**51Due****英国论文代写网精选****assignment****代写****范文：“****Application of
Artificial Neural Networks****”，这篇论文讨论了人工神经网络的应用。人工神经网络是一种非常先进的技术，其相关的数学模型也有许多，在很多领域都得到了应用。**

The ability of nonlinear approximation of wavelets, neural network and neuro-fuzzy models has been shown by many researchers. Combining the ability of wavelet transformation for revealing the property of function in localize region with learning ability and general approximation properties of neural network; recently, different types of wavelet neural network have been proposed.

Boubez and Peskin, used orthonormal set of wavelet functions as basis functions. Yamakawa and Wang applied non-orthogonal wavelet function as an activation function in the single layer feed-forward neural network. They have used a simple cosine wavelet activation function. Neural network with sigmoidal activation function has already been shown to carry out large dimensional problem very well.

WNN instigate a superior system model for complex and seismic application in comparison to the NN with sigmoidal activation function. Majority of the application of wavelet is limited to small dimension, though can handle large dimension problem.

In this paper two types of wavelet neural network namely summation wavelet neural network and multiplication wavelet neural network, are proposed. These two proposed WNN, lead to propose two types of wavelet neuro-fuzzy model namely summation wavelet neuro-fuzzy model and multiplication wavelet neuro-fuzzy model.

From the literature survey, it has been found that all studies show the efficacy of wavelets when used in wavelet network or/and in wavelet neuro-fuzzy model. But none of the reported work caters a comparative study for different types of the wavelets. The presented work is an attempt to brought a comparative study for three types of wavelet used in WNN or/and WNF, namely, Mexican hat, Morlet and Sinc wavelet function. The idea of this work is to use approximation of inputs by sigmoidal function and wavelet functions separately and then combine them.

The sigmoidal activation function in NN can modulate low frequency section of the signal and the wavelet activation function in WNN can modulate high frequency section especially sharp section of signal. The idea of proposing SWNN and MWNN is to combine the localize approximation property of wavelets with functional approximation properties of neural network. The temporal change in dynamic system, particularly when the changes are sharp, can be accumulated in wavelets.

The output of every neuron in SWNN is summation of the sigmoidal and wavelet activation functions and the output of each neuron in MWNN is the product of these two. With the proving capability of the ANFIS as a powerful approximation method, that has the both ability of the learning parameter in the neural networks and the localized approximation of the TSK fuzzy model, different types of networks based on neuro-fuzzy model has been proposed. In TSK fuzzy model the consequent part of each rule is approximated by a linear function of the inputs.

Essentially, neuro-fuzzy models based on TSK model are nonlinear, but conceptually, it is an aggregation of the linear models. If the system under consideration is chaos some forecasting able information in the system may not be predicted well, by the aggregation of these linear models. In nonlinear dynamic systems and time series application, the linear local models in TSK are adequate to predict the behavior of the system, but nonlinear local models in TSK are better to predict the nonlinear dynamic behavior of the system under consideration. For example, Wavelet neuro-fuzzy model can be used as a good general approximation.

In these models, the premise part of each fuzzy rule, represents a localized region of the input space in which a wavelet network is used as local model in the consequent part of fuzzy rules. In the present paper, proposed wavelet neural networks, i.e., SWNN and MWNN are used as a local model in the consequent part of fuzzy rules that leads to the proposition of summation wavelet neuro-fuzzy and multiplication wavelet neuro-fuzzy, respectively. By joining the localized region transformation of wavelet activation function with the localized approximation of each fuzzy rule; an increase in precision of models has been experienced.

In both wavelet network and wavelet neuro-fuzzy models three types of non-orthogonal wavelet function, namely Mexican hat, Morlet and Sinc, are used. Ability of proposed model is examined with four examples of time series.

The rest of the paper is organized as follow: In Section2 ,a brief discussion of the wavelet function and wavelet transform is presented. Section 3 proposes SWNN and MWNN models. Approximation properties and convergence analysis of the proposed networks also describes in this section. Wavelet neuro-fuzzy model are proposed in Section 4 . This section also dealt with the convergence analysis of SWNF and MWNF. Experimental results are revealed in Section5 and, finally conclusions are relegated to Section 6.

The wavelet transform in its continuous form provides a flexible time-frequency window, which narrows when observing high frequency phenomena and widens when analyzing low frequency behavior. Thus, time resolution becomes arbitrarily good at high frequencies, while the frequency resolution becomes arbitrarily good at low frequen-cies.

This kind of analysis is suitable for signals composed of high frequency components with short duration and low frequency components with long duration, which is often the case in practical situations. Here, a brief review from the theory of wavelets is described that gives basic idea about the wavelets and the related work.

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