Processamento de sinais de descargas parciais utilizando dicionários sobre-completos e representações esparsas

Abstract

The partial discharge (PD) phenomenon may cause the degradation of dielectric materials. Therefore, PD measurement is an important tool to diagnose the insulation conditions of electric equipment such as transformers, cables, and motors. However, on site PD measurement is usually limited due to the inherent characteristics of this type of signal, such as the low amplitude (millivolts) and broad frequency spectrum. Moreover, often the measurement becomes impossible due to interferences caused by the ambient noises, related to the high voltage amplitudes (kilovolts). The application of LTI filters for noise attenuation is limited since PD signals and noise typically occupy frequency bands not easily resoluble. Therefore, PD filtering requires the use of advanced signal processing techniques, especially those adapted to this specific type of signal. Generally, the signal processing techniques based on analytic dictionaries consist of searching for the best combination of a set of elementary signals (dictionary atoms) to compose a signal representation. As an example, the decompositions by Fourier or Wavelets may be cited. However, the use of overcomplete dictionaries composed by, for example, a blend of different wavelet families, allows closer representations of the signal properties in question. However, when using overcomplete dictionaries, an indeterminate system of equations is obtained (ill-posed system), which leads to infinite solutions. To find a particular solution, it is required to set restrictions to the problem (regularization) and to use an iterative approach that minimizes the representation error. This approach can be modeled as a typical optimization problem and one of its solutions consists of a search for sparse representations by minimizing the L1 norm, which is known as Basis Pursuit. This text presents a PD denoising method based on an iterative algorithm that uses wavelets overcomplete dictionaries and, from sparse representations, aims to obtain a noise-free reconstruction (Basis Pursuit Denoising). The optimization algorithm used in this method is named SALSA (Split Variable Augmented Lagrangian Shrinkage Algorithm) and is based on the Augmented Lagrangian approach associated with techniques for variable separation. The procedure is further detailed in the text along with its characteristics, limitations and methods for parameters setting, configure the algoritm and compose the overcomplete dictionary. The denoising performance was evaluated considering a PD signal database composed by real (measured in the laboratory) and synthetic (generated by numerical models) cases. It is shown that the proposed approach obtained signficant results in filtering AM and Gaussian noise types, with significant success, and obtaining also expressive results in the filtering of impulsive noise, although with some limitations in this case. The performance was evaluated by comparing the original and filtered signals, considering visual and numerical analysis obtained by commonly used denoising performance metrics