Induction motors are widely used in industrial processes since they offer a very high degree of reliability. But like any other machine, they are vulnerable to faults, which if left unmonitored, might lead to an unexpected interruption at the industrial plant. Therefore, the condition monitoring of the induction motors have been a challenging topic for many electrical machine researchers. Indeed, the effectiveness of the fault diagnosis and prognosis techniques depends very much on the quality of the fault features selection. However, in inductionmotor drives, rotor defects are the most complex in terms of detection since they interact with the supply frequency within a restricted band around this frequency, especially in the noloaded case. To overcome this drawback, this paper deals with an efficient and new method to diagnose the inductionmotor rotor fault based on the digital implementation of the monitoring algorithm based on the association of the Time Synchronous Averaging technique and Discrete Wavelet Transform. Experimental results are presented in order to show the effectiveness of the proposed method. The obtained results are largely satisfactory, indicating a promising industrial application of the combined “Time Synchronous Averaging – Discrete Wavelet Transform” approach.
1. Introduction
Nowadays, induction motors are the most important rotating electric machines within industrial applications. This is mainly due to their robustness, low cost, efficiency, and reliability.
However, in the practical applications, induction motors are subjected to electrical, environmental, mechanical and/or thermal stresses, which create failures in different parts of these machines
[1]
. Interruptions can be caused by rotor faults, stator faults, rotorstator eccentricity, and bearing failures
[1]
.
Therefore, a permanent condition monitoring of the induction machine is of high interest since it contributes to minimizing the downtime and improves its reliability and availability. Early diagnosis of these faults is an extensively investigated field for cost and maintenance time savings
[2]
.
Traditionally, several diagnosis techniques were used to supervise the induction motor faults, such as temperature measurements, infrared recognition, radio frequency emissions, noise monitoring, vibration measurement, speed fluctuations or torque sensing
[3

5]
. But the major problem of these methods is that they require direct access to the machine in order to place transducers for the monitoring.
To overcome this drawback, intensive research efforts have recently focused on electrical monitoring methods, which use only noninvasive sensors (i.e. current sensors)
[6]
.
Furthermore, it is known that an important factor of motor condition monitoring and fault diagnosis is how to extract the features of motor signals. From this perspective, three approaches have been developed by researchers:
1 Timedomain analysis
: It is the simplest form of signal processing, since the signal magnitude is examined in the time domain
[7]
.
2 Frequencydomain analysis
: It is widely adopted for condition monitoring and fault diagnosis of electrical motors. The most common frequencydomain analysis technique is the socalled Motor Current Signature Analysis (MCSA). MCSA focuses on the spectral analysis of the stator current and has been successfully used in the diagnosis of inductionmotor faults. The advantage of MCSA is that it needs only one current sensor and is based on straightforward signalprocessing techniques such as Fast Fourier Transforms
[8

9]
.
3Timefrequency domain analysis
: It consists of the time, frequency representation of a signal, which is inherently suited to indicate transient events in the signal. The most popular timefrequency domain analysis is the wavelet technique. Wavelet techniques for fault monitoring and diagnosis of induction motor are increasing, indeed, because they can be used for a localized analysis in a timefrequency or timescale domain. It is thus a powerful tool for condition monitoring and fault diagnosis. In this regard, intensive research efforts have focused on the use of approximation and detail signals for extracting the contribution of fault frequency components
[10

18]
.
Among the various induction motor defects, rotor faults are the most important, since the cumulative effect may lead to a major motor malfunction. Diagnosis of rotor failures has long been an important but complicated task in the area of induction motor condition monitoring. Indeed, especially at light load, it is difficult to distinguish between healthy and faulty rotors, as the rotordefect characteristic frequencies are very close to the fundamental component and their amplitudes are small in comparison
[19

20]
.
To alleviate this drawback, a method exploiting the cyclostationarity of electrical signals is developed for the motor condition monitoring. The “cyclostationarity” term was introduced by Bennett in 1958
[21]
and the theory of cyclostationarity was developed by Gardner
[22]
. More recently, Bonnardot et al. have shown that this theory can bring new solutions to fault detection and diagnosis problems
[23]
. Indeed, in the case of the cyclostationary signal, each period (or cycle) is considered as the same random process realization. Therefore, if these cycles are superposed, the overall average can be calculated: this average is also called Time Synchronous Average. Time Synchronous Averaging(TSA) is a method developed by McFadden in 1987; it allows the extraction of a deterministic component from a signal. TSA consists of averaging together a series of signal segments each corresponding to one period of a synchronizing signal
[24]
.
Nowadays, very little work has been done to exploit the electricalsignal cyclostationary characteristics in order to diagnose induction motor rotor fault. An approach associating TSA and a timedomain analysis was developed
[25]
and a combination of TSA with a frequencydomain analysis was depicted
[26]
.
This paper proposes a technique combining the TSA to a timefrequency domain analysis, based on the following steps:

1. Determination of the stator current TSA;

2. Residual current calculation by subtraction between the stator current and its TSA;

3. Application of DWT to the residual current in order to diagnose the inductionmotor rotor fault.
The main novelty of this article stems from the introduction of the notion of “combined TSA  DWT approach” in order to detect inductionmotor drive faults, even in the nonloaded case.
The rest of this paper is organized as follows. Section 2 depicts the architecture of the combined “Time Synchronous Averaging  Discrete Wavelet Transform” approach. Section 3 is devoted to the detailed description of the experiment. The comparison results and discussion are presented in Section 4. Finally, conclusions are mentioned in Section 5.
2. Architecture of the Combined “TSA  DWT” Approach
 2.1 Time Synchronous Averaging (TSA)
The asynchronous motor operating process and the electric supply fluctuations cause the nonstationary behavior of the stator current signal.
The idea is to exploit the electricalsignal cyclostationary characteristics in order to identify the faults which occur in an asynchronousmotor drive. Therefore, in this work, the firstorder cyclostationarity of stator current and voltage is largely exploited.
Furthermore, a rotor fault can be detected by highlighting a statorcurrent amplitude or phase modulation. However, the modulatedsignal weak frequency band makes it too difficult to detect modulation. An alternative to overcome this difficulty is proposed by MacFadden
[24]
: the Time Synchronous Averaging (TSA) method. It’s a way to reshape the signal before its processing.
The
T
period TSA of a signal
s
(
t
) is defined as follows:
The TSA method consists of averaging
s
(
t
)signal shifted versions of a whole number of
T
periods.
This method allows the separation between the excitation sources and, consequently, fault identification. Indeed, consider a signal
s
(
t
) sum of
T_{1}
period signal
s_{1}
(
t
),
T_{2}
period signal
s_{2}
(
t
) and noise. The application of the TSA method to
s
(
t
), at respectively
T_{1}
and
T_{2}
period allows the separation between
s_{1}
(
t
) and
s_{2}
(
t
). In fact, we can prove that:
By applying a similar approach, the stator current can be decomposed as follows:
where
I_{sh}
(
t
),
I_{smec}
(
t
) and
n
(
t
) are respectively the harmonic statorcurrent harmonic component, the mechanicalstructurerelated stator current and the noise.
In fact, the asynchronous motor monitoring consists of supervising the signal harmonic part. So, harmonic frequency (50Hz) which is related to electrical phenomena and mechanicalstructurerelated frequency must be separated.
For this purpose, the TSA method will be applied to the stator current. The
T_{h}
period TSA of stator current is done by the following relation, as established in (2) and (3):
where
T_{h}
=1/
f_{s}
is the harmonic period and
f_{s}
=50Hz the harmonic frequency corresponding to supply frequency.
Note that only the harmonic part of the stator current
I_{sh}
(
t
) corresponding to 50Hz frequency remains in the averaged signal. Thus, the synchronous averaging allows an effective separation between electricalrelated and mechanicalrelated components. The subtraction between the stator current and its TSA gives the residual current where only mechanicalrelated frequencies remain, as shown in (5):
It’s a very interesting property that will allow conditioning a mechanicalstructurerelated indicator monitoring an eventual rotor fault.
 2.2 Discrete Wavelet Transform (DWT)
For many years, Fourier Transform has been used for signal processing, since it is suitable for the study of a wide range of signals. The Fourier analysis consists in decomposing a signal into sine waves with different frequencies. Similarly, a wavelet analysis is the decomposition of a signal into shifted and scaled versions of a function called the ‘mother wavelet’.
There are two types of wavelet, the continuous wavelet transform (CWT) and discrete wavelet transform (DWT).
The CWT is the sum over time of the signal multiplied by scaled and shifted versions of the wavelet, as shown in (6).
where
s
(
t
) is the signal,
a
and
b
being real called dilation and translation parameters respectively and
ψ
is the wavelet function.
The DWT consists in sampling the scaling and shifted parameters. This leads to highfrequency resolution at low frequencies and hightime resolution for higher frequencies.
The DWT is preferred in the industry due to its less computational complexity and less computational time compared to CWT
[27]
.
DWT decomposes a signal by passing it successively through highpass and lowpass filters into its approximate and detailed versions using MultiResolution Analysis (MRA), and this is called the Mallat Algorithm as shown in
Fig. 1
.
[27]
.
The Mallat algorithm applied to stator or residual current
The original signal is denoted by
s
(
t
), with a sampling rate of
f
samples/sec. The lowpass filter is denoted by LPF while the highpass filter is denoted by HPF.
The first level of decomposition coefficients are
a
_{1}
and
d
_{1}
, where
a
_{1}
is the approximate version of the original signal and
d
_{1}
is the detailed version of the original signal. Further decomposition of
a
_{1}
gives
a
_{2}
and
d
_{2}
and so on. At each level, the HPF produces the detail coefficients (
d_{j}
), while the LPF produces the approximation coefficients (
a_{j}
).
Finally, the signal
s
(
t
) can be approximated using the DWT by
[27]
:
where
are respectively, the scaling and the wavelet coefficients,
φ^{n}
(
t
),
ψ^{j}
(
t
) are respectively the scaling function at level
n
and the wavelet function at level
j
,
n
is the decomposition level,
a_{n}
is the approximation signal at level
n
and
d_{j}
is the detail signal at level
j
.
[27]
.
In accordance with Nyquist rule, a downsampling by two for successive levels, halves the samples number of the previous level, with no information losses. If
f
(samples/sec) is the sampling rate used for capturing
s
(
t
), the detail
d_{j}
contains the information concerning the signal components whose frequencies are included in the interval [
f
/2
^{j+1}
,
f
/2
^{j}
]. The approximation signal
a_{n}
includes the low frequency components of the signal, belonging to the interval [0,
f
/2
^{n+1}
].
The high frequency band extends from half to full Nyquist frequency, where Nyquist frequency is given as
f
/2.
3. Detailed Description of the Experiment
 3.1 Experimental setup
The testing ground used includes an industrial threephase induction motor of 400V, 6.2A, 50Hz, 3kW, 1385 rpm. The data acquisition system (DAQ) has a resolution of 24bit, with 128MB of memory and the processor speed is 600MHz. The sampling rate taken is
f_{samp}
=25.6 kHz, so the number of samples per average cycle of 50 Hz is
N_{samp}
=512 (25600/50 = 512).
Supply voltage is measured by means of a voltage transducer (
Voltage LEM
) while stator current is measured by means of a current transducer (
Current LEM
). The velocity is measured with an optical tachometer. The block diagram of
Fig. 2
shows the implementation technique adopted during experimental testing.
Block Diagram of the implemented experimental device
The tests are first performed for the noloaded motor, in healthy and defective cases respectively. The same tests are carried out with the halfnominal loaded motor.
Indeed, under healthy operating conditions, the balanced threephase supply current system creates a forward rotating magnetic field, which rotates at synchronous speed. This airgap field induces currents in the rotor with a frequency proportional to the rotor slip
s
, and these currents generate a forward rotating field. So, for a symmetrical motor (healthy machine), there is not any backward field in the airgap
[28]
.
But, when a rotor failure occurs an electrical imbalance appears, since the rotor resistance values of the three phases are no longer equal to each other
[29]
.
Therefore, under rotor faults, an asymmetry appears in the rotor circuit and an additional backward field is produced by the imbalanced rotor currents
[30
,
31]
.
Note that the main effect of the rotor fault is the amplitude modulation of the stator current. It is characterized by the upper and lower sidebands. The formula used to calculate the components is given by
[31]
:
where
f_{s}
is the electrical supply frequency and s the per unit slip.
 3.2 Selection of DWT decomposition level
A suitable number of decomposition levels depends on the sampling frequency
f_{samp}
. It has to be chosen in order to allow the highlevel signals (approximation and details) to cover all the range of frequencies along which the sideband is localized.
Otherwise, several types of mother wavelets exist and have different properties. However, due to the wellknown properties of the orthogonal Daubechies family
[32]
, a mother wavelet of this family will be used in this paper.
Thereby, the DWT is carried out decomposing the current signal into 10 levels, each one of them having its own detailed coefficients and a determined range of frequencies, as shown in
Table 1
. The DWT is done using the Daubechies 5 (db5) wavelet with 10 decomposition levels
[33]
.
Frequency bands at different decomposition levels
Frequency bands at different decomposition levels
 3.3 Signal synchronization
During the acquisition of voltage signal, a problem of cycle drift from one electric cycle to another appears; it’s due to the electrical supply fluctuations. The cyclic statistic rules cannot be directly applied to these signals to extract desired information, except if a way to compensate these fluctuations is proposed.
A preliminary stage is needed: the current and voltage signals must be resampled according to a reference which “follows” these fluctuations: it’s “the synchronization of the current and voltage signals”. The purpose is to synchronize all electric cycles according to the same reference, so all cycles must be superimposed after the synchronization process. In this perspective, a resampling algorithm that allows electrical signals synchronization is developed, as illustrated in
Fig. 3
.
Signal synchronization algorithm
The voltage signal
V
is first cut out in slices, each one corresponding to one period (
T
=20ms), and each period containing an integer number of samples
N_{samp}
.
In this paper:

• The acquisition durationTais 20 seconds, so the number of voltage slices isN=Ta/T= 1000;

• The sample rate is 25.6 kHz, soNsamp=512 samples per period (512 = 25.6 kHz x 20 ms).
The shift between the first voltage period, taken as a reference, and the others are estimated: for this purpose, the firstperiod zero abscissa and the k
^{th}
period zero abscissa (for k=2 to N) are determined; the shift corresponds to the difference between these two abscissas. Then, each period is shifted to make it coincide with the first one (reference). If the two periods are already synchronous, the shift is then null.
The voltage signals before and after synchronization are represented in
Fig. 4
and
Fig. 5
respectively.
Superposition of 1000 voltage cycles before synchronization
Superposition of 1000 voltage cycles after synchronization
Once all cycles are synchronized, the signal is rebuilt by setting these cycles end to end. All cycles are now synchronous and the TSA can be carried out.
4. Comparison Results and Discussion
 4.1 Noloaded motor case
The DWT of the stator current
I_{s}
is applied in first.
Fig. 6
and
Fig. 7
show the stator current signal (
I_{s}
) and the upperlevel signals
a
_{10}
,
d
_{10}
,
d
_{9}
and
d
_{8}
, for the healthy and faulty cases respectively.
Highlevel wavelet signals results from the DWT signal analysis of stator current in healthy case at noload
Highlevel wavelet signals results from the DWT signal analysis of stator current in defective cases at noload
The comparison between the plots of DWT in the healthy and faulty case does not allow detecting the rotor fault.
So, the idea is to combine the TSA method and DWT in order to diagnose the inductionmotor rotor fault, as proposed by the algorithm of
Fig. 8
.
Flowchart of the proposed hybrid “TSA–DWT” rotorfaults detection algorithm
The DWT is now applied to the residual current
I_{res}
.
Fig. 9
and
Fig. 10
show the residual current signal (
I_{res}
) and the upperlevel signals
a
_{10}
,
d
_{10}
,
d
_{9}
and
d
_{8}
, for the healthy and faulty cases respectively.
Highlevel wavelet signals result from the DWT signal analysis of residual current in healthy case at no load
Highlevel wavelet signals results from the DWT signal analysis of residual current in defective case at no load
The difference between the 9
^{th}
detaillevel plots of residual current, in healthy and defective cases, is very clear. So, the DWT applied to residual current allows the detection of rotor fault.
 4.2 Halfnominal loaded motor test
Fig. 11
and
Fig. 12
show the statorcurrent signal (
I_{s}
) and the upperlevel signals
a
_{10}
,
d
_{10}
,
d
_{9}
and
d
_{8}
, for the healthy and faulty cases respectively.
Highlevel wavelet signals result from the DWT signal analysis of stator current in healthy case with a 50% nominal load
Highlevel wavelet signals result from the DWT signal analysis of stator current in defective case with a 50% nominal load
The comparison between the plots of DWT in the healthy and faulty case does not allow detecting easily the rotor fault. The 9
^{th}
detaillevel plot shows a little difference between the two cases, but this difference is too small to be significant.
So, the idea is to apply the DWT to the residual current
I_{res}
.
Fig. 13
and
Fig. 14
show the residual current signal (
I_{res}
) and the upperlevel signals
a
_{10}
,
d
_{10}
,
d
_{9}
and
d
_{8}
, for the healthy and faulty cases respectively.
Highlevel wavelet signals result from the DWT signal analysis of residual current in healthy case with a 50% nominal load
Highlevel wavelet signals result from the DWT signal analysis of residual current in defective case with a 50% nominal load
The difference between the 8
^{th}
and 9
^{th}
detaillevel plots of residual current, in healthy and defective cases, is very clear. So, the DWT applied to residual current allows the detection of rotor fault.
 4.3 Discussion
To show the effectiveness of the proposed approach, the signal will be conditioned in order to develop an inductionmotor diagnosing indicator. For this purpose, the energy concentrated in each detail level of wavelet decomposition will be calculated, for both the healthy and defective cases.
The detail energy at level
j
is given by:
where
j
is the level of detail,
d_{j}
is the detail signal at level
j
and
N
is the total number of samples in the signal. In this paper, the observation time is 2 seconds, so
N
= 512000 (
N
= 2 s x 25.6 kHz).
Detail energy of stator current signal is calculated using (9) up to level 10, for the healthy and defective cases and the results are given in
Table 2
(Total Energy).
Total Energies at different decomposition levels
Total Energies at different decomposition levels
From this experiment, it is observed that the total energy consumption in the faulty case is nearly the same as in the healthy case, since the two curves are quasi combined, as shown in
Fig.15
.
Total energy corresponding to stator current in healthy and faulty cases at no load and with a 50% nominal load
It is also noted that the 8
^{th}
leveltotalenergy value is the highest. This can be explained by the predominance of the fundamental component (50 Hz) at this level, since the frequency range associated to this level is 100 to 50Hz, as shown in
Table 2
.
Therefore, the diagnosis of rotor fault by this method is impossible: the total energy cannot be considered as a sensitive indicator of rotor fault.
To overcome the above inconvenience, the same procedure will be followed for the residual current, obtained by subtraction between the stator current and its TSA.
Detail energy of residual current signal is calculated for the healthy and defective cases and the results are given in
Table 3
(Residual Energy).
Residual Energies at different decomposition levels
Residual Energies at different decomposition levels
The corresponding graphs are shown in
Fig. 16
below.
Residual energy (corresponding to residual current) in healthy and faulty cases at no load and with a 50% nominal load
From this experiment, it is observed that the residual energy consumption in the faulty case is greater than in the healthy case, especially at the 9
^{th}
detail level.
Indeed, the speed value measured by the tachometer is 1467 rpm, so the slip value is
s
= 2.2% and the defect frequencies, given by (6) are 47.8 Hz and 52.2 Hz. These values are respectively contained in the 9
^{th}
(50  25 Hz) and 8
^{th}
(100  50 Hz) detail levels. Therefore, the residual energy allows an easy distinction between the healthy and defective cases.
In order to emphasize the fault effect, a ratio
k
will be computed as:
Table 4
below shows the computed
k
factor values at different detail levels, for both total and residual energies.
Ratio “k” values at different decomposition levels
Ratio “k” values at different decomposition levels
The
k
ratio value for the residual energy at the 9
^{th}
detail level is much higher than the other values which confirm the previous findings (235.5% at no load and 1241% at half nominal load).
5. Conclusion
This paper dealt with the induction motor rotor faults detection. A new stator currentbased fault detection approach is suggested. Indeed, it has been proposed to monitor induction motor rotor by means of the DWT of the residual current, obtained by subtraction between the stator current and its TSA. It was then found that the 9th detail level is the more energized level when a rotor fault occurs. The achieved results clearly demonstrate that the 9th detail levels of the residual current can be used as an effective indicator for rotor condition monitoring. The obtained results seem very promising for induction motor monitoring, since the approach is relatively simple. However, further investigations must be done toward the generalization of this approach to other types of faults which will be very beneficial for many industrial applications, including wind turbine monitoring.
Nomenclature
a_{n}Approximation signal at level n d_{j}Detail signal at level j E_{j}Detail energy at level j f_{defect}Rotorfault frequency f_{s}Supply frequency (50 Hz in this paper) f_{samp}Sampling rate (25.6 kHz in this paper) I_{res}(t)Residual current I_{s}(t) Stator current sh(t)>_{Th}Synchronous averaged current at T_{h} period I_{sh}(t) Statorcurrent harmonic component I_{smec}(t)Mechanicalstructurerelated stator current NTotal number of samples N_{samp}Number of samples per period SPer unit slip T_{h} Harmonic period (T_{h}=1/f_{s})
BIO
Nabil NGOTE was born in Casablanca, Morocco, in 1968. He received the diploma of “Ingénieur d’Etat” degree from the Ecole Nationale de l’Industrie Minérale, Rabat, Morocco, in 1990, in Electromechanical Engineering. He received Ph.D. degree, in Electrical Engineering from Ecole Mohammadia d’Ingénieurs, Université Mohamed V, Rabat, Morocco, in 2014. He is currently a Professor at “Ecole Nationale Supérieure des Mines de Rabat”, Rabat, Morocco. His research interests are monitoring of electrical drives condition operation.
Mohammed Ouassaid was born in Rabat, Morocco, in 1970. He received the M.Sc.A. and Ph.D. degrees, in Electrical Engineering from Ecole Mohammadia d’Ingénieurs, Rabat, Morocco, in 2002 and 2006, respectively. He is currently a Professor at Ecole Mohammadia d’Ingénieurs, Rabat, Morocco. His research interests are electric drives, power electronics, power systems and renewable energy.
Saïd Guedira was born in Rabat, Morocco, in 1960. He received the diploma of “Ingénieur d’Etat” degree from the Ecole Mohammedia d’Ingénieurs, Rabat, Morocco, in 1983, and the Ph.D. degree from the Faculté Polytechnique de Mons, Belgium, in 1995, in Electrical Engineering. He is currently a Professor at “Ecole Nationale Supérieure des Mines de Rabat”, Rabat, Morocco. His research interests include electrical network and predictive maintenance of rotating machines.
Mohamed Cherkaoui was born in Marrakech, Morocco, in 1954. He received the diplôme d’ingénieur d’état degree from the Ecole Mohammadia, Rabat, Morocco, in 1979 and the M.Sc.A. and Ph.D. degrees from the Institut National Polytechnique de la Loraine, Nancy, France, in 1983 and 1990, respectively, all in Electrical Engineering. In 1995, he joined the Department of Electrical Engineering, Ecole Mohammadia d’Ingénieurs, Rabat, Morocco, where is currently a Professor and University Research Professor. His current research interests include renewable energy, motor drives and power system.
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