An application of Genetic Algorithm and Fuzzy Logic for the induction motor diagnosis

H. Razik

Université Henri Poincaré - Nancy 1 GREEN-UHP - UMR-7037, BP 239

F - 54506 Vandœuvre-lès-Nancy, Cedex, France E-mail: Hubert.Razik@green.uhp-nancy.fr

M.B.R. Corrêa, E.R.C. da Silva Unidade Acadêmica de Engenharia Elétrica

LEIAM, Caixa Postal 10.105 58109-970 Campina Grande - PB - Brasil

E-mail: [mbrcorrea,edison]@dee.ufcg.edu.br

Abstract-The aim of this paper is the diagnosis of signatures of rotor broken bars when the induction machine is fed by an unbalanced line voltage. These signatures are given by the complex spectrum modulus of the line current. In order to make the diagnostic, a genetic algorithm is used to keep the amplitude of all faulty lines. Moreover, the fuzzy logic approach allows us to conclude to the load level operating system as to inform the operator of the rotor fault severity. Experimental results proof the performance of this method under various load levels and various fault severities. The conclusion resulting from this study is highlighted and proves the efficiency of the suggested approach.

I. INTRODUCTION

Even if the three-phase squirrel cage induction motor is frequently used because of its roughness, its robust construction and its low cost, it may show defects. They can come either from the stator, the rotor or from a mechanical problem. Knowing that industrial constraints are even stronger, the reliability and the safe operating system have to be considered. Consequently, the monitoring and the fault severity have been focused on for some decades. The most popular approach is the monitoring of the induction motor thanks to the spectral analysis of the stator line current absorbed by the induction motor. This technique is non-invasive and the current sensor is commonly used in industrial process as by electrical engineers. Some techniques are based on the classical FFT, others are based on a sliding FFT as on a time-frequency approach allowing the determination of the time where the fault was occurred. Although it lets be, these methods for the diagnosis of rotor broken rotor bar are based on the monitoring and the processing of the stator line current for the detection of the magnitude from some particular frequencies close to the fundamental frequency. These lines are the double slip frequencies close to the fundamental one. The fault severity is quantified thanks to the amplitude ratio of these lines on the supply one that increases with the defect level. This technique is rather simple to implement and it needs few parameters of the induction machine to monitor.

Extensive researches were developed in order to scan the whole range of possibilities from classical approaches to expert systems [1-7]. The main idea was to limit the number

of sensors. As the current monitoring is adapted to the detection of growing failure, different methods were performed to make an early detection using artificial intelligence “methods”. Among all these approaches used for the diagnostics, some are based on fuzzy logic, neural networks or on the mixed neuro-fuzzy logic [8-9]. The artificial intelligence methods based on neural networks require alas a training process in order to make efficient fault detection thanks to all data collected from the experimental plant you want to monitor. Consequently, the disadvantage of this method is that it is dedicated for only the fault training stages.

The diagnostic approach we propose in this paper is based on fuzzy fault detection thanks to a human knowledge of the process. The main goal of this approach is to better distinguish the symptoms from each others and to better obtain diagnosis. To do that, the procedure is composed of:

- data acquisition; - complex spectral analysis; - localisation of fault line frequencies; - computation of diagnostic indexes. This paper describes the different steps to make an efficient

diagnostic discerning a problem of a growing broken bar, a problem of the unbalanced line and the determination of the rotor fault severity as the load level operating system.

II. SPECTRAL COMPONENTS

One of the most well-known approaches regarding the diagnosis of rotor faults in induction machines is based on the processing of the stator currents to detect typical spectrum lines. An induction motor operating with rotor bars defect creates a negative sequence of stator current due to the rotor asymmetry. This principal component rises up at the frequency ( ) sfs21− close to the fundamental frequency. Moreover, due to reflection, the rotor asymmetry frequencies are thus: ssf± , 3 ssf± … Consequently, line components induced close to the fundamental frequency in the stator current spectrum are given by [1 2 ]bb sf ks f= ± (1) where k = 1, 2, 3 … is any positive integer, sf is the supply frequency and s is the slip.

Nevertheless, in case of an unbalanced supply line, the motor generates components both in the forward and the backward system. Moreover, interactions between the components due to the rotor asymmetry and the fundamental supply line frequencies give a novel expression of the principal components in the stator current flowing in the induction motor. These faulty lines are given as follows: [ ] [ ]2 , [1 2 ] , [1 2 ] , 2bb s s s sf s f s f s f s f= − − − ± ± − . (2)

Consequently, the frequency analysis of the stator currents in the range 2 ; 2s sf f−⎡ ⎤⎣ ⎦ will allow the computation of diagnostic indexes of the induction motor fed by an unbalanced line. The interesting components to monitor are:

1 [ 2] sf s f= − (3a) 2 [ 2 1] sf s f= − − (3b) 3 sf f= − (3c) 4 [2 1] sf s f= − (3d) 5 [1 2 ] sf s f= − (3e) 6 sf f= (3f) 7 [1 2 ] sf s f= + (3g) 8 [2 ] sf s f= − (3h)

The amplitudes of all these components are necessary for the fuzzy system fault detector. However, as line frequencies are both positive and negative, we have to analyse two stator line currents. To do that, the Concordia’s vector has to be deduced from the general expression as follows:

( ) ( )2( ) ( )

3 2B C

Ai t i t

i t i tα+⎛ ⎞

= −⎜ ⎟⎝ ⎠

(4)

( ) ( )

( )2

B Ci t i ti tβ

−= (5)

where iA(t), iB(t) and iC(t) are the line currents of the induction machine. The complex form of the Concordia’s current is: si i jiα β= + (6) where 2 1j = − . The Fast Fourier Transform of this signal will calculate to obtain the spectrum of the stator line current for the diagnosis purpose.

The fault detector presented (Fig. 1) is composed of 4 stages which are: the acquisition of the currents, the calculation of the Concordia’s vector, the amplitude search of the defective lines and finally the computation of diagnosis indexes thanks to an expert system based on fuzzy logic.

III. SPECTRUM LINES SEARCH

In this paper, we suggest to make the spectrum lines search by using a Genetic Algorithm (GA). This is based on a natural evolution as described below. It is adapted for the simultaneous evaluation of a large number of points in the search space. Here, the GA is used to find the global

maximum as well as to solve an optimization problem in the spectral lines identification process. A GA uses three fundamental operations which are: the selection, the crossover and the mutation.

The first operation consists in generating an initial population which has a size of N individuals which are the supply frequency and the slip frequency in our case. They are created through a random generator. Each one is constituted by the parameters vector [θ]. The elements of this vector are called genes and are the parameters for the optimization process. All genes can have both a lower and a higher limit in order to add constraints to the identification process. The N number defines the dimension of the search space.

In order to find the “best” individuals, we will have to choose a large dimension which is depending on the number of parameters. The quality of an individual, to be adequate for the problem, is characterized by its fitness F. The evaluation of F is made, for each individual, through an objective function. As our objective is to find the eight principal components in the current spectrum (3), eight Gaussian functions were used as a window. They depend only on the supply frequency (f s) and the slip frequency (sfs) which are the parameters to find. Figure 2 shows the spectral window allowing the calculation of the fitness.

Fig. 1. The stator line currents spectrum in case of one broken bar. The induction motor operates at full load.

0

1

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Fig. 2. The spectral window used for the fitness calculation.

The fitness is calculated as being the integral of the product of the current spectrum by the spectral window.

The passage from a generation of individuals (parents) to the next one (children) is based on: - Selection, the parents individuals with the highest fitness

are copied without any change in the children generation. - Crossover, two children are obtained thanks to an

artificial reproduction using the genes of two parents. The parents are selected among all the individuals upon fitness criterion, the better their fitness is, the more chances the parents have to take part in reproduction. A random number is generated, and a crossover is made if this one is less than the crossover probability pc. The children (Kn and Kn+1) are generated from the parents (Kp1 and Kp2) as follow: 1 2(1 )n p pK aK a K= + −

1 1 2(1 )n p pK a K aK+ = − + with 0 1.a≤ ≤ - Mutation, the genes of one parent are randomly altered

to give a child. The mutation is necessary to explore a larger space and to avoid local minima. Since the vector (individual) changes a lot, we proceed to the mutation with a low probability pm, less than 1%. Let Kn be the individual to be mutated, the gene to be altered is selected thanks to a random generator. It is then changed by an amount that is bounded in order to respect the constraints on the parameters.

- Final, all individuals of low Fitness are changing by new ones. They are computed randomly as in the initialization stage.

So, the new generation is composed of the individuals obtained thanks to selection, crossover, and mutation.

IV. THE FUZZY LOGIC

A fuzzy system is based on the three classical steps which are: the fuzzification step, the inference engine and the defuzzication step. The inputs of the fuzzy expert system are the controlled variables. All inputs can be bounded and normalized. Each input variable is described by membership functions (Small, Medium and High) which can be triangular or take other function shapes. Classically, the inference engine is based on the Max-Min method. The output membership functions are described by Dirac functions (False, True). The evaluation of the centre of gravity is thus easier to compute than using triangular or other functions shapes.

The inference engine is based on AND function and OR function which are described as follows:

- For the AND function applied to the two inputs A and B, the output is evaluated as min(μA, μB);

- For the OR function applied to the two inputs A and B, the output is evaluated as max(μA, μB).

The evaluation of the centre of gravity is made through this relation:

1 1

. /m m

si si sii i

Output Uμ μ= =

⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠∑ ∑ (6)

m denotes the number of membership functions for the output membership functions U. The membership degree is μsi and the weight is Usi.

The sense of velocity can be determined easily using the fuzzy logic. The rules are as follows:

IF (If6 is <high>) AND (If3 is <small>) THEN Velocity is <Positive> OR

IF (If6 is <small>) AND (If3 is <high>) THEN Velocity is <Negative>.

Moreover, we are able to monitor the connection of the motor to the line. A problem occurs when all the currents in the forward and backward have abnormal amplitude. The set of rules can be as follows:

IF (If6 is <high>) AND (If3 is <high>) THEN Current line is <abnormal> OR

IF (If6 is <small>) AND (If3 is <small>) THEN Current line is <abnormal>.

By the same way, we can determine the load level thanks to these three rules:

IF (s is <small>) THEN Load level is <Small> OR IF (s is <medium>) THEN Load level is <Medium> OR IF (s is <high>) THEN Load level is <Full>. The detection of the rotor fault is based on the ratio of the

sum of the two sideband currents on fundamental line current. This approach is advocated from one decade and gives a sufficient precision about the fault severity. As we study the forward and the backward sequence of the supply line, we have to calculate this ratio for the two sequences: Irf and Irb. These results will be the additional inputs for the expert system. The set of rules for the expertise of three phase induction motor, in case of broken bar defect, becomes:

IF (Irf is <small>) AND (If6 is <high>) AND (If3 is <small>) THEN Operating Condition is <Normal> OR

IF (Irb is <small>) AND (If6 is <small>) AND (If3 is <high>) THEN Operating Condition is <Normal> OR

IF (Irf is <medium>) AND (If6 is <high>) AND (If3 is <small>) THEN Operating Condition is <Fault in progress> OR

IF (Irb is < medium>) AND (If6 is <small>) AND (If3 is <high>) THEN Operating Condition is < Fault in progress > OR

IF (Irf is <high>) AND (If6 is <high>) AND (If3 is <small>) THEN Operating Condition is <Broken Bar> OR

IF (Irb is < high >) AND (If6 is <small>) AND (If3 is <high>) THEN Operating Condition is < Broken Bar >.

Thanks to these sets of rules, we are able to evaluate several diagnosis indexes. However, this technique requires the knowledge of the behavior for the determination of all membership functions.

V. EXPERIMENTAL RESULTS

In order to investigate the effectiveness of the proposed approach, we have performed invasive experiments on one type of induction motor (Fig.3). Its characteristics are listed in Table I.

Fig.3. View of the test bed for experimental setup TABLE I

CHARACTERISTIC OF THE INDUCTION MOTOR USED IN THE EXPERIMENT

Description Induction motor Manufacturer SEW USOCOME Power 3 kW Current 5.9 A Number of Poles 2 Number of rotor slots 28 Number of stator slots 36

The first experiments were considered thanks to a healthy

induction machine. Several tests were made for the motor operating at 50%, 75% and 100% of the full load level. This will serve as references in order to test the efficiency of the approach proposed in this paper. The second experiments were made with a machine where a partial hole was made in order to simulate a growing broken bar. This will be noted half broken bar. The third experiments were made with a complete hole in order to have one full broken bar. Two line currents measurements were made by a dedicated acquisition card. The sampling frequency ef was 10kHz and each data length was greater than to 217 values

The first step of this approach is the search lines of the supply frequency and the slip frequency which are inside of the Concordia’s vector spectrum. To do that, the GA was used and the convergence rate is listed in the table II. As we can observe, results are obtained after few iterations.

The second step to estimate or to calculate the fault indexes is the analysis of the amplitude of each lines researched in the spectrum (3). Consequently, these amplitudes will serve the fuzzy expert system. One of the major interests of this approach is the possibility of its extension to a remote system.

We summarize all information given by the expert system in the Table III for the Fuzzy detection of the velocity direction, in the Table IV for Fuzzy detection of the load level and finally in the Table V for the Fuzzy detection of the fault severity.

As we can see, all the results obtained by the fuzzy expert system are in full accordance with the test considered. We can conclude to an efficient fuzzy expert system dedicated for the monitoring of induction motors.

The Concordia’s current spectra of all the tests are presented here after. Their graphical analysis allows us to obtain indirectly the conclusion given by the fuzzy expert system.

TABLE II Convergence of the spectrum search lines (EXPERIMENTATION)

Iter fs sfs Fitness 1 49.896 1.831 256.2 2 49.896 2.899 284.1 3 49.896 3.051 303.5 4 49.896 3.051 303.5 5 49.896 3.051 303.5 6 50.048 3.051 304.1

TABLE III Fuzzy detection of the velocity direction (EXPERIMENTATION)

Backward Forward Direction

Rotor condition I-fs (dB) I+fs (dB) Negatif Positif Aberrant

0bb-100% -22.28 19.55 0 1 0

0bb-75% -18.35 15.83 0 1 0

0bb-50% -23.98 13.97 0 1 0

0.5bb-100% -25.70 21.39 0 1 0

0.5bb-75% -26.11 17.74 0 1 0

0.5bb-50% -35.88 13.11 0 1 0

1bb-100% -24.70 20.13 0 1 0

1bb-75% -27.79 16.30 0 1 0

1bb-50% -30.05 12.93 0 1 0 * 0bb-100%: faulty rotor with no broken bar operating under 100% of the full load

TABLE IV Fuzzy detection of the load level (EXPERIMENTATION)

Load level

Rotor condition Slip 0 - 50% ~75% ~100%

0bb-100% 0.076 0 0 1

0bb-75% 0.045 0 1 0

0bb-50% 0.027 1 0 0

0.5bb-100% 0.060 0 0 1

0.5bb-75% 0.045 0 1 0

0.5bb-50% 0.024 1 0 0

1bb-100% 0.085 0 0 1

1bb-75% 0.045 0 1 0

1bb-50% 0.027 1 0 0 * 0.5bb-75%: faulty rotor with an half broken bar operating under 75% of the full load

TABLE V Fuzzy detection of the fault severity (EXPERIMENTATION)

Amplitude of lines Fault severity

Rotor condition (1-2s)fs fs (1+2s)fs None Small High

0bb-100% -48.78 19.55 -49.99 1 0 0

0bb-75% -49.22 15.83 -55.05 1 0 0

0bb-50% -64.30 13.97 -44.77 1 0 0

0.5bb-100% -31.29 21.39 -41.21 0 1 0

0.5bb-75% -36.16 17.74 -45.62 0 1 0

0.5bb-50% -51.76 13.11 -44.59 0 1 0

1bb-100% -21.24 20.13 -32.50 0 0 1

1bb-75% -17.79 16.30 -36.20 0 0 1

1bb-50% -32.03 12.93 -29.05 0 0 1

* 1bb-50%: faulty rotor with one broken bar operating under 50% of the full load

Figure 4-6 show the spectrum obtained for the case of a full broken bar and the induction motor operates under 50%, 75% and 100% of the nominal load. The amplitude of the fundamental supply frequency allows us to conclude to the direction of the supply frame as to conclude about the defect severity of the rotor defect. Lines appeared close to the fundamental frequency. They are easier to distinguish from each other when the motor operates under high load condition. Nevertheless, the amplitude of these lines could be altered by the inter-bar currents [10].

By the same way, we show in Fig. 7-9 the case where the motor operates with a half broken bar and under several load level as previously described. Once again, we are able to conclude to the direction of the supply frame as to conclude to the rotor fault severity. Nevertheless, it is not obvious to quantify the fault severity whether we are in the presence of a half broken bar or whether we face a full broken bar. Really, lines amplitudes close to the supply frequency are changed a little bit though it is not significant enough for a graphic interpretation.

Spectrum (dB)

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Fig. 7. The stator line currents spectrum: 0.5bb-100%

Spectrum (dB)

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Fig. 8. The stator line currents spectrum: 0.5bb-75%

Spectrum (dB)

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Fig. 9. The stator line currents spectrum: 0.5bb-50%

Spectrum (dB)

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Fig. 4. The stator line currents spectrum: 1bb-100%

Spectrum (dB)

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Fig. 5. The stator line currents spectrum: 1bb-75%

Spectrum (dB)

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Fig. 6. The stator line currents spectrum: 1bb-50%

Spectrum (dB)

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Fig.10. The stator line currents spectrum: 0bb-100%

Spectrum (dB)

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Fig.11. The stator line currents spectrum: 0bb-75%

Spectrum (dB)

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Fig.12. The stator line currents spectrum: 0bb-50%

Finally we show in Fig. 10-12 the spectra obtained for the

case of a healthy machine. As we can observe, lines appear close to the supply frequency. They allow us to conclude that the motor has some natural asymmetries.

VI. CONCLUSION

In this paper we have presented an expert fuzzy system for the monitoring of the induction motor. It can operate under 50% to 100% of the nominal load. This approach allows us to distinguish a healthy machine from a machine operating with one broken bar. Moreover, the operator is alerted of a growing rotor fault. This system allows us to have information about the supply frame connection. This expert system is mainly based on the analysis of the Concordia’s current vector. The line spectrum search is made thanks to a Genetic Algorithm and the fault severity detection is based on a fuzzy approach. Naturally, this approach requires some knowledge about characteristics of the behavior of the motor in case of rotor fault. In that case the diagnosis will be efficient.

ACKNOWLEDGEMENT

This research has been supported by the GREEN laboratory at “Université Henri Poincaré”, Vandœuvre-lès-Nancy, France, the LEIAM laboratory at the “Universidade Federal de Campina Grande”, Brazil and by the CAPES-COFECUB.

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