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Induction Motor Broken Rotor Bars Diagnosisusing Stator Current Time-Frequency Analysis

A.F. Aimer, A. Bendiabdellah, A.H. Boudinar, C. Mokhtar and S. LaribiL.D.E.E Laboratory, Department of Electrical Engineering, USTO-Oran, Algeria

e-mail: [email protected]

Abstract--Recent advances in the field of power

electronics and control circuits, have contributed to the

increasing use of induction machines in electrical systems.

The use of induction machines is mainly due to their

robustness, their power/weight ratio and their low cost of

manufacture. Still, various faults may appear at such

machines. The Power Spectral Density (PSD) based on the

Fourier Transform (FT), is used as a method of analysis formany years for its simplicity and computing time relatively

low. However, it is ineffective in faults detection in the case

of a small slip (harmonics too near to the fundamental). In

addition, the fact that this method is based on the

calculation of the FT, implicitly implies that the spectral

properties of the signal are stationary. With the

development of variable speed applications, the spectral

characteristics of the stator current become non-stationary

and the spectra are much richer in harmonics. To resolve

these problems, we used in this paper, a time-frequency

representation called Short Time Fourier Transform, giving

therefore, an additional information on changes of the

frequencies over time in the stator current signal. We

conduct several simulations and experimental tests in theaim of validating our approach.

Index TermsInduction motor, fault diagnosis, time-

frequency analysis, broken rotor bars.

1.INTRODUCTION

With a simple technology, the induction motor iswidely used in most electric drives, especially forconstant speed applications. Advances in powerelectronics associated with modern controls techniqueshave led to consider variable speed applicationsefficiently, which was previously reserved exclusivelyfor DC motor and synchronous motor. Thus, given thisgrowing interest, a general reflection was engaged forfault detection and condition monitoring of inductionmachine.

Fault detection in electrical machinery has been thesubject of research and industrial achievements in recentyears. There are several types of techniques; the vibrationanalysis is the most used method [1], [2], [3]. Thismethod is mainly used for the detection of mechanicalfaults.

Another technique is also used increasingly in recent

years based on analysis of stator current also calledMotor Current Signature Analysis or MCSA, itsparticularity is that the stator current contains information

on almost all the faults that can appear on the inductionmotor [4], [5], [6].

Signal processing, spectral analysis in particular, isused for many years in detecting and locating faults ininduction machines [7]. This type of failures is wellsuited to this approach since many phenomena are

reflected by the appearance of sideband frequenciesdirectly related to the motor speed.

However, in most cases, induction motor operatesdirectly from the mains and running in the steady state,with known loads. The development of technology andthe advances in variable speed drives have given anotherdimension to various problems including non stationarycondition of measurable signals, disruptions anddistortions caused by power converters, etc. In addition,the requirements in terms of industrial maintenance guidethe research to a more effective fault diagnosis.

The power spectral density or PSD of the statorcurrent, calculated based on the Fourier transform (FT) isthe most currently tool used by researchers andindustrials [8]. This is justified by its simplicity and thelow cost of current sensors and the harmonic content ofstator current.

However, this technique has several disadvantageswhich are due to the problem of frequency resolution.Indeed, the calculation of the FT introduces a smoothingeffect and a side effect. These effects are reflected by theappearance of sideband lobes in the stator currentspectrum and reduce the analysis efficiency [9].

To analyze a signal, it has an interest in having a mainlobe as narrow as possible and sideband lobes of verylow amplitude when it is not possible to have both properties simultaneously. However, it is possible toreduce the amplitudes of sideband lobes by replacing therectangular window by a smoother and seamless window.

Following this resolution problem, the PSD findsdifficulties in detecting faults with a small motor slip(harmonics close to the fundamental).

Also, the fact that the PSD is based on the FT,implicitly implies that the spectral properties of the signalare stationary. In addition, the modulus of the FT of a

signal provides only a time average of the spectralcontent of the signal without giving details on possible


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changes in frequency over time. Therefore, informationregarding the location of the frequencies over time cannot be inferred from the Fourier transform.

To overcome these constraints, we use a time-frequency representation. Indeed, the Gabor works in the40s have conducted to the foundations of a new type ofanalysis called Short Time Fourier Transform or STFT.He was the first to imagine a local Fourier transformbased on a windowing signal analysis to observe changesin frequency over time. This transformation requires thedivision of the signal in consecutive short segments andthen calculates the Fourier transform of each segment.The idea is to introduce the local frequency parameter sothat the Fourier transform is applied to the signal througha sliding window on which the signal is approximatelystationary. This method represents the results into threedimensions; the description of the signal is carried out inthe time-frequency composed of spectral characteristics

as a function of time [10].The main disadvantage of this transformation is its

limited resolution. Indeed, it is impossible to have aperfect localization in both time and frequency. In otherwords, a good resolution in time (small time window)necessarily implies poor resolution in frequency (largefrequency window). Conversely, good resolution infrequency implies poor resolution in time. The windowwidth in each domain remains fixed as it is translated.This results in a fixed resolution across the entire time-frequency plane [11], [12].

In this context, this paper focuses on the application of

the Short Time Fourier Transform in detecting andlocating induction motor faults. To this end, the STFT isevaluated and used for the analysis of stator current in the presence of broken rotor bars faults. The results ofsimulations and experimental tests will support andvalidate our approach.

2.STATOR CURRENT SIGNATURE ANALYSIS

The stator current spectral analysis is the mostcommonly method used in recent years, because theresulting spectrum contains a source of information onmost faults that may appear on an induction machine.

It is important to note that, as in vibration analysiscase, the more the fault progresses, its characteristicspectral components continue to increase with time [6].

Induction motor broken rotor bars is consideredamong the most common fault studied because of itssimplicity of implementation. This fault induced changesin the stator current spectral component and thus theappearance of sideband frequencies in the currentspectrum produced by the magnetic field anomaly of thebroken rotor bars [7].

Indeed, broken rotor bars give rise to a sequence ofsidebands given by:

( ) sc fksf 21= (01)

Where: fs is the supply frequency and fc the sidebandfrequencies associated with the broken rotor bars, s is themotor slip and k= 1, 2, 3

3.TIME-FREQUENCY ANALYSIS

The Fourier transform is expressed by the following

equation [11]:

( ) ( )

= dtetxfFT ftjx2 (02)

We define the power spectral density or PSD as thesquare modulus of the Fourier transform. The PSD isthus independent of the signal phase.

Therefore, any information on the frequency changesover time is lost in the PSD.

It is really not necessary to present the problem of the

Fourier analysis as the overall weaknesses of this type ofrepresentation in the non stationary cases were identified[8], [10], [13].

Gabor's work in the 40s have laid the foundations ofthe Short Time Fourier Transform. It was the first toimagine a local Fourier transform based on a windowinganalyzed signal to observe changes in frequency overtime. The time-frequency distribution, known as ShortTime Fourier Transform or STFT is defined by [11]:

( ) ( ) ( )

+

=

dethxftSTFTfj

x

2

, (03)

( ) ( ) ( )+= deHfXftSTFT tjx

2, (04)

The second expression of the STFTx is inferred fromthe classical properties of the FT: conservation of thescalar product, shift properties and transformation of anormal product into a convolution one.

The STFT is constituted by the FT of ( ) ( )thx obtained by weighting ( )x by the window ( )th

witch is a short time analysis window localized around tand that shifts by varying the parameter t.

Join to ( )h , the family of functions depending ontwo parameters t and f, defined by [14]:

( ) ( ) ( ) 22, ,, = ftethhfj

ft

(05)

The numbers ( )ftSTFTx , are commonly calledprojections of ( )x on the functions system ht,f. Ifh isthe rectangle window ofTsupport, the STFT consists intaking the FT of a sequence of signals equal to x on the

support and zero elsewhere.


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We begin by the discrete-time signal [xn = x(nT)],T>0. Let hn = h(nT) and we mean by N the number ofsamples in the analysis window. Finally, we introduce adiscretization of the frequency variablef.

The STFT is then defined by the entire numbers Xk,ncalculated as follows [15]:

=

+=1

0

2

,

N

N

nTj

knk ehxXl

l

ll

, kZ, n = 1,2, (06)

As for the FT, the zero-padding technique allows theimprovement of the frequency resolution. The principleof this method is to complete by M zeros a set ofNsamples so thatM + Nis a power of 2 and thereafter can perform calculations using the Fast FT algorithm usingthe N + Mpoints. When M = N, the method use theDiscrete FT algorithms that are being made to calculate2Npoints from the spectrum, from only Npoints of the

signal.

3.HEISENBERG-GABOR UNCERTAINTY PRINCIPLE

The uncertainty principle, also called time-frequencyinequality, is based on the uncertainty relationshipsestablished by Werner Heisenberg in quantummechanics. The analogy with the work of Heisenberg forthe Fourier transform was made by Dennis Gabor in1946.

Let us consider the finite energy signalx(t), centred intime and frequency around zero.

Gabor defines the duration

tand the spectral bandfas follows [14]:

( )+

= dttxt

Et

x

221 (07)

( )+

= dffXf

Ef

x

221 (08)

Where Ex is the energy of the signal given by theParceval relationship:

( ) ( )+

+

== dffXdttxEx 22 (09)

Therefore, the time-frequency inequality is defined by[12]:

4

1 ft (10)

It expresses the fact that the duration-band product ofa signal is lower bounded for a t duration and a f spectral band. In other words, the greater the accuracy infrequency localization, the lower the accuracy in time

localization and vice versa. The STFT is subject to theuncertainty principle due to the use of Fourier transform.

This issue requires the search for the right time-frequency compromise suitable to the case considered indetermining the correct window width.

Gaussian window has the best time-frequencylocalization. Indeed, it verifies the following equality:

41= ft (11)

Finally, the choice of the window is important becauseit represents another compromise (comparable to thetime-frequency compromise) between the main lobewidth and the amplitude of the sideband in the frequencydomain.

4.SIMULATION RESULTS AND DISCUSSION

To simulate the presence of a rotor fault in a squirrelcage induction machine with a motor slip s = 5%, we

construct the signal to be analyzed as follows:( ) ( ) ( )

( ) ( )tbtf

tftftx

c

cs

++

+=

2

1

2sin068,0

2sin066,02sin5

(12)

With: b(t) a signal that represents the white noiseintroduced by using the concept of the SNR. The SNR being the Signal to Noise Ratio given by the followingequation:

b

s

P

PSNR 10log10= (13)

Where Ps and Pb are, respectively, the signal and noisepowers. The supply frequency used is equal tofs = 50Hz.The sideband frequencies of broken rotor bars arecalculated by equation (1). Therefore, the sidebandfrequencies of one broken bar are given by:

fc1 = 45Hz et fc2 = 55Hz.Figure 01 shows the signal of stator current in time

domain simulated with and without broken bars. We canobserve the change in the form of the stator current afterthe introduction of the broken rotor bar fault.

In Fig. 02, the STFT of the stator current is used forthe detection of harmonics corresponding to one broken

bar. This simulation is done with a motor slip of 5% andSNR = 50 dB corresponding to a moderately noisysignal. The sideband frequencies of the faults arehighlighted in the STFT using the three dimensional gridtechnique.

Fig. 03 represents the of stator current signal analysissimulation achieved by the STFT algorithm. Thesimulation parameters used correspond to one brokenrotor bar with a motor slip of 5% and a SNR of 10 dB.

The sideband frequencies corresponding to thesimulated fault are easily located for this value of theSNR which corresponds to a highly noisy signal. Thisverifies the robustness of the STFT against noise.


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4 4.2 4.4 4.6 4.8 5-10

-5

0

5

10

Temps (s)

Amplitude(A)

signal du courant statorique

4 4.2 4.4 4.6 4.8 5-10

-5

0

5

10

Temps (s)

Amplitude(A)


Healthy motor 1 broken bar

Time s Time s

Fig. 01: Stator current signal in time-domain for healthy and faulty cases.

0

2

4

0 50100 150

200

0

20

40

60

80

100

Spectre 3D

Frquence (Hz)Temps (s)

Puissance

(dB) 48,11dB

45Hz

47,18dB

55Hz

0

2

4

30 35 40 4550 55 60 65

70

0

20

40

60

80

100Spectre 3D


Puissance

(dB)

47,18dB

55Hz48,11dB

45Hz

Fig. 02: Stator current analysis by STFT for one broken bar, a motor slip of 5 % and an SNR=50 dB: (a): without zoom (b): with zoom.

(a) (b)

Power(dB)

Time (s)Time (s) Frequency (Hz)Frequency (Hz)

Power(dB)

STFT STFT

4 4.2 4.4 4.6 4.8 5-10

-5

0

5

10

Temps (s)

Amplitude(A)


Fig. 03: Time-domain representation and STFT analysis of stator current for one broken bar, a motor slip of 5 % and an SNR=10 dB.

0

2

4

30 35 40 4550 55 60 65

70

0

20

40

60

80

100

Spectre 3D


Puissance

(dB)

47,18dB55Hz

48,11dB

45Hz

STFT

Time (s)

Power(dB)

Time (s) Frequency (Hz)


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5.EXPERIMENTAL RESULTS AND DISCUSSION

5.1 Experimental Setup description

In order to validate the results obtained by thesimulation tests, we apply the time-frequency analysis inthe processing of experimental signals obtained from a

test conducted at the Laboratory of Automatics andIndustrial Informatics from the University of Poitiers(France). Indeed, this test creates an artificial fault of onebroken bar and two broken bars.

The block diagram of the experimental setup is givenin Fig. 04.

Fig. 04: Experimental setup bloc diagram.

The motor used in the experimental investigation is athree phases, 1.1 kW, 50Hz, 2 pole pairs, squirrel cageinduction machine.

All acquisitions were done in steady state with a

sampling frequency equal to 1428Hz. Each measuredsignal is acquired on 13347 samples.

5.2 Healthy motor test

The healthy motor test is established in order toprovide a reference which will be taken in considerationin the next tests to distinguish the normal operation ofinduction motor from the faulty ones.

Fig. 05 represents the time-domain signal of statorcurrent for the healthy motor case with a full load. Thestator current time-frequency analysis by STFT is givenby the following figure 06.

Fig. 05: stator current signal for the healthy motor test.

Fig. 06: stator current analysis by STFT for the healthy motortest.

In Fig. 06, we can observe through the time-frequencyanalysis of the stator current different harmonics on thespectrum. However, the most imposing harmonics are themultiples of the fundamental (150 Hz, 250 Hz, 350 Hz)

and the principal rotor slot harmonic observed at 621 Hz.Figure 07 represents a zoom of the time-frequency

spectrum produced around the fundamental in thefrequency band [30Hz-70Hz]. This band concerns usinsofar as the broken bars fault, studied in this paper, islocated in this frequency band.

5.3 One broken bar test

The motor slip calculated in this test is equal to4.06%. This value is obtained through the mechanicalspeed which is measured at 1432 rpm.

Electrical sensors

Butterworth Filters

Data AcquisitiondSPACE 1104

Shaft encoder1024 pts/r

isa , isb , isc

vsa , vsb , vsc

AC Grid380 V

3-phase InductionMotor

2 2.1 2.2 2.3 2.4 2.5-4

-2

0

2

4

Temps (s)

Am

plitude

(A)

Signal du courant statorique

Time (s)

0

2

4

60 100 200 300 400 500

600 700 800

-20

0

20

40

60

80Spectre temps-frqeunce


Am

plitude

621 Hz

29.40 dB

50 Hz

74.08 dB

150 Hz

24.64 dB

250 Hz

45.03 dB

350 Hz

33.20 dB

Power(dB)

Time (s)Frequency (Hz)

STFT


6/7

Fig. 07: stator current analysis by STFT for the healthy motortest with a zoom around the fundamental.

The theoretical sideband frequencies of one brokenrotor bar fault calculated according to the motor slip anddepending on the value of k=1,2 are given by:[41.88Hz;45.94Hz;54.04Hz;58.12Hz]. These frequenciesare located around the fundamental.

Through the zoom done on the time-frequencyspectrum shown in fig. 08, we can observe the sidebandfrequencies of the fault of one broken bar around thefundamental. Also, it should be noted that the detectedfrequencies are equal to the sideband frequenciescalculated theoretically based on the motor slip.

Fig. 08: stator current analysis by STFT for the one broken bartest with a zoom around the fundamental.

5.4 Two broken bars test

The sideband frequencies are calculated in the sameway regardless of the number of broken rotor bars.Indeed, stator current analysis in case of broken barsgives only an indication of the presence of the fault. Nevertheless, we can differentiate between the case ofone broken bar and the case of two broken bars bymonitoring the evolution of the power of the faultscomponent. Indeed, several experimental studies haveshown that increasing the number of rotor bars increasesthe power of the faults component [7].

Figure 09 shows the stator current signal in the time-domain for two broken rotor bars.

Fig. 09: stator current signal for the two broken bars test.

The zoom done on the time-frequency spectrumaround the fundamental is represented in fig. 10. We canobserve the sideband frequencies of the fault of twobroken bars.

Fig. 10: stator current analysis by STFT for the two broken bartest with a zoom around the fundamental.

0

2

4

30 35 40 45 50 5560 65 70

0

20

40

60

80



Puissance

(dB)

Time (s)Frequency (Hz)

STFT

Power(dB)

0

2

4

30 35 40 45 50 5560 65 70

0

20

40

60

80



Puissance

(dB) 58.44 Hz

33.00 dB

54.16 Hz

44.55 dB45.81 Hz

42.92 dB

41.85 Hz

30.81 dB

STFT

Frequency (Hz)Time (s)

Power(dB)

2 2.2 2.4 2.6 2.8 3-4

-2

0

2

4

Temps (s)

Am

plitude

(A)

Signal du courant statorique

Time (s)

0

2

4

30 35 40 45 50 5560 65 70

0

20

40

60

80



Puissance

(dB)

58.87 Hz

36.43 dB

54.48 Hz

45.79 dB

45,70 Hz

46,36 dB41.21 Hz

33.26 dB

STFT

Frequency (Hz)Time (s)

Power(dB)


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These frequencies are equal to the sidebandfrequencies calculated theoretically based on the motorslip. There is an increasing in the power of the faultscomponent compared to the case of one broken bar.

6. CONCLUSION

Through this paper, accent is placed on thepresentation of an effective diagnostic method capable ofdetecting and locating the sideband frequencies of rotorfaults particularly near the fundamental.

Indeed, it was used in this paper, a signalcorresponding to the stator current signal in the case of asquirrel cage induction motor with one and two brokenrotor bars. Therefore, an algorithm based on Short TimeFourier Transform is developed to perform a correctdiagnosis and relatively precise location of the sidebandfrequencies of the considered fault. Several tests have

been established to verify and to validate the robustnessand effectiveness of our approach.

Indeed, The STFT is robust to variations of the noiseand allows a clear and easy location of the faultsfrequencies for even low values of motor slip.

Also, we have experimentally validated our approachusing experimental signals acquired from a testconducted at the Laboratory of Automatics and IndustrialInformatics at the University of Poitiers (France). Thetime-frequency analysis of stator current from thedifferent tests led to the detection of fault sideband

frequencies.Finally, it should be noted that this work constitutes a

first step in analyzing non-stationary signals, throughwhich, we have validated the effectiveness of ourapproach in the case of stationary signals.

In this context, two perspectives should be consideredfor this work: extending the diagnosis to the transientstate (case of load changes) to solve the non-stationarityproblem observed in the variation of load of the inductionmachine and the experimental validation of this approachin the case of load changes.

ACKNOWLEDGEMENTS

The authors wish to thank all the team of theLaboratory of Automatic and Industrial Informatics ofthe University of Poitiers (FRANCE) and special thanksto Mr. Gerard Champenois for the aid he afforded for ourexperimental work validation.

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