Identification of Nonlinear Systems using Wavelets and Neural Network
Smriti Srivastava, Madhusudan Singh, Madasu Hanmandlu, A. N. JHA · IETE Journal of Research · 2006
By utilizing some of the important properties of wavelets like denoising, compression, multiresolution along with the concepts of neural network, two new wavelet neural networks (WNNs) are proposed for approximating any arbitrary non-linear function, hence identifying a non-linear system. We have discrete wavelet transform (DWT) block, which receives the given inputs, in the proposed two methods: one using compression property and other using multiresolution property. The compression property enables us to get less number of samples to be presented to the neural network, making approximation/identification fast. Here the wavelet also acts as a filter giving noise free output to the neural network. This method approximates the desired signal with a very good accuracy. Method II on the other hand multiresoluted every sample to represent a large class of signals exactly. Hence this method gives accurate results for few samples. It is shown that noise and disturbance in the reference signal is reduced with wavelets and also the variation of somatic gain, the parameter that controls the slope of the activation function in the neural network, leads to more accurate output. Identification results are found to be accurate and speed of their convergence is fast.