e
the costs of maintenance by allowing the early detection of faults, which could be
expensive to repair. In this paper some results on non-invasive detection of rotor faults in
wound rotor induction motors are presented. The applied method is the so-called motor
current signature analysis (MCSA), an often cited and investigated diagnosis method. The
method utilises the results of spectral analysis of the stator currents. Usually the FFT
(Fast Fourier Transform) is used to obtain the power density vs. frequency plots to be
analysed. In this paper the use of a novel versatile tool of harmonic analysis, of the
wavelet transform will be presented. The proposed wavelet based detection method
shows a good sensitivity. The theoretical basis of the method is proved by laboratory
tests.
1. Introduction
Induction motors play an important role in the safe and efficient operation of industrial
plants. Usually they are designed for 30 years fault-free lifetime, but most of them can
fail earlier.
Many of its components are especially susceptible to failures also in the case of
wound rotor induction machines. The stator or rotor windings are subject to insulation
break-down caused by mechanical stress and Transform-Based-Rotor-Faults-Detection-Method-for-/' >vibration, excessive heat, age, damage
during installation, carbon dust, etc.
Excessive heat can result from operation on continuous overload, motor stall, and too
many starts in succession without adequate cool down combined with excessive
accelerating time.
Mechanical stress failures are generally due to repetitive centrifugal loading on the
coil extensions or coil end-arm Transform-Based-Rotor-Faults-Detection-Method-for-/' >vibration, especially when the motor is subjected to
frequent starts.
One of the most common causes of coil faults in a wound rotor induction machine is
from winding contamination from carbon or graphite dust from the brushes. The fine
powder permeates all of the stator and rotor windings and can create a path between
conductors or between conductors to ground.
Machine bearings are subject to excessive wear and damage caused by inadequate
lubrication, asymmetric loading, or misalignment. The brushes or the slip ring of the
motor also can also damage.
In many applications these failures of the electrical machines can shut down an entire
industrial process. The unplanned machine shut downs cost both time and money that LOR�ND SZAB�, JEN BARNA DOBAI, K�ROLY �GOSTON BIR�
could be avoided if an early warning system is available against impending failures.
Such a system could also improve process safety, a key factor in many industrial
environments. Fault detection and diagnosis schemes are intended to provide advanced
warnings of incipient faults, so that corrective action can be taken without detrimental
interruption to processes [1].
Fault diagnosis of electrical machines can lead to greater plant availability, extended
plant life, higher quality products, and smoother plant operations.
Proper implementation of a maintenance program can reduce energy consumption in
plants by as much as 10�14%, while also reducing unplanned production downtime.
The average downtime costs can vary between 7.000 $ (in forest products) and
200.000 $ (in the automotive industry) [2].
Numerous fault detection methods have been proposed to identify the faults of
electrical machines. The fault detection methods involve several different types of fields
of science and technology and they are generally performed by mechanical and/or
electrical monitoring.
The most frequent used detection methods are [3]: motor current signature analysis
(MCSA), acoustic noise measurements, model, artificial intelligence and neural network
based techniques, noise and Transform-Based-Rotor-Faults-Detection-Method-for-/' >vibration monitoring, electromagnetic field monitoring
using search coils, or coils wound around motor shafts (axial flux related detection),
temperature measurements, infrared recognition, radio frequency (RF) emissions
monitoring, chemical analysis, etc.
For the detection of the induction motor's rotor faults here the motor current signature
analysis method was applied [4, 5].
2. The Wavelet Transform
In general terms, mathematical transformations are applied to signals to obtain a further
information from that signal that is not readily available in the unprocessed signal.
Most of the signals in practice, are time-domain signals in their raw format. That is,
whatever that signal is measuring, is a function of time. When time-domain signals are
plotted a time-amplitude representation of the signal is obtained. This is not always the
best representation of the signal for most signal processing related applications. In many
cases, as also in the case of electrical machines diagnosis, the most distinguished
information is hidden in the frequency content of the signal.
The frequency spectrum of a signal is basically the frequency components (spectral
components) of that signal. The frequency spectrum of a signal shows what frequencies
exist in the signal.
There are several transformations that can be applied, among which the Fourier
transform is probably by far the most popular. Although this transform is widely used
(especially in electrical engineering), it is not the only one, and it have several
disadvantages. The Fourier transform gives the frequency information of the signal
(how much of each frequency exists in the signal), but it does not marks when in time
these frequency components exist.
For better understanding the wavelet transform let take first an overlook on the short
time Fourier transform (STFT). There is only a minor difference between it and the
Fourier transform. DISCRETE WAVELET TRANSFORM BASED ROTOR FAULTS DETECTION...

The Fourier transform decomposes a signal to complex exponential functions of
different frequencies. The way it does this, is defined by the following equation:
+ =
dt
e
t
x
f
X
ft
j 2
)
(
)
(

(1)
where t is the time, f the frequency, and x denotes the analysed signal.
In short time Fourier transform (STFT), the signal is divided into small enough
segments, where these segments (portions) of the signal can be assumed to be
stationary. For this purpose, a window function is chosen. The width of this window
must be equal to the segment of the signal where its stationarity is valid. The window is
shifted along the time axis.
The definition of the STFT is the following:

=
t
ft
j
t
X
dt
e
t
t
t
x
f
t
STFT 2
*
)
(
)]
(
)
(
[
)
,
(
(2)
where (t) is the window function, and * marks the complex conjugate. As you can see
from equation (2), the STFT of the signal is nothing but the Fourier transform of the
signal multiplied by a window function.
For fast varying signals in order to obtain the stationarity, the window must be taken
as short as the signal within to be stationary. The narrower window means better time
resolution and better assumption of stationarity, but the frequency resolution is poorer.
A wide window means good frequency resolution, but poor time resolution and
furthermore, the condition of stationarity may be violated.
In electrical machines diagnosis both the continuous and the discrete wavelet
transform can be applied.
The continuous wavelet transform (CWT) was developed as an alternative approach
to the STFT to overcome its resolution problem. The wavelet analysis is done in a
similar way to the STFT analysis, in the sense that the signal is multiplied with a
function, with the wavelet, similar to the window function in the STFT, and the
transform is computed separately for different segments of the time-domain signal.
The continuous wavelet transform is defined by the following equation:




= =
dt
s
t
t
x
s
s
s
CWT
x
x
*
)
(
1
)
,
(
)
,
(

(3)

As it can be seen the transformed signal is a function of two variables ( and s, the
translation and scale parameters), respectively (t) is the transforming function, and it is
called the mother wavelet, a prototype for generating the other window functions.
The term translation is used in the same sense as it was used in the STFT; it is related
to the location of the window, as the window is shifted through the signal. This term,
obviously, corresponds to time information in the transform domain. The parameter
scale in the wavelet analysis is similar to the scale used in maps. High scales correspond
to a non-detailed global view (of the signal), and low scales correspond to a detailed
view. Similarly, in terms of frequency, low frequencies (high scales) correspond to a
global information of a signal, whereas high frequencies (low scales) correspond to a LOR�ND SZAB�, JEN BARNA DOBAI, K�ROLY �GOSTON BIR�
detailed information of a hidden pattern in the signal (that usually lasts a relatively short
time).
Once the mother wavelet is chosen the CWT computation starts with s=1 The wavelet
at this scale then is shifted towards the right by amount to the location t=, and the
equation (3) is computed to get the transform value at t= , s=1 in the time-frequency
plane. This procedure is repeated until the wavelet reaches the end of the signal. One
row of points on the time-scale plane for the scale s=1 is now completed. In this way the
continuous wavelet transform is computed for all the imposed values of s.
For the discrete wavelet transform (DWT) the main idea is the same as it is in the case
of CWT, but it is considerably easier and faster to implement.
A time-scale representation of a digital signal can be obtained using digital filtering
techniques. Filters of different cutoff frequencies are used to analyse the signal at
different scales. The signal is passed through a series of