Comparison of Wavenet and Neuralnet for System Modeling

Abstract

Abstract. This paper presents nonlinear static and dynamic system modeling using wavenet and neuralnet. Wavenet combines wavelet theory and feedforward neuralnet, so learning approach is similar to neuralnet. The selection of transfer function is crucial for the approximation property and the convergence of the network. The purelin and the tansig functions are used as the transfer functions for neuralnet and the first derivative of a gaussian function is used as the transfer function for wavenet. Wavenet and neuralnet parameters are optimized during learning phase. Selecting all initial values random, but for wavenet, it may be unsuitable for process modeling because wavelets have localization feature. For this reason heuristic procedure has been used for wavenet. In this study gradient methods have been applied for parameters updating with momentum. Error minimization is computed by quadratic cost function for wavenet and neuralnet. Nonlinear static and dynamic functions have been used for the simulations. Recently wavenet has been used as an alternative of the neuralnet because interpretation of the model with neuralnet is so hard. For wavenet learning approach, training algorithms require smaller number of iterations when compared with neuralnet. Consequently, according to the number of training iteration and TMSE, dynamic and static system modeling with wavenet is better as shown in results.

A Wavenet-Based Virtual Sensor for PM10 Monitoring

“…Wavelets are a family of orthonormal basis functions that can be used to perform transformations among spaces. Their use ranges from function approximation to audio compression [26][27][28]. The wavelet approximation theory is strictly related to multi-resolution analysis [26].…”

“…Up to now, a number of different functions has been considered and are currently used. More details about wavelet transformation can be found in [26][27][28].…”

Comparison of CNN-based methods for yoga pose classification

“…Wavelets have also been employed in many areas such as super-resolution, image registration, video coding, etc. [27][28][29][30][31][32][33][34] due to their nature of local extraction of spectral and temporal information of images.…”

Wavelet networks for nonlinear system modeling

“…The radial basis function is also local, but it does not have the spatial-spectral (time-frequency) zooming property of the wavelet function, and therefore cannot represent the local spatial-spectral characteristic of the function. So, for approximation and forecasting the wavelet network should have a better performance than the traditional neural network [5,15]. Families of wavelet functions especially, wavelet frames are universal approximators in identification of nonlinear systems.…”

“…Families of wavelet functions especially, wavelet frames are universal approximators in identification of nonlinear systems. Wavelet networks have been used both for static [12,20] and dynamic modeling [10,15]. System modeling is realized in three steps.…”