The higher-order analysis method of statistics analysis for response of linear structure under stationary non-Gaussian excitation

Power quality (PQ) event detection and classification is gaining importance due to worldwide use of delicate electronic devices. Things like lightning, large switching loads, non-linear load stresses, inadequate or incorrect wiring and grounding or accidents involving electric lines, can create problems to sensitive equipment, if it is designed to operate within narrow voltage limits, or if it does not incorporate the capability of filtering fluctuations in the electrical supply (Gerek et. al., 2006; Moreno et. al., 2006). The solution for a PQ problem implies the acquisition and monitoring of long data records from the energy distribution system, along with an automated detection and classification strategy which allows identify the cause of these voltage anomalies. Signal processing tools have been widely used for this purpose, and are mainly based in spectral analysis and wavelet transforms. These second-order methods, the most familiar to the scientific community, are based on the independence of the spectral components and evolution of the spectrum in the time domain. Other tools are threshold-based algorithms, linear classifiers and Bayesian networks. The goal of the signal processing analysis is to get a feature vector from the data record under study, which constitute the input to the computational intelligence modulus, which has the task of classification. Some recent works bring a different strategy, based in higher-order statistics (HOS), in dealing with the analysis of transients within PQ analysis (Gerek et. al., 2006; Moreno et. al., 2006) and other fields of Science (De la Rosa et. al., 2004, 2005, 2007). Without perturbation, the 50-Hz of the voltage waveform exhibits a Gaussian behaviour. Deviations from Gaussianity can be detected and characterized via HOS. Non-Gaussian processes need third and fourth order statistical characterization in order to be recognized. In order words, second-order moments and cumulants could be not capable of differentiate non-Gaussian events. The situation described matches the problem of differentiating between a transient of long duration named fault (within a signal period), and a short duration transient (25 per cent of a cycle). This one could also bring the 50-Hz voltage to zero instantly and, generally affects the sinusoid dramatically. By the contrary, the long-duration transient could be considered as a modulating signal (the 50-Hz signal is the carrier). These transients are intrinsically non-stationary, so it is necessary a battery of observations (sample registers) to obtain a reliable characterization. The main contribution of this work consists of the application of higher-order central cumulants to characterize PQ events, along with the use of a competitive layer as the classification tool. Results reveal that two different clusters, associated to both types of transients, can be recognized in the 2D graph. The successful results convey the idea that the physical underlying processes associated to the analyzed transients, generate different types of deviations from the typical effects that the noise cause in the 50-Hz sinusoid voltage waveform. The paper is organized as follows: Section on higher-order cumulants summarizes the main equations of the cumulants used in the paper. Then, we recall the competitive layer’s foundations, along with the Kohonen learning rule. The experience is described then, and the conclusions are drawn.

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Natural convection in a right-angle corner: higher-order analysis

International Journal of Heat and Mass Transfer ◽

10.1016/0017-9310(89)90123-3 ◽

1989 ◽

Vol 32 (11) ◽

pp. 2167-2177 ◽

Cited By ~ 5

Author(s):

D.B. Ingham ◽

I. Pop

Keyword(s):

Natural Convection ◽

Higher Order ◽

Order Analysis

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