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Expert Systems With Applications 211 (2023) 118588

Available online 19 August 2022

0957-4174/© 2022 Elsevier Ltd. All rights reserved.

Contents lists available at ScienceDirect

Expert Systems With Applications

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

A deep learning approach to predict the number of 𝑘-barriers for intrusion

detection over a circular region using wireless sensor networks

Abhilash Singh a, J. Amutha b, Jaiprakash Nagar c, Sandeep Sharma d,∗

aFluvial Geomorphology and Remote Sensing Laboratory, Indian Institute of Science Education and Research Bhopal, 462066, India

bUniversity School of ICT, Gautam Buddha University, Greater Noida, 201312, India

cSubir Chowdhury School of Quality and Reliability, Indian Institute of Technology Kharagpur, 721302, India

dDepartment of Electronics Engineering, Madhav Institute of Technology and Science, Gwalior, Madhya Pradesh, 474005, India

ARTICLE INFO

Keywords:

WSNs

Binary sensing model

Gaussian distribution

Uniform distribution

Barrier coverage

Deep learning

ABSTRACT

Wireless Sensor Networks (WSNs) is a promising technology with enormous applications in almost every walk

of life. One of the crucial applications of WSNs is intrusion detection and surveillance at border areas and in

the defence establishments. The border areas are stretched over hundreds to thousands of miles, hence, it is

not possible to patrol the entire border region. As a result, an enemy may enter from any point absence of

surveillance and cause the loss of lives or destroy the military establishments. WSNs can be a feasible solution

for the problem of intrusion detection and surveillance at the border areas. Detection of an enemy at the border

areas and nearby critical areas such as military cantonments is a time-sensitive task as a delay of a few seconds

may have disastrous consequences. Therefore, it becomes imperative to design systems that can identify and

detect the enemy as soon as it comes within the range of the deployed system. In this paper, we have proposed

a deep learning architecture based on a fully connected feed-forward Artificial Neural Network (ANN) for the

accurate prediction of the number of 𝑘-barriers for fast intrusion detection and prevention. We have trained

and evaluated the feed-forward ANN model using four potential features, namely area of the circular region,

sensing range of sensors, transmission range of sensors, and number of sensor for Gaussian and uniform sensor

distribution. These features are extracted through Monte Carlo simulation. In doing so, we found that the

model accurately predicts the number of 𝑘-barriers for both Gaussian and uniform sensor distribution with

correlation coefficient (R = 0.78) and Root Mean Square Error (RMSE = 41.15) for the former and R = 0.79

and RMSE = 48.36 for the latter. Further, the proposed approach outperforms the other benchmark algorithms

in terms of accuracy and computational time complexity.

1. Introduction

The unquenchable thirst of people for political and military power

is compelling them to extend their boundaries and grab other people’s

natural resources. In order to achieve this goal, they may try different

techniques such as gaining information about the military establish-

ments, the number of military personnel at a given place, regions of

natural resources, and the vulnerabilities of authorities that they can

exploit. In addition, illegal immigration, smuggling of drugs, and other

banned commodities across the boundaries are immediate concerns

that must be dealt with immediately. Therefore, it is crucial to identify

an intruder or an unauthorised activity accurately in a timely manner

as they all are time-sensitive issues that may result in havoc if not

prevented in time. Furthermore, encroachment in the border areas and

∗Corresponding author.

E-mail addresses: sabhilash@iiserb.ac.in (A. Singh), roniamutha@gmail.com (J. Amutha), jpnagar@iitkgp.ac.in (J. Nagar), sandeepsvce@mitsgwalior.in

(S. Sharma).

unauthorised entry into the prohibited regions is a serious issue making

border surveillance mandatory.

It is a well-known fact that most real-life problems can be solved

with the help of suitable technologies. Fortunately, WSNs are widely

used and is a popular technology that can resolve the concerned

issue (Huang et al.,2018;Keung, Li, & Zhang,2012;Singh, Sharma and

Singh,2021;Singh, Sharma, Singh, & Kumar,2019). WSNs are widely

deployed for various military applications such as intrusion detection in

border areas, combat monitoring, an unauthorised access to prohibited

areas, land mines detection, battlefield surveillance, reconnaissance,

and so on (Amutha, Sharma, & Nagar,2020;Kandris, Nakas, Vomvas,

& Koulouras,2020;Sharma & Nagar,2020;Si, Ma, Tao, Fu, & Shu,

2020).

https://doi.org/10.1016/j.eswa.2022.118588

Received 1 July 2021; Received in revised form 7 August 2022; Accepted 13 August 2022

Expert Systems With Applications 211 (2023) 118588

2

A. Singh et al.

Researchers have proposed various border surveillance and intru-

sion detection techniques using WSNs (Amutha, Nagar and Sharma,

2021;Arjun, Indukala, & Menon,2019;Aseeri, Ahmed, Shakib, Ghor-

bel, & Shaman,2017;Benahmed & Benahmed,2019;Gavel, Raghu-

vanshi, & Tiwari,2021;Karanja & Badru,2021;Karthick, Prabaharan,

& Selvaprasanth,2019;Mostafaei, Chowdhury, & Obaidat,2018). The

proposed techniques use either simulations or Internet of Things (IoT)

methods to validate their techniques. However, simulation methods for

the validation of proposed techniques have high time complexity, i.e.,

the time taken to obtain a single output at a given value of sensor and

sensing range is in several hours. Also, IoT devices are very expensive

and require a huge financial investment. The high time complexity

and financial issues can be minimised to a negligible level using ma-

chine learning approaches to validate and predict the performance

of WSNs before their actual deployment in a given region (Kotiyal,

Singh, Sharma, Nagar, & Lee,2021;Mishra, Varadharajan, Tupakula,

& Pilli,2018;Singh, Nagar, Sharma and Kotiyal,2021). However,

the accurate and timely detection and prevention of intrusion through

machine learning approaches is still an ill-posed problem that has been

insufficiently investigated. To address this issue, we propose a deep

learning architecture for accurate and timely intrusion detection and

prevention.

In this paper, we proposed a fully connected feed-forward ANN

architecture to predict the number of 𝑘-barriers for accurate intrusion

detection and prevention in WSNs using potential features. We have

extracted four features, namely area of the circular region, sensing

range of sensors, the transmission range of sensors, and the number

of sensors through the Monte Carlo simulation approach. Afterward,

we used these features to train and evaluate the performance of the

feed-forward ANN model using R, RMSE, bias, and computational time

complexity as performance metrics.

Further, the rest of the paper is divided into seven sections. In

Section 2, we have discussed the related works. In Section 3, we have

presented the system model. In this section, we have discussed the

sensor distribution models and the sensing model. In Section 4, we have

discussed the simulation experiment. In Section 5, we have discussed

the machine learning model. In this section, we have discussed the

feature importance, feature sensitivity, and model setup. In Section 6,

we have presented the results. Lastly, in Sections 7and 8, we have

presented the discussion and conclusion of this study, respectively.

2. Related works

Deep learning is a subset of machine learning algorithms which

has been applied for intrusion detection using WSNs (Amutha, Sharma

and Sharma,2021;Lee et al.,2021;Singh, Amutha, Nagar, Sharma, &

Lee,2022a,2022b;Sood, Prakash, Sharma, Singh, & Choubey,2022).

It is also employed for pattern matching and network security where

it identifies the malicious activities occurring in the network and is

termed as Network Intrusion Detection System (NIDS). The accuracy of

the NIDS can be improved with the help of Recurrent Neural Network

IDS (RNNIDS) (Sohi, Seifert, & Ganji,2021) which is capable of identi-

fying the complex patterns resulting in an enhanced intrusion detection

rate. Authors in Yin, Zhu, Fei, and He (2017) have proposed an RNNs

approach which examines the system behaviour, type of intrusion, and

the impact of intrusion on the intrusion detection accuracy with the

help of learning rate and the number of neurons. The major limitation

of RNNIDS is that it fails to minimise the false positives; thus, not

able to achieve the maximum detection rate. This issue has been dealt

with the help of a deep learning architecture that combines classifiers

with Convolution Neural Networks (CNN) having Long Short Term

Memory (LSTM), thus, offering maximum detection rate (Pektaş &

Acarman,2019). Here, the CNN acquires spatial information, and the

LSTM acquires temporal features from the received packets in the

network. The optimal parameters in the feature space are obtained by

employing an estimator known as tree-structured Parzen. This method

focuses on generating flow-based statistical features rather than data-

set features. Although the abnormal traffic can be detected with an

accuracy rate of 99.09% and a false alarm rate of 0.0227, it fails to

compute the computational time complexity of flow-based intrusion

detection method.

A deep learning approach that uses an auto-encoder strategy ex-

hibits an improvement in the time complexity by 18.12% (Abbasi,

Bashir, Qureshi, ul Islam, & Jeon,2021). This strategy uses multi-

layer perception to replace the detection of hierarchical features and

unsupervised feature learning. Thus, it enhances the pattern matching

mechanism for intrusion detection with the help of Deep Learning-

based Feature Extraction (DLFE), which is an Optimisation of Pattern

Matching (OPM) approaches. Another approach called Scale-Hybrid-

IDS-AlertNet (SHIA) (Vinayakumar et al.,2019) performs data com-

putation at the network and the host-level for the intrusion detection

and delivers the relevant alert notifications to the controller auto-

matically. A Deep Neural Network (DNN) can render an effective

IDS that can detect and classify the intruders crossing the Region of

Interest (RoI). Here, the performance of SHIA is measured in terms

of multi-class classification of the DNN, accuracy, True Positive Rate

(TPR), and False-Positive Rate (FPR). Although SHIA is scalable and

shows improved performance in handling large data-sets of real-time

systems, it does not compute the number of 𝑘-barriers and incurs high

computational costs.

Despite having a high computational complexity, ensemble-based

techniques have a high level of accuracy as compared to the base mod-

els. An ensemble based DNN framework for the continuous analysis of

intrusion detection along with the ability to learn hierarchical data-sets

automatically has been proposed in Folino, Folino, Guarascio, Pisani,

and Pontieri (2021). Here, a log-stream of an intrusion detection system

maintains an ensemble that contains classifiers trained on discrete

chunks of the data-set instance and a combiner model. The combiner

model performs reasoning on the instance parameters and classifier

predictions; after that, the efficacy is computed in terms of data scarcity

and accuracy that allows to analyse the diverse ensemble aggregation

strategies. This ensemble approach utilises the unstructured data that

does not comply with the transfer learning strategies and is found in

the log-stream of NIDS.

Barrier coverage using WSNs plays a crucial role in the detection

of an unauthorised personnel or object trying to enter the prohibited

region. Barriers are formed by the sensors deployed over the entire

given RoI. The early depletion of sensor’s energy leads to the failure of

the sensors causing blind spots in the barriers. To overcome this issue,

authors in Saraereh, Ali, Al-Tarawneh, and Khan (2021) have pro-

posed a set-based max-flow procedure for the re-deployment of mobile

sensors. This method determines the vulnerable locations and deploys

the mobile sensors which strengthens and prolongs the longevity of

the barrier. Although the algorithm exhibits higher efficiency in terms

of the computation time, it fails to predict the number of 𝑘-barriers

for the IDS. In Nagar and Sharma (2018), the authors have derived

an analytical closed-form expression using mobile sensors for the 𝑘-

barrier coverage probability of a WSN. Here, they have calculated

the total area covered by an intruder travelling at a given angle to

cross the RoI, Then, this total area is utilised to obtain the closed-

form expression for the 𝑘-barrier coverage probability of the WSN. In

another work presented in Singh, Nagar et al. (2021), the authors have

employed three machine learning approaches, namely Gaussian Process

Regression (GPR), Scaling GPR (S-GPR), and Center mean GPR (C-GPR)

to predict the 𝑘-barrier coverage probability of a WSN. The proposed

GPR technique quickly detects and prevents any intrusion from taking

place at any location in the RoI. A three-level hierarchy scheme to

detect a mobile intruder in distributed WSNs is proposed in Sharma

and Chauhan (2020) improving the precision of intrusion detection. To

maximise the probability of intrusion detection, the authors have used

diverse sensing techniques, 𝑘-mean clustering, and the Likelihood Ratio

Test (LRT) methods. The LRT fusion rule used in this scheme is efficient

Expert Systems With Applications 211 (2023) 118588

3

A. Singh et al.

Fig. 1. Illustration of (a) Gaussian sensor distribution and (b) Uniform sensor distribution. The blue-filled circles represent sensors.

in terms of metrics like detection probability and false alarm rate at a

given number of sensors and the speed of the mobile intruder.

The algorithms and strategies proposed in the literature fail to

accurately predict the number of 𝑘-barriers for intrusion detection.

Hence, the overall aim of this study is to overcome the limitation

of the previous studies in terms of accuracy and computational time

complexity using a deep learning approach.

3. System model

This section briefly discusses sensor distribution models, sensing

range model, and the performance metric, namely the number of

𝑘-barriers.

3.1. Sensor distribution model

The choice of sensor distribution model depends on the required

application. In this work, we consider two-sensor distribution models;

(i) Gaussian distribution model and (ii) uniformly distribution model.

3.1.1. Gaussian sensor distribution model

In this model, a finite number of sensors are installed in a finite

circular region of radius 𝑅meters following a 2D Gaussian distribution,

also known as a normal distribution (Fig. 1a). Thus, the Probability

Density Function (PDF) for a location (𝑥, 𝑦)to be installed with a sensor

is given by Wang, Xie, and Agrawal (2008)

𝑓(𝑥, 𝑦) = 1

2𝜋𝜎𝑥𝜎𝑦

𝑒

−( (𝑥−𝑥𝑐)2

2𝜎2

𝑥

+(𝑦−𝑦𝑐)2

2𝜎2

𝑦

)(1)

where (𝑥𝑐, 𝑦𝑐)represents the centre of the circular region, 𝜎𝑥and 𝜎𝑦

are the standard deviations of 𝑥and 𝑦location coordinates respec-

tively. Furthermore, the location of a sensor inside the circular region

represented by (𝛾, 𝜙)can also be modelled with the help of position

coordinates (𝑥, 𝑦)if

𝑓(𝑥, 𝑦) ∶ √(𝑥−𝑥𝑐)2+ (𝑦−𝑦𝑐)2≤𝑅=𝑓(𝛾, 𝜙) ∶ 𝛾≤𝑅(2)

3.1.2. Uniform sensor distribution model

In this model, a finite number of sensors are distributed uniformly

and randomly inside a finite circular region (denoted by ℜ) of radius

𝑅meters (Fig. 1b). The position of a random sensor within the circular

region is represented by 𝑃𝑐= (𝛾, 𝜙), where, 𝛾∈ [0, 𝑅], denotes the

distance of the sensor from the centre of the circular region, and

𝜙∈ [0,2𝜋], denotes the angle between the 𝑥-axis and the line that

passes through the sensor location. The resulting sensor distribution

probability density function is given by

𝑓𝑝(ℜ) = {1, 𝑖𝑓 𝑃𝑐∈ℜ

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (3)

Furthermore, the probability that a sensor is located at an arbitrary

position 𝑃𝑐= (𝛾, 𝜙)inside the circular region is given by

𝑓(𝑃𝑐) = 1

𝜋𝑅2(4)

3.2. Binary sensing range model

The binary sensing range model is one of the most widely employed

sensing range models for estimating the performance of WSNs (Laran-

jeira & Rodrigues,2014;Nagar, Chaturvedi, & Soh,2020). A point 𝑖

denoted by 𝑃𝑖(𝑥𝑖, 𝑦𝑖)inside the 2D circular region will be covered by a

sensor 𝑗located at 𝑆𝑗(𝑥𝑗, 𝑦𝑗), if the Euclidean distance of point 𝑖from

the sensor 𝑗is less than or equal to the sensing range 𝑟𝑠of the sensor.

Mathematically, it can be represented as

𝑃(𝑆𝑖) = {1, 𝑖𝑓 𝑑 (𝑆𝑖, 𝑃𝑖)≤𝑟s

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (5)

3.3. Coverage graph

Coverage measures how well sensors monitor the RoI in which they

are deployed. The 𝑘-coverage ensures that each point in the target RoI

is covered by at least 𝑘distinct sensors, where 𝑘is a positive integer

having a typical value greater than one. A connected 𝑘-coverage is

achieved when each point in the RoI is covered by at least 𝑘distinct

sensors and each sensor is able to communicate with each other. An

optimal 𝑘-coverage of the network is obtained when each point within

the RoI is covered by at least 𝑘distinct sensor without any overlapping

area. A Coverage Graph (CG) is denoted by CG(N) =(V, E), where V

denotes the number of vertices and Edenotes the number of edges.

Here, each vertex represents a sensor and an edge represents a link

between any two sensors if and only if they fall within the coverage of

each other. To construct a CG for a circular RoI, we have built sensor-

disjoint cycles within the entire RoI. A WSN rendering two-barrier

coverage inside a circular RoI is shown in Fig. 2a, and its respective

CG is depicted in Fig. 2b.

3.4. Barrier and barrier path

A barrier along the boundaries of a circular RoI can be constructed

by taking the union of distinct sensor coverage. Any arbitrary point

from where an intruder may enter the RoI is known as the point of

Expert Systems With Applications 211 (2023) 118588

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A. Singh et al.

Fig. 2. Illustration of (a) 2-Barrier coverage and (b) Coverage graph.

Table 1

Simulation parameters.

Parameters Values

Simulator NS-2.35

Radius of the circular region (R) 40 to 127 m

Number of sensors (N) 100 to 400

Sensing range (Rs) 15 to 40 m

Transmission range (Rtx) 30 to 80 m

Mac type IEEE 802.11

Sensor’s deployment type (a) Gaussian Distribution

(b) Uniform Distribution

Sensing model Binary sensing model

intrusion and any possible path that an intruder may follow to reach the

target point is called an intrusion path. In order to provide a guaranteed

barrier coverage, there must exist at least one barrier for every possible

intrusion path. In this way, any intrusion attempt can be identified and

prevented in a timely manner. The maximum number of barrier paths

𝐵𝑃𝑚𝑎𝑥 that can be constructed for a given intrusion path without any

overlapping coverage is given by Eq. (6).

𝐵𝑃𝑚𝑎𝑥 =⌊𝑁

𝑘⌋(6)

where Nrepresents the total number of sensors and 𝑘represents the

number of sensors required to ensure 𝑘barrier coverage for a possible

intrusion path.

4. Simulation experiment

We have obtained the simulation results using network simulator

NS-2.35, one of the widely used network simulators to obtain the per-

formance metrics of WSNs. Table 1 shows different network parameters

and their values used to get the simulation results for the number

of 𝑘-barrier paths. Here, we have assumed that any two sensors can

communicate with each other iff the transmission range of sensors (Rtx)

is at least twice the sensing range of sensors (Rs), i.e.,Rtx ≥2Rs.

5. Machine learning model

Machine learning algorithms are broadly classified into supervised

and unsupervised learning algorithms. In supervised machine learning,

we work with labelled data sets. It is mainly used to solve either

regression or classification problems. In contrast, unsupervised machine

learning algorithms deal with unlabelled data sets and are mainly used

to perform clustering and dimension reduction tasks.

In this study, our objective is to assess the potential of fully con-

nected feed-forward ANN to map the number of 𝑘-barriers using rele-

vant features. To evaluate the relevancy of the selected features, we

have calculated the feature importance score and performed feature

sensitivity analysis.

5.1. Feature importance

This study used the area of the RoI, sensing range, transmission

range, and the number of sensors as the potential features and 𝑘-

barriers as the predictand. In machine learning, the selection of input

features significantly affects its performance (Singh, Kotiyal, Sharma,

Nagar, & Lee,2020). Hence, before training the machine learning

model, we have evaluated the relative importance of each selected

feature on the predictand. In doing so, we opted regression tree ensem-

ble technique (Torres-Barrán, Alonso, & Dorronsoro,2019). We have

first trained a regression tree ensemble model by boosting hundred

regression trees using the Least Squares gradient Boosting (LSBoost)

ensemble aggregation method (i.e., 𝑟=100), each with a learning rate

of one (i.e., 𝛼=1), and the classical decision tree (i.e., decision stumps)

has been considered as a weak learner. The LBoost algorithm trains

one weak learner at a time and also detects its weak points. Based on

such weak points, it generates a new weak learner (li) and evaluates

its weight (i.e., 𝑤𝑖). According to (Eq. (7)), the algorithm improves the

current model (𝑀𝑖) by emphasising on the prior weak learner’s (𝑀𝑖−1)

weak point. After it has been trained, it integrates the weak learner

into the existing model, and creates a single strong learner (𝑀𝑟,i.e., an

ensemble of weak learners) iteratively.

𝑀𝑖=𝑀𝑖−1 +𝛼 . 𝑤𝑖. 𝑙𝑖(𝑖= 1,2,3,…, 𝑟)(7)

In addition, we determine the relative feature importance score by

evaluating the overall variations in the node risk (𝛥𝑅) due to the split

on each feature, and then normalising it by the total number of branch

nodes (𝑅𝑏𝑛). Mathematically, it is represented as in (Eq. (8));

𝛥𝑅 =

𝑅𝑝− (𝑅𝑐ℎ1+𝑅𝑐ℎ2)

𝑅𝑏𝑛

(8)

where 𝑅𝑝denotes the node risk of the parent and 𝑅𝑐ℎ1&𝑅𝑐ℎ2denotes

the node risk of two children. The node risk at an individual node (Ri)

is mathematically represented as in (Eq. (9));

𝑅𝑖=𝑃𝑖. 𝐸𝑖(9)

where 𝑃𝑖denotes the probability of node iand 𝐸𝑖denotes the mean

square error of the 𝑖𝑡ℎ node.

5.2. Feature sensitivity

Estimating the feature importance score only tells us about the

relative importance of each feature. However, it does not convey

how the features are associated with the predictand, i.e., whether the

predictand value increases with feature (positive impact) or decreases

with features (negative impact). To evaluate this, we have performed

the sensitivity analysis of the features using the Partial Dependence Plot

(PDP) (Friedman,2001;Singh, Nagar et al.,2021). PDP measures the

average effect of a single or more features by marginalising the effect of

all other features taken into consideration. We considered the combined

Expert Systems With Applications 211 (2023) 118588

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A. Singh et al.

Fig. 3. Structure of the fully connected feed-forward ANN model having four inputs, two hidden layers having 20 neurons each, and one output (i.e., 4:20:20:1).

impact of two features simultaneously from the input feature set (i.e.,

𝜗) on the predictand by marginalising the impact of the remaining

features. To do so, a subset 𝜗sand a complimentary set (𝜗c) of 𝜗sare

extracted from the feature set (𝜗= {k1, k2, .. . , kn}) where, nrepresents

the total features. Using (Eq. (10)), we can compute any prediction on

𝜗.

𝑓(𝜗) = 𝑓(𝜗𝑠, 𝜗𝑐)(10)

The partial dependence of the feature in 𝜗scan be determined by

calculating the expectation (Ec) of Eq. (11).

𝑓𝑠(𝜗𝑠) = 𝐸𝑐[𝑓(𝜗𝑠, 𝜗𝑐)]

=∫𝑓(𝜗𝑠, 𝜗𝑐). 𝜌𝑐(𝜗𝑐). 𝑑𝜗𝑐(11)

where 𝜌𝑐(𝜗𝑐)indicates the marginal probability of 𝜗𝑐, which is repre-

sented in Eq. (12).

𝜌𝑐(𝜗𝑐) ≈ ∫𝑝(𝜗𝑠, 𝜗𝑐). 𝑑𝜗𝑠(12)

Then, the partial dependency of the feature in 𝜗𝑠can be determined by

:

𝑓𝑠(𝜗𝑠) ≈ 1

𝑇

𝑇

∑

𝑖=1

𝑓(𝜗𝑠, 𝜗𝑐

𝑖)(13)

where 𝑇represents the total number of observations.

5.3. Model setup

In this subsection, we have discussed the architecture of the fully

connected feed-forward ANN including its working, activation function,

and the training algorithm.

5.3.1. Feed forward ANN

A Neural Network (NN) is a model which mimics the oversim-

plification of the brain performance that operates under a particular

specific function of interest. The primary objective of the NN model is

to discover a mapping function (f) that predicts a target function (f*)

through training the NN using labelled training data sets. During the

training phase, the network learns the range of parameters from the

training data. Once we trained the model, we need to validate and test

its performance using the unseen data.

A network can be subdivided into basic information-processing ele-

ments called neurons, which are the building blocks of ANN. Layers are

groups of neurons, and the network is comprised of interconnections

between these layers. There are diverse perspectives of linking layers

together that lead to several other forms of NNs like feed-forward

neural networks, recurrent neural networks, and convolutional neural

networks. In general, the optimisation problem of a neural network can

be represented by Eq. (14), where lrepresents the loss function, and W

is the learnable parameter. The main objective is to learn Wso that the

variance between the output of fcan be minimised, when the input x0

and the actual output yare provided.

𝑚𝑖𝑛 𝑙(𝑓(𝑥0, 𝑊 ), 𝑦)(14)

In this study, we have trained a fully connected feed-forward ANN.

It is a category of NN formed by organising neurons so that all neurons

in each layer are linked to every other neuron in the adjacent forward

layer. The data flows mainly in one direction, i.e., forward, from the

input neurons to the output, passing through the hidden layers (if any).

Since each neuron has one activation function, the total activation func-

tion for a layer equals the total output value. The training algorithm

utilises the output findings to calibrate the sensor connection weight

value (Moldovan, Caţaron, & Andonie,2020;Novickis, Justs, Ozols, &

Greit¯

ans,2020). Any continuous function can be approximated by a

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A. Singh et al.

feed-forward ANN with one hidden layer. However, the desired hidden

size might be high, making learning unfeasible. Feed-forward ANN is

well-suited for unstructured data, such as data that is not sequential or

time-dependent.

In this study, we structured a feed-forward ANN that consists of

two hidden layers and one output layer, as illustrated in Fig. 3. Each

hidden layers consist of twenty neurons. A common bias value is added

to each neuron in the hidden layers, which is followed by an activation

function.

5.3.2. Activation function

In feed-forward ANN, the activation function is one of the essential

key elements of the neuron (Duch & Jankowski,1999). It significantly

impacts the performance of the neural networks by modifying the

neuron output. The Universal Approximation Theorem states that a

feed-forward ANN with one hidden layer and an arbitrary sigmoidal

function with adequate sensors can estimate any continuous function

with no restrictions on the number of sensors or the size of the weights.

In this study, we have used the hyperbolic tangent sigmoid transfer

function at each layer because it is a bipolar sigmoid function that

has a positive response for a positive input and a negative response

for a negative input. Hence, it eliminates the problem of negative

responses for positive values. Further, as the complexity and non-

linear of the problems increases (when we increase the number of

sensors and the monitoring area in WSNs), the advantage of using the

hyperbolic tangent sigmoid transfer function becomes more apparent.

The mathematical model is expressed as:

𝑎=2

(1 + 𝑒(−2⋅𝑛))−1 (15)

This expression is mathematically equivalent to tanh(n). However,

the computational time complexity of Eq. (15) is lower than tanh(n).

5.3.3. Training algorithm

To minimise the error in the output, the values of weights and

biases need to be updated. This is done with the help of a backpropa-

gation training algorithm. In the backpropagation algorithm, the input

is transmitted to the hidden layer, which then perpetuates back the

sensitivity in order to minimise the error rate by updating the weights

and the bias during the process. This algorithm results in low conver-

gence, and in some cases, it also leads to over-fitting. To address these

issues, and for quick convergence without over-fitting, approaches like

Levenberg–Marquardt backpropagation (LM) and Bayesian Regular-

ization (BR) backpropagation, and Scaled Conjugate Gradient (SCG)

backpropagation have been developed. To minimise the sum of squares

at every iteration, LM utilises the conjugate gradient backpropagation

method. LM is used for curve fitting problems, while SCG is used for

pattern recognition problems. Bayesian regularization backpropagation

algorithm uses an objective function that incorporates the sum of

squared weights and the residual sum of squares in order to reduce

the prediction errors for attaining the desired model.

In this study, we have used the LM backpropagation algorithm. It is

a non-linear optimisation-based approach for training ANNs, by which

it uses second-order derivatives for improved convergence behaviour.

The LM algorithm offers the features of the steepest descent approach

along with the Gauss–Newton method, which provides an invertible

matrix, named Hessian matrix (H) which is shown in Eq. (16):

𝐻(𝑥) ≈ 𝐽𝑇(𝑥)𝐽(𝑥) + 𝜇𝐼 (16)

where, 𝜇represents the combination co-efficient, Jand Irepresents

the Jacobian and identity matrix respectively. The LM modification to

the Gauss–Newton algorithm (Hagan & Menhaj,1994) is represented

in Eq. (17):

𝛥𝑥 = [𝐽𝑇(𝑥)𝐽(𝑥) + 𝜇𝐼 ]−1𝐽𝑇(𝑥)𝑒(𝑥)(17)

The algorithm seems to be the steepest descent when the value of 𝜇

becomes high, whereas the algorithm is Gauss–Newton when the value

of 𝜇is minimal. The LM algorithm for the weight update rule (Mathew,

Griffin, Alamaniotis, Kanarachos, & Fitzpatrick,2018) is determined as

a function of Jacobian matrix and error vector (e), which is represented

in Eq. (18):

𝑤(𝑡+ 1) = 𝑤(𝑡)−(𝐽𝑇

𝑡𝐽𝑡+𝜇𝐼 )−1 +𝐽𝑡𝑒𝑡(18)

We have randomly divided (using the Mersenne Twister generator)

the complete data set (182 ×5) in a 55:15:30 ratio for training, vali-

dation, and testing of the feed-forward ANN algorithm. The complete

methodology is shown in Fig. 4.

6. Results

This section presents the results of feature importance analysis,

feature sensitivity analysis, and feed-forward ANN.

6.1. Feature importance of each features

Once we evaluated the feature importance of each feature for both

Gaussian and uniform sensor distribution, we plotted the relative im-

portance graph for both scenarios (Fig. 5). The higher the importance

score, the more important the feature is. We found that the relative

importance score of the sensing range, transmission range, and sensors

is the same and the maximum. In contrast, the area has the least relative

importance amongst all the features for both scenarios.

6.2. Feature sensitivity curve

To analyse the feature sensitivity, we have plotted the surface plot

of PDP considering two features at a time along with the corresponding

two-dimensional plot with an axis-aligned histogram representing the

distribution of the features. For four features, we have six possible

sensitivity plots. Again, we have plotted it for both scenarios i.e., for

Gaussian and uniform sensor distribution in Figs. 6 and 7, respectively.

For both scenarios, we observed that the area of the circular region

has a negative impact on the number of barriers. In contrast, sensing

range, transmission range, and the number of sensors positively impact

the number of barriers. In a nutshell, we observed a similar trend with

slight variation in the values for both scenarios.

6.3. Performance of the fully connected feed-forward ANN model

Once we trained the feed-forward ANN model for Gaussian and Uni-

form distribution scenarios, we evaluated its performance by plotting

a linear regression curve between the predicted and observed barriers.

We have used R, RMSE, and bias as the performance metrics. A high

value of R represents that the predicted values are well in accord with

the observed value. A low value of RMSE represents a more accurate

model. A positive value of bias shows overestimation, and a negative

value of bias shows underestimation. Afterward, we performed error

and residual analysis for a robust conclusion.

6.3.1. For Gaussian sensor distribution

To evaluate the performance of the trained feed-forward ANN for

Gaussian sensor distribution, we have reported the training, validation,

testing, and overall accuracy. For training accuracy, we fed the training

data set as input to the trained feed-forward ANN and evaluated its

performance. We found that the trained model work reasonably well on

the training data set with R =0.82, RMSE =43.38, and bias = −5.11

(Fig. 8a). The presence of a small negative bias indicates that the values

are slightly getting underestimated. Evaluating the model performance

using the test data results in bias study and hence its performance needs

to be evaluated using the unseen/new data sets. In doing so, we have

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Fig. 4. Flowchart of the methodology.

Fig. 5. Feature importance graph.

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Fig. 6. Partial dependency plot for circular region considering Gaussian sensor distribution.

Fig. 7. Partial dependency plot for circular region considering uniform sensor distribution.

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Fig. 8. Performance of the feed-forward ANN for Gaussian sensor distribution case (a) training accuracy, (b) validation accuracy, (c) testing accuracy, and (d) overall accuracy.

first validated the trained feed-forward ANN model through validation

data set (Fig. 8b). We found that the trained model performs well and

results in a good fit (with R =0.76, RMSE =34.79, and bias =3.99)

while tuning the hyper-parameters. Afterward, we used the test data

for unbiased evaluation of the trained model (Fig. 8c). We observed

that the trained model performed well on the test data (with R =0.76,

RMSE =29.86, and bias =17.31). The predicted value accord well

with the observed value with slight scattering. The presence of positive

bias represents that the values are slightly overestimated during the

testing phase. Finally, we combined all the data sets together (training,

validation, and testing) and fed it into the trained feed-forward ANN

model to calculate the model’s overall accuracy. We found that the

trained model performs reasonably well on the complete data sets with

R=0.78, RMSE =41.15, and bias =3.02 (Fig. 8d).

Further, to analyse the error distribution during the training, valida-

tion, and testing phase, we have performed error analysis and plotted

the combined error histogram using twenty bins (Fig. 9). The combined

error from the trained feed-forward ANN model ranges from −87.94

(leftmost bin) to 150.8 (rightmost bin) and follows a slightly right-

skewed Gaussian distribution. The peak of the distribution lies near

the zero error line indicating a more accurate model. The region left

to the zero error line indicates overestimated region, and the one on

the right represents an underestimated region. Overall, the number of

instances in the overestimated region is higher than the underestimated

region, results in the overestimation of predicted values by the trained

deep learning model. This statement is validated by the presence of a

positive bias of 3.02 (Fig. 8d).

Furthermore, to evaluate the appropriateness of the trained model,

we have performed the residual analysis and plotted the time series

plot of the test data along with the corresponding residual plot. We

have plotted the observed values (in blue) and predicted values (in

red) along with their 95% Confidence Interval (C.I). The dashed line

represents the RMSE value of the testing phase. The residuals are well

scattered and do not follows any specific pattern indicating a good fit

(Fig. 10).

6.3.2. For uniform sensor distribution

Similar to the Gaussian sensor distribution scenario, we have also

evaluated the performance of the deep learning model for uniform

sensor distribution. We reported the training, validation, testing, and

overall accuracy of the feed-forward ANN model that we trained for

uniform sensor distribution. For training accuracy, we have evaluated

the model over the training data sets. In doing so, we observed that the

model performs quite well over the training data sets (Fig. 11a). The

predicted values are close to the observed values (with R =0.79, RMSE

=55, and bias =3.65). However, the RMSE is high, and R is slightly

low as compared to the training accuracy of the Gaussian sensor distri-

bution. Afterward, we feed the validation data sets to the model input

to report the validation accuracy. The predicted values (while tuning

the hyper-parameters) are in agreement with the observed values with

R=0.81, RMSE =34.81, and bias =10.35 (Fig. 11b). For unbiased

evaluation, we have evaluated the trained model performance over the

test data set. We observed that the trained model performs well over

the test data with R =0.78, RMSE =34.58, and bias =19.89 (Fig. 11c).

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Fig. 9. Error analysis with error histogram with 20 bins for Gaussian sensor distribution case.

Fig. 10. Residual analysis of the feed-forward ANN output for Gaussian sensor distribution case.

Finally, we feed the combined data into the model to report the overall

accuracy.

We found that the trained model also performs well over the com-

plete data set with R =0.79, RMSE =48.36, and bias 9.55 (Fig. 11d).

Further, we perform the error analysis to understand the distribu-

tion of error in a uniform sensor distribution scenario. In doing so, we

plotted the combined error histogram using twenty bins (Fig. 12). We

observed a similar trend as for the Gaussian sensor distribution scenario

despite the high error range. The total error ranges from −111.1

(leftmost bin) to 169 (rightmost bin) and follows a slightly right-skewed

Gaussian distribution. Here also, the peak of the distribution lies near

the zero error line indicating an accurate model. The total number of

instances in the overestimated region is higher than the underestimated

region. Due to this, a positive bias is present in the model.

Furthermore, we have performed the residual analysis and plotted

the time series plot of observed–predicted values for the testing phase

along with the corresponding residual plot (Fig. 13). Here, the residuals

are well scattered and do not follow any particular path or pattern,

indicating that the linear plot is a good fit.

7. Discussion

This study uses fully connected feed-forward ANN to predict the

number of 𝑘-barriers for intrusion detection in WSNs. We trained two

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Fig. 11. Performance of the feed-forward ANN for uniform sensor distribution case (a) training accuracy, (b) validation accuracy, (c) testing accuracy, and (d) overall accuracy.

Fig. 12. Error analysis with error histogram with 20 bins for uniform sensor distribution case.

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Fig. 13. Residual analysis of the feed-forward ANN output for uniform sensor distribution case.

separate feed-forward ANN models for Gaussian and uniform sensor

distribution scenarios. We observed that the proposed architecture of

a fully connected feed-forward ANN model gives promising results for

both scenarios. Although the correlation coefficient value is nearly

equal for both scenarios, the RMSE and bias value for the Gaussian

sensor distribution scenario is better.

7.1. Comparing with different variant of feed-forward ANN

For an unbiased evaluation, we have generated different scenarios

of the feed-forward ANN model based on the number of hidden layers

used, ranging from shallow to deep feed-forward ANN model (Table 2).

To do so, we have selected six different scenarios corresponding to

1, 2, 3, 4, 5, and 10 hidden layers. A feed-forward ANN model with

more than ten hidden layers will result in high time complexity and

eventually not an optimal solution for intrusion detection, which is

a time-sensitive application. We have reported the training, valida-

tion, testing, and overall accuracy for all six scenarios. Based on the

overall performance, we have categorised the performance of each sce-

nario into poor, fair, and satisfactory. We found that the feed-forward

ANN with 2, 3, and 10 layers resulted in satisfactory performance.

Out of these three scenarios, feed-forward ANN with two layers (i.e.,

4:20:20:1) shows the best performance.

7.2. Comparison with the benchmark algorithms

Various other findings have been reported for high intrusion detec-

tion accuracy through the machine learning approach (Nancy et al.,

2020;Safaldin, Otair, & Abualigah,2021). Hence, any conclusion

based on comparing different scenarios of a single algorithm may

result in a biased conclusion. To ensure a fair evaluation of the pro-

posed approach, we have compared the results of feed-forward ANN

with the other benchmark algorithms using R, RMSE, and bias as the

performance metrics. We have selected Radial Basis Neural Network

(RBN), Exact Radial Basis Neural Network (ERBN), Recurrent Neu-

ral Network (RNN), LSTM, Boosting (Least-square boosting) Ensemble

Learning (EL), Bagging EL (Random Forest), Binary Decision Tree

(BDT), General Regression Neural Network (GRNN), Gaussian Process

Regression (GPR), and Support Vector Regression (SVR) as potential

benchmark algorithms because these algorithms are amongst best per-

forming algorithms in the black-box and explainable based machine

learning category (Belle & Papantonis,2021;Elias et al.,2020;Lin

et al.,2020;Lundberg et al.,2018;Mansor et al.,2020;Roscher, Bohn,

Duarte, & Garcke,2020;Singh, Gaurav, Rai and Beg,2021;Zhang,

Zhang, Ye, Fang, & Han,2020). On comparing, we found that the

feed-forward ANN outperforms all the benchmark algorithms in terms

of R, RMSE and bias (Table 3). Other than the feed-forward ANN,

SVR performs well and ranks second among the benchmark algorithms.

Interestingly, we found that some benchmark algorithms show a strong

correlation (i.e., high R value); however, they produce biased results.

The bias values are very high, indicating that these models strongly

overestimate the response variable.

7.3. Comparison of the computational time complexity

Further, we have also compared the performance of the algorithms

mentioned above in terms of computational efficiency. We have es-

timated and plotted the computational time complexity graph of all

the three algorithms for both scenarios (Fig. 14). We observed that

the feed-forward ANN algorithm exhibits the lowest, and the LSTM

exhibits the highest computational time complexity. Apart from this,

we have also plotted the time complexity of the Monte Carlo simulation

for three different scenarios. We have estimated the time-complexity

for sensors as 100, 200, and 300. We have kept the other features

constant (area ≈5000, sensing range =15, and transmission range =

30). We observed that the computation time-complexity of the Monte

Carlo simulation increases with the number of sensors. This shows the

efficacy and need of the proposed deep learning architecture to cut

down the computational cost during the network setup time.

8. Conclusion

This study presented a fully connected feed-forward ANN architec-

ture for the accurate mapping of the number of 𝑘-barriers for intrusion

detection using WSNs. In doing so, we have trained two separate

feed-forward ANN models for both Gaussian and uniform sensor dis-

tribution using four potential features extracted through simulations.

While evaluating the feature importance and feature sensitivity for

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Table 2

Comparison of the performance of different scenarios of feed-forward ANN.

Scenarios Training Validation Testing Overall Performance

R RMSE Bias R RMSE Bias R RMSE Bias R RMSE Bias

4:20:1 (Single layer) Gaussian 0.40 60.66 −11.69 0.28 53.27 −17.26 0.55 61.46 19.05 0.44 59.69 −3.23 Fair

Uniform 0.51 67.08 6.44 0.53 52.25 8.81 0.53 52.25 8.81 0.56 65.06 17.31 Fair

4:20:20:1 (Two layers) Gaussian 0.82 43.38 −5.11 0.76 34.79 3.99 0.76 29.86 17.31 0.78 41.15 3.02 Satisfactory

Uniform 0.79 55.00 3.65 0.81 34.81 10.35 0.78 34.58 19.89 0.79 48.36 9.55 Satisfactory

4:20:20:20:1 (Three layers) Gaussian 0.81 42.94 −2.91 0.75 44.94 13.66 0.72 37.51 2.08 0.76 42.93 1.06 Satisfactory

Uniform 0.82 49.54 14.69 0.80 48.62 18.31 0.66 47.90 22.24 0.77 50.17 17.51 Satisfactory

4:20:20:20:20:1 (Four layers) Gaussian 0.44 59.93 −10.18 0.30 58.59 −20.99 0.54 57.61 −12.55 0.47 58.74 −12.50 Fair

Uniform 0.08 78.32 −55.49 0.01 70.94 −43.85 0.12 81.12 −84.73 0.09 78.08 −62.60 Poor

4:20:20:20:20:20:1 (Five layers) Gaussian 0.46 62.44 −24.53 0.28 67.11 −17.13 0.42 50.32 −11.17 0.43 60.00 −19.40 Fair

Uniform 0.11 83.11 −102.25 0.06 84.13 −97.75 0.08 62.41 −70.25 0.07 78.22 −91.91 Poor

4:20:20: ... :20:20:1 (Ten layers) Gaussian 0.64 48.35 25.09 0.82 46.20 9.78 0.75 45.01 22.25 0.69 47.72 21.96 Satisfactory

Uniform 0.75 47.90 0.44 0.78 59.69 −3.47 0.70 59.17 5.20 0.73 53.23 1.30 Satisfactory

Table 3

Comparison with the benchmark algorithms.

Performance

metrics

Methods

Feed forward ANN RBN ERBN RNN LSTM Boosting EL Bagging EL (RF) BDT GRNN GPR SVR

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

Gaussian

Uniform

R 0.78 0.79 0.68 0.34 0.69 0.68 0.97 0.96 0.08 0.07 0.90 0.89 0.99 0.99 0.93 0.93 0.89 0.88 0.98 0.98 0.63 0.66

RMSE 41.15 48.36 65.67 168.51 75.12 89.68 15.71 22.27 1.16 1.42 37.31 46.00 11.37 12.63 29.29 32.90 39.66 48.80 11.49 13.72 48.44 52.22

Bias 3.02 9.55 39.19 137.51 60.11 71.11 61.45 65.36 −17.10 −20.9 59.06 69.96 53.90 62.35 57.42 63.22 60.70 71.69 53.18 61.07 18.24 20.26

Fig. 14. Comparison of the computational time complexity of the feed-forward ANN with the benchmark algorithms with three different scenarios of Monte Carlo simulations. A

log scale is used for the vertical axis.

Gaussian and uniform sensor distribution scenarios, we observed that

sensing range, transmission range, and number of sensors are the most

relevant features amongst all, which positively impact the predictand.

In contrast, the area is the least important feature, and it is negatively

related to the predictand. After training the models, we evaluated their

performance over the unseen data and found that both models provide

promising results.

Further, we have compared the performance of the feed-forward

ANN with the benchmark algorithms. We found that the proposed feed-

forward architecture outperforms the benchmark algorithms in terms of

accuracy and computational time complexity.

This study is a step towards the accurate and time-efficient predic-

tion of the number of 𝑘-barriers for intrusion detection using WSNs. Our

methodology can be used to cut down the time and cost requirements

during practical network setup.

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A. Singh et al.

CRediT authorship contribution statement

Abhilash Singh: Conceptualization, Methodology, Software, Data

curation, Validation, Writing – original draft, Visualization, Investi-

gation, Writing – review & editing. J. Amutha: Conceptualization,

Methodology, Software, Data curation, Validation, Writing – original

draft, Visualization, Writing – review & editing. Jaiprakash Nagar:

Conceptualization, Methodology, Data curation, Visualization, Writing

– original draft, Writing – review & editing. Sandeep Sharma: Method-

ology, Data curation, Visualization, Investigation, Writing – review &

editing, Supervision, Project Administration.

Declaration of competing interest

The authors declare that they have no known competing finan-

cial interests or personal relationships that could have appeared to

influence the work reported in this paper.

Data and code availability

The datasets generated during and/or analysed during the cur-

rent study can be downloaded from https://www.kaggle.com/datasets/

abhilashdata/ffannid-intrusion-detection-in-wsnshere (Data) and the

code can be downloaded from https://in.mathworks.com/matlabcentral/

fileexchange/116670-a-deep-learning-approach-to-predict-the- number-

of-k-barriers?s_tid=prof_contriblnkhere (Code) (accessed on 25 August

2022).

Acknowledgements

The authors would like to acknowledge IISER Bhopal, MITS Gwalior,

IIT Kharagpur, and Gautam Buddha University Greater Noida for

providing institutional support. They would like to thank to the editor

and all the anonymous reviewers for providing helpful comments and

suggestions.

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