Detection of Broken Rotor bar Fault in the Squirrel Cage Induction motor Using wavelet Packet Analysis
Dirci Djalel, Hichem MERABET, Aouabdi Salim, Boudiaf Adel
Research Center in Industrial Technologies CRTI, P.O. Box 64, Cheraga, Algeria Abstract
The fault of broken rotor bars in a three phase induction motor is diagnosed by using the wavelet Packet analysis. In this paper Daubechies wavelet is selected as the wavelet base and the wavelet coefficient is obtained from the wavelet transform of current signal of the faulty induction motor. The Energy of Wavelet components appear to be useful for detecting different electrical faults. In this paper we will study the problem of broken rotor bars
Keywords: wavelet Packet, analysis, diagnosis fault, induction motor, broken bar.
1. Introduction
During the last century, the optimal increase in world competitiveness in terms of production in a very competitive international environment has pushed manufacturers to look for ways to control and ensure the availability and dependability of their production tools.
These operational safety requirements have produced a new engineering science that is the monitoring of industrial equipment. The latter includes the detection and diagnosis of failures. Currently the diagnostic field has become an essential tool for corrective maintenance and therefore, companies equipped with monitoring systems tend more and more to automate the maintenance procedure.
The asynchronous machine, because of its construction, is the most robust machine and cheapest on the market. This machine is widely used in most of electric drives in several industrial fields, in particular for applications at a constant speed or variable speed. Like any other machine, the asynchronous machine is not safe from a malfunction. It can be affected by electrical or mechanical defects in the stator, or rotor, or both simultaneously [1][2]. The causes of the defects may be due to a simple problem of manufacture or improper use of the machine. Sometimes the environment in which the machine is used may be responsible for the
deterioration of the machine (corrosive environment, chemical environment).
Therefore, a sudden stop due to any abnormality can result in financial losses.
Therefore, it is recommended for early detection of a defect to be remedied in the shortest time possible and minimize induced effects. This pushed the majority of manufacturers to develop their production lines by sophisticated systems of detection and diagnosis of faults.These two functions aim firstly improving the safety of humans and property and also the increase in productivity gains.
In recent years rotor fault diagnosis has became a challenging topic for many electric machine researchers. The majority of all rotor failures are caused by combination of various stresses [3], namely:
Dynamic stresses arising from shaft torque centrifugal forces and cyclic stresses.
Magnetic stresses caused by electromagnetic forces, unbalanced magnetic pull, electromagnetic noise and vibration.
Thermal stresses due to thermal overload and unbalance, hot spot or excessive losses, sparking
Mechanical stresses due to lose lamination, fatigued parts, bearing failure etc
Since 1980 rotor bar fault detection has became a challenging issue and it still attracts researcher attention. Different diagnosis techniques have been developed
to identify rotor bar faults, Most of which are strongly dependent on detecting the twice slip frequency modulation due to the speed or torque in stator current [3][4].
Several published works are related to rotor bar failures in squirrel cage induction motors are based on machine current signature analysis [5].In this way fast Fourier transform is used to show the effect of this fault on frequency spectrum of current signal. Broken rotor bars in squirrel cage induction machine results the presence of two sidebands at frequency (1±2s)f around the main frequency component in the stator current spectrum [6]. Estimation of rotor resistance is another approach, which is reported in [7].
Although the Fourier transform is an effective method, it is useful for stationary signal processing and the transform signal may lose sometime domain information.
The limitation of Fourier transform is analyzing non-stationary signals lead to the introduction of time-frequency or time scale signal processing tools, assuming the independence of each frequency channel when the original signal is decomposed. The task of distinguishing the fault conditions from the normal conditions based on the resultant FFT spectrum is a difficult one.
This is due to the fact that the stator current is a non-stationary signal whose properties vary with respect to the time variant normal operation conditions of the motors such as load torque and power operation supply. Short-Time Fourier transforms, which windows the input signal, over comes time location problems to some extent. However by applying a fixed width window for all frequency components, this approach does not provide either multiple resolution or temporal resolution [8]. This assumption may be considered as the limitation of this approach. Wavelet transform is a method for time varies ignores non-stationary signal analysis, and uses a new description of spectral decomposition via the scaling concept.
Wavelet theory provides a unified framework for a number of techniques, which have been developed for various signals processing application [9]. Another method for detection of rotor broken bar is using wavelet transforms and signal energy in sixteenth level which is reported in [10].
In [10] the difference between levels is very close together therefore fault diagnosis is to be difficult. This paper proposes a method for mechanical fault feature extraction of three-phase squirrel cage induction motor based on wavelet packet decomposition of stator current. Wavelet is a time frequency analysis tool originated from seismic signal analysis, which uses narrow windows for high frequency component [11]. The window width of wavelet analysis is automatically adjusted for various frequency components. Two important characteristics, i.e. time localization ability and multi-resolution analysis, make wavelet very attractive for the purpose of fault detection and diagnosis. The underlying idea of proposed method is to use wavelet packet decomposition to decompose the stator current into time-frequency spectrum, and use the result to calculate energy to eight bands. The remainder of this paper is organized as follows. Section 2 describes the fundamentals of wavelet packet decomposition and the proposed feature coefficients to calculate energy level. Using the feature energy level analysis to the broken rotor bar is presented in section 3.
Simulation results on a reduced model of induction motor are presented in section 4
2. Mathematical Model of healthy machine
We consider that the induction machine consists of a stator winding back and a rotor squirrel cage. The proposed model is based on an approximation of magnetically coupled circuits where the current in each mesh in the rotor cage is an independent variable [12] [13]. Under classical simplifying assumptions, the model of induction motor is presented. The equation expresses the electrical functioning is:
U = M (1)
Where:
U: is a vector of the voltage;
I: is the vector of current power supplies, rod and ring;
M: is a matrix of connection between vectors, voltage and current vectors.
With:
U = v v v 0 0 0 … … 0 0 (2)
I = i i i i i i … i i (3)
M = R L
L R + L L
L L (4)
The stator resistance and inductance are expressed by:
R = !R 0 0
0 R 0
0 0 R " (5)
L = !L L L
L L L
L L L " (6)
The rotor of the squirrel cage motor consists of q isolated bars, uniformly distributed over the surface of the rotor. Each bar of the rotor cage is modelled by a resistance Rb in series with a leakage inductance Lb and each portion of the ring of short circuit with a resistance Re in series with a leakage inductance Le, as shown in Fig. 1.
#$ =
%&
&
&
&
' # −#) 0 ⋯ 0 − #) #+
−#) # – #) 0 ⋯ 0 #+
⋱ ⋱ ⋱ ⋱ ⋱ ⋱ ⋱
⋱ ⋱ ⋱ ⋱ ⋱ ⋱ ⋱
−#) 0 ⋯ 0 #) # #+ #+ #+ ⋯ ⋯ ⋯ ⋯ ⋯ .#+/00001
(7)
The application of Kirchhoff’s law on a grid gives us:
2. 4R + R 5. I6− R I67 − R I68 −
R . I = 0 (8)
9
9 4L 67 − L 5. I68 + ⋯ . −L I +
L 6 . I + ⋯ + L 6 : = 0 (9) For the stator, it is assumed that it is composed of three phases, each consisting of coils placed in series, regularly distributed in slots on its entire bore. We develop an analytical model of induction machine from the general equations we calculate different inductance of the machine. For this purpose, it suffices to consider the mechanical angle (θsisj) in the calculation of flux. This angle represents the angular difference between the phase i and phase j stator.
The resistance and inductance matrix are respectively represented by the following general form:
F = < F F 0
F F −F
0 −F q. F > (10) With:
F≡R, resistance matrix, F ≡L, inductance matrix.
Frs ≡Fsr =0, for considered resistance matrix.
The matrix of inductances of stator phases expressed by the relationship (10) is of the order (m, m) with m=3:
L ? = !L L L
L L L
L L L " (11) With:
Lsii if (i=j) : proper inductance of phase i ; Lsij if (i≠j) : mutual between i and j stators phases.
The matrix of rotor inductance is of the order (q+1, q+1).
Figure 1. Rotor mesh circuit
L =
%&
&
&
&
'L L … … L @ L
L L … … L @ L
⋮⋮ L@
L
⋮⋮ L@
L
⋮⋮…
…
⋮⋮…
…
⋮⋮ L@@
L
⋮⋮ qL /L 00001
(12)
The mutual inductance matrix between stator phases and rotor mesh is of the order (m, q):
L = <L LL
LL L
……
…
……
…
L @
L @
L @
> (13)
The rotor resistance matrix is:
[ ]
( )
( )
( )
( )
−
−
−
−
−
− +
−
−
−
− +
−
− +
−
−
−
− +
=
e b e e
e e e
e e b b b
e b e b
e b
e b b
e b b
e b
r
R N R R
R R R
R R R R R
R R R R
R R
R R R
R R R
R R
R
L L L
M M M
M M M M
M M M
M M M M
L L
2 0
0
2 0 0 0
0 0
2
0 0
2
(14) With:
L = L ;and R = 24R + R 5 (15)
The model presented in equation (2) is resolved as follows:
BICD = − L8 R + L I + L 8 V (16) Inductions can be calculated either by using the winding functions, knowing that it requires a precise knowledge of the shape of the winding machine, or by using decomposition into Fourier series of induction gap of the machine. The presence of a broken bar in the cage rotor produces a geometric and electromagnetic asymmetry in the rotor circuit, and induced currents are created in direct rotating field, another field is turning around.
These electrical equations must be added to the following mechanical equation:
J9G9 = T − TI+ fKΩ (17) The electromagnetic torque is following by:
T = M II N 9O9 M L L
L L N MI
I N (18) Where: [Ls], [Lr], [Lsr] and [Lrs] , are
respectively the matrix of proper and mutual inductances of stator and rotor windings.
3. Mathematical Model of machine in broken bar fault
The modelling of a fracture of a bar or a ring segment of a short circuit occurs (see Figure. 2) by increasing the value of its resistance so that the current crossing is the most close as possible to zero in steady state [14,15].
Modeling an electrical machine is an
This is introduced in the matrix of resistances by the addition of the matrix of the rotor resistance [Rr] with the default matrix [Rd]. In our study, the method of modelling by increasing the resistance of the broken bar, the value of this resistance is multiplied by a factor of M = 103.
#P =
%&
&
&
'0 0 0 … 0
⋮ 0 … … 0
⋮ #Q,Q #Q,Q7 0 ⋮ 0 #Q7 ,Q #Q7 ,Q7 ⋮ ⋮ 0 … … 0 0/0001
(19)
With:
Rk,k = Rk+1,k+1 = (M+1)*Rb+ 2*Re ; Rk+1,k= Rk,k+1=(-M)*Rb;
Figure 2. Broken Rotor bar in rotor mesh circuit
4. Wavelet Packet Decomposition
For any given signal x4t5 ∈ L , the discrete wavelettransform is defined as the inner product of the wavelet function and the signal, that is [16],
V4W, X5 = ∑^∈_Z4[5\4[5\],Q4[5 (20) Wherex4n5is the signal to be analyzed andψb,64n5 is the discretewavelet function.
The original signal can be approximatedwith the wavelet functions and the wavelet coefficients
Z4c5 = ∑ ∑]∈_ Q∈_V4W, X5\],Q4c5 (21) Wherej is the scale factor andk is the
displacement. Thewavelets are derived from a so-called mother wavelet by thedilation and translation factors. The mother wavelet is normalizedwith zero average and meets the following admissibility condition:
Vfghm∞|Ψ4f5|f jk < +∞ (22) Applying the wavelet transform to the
original signal divides the signal into two parts, the high-frequency part and the low frequency part. The low-frequency part is called an approximation of the original signal. A series of approximations can be obtained by reiterating such decompositions. The difference of the approximation between two successive decompositions is called the details. The multi resolution analysis (MRA) is an algorithm based on the reiterative decomposition of the low-frequency parts only. The peeling-off process in MRA can also be defined as decomposing the approximation spaceVbinto a subsequentapproximation subspace Vb7 and the correspondingdetail subspace Wb7 . The detail spaceWb related to the approxiamtionspaceVb, however, remains unrecompensed. Wavelet Packet decomposition WPD is an extension of wavelet transformation achieved by means of generalizing the link between multi resolution approximation nd wavelets. In WPD, both the approximation spaceVband
the detail spaceWb are decomposed further.
The transformation of the input sequence at scale can be described by [17, 18]:
Figure 3. Wavelet packet filters bank decomposition and corresponding binary
tree.
olow-pass filter; p high-pass filter.
Down sampling ↓ operator.
xm.m= x4n5 (23) Xb7 , s4n5 = ∑sxgmw8 h 4i5xb,su2bi − nv (24) Xb7 , s7 4n5 = ∑sxgmw8 hm4i5xb,su2bi − nv (25)
Wherehmandh represent low pass and high pass having a finite-impulse response of size. In Fig. 3(a), an example is shown for such a division using the conjugation mirror filter banks. The original space is divided into detail and approximation spaces by the low-pass filterhmand high-pass filterh , respectively. The resultant detail spaces further divided. The reiterative splitting of vector spaces is represented in a binary tree in Fig. 3 (b), where the binary tree nodes are labeled by their Depthj(a
dilation factor) and
nodenumberk(frequency factor), and the
ℎ ℎm ℎm
ℎ ℎ
zm.m
z.m z.
z.m z. z. zm.m
z.m z.m z.m z.m z.m z.m z.m z.m J=
0 J=1
J=
J=3 scale
corresponding space is denoted asWb6. It has been proven that there are more than2 b8 different wavelet packet orthonormal bases included ina full wavelet packet binary tree of Depthj. Each of thesepacket has a limitted time support as well as frequency support.
4.1. Feature Coefficients
the spectrum of the WPD. The Feature Coefficient for Node K at Depth j is defined in terms of WPD coefficients as:
W4j, k5 = {∑ g ….~xb,64|5} (26) Where N is the number of WPD
coefficients used for the calculation of the features at Depth j and Node k.
For a given frequency component, the energy of the component is localized at a certain number of Nodes at a given Depth, and the strength of the energy depends on the amplitude of the frequency component [19]. These coefficients are used for fault detection. This index can be interpreted as the amount of energy in the signal. Specific level. Using this index, we can explore the
“energy” distribution of the measured stator current to determine whether the motor is healthy or not.
4.2. Selection of the decomposition level
The approach is based on:
- A suitable number of decomposition levels (ns )depend on the sampling frequency f of the signal being analyzed.
For each one of the proposed approaches [20-22] it has to be chosen in order to allow the high-level signals (approximation and details) to cover all the range of frequencies along
which the sideband is localized.
- The minimum number of decomposition levels that is necessary for obtaining an approximation signal (A €) so that the upper limit of its associated frequencyband is under the fundamental frequency [23], is described by the following condition:
284^•‚7 5ƒ„< ƒ (27)
From this condition, the decomposition level of the approximation signal which includes the left side band harmonic is the integer ns given by:
ns = int …I†‡ˆI†‡4 5‰Š‰‹Œ (28)
For this approach, further decomposition of this signal has to be done so that the frequency band 0 − f will bedecomposed in more bands. Usually, two additionaldecomposition levels (that is, ns
+2) would be adequate for the analysis [24].
ns + 2 = int …I†‡ˆI†‡4 5•ŽŽŽŽ•Ž ‹Œ + 2 (29)
int47.645 + 2 = 9 levels
Several types of mother wavelets exist (Daubechies, coif let, smiled, biorthogonal, etc…..) and have different properties.
However, some authors showed that all these types of mother wavelets gave similar results. Due to the well-known properties of the orthogonal Daubechies family, we chose to use a mother wavelet of this family.
The multilevel decomposition of the stator current was then performed using Daubechies wavelet, the suitable level of decomposition is calculated according to Eq. (9). When the defect of the rotor bars, on the stator windings of the induction motor appear, the defect information in stator current is included in each frequency band determined by the decomposition in wavelet or in wavelet packet. By calculating the energy associated to each level or with the each node of decomposition, one can build a very effective diagnosis tool. The energy eigen value for each frequency band is defined by [25- 27]:
Eb= ∑ ˜D6g6g b,64n5˜ (30) Based on the energy eigenvalue, the
eigenvector is set up as:
T = š››Ž,››•,››w… …›wœ••› ž (31)
WhereDbis the amplitude in each discrete point of the wavelet coefficient of the signal in the corresponding frequency band, with:
E = ∑bgmœ8 ˜Eb˜ (32) The eigenvalue T contains information on
the signal of the stator current for a motor behavior. Besides, the amplitudes of the deviation of some eigenvalues indicate the severity of the defect, which makes T a good candidate to diagnose broken bars of the rotor.
5. Simulation of results
In this study we use a with the following characteristics.
Nominal power 3 kW reduced model for three phase squirrel cage induction motor simulation using MATLAB software Nominal voltage 220V
• Nominal current 5A
• Nominal speed 314 rpm
• the load torque 3.5 n.m
Then one, two, three rotor bar is broken for fault analysis and broken rotor bar detection Simulation results ‘’stator current’’ are shown in Fig. 2, 3, 4, 5 and 6 respectively.
f or stator current analysis we use stator current energy because in energy, signal variation is higher than signal and can be seen signal details better. ,in our case we using energy of node of wavelet packet decomposition analysis Fig. 9 and 13 show stator current energy for one and Three broken rotor bar respectively.
We calculate value of sixtieth node stator current energy for five conditions (healthy with load and without load, 1, 2, and 3 broken rotor bars) and put results in the table I. Daubechies or the normal wavelet basis of order 44 is used for this analysis. sample rate=10 KHz).
0 0.5 1 1.5 2 2.5 3 3.5
x 104 -20
-15 -10 -5 0 5 10 15 20
Time(S)
Current(A)
20 40 60 80 100 120 140
-10 -5 0 5 10 15
Time(S)
Feature Coefficients,node(9.7)
Figure 7. Feature coefficients for one broken rotor bar stator Figure 4.Healthy stator current without load
Figure 5. Feature coefficients for one broken rotor bar stator
Figure 6.Healthy stator current with a load
0 1 2 3 4
x 104 -20
-15 -10 -5 0 5 10 15 20
Time(S)
Current(A)
20 40 60 80 100 120 140
-6 -4 -2 0 2 4 6 8 10 12
Time(S)
Feature Coefficients ,node(9.7)
20 40 60 80 100 120 140 -8
-6 -4 -2 0 2 4 6 8 10
Time(S)
Feature Coefficients,node(9.7)
Figure 13 Feature coefficients for one broken rotor bar stator current, node (9.7)
0 1 2 3 4
x 104 -15
-10 -5 0 5 10 15
Time(S)
Current(A)
Figure 10. two rotor broken bar stator current
20 40 60 80 100 120 140
-8 -6 -4 -2 0 2 4 6 8 10
Time(S)
Feature coefficients,node(9.7)
Figure11. Feature coefficients for one broken rotor bar stator current, node (9.7)
0 1 2 3 4
x 104 -15
-10 -5 0 5 10 15
Time(S)
Current(A)
Figure 8. one broken rotor bar stator current
20 40 60 80 100 120 140
-8 -6 -4 -2 0 2 4 6 8 10
Feature coefficients,node(9.7)
Time(S)
Figure 9. Feature coefficients for one broken rotor bar stator current, node (9.7)
0 1 2 3 4
x 104 -10
-5 0 5 10 15
Time(S)
Current(A)
Figure 12.Three rotors broken bar stator current
130 135 140 -4
-2 0 2 4 6
Time(S)
Amplitude
Healthy machine with load Machine with three broken bars Healthy machine without load Machine with two broken bars Machine with a broken bar
Table 1 shows variation of energy of each node stator current and certainly in node (9.7). According table I results energy in level nine and node (9.7) is different by number of rotor bars clearly that can be used in broken rotor bar detection.
Figure 14. distribution of energy obtained
The difference between signals is on the energy level that is shown in table 1. In table 1, energy levels in sixtieth nodes at level nine are shown that in node (9.7) difference between broken rotor bars is higher than others. Energy level node (9.7) is the best way for broken bar rotor detection.
Table 1: energy of each 9th scale in healthy and faulty cases
Node level 9
Energy of current stator of Induction Motor
Without load
With load With broken bar
With two broken bar
With three broken bars
(0,9) 63.6323 52.6170 125.7223 225.0106 328.7514
(1,9) 3.9499 5.1568 10.3390 8.3000 3.7395
(2,9) 4.0583 3.5930 5.8803 4.3370 4.7646
(3,9) 2.2468 2.2027 4.0443 3.0528 1.7067
(4,9) 1.1226 1.0992 1.5210 1.5545 1.6725
(5,9) 20.5893 19.9125 23.6286 24.6516 25.6629
(6,9) 93.3223 82.0895 45.3727 40.0925 41.3209
(7,9) 356.9241 577.8219 587.8057 704.4820 939.4306
(8,9) 0.0012 0.0019 6.84 10-4 7.46.10-4 6.81 10-4
(9,9) 0.0048 0.0086 0.0011 0.0013 0.0012
(10,9) 0.0387 0.0944 0.0146 0.0194 0.0869
(11,9) 0.1401 0.1302 0.0088 0.0115 0.0732
(12,9) 0.1167 0.1000 0.2735 0.2920 0.3531
(13,9) 0.2818 0.2666 0.3645 0.3733 0.3783
(14,9) 0.0011 0.0038 0.0053 0.0065 0.0137
(15,9) 0.001 0.0036 0.0054 0.0076 0.0183
0 5 10 15 0
100 200 300 400 500 600 700 800 900 1000
energy eigenvalue
16 Node at level 9
healthy machine without load healthy machine with load machine with broken bar machine with two broken bar machine with three broken bars
The figure 15 clearly shows the variation of the energy eigenvalue. One can observe that the energy stored in node (9.7) depends on the degree of the default. Obviously, the energy in level 9 represents the number of broken bars of the squirrel cage rotor.
The band of detection of broken rotor bars can’t be influenced by mechanical vibrations and load effect because the frequencies accompanying the mechanical problem are very far from the band of detection which is located in [39.06-78.12] Hz. The broken bar induce supplementary frequencies near the fundamental component which are described by (1±2s)f. These frequencies are influenced only by the operating frequency f and the slip s
Figure 15. Eigenvector analysis results obtained from db44
6. Conclusions
Signal decomposition via wavelet transform and wavelet packet provides a good approach of multi resolution analysis.
The decomposed signals are independent duet the orthogonality of the wavelet function. There is no redundant information in the decomposed frequency bands.
Based on the information from a set of independent frequency bands, mechanical condition monitoring and fault diagnosis can be performed effectively.
This work shows a new approach in detection of broken rotor bars in squirrel cage induction motors having only stator line current energy as input. The detection is based on the Discrete Wavelet Decomposition method.
It shows that the effectiveness of the proposed method for this kind of fault. 3-hp squirrel cage induction motor
The result can be used as an extra feature for the proposed SVM classifier.
Acknowledgment
This work is realised in the Research Center in Industrial Technologies CRTI, Algeria, in framework of validation the results of our reserche project
“Monitoring of faults in elctro-energy systems besed on intelgence artificielle ”.
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application de la techinque des ondelettes au diagnostic de défaurs de la machine asynchrone a rotor à cage”, RerN VOL 15, N°4 ? PP 549-557, 2014.
[25] Haitham Abu-Rub, S. M.Ahmed , Shady S.
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Vol.3, No.1, , pp. 129~135 ISSN: 2088 February 2012.
[27] Merabet Hichem, BAHI Tahar,
and Detection of Eccentricity Faults in a Doubly-Fed Induction Generator Electrotehnicà, Electronicà, Automaticà (EEA) , Volume 64 , Issue 3 , pp 60
8. Biography
Drici Djalel: received the Engineering degree in electronics engineering in 2005 and the Magister degree in electronics engineering in 2008, both from the 8 Mai 1945 University, Guelma, Algeria. His main research fields include signal processing, fault diagnosis, and Renewable energy. Email: [email protected]
Hichem Merabet:
Engineering, Magister and Doctorate degrees in electrical engineering from Badji Mokhtar University, Annaba, Algeria in
2006, 2009 and
2016,respctively.His main research fields
include signal processing, control of system, faults diagnosis, monitoring of system electro energy and Renewable energy.
Email: [email protected]
Adel Boudiaf:
barika/ Batna, Algeria, in 1977. he received the Engineering,
University in 2004
Magister degrees in electrical engineering from
University, Algeria, in 2009, he received his PhD in electrical engineering from the
Gualma, Algeria in 2016. He is a senior researcher in the field of quality and
monitoring, control in Research Center in Industrial Technologies CRTI, ex -
Aouabdi Salim:
Engineering,
degrees in automatics electrical engineering from Badji Mokhtar
Annaba, Algeria in 2005 and 2016,respctively.His main main
fields of diagnosis of non-linear systems via statistical multivariate analysis.
Vol.3, No.1, , pp. 129~135 ISSN: 2088-8708, Merabet Hichem, BAHI Tahar, Diagnosis and Detection of Eccentricity Faults in a Fed Induction Generator, Electrotehnicà, Electronicà, Automaticà Volume 64 , Issue 3 , pp 60-67, 2016.
received the Engineering degree in electronics engineering in 2005 and the Magister degree in electronics engineering in 2008, both from the University, Guelma, His main research fields include signal processing, fault diagnosis, and
[email protected] : received the Engineering, Magister and Doctorate degrees in electrical engineering from Badji Mokhtar University, Annaba, Algeria in
2009 and
His main
, control of system, system electro-
Adel Boudiaf: was borne in barika/ Batna, Algeria, in received the frome Batna in 2004 and the Magister degrees in electrical engineering from Beskra he received his PhD in electrical engineering from the University of He is a senior researcher in the field of quality and process monitoring, control in Research Center in
CSC.
Aouabdi Salim: received the and Magister automatics and engineering from Badji Mokhtar University, Annaba, Algeria in 2005, 2009 His main main research linear systems via
