills Based on K-means Cluster and Radial Basis Function Neural Network

Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps： first, decomposing cutting torque components from the original signals by wavelet packet decomposition （WPD）; second, extracting wavelet coefficients of different wear states （i.e., slight, normal, or severe wear） with signal features adapting to Welch spectrum. Finally, monitoring and recognition of the feature vectors of cutting torque signal are performed by using the K-means cluster and radial basis function neural network （RBFNN）. The experiments on different tool wears of the multivariable features reveal that the results of monitoring and recognition are significant and effective.

The construction and approximation of feedforward neural network with hyperbolic tangent function

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are con- structed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.

Establishment of a Fault Prognosis Model Using Wavelet Neural Networks and Its Engineering Application

Fault diagnosis is confronted with two problems; how to '' measure'' the growthof a fault and how to predict the remaining useful lifetime of such a failing component or machine.This paper attempts to solve these two problems by proposing a model of fault prognosis usingwavelet basis neural network. Gaussian radial basis functions and Mexican hat wavelet frames areused as scaling functions and wavelets, respectively. The centers of the basis functions arecalculated using a dyadic expansion scheme and a k-means clustering algorithm.

Performance Comparison of Neural Networks for HRTFs Approximation

In order to approach to head related transfer functions (HRTFs), this paper employs and compares three kinds of one input neural network models, namely, multi layer perceptron (MLP) networks, radial basis function (RBF) networks and wavelet neural networks (WNN) so as to select the best network model for further HRTFs approximation. Experimental results demonstrate that wavelet neural networks are more efficient and useful.

Modeling of coal consumption rate based on wavelet neural network

In this paper,two wavelet neural network(WNN)frames which depend on Morlet wavelet function and Gaussian wavelet function were established.In order to improve the efficiency of model training,the momentum term was applied to modify the weights and thresholds,and the output of the network was summed up by function transformation of output layer nodes.When the Gaussian Wavelet Neural Networks(GWNN)and Morlet Wavelet Neural Networks(MWNN)were applied to coal consumption rate(CCR)estimation in a thermal power plant,the results confirmed their potency in function approximation.In addition,the influence of learning rate on the models was also discussed through the orthogonal experiment.

The construction and approximation of some neural networks operators

In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of the operators approximating continuous functions defined on a compact interval are estimated. Furthmore, Bochner-Riesz means operators of double Fourier series are used to construct networks operators for approximating bivariate functions, and the errors of approximation by the operators are estimated.

The Neural Network Model of Sinusoid Activation Transfer Function

A new type of neural network is described, which is basing on Fourier series, and the activation transfer function in its neuron model is sinusoid, ft can approximate to any function, which is continuum in every segment, with any precision with by layers only. We also provide the computer approach emulation results of different kinds of static function.

Simulation and prediction of monthly accumulated runoff,based on several neural network models under poor data availability

Most previous research on areas with abundant rainfall shows that simulations using rainfall-runoff modes have a very high prediction accuracy and applicability when using a back-propagation(BP), feed-forward, multilayer perceptron artificial neural network(ANN). However, in runoff areas with relatively low rainfall or a dry climate, more studies are needed. In these areas—of which oasis-plain areas are a particularly good example—the existence and development of runoff depends largely on that which is generated from alpine regions. Quantitative analysis of the uncertainty of runoff simulation under climate change is the key to improving the utilization and management of water resources in arid areas. Therefore, in this context, three kinds of BP feed-forward, three-layer ANNs with similar structure were chosen as models in this paper.Taking the oasis–plain region traverse by the Qira River Basin in Xinjiang, China, as the research area, the monthly accumulated runoff of the Qira River in the next month was simulated and predicted. The results showed that the training precision of a compact wavelet neural network is low; but from the forecasting results, it could be concluded that the training algorithm can better reflect the whole law of samples. The traditional artificial neural network(TANN) model and radial basis-function neural network(RBFNN) model showed higher accuracy in the training and prediction stage. However, the TANN model, more sensitive to the selection of input variables, requires a large number of numerical simulations to determine the appropriate input variables and the number of hidden-layer neurons. Hence, The RBFNN model is more suitable for the study of such problems. And it can be extended to other similar research arid-oasis areas on the southern edge of the Kunlun Mountains and provides a reference for sustainable water-resource management of arid-oasis areas.

Crack identification in functionally graded material framed structures using stationary wavelet transform and neural network

In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution.Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth.The dynamic stiffness method(DSM)is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams.The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification.The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures,even with noisy measured mode shapes and a limited amount of measured data.

Performance comparison of three artificial neural network methods for classification of electroencephalograph signals of five mental tasks

In this paper, performance of three classifiers for classification of five mental tasks were investigated. Wavelet Packet Transform (WPT) was used for feature extraction of the relevant frequency bands from raw Electroencephalograph (EEG) signal. The three classifiers namely used were Multilayer Back propagation Neural Network, Support Vector Machine and Radial Basis Function Neural Network. In MLP-BP NN five training methods used were a) Gradient Descent Back Propagation b) Levenberg-Marquardt c) Resilient Back Propagation d) Conjugate Learning Gradient Back Propagation and e) Gradient Descent Back Propagation with movementum.

Adaptive Control by Using Neural Networks

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Applications of Wavelets in 3-D Audio Simulation

Wavelet has been used as a powerful tool in the signal processing and function approximation recently. This paper presents the application of wavelets for solving two key problems in 3-D audio simulation. First, we employ discrete wavelet transform (DWT) combined with vector quantization (VQ) to compress audio data in order to reduce tremendous redundant data storage and transmission times. Secondly, we use wavelets as the activation functions in neural networks called feed-forward wavelet networks to approach auditory localization information cues (head-related transfer functions (HRTFs) are used here). The experimental results demonstrate that the application of wavelets is more efficient and useful in 3-D audio simulation.

RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function （RBF） neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.

Approximation by Neural Networks with Sigmoidal Functions

In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the ap- proximation. To improve the approximation rate, we further introduce a type of combinations of neurM networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals.

Face Representation Using Combined Method of Gabor Filters, Wavelet Transformation and DCV and Recognition Using RBF

An efficient face representation is a vital step for a successful face recognition system. Gabor features are known to be effective for face recognition. The Gabor features extracted by Gabor filters have large dimensionality. The feature of wavelet transformation is feature reduction. Hence, the large dimensional Gabor features are reduced by wavelet transformation. The discriminative common vectors are obtained using the within-class scatter matrix method to get a feature representation of face images with enhanced discrimination and are classified using radial basis function network. The proposed system is validated using three face databases such as ORL, The Japanese Female Facial Expression (JAFFE) and Essex Face database. Experimental results show that the proposed method reduces the number of features, minimizes the computational complexity and yielded the better recognition rates.

Exponential convergence of the deep neural network approximation for analytic functions Dedicated to Professor Ta Tsien Li on the Occasion of His 80th Birthday

We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.