The next advantage of this conversion is having different resolutions in different scales so that for high frequency phenomenon, the frequency resolution increases and the time resolution decreases and vise versa for low frequency phenomenon. This theory has a special application in concentration and time locating of transient phenomenon in power electrical engineering. Recently, this theory is appeared as an important mathematical model in electrical engineering community.
They offer a presentation of signal at both time and frequency domain, so the Wavelets analysis is preferable, from this aspect, compare with the Fourier analysis and efficiently is used in many different fields such as: astronomy, Acoustic, nuclear engineering, signal and image processing, neurophysiology, music, magnetic resonances, xerography, speech distinction, earthquake predication, radar, Optic and the applications of pure math. They convert a signal to the arbitrary signals with different scales and different levels of resolution using the scaling and transmission properties. Wavelets have the specific scaling properties. Against the Fourier analysis, the Wavelet analysis doesn't extend the functions as the trigonometric or polynomial functions, but according to the wavelets that themselves have created by delaying and transmission of a mother wavelet. Like the Fourier analysis, Wavelet analysis also extends the functions according to a set of basic functions. Wavelet theory application in signal analysis: The wavelet expression is applied to a family of functions, produced from translation and dilation of a function, called mother wavelet ( Chik et al., 2009 Sanchez-Lopez et al., 2003). In this study, discrete wavelet transform has been used for detecting the broken bars in the induction motors. It is therefore desirable to select a wavelet that produces the best results for the signal being analyzed ( Halbaoui et al., 2009 Lasaad et al., 2007 Sarhan and Issa, 2006). Some wavelets are more efficient at encoding, de-noising, compressing, decomposing and reconstructing signals than others. However in wavelet analysis the basis function could be any permissible wavelet and the results produced are unique to the selected wavelet. In Fourier analysis the basis functions are complex exponentials producing the same results for a particular waveform being analyzed. Wavelet analysis was introduced to overcome the shortcomings of Fourier analysis. These diagnostic techniques include computation of the negative sequence components of motor terminal quantities ( Kliman et al., 1996 Kohler et al., 1992 Tallam et al., 2003) detection of the frequency spectrum sideband components ( Bellini et al., 2001 Elkasabgy et al., 1992), motor parameter estimation methods ( Vas, 1993 Said et al., 2000) Artificial Intelligence (AI) based statistical machine learning approach ( Yeh et al., 2004 Povinelli et al., 2002), artificial neural networks ( Filippetti et al., 1998 Murray and Penman, 1997 Bernieri et al., 1996) as well as the recently proposed motor magnetic field pendulous oscillation phenomenon ( Mirafzal and Demerdash, 2003, 2005, 2006). Numerous diagnostic techniques for induction motors have been reported in the literature to diagnose electric machine faults, such as stator winding inter-turn shorts, broken rotor bars, broken end-ring connectors and bearing faults.
Accordingly, an online fault diagnostic system becomes a valuable tool to increase the system efficiency and reliability ( Tallam et al., 2003 Bellini et al., 2001 Elkasabgy et al., 1992). On the other hand, increasing the frequency of scheduled maintenance increases the cost and decreases the productivity of a system. Maintenance schedules can proactively be implemented to reduce or prevent these failures although the probability of a sudden machine failure cannot be entirely ruled out. These machine failures reduce productivity in industrial and power systems. Sudden machine failure is very damaging or catastrophic in applications such as large industrial systems or central station power plant auxiliaries in which the electric machine is the prime mover. In the past two decades, there have been many investigations on condition monitoring and fault diagnostics in electric machines, especially squirrel-cage induction motors ( Haji and Toliyat, 2001 Kliman et al., 1996 Kohler et al., 1992 Tallam et al., 2003). Therefore, there is a considerable demand to reduce maintenance costs and prevent unscheduled downtimes for electrical drive systems, especially ac induction machine. Since, induction motors present numerous advantages due to their robustness and their power to weight ratio, they are widely used in the industry.
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