Representação esparsa utilizando Wavelets e variação total aplicados ao processamento de sinais de descargas parciais

Abstract

Partial discharges are transient electrical discharges in the form of short pulses that occur inside insulation systems. In order to verify the existence of partial discharges, signal processing techniques are developed and used to enable interventions and scheduled maintenance in equipment, thus avoiding major financial losses. Several are the existing signal processing techniques that allow denoising, however, because they have specific characteristics, partial discharge signals are better processed when using the Wavelet Transform. Such a transform allows, among other characteristics, the decomposition of the signal into components localized in time (signal translation) and in the scale (signal dilation/contraction), which favors the representation of strictly localized signals. Specifically, in a variation of the Wavelet Transform known as Stationary Wavelet Transform, it is possible to reconstruct a signal from its circularly shifted versions by obtaining an overcomplete dictionary. However, by using an overcomplete dictionary, an indeterminate system is obtained, allowing infinite solutions. In order to find the best solution (least reconstruction error) among existing ones, it is necessary to apply an optimization method. This work presents the method known as Wavelet Total Variation, which based on the algorithm Split Variable Augmented Lagrangian Shrinkage Algorithm, aiming to eliminate noise in signals of partial discharges. The method is applied to signals of partial discharges measured in laboratory and generated by numerical models containing noises of harmonic, gaussian and impulsive type. The obtained results show that the method allows expressive levels of attenuation of the three types of noise investigated and produces little degradation in the partial discharges. The method is analyzed against another method in the literature and presents better quantitative results when comparing the resulting errors between original signals and the obtained signals.