What are the estimated values of the stator and rotor resistances?

In this test, the six winding resistances (RsA, RsB, RsC, Rra, Rrb, Rrc) are again the parameters to be optimized in order to minimize the IAE (2).

(Open Access) Induction machine Winding Faults Identification using Bacterial Foraging Optimization technique (2014) | Salaheddine Ethni

Q: What is the success rate of the BFO algorithm?

The BFO algorithm had a success rate of about 75% when used with the no-load measured current data compared with a success rate of about 85% for the PSO algorithm.

Q: How long did the data take to be collected?

Data are collected over a time window of 0.2 sec, with a sampling interval of 1ms, as the machine was operating atsteady state with no load.

Q: What is the purpose of the experiment?

The experiment work was conducted on a 1.5kW, 50 Hz, 240V, 2-pole wound rotor induction machine coupled to a 3kW DC machine used as a generator to provide the necessary load torque.

Q: What is the name of the algorithm?

B. SwarmingSwarming is a technique used in some versions of the algorithm to smooth the progress of the convergence of cells of bacteria to form groups around areas in the solution with high nutrient concentration, thereby improving the efficiency of the search and foraging process.

Q: How many investigations were required to obtain convergence?

The number of investigations required to obtain convergence is 1844 where the calculation error falls from a maximum value of 0.068 A.s to 0.022112 A.s. Figs.

Q: Why are the final values of stator resistances higher than the nominal values?

The final values of stator resistances are higher than the nominal values identified in Table 1 due to the fact that the algorithm is limited to changes in resistance values alone and has to find a way to compensate for the effect of the fault on other machine parameters.

Induction Machine Winding Faults Identification

using Bacterial Foraging Optimization Technique

S. A. Ethni, S. M. Gadoue and B. Zahawi

School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, UK

Email: salaheddine.ethni@ncl.ac.uk

Abstract-The performance of a stochastic search algorithm,

Bacterial Foraging Optimization (BFO), when used for fault

identification of induction machine stator and rotor winding

faults, is investigated in this paper. The proposed condition

monitoring technique uses time domain terminal data in

conjunction with the optimization algorithm and an induction

machine model to indicate the presence of a fault and provide

information about its nature and location. The proposed

technique is evaluated using experimental data obtained from a

1.5 kW wound rotor three-phase induction machine. BFO is

shown to be effective in identifying the type and location of the

fault without the need for prior knowledge of various fault

signatures.

Index Terms-- Induction machine, bacterial foraging algorithm,

condition monitoring.

I. INTRODUCTION

Induction motors are used in a wide variety of domestic and

industrial applications due to their simple construction,

ruggedness, low price and efficiency. The monitoring the

condition of the motor is essential to detect any developing

fault at an early stage, reducing the risks of severe motor

faults. Faults can then be treated before completely damaging

the motor, thus decreasing the maintenance cost and

shutdown time. Consequently, there is an increasing need for

a simple and reliable technique to detect incipient motor

faults. Traditional induction machine condition monitoring

techniques [1] usually involve the use of sensors embedded in

the machine to measure, for example, temperature or

vibration [2]. There has also been considerable interest in

detecting windings and other machine faults by examination

of terminal current waveforms [3] using data gathered under

steady-state operating condition. This may involve the

calculation of quantities such as input power [4] or negative

sequence components [5]. Recent trends in condition

monitoring include the detection of machine faults using data

acquired during speed transients [6] and the estimation of

machine parameters [7-11].

A new fault identification technique using machine terminal

data and rotor position information has been recently

proposed by the authors [8-10]. In this method, a stochastic

search is carried out to estimate the values of machine

parameters which give the best possible match between the

performance of the faulty experimental machine and its

mathematical model, thus identifying both the location and

nature of the winding fault. Figure 1 shows a schematic

diagram of the fault identification technique. Stator currents

are calculated from an induction motor dynamic model and

compared to the actual measured currents to produce a set of

current errors that are integrated then summed to give an

overall error function. When the machine is in its healthy

state, there is a high correlation between its effective

parameters and the model parameters resulting in a small

calculation error. If a fault develops in the machine, its

electrical parameters are of course modified and when the

measured currents are compared with calculated currents

there will be a large calculation error giving a fast indication

that a fault of some type is present. Fault identification is

carried out by adjusting the model parameters, using a

stochastic search method to minimize the error. The new set

of model parameters then defines the nature and location of

the fault. Unlike many other methods, it should be noted here

that the new stochastic search based approach does not

require any expert prior knowledge of the type of fault or its

location; both are identified as an integral part of the

optimisation process.

The Fault identification technique proposed in this paper is

based on Bacterial Foraging Optimization (BFO). This

stochastic algorithm continuously adjusts the induction

machine model parameters off-line to achieve the minimum

error between the measured and calculated stator currents.

The new set of model parameters defines the nature and

location of the fault.

Experimental tests based on a 1.5 kW wound rotor three

phase induction machine have been carried out to validate the

proposed fault identification algorithm with stator and rotor

faults considered. Results confirm the capability of BFO to

identify and locate the fault without the need for a previous

knowledge of different fault current signatures.

Measured

Stator

Currents

Machine

Model

Measured Voltage

and

Rotor Speed

Stochastic

Algorithm

∫|e|dtMachine

parameters

Error

Fault

Alert

Calculated Stator

Currents

Fault Identification

Fig. 1 Block diagram of the stochastic search based fault identification

technique

II. INDUCTION MACHINE MATHEMATICAL MODEL

The mathematical ABCabc model of an induction motor is

developed using Simulink software and used with BFO to

identify different machine winding faults. This ABCabc

model is obtained from the standard machine voltage

equations and represented by (1):





rsr

TTT

cos

coscos

cos

coscos

cos

coscos

cos

coscos

(1)

where (V

, V

) ,(I

, I

) are the stator winding

voltages and currents, (V

, V

), (I

, I

) are the rotor

winding voltages and currents, (R

, R

), (R

, R

)

are the stator and rotor winding resistances respectively, L

and L

are the stator and rotor winding self-inductances

respectively, M

and M

are the mutual inductance between

pairs of stator and rotor windings respectively, M

is the peak

value of the rotor position dependent mutual inductance

between stator and rotor winding pairs,

is the rotor position

angle,

+2Se3,

+4Se3 and p is the differential

operator.

III. B

ACTERIAL FORAGING OPTIMIZATION

Bacterial Foraging Optimization (BFO) was introduced in

2002 by Passino [12]. The BFO is a stochastic search and

optimization technique based on the foraging behaviour of

Escherichia coli (E. coli) bacteria which takes advantage of a

variety of bacterial swarming and social foraging behaviours.

Unlike Particle Swarm Optimization (PSO) [13] the bacterial

foraging is based on the idea of the survival of the fittest. In

contrast, PSO is a collective method in which members of the

population cooperate to find a global optimum in a partially

random way and without any selection. Members of the

population with the lower fitness functions are not discarded

but do survive and can potentially be the future successful

members of the swarm.

The bacterial foraging system consists of four principal

mechanisms, namely chemotaxis, swarming, reproduction,

and elimination dispersal.

A. chemotaxis

A chemotactic step can be described as a tumble followed by

another tumble or a tumble followed by a swim. The

chemotactic process of E. coli is modelled within the BFO

algorithm according to the possible mediums the bacteria

discovers and its reaction within such mediums.

This can be simply described as follow:

If the matrix X

(j, k, l) represents the current position of the i

bacterium at the j

chemotactic, k

reproductive and l

elimination-dispersal step the new position X

(j+1, k, l) is then

determined by:

)(),,(),,1( jClkjlkj

λΧΧ  

i = 1,2,…S

where S is the number of bacteria to be used in the search, C

is the maximum step size taken to the next possible position,

and the elements of the matrix O

(j) are random functions used

to define the size of the step and the direction of movement

given by:

)()(

)(

ΔΔ

)(i

is the transpose of

)(i'

and

],...,[)(

1 mii

rri '

, r

is a

random number between [-1, 1] and m = 1, 2,…, p, where p is

the number of dimensions of the search space (i.e. the number

of variables).

B. Swarming

Swarming is a technique used in some versions of the

algorithm to smooth the progress of the convergence of cells

of bacteria to form groups around areas in the solution with

high nutrient concentration, thereby improving the efficiency

of the search and foraging process. Swarming was not

implemented in the simple form of the algorithm used in this

study.

C. Reproduction

After N

chemotactic steps, a reproduction step takes place.

All bacteria are arranged in order according to their fitness,

only the first half of the population survives and each

surviving bacterium splits into two new bacteria, located at

the same position.

D. Elimination-dispersion

The chemotaxis gives a basis for a local search, while the

reproduction process speeds the convergence of the

algorithm. However, chemotaxis and reproduction are not

enough for global optima searching since bacteria may get

stuck around the initial positions or local optima. In the BFO,

a dispersion event takes place after a certain number of

reproduction processes. In each elimination-dispersal step, all

members are subjected to elimination-dispersal with a

probability of P

. For each bacterium, if P

is greater than a

random number in the interval [0–1] the bacterium is

eliminated and replaced by another bacterium dispersed to a

new, random location within the search space.

At the beginning of the algorithm, the E. coli are randomly

distributed in the solution space, which has different

concentrations of nutrients and noxious substances (different

function values). The fitness function (function value or

nutrient concentration value J) for each randomly distributed

bacterium is then calculated at its initial location. A tumble

then takes place in a random direction and the fitness value J

corresponding to the new position is calculated. This value of

J(i, j, k, l) is then compared with the previously calculated

value and if the new value of J is better, a swim in the same

direction as the previous tumble follows. If the fitness value is

less at the new position, a second tumble takes place to a new

random position, and so on. The maximum number of

successive steps in any one swim sequence is limited to N

steps. The cumulative fitness function of each bacterium is

calculated after N

steps as the sum of the nutrient

concentration value

lkjiJ

),,,(

obtained during its life

time, i.e. the previous N

chemotactic steps. The bacteria are

then arranged in order according to their fitness values. The

healthier half of the population survives and the less healthy

half dies out. Each surviving bacterium split into two new

bacteria, located at the same position and begins the

exploration of the search space from a healthier starting

position than the previous generation.

Step 1: Initialize, the BFO algorithm parameters p, S, N

, N

, P

, C(i), i = 1,…,S. Distribute the initial

population (X

(j,k,l)|i=1,2,…,S) randomly within the solution

space.

Step 2: Elimination-dispersal loop: l = l +1

Step 3: Reproduction loop: k = k+1,

Step 4: Chemotaxis loop: j = j+1,

substep a: for i = 1,2,…S, take a chemotactic step

for bacterium i

substep b: calculate the fitness function, J (i, j,k,l).

substep c: Let J

last

= J(i, j,k,l) to save this value since

the algorithm may find a better cost via a run.

substep d: Tumble: generate a random vector

i ' )(

with each element

)(i

, m= 1,2,. . . ,p, a

random number on [-1, 1].

substep e: Move: Let

)()(

)(

),,(),,1(

Clkjlkj

& &

Use the new value of

),,1( lkj

&

to calculate the

concentration function of bacterium i.

substep f: compute J(i,j+1,k,l), of the two feasible

solutions (J

and J

j+1

), the one with the lowest value of J is

selected.

substep g: Swim

i) Let m = 0 (counter for swim length).

ii) While m < Ns

Let m=m+1.

If J(i,j+1,k,l) < J

last

, let J

last

= J(i,j+1,k,l) and let

)()(

)(

),,(),,1(

Clkjlkj

& &

use the value

of X

(j+1,k,l) to calculate the new J(i,j+1,k,l) as in

(substep f)

Else let m = Ns. (end while statement).

Substep h: Go to next bacterium (i + 1) if i ≠ S (go to

substep b)

Step 5: If j < Nc, go to step 4. In this case, continue

chemotaxis, since the life of the bacteria is not over.

Step 6: Reproduction

For the given k and l, and for each i = 1,2,…,S, let



),,,(

health

lkjiJJ

be the health of bacterium i (a measure of

how many nutrients it got over its lifetime and how successful

it was at avoiding noxious substances). Sort bacteria and

chemotactic parameters C in order of ascending cost J

health

higher cost means lower health.

The S

(S/2) bacteria with the highest J

health

values die and the

other S

bacteria with the best values split (and the copies that

are made are placed at the same location as their parent).

Step 7: If k < Nre, go to step 3. In this case, we have not

reached the number of specified reproduction steps, so we

start the next generation in the chemotactic

loop.

Step 8: Elimination-dispersal: For i = 1,2,…,S, with

probability P

, eliminate and disperse each bacterium

which keeps the swarm size constant. When eliminate

a bacterium, simply disperse one to a random location within

the search space.

Step 9: If l < N

, then go to step 2; if not end.

The BFO parameters necessary for its implementation are

first specified including the number of bacteria within the

population S = 8, P

= 0.25, and C = 0.1, the initial position

of each bacterium within the solution space, the number of

chemotactic steps N

= 10 taken during each bacterium

lifetime, the maximum number of successive steps in any one

swim sequence N

= 4 steps and the number of reproduction

= 4 and elimination/ dispersal events N

= 2 that would

occur during the BFO implementation.

IV. E

XPERIMENTAL RESULTS

The experiment work was conducted on a 1.5kW, 50 Hz,

240V, 2-pole wound rotor induction machine coupled to a

3kW DC machine used as a generator to provide the

necessary load torque. The induction motor has a star

connected stator windings and a short circuited delta

connected rotor winding. Standard tests (dc resistance, no-

load and locked rotor tests) [14] were carried out to determine

the nominal values of the machine parameters, giving the

following results in Table 1.

Tests are carried out emulating stator and rotor open-circuit

winding fault conditions. In all tests, the measured waveforms

are the three terminal voltages, three stator currents and rotor

speed. Voltage differential probes, current probe amplifier

and a digital tachometer are used to measure these signals.

Data are collected over a time window of 0.2 sec, with a

sampling interval of 1ms, as the machine was operating at

steady state with no load. The acquired data were then

processed off-line using the BFO algorithm to determine the

effective resistances of the six windings. The position of each

bacterium within the solution space X

= (R

, R

) is a potential solution which can be applied to

the induction motor model to evaluate a set of stator currents.

Each parameter value must lie within a pre-defined search

space and the overall calculation error; the Integral Absolute

Error (IAE) as defined in (2). This error function is the cost

function to be minimized by BFO.



' TiiiiiiIAE

sCcsCmsBcsBmsAcsAm

(2)

where (

sAm

sBm

sCm

) are the measured currents,

(

sAc

sBc

sCc

) are the calculated currents and ΔT is the

sampling period.

TABLE 1

NDUCTION MOTOR PARAMETERS

alues

Stator resistances

= 5. 88 Ω

Rotor resistances

= 6.83 Ω

Stator self-inductances

= 0.729 H

Rotor self-inductances

= 0.578

Mutual inductances between the stator

windings

= 0.25 H

Mutual inductances between the rotor

windings

= 0.7 H

Mutual inductance between stator and

rotor winding pairs

= 0.769

rs=

A. Stator winding open-circuit fault

A developing stator open-circuit winding fault is emulated by

connecting a 7: resistor in series with a stator phase winding

(winding B) as shown in Fig. 2.

Stator

Three- Phase

Power

Supply

7 Ω

Fig. 2 Developing stator winding open-circuit fault test circuit

Results of the identification algorithm are shown in Figs. 3-5.

The BFO algorithm successfully identifies the presence of the

stator winding fault as indicated by the high values of R

compared with R

and R

. The number of investigations

required to obtain convergence is 1844 where the calculation

error falls from a maximum value of 0.068 A.s to 0.022112

A.s. Figs. 3-4 show the estimated stator and rotor resistances,

respectively. The error function corresponding to the existing

best solution is shown in Fig. 5. The final estimated values of

the stator and rotor resistances are given in Table 2.

1 6 11 16 21 26 31 36 41 46 51 56 61

Number of accepted steps

Stator resistances

Fig.3 Stator resistance estimation using BFO for operation with stator

winding fault

1 6 11 16 21 26 31 36 41 46 51 56 61

Number of accepted steps

Rotor resistances

Fig. 4 Rotor resistance estimation using BFO for operation with stator

winding fault

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 6 11 16 21 26 31 36 41 46 51 56 61

Number of accepted steps

Error (A.s)

Fig. 5 Current estimation error using BFO for operation with stator winding

fault

TABLE 2

INAL VALUES OF WINDING RESISTANCES OBTAINED USING BFO WITH

STATOR

OPEN-CIRCUIT FAULT

(Ω)

5.75

12.31

6.7

6.6

7.5

8.47

B. Rotor open-circuit fault

A developing open-circuit rotor winding fault is emulated by

connecting a 7 : resistor in series with the line connected to

the two ends of the b-c rotor delta windings as shown in Fig.

6. This arrangement was used because it was not possible to

gain access to the three separate delta connected windings.

7 Ω

Fig. 6 Developing rotor winding open-circuit fault test circuit

The BFO algorithm is implemented to identify the presence

of a developing rotor winding open-circuit fault based on the

experimental measurements. In this test, the six winding

resistances (R

, R

) are again the

parameters to be optimized in order to minimize the IAE (2).

Figs. 7 and 8 show the estimated stator and rotor resistances,

respectively obtained by the BFO algorithm. The error

function corresponding to the existing best solution is shown

in Fig. 9. The number of steps or investigations required to

obtain convergence of the two data sets was 1882. The

calculation error falls from a maximum value of 0.068 A.s,

before reducing to 0.02 A.s. Because of the simplicity of the

machine model used in the investigation, it would be

unrealistic to expect this error to reduce to zero, even with a

much larger number of iterations. Clearly, the algorithm

successfully detects the presence of the rotor winding fault as

indicated by the high values of R

and R

in Fig. 8. The final

estimated values of the stator and rotor resistances are given

in Table 3. The final values of stator resistances are higher

than the nominal values identified in Table 1 due to the fact

that the algorithm is limited to changes in resistance values

alone and has to find a way to compensate for the effect of the

fault on other machine parameters.

1 7 13 19 25 31 37 43 49 55 61 67

Number of accepted steps

Stator resistances

Fig. 7 Stator resistance estimation using BFO for operation with rotor

winding fault

1 7 13 19 25 31 37 43 49 55 61 67

Number of accepted steps

Rotor resistances

Fig. 8 Rotor resistance estimation using BFO for operation with rotor

winding fault

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 7 13 19 25 31 37 43 49 55 61 67

Number of acce pted steps

Error (A.s)

Fig. 9 Current estimation error using BFO for operation with rotor winding

fault

TABLE

INAL VALUES OF WINDING RESISTANCES OBTAINED USING BFO WITH

ROTOR

OPEN-CIRCUIT FAULT

(Ω)

7.58

7.624

7.61

6.88

11.1

12.534

C. Comparison with PSO algorithm

Table 4 shows a comparison of the BFO results with those

obtained using the PSO algorithm [8, 9]. The BFO algorithm

had a success rate of about 75% when used with the no-load

measured current data compared with a success rate of about

85% for the PSO algorithm. PSO was also substantially faster

than BFO which requires a much larger number of

investigations to produce consistent values for the estimated

rotor and stator resistances (the number of investigations

when conducting a BFO search being noticeably larger than

the number of accepted solutions). This demonstrates the

robust nature of the PSO process and its suitability to this

type of nonlinear multivariable optimization problem. Both

algorithms showed estimated stator and rotor resistances to

converge to similar values, confirming that there is fault in

the machine's stator and rotor windings.

Induction machine Winding Faults Identification using Bacterial Foraging Optimization technique

Figures

Citations

Online condition monitoring of induction motors using signature analysis

Detection of Induction Machine Winding Faults Using Genetic Algorithm

Inter-turn short circuit stator fault identification for induction machines using computational intelligence algorithms

A novel evolutionary technique to estimate induction machine parameters from name plate data

On the identifiability, parameter identification and fault diagnosis of induction machines

References

Particle swarm optimization

Biomimicry of bacterial foraging for distributed optimization and control

A review of induction motors signature analysis as a medium for faults detection

Particle Swarm Optimization

A review of induction motors signature analysis as a medium for faults detection

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Frequently Asked Questions (13)

Q1. What contributions have the authors mentioned in the paper "Abstract" ?

Q2. What is the success rate of the BFO algorithm?

Q3. How long did the data take to be collected?

Q4. What is the purpose of the experiment?

Q5. What is the name of the algorithm?

Q6. What is the cumulative fitness function of each bacterium?

Q7. How many investigations were required to obtain convergence?

Q8. What are the estimated values of the stator and rotor resistances?

Q9. What is the chemotaxis of the algorithm?

Q10. Why are the final values of stator resistances higher than the nominal values?

Q11. What is the definition of a bacterial foraging system?

Q12. What were the tests carried out to determine the nominal values of the machine parameters?

Q13. Why is the error function shown in Fig. 3?