Computers and Electrical Engineering 40 (2014) 2236–2245

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Computers and Electrical Engineering

journal homepage: www.elsevier .com/ locate /compeleceng

Diagnosis of wiring networks using Particle SwarmOptimization and Genetic Algorithms q

http://dx.doi.org/10.1016/j.compeleceng.2014.07.0020045-7906/� 2014 Elsevier Ltd. All rights reserved.

q Reviews processed and recommended for publication to the Editor-in-Chief by Guest Editor Dr. Zhihong Man.⇑ Corresponding author.

E-mail address: mostafa.kamel.smail@gmail.com (M.K. Smail).

M.K. Smail a,⇑, H.R.E.H. Bouchekara b, L. Pichon c, H. Boudjefdjouf b,d, R. Mehasni b

a Université Paris-Est, IFSTTAR, Boulevard Newton, F-77747 Champs sur Marne, Franceb Electrical Engineering Laboratory of Constantine, LEC, Department of Electrical Engineering, University of Constantine 1, 25000 Constantine, Algeriac Laboratoire de Génie Electrique de Paris, UMR 8507 CNRS, SUPELEC, Université Paris-Sud, Université Pierre et Marie Curie, 91192 Gif-sur Yvette cedex, Franced UAq EMC Laboratory, Dept of Industrial and Information Engineering and Economics, via G. Gronchi, 18, 67100 L’Aquila, Italy

a r t i c l e i n f o a b s t r a c t

Article history:Available online 11 August 2014

Keywords:Time Domain ReflectometryWiring diagnosisFinite Difference Time Domain methodGenetic AlgorithmParticle Swarm Optimization

The performances of Particle Swarm Optimization and Genetic Algorithm have beencompared to develop a methodology for wiring network diagnosis allowing the detection,localization and characterization of faults. Two complementary steps are addressed. In thefirst step the direct problem is modeled using RLCG circuit parameters. Then the FiniteDifference Time Domain method is used to solve the telegrapher’s equations. This modelprovides a simple and accurate method to simulate Time Domain Reflectometry responses.In the second step the optimization methods are combined with the wire propagationmodel to solve the inverse problem and to deduce physical information’s about defectsfrom the reflectometry response. Several configurations are studied in order to demon-strate the applicability of each approach. Further, in order to validate the obtained resultsfor both inversion techniques, they are compared with experimental measurements.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Fault occurrence in wiring is a major cause for concern in aircrafts, cars and other transport means. As transport meanwires age they become brittle and are subject to several electrical, chemical and mechanical stresses. This leads to the occur-rence of defects in the wiring. Arcs in aircraft wires are involved in several serious accidents including the explosion of SwissAir Flight 111 and TWA Flight 800 [1]. In this area, reliability becomes a safety issue.

There are several emerging technologies that may help to locate and characterize faults in wiring networks. The mostwidely used technique for fault location in automobile wiring is reflectometry [1]. It is based on the same principle of radar.A high frequency electrical signal is sent down the wire, where it reflects from any impedance discontinuity such as open orshort circuits. The difference (time delay or phase shift) between the incident and reflected signal is used to locate the faulton the wire. The nature of the input signal is used to classify each type of reflectometry: Time Domain Reflectometry (TDR)uses a fast rise time pulse [2], Frequency Domain Reflectometry (FDR) uses a sine wave signal [3], Sequence Time DomainReflectometry (STDR) uses a pseudo-noise (PN) code, and Spread Sequence Time Domain Reflectometry (SSTDR) used a sine-wave-modulated PN code [4]. These last two techniques can test wire on live. Also a new method called, Time–FrequencyDomain Reflectometry (TFDR) was presented in [5]. All these methods present some limitations to characterize the imped-ance of the fault as well as the position in some cases.

M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245 2237

Interpreting the results obtained with reflectometry instrument for a wiring network requires great expertise, as thereflectometry response can be very complex. Moreover, the reflectometry response itself is not self-sufficient to identifyand locate the defects in wiring networks. There is the need to solve efficiently the inverse problem which consists of deduc-ing some knowledge about the defects from the response at the input of the line.

Several methods have been proposed to locate and characterize faults on wiring networks. In a baseline approach, theresponse of the faulty network is compared with either the pre-measured or simulated response of its (known) healthy con-figuration. With this method it is extremely difficult to detect and locate defects in faulty wiring networks affected by two ormore faults. Only the first fault near to the test point can be detected. Also the location of the fault on the branches cannot beidentified. In Bayesian approaches, the essential idea is to assign a quantifiable measure of certainty of belief to all possiblevariables (permittivity, impedance, location of the faults) [6]. In [7] Time domain signal restoration and parameter recon-struction of a simple nonuniform RLCG transmission line is performed using the wave-splitting technique and the compactGreen functions technique. These two last methods allow to find faults in simple electrical wirings only.

Wiring networks can be affected by two types of faults namely soft and hard faults. Soft ones are created by the change ofthe impedance along the line due to simple deformation in the wire or local modification of the electrical parameters [8].Hard ones are open and short circuits. For the first type of faults, the reflectometry response of the faulty network presentsa simple deviation or variation versus the impedance of the fault in the defects location. In the case of hard faults, both thestructure of network and the response change.

In this paper, a comparative evaluation of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) for detection,localization and characterization of defects in faulty wiring networks using measured reflectometry response is achieved.Solving the inverse problem, when a hard fault occurs consists of reconstructing the structure of the faulty wiring networkby minimizing the error between the reflectometry response and the one given by the direct model. This model describes thepropagation of the electromagnetic wave along Multiconductors Transmission Lines (MTL) in the time domain.

The reminder of this paper is organized as follow: in Section 2 the direct model and network analysis are presented. InSection 3 the resolution of the inverse problem using GA and PSO are described. In Section 4 the inversion results obtainedusing GA and PSO are compared to the measured ones. Finally, the conclusion is drawn in Section 5.

2. The direct model

The propagation in a MTL (including n conductors) can be modeled by a RLCG circuit model [9]. The position along theline is denoted by z and time is denoted by t. The n � n matrices [R] (resistance), [L] (inductance), [C] (capacitance) and[G] (conductance) contain the per-unit-length parameters which are computed either by finite element approach or analyt-ically for simple configurations.

The model is based on the telegrapher’s equations. The wave propagation equations are solved using the Finite DifferenceTime Domain (FDTD) method.

In order to validate the direct model, we have chosen a MTL composed of three conductors with a characteristic imped-ance of 120 ohms and a length of 1 m as shown in Fig. 1. The height above the ground plane is 5 cm. To study the twistedwire configuration (Fig. 1(a)) by the transmission line theory, it has been discretized into small section (Si) of same length D

(a)

)c()b(

D

D D h3h1

h2

Δ

S1 S2

Open Circuit

5 cm 50Ω p

p

50Ω

1m

~

Δ

Fig. 1. (a) Twisted wire configuration, (b) discretization into uniform MTL sections Si of length D = p/N and (c) cross sectional of MTL.

2238 M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245

(Fig. 1 (b)). The distance between the wires is D, and the height of these wires with respect the ground are h1, h2 and h3 whichis variable along the MTL (Fig. 1(c)). The sections length is equal to the ratio p/N, where p represents the twist pitch and N thenumber of sections in each p. Thus, the initial non-uniform MTL is replaced by a uniform one, which can be modeled byequivalent lumped parameter circuit.

As aforementioned, the time-domain analysis of the MTL is determined by the FDTD method. Where the line axis z is dis-cretized in Dz increments, the time variable t is discretized in Dt increments.

In this application the length of the spatial cell size Dz is chosen to be small compared to the wavelength of the sourcekmin signal, generally of the order of Dz = kmin/60. The sampling interval Dt chosen in the study is given by Dt = Dz/(2v),where v is the velocity of the propagation of the wire with 0.5 c < v < 0.8 c, c being the speed of the light. This choice insuresthe stability on the time stepping algorithm.

The direct model results are compared with the experimental data obtained from measurement of S11 parameters with aVector Network Analyzer (VNA) in frequency domain from 600 kHz to 2 GHz (Fig. 2). The TDR is obtained using inverse Fou-rier transform. It is worth mentioning that the measurements i.e., the experimental part of this paper has been done in Lab-oratoire de Génie Electrique de Paris (LGEP) France.

For the simulated response, a raised cosine pulse with a rising time of 2 ns, and the voltage at high state of 1 V is used assource. The first reflection occurs because of the mismatch between the input impedance (ZI = 50 ohms) and the impedanceof the MTL (ZC = 120 ohms). The second reflection at 1 m gives information about the length and the load (open end) of theMTL. The third, fourth and fifth reflections respectively in 2 m, 3 m and 4 m are due to the round-trips. The small fluctuationsbetween these main reflections are due to the difference between real and simulated distribution of the MTL and change inimpedance along the wire.

2.1. Network analysis

The analysis of single wires is very important but in a real automobile or aircraft environment all wirings are part ofbranched wiring networks and the faults must be analyzed as part of these networks. The FDTD method provides the suitablesolution for such analysis. To model networks, transmission conditions have to be implemented at the junctions. The reflec-tion coefficient C at a junction or termination can be evaluated using Eq. (1), where Z0 is the characteristic impedance of thecables and Z is the impedance at the mismatch. The quantities Vreflected and Vincident are the reflected and incident wavesrespectively.

C ¼ Vreflected

Vincident¼ Z � Z0

Z þ Z0ð1Þ

For short ended termination, Z is equal to 0 while it is 1 for an open ended termination. At a junction, the value of Zdepends on the number of branches linked to that junction. If wires have the same impedances, Z takes the value of Z0/n(parallel combination of electrical lines) where n is the number of branches linked at the junction. Eq. (2) gives the relation-ship between the C at a junction and the number of branches present at that junction.

C ¼ Z0 � Z0=nZ0 þ Z0=n

¼ n� 1nþ 1

ð2Þ

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Distance (m)

Ref

lect

ion

Coe

ffic

ient

(U

nitl

ess)

Measured Response of Twisted Wire Simulated Response of Twisted Wire

Fig. 2. Comparison between simulation results and measures for the TDR response.

M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245 2239

When the lines are of unequal impedances, Eq. (2) is no more valid to determine C. The value of Z in these cases should beevaluated by taking into consideration individual impedances. The complexity of this problem increases when the number ofstages in the network is increased. The network model has been validated in [10]. For illustration the simulation response fora simple Y network is presented in Fig. 3. The approach is equivalent to simulating the reflection diagram of the Y wiringnetwork. The reflection diagrams are graphical representations of the reflection distribution along the length of a transmis-sion line. The abscissa of the reflection diagram denotes the distance along the network, and the ordinate represents the timerequired by the reflection to reach the reflectometer.

3. The inverse problem

3.1. Formulation of the problem

In this problem, both the measured TDR and the direct model are used to reconstruct the wiring network. The designvariables are the lengths of the different branches Li. From the reflectometry data of the wiring network under test, themethodology of reconstruction leads to the resolution of an inverse problem: GA and PSO are used to minimize the objectivefunction given by (3), where vTDR(t) is the given initial impulse response, vMod(t) the response calculated using the directmodel and Nstop is the total number of data.

FðvÞ ¼ 1Nstop

Z T

0

jvTDRðtÞ � vModðtÞj2

jvTDRðtÞj2dt

!1=2

ð3Þ

3.2. Approach 1: Genetic Algorithm

GA is a global optimization method based on genetic recombination and evolution in nature [11]. GAs use an approachthat commonly involves starting with a random selection of design space points of M populations. The system is discretized

A

B

C

O

Time

- (2/3) (2/3)

- (2/3) (2/3)

- (2/3) (1/3) (2/3)

(2/3)

- (2/3) (2/3)

- (1/3)

Γ0 = 0 ΓA =-(1/3) ΓC =-1 ΓB =-1 O

1

(2/3)

- (2/3)

- (2/3) (2/3) (1/3)

- (2/3) (1/3)

(2/3) (1/3) (1/3)

(2/3) (1/3)

2((2/3) (2/3))

- (2/3) (2/3)

A B C

OA

AB

AC BA

AO

OA

Normalized Γ

Fig. 3. Diagram of the simulation for a Y wiring network.

2240 M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245

into P parameters in a model vector m called a chromosome. Each parameter mj, (j = 1 . . .P) is called a gene in accordancewith the natural terminology of the genetic theory. A gene is a binary encoding of a parameter given by:

mj ¼ mminj þ

ðmmaxj �mmax

j Þ2n � 1

�Xn�1

i¼0

bi2i ð4Þ

The parameters mj represent the length of a branch Li in our application. The set of values b1,b2 . . .bn�1 is the n-bit string ofthe binary representation of mj, mj

min and mjmax are the minimum and maximum admissible values for mj, respectively. Using

a sufficient number of bits per parameter provides a fine-grained set of values.The genes of these initial individuals are combined in meaningful ways to produce new solutions, and these are evaluated

and ranked by an objective function value [10]. Finally, the GA iteratively generates a new population, which is derived fromthe previous population through the application of the genetic operations which are: Selection, Crossing and Mutation. Therole of the selection is to select individuals in the population from their fitness. The crossover operation combines the fea-tures of two parent chromosomes to form two offsprings. The mutation implies small random changes to one or several ofgenes in a chromosome in order to promote variation and diversity in the population [12]. Selection, mutation and crossingeach operation are controlled with probabilities Ps, Pm, and Pc respectively, that allow the algorithm to explore new regions ofthe problem space. The new population will contain increasingly better chromosomes (best individuals or parameters) andwill eventually converge to an optimal population that consists of the optimal chromosomes.

The control parameters involved in GA are: the population size, the number of encoding bits, the selection mechanism,the crossover rate, the mutation rate and the maximum number of iterations [13].

3.3. Approach 2: Particle Swarm Optimization (PSO)

PSO is an evolutionary algorithm for the solution of optimization problems. It belongs to the field of Swarm Intelligenceand Collective Intelligence and is a sub-field of Computational Intelligence [14]. It was developed by Eberhart and Kennedyand inspired by social behavior of bird flocking or fish schooling [14]. Several modifications in the PSO algorithm had beendone by various researchers [15]. PSO is simple in concept, as it has a few parameters only to be adjusted. It has found appli-cations in various areas like constrained optimization problems, min–max problems, multi-objective optimization problemsand many more [15].

The PSO method is regarded as a population-based method, where the population is referred to as a swarm [16]. Theswarm consists of n individuals called particles, each of which represents a candidate solution [17]. Each particle i in theswarm holds the following information: (i) it occupies the position xi, (ii) it moves with a velocity vi, (iii) the best position,the one associated with the best fitness value the particle has achieved so far pbesti, and (iv) the global best position, the oneassociated with the best fitness value found among all of the particles gbest.

Similarly to the GA, in our application, the positions of particles xi represent the lengths of the branches Li. The fitness of aparticle is determined from its position. The fitness is defined in such a way that a particle closer to the solution has higherfitness value than a particle that is far away. In each iteration, velocities and positions of all particles are updated to persuadethem to achieve better fitness according to the following equations:

v tþ1ij ¼ wv t

ij þ c1randt1jðpbestt

ij � xtijÞ þ c2randt

2jðgbesttj � xt

ijÞ ð5Þxtþ1

ij ¼ xtij þ v tþ1

ij ð6Þ

for j 2 1 . . .d where d is the number of dimensions, i 2 1 . . .n where n is the number of particles, t, is the iteration number, w isthe inertia weight, rand1 and rand2 are two random numbers uniformly distributed in the range [0,1], and c1 and c2 the accel-eration factors. c1 is the cognitive acceleration constant. This component propels the particle towards the position where ithad the highest fitness. c2 is the social acceleration constant. This component steers the particle towards the particle thatcurrently has the highest fitness.

In Eq. (5), the inertia weight w affects the contribution of v tij to the new velocity v tþ1

ij . If w is large, it makes a large step inone iteration (exploring the search space), while if w is small; it makes a small step in one iteration, therefore tending to stayin a local region [18].

Typically, the velocity of a particle is bounded between properly chosen limits vmin < vid < vmax (in most cases vmin = �vmax).Likewise, the position of a particle is bounded as follows: xmin < xid < xmax.

Afterwards, each particle updates its personal best position using the following equation:

pbesttþ1i ¼

pbestti if f ðpbestt

i Þ 6 f ðxtþ1i Þ

xtþ1i if f ðpbestt

i Þ > f ðxtþ1i Þ

(ð7Þ

Finally, the global best of the swarm is updated using the following equation:

gbesttþ1 ¼ arg min f ðpbesttþ1i Þ ð8Þ

where f is a function that evaluates the fitness value for a given position.

Fig. 4. The two studied configurations, (a) the ‘Y’ wiring network and (b) the complex ‘YY’ wiring network.

M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245 2241

The PSO process is repeated iteratively until one of the following termination criteria occurs [19]: if the maximum num-ber of iterations has been reached, an acceptable solution has been found or no improvement is observed over a number ofiterations.

The tuning parameters of PSO are: the population size, the inertia weight (w), the acceleration factors (c1 and c2) and themaximum number of iterations.

4. Application results and discussion

To illustrate the application of each optimization method i.e., GA and PSO, two configurations have been studied. The firstone consists of the simple Y shaped network shown in Fig. 4(a). The second one consists of a more complex network struc-ture represented by a double Y (YY) shaped network shown in Fig. 4(b).

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Distance (m)

Ref

lexi

on c

oeff

icie

nt (

Uni

tles

s)

Reflectometry Response of healthy network - MeasuredReflectometry Response of Faulty network in L1 - Measured

Fig. 5. Comparison between the reflectometry responses of the healthy network and the one affected by an open ended circuit fault in L1 (measures).

Table 1Parameters used for GA and PSO.

GA Parameters PSO Parameters

Y configurationPopulation size: 60 Population size: 60Iteration max: 50 Generation max: 100Mutation, crossing probabilities: 1.5%, 70% c1 = 0.5, c2 = 1.25Bits number: 5 bits w = 0.6

YY configurationPopulation size: 100 Population size: 100Iteration max: 50 Generation max: 200Mutation, crossing probabilities: 1.5%, 70% c1 = 0.5, c2 = 1.25Bits number: 5 bits w = 0.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.4

-0.2

0

0.2

0.4

0.6

0.8

Distance (m)

Ref

lexi

on c

oeff

icie

nt (

Uni

tles

s)

Reflectometry Response of Healthy Network -Measured

Reflectometry Response of Faulty Network -Measured

Fig. 6. Comparison between the reflectometry responses of the healthy network and that affected by open ended circuit fault in L2 (measures).

0 0.5 1 1.5 2 2.5 3 3.5 4-0.4

-0.2

0

0.2

0.4

0.6

0.8

Distance (m)

Mag

nitu

de

Reflectometry Response of the Faulty Network - GA Reflectometry Response of the Faulty Network - MeasurementReflectometry Response of the Faulty Network PSO

Fig. 7. Comparison between the reflectometry responses measured and reconstructed by GA and PSO of the faulty network.

2242 M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245

Recall that our goal is the reconstruction of the network structure under test by computing the lengths of the networkbranches from the reflectometry response. By simple comparison between the reflectometry response of the network undertest and the healthy one we can check if the first (main) branch is affected or not. Hence, when the main branch is not

M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245 2243

affected the number of design variables is reduced by removing L1 from the research area. For instance, the identification,location and characterization of one fault affecting the Y network displayed in Fig. 4(a) can be deduced using the reflectom-etry responses of Fig. 5. We can see that in this case the fault is in L1, located at 0.75 m and it is an open circuit. Therefore, inour methodology the first step consists of checking if L1 (the main branch) is affected or not. If the main branch is healthy thenumber of design variables is reduced to n � 1 where n represents the total number of branches in the wiring network.

Table 1 gives the GA and PSO control parameters used in this study (for both configurations). It is noteworthy to mentionthat all the developed programs are under the commercial software Matlab and all simulations are carried out a Pentium 4Core 2 Due Processor and 4 GB of RAM. Notice that in our inversion procedure, in order to compare both optimization tech-niques the same discretizations of the wiring network branches are used.

4.1. Configuration 1

In the first configuration (Fig. 4(a)), the faulty wiring network (affected in L2) and its reflectometry response shown inFig. 6 are considered. In this case the optimization parameters are L2 and L3.

The obtained results are shown in Fig. 7. We can see that both optimization methods give a good agreement comparedwith the measured (actual) response. This last observation confirms the applicability of GA and PSO techniques to the diag-nosis of faulty wiring networks.

Table 2Optimized branches length parameters obtained by GA and PSO.

Exact values L2 L3 Computational time (min) Error Fitness value1.5 0.75

GA 1.4320 0.7755 9.57 9.54e�4 0.0223PSO 1.4408 0.7779 2.41 9.54e�4 0.0223

Open Circuit

L3=0.77m for GA and PSO

Fig. 8. The reconstructed network for Configuration 1 using the developed approaches.

0 1 2 3 4 5 6 7 8 9-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Distance (m)

Mag

nitu

de

Reflectometry Response of the Healthy Network - MeasuredReflectometry Response of the Faulty Network - Measured

Fig. 9. Comparison between the reflectometry responses of the healthy network and the one affected by two open ended circuit faults in L2 and L4

(measures).

0 1 2 3 4 5 6 7 8-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Distance (m)

Mag

nitu

de

Reflectometry Response of the Faulty Network - Partial Swarm Optimization

Reflectometry Response of the Faulty Network - Measurement

Reflectometry Response of the Faulty Network -Genetic Algorithm

Fig. 10. Comparison between the reflectometry responses measured and reconstructed using GA and PSO of the faulty network.

2244 M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245

Table 2 summarizes the obtained design variables for both approaches. We can notice from this table that where the per-formance of both GA and PSO is similar in terms of the obtained best fitness value. However, PSO outperforms GA in terms ofcomputational time, where in typical PSO optimization process the best fitness value decreases rapidly (less than 3 min)whereas for GA it takes about 9.75 min.

The comparison of the branches lengths obtained by PSO and GA with actual ones is shown in Table 2, the proposed meth-odology allows the characterization of the fault, by finding the nature of the charge in the affected branch in this case L3, forboth method (GA & PSO) we find open circuit as fault characterization. The new lengths of the different branches illustratethe location of the fault in L3 (Fig. 8).

4.2. Configuration 2

In the second configuration, the wiring network shown in Fig. 4(b) is considered. It includes two hard faults (open cir-cuits) in branches L2 and L4. The measured reflectometry responses of the wiring network before and after the occurringof faults are shown in Fig. 9. From this figure the distance between the location of the fault and the test point is clear. Nev-ertheless, it is still not clear which branch the fault lies on. The locations of the faults in the wiring network are masked byother prominent reflections resulting from junction and terminations in the network. In this case, there are four design

Table 3Optimized branches length parameters obtained by GA and PSO.

Exact values L2 (m) L5 (m) L4 (m) Computational time (min) Error Fitness value0.75 1.5 0.38

GA 0.7923 1.4170 0.4125 94.60 5.75e�4 0.0018PSO 0.7648 1.4293 0.4120 26.36 4.75e�4 0.0154

Open Circuit

L4=0.41 m for GA and PSO

Open Circuit L2=0.79 m for GA L2=0.76 m for PSO

Fig. 11. The reconstructed network for Configuration 1 using the developed approaches.

M.K. Smail et al. / Computers and Electrical Engineering 40 (2014) 2236–2245 2245

variables that are L2, L3, L4 and L5 where L1 is not a design variable due to same reasons explained in Configuration 1. Theinput of both optimization methods is the measurement reflectometry response of the faulty wiring network (C,L) givenby Fig. 9. The control parameters of GA and PSO used for this configuration are tabulated in Table 1.

The results obtained for this configuration are given in Fig. 10 and Table 3. We can clearly see that the reflectometryresponses obtained are close to the measured response. In one side, the comparison of the actual branches lengths withthe obtained ones show ones again the applicability of both methods for the diagnosis of wiring networks. In the other side,a comparison between the two developed approaches shows that PSO outperforms GA in terms of convergence and compu-tational time. With GA obtaining the state of the wiring network takes 94.60 min while with PSO it takes 26.36 min only.

The reconstructed wiring network using the developed approaches is shown in Fig. 11 and it shows the location of faultsin L2 and L5.

5. Conclusion

In this paper, we have described and shown the applicability of the GA and PSO techniques for wiring diagnosis. Theobjective of this work is to compare the performance of these two optimization techniques for the development of accuratediagnosis methodology. This improves the process of detection, location and characterization of faults. It is observed that theperformance of the PSO is better than that of GA, where the PSO algorithm seems to arrive at its final parameter values infewer generations than the GA. It is also noticed that, the computational time for PSO is low compared to the GA technique.This is a major advantage for the wiring diagnosis because the identification of the status of the wiring network quickly ispreferable. The two approaches were tested against experimental data and demonstrated to be effective for wiring diagnosis.These methods can be extended to soft faults. In this case, the optimization parameters are inductances and capacitances orimpedances. This challenge represents the objective of our future paper.

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Mostafa Kamel Smail has received the master degree in 2007 and the PhD degree in 2010 from University of Paris-Sud XI, France. He is currently researcherat the Institut Français des Sciences et Technologies des Transports, de l’Aménagement et des Réseaux (IFSTTAR). His current research interests are wavepropagation modeling, reliability of wiring, electromagnetic compatibility and Inverse modeling.

Houssem Bouchekara was born in Constantine Algeria in 1981. He received his Ph.D. degree in electrical engineering from Grenoble Electrical EngineeringLaboratory, France, in 2008. He is now an Assistant Professor at the Electrical Engineering Department of University of Constantine 1 Algeria. His researchinterests include: optimization techniques, magnetic refrigeration, electromagnetics, electrical machines, and power systems.

Lionel Pichon obtained the Dip. Eng. from Ecole Supérieure d’Ingénieurs en Electronique et Electrotechnique in 1984. In 1985 he joined the Laboratoire deGénie Electrique de Paris where he earned a PhD in electrical engineering in 1989. He got a position at the CNRS (Centre National de la RechercheScientifique) in 1989. He is now Directeur de Recherche.

Hamza Boudjefdjouf was born in Mila, Algeria, in 1982. He received his master degree in 2009 from the University of Constantine 1 Algeria. He is currentlya PhD student in the University of Constantine 1 and the University of L’Aquila in Italy. His current research interests are wave propagation, wiring networksdiagnosis, electromagnetic compatibility and dams control and monitoring.

Rabia Mehasni has received his PhD in electrical engineering from University Mentouri Constantine, Algeria, in 2007. He is now an Associate Professor atthe Electrical Engineering Department of University of Constantine 1 Algeria. His area of specialization includes: wiring diagnosis with reflectometry andthe industrial applications of the magnetic induction like magnetic separation, magnetic bearings and induction heating.