TELKOMNIKA Telecommunication Computing Electronics and Control Vol.
No.
April 2026, pp.
ISSN: 1693-6930.
DOI: 10.
12928/TELKOMNIKA.
Simultaneous faults diagnosis and prognostic in induction motor drives under nonstationary conditions Ameur Fethi Aimer1,2.
Ahmed Hamida Boudinar2,3.
Mohamed El-Amine Khodja2,3.
Azeddine Bendiabdellah2,3 LDEE Laboratory.
Department of Electrotechnics.
University Tahar Moulay of Saida.
Saida.
Algeria Department of Electrotechnics.
University of Sciences and Technology of Oran.
Bir El Djir.
Algeria LDEE Laboratory.
University of Sciences and Technology of Oran.
Bir El Djir.
Algeria
Article Info
ABSTRACT
Article history:
In this paper, an auto regressive (AR) model-based approach is applied in the stator current analysis under non-stationary conditions .
ase of frequency variation due to variable speed operatio.
Under these conditions, the identification of fault signatures is almost impossible due the variation of the fundamental frequency using conventional analysis methods.
Moreover, this approach is used in the diagnosis of multiple faults occurring simultaneously in induction motor drives.
In this aim, the stator current signal is decomposed into short segments then the AR modeling approach is applied on each segment.
This approach called short-time ROOT-AR is then applied to solve the problem of the non-stationarity of the stator current signal under variable speed operation.
The efficiency of the short-time ROOT-AR approach is evaluated through experimental tests in the diagnosis of multiple faults occurring simultaneously in induction motor drive.
Finally, the superiority of the proposed approach is highlighted in comparison with conventional techniques in terms of accuracy, computational time and robustness against the noise.
Received Oct 22, 2025 Revised Dec 8, 2025 Accepted Jan 30, 2026 Keywords:
Fault diagnosis Induction motor Simultaneous faults Time-frequency analysis Variable speed drive This is an open access article under the CC BY-SA license.
Corresponding Author:
Ameur Fethi Aimer LDEE Laboratory.
Department of Electrotechnics.
University Tahar Moulay of Saida BP 138 city ENNASR 20000.
Saida.
Algeria Email: ameurfethi.
aimer@univ-saida.
INTRODUCTION
Induction motor represents a large part of the industrial machinery field, accounting for over 80% of installed machines.
This is primarily due to its robustness, high power-to-weight ratio, and low manufacturing cost.
However, diagnosing potential faults that may occur during the operation of an induction motor is essential to ensure continuous operation, improve efficiency, and minimize energy losses .
Ae.
Furthermore, it is more common for several faults to occur simultaneously, making the process of identifying a single isolated fault ineffective.
Therefore, it is more practical to design a diagnostic process that allows the monitoring of multiple faults at the same time.
Indeed, several incipient faults, such as eccentricity, broken rotor bars, or scratches on bearing surfaces, can occur simultaneously but with a very low amplitude, making their detection almost impossible using conventional diagnostic methods .
Ae.
Therefore, the use of high-resolution techniques is essential for better discrimination of the resulting frequency signatures, particularly in variable-speed applications where the static converter introduces harmonics that contaminate the signal, thus increasing the noise level.
Moreover, these variable-speed applications introduce non-stationarity into the electrical signals due to the variation of the supply frequency.
Journal homepage: http://journal.
id/index.
php/TELKOMNIKA A ISSN: 1693-6930 This is particularly important since this frequency is crucial in the calculation of most fault-related frequency signatures .
Ae.
To fix these problems, an improved auto regressive (AR) method called ROOT-AR is first introduced by improving two aspects on the AR modeling.
The first one consists in processing the signal only on a limited frequency band where the signature of the faults is supposed to This will reduce the samples number, and thus reduce the computation time.
In addition, this solution allows the determination of the number of searched harmonics instead of its estimation.
The second one provides a better display by representing the signal frequencies obtained using the ROOT-AR approach .
This approach is reliable in the case of stationary signals .
onstant frequencie.
Nevertheless, it is limited in the case where the frequencies vary over time.
this is the case of a load variation or a variable speed drive.
this case, the electrical signals become non-stationary .
ariable frequencie.
Several techniques address the problem of the analysis under non-stationary conditions.
The basic technique in the analysis of non-stationary signals is the short time fourier transform (STFT) .
, .
also known for its limited time-frequency resolution.
Other techniques such as discrete wavelet transform (DWT) .
Wigner-Ville distribution (WVD) .
, minimum norm spectral estimation technique .
, demodulation technique .
or empirical mode decomposition (EMD) .
present interesting results but with drawbacks related to the complexity of implementation and high computation time.
Also, the resulting time-frequency spectrum is often difficult to read and to discuss.
Moreover, several artificial intelligence (AI)-based diagnostic methods are presented in .
in order to achieve a classification of multiple faults.
Nevertheless, these AI techniques based on machine learning algorithms needs a large database necessary to the learning procedure.
To overcome these problems, the short time ROOT-AR approach is applied in the analysis of nonstationary signals.
In this aim, the non-stationary signal is decomposed into short segments while applying the ROOT-AR approach on each segment, this adaptation aims to obtain a time-frequency spectrum where frequency variations over time can be observed.
Indeed, since the proposed approach is based on the STFT principle, the window size width is fixed in order to reduce the complexity of the algorithm .
n comparison with DWT for exampl.
In the other hand, the fourier computation is replaced with ROOT-AR spectrum which improves the frequency resolution and the readability of the spectrum.
Also, the analysis over a limited frequency band leads to a reduced computation time allowing a real-time diagnosis.
In addition, several faults operating simultaneously are identified in the case of non-stationary signals .
ith a variable fundamental frequency necessary for speed variatio.
Moreover, this variation is achieved using a pulse width modulation (PWM) inverter, which increases the harmonics in the stator current spectrum and, consequently, the noise.
The distinctive feature of the short time ROOT-AR is the adaptation of the ROOT-AR method .
obust against noise compared to fourier analysis: FT and STFT) in the analysis of non-stationary signals.
Finaly, the resulting time-frequency spectrum is easy to read thanks to the robustness of the ROOTAR against noisy signals .
ue to the PWM inverte.
To verify the effectiveness of the SHORT TIME ROOT-AR in the analysis of signals in the presence of multiple faults under non-stationary operation cases, the diagnosis of bearing faults, eccentricity faults and broken rotor bars faults in variable speed induction motor is achieved through experimental tests.
FAULT DIAGNOSIS THEORY
Due to the rich information content of the stator current spectrum, several research studies have demonstrated that its analysis constitutes an effective tool not only for the detection, but also for the identification of faults affecting induction motors.
This identification capability is essentially based on the precise monitoring of the frequency positions of certain harmonic components, as well as the analysis of their respective amplitudes, thus making it possible to identify the nature of the searched fault .
In this paper, multiple faults among most recurrent faults are investigated using experimental tests.
These faults are presented in the following section.
Broken rotor bars Manufacturing faults, porosity in materials, mechanical overloads, and gear damage are among the main causes of rotor bar breakage.
When one or more rotor bars are broken, the electromechanical stresses applied on adjacent bars can lead to rapid propagation of the damage.
In certain critical cases, this can lead to catastrophic motor failure, particularly if bar fragments detach from the cage during operation .
Thus, rotor bar breakage results in the occurrence of a series of frequencies calculated using .
yceyca = .
A 2ycoy.
yceyc with yco = 1,2,3 A TELKOMNIKA Telecommun Comput El Control.
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April 2026: 717-726 TELKOMNIKA Telecommun Comput El Control where: yceyc is the supply frequency, yceyca denotes the sideband frequencies associated with the rotor broken bar fault, and finally yc represents the motor slip.
Eccentricity faults In induction motors, residual eccentricity is inevitable, even when the motor is new.
Eccentricity faults, caused by a variation in the air gap, cause vibrations and damage to the bearings, which can lead to rotor-stator contact.
They are divided into three types: static, dynamic, and mixed.
In the presence of static eccentricity, the area of the smallest air gap remains fixed during rotation.
This type of eccentricity generally results from improper rotor assembly or deformation of the stator core .
In contrast, dynamic eccentricity is characterized by a misalignment between the geometric center of the rotor and its axis of rotation, which causes the position of the minimum air gap point to vary during rotation.
This phenomenon can be caused by factors such as resonance at a critical speed, rotor shaft deflection, bearing wear, or misalignment.
If both static and dynamic eccentricity are present at the same time, a low-frequency component is formed near the main frequency, expressed by .
yceyceycayca = yceyc UI .
A 1Oeyc ycy .
Bearing faults Bearings are designed as an electromechanical interface between the rotor and the stator of electric In addition, they maintain the shaft of the machine in order to guarantee a proper rotation of the The rolling-element bearings consist of four parts: inner and outer races, balls and cage which guarantees an equidistant separation between balls.
Bearing faults can be located on the stator current spectrum at the following frequencies .
yceycayceycayc [H.
= .
ceyc A yco UI yceyc | with yco = 1,2,3 A .
where yceyc is the fault vibrational frequency corresponding to one of the faults that can be observed on bearings element .
nner race, outer race, ball or cag.
, while yceyc is the supply frequency.
In this paper, the outer race fault is considered as the selected bearing fault.
The characteristic frequency in the case of an outer race fault is given by the frequency yceycu :
yceycu = ycAyca yceyc .
Oe yaAya yaya ycaycuyc y.
where yaAya and yaya respectively, are the ball and the cage diameters, ycAyca is the bearing balls number.
A is a contact angle and yceyc the mechanical rotor frequency.
AUTOREGRESSIVE MODEL OF STATOR CURRENT
The spectrum of stator current is composed of the following frequencies .
Supply frequency: yceyc Time harmonics caused by the supply pollution: .
yceyc Harmonics due to eccentricity located around the fundamental Space harmonics due to non-sinusoidal distribution of windings Therefore, the stator current can be presented as a sum of trigonometric functions given by:
ycA ya ycnyc .
= Ocycn=1 yaycn ycaycuyc.
yuUyceycn yc yuoycn ) yc.
where yaycn , yceycn .
Aycn are respectively, the magnitude, frequency and initial value of the ycn ycEa cosine phase, ycAya being the number of harmonics, yc.
is the measurement noise.
Using the EulerAos decomposition, the numerical expression of stator current of .
can be presented as a sum of 2.
ycAya complex exponentials given by:
2ycA ya ycnyc .
= Ocycn=1ya ycn .
yce yce yc.
yuU ycn ycu yucycn ) yceyce yc.
with ycu = 0,1,2, .
, ycA Oe 1 where ycA is the number of samples number and yceyce is the sampling frequency.
As a matter of fact, the AR model is considered as an all-pole filter with a white noise as an input and a variance equal to yuayc2 .
The AR model of stator current is given by the following difference:
Simultaneous faults diagnosis and prognostic in induction motor drives under A (Ameur Fethi Aime.
A ISSN: 1693-6930 yce.
= ycnyc .
Oe ycnCyc .
= ycnyc .
Ocyayco=1 ycaCyco ycnyc .
cu Oe yc.
Therefore, the transfer function of the system is expressed by:
= .
C yco yc Oeyco 1 Ocya yco=1 yca where ya represents the order of the AR model, yce.
the prediction error illustrated by a white noise and yyco represent the filter coefficients obtained by minimizing the prediction error yce.
The power spectral density (PSD) of the AR model given in .
, leads to:
ycEycIyayaycI .
= yuaycu Oeyc2yuU yco yceyce | C ycoyce .
Ocya
yco=1 yca
PROPOSED SHORT-TIME ROOT-AR APPROACH
A non-stationary signal is characterized by frequency components varying over time.
Consequently, the fault signatures, depending on the supply frequency, also vary over time, thus leading to an ineffective fault detection process.
To solve this problem and to be able to introduce the notion of time into the resulting spectrum, the analysis must be shifted to a time-frequency plane.
For this, the ROOT-AR approach is adapted to the analysis of non-stationary signals inspired from the STFT developed in our previous works.
Furthermore, since the STFT is based on the calculation of the fourier transform, it presents problems related to limited time-frequency resolution .
ue to the Heisenberg-Gabor uncertainty principl.
By applying the high-resolution approach ROOT-AR, a time-frequency approach superior in frequency resolution is applied.
The idea is to introduce a sliding window through which we apply the ROOT-AR approach.
this sliding window Figure 1 makes it possible to have portions or segments of the nonstationary signal where each portion of signal is considered stationary.
These signal portions will then be analyzed by the ROOT-AR approach.
The procedure of the proposed approach is given in the flowchart in the Figure 2.
The resulting approach, called SHORT-TIME ROOT-AR or ST-AR, will allow us to observe the different signal components in a time-frequency plane.
Figure 1.
Sliding window analysis concept Figure 2.
Flowchart of the short-time ROOT-AR
EXPERIMENTAL VALIDATION OF THE SHORT-TIME ROOT-AR APPROACH
The experimental setup described in Figure 3 used for experimental tests is composed of a threephase squirrel cage induction motor .
kW, 7 A, 50 Hz, 1410 rpm, and 4 pole.
coupled to a direct current (DC) generator associated to a resistive load.
The stator current signals are measured using three Effect-Hall sensors and an anti-aliasing filter .
n experimental tests, the cutoff frequency of the filter is equal to 400 H.
TELKOMNIKA Telecommun Comput El Control.
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April 2026: 717-726 TELKOMNIKA Telecommun Comput El Control while the motor mechanical speed is measured using a tachometer.
All acquisitions are obtained for an acquisition time of 40 s and a sampling frequency of 3 kHz.
This leads to a frequency resolution equal to 025 Hz.
The entire set is connected to a computer for processing the measured signals and generating those necessary for the control of the PWM inverter.
These control signals are obtained using a space vector PWM through a digital signal processing and control engineering (DSPACE) 1104 card.
The bearing considered in this paper is a 6205-ZZ rolling-element bearing detailed in the Tables 1 and 2.
For the fault diagnosis, an outer race fault is created artificially using a scratch of 2 mm width and 2 mm deep in the outer race.
This configuration is illustrated in Figure 4.
Figure 3.
Experimental setup description Table 1.
Induction motor parameters Parameter Rated power Supply frequency Rated voltage Rated current Rated speed Number of rotor bars Number of poles pairs Value 3 kW 50 Hz 1440 rev/min Table 2.
Geometric parameters of rolling-element bearing Aureference ZZ-6205 coupling opposite sideAy Parameter Ball diameter Db Cage diameter Dc Number of balls Nb Contact angle A Value 835 mm 5 mm Figure 4.
Artificial bearing fault .
uter race faul.
In experimental tests, the induction motor operates at a variable supply frequency from 30 to 50 Hz.
The acquisition of the stator current during this variation makes the stator current non-stationary.
Consequently, the frequency signatures of all considered faults .
ependent on the supply frequenc.
vary Simultaneous faults diagnosis and prognostic in induction motor drives under A (Ameur Fethi Aime.
A ISSN: 1693-6930 with the variation of the supply frequency.
Indeed, the outer race fault signature for both supply frequencies 50 Hz and 30 Hz .
or yco = .
is determined from .
These fault signatures are given in Table 3.
Table 3.
Theoretical frequencies of bearing fault Supply frequency Theoretical frequency For yco = 1 50 Hz 30 Hz yceycayceycayc [H.
= .
ceyc A yco UI yceyc | 16 Hz 29 Hz In the other hand, theoretical frequencies of broken rotor bars are given in Table 4 for both supply frequencies and for a motor slip equal to 4.
6% corresponding to a measured speed of 1431 rpm in experimental tests.
Also, theoretical frequencies of eccentricity fault calculated according to .
are given in Table 5 for both supply frequencies.
The purpose of the test is to show the ability and the efficiency of the proposed short-time ROOT-AR approach compared to the conventional method in the detection of multiple failures signatures when the frequency changes over time.
For this aim.
Figure 5 illustrates the stator current PSD using the periodogram technique for a supply frequency of 30 Hz, 50 Hz and when the supply frequency changes from 30 Hz to 50 Hz.
This test shows the existence of two main frequencies observed at 30 Hz and 50 Hz frequencies.
Table 4.
Frequency signatures of rotor fault .
ase of a motor slip of 4.
6 %)
Sideband type yceyca = .
A 2ycoy.
yceyc Theoretical frequencies .
or 30 H.
Theoretical frequencies .
or 50 H.
Lower sideband yco=1 2 Hz 4 Hz Upper sideband yco=1 7 Hz 6 Hz Table 5.
Frequency signatures of eccentricity fault .
ase of a motor slip of 4.
6 %)
Sideband type 1Oeyc yceyceycayca = yceyc UI .
A ycy Theoretical frequencies .
or 30 H.
Theoretical frequencies .
or 50 H.
Lower sideband Upper sideband yco=1 yco=1 3 Hz 8 Hz 7 Hz 1 Hz Figure 5.
PSD using periodogram for a supply frequency of 30 Hz, 50 Hz and a variation from 30 to 50 Hz TELKOMNIKA Telecommun Comput El Control.
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April 2026: 717-726 TELKOMNIKA Telecommun Comput El Control In the first and second spectrum .
tationary cas.
, the searched harmonics related to the faults (Table 3 to .
are visible but drowned in the other harmonics due to the PWM inverter.
However, the identification of the fault signatures in the third spectrum .
on-stationary cas.
is impossible.
Indeed, it is impossible in this case to identify the rotor cage faults signature, for example, from the outer race fault signatures.
In addition, this spectrum cannot indicate the initial supply frequency and the final one.
This is the major drawback of this method of analysis using the PSD estimation by periodogram.
Figure 6 shows the time-frequency representation of the stator current obtained by the proposed short-time ROOT-AR approach.
From Figure 6, the proposed approach is validated in the detection of the fundamental frequency, the rotor cage fault signature, the eccentricity fault signature and the outer race fault signature in both stationary and non-stationary conditions and especially in time-frequency plane.
comparing the spectrum of both approaches .
eriodogram and short-time ROOT-AR), the importance of introducing the notion of time in the analysis of non-stationary signals .
ariable frequenc.
and the amount of information lost in the absence the information of time in the spectrum are highlighted.
In addition.
Table 6 summarizes the main feature of each signal processing technique .
Figure 6.
PSD using short time ROOT-AR approach for a supply frequency of 30 Hz, 50 Hz and a variation from 30 to 50 Hz Table 6.
Comparison between high resolution/time-frequency methods Method
Peridogram
STFT
ROOT-music
ROOT-AR
Short time ROOT-AR
Frequency resolution Low
Low
Very high
Very high
Very high
Noise robustness Low
Low
High
High
High
Computation time
Very low
Low
High
Low
Low
Complexity Low
Low
High
Low
Low
Nonstationary analysis Yes
Yes
CONCLUSION
Through this paper, an experimental test setup of the induction motor fed with a PWM inverter for multiple faults diagnosis is presented.
As a result, the effectiveness of the proposed approach and its superiority compared to the conventional periodogram based on fourier transform technique is highlighted.
Moreover, in the aim of adapting the ROOT-AR approach to the analysis of non-stationary signals, a variant of ROOT-AR called short-time ROOT-AR is proposed.
This approach has been applied in the detection of simultaneous faults in the case of a variation of the supply frequency .
on-stationary signal.
We were able to experimentally verify the effectiveness of the proposed approach and see its superiority compared to the classic periodogram method in the analysis of non-stationary signals.
However, the proposed approach Simultaneous faults diagnosis and prognostic in induction motor drives under A (Ameur Fethi Aime.
A ISSN: 1693-6930 focuses on the analysis over a well-defined frequency band in order to reduce the computation time.
This frequency band is chosen depending on the searched faults.
Therefore, it is interesting to develop an algorithm based on deep learning techniques in order to select the appropriate frequency band used in the This will be investigated in future works.
FUNDING INFORMATION
Authors state no funding involved.
AUTHOR CONTRIBUTIONS STATEMENT
This journal uses the Contributor Roles Taxonomy (CRediT) to recognize individual author contributions, reduce authorship disputes, and facilitate collaboration.
Name of Author Ameur Fethi Aimer Ahmed Hamida Boudinar Mohamed El-Amine Khodja Azedine Bendiabdellah C : Conceptualization M : Methodology So : Software Va : Validation Fo : Formal analysis ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue I : Investigation R : Resources D : Data Curation O : Writing - Original Draft E : Writing - Review & Editing ue ue ue ue ue ue ue ue ue ue ue Vi : Visualization Su : Supervision P : Project administration Fu : Funding acquisition CONFLICT OF INTEREST STATEMENT Authors state no conflict of interest.
INFORMED CONSENT
We have obtained informed consent from all individuals included in this study.
DATA AVAILABILITY
The data that support the findings of this study are available on request from the corresponding author [Ameur Fethi Aime.
The data, which contain information that could compromise the privacy of research participants, are not publicly available due to certain restrictions.
Derived data supporting the findings of this study are available from the corresponding author [Ameur Fethi Aime.
on request.
REFERENCES