SETIT 2007

4th International Conference: Sciences of Electronic,

Technologies of Information and Telecommunications
March 25-29, 2007 – TUNISIA

On-line diagnosis of induction motor faults

LEBAROUD Abdesselam
CLERC Guy
Université Claude Bernard, Lyon 1 – CEGELY – Bâtiment OMEGA 43, boulevard du 11
novembre 1918 69622 VILLEURBANNE cedex France
E.mail : lebaroud@yahoo.fr

Abstract: A new method of automatic diagnosis of induction motor faults based on the time-frequency ambiguity plane
analysis of the current waveforms. This method is composed of two sequential processes: a feature extraction and a
classification. In the process features extraction, the time-frequency representation (TFR) have been designed for
maximizing the separability between classes representing the different faults; bearing fault, stator fault and rotor fault.
The classification of a new signal is based on the Mahalanobis distance.
Key words: automatic diagnosis, time-frequency representation, bearing fault, stator fault, rotor fault

1.1. Bearing Faults

INTRODUCTION
Bearing faults such as outer race, inner race, ball
In many classification applications, features are
fault, and train fault cause machine vibration. These
traditionally extracted from standard Time-Frequency
faults have vibration frequency components, fv, that
Representations (TFRs) [1]. Quadratic class of time–
are characteristic of each fault type. The mechanical
frequency representations can be uniquely
vibration caused by the bearing fault results in air gap
characterized by an underlying function called a
eccentricity. Oscillations in air gap length induce
kernel. In previous time-frequency research, kernels
variations in flux density. These variations produce
have been derived in order to fulfil properties, such
harmonics on the stator current. The characteristic
minimizing quadratic interference. Although some of
current frequencies, f c , due to bearing characteristic
the resulting TFRs can offer advantages for
classification of certain types of signals the goal of vibration frequencies are calculate by [7]:
sensitive detection or accurate classification is rarely f c = f s ± mfν (1)
an explicit goal of kernel design [2]. Those few
methods that optimize the kernel for classification Where f s is fundamental frequency, fν
purpose, constrain the form of the kernel to predefined Characteristic vibration, frequency m Positive integer
parametric functions with symmetries that can not be multiplier.
suitable to detection or classification [3], [4].
Traditionally, the objective of time–frequency research 1.2. Rotor faults
is to create a function that will describe the energy A fault on the rotor, such as a broken rotor bars,
density of a signal simultaneously in time and causes asymmetrical working conditions within the
frequency. For explicit classification, it is not rotor. The current rotor bars, which are at the
necessarily desirable to accurately represent the frequency s f , can be expressed into positive and
energy distribution of a signal in time and frequency.
In fact, such a representation may conflict with the negative sequence components ± s f within the rotor,
goal of classification, generating a TFR that where s is the slip. Consequently, the negative
maximizes the separability of TFRs from different sequence rotor current results in stator currents at
classes. It may be advantageous to design TFRs that frequency [8]:
specifically highlight differences between classes − sf + f r = − sf + f − sf = (1 − 2 s) f (2)
[5],[6]. In this paper we propose a technique for
designing an optimized time-frequency representation The interaction of the (1 − 2 s) f harmonic of the
(TFR) from a time-frequency ambiguity plane applied motor current with the fundamental air-gap flux
for a precise classification of motor faults; such as; produces speed ripple at 2sf and gives rise to
bearing fault, stator faults and broken bars. additional motor current harmonics at frequencies
1. INDUCTION MACHINE FAULTS (1 ± 2ks) f , k=1,2,3.. [9] with k = 1 , the frequency
sidebands (1 ± 2s) f of the fundamental are very

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commonly used to detect broken bar faults. The 3. INDUCTION MACHINE FAULTS
motor-load inertia also affects the magnitude of these CLASSIFICATION
sidebands [10]. The optimal TFR method is applied to classification
of three kinds of induction machine faults, which are;
1.3 STATOR FAULTS bearing fault, stator fault and rotor fault. Thus, four
In ideal conditions, the motor supply current classes are considered: healthy motor, bearing fault,
contains only a positive-sequence component, leading stator fault and broken bars. The goal of the feature
to a constant space vector current modulus. If there is extraction is to generate a N-point feature vector from
inter-turn short circuit in the motor stator winding, the the original 10000-point current signal. The feature
supply current will exhibits some sort of unbalance. vectors are classified with Mahalanobis distance. The
When explained by symmetrical components theory, characteristic frequencies of the three faults
the stator asymmetry produces a component at considered, are located near to the fundamental
frequency − f (i.e., a negative sequence component). frequency and, in order to preserve relevant
This component gives rise to torque ripples at information, the original signal is resample with a
frequencies of 2sf and consequently produce speed downsampling rate 25. Only the range of the required
frequencies is preserved. By downsampling, the signal
ripples of different amplitude, being differently
dimension has been reduced greatly. This leads to a
filtered by the machine-load inertia [11].
great reduction of the computation complexity. In
addition, electrical noise has also been attenuated.
2. USE OF THE KERNEL AND AMBIGUITY
After this step, a new 200-point signal that keeps the
PLANE FOR CLASSIFICATION
signature of the original signal is obtained. The time-
frequency ambiguity plane of the signal is calculated
The discrete version of ambiguity function [5] is: by eq. (3). We will construct the TFR optimal for our
classification task by smoothing the ambiguity plane
N −1 2π
with a class-dependant kernel. Here, the dimension of
A[η ,τ ] = Fn→η {R[n,τ ]} = ∑R[n,τ ]e
-j nη
N
(3) ambiguity plane is 200*200. Basically we will directly
n=0 select N points from this plane as our feature vector.
Where F represents the Fourier transform, is1 i s2 i si
η represents discrete frequency shift, and τ
represents discrete time lag. The instantaneous
autocorrelation function R[n,τ ] is defined as:
(TFR)1 (TFR)2 … (TFR)i
R[n,τ ] = x * [n ]. x[(n + τ )N ] (4)

This method, used to design kernels (and thus

TFRs), optimizes the discrimination between
predefined sets of classes. The resulting kernels are Classification
not restricted to any predefined function but, rather,
are arbitrary in shape. This approach requires the
necessary smoothing in order to achieve best
classification performance. The use of the kernel and
ambiguity plane includes two sequential processes: Level 1
Stator fault Bearing Fault Rotor fault
feature extraction and classification. Our goal is to
design a classification-optimal representation that
specifically emphasizes the differences between
Level 2 Severity degree
classes. It is not necessary for the representation to
accurately describe the time-frequency information of
the signal. This technique has been successfully Figure.1 Procedure of Faults classification
applied for tool-wear monitoring and radar transmitter
identification [5].
3.1 Fisher’s discriminant ratio kernel (FDR)
The kernel determines the representations and its
properties. A kernel function is a generating function The kernel φ opt (η ,τ ) is designed for each specific
that operates upon the signal to produce the TFR. The classification task. We determine N locations from the
characteristic function for each TFR is A(η ,τ )φ (η ,τ ) 200*200 ambiguity plane, in such a way that the
In other words, for a given a signal, a TFR can be values in these locations are very similar for signals
uniquely mapped from a kernel [3]. The classification- from the same class, while they vary significantly for
optimal representation TFRi can be obtained by signals from different classes. The notation
smoothing the ambiguity plane with an appropriate Aij [η ,τ ] represents the ambiguity plane of the jth
kernel φ opt , which is a classification-optimal kernel. training example in the ith class. We design and use
The problem of designing the TFRi becomes Fisher’s Discriminant Ratio kernel to get those N
equivalent to designing the classification-optimal locations.
kernel φ opt (η , τ ) .

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The kernels are designed by I training example Feature points are ambiguity plane points of
signals from each class with the equation as follows: locations (η ,τ ) where φopt
(c)
[η ,τ ] = 1 . Therefore, the
process of feature extraction is to select points that are

FDR(η ,τ ) =
(m [η ,τ ] − mFault Healthy
[η ,τ ]) 2

(5)
optimal for the classification task from the ambiguity
2
VFault [η ,τ ] + VHealthy
2
[η ,τ ] plane. The optimal number of nonzero points is
determined by evaluating the classifier performance
Where using the K best kernel points (i.e., the K points with
N1 N2
the largest Fisher’s discriminant ratio). Kopt is selected
m Fault [η ,τ ] = ∑∑ A [η ,τ ]
1 to be the number K for which the probability of
ij Fault
(6)
I i =1 j =1 correct classification is the greatest. Selection of
points in the Doppler-delay plane is interpreted as
N1 N2

m Healthy [η ,τ ] = ∑∑ A [η ,τ ]
1 masking of ambiguity function of the signal by an
ij Healthy
(7)
I i =1 j =1 adapted binary function providing an optimal kernel
According to the symmetries of the ambiguity plane,
mFault [η ,τ ] and mHealthy [η ,τ ] average of fault and only points on a quarter plane are considered.
healthy classes of ambiguity plane
I = N1.N 2 number of examples per class 3.3 Classification by Mahalanobis distance
N 2 : Number of current examples of same load level
N1 : Number of load levels After designing the kernels, using examples from
2
VFault [η ,τ ]2 and VHealthy
2
[η ,τ ] variances of the fault and each of the C classes, actual classification is
healthy classes in the ambiguity plane performed. Given a particular unknown test signal
vector (the classifier is not trained on this example),
[η ,τ ] = ∑ (A [η ,τ ] − m [η ,τ ])
N
2 1 2
the classifier estimates the class membership of this
VFault ij Fault Fault
(8)
I j =1 example. The classification of the point x in one of c
classes can be realized by standard classification
[η ,τ ] = ∑ (A [η ,τ ] − m [η ,τ ])
N
2 1 2 techniques (e.g. linear or quadratic discriminant
VHealtyn ij Healthy Healthy
(9)
I j =1 functions, distance, neural networks, ..). We choose to
classify with a Mahalanobis distance. The feature
The system is trained by using ten current signals at vector of signal x given by:
0% and 100% load levels. We take N 1 = 2 in order to
FVx = φopt
(c)
o Ax (12)
solve the problem of the load levels. Test is then
performed on current signals collected at the 25% and Where Ax Ambiguity Plane of signal x
70% load levels. For C -classes must be designed x is affected to the class ci ⇔ i = arg min {d M (FVx )}
C − 1 kernels. As we have four classes (three fault Where d M (FV x ) is the FVx Mahalanobis i =1...c
distance of
cases and the healthy case of the machine), we must class ci, arg min {d M (FV x )} is the minimal value of the
design three kernels: bearing fault kernel, stator fault d M (FV x ) i =1...c

kernel and rotor fault kernel. Each kernel separates the

healthy case of the fault case. (
d M (FVx ) = (FVx − FVtrain
(c)
) .∑c (FVx − FVtrain
(c )
T
) −1
)12
(13)
Where (.) denotes matrix transpose. Covariance
T
3.2. Features Extraction
∑c are estimated from the training data. A reject
We transform the Fisher’s Discriminant Ratio decision is taken when the response x(t ) to be classified
(FDR) to φ opt kernel in a binary matrix by replacing is far from any class.

the maximum N points with 1‘s and the other points

with 0’s. Features can be extracted directly ⎧ x is affected if d M (FVx ) p η
from φ opt [η , τ ]o A[η ,τ ] where o is an element-by- ⎨ (14)
⎩ x is reject otherwise
element matrix product. The kernel has the same
dimensions as the ambiguity plane. By multiplying the Where η is a given reject threshold
φopt kernel with a certain signal’s ambiguity plane, we The error of the badly classified points of the feature
vectors FVx is calculated by:
will find k feature points for this signal. We put them
into a vector in order to create the training feature N1 N2 FV train − FV x
(k ) of class c: e(i, j )% = ∑∑
(c)
vector FVtrain 1 i, j i, j
.100 (15)
I i =1 j =1 FVtrain i , j
(c)
FVtrain (k ) = φopt(c ) [η ,τ ] o A (c ) [η ,τ ] (10)

φopt(c ) [η ,τ ] Training optimal kernel Where

A (c ) [η ,τ ] Mean class of ambiguity plane I = N1.N 2 Examples number per class
Where N 2 : Current examples number of same load level
N1 : load level number
⎧⎪ A ( c ) [η ,τ ], if φ opt
(c )
[η ,τ ]= 1
φ opt( c ) [η ,τ ]o A ( c ) [η ,τ ] = ⎨ (11)
if φ opt [η ,τ ]= 0
4. EXPERIMENT RESULTS
⎪⎩0,
(c)

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SETIT2007

An acquisition of current signals was carried out on the locations which have values close or similar of
a test bench, which is made of a 5.5 KW induction points those of other classes.
motor (fig.2).
150

Bearing fault

Doppler (Hz)
100

50
Rotor fault

Fig.2. test bench of induction motor Stator fault

0
0 50 100 150
Delay (points)

Fig.5. Ambiguity plane smoothed by three kernel

The features vector of the signal to be classified

FVx was compared with features vectors of the
training by using the Mahalanobis distance from
Fig.3. Broken bars Fig.4. Bearing faults eq.14. The decision rule of signal assignment is made
by eq.15. The threshold λ = 0.4 was tested
The sampling rate is 10 KHz. The number of successfully on several signals in order to obtain a
samples per signal is N=10000. The data acquisition correct classification. We have tested signals which do
set on the machine consists of 15 examples of stator not belong to the training set of the three faults;
current recorded with different levels (0%, 25%, 50%, bearing fault, stator fault and rotor fault with various
75%, 100%). Different operating conditions from the levels of load (25%, 50%, 75%). Five signals
machine were considered; healthy, bearing fault examples are taken for each fault and for each load
(fig.4), stator fault (fig.2) and rotor fault (fig.3) .The level. Thus we will have 5 X 3=15 signals test for
training set is carried out on 10 current examples. The each fault. After extraction, the features vectors of
last five current examples are used to test the system signal to be classified, we took 50 points at each
classification. feature vector with various levels of load. The
The training set for the three faults and for the calculation of the Mahalanobis distance d M (Vx ) is
healthy machine was made, each one, from 10 done along these features vectors. The figure 8 shows
examples of no-load current and 10 other examples for that the error is null for the first eight points of the
full load. Consequently we have 20 examples of vectors tests concerning the bearing fault. This is for
training for each of three faults and 20 examples of 25% 50% and 75%.levels of load. Finally, bearing
training for the healthy machine. The bearing fault fault is only characterized by three points that are
kernel is designed for obtaining the points location of belonging to the first eight points. Consequently the
maximum separation between two classes: fault signals tested are identified with precision.
bearing class and the healthy motor class. The
dimension of ambiguity plane contains initially 200 x 50
25%
200 = 40000 points; considering symmetry compared 50%
40 75%
to the origin, we take the quarter of ambiguity plane,
which corresponds to N=10000. The stator fault kernel 30
is designed for obtaining the points location of
Error %

maximum separation between stator fault class and the 20

healthy motor class. Rotor fault kernel is designed
10
also for obtaining the points location of maximum
separation between rotor fault class and the healthy 0
motor class. Ambiguity plane of three kernels is 0 10 20 30 40 50
computed from N=10000 points. The classification
consists on the separation of faults classes. The Fisher’s Points
Fisher’s point locations are represented in the Fig.8. Classification errors for bearing fault
Doppler-delay plane (Fig.5). We retained 03 points
location per kernel {(ξ ,τ )1 ,L, (ξ ,τ )9 } of stronger For stator fault, the figure 9 shows that the
contrast. These locations are ranged in the feature classification error is null for the first twelve points of
vector for training {FV1 ,L, FV9 } . This selection is the vectors tests. Different load level 25% 50% and
75% are considered. The stator fault is characterized
made on the basis of contrast value and a compact by three points that belong to the first twelve points.
localization in the ambiguity plane. We also removed Consequently the signals are identified with precision.

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SETIT2007

Current," IEEE Trans. Industry Applications, vol.

80
25% 35, no. 2, March/April 1999
70 50%
75% [2] L. Atlas, J. Droppo, and J. McLaughlin,
60
"Optimizing time-frequency distributions via
Error %

50 operator theory", in Proceedings of the 1997 SPIE,

40 vol. 3162, pp. 161–171.
30 [3] C. Heitz, "Optimum time-frequency
20 representations for the classification and
10 detection of signals," Appl. Signal Process., 1995,
0 vol. 2, no. 3, pp. 124–143.
0 10 20 30 40 50
[4] M. Davy and C. Doncarli, "Optimal kernels of
Fisher’s Points time-frequency representations for signal
Fig.9. Classification errors for stator fault classification," in Proc. IEEE-SP Int. Symp.
Time-Freq. Time-Scale Anal., 1998, pp. 581–
Figure 10 shows that for the rotor fault the 584.
classification mean error is null for the first thirteen [5] B.W. Gillespie and L. Atlas, "Optimizing Time–
points of the vectors tests for different load level 25% Frequency Kernels for Classification," IEEE
50% and 75%. The rotor fault is characterized by three Trans. Signal Processing, March 2001, VOL. 49,
points that belong to the first thirteen points. NO. 3,
Consequently the signals tested are also identified [6] M. Wang, G. I. Rowe, and A. V. Mamishev,
with precision. "Classification of power quality events using
optimal time-frequency representations—Part 1:
60
25%
50%
application," IEEE Trans. Power Delivery, 2004,
75%
50 vol. 19, pp. 1496–1503,
[7] M J. Devaneyand L. Eren, "Detecting Motor Bearing
Error %

40
faults”, IEEE Instrumentation & Measurement
30 Magazine", December 2004
20 [8] D.K. Perovic, M. Arkan, and P. Unsworth.
"Induction motor fault detection by space vector
10
angular fluctuation," IEEE IAS, Rome 2000, Vol 1,
0 pp 388-394,
0 10 20 30 40 50
[9] F. Filipetti, G. Franceschini, C. Tassoni, and P. Vas, "
Fisher’s Points
AI techniques in induction machine diagnosis
Fig.10. Classification error for rotor fault including the speed ripple effect," vol 1, IEEE IAS,
California 1996, pp 655-662,
[10] A. Lebaroud, A. Bentounsi, G. Clerc, "Detailed
CONCLUSION Study of the Rotor Asymmetry Effects of Induction
Machine Under Different Supply Conditions,” 11th
In this study we proposed a method based on time- European conference of power electronics and
frequency representation (TFR) for the diagnostic of applications (EPE’05), Dresden, Germany, 11-14
induction motor faults. We demonstrate that the September 2005.
classical TFR have parametric kernel and a priori [11] A. Lebaroud, A. Bentounsi, A. Kkhezzar, M.
preset which are inappropriate for classification. Thus, Boucherma, " Effects of Broken Bar Induction
we use the plane of ambiguity where all the TFR can Motor with Stator Asymmetry and Distorted
be derived by a suitable choice of the kernel. It gives a Supply," International conference in electrical
precise classification of the signal. The diagnosis machines (ICEM’04), Poland, September 2004.
system classifies the different faults : bearing fault, [12] L. Cohen, "Time-Frequency Analysis," Englewood
stator fault and rotor fault. Each fault was Cliffs, NJ: Prentice-Hall, 1995.
characterized by a kernel. The optimized kernels allow
extracting nine discriminated locations in the Doppler
delay plane {(ξ ,τ )1 , L , (ξ ,τ )9 } . The assignment of an
unclassified signal was made with the Mahalanobis
distance. The mean error of points which are badly
classified is null. The diagnosis by TFR takes into
account the level of load and provides a reduced
computing time and an accurate classification.

REFERENCE

[1] B. Yazıcı, G. B. Kliman, "An Adaptive Statistical

Time–Frequency Method for Detection of Broken
Bars and Bearing Faults in Motors Using Stator

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