Neural Networks and Wavelet Transform in Waveform Approximation

To fully analyze the time response of a complex system, in order to discover its critical operation points, the output waveform (under all conceivable conditions) needs to be generated. Using conventional methods as physical experiments or detailed simulations can be prohibitive from the resources point of view (time, equipment). The challenge is to generate the waveform by its numerous time samples as a function of different operating conditions described by a set of parameters. In this paper, we propose a fast to evaluate, but also accurate model that approximates the waveforms, as a reliable substitute for complex physical experiments or overwhelming system simulations. Our proposed model consists of two stages. In the first stage, a previously trained artificial neural network produces some coefficients standing for "primary" coefficients of a wavelet transform. In the second stage, an inverse wavelet transform generates all the time samples of the expected waveform, using a fusion between the "primary" coefficients and some "secondary" coefficients previously extracted from the nominal waveform in the family. The test results for a number of 100 different combinations of three waveform parameters show that our model is a reliable one, featuring high accuracy and generalization capabilities, as well as high computation speed.