Diagnosis and classification using ANFIS approach of stator and rotor faults in induction machine Hichem Merabet*

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Diagnosis and classification using ANFIS approach of stator and rotor faults in induction machine

Hichem Merabet*

Research Center in Industrial Technologies (CRTI), P.O. Box 64, Cheraga, Algeria

Email: h.merabet@csc.dz

*Corresponding author

Tahar Bahi

Electrical Department,

Faculty of Science Engineering, University of Annaba, Algeria Email: tbahi@hotmail.com

Djalel Drici

Research Center in Industrial Technologies (CRTI), P.O. Box 64, Cheraga, Algeria

Email: d.drissi@csc.dz

Abstract: Three-phase squirrel cage induction motors are one of the important elements of the industrial production system, and are mostly used because of their robustness, reliability, relatively simple construction and their low cost.

Nevertheless, during their function in different process, this machine types are submitted to external and internal stresses which can lead to several electrical or mechanical failures. In this paper, we proposed a reliable approach for diagnosis and detection of stator short-circuit windings and rotor broken bars faults in induction motor under varying load condition based on relative energy for each level of stator current signal using wavelet packet decomposition which will be useful as data input of adaptive neuro-fuzzy inference system (ANFIS). The adaptive neuro-fuzzy inference system is able to identify the induction motor and it is proven to be capable of detecting broken bars and stator short-circuit fault e with high precision. The diagnostic ANFIS algorithm is applicable to a variety of industrial process based on the induction machine for detection and classified the any faults types. This approach is applied under the MATLAB software®.

Keywords: induction machine; diagnosis; detection; neuro-fuzzy inference system, modelling; simulation.

Reference to this paper should be made as follows: Merabet, H., Bahi, T. and Drici, D. (2017) ‘Diagnosis and classification using ANFIS approach of stator and rotor faults in induction machine’, Int. J. Intelligent Engineering Informatics, Vol. 5, No. 3, pp.267–282.

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Biographical notes: Hichem Merabet received his Engineering degree in Electrical Engineering in 2006, the Magister and Doctorate degree in Electrical Engineering in 2009 and 2016, respectively both from the University of Badji Mokhtar University, Annaba, Algeria. His main research fields include the control of electrical machines, fault diagnosis, system electro-energy and renewable energy.

Tahar Bahi received his Engineering, Magister and Doctorate degrees in Electrical Engineering from Badji Mokhtar University, Annaba, Algeria in 1983, 1986 and 2006, respectively. Since 1983, he has been with the Department of Electrical of the University of Annaba, Algeria where he is currently a Professor of Electrical Engineering. His main research fields include the control of electrical machines, power electronic applications and Renewable energy.

Djalel Drici received his 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.

This paper is a revised and expanded version of a paper entitled ‘Diagnosis of stator turn-to-turn fault and rotor broken bars fault using neuro-fuzzy inference system’ presented at the 3rd International Conference on Automation, Control, Engineering and Computer Science, ACECS-2016, Hammamet, Tunisia, 20–22 March 2016.

1 Introduction

Squirrel cage induction motors have dominated in the field of electromechanical energy conversion and are very often used different industrial systems based on rotating machinery to transform electrical energy into mechanical driving because of their robustness, high power efficiency and high reliability, and low charge (Yahia et al., 2014;

Godoy et al., 2015; Srinivasan et al., 2015). In spite of their low cost, reliability and robustness, in case of heavy load or high temperature, some pivotal components of rotating machinery would inevitably generate multi various faults lead to breakdown in electrical machines of the entire production system which cause considerable financial losses (Babaa et al., 2013).

According to major faults found in squirrel cage induction motors are derived from electrical or mechanical problem, among the electrical faults, the stator windings faults represent approximately to 30% to 40% of the machines faults are related to stator inter turn fault in the stator winding, which cause a large circulation current in the shorted turns (Asfani et al., 2012; Siddiqui et al., 2014; Drif and Cardoso, 2014). In generally the inter-turn short-circuit fault is caused by mechanical stress, moisture and partial discharge, which is accelerated for electrical machines supplied by inverters. But really, as well known, the primary or the main cause of inter-turn short circuit is degradation of the winding insulation, which leads to. When an inter-turn short circuit occurs, and the big problem that the inter-turn short circuit propagate and takes a large area in the winding which effectively lead to generate, phase-ground or phase-phase faults (Wang et al., 2014; Ukil et al., 2011).

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In another side from the investigations on different mechanical faults types in induction machine that the rotor related faults is around 20% including broken rotor bar faults (Pu et al., 2014; Soufi et al., 2013).

The presence of the broken rotor bar fault in produces a geometric and electromagnetic asymmetry in the rotor circuit, and induced currents are created in direct rotating field, another field is turning around (Singh et al., 2016). However, if a sufficient number of rotor bars are broken, the motor cannot start because it cannot develop sufficient torque. Breakage of broken rotor bar occurs in large induction machines (da Costa et al., 2015).

The induction machine under stator or rotor faults in monitoring and diagnosis stage, many kinds of fault signature have been used in several tasks. Such as vibration signal monitoring, temperature measurements, flux magnetic, electromagnetic torque and speed, among these various parameters in case of electrical and mechanical fault types, stator current is widely used for diagnosis purposes, availability of need sensors in the existing drive system and possessing informative instinct are the main reasons that make the stator current more preferable then other fault signatures (Lashkari et al., 2015; El-Bouchikhi et al., 2015; Faiz and Moosavi, 2016).

According to the literature, there are several techniques of the detection of stator and rotor faults in induction machines drives, especially, the methods based on time domain or frequency domain techniques, which have been proposed to detect stator failures. A more intensive research efforts have been focused on frequency signature analysis for stator and rotor faults using different signals such as; machine currents, the motor current signature analysis (MCSA) combined with wavelet, wavelet transform (WT) applied to different signals, current envelope (CE), extended Park’s vector approach (EPVA), instantaneous power signature analysis (IPSA), short-time fourier transform (STFT), support victor machine (SVM), etc. (Pons-Llinares et al., 2014; Zhang et al., 2015;

Kusuma et al., 2015).

The artificial intelligences based on fuzzy logic system inference, artificial neural network (ANN) or combined structure techniques of artificial neural fuzzy interference system (ANFIS) are widely used in the new monitoring and fault classification techniques of induction machines (Eristi et al., 2013; Subbaraj and Annapurna, 2014;

Souli-Jbali and Minyar, 2015; Vaidyanathan and Azar, 2016).

Therefore, in order to increase the efficiency and the reliability of the monitoring in the field of the (IM) supervision, the proposed technique is based on neuro-fuzzy inference system (ANFIS).

In the aim to analysing the faults, the global mathematical model of induction machine is developed and simulated via software MATLAB^®/SIMULINK.

2 Induction motor model

2.1 Multi meshes model of rotor broken bars fault

The mathematical model of squirrel cage induction motor can be written in vector matrix from as follows (Pu et al., 2014).

( )

[ ] [ ][ ] d [ ][ ]

V R I L I

= +dt (1)

(4)

where

[ ]

^S

R

V V V

⎡ ⎤

= ⎢ ⎥

⎣ ⎦ (2)

and

[ ]

^S

R

I I I

⎡ ⎤

= ⎢ ⎥

⎣ ⎦ (3)

With

[ ] [ ]

[ ]

[ ] [ ]

1

1 2 3

1

1 2 3 1

[0 0 0 0] _R

R R

t

S S S S

t

s S S S

r t N

t

r R R R Rk RN e N

V V V V

I I I I

V

I I I I I I I

+

×

⎧ =

⎪⎪ =

⎪⎨

⎪ =

⎪⎩

…

… …

(4)

We applied Park transformation extended to the rotor system so as to convert this system in Nr phases in a (d, q) system written as follows:

3 ( )

1 1 1

2 2 2

2 cos cos . .2 cos ( 1) .2

sin sin . .2 sin ( 1) .2

n R R

R R

R

R R

T θ n θ θ k p π θ n p π

n n

θ θ k p π θ n p π

n n

⎡ ⎤

⎢ ⎥

⎡ ⎤ = ⎛ ⎞ ⎛ ⎞

⎣ ⎦ ⎢⎢⎢ ⎜⎝ − ⎟⎠ ⎝⎜ − − ⎠⎟ ⎥⎥⎥

− ⎛ ⎞ ⎛ ⎞

⎢ − ⎜ − ⎟ − ⎜ − − ⎟⎥

⎢ ⎝ ⎠ ⎝ ⎠⎥

⎣ ⎦

…

(5)

The inverse Park transformation as follow

( ) ¹

3

1 cos sin

1 cos . .2 sin . .2

1 2 2

( 1) . sin ( 1) .

R R

n R

R R

θ θ

π π

θ k p θ k p

n n

T θ

π π

θ n p θ n p

n n

−

⎡ − ⎤

⎢ ⎛ ⎞ ⎛ ⎞ ⎥

⎢ ⎜ − ⎟ − ⎜ − ⎟ ⎥

⎢ ⎝ ⎠ ⎝ ⎠ ⎥

⎡ ⎤ =

⎣ ⎦ ⎢ ⎥

⎢ ⎥

⎢ ⎛ − − ⎞ − ⎛ − − ⎞⎥

⎢ ⎜⎝ ⎟⎠ ⎜⎝ ⎟⎠⎥

⎣ ⎦

(6)

with

• kε[0 … (n –1)] kεN

(8) With θs: position of stator quantities.

Either the stator part

[ ][ ] { [ ][ ] } { [ ][ ] }

[ ] s s d s s d sr rk

V R i L i M i

dt dt

= + + (9)

The application of the transformation given:

( )

{ } [ ]

[

( )

] { [ ] [

( )

] } [ ]

1

33 33

1

33 33

1

33 33

1

33 3

1

33 3

odqs s s s odqs

s s s odqs

s sr Nr R odqr

s sr Nr s odqr

V T θ R T θ i

T θ L T θ d i

dt

T θ L d T θ i

dt

T θ M T θ d i

dt

T θ d M T θ i

dt

−

= + +

⎡ ⎤

+ ⎣ ⎦

+

(10)

For rotor part:

[ ] [ ][ ]

Vr Rr irk d

{ [ ][ ]

Lr irk

}

d

{ [

Msr

][ ]

is

}

dt dt

( )

]

{ } [ ]

( )

[ ] [

( )

]

{ } ^{[ ]}

1

3 3

1

3 3

1

3 33

1

3 33

odqr Nr R r Nr R odqr

Nr R r Nr R odqr

Nr R r s odqs

Nr R rs s odqs

V T θ R T θ i

T θ L T θ d i

dt

T θ Ms T θ d i

dt

T θ d M T θ i

dt

−

⎡ ⎤ ⎡ ⎤

= ⎣ ⎦ ⎣ ⎦

⎡ ⎤ ⎡ ⎤

+ ⎣ ⎦ ⎣ ⎦

⎡ ⎤

+ ⎣ ⎦

⎡ ⎤

+ ⎣ ⎦

(12)

When choosing a reference related to the rotor:

, 0

s R

θ =θ θ =

According simplifications we obtain smaller model for the asynchronous machine:

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0 0 0 2

0 0 0

2

*

3 0 0 0

2

0 3 0 0

2

0 0 0 0

0 0

2

0 0

0 2

0 0 0 0

0

0 0 0 0

0

0 0 0 0

sc r sr

r ds

sc sr

qs

sr rc dr

qr

sr rc e

e

s sc r sr

ds

qs r

sc s sr

r

r e

L N M

N i

L M i

d i

M L dt

i

M L i

L

R wL N wM

V

V wL R N wM

R

R R

⎡ − ⎤

⎢ ⎥

⎢ ⎥ ⎡ ⎤

⎢ − ⎥ ⎢ ⎥

⎢ ⎥ ⎢ ⎥

⎢− ⎥ ⎢ ⎥

⎢ ⎥ ⎢ ⎥

⎢ ⎥ ⎢ ⎥⎣ ⎦

⎢ − ⎥

⎢ ⎥

⎣ ⎦

⎡ −

⎡ ⎤ ⎢

⎢ ⎥ ⎢

⎢ ⎥ ⎢⎢ −

⎢ ⎥

=⎢ ⎥−⎢

⎢ ⎥

⎣ ⎦

⎣

ds qs dr qr e

i i i i i

⎤⎥ ⎡ ⎤

⎥ ⎢ ⎥

⎢ ⎥ ⎢ ⎥

⎢ ⎥ ⎢ ⎥⎣ ⎦

⎢ ⎥

⎦

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with

( )

2 2 1 cos

rc rp rr e e

r

r e b

r

L L M L L

N

R R R

N

⎧ = − + + −

⎪⎪⎨

⎪ = + −

⎪⎩

α α

(14)

For the mechanical part, after the application of the general transformation on the expression of the torque, we obtained:

( )

3 .

e 2 r sr ds qr qs dr

C = PN M i ⋅i −i ⋅i (15)

In the rotor broken bars faults we are considered, they in an increase in the resistance of elements presents a defect. They do not cause topology changes of the rotor, but only certain elements of the matrix [Rr] which are changed. For this, the simplest procedure is to add to the array of resistance [Rr] a new matrix [ ]R′r where the non-zero elements correspond to the faulty elements. In the if the defect concerns the k bar, the new array of rotor resistance is written:

[ ]

Rrf =

^{[ ] [ ]}

Rr + R′r (16)

where

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[ ]

0 0 0 0

0 0 0 0 0

0 0 0

0 0 0 0 0

0

r bk bk

bk bk

R R R

R R

⎡ ⎤

⎢ ⎥

′ =⎢ ′ − ′ ⎥

⎢ − ′ ′ ⎥

⎢ ⎥

⎣ ⎦

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The new rotor matrix resistances, after transformations are:

[ ]

^{( )}

[ ]

^{( )}

[ ]

( )

{ [ ] [ ] }

( )

1

2 2

1

2 2

rfdq Nr R rf Nr R abcs

Nr R r r Nr R

R T θ R T θ x

T θ R R T θ

−

⎡ ⎤ ⎡ ⎤

=⎣ ⎦ ⎣ ⎦ =

⎡ ⎤ ′ ⎡ ⎤

=⎣ ⎦ + ⎣ ⎦

(18) The fault resistance matrix becomes:

[

rfdq

]

^rdd ^rdq

rqd rqq

R R

R R R

⎡ ⎤

= ⎢ ⎥

⎣ ⎦ (19)

Where the four terms of this matrix are

( )

2 (1 cos ) 2 2 (1 cos ) 1 cos(2 1)

2 (1 cos ) sin(2 1) 2 (1 cos ) sin(2 1)

2 (1 cos ) 2 2 (1 cos ) 1 cos(2 1)

rdd b er r k bfk

rdq bfk

r k

rqd r k bfk

rqq b er r k bfk

R R R R k

N N

R R k

N

R R k

N

R R R R k

N N

⎧ = − + + − ⋅ − − ⋅

⎪⎪

⎪ = − − ⋅ − ⋅

⎪⎪⎨

⎪ = − − ⋅ − ⋅

⎪⎪

⎪ = − + + − ⋅ − − ⋅

⎪⎩

∑

α α α

α α

α α α

(20)

The index k characterises the broken bar, Rbfk: resistance of a rotor broken bar.

2.2 Model of stator inter turns short-circuit fault

Assuming that motor function under stator inter-turns short-circuits faults in phase ‘a’ the flux stator winding and short-circuit winding equations in dq frame (Lashkari et al., 2015):

2 cos

3

qs qs S qs ds S f

dλ v R I ωλ μR I θ

dt = − + + (21)

2 sin

3

ds ds S ds qs S f

dλ v R I ωλ μR I θ

dt = − + + (22)

( )

1 cos sin

as f f S ds qs f

dλ R I μR I θ I θ I

dt = − + − (23)

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The stator and winding currents in dq frame

( )

1 2 3 4 cos

sq qs qr r m f

I =λ σ −λ σ + Lσ +L σ I θ (24)

( )

1 2 3 4 sin

sd ds dr r m f

I =λ σ −λ σ + Lσ +L σ I θ (25)

( ) ( )

(

² ⁵ ⁶ ^cos ⁵ ⁶ ^sin ⁴

)

f as sq rq sq rq

I = −λ + σ I +σ I θ+ σ I +σ I θ σ (26)

The constant coefficients σi are shown in Table 1.

Table 1 Coefficient of currents equations

σ0 σ1 σ2 σ3 σ4 σ5 σ6

s r 2m

L L −L

0

1 σ Ls

1 m

r

L σ

L ₀

2 3

μLs

σ ₀

2 3

μLm

σ

μLs μLm

Figure 1 present the schematic of induction machine under inter turns short-circuit fault in phase ‘a’

Figure 1 Stator windings with short circuit fault in phase ‘a’ (see online version for colours)

3 Wavelet packet method

The wavelet method requires the use of time-frequency basis functions with different time supports to analyse signal structures of different sizes. The WTs extension of the STFT, projects the original signal down onto wavelet basis functions and provides a mapping from the time domain to the time-scale plane. The wavelet ψ(t) is a zero mean function (Jinglong et al., 2016; Bouzida et al., 2013; Kahkashan et al., 2014).

( ) 0 ψ t dt

+∞

−∞ =

∫

⁽²⁷⁾

The equation (27) is dilated with a scale parameter s, and translated by u:

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, ( ) 1

u s u

ψ t ψ t

s s

⎛ ⎞

= ⎜⎝ − ⎟⎠ (28)

The WT of a function f at the scale s and position u is computed by correlating f with a wavelet atom:

( , ) ( ) 1

f u

W u s f t ψ t

s s

+∞

−∞

⎛ ⎞

=

∫

⎜⎝ − ⎟⎠⁽²⁹⁾

A real WT is complete and conserves energy as long as it satisfies a weak admissibility condition

2 0 2

0

( ) ( )

| | | | ^ψ

ψ ω ψ ω

dω dω C

ω ω

+∞

= −∞ = < +∞

∫ ∫

⁽³⁰⁾

The multi-resolution analysis can analyse a signal into different frequency bands.

Either φ the scale function. It must be in L² and having a non-zero mean. Base scaling functions are formed for all i∈Z as follows:

( )

, ( ) 2 ⁱ/2 2 ^l

λi j t = ⁻ φ ⁻ t− j (31)

In the same manner, the wavelet base is:

( )

, /2

Ψi j( ) 2t = ⁻ⁱ Ψ 2⁻^lt−j (32)

The following equations represent the decomposition of the scaling function and the wavelet linear combinations of the scale function to the full resolution directly. The dyadic scaling factor leads to:

( ) 2 ( ) (2 )

λ t =

∑

j h j φ t− j ⁽³³⁾

Ψ( ) 2 ( )Ψ(2 )

t =

∑

j g j t− j ⁽³⁴⁾

The terms h(j) and g(j) are the low-pass filters and high pass respectively in wavelet decomposition.

The Mallat algorithm allows decomposing the signal f(n) in several decomposition levels as shown in Figure 2:

Figure 2 Decomposition of wavelet packet (see online version for colours)

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We obtain 2^l frequency bands each with the same bandwidth as:

( ) 2 , 2 i l− ifn

⎡ ⎤

⎢ ⎥

⎣ ⎦ (34)

with i = 1,2…2^l.

Such that fn is the Nyquist frequency in the frequency bands i. When h(n) and g(n) are f(n) decomposition filters in D1 and A1 respectively. The next level of decomposition is based on A1 and coefficients are expressed as follows:

2( ) ( 2 ) ( )1

A n =

∑

jh k− n A k ⁽³⁵⁾

2( ) ( 2 ) ( )1

A n =

∑

jh k− n A k ⁽³⁶⁾

When the mechanical and electrical faults, of the induction motor occur, the fault information of the current signal is included in each frequency band resulting from the wavelet decomposition or wavelet packet.

By calculating the energy associated with each level or each decomposition, one can build a very effective diagnostic tool. The clean energy value of each frequency band is defined:

2

1 , ( )

k n

j k j k

E ⁼ D n

=

∑

+ ⁽³⁷⁾

where j is the decomposition level. Based on the value of clean energy, the vector is given by:

0, 0, 2, , 2 1,

E E E E m

T E E E E

⎡ − ⎤

= ⎢⎣ … ⎥⎦ (38)

Such as:

2 1 2

0 m j j

E ⁻ E

=

∑

= ⁽³⁹⁾

4 Adaptive neuro-fuzzy inference system

Adaptive neuro-fuzzy inference system (ANFIS) is one of the most significant approaches for offline or online electrical machines drives monitoring and has been effectively applied tasks in recent years (Ahmed et al., 2012).

ANFIS is a hybrid controller structure using fuzzy logic inference system and the architecture of a neural network having five-layer feed-forward structure. With this way ANFIS use the advantage of learning ability of neural networks inference mechanism similar human brain provided by fuzzy logic. A typical architecture of ANFIS having n inputs, one output, and m rules is illustrated in Figure 4 (Ayaz, 2014; Shibendu et al., 2013). Here x, y, z and up to n are inputs, f is output, the cylinders represent fixed node functions and the cubes represent adaptive node functions. This is a Sugeno type fuzzy system, where the fuzzy IF-THEN rules have the following form:

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• rule 1: if x is A1 and y is B1,…n is k1 then f1 =(p1x + q1y + r1z + … v1)

• rule 2: if x is A2 and y is B2,…n is k2 then f2 = (p2x + q2y + r2z + … v2)

• …

• rule m: if x is Am and y is Bm,…n is km then f2 = (pmx + qmy + rmz + … vm).

Figure 3 Decomposition of wavelet packet (see online version for colours)

5 Interpretation simulation

The ANFIS model generates eight input membership functions of Gaussian structure and is run for 500 Epochs. The error for the training and checking output are found to be 0.004%. The trained and checked ANFIS output for fault type’s diagnosis are shown in Figure 4 and Figure 5.

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Figure 4 Training, testing and checking output for the ANFIS (broken rotor bars faults) (see online version for colours)

0 50 100 150 200 250 300 350 400 450 500

-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Index Data

faults type

Training Data ANFIS Output Checking Data ANFIS Checking Output

Healthy case

4 broken rotor bar

1 broken rotor bar 3 broken rotor bar

2 broken rotor bar

Figure 5 Training, testing and checking output for the ANFIS (stator inter-turns short circuit) (see online version for colours)

0 50 100 150 200 250 300 350 400

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

Index Data

faults type

Training Data ANFIS Output Checking Data ANFIS Checking Output

Healthy case

5% inter-turns 15% inter-turns

35% inter-turns

Figure 6 Testing data and testing output for the ANFIS (broken rotor bars faults) (see online version for colours)

1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Index Data

faults type

Testing-Data

ANFIS Output-Test 4 broken rotor bar 3 broken rotor bar

2 broken rotor bar 1 broken rotor bar Healthy case

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Figure 7 Testing data and testing output for the ANFIS (stator inter-turns short circuit)

1 2 3 4 5 6 7 8

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

Index Data

faults type

Testing-Data

ANFIS Output-Test 35% inter-turns

15% inter-turns

Healthy case

5% inter-turns

To validate our network (shown Figure 6 and Figure 7), a test of recognition is carried out. The results are consigned in the table (show Table 1).

Table 2 Numerical values of input-output for validate ANFIS Input

x y Desired output Estimated

output Observations of the error Rotor broken bars faults

95.5056 366.6240 0.0000 0.0000 0.0000 98.1150 405.8460 0.0000 0.0000 0.0000

61.6177 351.4025 1.0000 1.0011 –0.0011

65.3050 412.7210 1.0000 0.9987 0.0013 56.7994 381.6860 2.0000 1.9998 0.0002

58.1560 398.6990 2.0000 2.0022 –0.0022

57.3547 434.1678 3.0000 3.0076 0.0024

62.5511 520.7533 3.0000 3.0009 –0.0009

55.8730 500.4854 4.0000 4.0011 –0.0011

59.0201 550.6706 4.0000 3.9993 0.0007 Stator inter turns short-circuit faults

392.4010 4.8310e+03 1.0000 0.9999 0.0001

383.1424 4.8413e+03 1.0000 1.0059 –0.0059

492.4003 5.8319e+03 2.0000 1.9999 0.0001

505.7650 5.7690e+03 2.0000 2.0103 –0.013

592.4005 6.8309e+03 3.0000 2.9994 0.0006

601.8990 6.8240e+03 3.0000 3.0151 –0.0151

The new data are checked with the developed ANFIS model. The error is about 0.025%

and the efficiency of our developed ANFIS is about 99%. Both the error curves are illustrated in Figure 8 and Figure 9.

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Figure 8 Error curve of the ANFIS (rotor broken rotor bars) (see online version for colours)

0 100 200 300 400 500

0 0.005 0.01 0.015 0.02 0.025

Epoche

Error

Train Error Checking Error

Figure 9 Error curve of the ANFIS (stator inter-turns short circuit) (see online version for colours)

0 50 100 150 200 250 300 350 400 450 500

-1 -0.5 0 0.5 1 1.5 2 2.5

Epoche

Error

Train__Error Check__Error

The input relationships or dependency for the ANFIS output are in addition analysed.

These are the unique characteristics of ANFIS. The mapping is optimised by neuro adaptive learning techniques by fuzzy modelling procedure to learn information about the data set for monitoring the stat of induction machine in our case study.

6 Conclusions

In this paper, we presented the development of a fault model of the induction machine then the simulations of stator short-circuit and rotor broken bar faults.

We initially presented in the first part the mathematical model of rotor broken bars faults then the model of stator inter turns short-circuit faults.

In the second part of this work, the ANFIS approach is used to diagnose and classifier the electrical and mechanical faults in the induction machine, the adaptive neuro-fuzzy system inference indicator is based on the analysis of magnitude of energy level of the

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wavelet decomposition for stator current, in addition used for off-line training and checking of ANFIS in deferent fault types.

References

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