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312
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 16, NO. 4, DECEMBER 2001
Pattern Recognition—A Technique for Induction
Machines Rotor Broken Bar Detection
Masoud Haji, Student Member, IEEE and Hamid A. Toliyat, Senior Member, IEEE
Abstract—A pattern recognition technique based on Bayes
minimum error classifier is developed to detect broken rotor
bar faults in induction motors at the steady state. The proposed
algorithm uses only stator currents as input without the need for
any other variables. First rotor speed is estimated from the stator
currents, then appropriate features are extracted. The produced
feature vector is normalized and fed to the trained classifier to
see if motor is healthy or has broken bar faults. Only number of
poles and rotor slots are needed as pre-knowledge information.
Theoretical approach together with experimental results derived
from a 3 hp ac induction motor show the strength of the proposed
method. In order to cover many different motor load conditions
data are obtained from 10% to 130% of the rated load for both
a healthy induction motor and an induction motor with a rotor
having 4 broken bars.
Index Terms—Broken bars fault, fault diagnosis, induction
motor, speed estimation, statistical classifier.
I. INTRODUCTION
M
OST electric motor failures interrupt a process, reduce
production, and may damage other related machinery.
In some factories, a very expensive scheduled maintenance is
performed in order to prevent sudden motor failures. Therefore,
there is a considerable demand to reduce maintenance costs and
prevent unscheduled downtimes for electrical drive systems, especially ac induction motors. In the past two decades, there has
been a substantial amount of research to provide new condition monitoring techniques for ac induction motors based on
analyzing vibration signals [1]–[4], or signals other than currents [5]. Vibration transducer is expensive and care should be
taken into account for mechanical installation and transmitting
the signal [6]. Similar problems exist while working with other
sensors like speed and temperature. Interestingly, signatures of
all signals are available on electrical terminals (currents) of electric machines including the vibration signals [22].
Current signals can easily be monitored for condition monitoring and control purposes. The objective is how to extract different features from the current signal and discriminate among
various machine conditions. Noise together with nonlinear behavior of machine with or without faults make this task very
difficult. Most of the works on motor current signature analysis (MCSA) use second order based techniques like FFT analysis [7]–[12] or Eigenanalysis-based frequency estimation (high
Manuscript received April 19, 2001. Paper was approved for presenting at the
IEMDC01, Cambridge, MA USA, June 2001.
The authors are with the Electric Machines and Power Electronic Laboratory,
Department of Electrical Engineering, Texas A&M University, College Station,
TX 77843-3128 (e-mail: [email protected]).
Publisher Item Identifier S 0885-8969(01)10054-9.
resolution spectral analysis) [21] and a few time-frequency analysis such as wavelet [13], [14]. Yazici and Kliman [15] have
presented a second order time frequency statistical method for
detection of broken bars and bearing faults for induction motors.
They have estimated torque, then knowing machine nameplate
information speed has been linearly estimated, finally a spectral
feature vector is produced which can be used for classification.
Recent developments in hardware and software make it possible to produce a system for condition monitoring of induction machines if we utilize signal processing and classification
techniques for fault diagnosis. In the following section, a brief
transformation approach
review of faults is presented. The
comes in Section III. Section IV deals with estimating speed
from current signal as a necessary element. In Section V, a brief
review for statistical pattern recognition and Bayes classifiers
are discussed. Feature extraction and the classifier are covered
in Section VI. A block diagram of the proposed method plus the
details of the developed algorithm and experimental results are
presented in Sections VII and VIII.
II. FAULTS IN AC INDUCTION MACHINES—A BRIEF REVIEW
[9]
Faults in electric machines produce one or more of the following symptoms:
a) Unbalanced air-gap voltages and line currents,
b) Increased torque pulsation,
c) Decreased average torque,
d) Increased losses and reduction in efficiency,
e) Excessive heating.
The most prevalent faults in AC induction machines are
briefly described in the following four categories:
1) Bearing Faults: Though almost 40–50% of all motor failures are bearing related, very little has been reported in the literature regarding bearing related fault detection using motor current techniques. Bearing faults might manifest themselves as
rotor asymmetry faults from the category of eccentricity related
faults.
2) Stator or Armature Faults: These faults start as undetected turn-to-turn faults, which grow and culminate into major
ones. Almost 30–40% of all reported faults of induction motor
failures falls in this category. Toliyat and Lipo have shown
through both modeling and experimentation that these faults
result in asymmetry in the machine impedance causing the
machine to draw unbalance phase currents [16].
3) Broken Rotor Bar and End Ring Faults: Rotor failures
now account for 5–10% of total induction motor failures.
0885–8969/01$10.00 © 2001 IEEE
HAJI AND TOLIYAT: PATTERN RECOGNITION—A TECHNIQUE FOR INDUCTION MACHINES ROTOR BROKEN BAR DETECTION
Broken rotor bars give rise to a sequence of side-bands given
by:
313
Equation (3) under ideal condition has physical meaning and
in steady state reduces to:
(1)
where is the supply frequency and is the slip. Frequency
domain analysis (second order) and parameter estimation techniques have been widely used to detect this type of faults. As
suggested in [17], presence of interbar currents in uninsulated
rotor cages, where the contact between the rotor core and the
bars are good, might make broken bar detection difficult.
In practice, the current side bands around fundamental may
exist even when the machine is healthy [9]. Also rotor asymmetry, resulting from rotor ellipticity, misalignment of the shaft
with the cage, magnetic anisotropy, etc., shows up at the same
frequency components as the broken bars [15]. Therefore, other
features of this fault need to be investigated.
4) Eccentricity Related Faults: is the condition of unequal
air-gap between the stator and rotor. It is called static air-gap eccentricity when the position of the minimal radial air-gap length
is fixed in the space. This maybe caused by the ovality of the
stator core or by the incorrect positioning of the rotor or stator
at the commissioning stage.
In case of dynamic eccentricity, the center of rotor is not at
the center of rotation, so the position of minimum air-gap rotates with the rotor. This maybe caused by a bent rotor shaft,
bearing wear or misalignment, mechanical resonance at critical
speed, etc. In practice, an air-gap eccentricity of up to 10% is
permissible. Both static and dynamic eccentricities tend to exist
in practice.
Using Motor Current Signature Analysis (MCSA) the equation describing the frequency components of interest is:
(2)
for static eccentricity, and (1, 2, 3, …) for dywhere
namic eccentricity. is the number of rotor slots and is the
1, 3, 5, … .
number of poles, and
Other equations are also presented in the literature as low frequency components for mixed eccentricity [9]. As it is obvious,
sometimes different faults produce nearly the same frequency
components or behave like healthy machine, which make the diagnosis impossible. Specially, if it is only based on second order
frequency analysis. This is the reason why new techniques must
also be considered to reach a unique policy for distinguishing
among faults.
(4)
Under abnormal conditions, such as the broken rotor bars, (4)
is no longer valid, however, without loss of information we can
still work with and in (3).
Benbouzid and Nejjari have shown that – pattern differs
from each other in healthy machine and under open phase or
stator unbalance faults [18]. Cardoso et al.have shown different
– pattern for faults in rectifier diodes and power switches
for ac drive systems and for broken rotor bars in ac induction
motors [19].
transformation by itself is not enough for
Use of Park’s
fault diagnosis for a number of reasons; first, it is not obvious if
patterns are unique for different faults, secondly classification
is very difficult if noise and practical problems are considered.
transformation keeps all
However, as mentioned above the
information in the currents while reduces the number of variables from three to two. In this paper, and variables are used
in the proposed approach.
IV. SPEED ESTIMATION—RSH APPROACH
Effective sensorless speed estimation is desirable for both
on-line condition monitoring of induction motor and sensorless adjustable speed ac drive application [20]. The mechanical speed information of an induction machine is embedded in
the stator currents. The slots produce a continuous variation of
the air-gap permeance in squirrel cage induction motors. During
operation, the rotor slot MMF harmonics will interact with the
fundamental component of the air-gap flux because of the rotor
currents. Therefore, the air-gap flux will be modulated by the
passing rotor slots, producing rotor slot harmonics (RSH). A
number of researches have been performed to extract rotor speed
from RSH [23]–[25].
The induction motor speed, , can be calculated using RSH
at any slip condition from the following expression:
(5)
III. DQ TRANSFORMATION
In a 3-phase induction motor, the sum of stator currents is
zero. Therefore, only two currents are sufficient for processing
and the third one can be obtained from the other two phases. A
suitable representation is the use of Park’s transformation given
by:
(3)
where and are as in (2). Since the rotor slot harmonics are
related to the rotor currents, their magnitude reduce with decreasing load making it difficult to detect RSH. In the absence
of detectable RSH, the use of eccentricity-related harmonics has
been proposed [26].
In the proposed approach, the rotor speed is needed first as
a normalizing factor for features and secondly for windowing
broken bars harmonics from current spectrum. It will be shown
later that the power of signal in this window plus phase at desired
harmonics, will be other features.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 16, NO. 4, DECEMBER 2001
V. PATTERN RECOGNITION AND BAYES MINIMUM ERROR
CLASSIFIER—A BRIEF REVIEW [27]
A pattern recognition system contains three parts, a transducer, a feature extractor and a classifier. The transducer senses
the input and converts it into a form suitable for machine processing. The feature extractor extracts presumably relevant information from the input data. The classifier uses this information to assign the input data to one of a finite numbers of category . The fundamental theory and the necessary formulas of
the statistical pattern recognition technique are presented next.
More details can be found in [27].
A. Bayes Decision Theory
Bayes decision theory is a fundamental statistical approach to the problem of pattern classification. Let
be the finite set of states of nabe the probability of each state (or class).
ture (class) and
Having an observed vector (or feature vector), the Bayes
theory is based on the formula:
Fig. 1.
Power spectral density of stator currents.
normal density is completely specified by two parameters, mean
vector and covariance matrix:
(8)
(6)
where
(9)
is the state-conditional probability density funcwhere
tion for , i.e., the probability density function for given that
is the probability of selected class
state of nature is .
, given the feature vector . The strength of the above formula is that it relates our observation and priori probability,
, to a posteriori probability,
.
. It is
For simplicity it is often abbreviated as
shown that by using normal distribution in our analysis, which
in most cases is a fair assumption, we can have a very simple
form for the discriminant function for the Bayes minimum error
classifier:
(10)
B. Bayes Minimum Error Classifier
The problem of classification comes with the optimization
problem. We want to have a threshold or boundary conditions
in the space of feature vectors in order to discriminate different
classes. This boundary condition is called discriminant function
or decision surface. Different decision surfaces have different
properties. If the decided class is but the true class is , then
and in error if not. If errors are to
the decision is correct if
be avoided, it is natural to seek a decision rule that minimizes the
average probability of error, i.e., the error rate. It is proved that
in (6) as the discriminant function
if we use
(or decision surface), then we will minimize the probability of
error by:
Decide
if
(7)
This is called Bayes Minimum Error Classifier. Another important classifier is Bayes Minimum Risk where different errors
have different weights.
C. Simplified Formula for Normal Distribution
Primarily the conditional densities determine the structure of
a Bayes classifier. Of the various density functions that have
been investigated, none has received more attention than the
multivariate normal density function. The general multivariate
where is the feature vector and and are the covariance
matrix and the mean vector for each class.
VI. FEATURE EXTRACTION AND THE CLASSIFIER
Based on the discussion in the previous sections, torque developed at the broken rotor bar frequency (Fig. 1) in and
are assumed to be features. Another feature is phase at that frequency. In this paper, experiments were performed on a broken
rotor bar and a healthy rotor induction motors.
Without loss of generality, the appropriate features can be extracted from eccentricity related harmonicas as well. All features are normalized according to the running speed and load to
have comparable data for different conditions.
The classifier is Bayes minimum error assuming that features
have normal distribution with equal likely classes. This is a fair
assumption at this level but in case of multiple classes and online
monitoring, different probability should be assigned to different
classes. For example: in online monitoring techniques, statistical rate of occurrence of main faults can be used as a probability measure (refer to Section II).
The utilized discriminant function has the form in (10), where
is the feature vector and and are the covariance matrix
, respectively.
and the mean vector for each class
Further details plus the block diagram of the proposed method
HAJI AND TOLIYAT: PATTERN RECOGNITION—A TECHNIQUE FOR INDUCTION MACHINES ROTOR BROKEN BAR DETECTION
315
Fig. 3. Normalized torque and phase produced by broken bar harmonics (Id
current). Horizontal axis shows number of samples in each class.
number of columns (features) and refers to each sample. The
normalized feature vector is calculated by:
Fig. 2. Block diagram of the proposed algorithm.
and experimental results derived from both a healthy induction
motor and the one having four broken bars are covered in the
next two sections.
VII. BLOCK DIAGRAM
Fig. 2 shows the proposed algorithm. Stator currents are meatransformation they are consured first, and then using the
verted to – form. For normalization and getting features, rotor
speed is important. Therefore, the rotor speed is estimated first
by using RSH technique. Knowing the number of rotor bars and
stator poles, rotor speed is estimated from the power spectral
density of the – currents. Then, necessary features are extracted, normalized and fed to the classifier. Applying the discriminant function (10) on the produced vector, the classifier
decides whether it comes from a healthy motor or a motor with
broken rotor bars. Normalization has a two step procedure:
1) For the 1st and 3rd features; first the integral of power
spectral density (PSD) in a window around broken rotor
bar harmonics and fundamental harmonics are calculated
(Fig. 1). Then, division of these two gives a normalized
, if
power of the broken bar harmonics. Since
we divide the result by (1-s), we will have a normalized
torque produced by the broken bar harmonics (the desired
feature).
2) In order to give the same weight to different features, all
produced data from healthy and broken bar faults are put
together and normalized according to (11).
(11)
where
equation for
, and 1 in the
is for the unbiased estimation [27]. is the
(12)
is the dimension of our feature space and the feawhere
. To be able to classify, acture vector is:
cording to Bayes minimum error classifier, we should find mean
, and covariance matrix
of each class (healthy
vector
and rotor broken bar fault) which is called offline training. For
simplicity, we assumed that features have normal distribution.
Therefore, the maximum likelihood estimate for the mean and
covariance of each class are [27]:
(13)
(14)
and
in (11) with
and
One should not confuse
in (13) and (14). The first two are used for normalizing the ex, while the last two are used for classitracted feature vector
fication in discriminant function (10).
VIII. EXPERIMENTAL RESULTS
The proposed algorithm was implemented on a 3 hp, 3-phase
induction motor with a rotor having 44 bars. The induction
motor was run from 10% to 130% of rated load with a healthy
rotor and a 4 broken bar rotor. Therefore, 47 sets of different
data were collected and processed to cover all different
torque-speed machine conditions. Figs. 3 and 4 show features
derived from these data. First and third features in these
figures are normalized power in a window around broken bar
transformation
harmonics in and , respectively. Use of
will be more useful in case of stator unbalances or eccentricity.
As can be seen, there is not much difference between first and
third features. But, the algorithm remains more robust if we
consider both features. The second and fourth features are the
316
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 16, NO. 4, DECEMBER 2001
steady state. Only number of poles and rotor slots are needed
as pre-knowledge information. Stator currents are the only inputs to this algorithm. For normalization and getting features,
rotor speed is important. Therefore, the rotor speed is estimated
first by using rotor slot harmonics method, then features are extracted. Once normalized mean and variance plus mean and covariance of each class are determined for an ac induction motor,
the technique can be used in online condition monitoring of the
motor. Theoretical approach plus experimental results from a
3 hp induction motor show the strength of the proposed method.
Without loss of generality, the algorithm can be revised to include other faults such as eccentricity and phase unbalance.
Also, if appropriate features are derived, this method can be
applied for fault classification in other electric machines like DC
machines.
Fig. 4. Normalized torque and phase produced by broken bar harmonics (
current). Horizontal axis shows number of samples in each class.
Iq
ACKNOWLEDGMENT
The authors would like to express their gratitude to Prof N.
Kehtarnavaz, and B. N. Araabi from Texas A&M University for
their remarks.
REFERENCES
Fig. 5. Classification results. Horizontal axes 1 corresponds to healthy class
and 2 to rotor broken bar faults. Only 1 out of 47 samples is misclassified (error
2.1%).
=
normalized phase information, which as the results show, do
not carry much information for this case.
Since not very many data for training and test were available, one suitable approach is to take one sample out from the
data pool as a test sample and use the remaining for training the
classifier. This procedure was iterated 47 times and results were
compared with the true classes.
Fig. 5 shows the classification results. Only one sample was
misclassified which means that we have near 2 percent error.
This is because of the limited number of training and test samples. The real error in online monitoring is higher than this, as
machine parameters change in different speed and torque conditions. If motor manufacturers use this algorithm, error can reasonably be kept low because of the huge number of training and
test data that they might have.
To get better and more accurate results, rotors with different
number of broken bars should be used. Also, with inverter we
can have very many samples at each load with varying speed.
IX. CONCLUSION
A well known pattern recognition technique, Bayes minimum
error classifier is utilized to distinguish between broken rotor
bar fault and healthy condition of an ac induction machine at
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