Soft Fault Detection and Localization in an Unshielded Twisted Pair

Network using Power Line Communication

Abdel Karim Abdel Karim

1,2 a

, Virginie Degardin

2 b

, Vincent Cocquempot

1 c

and M. Amine Atoui

1,2 d

Universit

e de Lille, CNRS, Centrale Lille, UMR 9189 - CRIStAL, F-59000 Lille, France

Univ. Lille, CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, UMR 8520 - IEMN, F-59000 Lille, France

Keywords:

Vehicular Embedded Networks, Monitoring, Fault Detection, Fault Localization, Soft Fault, Transmission

System.

Abstract:

Vehicular electrical wires and communication systems can be affected by faults. Depending on their severity,

faults can be divided into two families: hard and soft faults. Hard faults indicate open/short circuits that can

lead to serious breakdowns because they prevent the ﬂow of energy or information. Even though soft faults

do not have such severe impacts on the system, they may develop into hard faults in the long term, hence the

need to detect them. In this paper, an unshielded twisted pair cable that undergoes a water-tree degradation

is considered. A soft fault, which may correspond to the effect of a mechanical constraint on the cable, is

introduced as a series resistor. The studied network is a tree-shape network composed of one source and

multiple receivers, one at each end of a branch. Assuming that these receivers operate in a healthy state, to

detect the fault, the transfer function from each receiver are monitored and a detection index is used. Another

index, based on the comparison of the effect of the fault at each endpoint, is proposed to locate the affected

branch. To summarize the detection and localization algorithm, a signature matrix is generated. Simulation

results are presented to illustrate our approach.

1 INTRODUCTION

As part of autonomous/electric vehicles, Advanced

Driver Assistance Systems (ADAS) have been inte-

grated into vehicles to ensure road safety and driving

comfort (Lindgren and Chen, 2006). These systems

rely on electronic equipments that exchange informa-

tion via dedicated communication networks. Since

the One-Pair Ether-Net Alliance has encouraged the

adoption of the automotive Ethernet for modern ve-

hicular networks, the studied network is based on

Unshielded Twisted Pair (UTP) cables (Zweck and

Communication, 2019). This network is subject to

failures that can have fatal consequences. Hence the

need of a monitoring system that can distinguish be-

tween healthy and faulty states. Reﬂectometry and its

derivatives are the main used monitoring methods for

fault detection in networks (Furse et al., 2020). Time

https://orcid.org/0000-0003-4390-9858

https://orcid.org/0000-0002-8716-7940

https://orcid.org/0000-0001-7281-911X

https://orcid.org/0000-0003-1893-5819

Domain Reﬂectometry (TDR) and Frequency Do-

main Reﬂectometry (FDR) form the two main classes

of reﬂectometry systems (Furse et al., 2003). The

experiments using reﬂectometry realized by (Kafal

and Benoit, 2018), on a two-wire transmission line,

demonstrate that soft faults can have signatures which

are much weaker than changes in impedance which

can affect a cable during actual installation condi-

tions. Furthermore, the measurement and simulations

in (Grifﬁths et al., 2006), on a two-wire conductor

General Cable SKU 02301.R5.02 lamp cord (Corpo-

ration, 2017), have also shown that these signatures

are invisible using TDR, FDR and Spread-spectrum

TDR in the frequency range of 100 MHz – 200 MHz

due to the normal impedance variation in the realistic

environment of the cable. Moreover, even if the lat-

ter was detected, reﬂectometry based methods have a

major drawback due to the use of special, expensive

and bulky sensors and instruments (Huo et al., 2019).

Finally, according to (Kafal and Benoit, 2018), the ef-

fect of nodes on a reﬂectogram can be much stronger

than the effect of a soft fault. A Power Line Commu-

nication (PLC) system can also be used to monitor the

Abdel Karim, A., Degardin, V., Cocquempot, V. and Atoui, M.

Soft Fault Detection and Localization in an Unshielded Twisted Pair Network using Power Line Communication.

DOI: 10.5220/0010438000820089

In Proceedings of the 7th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2021), pages 82-89

ISBN: 978-989-758-513-5

network. In (Lallbeeharry et al., 2018), a PLC system

implemented a real time fault detection between two

modems. The time evolution of the transfer function

H( f ) between the two ends of a UTP cable is moni-

tored, and statistical coefﬁcients (i.e. Correlation co-

efﬁcient ρ and Euclidean distance Eu) are used to de-

tect soft faults.

In this paper, a soft fault detection and localization

method is proposed and analyzed in a tree-shape net-

work composed of one source and multiple receivers,

one at each end of a branch. The soft fault - which

can appear, for example, after an electric discharge

or may be due to a bad contact between a wire and a

connector - is represented by the insertion of a series

resistance such as in (Lallbeeharry et al., 2018), while

the network is being degraded by a Water Tree (WT)

phenomenon as described in (Huo et al., 2019). This

phenomenon represents the change in the dielectric

permittivity of a cable insulation caused by humid-

ity. The transfer function from each point of view of

the receivers, between the source and each receiver is

measured by the receivers at the end of each branch of

the network, through Orthogonal Frequency Division

Multiplexing (OFDM) pilot symbols sending by the

source. Afterwards, two indices extracted from H( f )

are used to detect the presence of a soft fault then to

locate the affected branch. The detection index is cal-

culated between a reference H( f ) and the successive

ones which are measured. Once the presence of a fault

is conﬁrmed, a localization index is then computed

to determine the branch where the fault is located.

The fault detection and localization methodology pro-

posed in this paper is general, but for presentation rea-

son, a network comprising one source, three receivers

and two nodes is studied. In section 2, the detection

and localization indices is presented along with the

proposed method. To validate this work, data are gen-

erated using cable, degradation and soft fault models

that are detailed in section 3.1. Simulations and the

results are carried on in section 3.2. Conclusions and

future work to be conducted close this paper.

2 FAULT DETECTION AND

LOCALIZATION

2.1 Fault Diagnostic Indices

The indices presented in this section are based only

on the transfer function H( f ) of the network.

Deﬁnition 1. CORRELATION COEFFICIENT. The

correlation coefﬁcient ρ

expresses the distance be-

tween the reference transfer function and the succes-

sive acquisitions (measurements) of the transfer func-

tion at each receiver R

∑

Re f erence

( f

) · H

∗Test

( f

∑

Re f erence

( f

(1)

Re f erence

is the ﬁrst acquisition that is supposed to

be the transfer function for the healthy network at the

receiver R

. H

Test

is the measured transfer function

that needs to be tested at a given time at the receiver

. f

denotes the frequency in the range of 1 MHz

to 100 MHz with a step of 10 kHz. X

∗

denotes the

conjugate of X, and |X | is the module of X.

Deﬁnition 2. DETECTION INDEX. The detection in-

dex I

is deﬁned as :

= |1 − ρ

| (2)

In a healthy case, I

computed at each receiver

i, is equal or close to zero and it deviates from

zero when a fault occurs or in presence of network

degradation. Once the fault is detected by one of the

receiver, the network is considered as faulty.

Deﬁnition 3. LOCALIZATION INDEX. The localiza-

tion index I

is deﬁned as the ratio between trans-

fer function measured after fault detection at each re-

ceiver R

and the transfer function measured before

fault detection at each receiver R

Faulty

( f )

Healthy

( f )

(3)

where I

denotes the localization index at the receiver

. H

Healthy

( f ) and H

Faulty

( f ) are respectively the

transfer function before and after the fault detection.

2.2 Illustration on a Study Case

To show the usefulness of the localization index, the

three cases in Fig. 1 are explored. Let consider the

multipath model found in (Zimmermann and Dostert,

1999), (Zimmermann and Dostert, 2002) that de-

scribes the propagation of the waves in a network.

According to the multipath signal propagation model,

there are several possible paths from the source S to

the receiver R

. Furthermore, the signal is reﬂected

at each impedance discontinuity (localized fault and

node). The received signal is thus a superposition of

the ﬁrst M signiﬁcant paths considered. Hence, the

transfer function H( f ) can be represented by the fol-

lowing equation :

H( f ) =

∑

i=1

· e

−γ·d

(4)

Soft Fault Detection and Localization in an Unshielded Twisted Pair Network using Power Line Communication

Figure 1: Y-Shaped networks.

where M represents the number of the most signiﬁ-

cant paths, g

denotes the weighting factor of the path

i representing the product of the reﬂection and trans-

mission factors along the path, γ is the complex prop-

agation constant and d

is the length of the path i. γ

and g

are both depending on the frequency f .

To simplify and to limit the number of paths M,

the source and the receivers are considered matched

to the network and the ﬁrst two paths are taken into

consideration.

1. Healthy Network.

In a healthy network, only the direct path between

the source and each receiver exists. Thus, the

transfer function from the point of view of each

receiver is :

Healthy

( f ) = t

· e

−γ·(l

)

(5)

Healthy

( f ) = t

· e

−γ·(l

)

(6)

where t

is the transmission factor of the node

N, l

, l

and l

are the lengths of each branch

presented in Fig. 1.

2. Appearance of a Soft Abrupt Fault Before the

Node.

If a fault occurs at the branch situated before the

node N, several paths are possible.

From the point of view of R

, the two most signif-

icant paths are :

- Path no.1 : S - F - N - R

- Path no.2 : S - F - N - F - N - R

Therefore, the frequency response from S to R

can be expressed as:

( f ) = t

·t

· e

−γ·(l

)

+ (7)

· r

· e

−γ·2·(l

−x)

·t

· e

−γ·(l

)

= t

· (1 +r

· r

· e

−γ·2·(l

−x)

) · t

· e

−γ·(l

)

By analogy for the second receiver R

( f ) = t

·t

· e

−γ·(l

)

+ (8)

· r

· e

−γ·2·(l

−x)

·t

· e

−γ·(l

)

= t

· (1 +r

· r

· e

−γ·2·(l

−x)

) · t

· e

−γ·(l

)

where t

and r

represent respectively the trans-

mission and reﬂection factors of the fault. t

the transmission factor of the node N. The at-

tenuation due to the signal propagation from the

source to each receiver i, e

−γ·(l

)

, are multiplied

by the same value in (7) and (8).

Hence, I

and I

are equal :

= I

= t

·(1 + r

·r

·e

−γ·2·(l

−x)

)·

(9)

3. Appearance of a Soft Abrupt Fault after the

Node.

If a fault occurs after the node N in the branch

directly linked to the receiver R

, several paths are

also possible. From the point of view of R

, the

transfer function is expressed as:

( f ) = t

·t

· e

−γ·(l

)

+ (10)

· r

· e

−γ·2·x

·t

· e

−γ·(l

)

= t

· (1 + r

· r

· e

−γ·2·x

· e

−γ·(l

)

From the point of view of R

, the transfer function

is expressed as :

( f ) = t

· e

−γ·(l

)

+ (11)

· r

· e

−γ·2·x

·t

· e

−γ·(l

)

= (1 +t

· r

· e

−γ·2·x

· e

−γ·(l

)

where r

denotes the reﬂection coefﬁcient of the

fault. t

and r

are respectively the transmission

and reﬂection coefﬁcient of the node N. In this

case, the weighting factors from (10) and (11) are

different. Therefore, I

is different than I

= t

· (1 + r

· r

· e

−γ·2·x

) ·

(12)

= (1 +t

· r

· e

−γ·2·x

) ·

(13)

This index allows us to eliminate the effect of the

attenuation due to the signal propagation from the

source to the i

receiver : e

−γ(l

)

. This index de-

pends on the attenuation due to the propagation be-

tween the node and the fault positions : e

−γ·2·x

, the

severity of the fault represented by r

and/or t

and

the impact of the fault on the node represented by the

change of the transmission and the reﬂection factors

of the node.

VEHITS 2021 - 7th International Conference on Vehicle Technology and Intelligent Transport Systems

2.3 Fault Detection and Localization

Method

The proposed fault detection and localization method

(see Fig. 2) is based on the two aforementioned in-

dices.

Compute the localization indices: 





Compute the detection indices: 





Healthy

network







 



Faulty network

Compare to the signature matrix

Yes











Fault is at branch 













Detection

Localization

Evaluate their equality and minimum inequality

Figure 2: Fault detection and localization algorithm.

It is divided into two phases : ”Detection” then

”Localization”. These phases are discussed in the

following.

1. Detection Phase:

The network is considered as faulty, if, at least,

one of the indices, I

, computed at each re-

ceiver is higher than its predeﬁned threshold ψ

Otherwise the network is considered as healthy.

The threshold ψ

is empirically deduced to detect

abrupt soft faults while taking into account the

slow variation due to WT. The localization phase

is triggered after the presence of a fault is con-

ﬁrmed.

2. Localization Phase:

When a fault is detected, the indices I

are com-

puted. To determine the branch where the present

fault is located, they are evaluated and compared

to each branch’s fault reference signature. This

comparison would suggest a set of candidates.

A candidate stands for the presence of fault in a

branch j, denoted F

. Multiple faults are out of

the scope of this paper. Only single faults are as-

sumed.

Table 1: Signature matrix.

. . . F

1,1

··· α

1,N

m,1

. . . α

m,N

min

) β

. . . β

The proposed signature matrix is derived and de-

pends on the considered network’s topology. The ma-

trix rows correspond to the behaviour of m + 1 indica-

tors, the m receiver’s localization indices plus the set

of receivers at which the localisation indices values

are minimum, towards the presence of a fault F

. Its

columns describe the N branch’s fault reference sig-

natures.

A general signature matrix is provided in table 1.

It is characterized by two types of parameters: α and

β. A parameters α

i, j

represents a Boolean variable

which takes its values in the set {0, 1}. Equal local-

ization indices relative to a fault in a branch j, admit

a value 1 for their Boolean variables in the column

j of the signature matrix. The Boolean variables of

those with different values take 0. A parameter β

is a subset, in respect to F

, of receivers at which

the localisation indices’ values are the lowest, such as

⊂ {R

, . . . , R

The signature matrix is build in such a way that

faults are decoupled in a set of tests such as the m +1

indicators reacts to a particular subset of faults and

each branch’s fault j is characterised by a certain con-

ﬁguration of the indicators values. Different conﬁgu-

rations arise depending on where the fault is located

on the network. These conﬁgurations can be gener-

alised by four cases.

• If a fault F

occurs prior to all the network’s

nodes, the closest branch to the source: all the m

indices computed at the receivers situated after it

lead to a same value. The localization indices are

equal, ∀i, α

i, j

= 1.

• If a fault F

occurs behind all the network’s

nodes, at the end of the network: all the m indices

computed at the receivers situated before it take

different values, ∀i, k, α

i, j

6= α

k, j

. The localization

index i directly linked to the affected branch has

the lowest value among all the indices, β

= I

• If a fault F

is located at the branch directly

linked to a receiver i: only the indices computed

at the receivers situated after the nearest node

to the receiver i share the same values, for each

k, k > i, α

k, j

= 1. The index of localization related

to the receiver i has the lowest value among all the

indices, β

= I

• If a fault F

occurs between two nodes, a branch

not linked to any receiver: only the indices com-

puted at the receivers situated before the farthest

node, among the two nodes, to the source take dif-

ferent values, for each k, k < i, α

i, j

6= α

k, j

. The

receivers sharing the same values have the lowest

values compared to the remaining indices’ values.

for each k, k > i, I

∈ β

Soft Fault Detection and Localization in an Unshielded Twisted Pair Network using Power Line Communication

2.4 Summary

The step-by-step procedure of the proposed fault de-

tection and localization scheme based on PLC is sum-

marized as follows:

1. Construct the signature matrix with respect to the

network topology.

2. Deﬁne the reference H( f ) from each receiver’s

point of view.

3. Acquire successive H( f ) from each receiver i,

compute and monitor I

4. If no change is detected, return to step (3), other-

wise go to the next step.

5. Compute the localization indices I

and evaluate

their equality and minimum inequality.

6. Compare the resulting evaluation vector of step 5

to the fault signature in the signature matrix.

7. From step (6), deduce the faulty branch.

3 APPLICATION CASE STUDY

3.1 Data Generation

In this work, the studied network is the automotive

Ethernet, which is based on Unshielded Twisted Pairs

(UTP). This type of network is chosen for its ability

to meet the needs of ADAS (Hank et al., 2013).

Simulations of such a network are used to vali-

date the proposed method, before applying it in a real

network. In this paper, a deterministic chain matrices

-based model (Galli and Banwell, 2005) of the net-

work is used to compute H( f ). The model is based

on the physical characteristics of the network (topol-

ogy, type of cable, terminal devices i.e. source and

receivers) and on the transmission line theory. Each

quadripole element of the network is represented by

its corresponding ABCD chain matrix and the global

ABCD chain matrix is obtained by the product of

each individual element matrix (Peres et al., 2003).

For UTP networks, chain matrices can be computed

using the equations found in (Al-Asadi et al., 2000),

(El Sahmarany, 2013), (Truong, 2000) and (Ramo

et al., 1994). To our knowledge, the work by (El Sah-

marany, 2013) is the only one between them that took

the twisting phenomenon in consideration. Thus, the

equations found in the latter one are used to compute

those parameters in the marge of frequencies going

from 1 MHz to 100 MHz. These parameters are used

in the deterministic model to deduce H( f ).

3.1.1 Degradation and Soft Fault Model

Degradation: The degradation is deﬁned by an irre-

versible process in one or more of the primary param-

eters of the cable with either time, duration of use or

an external cause (e.g. humidity, heat, etc . . . ). The

WT degradation caused by humidity affects the di-

electric permittivity of the wire ε. Since the capaci-

tance of the cable is directly related to ε, then the WT

degradation is represented as two capacitors as shown

in Fig. 3 (Mugala, 2005).

Figure 3: Representation of an aged sample.

A model of the WT degradation seen in (F

orstel

and Lampe, 2017) and (Sanniyati et al., 2016) is used

to reproduce a degradation going from 0% to 5% with

a step of 0.1% (y = 0 to y = 0.05). The total permit-

tivity of an aged sample given by (Huo et al., 2019) is

computed using (14) :

total

insulator

W T

y ε

insulator

+ (1 − y)ε

W T

(14)

where ε

W T

is the permittivity of the affected zone

shown in blue in Fig. 3. ε

insulator

is the permittivity of

the pure insulation and y is the percentage of affected

zone.

In the following, the WT degradation is considered

as a normal evolution of the cable characteristics.

Soft Fault: This type of faults only produces

very small impedance changes (Auzanneau, 2013).

Therefore, a soft fault is usually represented by a

small localized modiﬁcation of the characteristic

impedance of the line. In this paper, the soft fault is

represented by a sudden insertion of series resistor.

3.2 Simulations and Results

As an example, several simulations are conducted on

the network shown in Fig. 4. This network has one

source, three receivers, two nodes and ﬁve branches.

Note that the source and all the receivers are matched

to the line (Same impedance of the characteristic

impedance of the network Z

= 120 Ω).

The three transfer functions of the network are com-

puted and their corresponding Bode diagram are

shown in Fig. 5 and 6.

1. Detection: We assume that the level of degrada-

tion increases by 1% every 50 successive acquisi-

VEHITS 2021 - 7th International Conference on Vehicle Technology and Intelligent Transport Systems

Figure 4: Unshielded twisted pair network.

0 1 2 3 4 5 6 7 8 9 10

Frequency(Hz)

-14

-12

-10

-8

-6

-4

-2

|H(f)|dB

Module of the transfer functions H

(f)

Receiver 1

Receiver 2

Receiver 3

Figure 5: Module of the transfer function of each receiver

( f )|.

tions of H

( f ). In this case, where the cable un-

dergoes a WT degradation with the absence of a

soft fault, the computed I

between H

re f erence

( f )

and H

test

( f ) increases at a slow pace as shown in

Fig. 7 for each receiver. H

test

( f ) denotes the suc-

cessive test data that needs to be tested at a given

time. When an abrupt soft fault occurs, its effect

differs from one receiver to another. A 5 Ω resis-

tor is inserted in series in the branch B

at t = t

a rupture in the variation of the detection index

appears as shown in Fig. 8. Therefore, to detect

the abrupt soft fault, it is sufﬁcient to detect the

rupture by one of the receiver.

2. Localization: Once the fault is detected, to locate

the affected branch, the localization index I

computed at each receiver. Since I

is a complex

index, its module |I

| and phase φ(I

) are pre-

sented in Fig. 9.

The results show that I

is equal to I

and both of

them are different from I

as it has been proven

0 1 2 3 4 5 6 7 8 9 10

Frequency(Hz)

-4

-2

(H(f)) rad

Phase of the transfer functions H

(f)

Receiver 1

Receiver 2

Receiver 3

Figure 6: Phase of the transfer function of each receiver

φ(H

( f )).

0 500 1000 1500 2000 2500 3000

Observation

-2

-3

Variation of the detection index with observations

Figure 7: Variation of the detection indices (Degraded net-

work without abrupt soft fault).

0 500 1000 1500 2000 2500 3000

Observation

0.01

0.02

0.03

0.04

Variation of the detection index with observations

Figure 8: Variation of the detection indices (Degraded net-

work with the appearance of a soft fault at t

in section 2. By changing the position of the fault

from one branch to another and observing the be-

havior of the localization indices a topology de-

pendent signature matrix can be obtained.

Table 2: Signature matrix of the network in Fig.4.

1 1 1 0 0

1 0 0 0 0

min

) R

∩ R

Note that a 1 in the table represents equality and a

0 represents a difference. All the indices holding

the number 1 are equal and the index holding the

number 0 is different from all the other indices.

For instance, let consider that the localized soft

fault occurs at the branch B

or the branch B

. The

fault is then located before the node connected to

the receivers R

and R

, therefore I

is equal to

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Frequency(Hz)

0.95

1.05

Variation of the localization index module with frequency

Receiver 1

Receiver 2

Receiver 3

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Frequency(Hz)

-0.05

0.05

) rad

Variation of the localization index phase with frequency

Receiver 1

Receiver 2

Receiver 3

Figure 9: Variation of the localization index. A 5 Ω resistor

is inserted in series in the branch B

at t = t

Soft Fault Detection and Localization in an Unshielded Twisted Pair Network using Power Line Communication

. To differentiate between these two cases (fault

at B

or at B

), the minimum index should then be

computed. The branch B

is directly linked to R

thus if the fault is in this branch, the minimum

index is I

. If there was no exclusive minimum

min(I

) = I

= I

, then the fault is in the com-

mon branch of the two receivers as in the case of

fault in B

4 CONCLUSIONS AND FUTURE

WORK

In this paper, a fault detection and localization

methodology based on the transfer function H( f ) is

proposed to detect a soft fault. This methodology is

based on two indices. At ﬁrst, the detection index is

computed. Once the fault is detected by one of the

receivers, the localization index is computed at each

endpoint of the network. The localization indices are

checked against one another to verify whether they

are equal or not. The results of these tests are com-

pared to each branch fault’s signature in the proposed

signature matrix. The proposed matrix is constructed

with respect to the network topology. To illustrate our

proposal, two bus networks are considered: a degrad-

ing two nodes network and an Y-shaped (one node)

network.

Further work will be realized to expand the valid-

ity and study the sensitivity of the detection and lo-

calization indices, in more complex networks. Also,

it would be interesting to introduce statistical equal-

ity tests for better and accurate comparison between

localization indices when noise is considered. This

approach will be also validated on a test bench that is

under construction.

ACKNOWLEDGEMENTS

This research work is done in the framework of the

ELSAT2020 project which is co-ﬁnanced by the Eu-

ropean Union with the European Regional Develop-

ment Fund, the French state and the Hauts-de-France

Region Council.

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