energies
Article

FEHCA: A Fault-Tolerant Energy-Efficient Hierarchical
Clustering Algorithm for Wireless Sensor Networks
Ankur Choudhary 1 , Santosh Kumar 1 , Sharad Gupta 1 , Mingwei Gong 2, * and Aniket Mahanti 3, *
1

2

3

*







Citation: Choudhary, A.; Kumar, S.;
Gupta, S.; Gong, M.; Mahanti, A.
FEHCA: A Fault-Tolerant
Energy-Efficient Hierarchical
Clustering Algorithm for Wireless
Sensor Networks. Energies 2021, 14,
3935. https://doi.org/10.3390/

Department of Computer Science and Engineering, Graphic Era Deemed to be University,
Dehradun 248002, India; ankurchoudhary.cse@geu.ac.in (A.C.); drsantosh.cse@geu.ac.in (S.K.);
sharadgupta@geu.ac.in (S.G.)
Faculty of Science and Technology, Mathematics and Computing, Mount Royal University,
Calgary, AB T3E 6K6, Canada
School of Computer Science, University of Auckland, Auckland 1010, New Zealand
Correspondence: mgong@mtroyal.ca (M.G.); a.mahanti@auckland.ac.nz (A.M.)

Abstract: Technological advancements have led to increased confidence in the design of large-scale
wireless networks that comprise small energy constraint devices. Despite the boost in technological
advancements, energy dissipation and fault tolerance are amongst the key deciding factors while
designing and deploying wireless sensor networks. This paper proposes a Fault-tolerant Energyefficient Hierarchical Clustering Algorithm (FEHCA) for wireless sensor networks (WSNs), which
demonstrates energy-efficient clustering and fault-tolerant operation of cluster heads (CHs). It treats
CHs as no special node but equally prone to faults as normal sensing nodes of the cluster. The
proposed scheme addresses some of the limitations of prominent hierarchical clustering algorithms,
such as the randomized election of the cluster heads after each round, which results in significant
energy dissipation; non-consideration of the residual energy of the sensing nodes while selecting
cluster heads, etc. It utilizes the capability of vector quantization to partition the deployed sensors
into an optimal number of clusters and ensures that almost the entire area to be monitored is alive
for most of the network’s lifetime. This supports better decision-making compared to decisions
made on the basis of limited area sensing data after a few rounds of communication. The scheme is
implemented for both friendly as well as hostile deployments. The simulation results are encouraging
and validate the proposed algorithm.

en14133935

Keywords: WSN; energy efficiency; hierarchical clustering; fault tolerance
Academic Editor: Alon Kuperman
Received: 25 May 2021
Accepted: 24 June 2021
Published: 2 July 2021

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4.0/).

1. Introduction
The world is witnessing the increasing involvement of sensors in human life due
to the technological advancements that have been achieved in recent decades. Various
arrangements of sensors are serving humankind in the present scenario. Wireless sensor
networks can be visualised as various sensing nodes sensing a specified domain, gathering
information normally pertaining to environmental changes (movement of human beings,
animals or vehicles; temperature changes, etc.) and forwarding it to a central control station,
generally referred to as a sink or base station (BS), for decision-making purposes [1–3].
Figure 1 shows a typical hierarchical architecture, where sensing nodes collect the
data from the environment and forward it to a leader node in the cluster, referred to as a
cluster head (CH), which, after aggregation, further forwards it towards the base station.
The analysis of data for decision-making purposes is generally performed at the BS level,
but some basic computations can also be performed at the CH level or even at the normal
sensing node level depending on the approach used [1,4].
Inherent to the wireless networks are a few constraints such as limited battery life,
bandwidth, memory, processing capabilities, abrupt sensor breakdown or abrupt behaviour,
etc., which all need to be efficiently addressed. These networks may be deployed in friendly

Energies 2021, 14, 3935. https://doi.org/10.3390/en14133935

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environments such as homes and offices or may be air-dropped into hostile environments
where sometimes it is not possible to replace the batteries of the sensors or calibrate
Energies 2021, 14, x FOR PEER REVIEW
2 ofthe
22
sensors [1,3]. The sensing nodes of WSNs are generally fixed but they may have limited
mobility as well, such as sensors floating on water bodies.

Figure
Figure 1.
1. Typical
Typical hierarchical
hierarchical architecture.
architecture.

Inherent
to the
wireless networks
are a few constraintssystems
such as (MEMS)
limited battery
life,
Continuing
advancements
in micro-electro-mechanical
technology
bandwidth,
processing
capabilities,
abrupt sensorenergy-efficient
breakdown or abrupt
behavhave made memory,
it possible
to fabricate
smaller, inexpensive,
sensors
with
iour,
etc., which
all and
needincreased
to be efficiently
addressed.
These networks
may
be deployed
in
increased
memory
computational
capability
[1,5–7] (e.g.,
Mica
motes from
friendly
environments
such as
homesthe
and
offices
or may
air-dropped
into hostile
Crossbow,
Tmote Sky from
Moteiv,
MKII
nodes
frombeUCLA
and SunSpot
from enviSun),
ronments
where
sometimes
is not possible
to use
replace
the batteries
of the sensors
or calwhich have
further
boosteditconfidence
in the
of WSNs.
The integration
of sensing
capabilities,
computation
and
communication
into a are
single
unit hasfixed
also but
beenthey
much
refined.
ibrate
the sensors
[1,3]. The
sensing
nodes of WSNs
generally
may
have
This has
tempted
analyse
the sensors’
data
for the purpose of efficient
limited
mobility
as researchers
well, such astosensors
floating
on water
bodies.
decision-making.
Continuing advancements in micro-electro-mechanical systems (MEMS) technology
have smaller,
been adopted
in relation
to WSNs; of
late, many
rehave Various
made it methodologies
possible to fabricate
inexpensive,
energy-efficient
sensors
with insearchers
have been
to computational
use machine learning
(ML)
in the(e.g.,
context
of motes
WSNs from
[8,9].
creased
memory
andtempted
increased
capability
[1,5–7]
Mica
It providesTmote
generalised
solutions
through
an nodes
architecture
that can
learn
and improve
its
Crossbow,
Sky from
Moteiv,
the MKII
from UCLA
and
SunSpot
from Sun),
performance.
The
application
of
ML
has
led
to
great
improvements
in
the
performance
which have further boosted confidence in the use of WSNs. The integration of sensing
of WSNs. Thus,
advancements
in machine learning
and
arehas
being
to solve
capabilities,
computation
and communication
into ahave
single
unit
alsoapplied
been much
revarious
WSN
issues
[10,11].
fined. This has tempted researchers to analyse the sensors’ data for the purpose of efficient
Routing strategies also play a key role in the efficient working of WSNs. These
decision-making.
strategies
in WSNs,
on the basis
the network
aretobroadly
into flat
Various
methodologies
haveofbeen
adoptedstructure,
in relation
WSNs; classified
of late, many
renetwork
routing,
location-based
routing
and
hierarchical
network
routing.
In
flat
network
searchers have been tempted to use machine learning (ML) in the context of WSNs [8,9].
routing,
all the
sensors are
uniformly
deployed
at the same that
levelcan
andlearn
eachand
sensor
serves its
as
It
provides
generalised
solutions
through
an architecture
improve
the
other’s
peer.
This
can
further
be
divided
into
proactive
or
reactive
routing
[12].
On
the
performance. The application of ML has led to great improvements in the performance of
other hand,
the case of location-based
routing,have
the sensors
clustered
based
on their
WSNs.
Thus,inadvancements
in machine learning
and areare
being
applied
to solve
varlocation
in
the
deployment,
which
is
determined
by
the
received
signal
strength
[13,14].
ious WSN issues [10,11].
Amongststrategies
the three,also
hierarchical
routing
protocols
haveworking
attractedof
the
attention
of many
Routing
play a key
role in
the efficient
WSNs.
These
stratresearchers
as
they
ensure
better
energy
efficiency
[15,16].
Here,
the
protocols
arrange
the
egies in WSNs, on the basis of the network structure, are broadly classified into flat netdeployed
sensors
into
groups
and
each
group
has
a
designated
cluster
head
(generally
the
work routing, location-based routing and hierarchical network routing. In flat network
sensor with the maximum energy). The cluster head coordinates with all the nodes inside
routing, all the sensors are uniformly deployed at the same level and each sensor serves
the group, generally called a cluster, and with the activities outside the cluster, whether
as the other’s peer. This can further be divided into proactive or reactive routing [12]. On
communicating with other CHs or the BS.
the other hand, in the case of location-based routing, the sensors are clustered based on
One of the most prominent hierarchical routing protocols is Low-Energy Adaptive
their location in the deployment, which is determined by the received signal strength
Clustering Hierarchy (LEACH). It has shown great energy efficiency and is the basis of
[13,14].
various other subsequent routing protocols [17]. It makes use of randomisation for the
Amongst the three, hierarchical routing protocols have attracted the attention of
purpose of evenly distributing the energy load across all the sensing nodes and arranges
many researchers as they ensure better energy efficiency [15,16]. Here, the protocols arvarious sensors into groups, where each group has a special sensor behaving as the leader
range the deployed sensors into groups and each group has a designated cluster head
of the group, coordinating the activities of the group. Here, a few sensors designate
(generally the sensor with the maximum energy). The cluster head coordinates with all
the nodes inside the group, generally called a cluster, and with the activities outside the
cluster, whether communicating with other CHs or the BS.
One of the most prominent hierarchical routing protocols is Low-Energy Adaptive
Clustering Hierarchy (LEACH). It has shown great energy efficiency and is the basis of

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purpose of evenly distributing the energy load across all the sensing nodes and arranges
various sensors into groups, where each group has a special sensor behaving as the leader
of the group, coordinating the activities of the group. Here, a few sensors designate themselves as cluster heads based on a certain probability and the number of times they have
themselves as cluster heads based on a certain probability and the number of times they
been the cluster head so far. This leader’s role is rotated so that it does not drain any single
have been the cluster head so far. This leader’s role is rotated so that it does not drain any
sensor’s energy [15].
single sensor’s energy [15].
Since, the deployed battery-operated sensing nodes are energy-constrained, it is imSince, the deployed battery-operated sensing nodes are energy-constrained, it is
portant to utilize the energy wisely to extend the network’s lifetime. Moreover, the nodes
important to utilize the energy wisely to extend the network’s lifetime. Moreover, the
deployed in hostile environments are very prone to faults, which may be related to a harsh
nodes deployed in hostile environments are very prone to faults, which may be related to
environment, energy depletion or hardware failure. Although it is quite evident that a
a harsh environment, energy depletion or hardware failure. Although it is quite evident
non-CH
faultyfaulty
nodenode
will will
degrade
the the
network
performance,
a afaulty
can be
be
that
a non-CH
degrade
network
performance,
faultyCH
CH node
node can
much
more
problematic,
as
it
will
hamper
the
whole
data
aggregation
and
dissemination
much more problematic, as it will hamper the whole data aggregation and dissemination
process of
of this
this cluster
cluster and
and will
will make
make normal
normal working
workingnodes
nodesuseless.
useless. This
This paper
paper discusses
discusses
process
the
basic
concept
of
the
hierarchical
clustering
protocols
and
proposes
a
base-station-conthe basic concept of the hierarchical clustering protocols and proposes a base-stationtrolled Fault-tolerant
Energy-efficient
Hierarchical
Clustering
Algorithm
(FEHCA),
which
controlled
Fault-tolerant
Energy-efficient
Hierarchical
Clustering
Algorithm
(FEHCA),
focusesfocuses
on: on:
which

••
••
••
••
••
••

The issue
issue of
of energy
energy efficient
efficientclustering
clusteringto
toenhance
enhancethe
thenetwork
networklifetime;
lifetime;
The
The
optimal
cluster
counts
for
the
network;
The optimal cluster counts for the network;
The use
use of
of k-means
k-means clustering
clustering that
that partitions
partitions N-nodes
N-nodes into
into k-clusters,
k-clusters, in
in which
which each
each
The
node
is
associated
with
the
cluster
with
the
nearest
mean;
node is associated with the cluster with the nearest mean;
The election
election of
of CHs
CHs near
near the
the centroids
centroids of
of the
the respective
respective clusters
clusters for
for effective
effective interinterThe
cluster communication;
communication;
cluster
Minimization of
deferring
thethe
re-election
of new
CHsCHs
afterafter
each
Minimization
of energy
energydissipation
dissipationbyby
deferring
re-election
of new
round;
each
round;
Attempting to
to make
make the
the cluster
cluster heads
heads (CHs)
(CHs) fault-tolerant
fault-tolerant by
by appointing
appointing aa secondary
secondary
Attempting
cluster
head
(sCH)
in
case
the
current
cluster
head
goes
down
between
two
cluster head (sCH) in case the current cluster head goes down between two successuccessive
sive
rounds.rounds.

In essence,
essence, this
this paper
paper proposes
proposes aa centralised
centralised cluster
cluster formation
formation technique
technique controlled
controlled
In
by the
the base
base station
station (BS),
(BS), where
where the
the deployed
deployed sensors
sensors are
are divided
divided into
into an
an optimal
optimal number
number
by
of
Oncethe
thenumber
numberofofclusters
clustersisisdecided
decidedand
and
cluster
formation
is done,
of clusters. Once
cluster
formation
is done,
thethe
alalgorithm,
instead
electing
any
arbitrary
CH,
shown
in Figure
2, elects
near
gorithm, instead
ofof
electing
any
arbitrary
CH,
as as
shown
in Figure
2, elects
thethe
CHCH
near
the
the
centroid
of respective
clusters.
algorithm
been
developed
fault-tolerant
centroid
of respective
clusters.
TheThe
algorithm
hashas
been
developed
to to
bebe
fault-tolerant
in
in
the
context
of
the
CH
and
does
not
require
re-cluster
formation
between
two
successive
the context of the CH and does not require re-cluster formation
successive
rounds
rounds ifif the
the CH
CH is
is found
found to
to be
be permanently
permanently defective.
defective.

Figure 2.
2. Depiction
Depiction of
of random
random distribution
distribution of
of cluster
cluster heads
heads in
in conventional
conventional LEACH
LEACH protocol.
protocol.
Figure

The work was carried out by considering both friendly and hostile environments;
thus, the placement of the BS was assumed to be within the deployment and far away from

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4 of 21
The work was carried out by considering both friendly and hostile environments;
thus, the placement of the BS was assumed to be within the deployment and far away
from the hostile environment, respectively. The performance of the network highly depends
on the
placement of
the base station.
Suppose thatof
a BS
placed within
monithe
hostile
environment,
respectively.
The performance
theisnetwork
highly the
depends
tored
area
(user-friendly
environments
such
homes
and
offices,
etc.);
it
will
be
in
close
on the placement of the base station. Suppose that a BS is placed within the monitored
proximity
to
the
cluster
heads,
as
compared
to
a
base
station,
which
is
outside
the
moniarea (user-friendly environments such homes and offices, etc.); it will be in close proximity
tored
area (generally
the case of
deployments
as harsh
terrains, border
to
the cluster
heads, asincompared
to hostile
a base station,
which such
is outside
the monitored
area
areas, etc.),inwhere
most
the cluster
heads generally
will beterrains,
at a distance
from
the etc.),
base
(generally
the case
of of
hostile
deployments
such as harsh
border
areas,
station.
where most of the cluster heads generally will be at a distance from the base station.
Most of
of the
the implementations
implementations discuss
discuss either
either friendly
friendly environment
environment deployments
deployments or
or
Most
hostile
environment
deployments,
but
the
proposed
algorithm
was
simulated
and
valihostile environment deployments, but the proposed algorithm was simulated and validated
dated
forscenarios.
both scenarios.
also compared
our
work
with
some
of the state-of-the-art
for
both
We alsoWe
compared
our work
with
some
of the
state-of-the-art
existing
existing technologies
with common
parameters
by positioning
the BS
the monitechnologies
with common
parameters
by positioning
the BS within
thewithin
monitored
area.
tored area. Furthermore,
the paper the
simulates
the proposed
hostile environFurthermore,
the paper simulates
proposed
algorithmalgorithm
in hostile in
environments
by
ments by integrating
high
energy
into thewith
network,
with theaim
primary
aim of
keeping
integrating
high energy
nodes
intonodes
the network,
the primary
of keeping
the
entire
the entire monitored
area
for the
of the
lifetime
of the
network
rather than
monitored
area alive for
thealive
majority
of majority
the lifetime
of the
network
rather
than monitoring
monitoring
only
the
surrounding
region
after
certain
rounds
of
communication,
shown
only the surrounding region after certain rounds of communication, as shown in as
Figure
3,
in Figure
3, andare
thepromising.
results are promising.
and
the results

Figure
Figure 3.
3. Scenario where
where most
most of
of the
the area
area is
is unmonitored
unmonitored in
inaalive
livenetwork.
network.

The
The rest
rest of
of the
the paper
paper isis organized
organized as
as follows.
follows. Section
Section 22 presents
presents aa summary
summary of
of the
the
related
work
done
in
this
domain,
whereas
the
proposed
system
model
is
explained
related work done in this domain, whereas the proposed system model is explained in
in
Section
Section 3,
3, which
which includes
includes the
the network
network model
model and
and energy
energy model
model for
for the
the proposed
proposed system.
system.
Section
Section 44 discusses
discusses the
the proposed
proposed algorithm
algorithm for
for cluster
cluster head
head selection
selection and
and fault
fault tolerance.
tolerance.
Investigational
outcomes
are
discussed
in
detail
in
Section
5,
which
also
contains
the
Investigational outcomes are discussed in detail in Section 5, which also contains the comcomparative
study
of
our
algorithm.
Finally,
the
summary
and
conclusions
are
presented
parative study of our algorithm. Finally, the summary and conclusions are presented in
in
Section
Section
6. 6.
2. Related Work
2. Related Work
Clustering and fault tolerance are the focus of various researchers working on wireClustering and fault tolerance are the focus of various researchers working on wireless senor networks [3,18]. Clustering is generally studied as either centralised or disless senor networks [3,18]. Clustering is generally studied as either centralised or distribtributed [18]. Centralised clustering involves clustering that is dictated by the base station
uted [18]. Centralised clustering involves clustering that is dictated by the base station
and the decisions are communicated in the field to the elected CHs; it is generally used in
and the decisions are communicated in the field to the elected CHs; it is generally used in
location-aware sensor networks. On the other hand, distributed clustering can be utilised
location-aware
sensor networks.sensor
On the
other hand,
distributed
clustering
be of
utilised
in
the case of location-unaware
networks,
where
the sensors
are not can
aware
their
relative positioning in the network.
Various hierarchical routing protocols for WSNs have also been presented in the
past [15,19–22]. Heinzelman et al. [15] presented a two-phase (setup phase and steady

Energies 2021, 14, 3935

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phase) cluster-based protocol for WSNs, known as Low Energy Adaptive Clustering
Hierarchy (LEACH). Though LEACH was one of the earliest clustering protocols and
formed the basis for various forthcoming protocols, it has its own share of shortcomings,
which have been addressed by various researchers [23–29].
Mechta et al. [30] have proposed a protocol named LEACH-CKM that makes use of kmeans classification for grouping the nodes. The proposed protocol is based on Centralised
LEACH, where CHs are appointed centrally with the help of the CH’s and sensing node’s
local information. LEACH-CKM addresses the node isolation problem where a remote
node is not able to communicate with the base station. It utilises a Minimum Transmission
Energy routing algorithm for routing the information from remote nodes.
An energy-efficient, fault-tolerant, distributed clustering and routing scheme for
wireless sensor networks has been proposed by Azharuddin et al. [31]. The proposed
scheme is a set of two algorithms jointly named Distributed Fault-tolerant Clustering and
Routing (DFCR). It makes use of a distributed run time recovery strategy for the sensor
nodes in case of unexpected failure of the cluster heads. The scheme is shown to be capable
of handling the sensor nodes that do not have any cluster head to be associated with.
In another work, LEACH’s threshold formula has been modified and presented by
Xingguo L et al. [20], where the residual energy is taken into account while selecting a
cluster head, as the traditional LEACH does not pay attention to the residual energy of the
nodes while choosing the cluster heads, which might lead to a low energy sensor node
being elected as the cluster head, which will exhaust early, leading to wastage of resources
utilised for cluster head selection. The protocol uses direct BS and CH communication.
Bhatti et al. [32] have proposed a clustering technique using fuzzy c-means. The
paper presents a cluster-based cooperative spectrum sensing scheme to reduce energy
consumption and proposes an algorithm that creates clusters and elects the cluster heads
in such a way that focuses on both the issues of energy consumption and efficiency in a
positive manner. The proposed scheme ensures maximum probability of detection under
an imperfect channel, utilising minimal consumption of energy when compared with the
conventional clustering approaches.
Further, the role of energy balancing in extending the network lifespan has been
explored by Azharuddin et al. [33]. The authors propose a Particle Swarm Optimization
(PSO)-based routing and clustering algorithm for wireless sensor networks, where the
routing algorithm creates a balance between energy efficiency and energy balancing. The
clustering algorithm is responsible for the CH and normal sensing node’s energy consumption. The proposed algorithms are also sophisticated enough to handle the failure of
cluster heads.
A comparison between Particle Swarm Optimisation and Genetic Algorithm when
applied to wireless sensor networks for network optimisation has been presented by
Parwekar et al. [34]. It shows how both the algorithms can optimise cluster formation.
Their experimental results found that PSO outperformed GA for clustering purposes.
Saveros et al. [35] have proposed a low-power handover design algorithm for wireless
sensor networks (WSNs). The algorithm is designed to place the majority of the scanning
responsibility on the mains-powered access points. The proposed algorithm has been
implemented and empirically evaluated. The evaluation results show that the energy consumption can be reduced by several orders of magnitude compared to existing algorithms
for WSNs.
Nigam, G.K et al. [36] have pointed out at some of the drawbacks of the LEACH
protocol, such as the unnecessary cluster head election after each round, which results
in significant energy depletion, discarding the remaining energy of the sensors, nonuniformity of number of cluster heads, etc. The paper proposes an algorithm, namely
ESO-LEACH, for addressing some of these issues. It makes use of metaheuristic particle
swarm enhancement for the initial clustering of the nodes, introduces the concept of
advanced nodes and also takes the residual energy of the nodes into consideration. An
enhanced set of rules and a fitness function are also defined for the purpose of cluster

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head selection. The algorithm demonstrates enhanced network lifetime as compared to
conventional LEACH.
Based on the above observations, it seems that there is a need for a centrally administered fault-tolerant and energy-efficient clustering algorithm. In order to achieve this, we
have proposed an improved, centrally administered, fault-tolerant and energy-efficient
clustering algorithm that is capable of enhancing the energy load balance and able to
achieve encouraging results. Therefore, in the next section, a system model is considered
for implementing the proposed algorithm.
3. System Model
A system model has prime importance when it comes to algorithm discussions. In
this section, the system model considered in the proposed algorithm is discussed in terms
of network model, energy model and fault model.
3.1. Network Model
The proposed work assumes the random deployment of N-sensing nodes that, once
deployed, are stationary. The deployed nodes are homogeneous in nature, with identical
initial energy and hardware. The basic working principle is divided into rounds as in [37],
where each round comprises local data gathering by the sensing nodes, which is forwarded
to the cluster head of the particular clusters. On receiving the data, the cluster head
aggregates the received data, removes the redundancies and transmits these data to the
base station (BS). In between the successive rounds, the nodes are assumed to switch off
their radios in order to conserve their batteries. The following assumptions have been
considered for this purpose:
Assumption 1. All the sensing nodes, once deployed, and the base station are stationary.
Assumption 2a. All the sensing nodes start with the same initial energy (in the case of BS
positioned at the centre of the deployment).
Assumption 2b. The deployment is equipped with advanced nodes in incremental fashion with
increasing distance from the BS as per Lemma 2 (in the case of BS positioned outside the deployment area).
Assumption 3. The BS controls the clustering process and has high computational power and is
also not energy-constrained.
Assumption 4. The BS is within the direct communication range of all the nodes and thus the
elected CHs (which communicate directly with the BS).
Assumption 5. The sensing nodes sense the region at a fixed rate and then communicate the sensed
data to the respective CHs.
Assumption 6. The sensors can adjust the transmission power as the distance to the target changes.
Assumption 7. The sensors are homogeneous in nature and energy-constrained.
The above-listed assumptions are taken into consideration in order to study the
performance of the proposed scheme in line with the other popular schemes mentioned
in the paper and highlight the improvements of the proposed scheme in terms of the
common parameters.
3.2. Energy Model
The proposed work makes use of the popular energy model described in [37], which
makes use of both the free space (d2 power loss) and the multipath propagation (d4 power
loss) model depending on the distance between the communicating entities.
If the distance between the sender and the receiver is less than a threshold do , then
the free space model is utilised; otherwise, the multipath model is utilised. If Eelec is the
amount of energy dissipated by the radio to run the transmitter or receiver circuitry per bit,

Energies 2021, 14, 3935

7 of 21

εfs and εmp are the energy required for amplification in the free space and multipath model,
respectively. The energy required by the radio to transmit a k-bit message over a distance d
is given by Equation (1) as:

ETx (k, d) =

k ∗ Eelec + k ∗ ε f s ∗ d2 ,
k ∗ Eelec + k ∗ ε mp ∗ d4 ,

d < do
d ≥ do

(1)

To receive the k-bit message, the radio expends ERx energy, as given by Equation (2).
ERx (k) = k ∗ Eelec

(2)

The given parameter Eelec depends on numerous factors, such as digital coding, modulation, filtering and spreading of the signal, while the amplification energy εfs and εmp
is subject to the distance between the sender and the receiver and to the acceptable bit
rate error.
For simulation purposes, the parameters are set to: Eelec = 50 nj/bit, εfs = 10 pj/bit/m2 ,
qε
fs
εmp = 0.0013pj/bit/m4 and EDA = 5 nj/bit/signal. Threshold do is calculated as d0 = ε mp
.
3.3. Fault Model
Failures are an inherent part of WSNs; different types of faults may affect them [38].
If, in between the CH selection rounds, the CH goes down, then either the data aggregated
of that cluster will be lost or a new CH selection will be initiated immediately. The
proposed Fault-tolerant Energy-efficient Hierarchical Clustering Algorithm (FEHCA) does
not introduce immediate CH selection in between two successive rounds as such a practice
leads to energy depletion. The CH going down in between two successive rounds is
managed by the sCH node of each cluster, which is on standby in every cluster and takes
over the task of CH temporarily.
The algorithm ascertains the selection of the CH at the centroid or near the centroid
of the clusters. As a random CH selection does not present an ideal scenario, as shown in
Figure 2, unpredictable CH selection generally leads to non-uniform energy dissipation
in the network, which ultimately reduces the network lifetime due to the rapid energy
discharge. Election of the CH near the centroids makes it easily accessible and helps
in achieving uniform energy dissipation, and, once the current CH’s energy is depleted
beyond a certain threshold, preference is given to the eligible sensors near the previous
round’s CH and the defined energy threshold is satisfied.
4. Proposed Algorithm
In the proposed algorithm, the network lifetime is divided into several rounds. The
algorithm works in two phases, the setup phase and the steady-state phase, as shown
in Figure 4. In the setup phase, the base station (BS) gathers the energy and location
information of the deployed nodes, based on which it clusters the entire region into an
optimal number of clusters (7 optimal clusters in our case), as shown in Figure 5. The BS,
after deciding the optimal cluster ratio (Cr ) in the network, performs the clustering using
the k-means clustering algorithm [39]. Once the clusters are determined, the BS elects the
CHs at or near the centroid of the clusters, which is followed by the steady-state phase.
In the steady-state phase, when the cluster formation is accomplished, the non-cluster
head sensing nodes sense the region and forward the sensed data to the appropriate CHs.
The CHs aggregate the data, look for any redundancy and uncorrelated data and send
it to the BS in a single hop. For better energy efficiency, the proposed algorithm elects
the CHs near the centroid of the cluster and delays the subsequent setup phases, unlike
in LEACH, until the residual energy of the current CH (CH_Eres ) >= specified threshold
energy (Cluster_Eavg ), thus conserving energy, as each setup phase consumes a significant
amount of energy in exchanging the control packets required for the cluster formation.

Energies 2021, 14, 3935

CHs.
The
CHs
aggregate
thethe
data,
look
forfor
any
redundancy
and
uncorrelated
data
and
CHs.
The
CHs
aggregate
data,
look
any
redundancy
and
uncorrelated
data
and
send
it to
thethe
BSBS
in in
a single
hop.
ForFor
better
energy
efficiency,
thethe
proposed
algorithm
elects
send
it to
a single
hop.
better
energy
efficiency,
proposed
algorithm
elects
thethe
CHs
near
thethe
centroid
of of
thethe
cluster
and
delays
thethe
subsequent
setup
phases,
unlike
CHs
near
centroid
cluster
and
delays
subsequent
setup
phases,
unlike
in in
LEACH,
until
thethe
residual
energy
of of
thethe
current
CH
(𝐶𝐻_𝐸
specified
threshold
LEACH,
until
residual
energy
current
CH
(𝐶𝐻_𝐸 ) >=
) >=
specified
threshold
8 of 21
energy
(𝐶𝑙𝑢𝑠𝑡𝑒𝑟_𝐸
conserving
energy,
as as
each
setup
phase
consumes
a significant
energy
(𝐶𝑙𝑢𝑠𝑡𝑒𝑟_𝐸 ), thus
), thus
conserving
energy,
each
setup
phase
consumes
a significant
amount
of of
energy
in in
exchanging
thethe
control
packets
required
forfor
thethe
cluster
formation.
amount
energy
exchanging
control
packets
required
cluster
formation.

Figure
4.
showing
the
overall
operation
of of
thethe
algorithm.
Figure
4.
Timeline
showing
the
overall
operation
of
the
algorithm.
Figure
4. Timeline
Timeline
showing
the
overall
operation
algorithm.

Figure
5. Optimal
Optimal
number
clusters
the
network.
5.
number
ofofof
clusters
inin
the
network.
Figure
5.
Optimal
number
clusters
in
the
network.

Algorithm
the
proposed
scheme,
followed
by
Lemma
10 sanalysis
analysis
Algorithm
11describes
the
proposed
scheme,
followed
byby
Lemma
1′s1′s
analysis
of of
itsof
Algorithm
1describes
describes
the
proposed
scheme,
followed
Lemma
itsits
complexity.
The
clustering
and
cluster
head
selection
processes
used
in
the proposed
complexity.
The
clustering
and
cluster
head
selection
processes
used
in
thethe
proposed
al-alcomplexity.
The
clustering
and
cluster
head
selection
processes
used
in
proposed
algorithm
discussed
inthe
the
following
section.
gorithm
areare
discussed
in in
the
following
section.
gorithm
discussed
following
section.
4.1.4.1.
Clustering
Phase
Clustering
Phase
Clustering
Phase
The
proposed
algorithm
uses
unsupervised
vector
quantisation
k-means
The
proposed
algorithm
uses
a apopular
unsupervised
vector
quantisation
k-means
The
proposed
algorithm
uses
apopular
popular
unsupervised
vector
quantisation
k-means
algorithm
toto
divide
the
randomly
distributed
sensors
into
clusters
and
performs
iterative
algorithm
to
divide
the
randomly
distributed
sensors
into
clusters
and
performs
iterative
algorithm
divide
the
randomly
distributed
into
clusters
and
performs
iterative
computations
optimise
centroids.
The
algorithm
tries
to minimise
the distance
computations
tototo
optimise
thethe
centroids.
The
algorithm
tries
to
minimise
thethe
distance
be-becomputations
optimise
centroids.
The
algorithm
tries
to
minimise
distance
tween
thethe
sensor
nodes
within
thethe
clusters
with
the
respective
centroids.
FEHCA
implebetween
the
sensor
nodes
within
the
clusters
with
the respective
centroids.
FEHCA
tween
sensor
nodes
within
clusters
with
the
respective
centroids.
FEHCA
implements
a centralised
approach
where
the
BSBS
performs
thethe
task
of
clustering.
The
BSBS
elects
ments
a centralised
approach
where
the
performs
task
of
clustering.
The
elects
implements
a centralised
approach
where
the
BS performs
the
task
of clustering.
The BS
thethe
sensor
node
nearest
to to
thethe
centroid
energy
greater
than
or or
equal
to to
the
average
sensor
node
nearest
centroid
with
energy
greater
than
equal
average
elects
the sensor
node
nearest
to
the with
centroid
with
energy
greater
than
orthe
equal
to the
cluster
energy,
i.e.,
EresE>=
Cluster_E
.avg
Here,
theavg
current
retains
itsCH
role
until
itsits
energy
cluster
energy,
i.e.,
resi.e.,
>=
Cluster_E
. Here,
the
CH
retains
its
role
until
its
energy
average
cluster
energy,
Eres >=avgCluster_E
. current
Here,CH
the
current
retains
role
until
falls
below
thethe
average
ofenergy
thethe
cluster.
thethe
number
of of
clusters
to to
bebeto
falls
below
average
energy
of
cluster.
Moreover,
number
clusters
its
energy
falls
below
theenergy
average
of theMoreover,
cluster.
Moreover,
the number
of clusters
formed
is is
not
changed
unless
thethe
ideal
number
of of
clusters
required
changes.
In In
essence,
formed
changed
unless
ideal
number
required
changes.
essence,
be
formed
isnot
not
changed
unless
the
ideal
number
ofclusters
clusters
required
changes.
In
essence,
the
clustering
phase
is
divided
into
two
phases,
namely
centralised
clustering
and
cluster
the
clustering
phase
is
divided
into
two
phases,
namely
centralised
clustering
and
the clustering phase is divided into two phases, namely centralised clustering andcluster
cluster
head
selection.
head
selection.
head
selection.
4.2.4.2.
Centralised
Clustering
Centralised
Clustering
Centralised
Clustering
In
centralised
clustering,
each
ithith
node
is represented
byby
Nby
i,N
where
i ∈i {1,
n},2,n},
and
centralised
clustering,
node
isisrepresented
i,N
where
∈ {1,
2,{1,
...,
InIn
centralised
clustering,
each
ith
node
represented
i2,∈...,
. .and
. , n},
i , where
+. Therefore,
+. Therefore,
+
the
base
station
is
represented
as
N
the
overall
entities
participating
are
N=
the
base
station
is
represented
as
N
the
overall
entities
participating
are
N=
and the base station is represented as N . Therefore, the overall entities participating
+}. +N+, based
+, based
+
+
{N
1, N
2N
,
...,
N
nN
,
N
on
the
sensor’s
location
and
residual
energy,
partitions
the
{N
1
,
2
,
...,
n
,
N
}.
N
on
the
sensor’s
location
and
residual
energy,
partitions
the
are N= {N1 , N2 , . . . , Nn , N }. N , based on the sensor’s location and residual energy,
network
into
clusters;
for
this,
thethe
proposed
scheme
makes
use
of of
k-means
as as
network
into
clusters;
for
this,
proposed
scheme
makes
use
k-means
clustering
partitions
the
network
into
clusters;
for this,
the
proposed
scheme
makesclustering
use
of k-means
+ conveys
+ conveys
shown
in
Algorithm
2.
Once
the
clustering
decision
is
made,
N
the
clustering
+
shown
in
Algorithm
2.
Once
the
clustering
decision
is
made,
N
the
clustering
clustering as shown in Algorithm 2. Once the clustering decision is made, N conveys
the clustering information to the sensing nodes (Ni ). N+ elects the CHs and sends the
corresponding CH parameters to Ni . On receiving the values from the BS, each node
determines whether it is the CH or a normal participating node in the current round. If
any node is not selected as a CH in the current round, then the N+ directly transmits
the Ni value corresponding to the CH with which that node needs to associate. The
k-means clustering initially performs a random partition of the network into centroid
based k-clusters; then, it repeatedly performs the task of minimising the distance between
each node and the respective centroid. Ultimately, this process ensures that the sensor
nodes within the cluster are in close proximity. This leads to reduced energy dissipation

Energies 2021, 14, 3935

9 of 21

and efficient communication of the CH with the member nodes, as well as supporting
efficient monitoring of the cluster.
4.3. Cluster Head Selection
In this process, the BS (N+ ) elects the CHs based on the distance from the centroid
and the specified energy requirements, and it communicates the Ni value corresponding
to the selected CH to the participating nodes in the network. If the received Ni value
corresponds to the value of the receiving node, then the recipient recognises itself as
the CH and creates and broadcasts to its member nodes for the coordination of the data
transmission in the specified schedule. Otherwise, if the Ni value does not correspond
to the value of the receiving node, then it recognises itself as a normal member node
of the cluster, sends a cluster joining request to the CH whose Ni value it has received
from N+ and subsequently waits for the schedule to be generated by its CH. Once this
process is completed, each member node in the cluster transmits the sensed data and
the corresponding residual energy to the respective CH as per the received schedule.
Between the subsequent transmission schedule, the sensor switches off the radios to
conserve the energy. The CH compares its energy with the average energy of the cluster
and communicates this information to the BS. If its energy is greater than or equal to the
average energy of the cluster, then it remains the CH; otherwise, the BS elects a new CH by
considering the residual energy and the distance from the centroid in the next round. New
CHs are elected from the sensors within the current clusters only, and new clusters are
created only when the ideal number of clusters to be formed is changed (depending on the
Cr ). The cluster head election in FEHCA is shown in Algorithm 1 which has a worst-case
time complexity of O (Cn2 + Cn CN2 log CN) and is discussed in Lemma 1.
Algorithm 1. Cluster head election in FEHCA.
Input: ( N, Ei , n, Cr )
N ( Ni , ∀ i ∈ {1, 2, . . . , n}) alive nodes with co-ordinates ( xi , yi )
E: initial energy ( E1 , E2 , E3 , . . . , En )
n: number of alive nodes
Cr: Optimal cluster ratio
Output: CH
where CH represents cluster heads
Procedure: FEHCA( N, Ei , Cr, n)
Cn = round(n ∗ Cr )
1:
//Number of clusters in the network
Centroid, CN ← KMEANS( N, Cn, n)
//Calculating cluster(s) centroid, and
2:
respective participating members
f or i = 1 to all centroids in Centroid
//For
finding the minimum distance node
3:
in a cluster
4:
Cluster_Eavg ← 0
5:
f or j = 1 to all member nodes in CN
//For all nodes in a cluster
6:
Cluster_Eavg ← Cluster_Eavg + Ej
7:
dij ← distance between centroid and cluster node
8:
end f or
9:
10:
11:
12:
13:
14:
15:

Cluster_E

Cluster_Eavg ← number o f nodeavgin CN
while CH_Eres < Cluster_Eavg
do
CH ← min(di )
//CH is elected cluster head
remove CH f rom di
end while
end f or

Energies 2021, 14, 3935

10 of 21

Algorithm 2. K-Means algorithm.
Input: ( N, Cn, n)
N ( Ni , ∀ i ∈ {1, 2, . . . , n}) alive nodes with co-ordinates ( xl , yl )
Cn represents number of clusters in the network
n is number of alive nodes
Output: Centroid, CN
Procedure: KMEANS( N, Cn, n)
1:
(s1 , s2 , s3 , . . . , sCn ) ← Select random seed points( N, Cn)
∀ i ∈ {1, 2, . . . , n}
2:
f or k ← 1 to Cn
3:
do Centroidk ← sk
4:
end f or
5:
while stopping condition is not met
6:
do
7:
f or k ← 1 to Cn
8:
CNk ← { }
9:
end f or
10:
f or m ← 1 to n

p 1/p
11:
j ← argmin( ∑i Nm − Centroid j
)
j

12:
13:
14:
15:
16:
17:
18:

//distance computation
CNj ← CNj ∪ { Nm }
//reassignment of vectors
end f or
f or k ← 1 to Cn
1
Centroid ← |CN
∑ N ∈CNk N
k|
//recompilation of centroids
end f or
end while
return {Centroid, CN }

Generally, the network lifetime is considered till the last cluster head is able to communicate with the base station; once the base station stops receiving the sensed data of the
region, the network is assumed to be exhausted. Though this is a valid way of computing
the lifetime of a network, it does not give a true picture of the sensed region. This is because,
initially, the BS receives sensed values from the entire region being monitored but, as the
time elapses, the CHs far away from the BS start dying earlier than the CHs near the BS (in
the case of direct non-multi-hop networks) and, as the time elapses, only the CHs near the
BS are able to communicate, as depicted in Figure 3, this fact is later validated in the results
analysis section. Then, based on the nearby cluster readings, the BS is forced to either made
decisions for the entire monitored area (which is not justified) or make decisions for only
the areas from which it can communicate and preserving the rest of the area for further
monitoring. The same issue occurs when CHs transmit multi-hop data to the BS, with
the exception that CHs closer to the BS wear out faster than CHs farther away due to the
overhead of transmitting the additional packets from faraway nodes to the BS.
This is taken into account by the proposed algorithm (FEHCA), which focuses on
controlling the entire region for almost the entire network lifespan. It demonstrates the
inclusion of advanced nodes within the clusters in uniform fashion (in case the BS is within
the deployment zone) as well as in increasing fashion when the distance between the cluster
and BS increases (in case the BS is far away from the deployment zone). This is crucial in
order to monitor a larger area rather than only monitoring clusters in close proximity to
the BS for most of the time and making decisions for the entire area based solely on inputs
from neighbouring CHs only. With or without the same number of high energy nodes,
the CHs far away from the BS die out early and only the CHs and the clusters near the BS
remain alive for a longer period of time. We need sensed data from the entire area being
monitored for better decision-making, which means that the CHs of the entire area must be

Energies 2021, 14, 3935

11 of 21

alive, and one way to achieve this is to deploy advanced nodes in increasing order as the
distance from the BS increases.
If two CHs are at different distances from the BS, then the transmission energy consumption must be different according to Equation (1). Therefore, in order to equate the
transmissions of both the CHs to the BS, we require additional energy for the distant CH.
The computation of the additional amount of energy is given in Lemma 2.
Lemma 1. The cluster head election in FEHCA has a worst-case time complexity of O (Cn2 + Cn
CN2 log CN).
Proof: The major components in the FEHCA algorithm that dominate the complexity
from Step 2 and Steps 3 to 15. As in Step 2, we use the k-means algorithm, which has a
complexity of O (CN). Steps 3 to 15 mainly consist of two parts. For Part 1 (Steps 5 to 8),
the complexity of this part is O (CN). For Part 2 (Steps 10 to 14), in Step 12, we have used a
sorting technique, which has a time complexity of O (CN log CN). Thus, the complete Steps
10 to 14 have a time complexity of O (CN2 log CN). Therefore, the time complexity from
Steps 3 to 15 is O (Cn2 ) + O (Cn CN2 log CN). Now, the overall complexity of Algorithm 1
is O (Cn2 ) + O (Cn CN2 log CN) + O (CN) ≈ O (Cn2 + Cn CN2 log CN). 
Lemma 2. Let the energy requirement for the transmission of k-bits from a cluster head (CH) to
the base station (BS) in the case of a multipath be ETx (k, d) = k ∗ Eelec + k ∗ ε mp ∗ d4 , where ‘d’ is
the distance between BS and a CH. If the distance between two CHs (CH1 and CH2 ) from the BS
is d1 and d2 such that d2 >d1 , then, in order to equate the transmissions of CH1 and CH, we need
additional energy for CH2, which is given by
∆=

θ k ∗ ε mp d42 − d41




k ∗ Eelec + k ∗ ε mp ∗ d41

where θ is the initial energy with CH1 and CH2 .
Proof. The energy requirement for transmitting k-bits over the distance d as discussed in
Equation (1) is given by:
ETx (k, d) = k ∗ Eelec + k ∗ ε mp ∗ d4

(3)

Since ETx () is a strictly increasing function over ‘d’, ETx (k, d2 ) > ETx (k, d1 ) for given
d2 > d1. Now, using Equation (3), we obtain
k ∗ Eelec + k ∗ ε mp ∗ d42 > k ∗ Eelec + k ∗ ε mp ∗ d41

(4)

Reversing the inequality in Equation (4) produces
1
1
<
4
k ∗ Eelec + k ∗ ε mp ∗ d2
k ∗ Eelec + k ∗ ε mp ∗ d41

(5)

Further, multiplying θ in (5), we obtain
θ
θ
<
4
k ∗ Eelec + k ∗ ε mp ∗ d2
k ∗ Eelec + k ∗ ε mp ∗ d41

(6)

Then, equating Equation (6), we obtain
θ+∆
θ
=
4
k ∗ Eelec + k ∗ ε mp ∗ d2
k ∗ Eelec + k ∗ ε mp ∗ d41

(7)

Energies 2021, 14, 3935

12 of 21

Finally,
∆=

θ k ∗ ε mp d42 − d41




k ∗ Eelec + k ∗ ε mp ∗ d41

.


5. Results Analysis
In this section of the paper, a simulation setup along with two scenarios is considered.
The setup was prepared for the purpose of evaluation of the proposed algorithm (FEHCA).
The LEACH and the proposed algorithm were simulated in Python on an Intel Core i5-9300
H CPU @ 2.40 GHz and 8GB RAM running on Windows 10. The sensors were randomly
deployed in a 100 m × 100 m area; the initial energy of the sensor was assumed to be
0.5 J. The CH probability was not fixed in advance as in LEACH and was computed
at run time, as depicted in Figure 5. FEHCA’s effectiveness was assessed on the same
basic parameters as in [37], and the results are shown in Table 1. We tested our proposed
algorithm extensively for the following two scenarios and compared the results with the
existing LEACH protocol and ESO-LEACH [36].
Table 1. Simulation parameters for FEHCA.
Parameters

Values

Area
Number of nodes
Sink location
Optimal cluster ratio (Cr )
Initial energy of node, Ei
Data packet size
Energy consumption: power amplifier, εfs
Energy consumption: power amplifier, εmp
Energy dissipated to run the transmitter or receiver circuitry, Eelec
Energy consumption: aggregation (EDA)
Threshold distance, do
Initial energy of high energy node

100 m × 100 m
100
centre and 50,200
07
0.5 J
4000 bits
10 × 10−12 J/bit/m2
0.0013 × 10−12 J/bit/m4
50 × 10−9 J/bit
5 × 10−9 j/bit/signal
87.7 m
1J

Scenario 1. A wireless sensor network (WSN1 ) is deployed and BS is placed at the middle position
(50, 50) in the deployment area (x, y).
Scenario 2. A wireless sensor network (WSN2 ) is deployed and BS is placed at position (50, 200),
which is far away from the deployment area (x, y).
5.1. Experimental Evaluation for Scenario 1
In Scenario 1, the deployment area (x, y) is 100 m × 100 m, and 100 nodes are deployed
at random, with the base station at the centre (50, 50), as shown in Figure 6. Using k-means
clustering, the randomly deployed nodes are grouped into an optimal number of clusters,
and the centroid of each cluster (marked as ‘x’) is chosen, as shown in Figures 7 and 8.
The results were collected by keeping the base station at position (50, 50) in a
100 m × 100 m area, which was monitored. We first simulated the LEACH algorithm
and then the proposed FEHCA with the same simulation parameters and found the proposed algorithm to last, on average, 70 percent longer than the LEACH algorithm, as shown
in Figure 9 and Table 2a.

which is far away from the deployment area (x, y).

Energies 2021, 14, 3935

5.1.
5.1. Experimental
Experimental Evaluation
Evaluation for
for Scenario
Scenario 11
In
Scenario
1,
the
deployment
In Scenario 1, the deploymentarea
area(x,
(x,y)
y)is
is100
100m
m××100
100m,
m,and
and100
100nodes
nodesare
aredeployed
deployed
at
atrandom,
random,with
withthe
thebase
basestation
stationat
atthe
thecentre
centre(50,
(50,50),
50),as
asshown
shownin
inFigure
Figure6.
6.Using
Usingk-means
k-means
13 of 21
clustering,
clustering,the
therandomly
randomlydeployed
deployednodes
nodesare
aregrouped
groupedinto
intoan
anoptimal
optimalnumber
numberof
ofclusters,
clusters,
and
and the
the centroid
centroid of
of each
each cluster
cluster (marked
(marked as
as ‘x’)
‘x’) is
is chosen,
chosen, as
as shown
shown in
in Figures
Figures 77 and
and 8.
8.

Figure
area
of
100
m
×× 100
Figure
Random
100
Figure 6.
6. Random
Random deployment
deployment of
of 100
100sensor
sensornodes
nodesin
inan
anarea
areaof
of100
100m
m×
100 m
m with
with BS
BS positioned
positioned
inside
inside
insidethe
thedeployment
deploymentarea.
area.

Energies 2021, 14, x FOR PEER REVIEW

14 of 22

Figure
Network
clustering
using
k-means
Figure
Figure7.
7.Network
Networkclustering
clusteringusing
usingk-means
k-meansalgorithm.
algorithm.

Figure 8. Depiction of network clusters with centroids.

The results were collected by keeping the base station at position (50, 50) in a 100 m
× 100 m area, which was monitored. We first simulated the LEACH algorithm and then
the proposed FEHCA with the same simulation parameters and found the proposed algorithm to last, on average, 70 percent longer than the LEACH algorithm, as shown in
Figure 9 and Table 2a.

Figure 8. Depiction of network clusters with centroids.

The results were collected by keeping the base station at position (50, 50) in a 100 m
× 100 m area, which was monitored. We first simulated the LEACH algorithm and then
the proposed FEHCA with the same simulation parameters and found the proposed
14 ofal21
gorithm to last, on average, 70 percent longer than the LEACH algorithm, as shown in
Figure 9 and Table 2a.

Energies 2021, 14, 3935

Figure
9. Performance
FEHCA and
and LEACH
LEACH in
in terms
terms of
of operational
operational nodes
nodes per
per round
round when
when base
base
Figure 9.
Performance of
of FEHCA
station
is
positioned
inside
the
deployment
area.
station is positioned inside the deployment area.
Table 2. (a) Network lifetime comparison of LEACH and FEHCA; (b) network lifetime comparison
Table 2. (a) Network lifetime comparison of LEACH and FEHCA; (b) network lifetime comparison of ESO-LEACH and
of ESO-LEACH and FEHCA:H_energy_UD.
FEHCA:H_energy_UD.

(a)

(a)
No. of Rounds

No. of Alive Nodes
No. ofNo.
Aliveof
Nodes
Alive
in LEACH No. of
in FEHCA

100

100

200

100

Rounds

Nodes in
100
LEACH
99

100
200
300
400
500
600

100
99
100
99
100
99
100
97
100
96
100

300

100

400

100

500

100

600

100

700

100

750

89

800

39

95

850

0

96

(b)
No. of Alive No. of Alive
No. of Alive Nodes
No. of Alive Nodes in
No.
of
Nodes
Nodes in
in ESO- LEACH
[36] inFEHCA:H_energy_UD
Rounds 100
ESO- LEACH FEHCA:H_en99
[36]
ergy_UD
93
99
100
100
99
88
99
200
93
99
85
99
300
88
99
81
99
400
85
99
71
99
500
81
99
64
99
600
71
99
(b)

No.
of Alive
No. of Rounds
Nodes in
100
FEHCA
200

100300
99400
99500
99600
99
700
97
800

57

99

900

51

98

94

1000

45

98

900

93

1100

37

98

1000

93

1200

32

98

1100

92

1300

28 *

93

1150

73

1350

24 *

13

1200

05

1500

18

5

1300

05

1650

13 *

0

1350

04

1800

10

1400

02

2000

4

0

2200

0

1450

* Approximate values ascertained from the results [36].

Furthermore, we discovered that, similar to LEACH, most of the nodes in FEHCA
were operational for the majority of the time, as shown in Figure 9, whereas this is not the
case in many proposed algorithms [36], where the nodes’ batteries start to become depleted
immediately, as shown in Table 2b; after a certain number of communication rounds, this
forces a decision to be made on the data received from limited regions only. Furthermore,
FEHCA lasted 50 percent longer than LEACH, with over 90% of nodes still alive.

Energies 2021, 14, 3935

Furthermore, we discovered that, similar to LEACH, most of the nodes in FEHCA
were operational for the majority of the time, as shown in Figure 9, whereas this is not the
case in many proposed algorithms [36], where the nodes’ batteries start to become depleted immediately, as shown in Table 2b; after a certain number of communication
15only.
of 21
rounds, this forces a decision to be made on the data received from limited regions
Furthermore, FEHCA lasted 50 percent longer than LEACH, with over 90% of nodes still
alive.
The LEACH
LEACH protocol
protocol is
with
almost
all all
nodes,
resultThe
is valued
valuedfor
forits
itsability
abilitytotoperform
perform
with
almost
nodes,
reing
in
higher
area
coverage
for
the
majority
of
its
lifetime,
but
its
random
clustering,
unsulting in higher area coverage for the majority of its lifetime, but its random clustering,
predictable and
random
cluster
head
election
mechanism
results
in high
energy
dissipaunpredictable
and
random
cluster
head
election
mechanism
results
in high
energy
distion
fluctuations,
as
shown
in
Figure
10,
which
must
be
addressed.
Furthermore,
LEACH
sipation fluctuations, as shown in Figure 10, which must be addressed. Furthermore,
makes no
mention
of the data
packets
lost during
algorithm’s
operation.
FEHCA,FEon
LEACH
makes
no mention
of the
data packets
lost the
during
the algorithm’s
operation.
the
other
hand,
addresses
both
of
these
issues
and
the
findings
are
supported
by
Figures
HCA, on the other hand, addresses both of these issues and the findings are supported by
11 and 12.
Figures
11 and 12.

Energies 2021, 14, x FOR PEER REVIEW
Energies 2021, 14, x FOR PEER REVIEW

16 of 22
16 of 22

Figure10.
10.Energy
Energydissipation
dissipationper
perround
roundin
inLEACH.
LEACH.
Figure

Figure
11.
Energy dissipation
comparison
per
round
in
LEACH
and
FEHCA.
Figure 11.
11. Energy
Energy
dissipation comparison
comparison per
per round
round in
in LEACH
LEACH and
and FEHCA.
FEHCA.
Figure
dissipation

Figure 12. Retransmissions per round in FEHCA.
Figure 12. Retransmissions
per round in FEHCA.

The Fault-tolerant
Fault-tolerant Energy-efficient
Energy-efficient Hierarchical
Hierarchical Clustering
Clustering Algorithm
Algorithm (FEHCA),
(FEHCA),
The
similarly
to
LEACH,
operates
at
nearly
full
strength
for
the
majority
of
its
lifespan,
which
similarly to LEACH, operates at nearly full strength for the majority of its lifespan, which
is critical
critical for
for reliable
reliable networks.
networks. It
It achieves
achieves minimum
minimum energy
energy dissipation
dissipation variation
variation due
due to
to
is
the
determination
of
optimum
number
of
cluster
heads
and
then
by
focusing
on
cluster
the determination of optimum number of cluster heads and then by focusing on cluster

Energies 2021, 14, 3935

16 of 21

The Fault-tolerant Energy-efficient Hierarchical Clustering Algorithm (FEHCA), similarly to LEACH, operates at nearly full strength for the majority of its lifespan, which is
critical for reliable networks. It achieves minimum energy dissipation variation due to the
determination of optimum number of cluster heads and then by focusing on cluster head
placement at or near the centroids, as opposed to LEACH, which elects cluster heads at random. The fault-tolerant behaviour of cluster heads has been also demonstrated by FEHCA.
In the event of a cluster head failure, secondary cluster heads (sCHs) take over the task. As
shown in Figure 12, failed packet transmissions have been handled and re-transmitted.
In addition, the paper compares FEHCA: H_energy_UD to ESO-LEACH [36] with
the same parameters. FEHCA: H_energy_UD uniformly distributes high energy nodes
with twice the energy of normal nodes (i.e., 1J initial energy) in each cluster. High energy
nodes are contained in the set of N-normal nodes; thus, normal node count = N- high
energy nodes.
FEHCA: H_energy_UD, on average, keeps 90% of the network alive for more than
80% of the network life time, while ESO-LEACH keeps around 50% of the network alive
for approximately 40% of the network life time, as shown in Table 2b.
5.2. Experimental Evaluation for Scenario 2
In Scenario 2, the deployment area (x, y) is 100 m × 100 m, 100 sensor nodes are
Energies 2021, 14, x FOR PEER REVIEW
of 22
randomly deployed and the base station is placed in position (50, 200), i.e., far17away

from the deployment area, as in hostile environments such as inaccessible border regions,
wildlife monitoring, etc., as shown in Figure 13.

Figure 13. Random deployment of 100
100 sensor
sensor nodes
nodes in
in an
an area
areaof
of100
100m
m×
× 100 m with BS positioned
outside the deployment area at position (50, 200).

Figure 14
network
after
the the
optimal
clusters
have have
been determined,
Figure
14shows
showsthe
theclustered
clustered
network
after
optimal
clusters
been deterwith
the
CHs
chosen
by
the
BS
near
or
at
the
centroids.
Each
cluster
communicates
directly
mined, with the CHs chosen by the BS near or at the centroids. Each cluster communicates
with
the
BS
with
the
help
of
the
elected
CH,
as
depicted
by
Figure
15.
directly with the BS with the help of the elected CH, as depicted by Figure 15.
In Figure 16, a typical scenario involving the distance between the BS and the communicating CHs is illustrated, in which three CHs with 0.5 J of initial energy communicating
directly with the BS are located at 117 m, 151 m and 185 m distances from the BS. When
considering multipath propagation εmp , we can see that the CH furthest from the BS is
functional for 80 rounds, while the CHs closer to the BS are able to communicate for 173
and 426 rounds, respectively.

Figure 13. Random deployment of 100 sensor nodes in an area of 100 m × 100 m with BS positioned
outside the deployment area at position (50, 200).
Energies 2021, 14, 3935

Figure 14 shows the clustered network after the optimal clusters have been 17
deterof 21
mined, with the CHs chosen by the BS near or at the centroids. Each cluster communicates
directly with the BS with the help of the elected CH, as depicted by Figure 15.

Energies 2021, 14, x FOR PEER REVIEW

18 of 22

Energies 2021, 14, x FOR PEER REVIEW

18 of 22

Figure 14. Network clustering using k-means algorithm.

Figure 15. Depiction of network clusters along with respective centroids (each cluster communicates directly with the BS).

In Figure 16, a typical scenario involving the distance between the BS and the communicating CHs is illustrated, in which three CHs with 0.5 J of initial energy communicating directly with the BS are located at 117 m, 151 m and 185 m distances from the BS.
When considering multipath propagation εmp, we can see that the CH furthest from the
BS is functional
forof
rounds,
whilealong
the CHs
to the
BS are(each
able cluster
to
communicate
Figure
15.
network
clusters
with
respective
centroids
(each
cluster
communi- for
Figure
15.Depiction
Depiction
of80
network
clusters
along
withcloser
respective
centroids
communicates
173 and
426with
rounds,
respectively.
cates
directly
the BS).
directly
with
the
BS).
In Figure 16, a typical scenario involving the distance between the BS and the communicating CHs is illustrated, in which three CHs with 0.5 J of initial energy communicating directly with the BS are located at 117 m, 151 m and 185 m distances from the BS.
When considering multipath propagation εmp, we can see that the CH furthest from the
BS is functional for 80 rounds, while the CHs closer to the BS are able to communicate for
173 and 426 rounds, respectively.

Figure
Figure 16.
16. Effect
Effect of
of distance
distance of
of cluster
cluster heads
heads (CHs)
(CHs) from
fromBS
BSon
onthe
thenetwork
networklifespan.
lifespan.

Thus,
)
Thus, with
with knowledge
knowledgeof
ofthe
thedistance
distance(d
(di )i) from
fromthe
theBS
BSand
andthe
theresidual
residualenergies
energies(E
(Eres
res)
of
the
member
nodes
in
the
network,
a
ratio
of
the
energy
requirements
in
accordance
with
of the member nodes in the network, a ratio of the energy requirements in accordance
the
increasing
distance
can becan
formulated
to keep
entire
monitored
area operational.
with
the increasing
distance
be formulated
to the
keep
the entire
monitored
area operaWe
can
compute
the
lifetime
of
the
closest
node
in
terms
of
the
number
of
roundsof
required
tional. We can compute the lifetime of the closest node in terms of the number
rounds
for it to function, and we can then calculate the energy requirements of the farthest nodes
required for it to function, and we can then calculate the energy requirements of the farto match the performance in terms of rounds. As a result, as the distance from the base
thest nodes
to of
match
the of
performance
termsfrom
of rounds.
As
a result,
as the distance from
Figure
16. Effect
distance
cluster headsin(CHs)
BS on the
network
lifespan.
station increases, and we will need to introduce a greater number of high energy nodes.
the base station increases, and we will need to introduce a greater number of high energy
Thus, with knowledge of the distance (di) from the BS and the residual energies (Eres)
nodes.
of theDue
member
nodes energy
in the network,
a ratiocluster
of theheads
energy
requirements
accordance
to different
requirements,
that
are far awayinfrom
the base
with
thetend
increasing
cana be
formulated
to than
keep cluster
the entire
monitored
station
to losedistance
energy at
much
faster rate
heads
that arearea
closeoperato the
tional.
We canAs
compute
the
lifetime
the closest
node in terms of
thethe
number
of rounds
base station.
a result,
after
a fewofrounds
of communication
with
base station,
the

Energies 2021, 14, 3935

18 of 21

Due to different energy requirements, cluster heads that are far away from the base
Energies 2021, 14, x FOR PEER REVIEWstation tend to lose energy at a much faster rate than cluster heads that are close to19
22
theofbase
Energies 2021, 14, x FOR PEER REVIEW

station. As a result, after a few rounds of communication with the base station, the network
19 of
22 are
is left with only nearby cluster heads that are communicating with the base station
and
responsible for increasing the network lifetime. The simulation results validate this, and is
shown in Figure 17.

Figure 17. Placement of alive nodes when the count is less than 10 with uniform distribution of high
energy nodes.
Figure
17. Placement
of alive
nodes
when
the count
is less
10 with
uniform
distribution
of high
Figure
17. Placement
of alive
nodes
when
the count
is less
thanthan
10 with
uniform
distribution
of high
Based
on the distance from the BS and the initial energy known, the lifetime of the
energy
nodes.
energy
nodes.

nodes closer to the BS and the farthest nodes in terms of number of rounds can be calcuBased
on the
distance
from
BSLemma
and
energy
known,
the
lifetime
ofbe
the
Based
on the
distance
from
the the
BS
and
the the
initial
energy
known,
the
lifetime
of the
lated.
Furthermore,
in accordance
with
2,initial
the
ratio
of high
energy
nodes
to
nodes
closer
to the
and
the
farthest
nodesininterms
terms
ofnumber
number
of rounds
calculated.
nodes
closer
the
BSBS
and
the
farthest
of
of
can
be
calcudeployed
astothe
distance
from
the BSnodes
increases
has been
determined,
andcan
thebe
results
are
Furthermore,
in accordance
Lemma
2, from
the2,ratio
of high
nodes
to be deployed
lated.
Furthermore,
in18,
accordance
with
Lemma
the
ratio
of energy
high for
energy
nodes
toofbethe
presented
in Figure
whichwith
presents
data
distant
clusters
the majority
as
the
distance
from
the
BS
increases
has
been
determined,
and
the
results
are
presented
deployed
the distance from the BS increases has been determined, and the results are in
networkas
lifetime.
Figure
18,
which presents
data
from distant
clusters
for the
majority
networkoflifetime.
presented in Figure
18, which
presents
data from
distant
clusters
for of
thethe
majority
the
network lifetime.

Figure 18. Placement of alive nodes when the count is less than 10 with incremental distribution of
Figure 18. Placement of alive nodes when the count is less than 10 with incremental distribution of
high
energy
nodes.
high
energy
nodes.
Figure 18. Placement of alive nodes when the count is less than 10 with incremental distribution of
Compared to the result of uniform distribution of high energy nodes as shown in
Compared
high energy
nodes. to the result of uniform distribution of high energy nodes as shown in

Figure 17, the induction of high energy nodes in an increasing manner shows promising
Figure 17, the induction of high energy nodes in an increasing manner shows promising
results, and the base station is able to receive data from a larger area rather than only from
Compared
the station
result of
uniform
distribution
of high
energy
nodes than
as shown
in
results,
and thetobase
is able
to receive
data from
a larger
area rather
only from
the nearby region, as shown in Figure 18, for a prolonged period of time. This assists in
Figure
17, theregion,
induction
of highinenergy
increasing
manner
showsThis
promising
the nearby
as shown
Figurenodes
18, forinaan
prolonged
period
of time.
assists in
making practical decisions that are much more reliable than decisions made solely on the
results,
and
the basedecisions
station isthat
ableare
to receive
data reliable
from a larger
area rather
thansolely
only from
making
practical
much more
than decisions
made
on the
basis of nearby region cluster heads.
the
nearby
region,region
as shown
in heads.
Figure 18, for a prolonged period of time. This assists in
basis
of nearby
cluster
The simulation results depicted in Figure 19, also shows that the proposed FEHCA,
makingThe
practical
decisions
that
are much
more
decisions
made solely FEHCA,
on the
results
depicted
Figurereliable
19,variations
alsothan
shows
thattothe
with thesimulation
help of controlled
energy in
dissipation
due
(a)proposed
optimal number of
basis
of
nearby
region
cluster
heads.
with
the selection,
help of controlled
dissipation
variations
due (c)
to (a)
optimal
number ofby
cluster
(b) betterenergy
positioning
of cluster
heads and
energy
conservation
The simulation
results
in Figure
19, also
shows
proposed
FEHCA,by
cluster
selection, (b)
betterdepicted
positioning
of cluster
heads
andthat
(c) the
energy
conservation
with
the help
controlled
energy
dissipation
variations
optimal
number
ofin
delaying
theofnew
cluster head
election
procedure
in thedue
casetoof(a)CH
failures,
helped
cluster
selection,
positioning
of clustertoheads
andfor
(c)the
energy
almost
doubling(b)
thebetter
performance
as compared
LEACH
sameconservation
parameters. by
delaying the new cluster head election procedure in the case of CH failures, helped in
almost doubling the performance as compared to LEACH for the same parameters.

Energies 2021, 14, 3935

19 of 21

Energies 2021, 14, x FOR PEER REVIEW
20 of 22
Energies 2021, 14, x FOR PEER REVIEW
20 of in
22
delaying the new cluster head election procedure in the case of CH failures, helped

almost doubling the performance as compared to LEACH for the same parameters.

Figure 19. Performance of FEHCA and LEACH in terms of operational nodes per round when BS
Figure 19. Performance of FEHCA
LEACH
FEHCA and
and
LEACH in
in terms
terms of
of operational
operationalnodes
nodesper
perround
roundwhen
whenBS
BSis
is positioned
outside the deployment
area.
positioned
outside
thethe
deployment
area.
is positioned
outside
deployment
area.

As shown in Figure 19, the proposed algorithm has been tested with high energy
As shown
ininFigure
19,19,
thethe
proposed
algorithm
has been
testedtested
with high
nodes
shown
Figure
proposed
algorithm
has been
withenergy
high distribenergy
nodesAsthat
are uniformly
distributed
(FEHCA:
H_energy_UD)
and incrementally
that
are
uniformly
distributed
(FEHCA:
H_energy_UD)
and incrementally
distributed
nodes
that
are uniformly
distributed
(FEHCA:
H_energy_UD)
and incrementally
distributed
(FEHCA:
H_energy_ID).
(FEHCA:
H_energy_ID).
uted When
(FEHCA:
H_energy_ID).
comparing FEHCA
and
variants to
LEACH, Figure
Figure 20
20 shows
shows the
the energy
energy
When
FEHCA
and its
its
to
When comparing
comparing
FEHCA
and
its variants
variants
to LEACH,
LEACH,
Figure
20 shows
the case
energy
consumption
variations
per
transmission,
which
are
again
minimised
in
the
of
consumption
variations
per
transmission,
which
are again
minimised
in the case
of FEHCA
consumption
variations
per
transmission,
which
are
again
minimised
in
the
case
of
FEHCA
and
its
variants.
and
its variants.
FEHCA
and its variants.

Figure 20. Energy dissipation per round in LEACH and FEHCA when BS is positioned outside the
Figure 20. Energy
area. dissipation per round in LEACH and FEHCA when BS is positioned outside the
deployment
deployment area.

6. Conclusions

6. Conclusions
6. Conclusions
Energy conservation and fault tolerance are two major aspects when it comes to wire-

Energy conservation and fault tolerance are two major aspects when it comes to wireless sensor
networks.
This paper
presents
aare
centralised
clustering
mechanism
with
an
Energynetworks.
conservation
fault
tolerance
two major
aspectsmechanism
when
it comes
wireless sensor
Thisand
paper
presents
a centralised
clustering
withtoan
enenergy-efficient
data
dissemination
scheme
that
can
cope
with
a
certain
number
of
faulty
less sensor networks.
This paper presents
centralised
mechanism
with
energy-efficient
data dissemination
scheme athat
can copeclustering
with a certain
number
of an
faulty
cluster
heads. We
simulated
the proposed
Fault-tolerant
Energy-efficient
Hierarchical
Clusergy-efficient
data
dissemination
scheme
that
can
cope
with
a
certain
number
of
faulty
cluster heads. We simulated the proposed Fault-tolerant Energy-efficient Hierarchical
tering
(FEHCA)
for the scenarios
with
the base station
inside as well
as outside
clusterAlgorithm
heads.
We
simulated
Fault-tolerant
Energy-efficient
Hierarchical
Clustering
Algorithm
(FEHCA)
forproposed
the scenarios
with the base
station inside
as well as
the
monitored
area and(FEHCA)
found thefor
results
encouraging.
The
energy
consumption
perwell
transClustering
Algorithm
the
scenarios
with
the
base
station
inside
as
as
outside the monitored area and found the results encouraging. The energy consumption
mission
wasmonitored
much better
as compared
tothe
LEACH.
The
proposed FEHCA
demonstrated,
on
outside
the
area
and
found
results
encouraging.
The
energy
consumption
per transmission was much better as compared to LEACH. The proposed FEHCA demonaverage,
a 70 percent
increase
in network
performance
in terms
of the number
of demonrounds
per transmission
wasa much
better
as compared
to LEACH.
The proposed
FEHCA
strated,
on average,
70 percent
increase
in network
performance
in terms
of the number
as
compared
to
LEACH
when
the
base
station
was
positioned
inside
the
deployment.
strated,
onas
average,
a 70 to
percent
increase
network
performance
in terms of
the number
of
rounds
compared
LEACH
wheninthe
base station
was positioned
inside
the deFEHCA
surpassed
LEACH
in keeping
mostthe
of base
the nodes
alive
forpositioned
the majority
of the
of
rounds
as
compared
to
LEACH
when
station
was
inside
thetime,
deployment. FEHCA surpassed LEACH in keeping most of the nodes alive for the majority
unlike
many
well-known
proposed
schemes
with most
the proper
energy
management;
in fact,
ployment.
FEHCA
surpassed
LEACH
in
keeping
of
the
nodes
alive
for
the
majority
of the time, unlike many well-known proposed schemes with the proper energy manageof the in
time,
unlike
many
well-known
proposed
proper
energy
ment;
fact,
FEHCA
lasted
for 50 percent
moreschemes
rounds with
than the
LEACH
with
moremanagethan 90
ment; inoffact,
FEHCA
for 50 percent
morewas
rounds
LEACH
with
more than 90
percent
nodes
alive.lasted
The proposed
algorithm
also than
compared
with
ESO-LEACH
in
percent of nodes alive. The proposed algorithm was also compared with ESO-LEACH in

Energies 2021, 14, 3935

20 of 21

FEHCA lasted for 50 percent more rounds than LEACH with more than 90 percent of nodes
alive. The proposed algorithm was also compared with ESO-LEACH in terms of common
parameters and it succeeded in keeping more than 90 percent of the nodes alive for more
than 80 percent of the network lifetime, as compared to ESO-LEACH, where almost 50% of
the network was down within approximately 40% of the network lifetime. The algorithm
also doubled the communication rounds as compared to LEACH in the case of the base
station being placed far away from the deployment. Moreover, with the induction of
high energy nodes in an increasing manner in each cluster as per the increasing distance
from the base station in accordance with Lemma 2, we observed extended coverage for a
prolonged period of time, with the last few sensing nodes left from the entire area to be
monitored. FEHCA is also capable of handling lost packets in the case of faulty cluster
heads. However, for fault tolerance, FEHCA considers only permanent failures of CHs. In
the future, we will attempt to introduce multi-hopping in FEHCA in order to minimise
energy consumption and prolong the network lifetime.
Author Contributions: Conceptualization, A.C. and S.K.; Formal analysis, A.C.; Investigation, A.C.
and S.G.; Methodology, A.C. and S.K.; Project administration, S.K.; Supervision, S.K.; Validation, A.C.
and S.G.; Visualization, A.C.; Writing—original draft, A.C.; Writing—review & editing, S.K., S.G.,
M.G. and A.M. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.

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