Indian Journal of Science and Technology, Vol 8(30), DOI: 10.17485/ijst/2015/v8i30/70494, November 2015
ISSN (Print) : 0974-6846
ISSN (Online) : 0974-5645
Information Theoretic Criteria for Induction
Motor Fault Identification
W. Abitha Memala* and V. Rajini
EEE, SSNCE, Chennai - 603110, Tamil Nadu, India; abithamemalaw82@yahoo.com, rajiniv@gmail.com
Abstract
The objective of our work is to identify the inter-turn incipient short fault that occurs in the induction motor at no
load condition. The method used in fault identification is Information Theoretic Criteria, which uses Frequency Signal
Dimension Order (FSDO) estimator and fault decision module. The FSDO estimator estimates the number of frequencies
in stator current signatures using Minimum Description Length (MDL) criterion and Akaike Information Criteria (AIC).
Fault decision module uses the number of frequencies as fault index in detecting the fault and identifying the fault severity.
The proposed method is able to identify the fault from the data buried in noise. MDL yields consistent estimate, the fault
index obtained using MDL criterion is considered for diagnosing the faults. The CDF plot of MDL and AIC helps in proving
the fault severity results obtained from fault index value. With very lesser values of sampled data, the proposed method is
able to distinguish between healthy and faulty conditions. This novel approach diagnoses the inter-turn incipient fault with
very simple calculation and it needs only very few number of measured data for estimating the number of fault frequencies
associated with the faulty conditions.
Keywords: Akaike Information Criteria (AIC), Cumulative Density Function (CDF), Information Theoretic Criteria (ITC),
Inter-turn incipient short circuit fault, Minimum Description Length (MDL) Criteria and Stator Faults
1. Introduction
For the last 20 years, FFT is used for diagnosing the faults
by extracting the frequency information from stator
current to detect stator inter-turn short circuit faults,
broken bar faults and other mechanical faults1,2.
To overcome the frequency resolutions problems
of FFT, the subspace methods like Multiple Signal
Classification (MUSIC) algorithm, Estimation of Signal
Parameters via Rotational Invariance Techniques
(ESPRIT), Zoom FFT (ZFFT), Zoom MUSIC (ZMUSIC)
and Zoom ESPRIT (ZESPRIT) are used3-6. But it has the
inconvenience of long computational time. To detect
fault sensitive frequencies the MUSIC algorithm and
ESPRIT with zooming methods was proposed7. This
method works well with various load conditions. But
the difference in the healthy and faulty spectrum during
the no load condition is not so good when the motor is
running at no load condition.
* Author for correspondence
In our work a novel approach for identification of
the inter-turn incipient stator fault is proposed for the
induction motor running at no load condition. When
fault appears, the frequency corresponds to the faulty
condition is introduced in the stator current spectrum.
The numbers of fault frequencies appearing in the faulty
spectrum is determined from the Eigen values of the
auto correlation matrix and it is used as the fault index
in determining the faulty condition. The proposed
approach uses the Information Theoretic Criteria (ITC)8
by Schwarts and Rissanen (Minimum Description Length
(MDL) criterion) and Akaike Information Criteria (AIC)
in identifying the fault index and CDF of MDL&AIC in
recognizing the fault severity. The inter-turn short circuit
stator fault is identified based on the calculation of the
number of frequency calculated from the Minimum
Description Length (MDL) and Akaike Information
Criteria (AIC)9 and the Cumulative Density Function
(CDF) of the Minimum Description Length (MDL) and
Information Theoretic Criteria for Induction Motor Fault Identification
Akaike Information Criteria (AIC). CDF of MDL and AIC
is plotted for easy recognition of the fault severity. The
advantage of the proposed approach is it doesn’t require
any subjective judgment for deciding the threshold levels
as it is not using the same. The number of frequencies is
calculated as the value for which the MDL criteria or AIC
is minimized. The CDF plot of the MDL and AIC makes
the diagnosing process easier by providing the graphical
representation to identify the fault severity. This method
is an easy method of diagnosing compared with other
techniques11-15.
2. Data Model
The problem associated is to identify the inter-turn short
circuit stator fault of the induction motor, working under
no load condition, with the available measured datax (n),
which is buried in a noise signal. In subspace methods,
the N number of discrete time signals x(n) is represented
by L complex sinusoids s(n), in a white noise w(n) and is
given in equations (1-3).
x(n) = s(n) + w(n), n = 0, 1, 2,......N-1
(1)
s(n) consists of sinusoids and w(n) is white noise with
zero mean and a variance of σ2 .
Where,
L
s (n) = å A i e j2(fi n) (2)
i=1
e
Ai = ai ((i)) (3)
N – Number of sample data, fi-The frequency, |ai|–
The magnitude, Rx - The phase of the ith complex sinusoid.
The auto correlation matrix Rx of the measured data
x[n] is expressed as equations(4 and 5).
2
R =
M  a f ( f ) f H ( f )+(2 I (4)
x
å
(i =1)
i
i
i
L
Where,
T
e
(5)
f ( fi ) = éê1e ( j2"(" f(i ) )) ( j 4"(" fi )... e( j2"("(N -1) fi ))ùú
ë
û
The exponent H represents Hermitian transpose and
IL represents identity matrix.
2
fault. The FSDO estimator and fault decision module
are used in diagnosing the fault. The FSDO estimator
estimates the number of frequencies in the measured data,
which is buried in a noise signal, using the Information
Theoretic Criteria (ITC). ITC includes MDL criterion and
AIC in estimating the number of fault frequencies. The
number of frequencies is used as fault index in identifying
the faults. The Cumulative Distribution Function (CDF)
plot is obtained from the MDL criterion and AIC and is
used in identifying the fault severity. The fault decision
module uses the fault index and CDF plot for diagnosing
the inter turn incipient stator fault.
3.1 FSDO Estimator
FSDO estimator uses ITC to estimate the number of
frequencies8. The auto correlation matrix Rx given in
equation (4), is unknown in practice13. Therefore, it is
necessary to use the sample correlation matrix, Rx which
is equivalent to Rx to proceed with FSDO estimator. A
Special Smoothing (SS) method is applied to calculate Rx
, given in equation(6).
x =
R
æN -L+1
ö
1
çç å x (n) x T (n)÷÷(6)
÷ø
N - L + 1 çè n=1
Eigen based decomposition of the equation(6) yields
the Eigen values as λ1, λ2, λ3, ……λL and Eigen vectors
v1,v2,v3…vL. Full rank of Rx is M.
The sorted eigen values are as the following equation (7).
λ1>λ2>λ3, ……>λL (7)
The smallest Eigen value of corresponds to σ2.
i.e. λM = λM+1 = λM+2, …… = λL = σ2(8)
The MDL criterion of ITC is used in estimating the
number Rx of frequencies. The MDL criterion is given by,
(
MDL(k ) = - log  (P(i=k) (L -1)(i(1/(L - k )))/1/(L - k )
å
( i =k )
(L -1) (i) )(Ps (L - k )) + 1/2k (2L - k ) log (N - L +1)
(9)
The number of frequencies d is the value for which
MDL is minimized.
3. Proposed Algorithm

d = arg k min MDL (k)(10)
A new fault diagnosing algorithm is proposed for
diagnosing the inter-turn incipient short circuit stator
k = 0,1,2, ……. L-1.
The CDF plot of d gives the graphical representation
Vol 8 (30) | November 2015 | www.indjst.org
Indian Journal of Science and Technology
W. Abitha Memala and V. Rajini
of fault identifications from the healthy condition.
The AIC of ITC is also can be used in estimating the
number of frequencies. The AIC is given by,
(
AIC(k ) = -2log  (P(i=k) (L -1)(i(1/(L - k )))/1/(L - k )
å(i=k)(L -1) (i) )(Ps (L - k)) +1/2k (2L - k)log (N - L +1)
(11)
The number of frequencies 
g is the value for which
AIC is minimized.

g = arg k min aic (k)(12)
k = 0,1,2, ……. L-1.
The CDF plot of 
g gives the graphical representation
of fault identifications from the healthy condition.
The CDF plot of the MDL and AIC is generated as
it is not only distinct the healthy motor from the faulty
conditions, but also identifies the severity of the fault.
4. Experimental Setup
The stator current data of the induction motor under
healthy and faulty conditions are recorded at no load
working condition, using the experimental setup shown
in Figure 2. The tested motor has the following ratings:
3 hp, 415V, 3Φ, 50Hz, pole changing induction motor,
made to run as a 4 pole induction motor.
3.2 Fault Decision Module
The fault decision module can be represented with the
following Figure 1. The FSDO estimator estimates the
Figure 1. Fault Decision Module.
number of frequencies and the fault decision module
identifies the fault occurrence, using the number of fault
frequencies from the FSDO estimator. This number of
frequencies is used as fault index in identifying the faulty
condition of the induction motor.
The measured data is used in calculating Rx the sample
auto correlation matrix using the equation (6). In practice,
it is difficult to identify the number of frequencies from
the Eigen values, although it is able to provide the noise
level of the measured data7.
The ITC uses the Eigen values of Rx in calculating the
values of MDL and AIC given by equation 9 and 11. In large
sample limit, AIC tends to overestimate the number of
frequencies, but MDL yields consistent estimate always8.
In our work, the considered value of L in calculating MDL
and AIC is 50.
FSDO estimator uses the k value (equation 10 and 12)
at which MDL criterion and AIC of ITC is minimized,
to calculate the number of frequencies. This value of k
is used as the fault index in identifying the fault of the
induction motor.
Vol 8 (30) | November 2015 | www.indjst.org
Figure 2. Experimental Setup.
The inter-turn incipient short circuit fault is artificially
created in the motor. The fault creation of the induction
motor is explained in this session. The healthy and faulty
stator voltage and current waveform is also given in this
session. The measured stator current data has the influence
of the operating condition of the faulty induction motor.
For analysis, 1000 number of samples (N) is collected.
From sample correlation matrix, the Eigen values are
estimated. The sorted Eigen values are considered for
calculating the MDL and AIC values.
4.1 Creation of Inter-Turn Incipient Short
Circuit Fault
The inter-turn short circuit stator fault is created in the
stator lead to critical faulty condition within a very few
seconds. It is necessary to identify the inter-turn short
Indian Journal of Science and Technology
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Information Theoretic Criteria for Induction Motor Fault Identification
circuit fault at the early stage to avoid severe damage to
the machine. A new methodology based on ITC is used to
identify the inter-turn short circuit fault is at the incipient
stage.
The inter-turn short circuit fault is created artificially
in the test motor. A resistance is connected across the
terminals to be shorted. This parallel path across the
turns to be shorted creates the situation which is similar
to the partial insulation failure which appears prior to the
complete break down due to inter turn short circuit fault.
A circulating current is created in the short circuited path
which may lead to an unbalance in the stator current.
Therefore fault harmonics are induced on it. This creates
the inter-turn incipient faulty condition and leads to the
unsymmetrical working condition of the machine. Figure
3, Shows the inter turn incipient fault creation in the
induction motor.
Figure 3. Creation of Inter-Turn Incipient Short Circuit
Stator Fault.
In real time situations, this R value may be very small
or zero, which will ultimately increase the current intake.
The considered fault for analysis is inter-turn incipient
short circuit stator fault with 3 turns shorted in R phase,
6 turns short in R phase and 3 turns shorted in R and Y
phase.
4.2 Stator Voltage and Current Waveform
The voltage and current waveform of the motor under
healthy and faulty condition is obtained using DSO
(Agilent Technologies). Figure 4 shows the voltage and
current waveform of the healthy motor and Figure 5
shows the voltage and current waveform of the faulty
motor.
4
Vol 8 (30) | November 2015 | www.indjst.org
Figure 4. Voltage and Current Waveform of the Healthy
Motor.
Figure 5. Voltage and Current Waveform of the Faulty
Motor.
5. Results and Discussions
The stator current samples are collected for healthy and
faulty working condition of the induction motor, using the
above experimental setup. The FSDO estimator estimates
the number of frequencies introduced in the stator
current because of the faulty condition of the motor. The
fault decision module uses this number of frequency as
the fault index in diagnosing the faults. Table1 shows the
fault index of the motor under healthy and various faulty
conditions calculated using equations 10 and 12.
Fault index is calculated using both MDL and
ATC. From Table1, it is understood that the fault index
calculated using AIC is higher than the MDL results. Even
though the fault index can be calculated using MDL and
Indian Journal of Science and Technology
W. Abitha Memala and V. Rajini
AIC, AIC yields inconsistent estimate therefore tends
to overestimate the number of frequencies in the large
sample limits, whereas MDL yields a consistent estimate8.
The fault index calculated using MDL criterion gives
better results compared to AIC8. Therefore the fault index
calculated using MDL criterion is considered in diagnosis.
Table 1. Fault index of the induction motot under various
conditions.
ITC
Healthy 3 turns 6 turns 3 turns short
motor short R short in R in R and Y
phase
phase
Fault index of
14
33
36
37
MDL (
Fault index of
29
40
41
43
AIC (
The fault index i.e. number of frequencies in the
healthy motor current spectrum is 14. Therefore, there
is one supply frequency in addition to the other 13
frequencies appearing in the healthy spectrum of the
induction motor with the considered Eigen value. This
is due to the reason that some of the harmonics appear
in the healthy machine due to standard misalignment,
supply misalignment in phase, rotor eccentricity faults
and noise added with the signal3. The fault index of the
healthy motor value is the reference value for diagnosing
the faulty conditions of this motor at no load conditions.
The fault index å of the faulty motor is higher
than the healthy motor. Any value above this value
represents the faulty condition of the induction motor.
For the motor with inter-turn short circuit fault, there is
an apparent increase in high frequency components to
represent the fault8.
When analyzing the inter-turn incipient short circuit
stator fault, the 3 turns short in R and Y phase of the
induction motor represents the greater fault index value
compared to other faulty conditions. The difference in
the fault frequency components between healthy and this
faulty condition is 23. Therefore 23 extra frequencies are
added in the faulty current spectrum of 3 turns shorted in
R and Y phase of the motor.
The fault index of the 6 turns short in R phase is
greater than the 3 turns short in R phase. In 6 turns short
in R phase, 22 fault frequencies are added in the current
spectrum. In 3 turns short in R phase 19 fault frequencies
are added in the current spectrum. The increase in fault
s ( n) =
L
i=1
index beyond the healthy fault index indicates the faulty
condition of the motor. As the fault severity increases the
number of frequencies in the spectrum also increases.
The increase in fault index value represents the severity of
the fault occurred.
The CDF plot of the MDL and AIC proves the fault
severity result obtained from the fault index value. The CDF
plot of MDL and AIC, for various working condition of the
motors is shown in Figure 6 and 7 respectively. The CDF plot
is plotted, with the help of the auto correlation matrix.
Figure 6. CDF Plot of MDL.
A i e j2(fi n)
Vol 8 (30) | November 2015 | www.indjst.org
Figure 7. CDF Plot of AIC.
Even though all the operating conditions have the
same destination, the starting point of the MDL&AIC
values differ for every conditions of the motor. The
starting point of the healthy motor is lesser compared
with all the faulty conditions. Therefore it has the broad
MDL and AIC values (which is the difference between the
destination and starting points) compared to the faulty
conditions.
The CDF plot of the Minimum Description Length
Indian Journal of Science and Technology
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Information Theoretic Criteria for Induction Motor Fault Identification
(MDL) and AIC give clear distinction between healthy
and faulty conditions and identify the severity of the fault.
When comparing the faulty data, the destination point
is same for all the measured data. The starting point for 3
turns short in R phase is very much lesser compared with
the 6 turns short in R phase, which is even more lesser
than the 3 turns short in R and Y phase. The value of 3
turns short in R phase fault is closer to the healthy value.
The severity of the fault level increases as they deviates
from the healthy plot. The similarities in CDF plot of
MDL and AIC confirms the fault severity result obtained
from the fault index of the induction motor.
6. Conclusion
A novel approach is proposed for identifying the interturn incipient stator fault of the induction motor from
the stator current data buried in noise. The proposed
approach uses the number of fault frequencies as fault
index in calculating the severity of the faults and CDF
plot of Minimum Description Length (MDL) and Akaike
Information Criteria (AIC) to prove the severity of the
fault result obtained.
The proposed approach is based on Information
Theoretic Criteria (ITC). The number of frequencies
related to the operating condition of the induction
motor is obtained using ITC (MDL and AIC). As AIC
yields inconsistent estimate and tends to overestimate
the number of frequencies. As MDL yields consistent
estimate, the fault index obtained using MDL criterion is
considered for diagnosing the faults.
The FSDO estimator estimates the number of fault
frequencies associated with the faulty working condition
of the motor. The fault decision module uses the FSDO
estimator output as fault index to estimate the fault & its
severity.
The proposed approach plots CDF plot for the MDL
and AIC. This method helps in proving the fault severity
results obtained from fault index value. With very lesser
values of sampled data, the proposed method is able to
distinguish between healthy and faulty conditions.
The proposed approach is a new method in diagnosing
the inter-turn incipient fault of the induction motor. This
approach has very simple calculation; it needs only very
few number of measured data for estimating the number
of fault frequencies associated with the faulty conditions;
takes very lesser calculation time; online implementation
is easier; can be implemented to identify other types of
faults also.
6
Vol 8 (30) | November 2015 | www.indjst.org
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Indian Journal of Science and Technology