Advance in Electronic and Electric Engineering.
ISSN 2231-1297, Volume 3, Number 8 (2013), pp. 1019-1030
© Research India Publications
http://www.ripublication.com/aeee.htm
Tradeoff Analysis of Wavelet Transform Techniques for the
Detection of Broken Rotor Bars in Induction Motors
S.M. Shashidhara1, Member, IEEE and Dr. P. Sangameswara Raju2
1
Research Scholar, Dept of of EEE, SVU College of Engineering, Tirupati, India.
2
Professor, Dept of EEE, SVU College of Engineering, Tirupati.
Abstract
This paper presents the fault detection of broken rotor bars using
different mother wavelets and the tradeoff analysis of these wavelets is
performed. The stator phase current was used as input to the fault
detecting module based on wavelet analysis. DWT coefficients of the
stator current in a particular frequency band are calculated and
analysed. Daubechies db8, db9, db10 and Symlet sym7 and sym8
wavelets are applied to analyse stator current disturbed due to broken
bars . The sensitivities of these wavelets to fault signals do vary and
they are compared and evaluated to choose the most optimal one. This
facilitates the diagnosis of broken rotor bar and also indicates the
number of broken bars. This paper presents the results and
demonstrates the effectiveness of the proposed approach for fault
diagnosis.
Index Terms: Induction motor, fault detection, tradeoff analysis,
broken rotor bar, wavelet, DWT, Stator current.
1. Introduction
Fault diagnosis on Induction motor is a major concern in the in the electric drives
industry as 80% of the electric drives industry works on Induction motors. The fault
diagnosis based on the signal processing methods is very widely used as it is a
noninvasive method. While using signal processing based fault diagnosis we need to
reduce the time taken for the diagnosis. The sample-by-sample comparison and
analysis would be time taking and the computational complexity would be high. That
is why feature based methods were used like the Fast Fourier Transform (FFT), Short
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S.M. Shashidhara et al
Time Fourier Transform (STFT) and recently Wavelet Transforms (WT). Wavelet
transform takes its seat in this application because of its feature extracting capability
from the signals. Motor current Signature Analysis (MCSA) is the method that would
be appropriate to deal with because it is sensorless and is the most effective way of
analysing the faults in the induction motors.
A comparison of stator current, vibration, and acoustic methods in detecting broken
bar and bearing faults were presented by [1] The MCSA method using Wavelet
Transform was used in [2] for broken rotor bar method in an induction motor. The
Sensorless Induction motor control technique used the Wavelet Based fault diagnosis
was presented in [3]. Empirical model decomposition was used for detecting the
nonlinear system of the broken rotor fault was detected by the Wavelet Transform[4].A
fault linearizing method called stepping finite element was introduced ,which would be
got by filtering ,differentiating and transforming the fault signal using the Daubecheis
wavelet for 5 times was presented in [5]. This paper takes up the tradeoff analysis
among different mother wavelets for fault detection of rotor bars. In spite of
satisfactory performance of DWT, it has some drawbacks. Selection of optimal mother
wavelet is somewhat arbitrary, not a known priori which may introduce error in the
detection parameters. Besides, the overlap between bands associated with wavelet
signals appearing mainly for lower order wavelet. In this paper, the proposed approach
is focused on the study of different wavelet performance by analysis the coefficients
derived from the DWT [11] [12]. A best representative wavelet is selected for rotor
fault detection by comprehensive analysis these coefficients. This permits a good
interpretation of the phenomenon due to the variation of these signals reflects distinctly
the development of the harmonics associated with broken rotor bars during the
transient. Moreover, the use of the wavelet signals (approximation and high order
details) resulting from the DWT constitutes an advantage because these signals act as
filters, according to Mallat algorithm, allowing the automatic extraction of the time
evolution of the low frequency components that are present in the signal during the
transient [13].
2. Wavelet Transforms
To extract data from signals and bring out the dynamics that agrees to the signals, a
right signal processing technique is to be chosen. Generally, the process of signal
processing translates a time domain signal into another domain as the diagnostic
information embedded within the time domain is not readily evident in its original
form. Mathematically, this can be accomplished by mapping the time domain signal as
a series of coefficients, based on a equivalence between the signal x(t) and template
functions {Ψ*n(t)}.
∞
∞
(1)
Tradeoff Analysis of Wavelet Transform Techniques for the Detection of Broken 1021
The inner product between x(t) and Ψ*n(t) is
,
(2)
2.1 Representative Signals
There are many commonly used wavelets for performing the DWT. Haar is orthogonal
and symmetric. The property of symmetry ascertains that the Haar wavelet bears linear
phase characteristics, meaning that when a filtering is performed on a signal with this
mother wavelet, there will be no phase deformation in the filtered signal. Moreover, it
is the simplest base wavelet with the highest time resolution.
However, the rectangular contour of the Haar wavelet makes its corresponding
spectrum with slow decay, heading to a low frequency resolution. Another is
Daubechies, is orthogonal and asymmetrical, which brings in a large phase distortion.
This means that it cannot be employed in applications where a phase data needs to be
kept. It is also a compact support mother wavelet with a given support width of 2N -1,
in which N is the order of the base wavelet.
One of the major advantages of wavelet transform for signal analysis is the
abundance of the mother wavelets. From such abundance comes up a question of how
to pick out a base wavelet that is most appropriate for analysing a specific signal. Since
the choice in the first place may bear on the result of the wavelet transform at the end,
the question is logical. For example, as shown in Figure 1.
Therefore, in the following section, a general strategy for base wavelet selection is
presented. Then, several quantitative measures that can be used as guidelines for
wavelet selection are given. While Morlet wavelet is efficient in pulling out the
impulsive component, the Mexican-hat and Daubechies wavelets did not amply reveal
the characteristics of impulsive component
.
Figure 1
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S.M. Shashidhara et al
2.2 Selection Criteria
There are two means to assess the performance of wavelet , one is qualitative and the
other is quantitative. Base wavelets are defined by orthogonality, symmetry, and
compact support. Understanding these attributes will help pick out a candidate mother
wavelet from the wavelet families for examining a specific signal. For example, the
orthogonality dimension indicates that the inner product of the base wavelet is unity
with itself, while it is zero with other scaled and shifted wavelets. As an outcome, an
orthogonal wavelet is efficient for signal decomposition into non-overlapping subfrequency bands. The symmetric property ascertains that a base wavelet can serve as a
linear phase filter. A compact support wavelet is one whose basis function is non-zero
only within a finite interval. This allows the wavelet transform to efficiently map
signals that have localized features.
a. Db Wavelet
b. Sym Wavelet
Fig. 2: Demonstration of wavelet family
Tradeoff Analysis of Wavelet Transform Techniques for the Detection of Broken 1023
In this paper, the approach for the diagnosis of broken rotor bars is discussed and
applied to industrial induction machines. Several experiments are conducted for
different operating conditions and fault cases such as one-bar breakage, two-bar
breakages and also a variation of load. For the purposes of testing, the bar breakages
were forced in the workshop in motors.
3. Experimental Setup
In this part, an on-line experimental rig is developed in order to test and verify the
performance of the diagnosing system. The on-line current monitoring system is
shown in Figure1. The experimentation is conducted under the self-designed test rig
which is mainly composed a set of three phase induction machines, DC generate,
current transducer, A/D converter, and computer. Firstly, transient stator current
signals are collected from tested motors and signal preprocessing is conducted which
contains smoothing and subtraction. Moreover, Matlab & Wavelet toolbox is used to
decompose the acquired time domain signal into time-frequency domain. Then, fault
features waveband is extracted from all intended wavelet transform level. Finally, the
individual diagnosis results are applied to validate the developed model.
The tested motors are three identical three-phase, 2-pole, 36 stator slots and 28
rotor slots induction motors. The specifications of the proposed induction motors used
in our experiment are 5.5KW, 3000 rpm, 20.6A, 50Hz, 2 poles, 36 stator slots, 28 rotor
slots. The tests are carried out on a healthy motor and a motor with drilled bars. The
rotor bar breakages were broken deliberately by drilling holes in the workshop.
Stator currents of the motor are sampled by a Hall Effect sensing element which is
positioned in one of the phase line current wires. The stator current is sampled at 1.92
KHz rate and interfaced to a PC by a data acquisition system. The quantities have been
measured for healthy and three broken rotor bars at varied load.
The motor load is operated through the generator shaft speed. A DC generator is
coupled to the motor as the load. The excitation current of the generator has been
adjusted in order to regulate the output voltage. A resistance box is connected to the
terminals of the generator. The resistance of this box can be selected step by step by a
selector switch on the box.
Sampling frequencies of 1920 samples/s which enable good resolution analyses,
Table I shows the frequency levels of the wavelet function coefficients.
Table 1: Frequency levels of wavelet.
Wavelet
Analysis
A5
D5
Frequency
Components
(Hz)
0-30
30-60
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S.M. Shashidhara et al
D4
D3
D2
A1
60-120
120-240
240-480
480-960
4. NDICES for Diagnosis of Fault
As already mentioned, Rotor broken bars render side band components around the
fundamental frequency. Moreover, referring to Table I indicates that the wavelet
coefficients in D5 consist of side band components around the fundamental frequency.
Therefore, in this paper, a different wavelet (db8, db9, db10, sym7, sym8) coefficient
in D5 has been used to diagnose the fault and also the number of the broken bars. By
comparing these coefficients in D5, the best wavelet was selected for diagnosis of rotor
fault and the number of broken rotor bars.
Fig. 3: Wavelets coefficients for healthy motor.
Fig. 4: Wavelets coefficients for one broken rotor bar.
Tradeoff Analysis of Wavelet Transform Techniques for the Detection of Broken 1025
Fig 5: Wavelets coefficients for two broken rotor bars.
Fig. 6: Wavelets coefficients for three broken rotor bars.
Fig. 7: Different Wavelet coefficients in D5 for two broken rotor
bar motor under experimental results.
Fig. 8: Criterion function 1.
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S.M. Shashidhara et al
Fig. 9: Criterion function 2.
Table 2: Criterion function for different wavelets under healthy condition.
Wavele Mea STD Mean
ts
n
fluctuatio
ns
Db8
4.393 2.113 0.0769
Db9
4.399 2.115 0.0782
Db10 4.421 2.116 0.0782
Sym7 4.432 2.117 0.0783
Sym8 4.462 2.118 0.0789
Index1
Index2
0.4809167
0.4808627
0.4785932
0.4777557
0.4747243
0.0175015
0.0177735
0.0176863
0.0176645
0.0176794
Table 3: Criterion function for different wavelets under one broken bar.
Wavele Mea STD Mean
ts
n
fluctuatio
ns
Db8
4.199 2.121 0.1097
Db9
4.196 2.122 0.1095
Db10 4.173 2.205 0.1221
Sym7 4.195 2.136 0.1001
Sym8 4.182 2.203 0.1173
Index1
Index2
0.5051077
0.5058027
0.5285392
0.5091524
0.5268884
0.0261221
0.0260944
0.0292581
0.0238583
0.0280481
Table 4: Criterion Function For Different Wavelets under Two Broken Bars.
Wavele Mea STD Mean
Index1
ts
n
fluctuatio
ns
Index2
Tradeoff Analysis of Wavelet Transform Techniques for the Detection of Broken 1027
Db8
Db9
Db10
Sym7
Sym8
3.995
3.985
3.897
3.992
3.988
2.167
2.168
2.168
2.169
2.171
0.1235
0.1296
0.1311
0.1357
0.1388
0.5425854
0.5441087
0.5564849
0.5434984
0.5443377
0.0309097
0.0325170
0.0336369
0.0339921
0.0347983
Table 5: Criterion Function For Different Wavelets under Three Broken Bars.
Wavele Mea STD Mean
ts
n
fluctuatio
ns
Db8
3.779 2.186 0.1635
Db9
3.791 2.188 0.1696
Db10 3.796 2.189 0.1711
Sym7 3.801 2.190 0.1757
Sym8 3.810 2.191 0.1788
Index1
Index2
0.5786521
0.5772567
0.5767417
0.5762836
0.5749560
0.0432619
0.0447269
0.0450678
0.0462173
0.0469180
By the numerical analysis of mean, STD and variations, the change tendencies can
be evolved when broken rotor bars occur in induction motor. However, these
tendencies are not easy for operator to judge due to the values are too small to separate
them. To resolve this problem, according to the above cited facts the following indices
are proposed for the diagnosis of the broken bar:
Criterion function=
Criterion function=
Table 6: Criterion Function for Different Wavelets for three Broken Bars in
Experimental Results.
Wavele Mea STD Mean
ts
n
fluctuatio
ns
Db8
4.179 2.436 0.1935
Db9
4.191 2.438 0.1996
Db10 4.196 2.439 0.2011
Sym7 4.201 2.440 0.2057
Sym8 4.210 2.441 0.2088
Index1
Index2
0.5830880
0.5818125
0.5813415
0.5809215
0.5797098
0.0462996
0.0476156
0.0479208
0.0489575
0.0495855
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S.M. Shashidhara et al
Wherever the average of the absolute value of the wavelet coefficients in D5 is
expressed in per-unit with reference to the average amplitude of the currents. The value
of index 1 increases by occurrence of the breaking in the bars of the rotor and has
rising trend as shown in Figure 9. According to Table II-VI, the value of index 1 for a
healthy motor is 47-48% and for the motor with one broken rotor bar is 50-51%. An
evident difference between these values makes the proposed index enable to diagnose
faulty motor from healthy motor. On the other hand, comparison of this index for one
and two broken bars indicates that this is a convenient index for the diagnosis of the
number of broken bars.
Figure 7 shows the experimental results for 3 rotor broken bars which are in good
correspondence with the computer simulation results. Although by introducing these
two indexes, boundaries between healthy and faulty and also the numbers of broken
bars is clearly depicted in Figure 8, 9. To increase the accuracy of diagnosis, the most
suitable wavelet must be selected. However, there is no definite rule to lead how to
pick out the right wavelet until now. Most of the inquiries are based on trial and error
approach. In this paper, Daubechies db8, db9, db10 and Symlet sym7 and sym8
wavelets were used to diagnose broken rotor bars. According to Figure 8, 9, wavelet
sym8 has the most apparent gap to detect 1, 2 and 3 broken rotor bar faults.
5. Conclusion
In this paper, the proposed fault detecting algorithm is implemented on the stator
current of a healthy and faulty induction motor. Two novel criterion functions are
presented to select the optimal mother wavelet to diagnose the broken rotor bars fault
and also the number of broken bars in induction motors. Both simulations and
experiments prove that increase of the load and broken bars is followed by a growth in
amplitude of harmonic components of a faulty induction machine.
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Authors
Prof. S. M. Shashidhara is working as Professor in Electronics &
Communication Engineering dept of Proudadhevaraya Institute of
Technology, Hospet, India. Member of ISTE, IEEE, Execom Member
of Communications Society, Bangalore. His areas of interest include
Power Electronics, Power Systems Protection, Digital Signal
Processing and Communication Systems.
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S.M. Shashidhara et al
Dr. P. Sangameswara Raju, received Ph.D from Sri Venkateswara
Univerisity, Tirupati, Andhra Pradesh. He is working as Professor and
Head of the Department of Electrical & Electronics Engineering, S.V.
University. Tirupati, Andhra Pradesh, India. He has over 50
publications in National and International Journals and conferences to
his credit. His areas of interest are Power Systems operation, control
and stability.