Area Coverage improvement of a Fixed Sensors

Network System using Fuzzy Control

MARIOS SFENDOURAKIS

Department of Electronic and Computer Engineering, Brunel University- UB8 3PX Kingston Lane, Uxbridge Middlesex,

UNITED KINGDOM

ALEXIOS STARIDAS

Department of Electrical and Computer Engineering, Hellenic Mediterranean University, Romanou 3, Chania, GREECE

IASON DIMOU

Department of Electronic Engineering, Hellenic Mediterranean University, Romanou 3, Chania, GREECE

ALEXIA DIMA

Department of Electronic Engineering, Hellenic Mediterranean University, Romanou 3, Chania, GREECE

THEODORE PAPADOULIS

Department of Electronic Engineering, Hellenic Mediterranean University, Romanou 3, Chania, GREECE

LAMBROS FRANTZESKAKIS

Department of Electronic Engineering, Hellenic Mediterranean University, Romanou 3, Chania, GREECE

ZISIS MAKRIS

Department of Electronic Engineering, Hellenic Mediterranean University, Romanou 3, Chania, GREECE

RAJAGOPAL NILAVALAN

Department of Electronic and Computer Engineering , Brunel University, UB8 3PX Kingston Lane, Uxbridge Middlesex,

UNITED KINGDOM

Abstract: - This paper presents a novel work on localization of transmitters using triangulation with sensors at

fixed positions. This is achieved when three or more sensors cover the whole area, a factor which enables the

system to perform localization via triangulation. The network needs to keep a high detection rate which, in

most cases, is achieved by adequate sensor coverage. Various tests using various grids of sensors have been

carried out to investigate the way the system operates in different cases using a lot of transmitters. Detection

complexity is tackled by finding the optimal detecting sensor radius in order for the network to continue

operate normally. The coverage quality changes in the area of interest and the network is able to detect new

transmitters that might enter the area of interest. It is also shown that as the number of transmitters increases the

network keeps its high performance by using additional groups of sensors in a sub-region area of that of

interest. This way, even when the network is saturated by many transmitters in one region, new transmitters can

still be detected.

Keywords: Fixed Sensors Network, Triangulation, Localization, Sensor Blindness, Detection Range.

Received: July 13, 2021. Revised: May 26, 2022. Accepted: June 19, 2022. Published: August 3, 2022.

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Marios Sfendourakis, Alexios Staridas,

Iason Dimou, Alexia Dima, Theodore Papadoulis,

Lambros Frantzeskakis, Zisis Makris,

Rajagopal Nilavalan

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1.Introduction

In this research we are providing a solution to the

problem of localization with the process of triangulation.

The process of positioning with triangulation is currently

under research for a large number of applications. In our

case we use various grids of fixed Sensors (SRs) in order

to detect possible transmitters (TRs) which might enter an

area. In the last decade, coverage was a fundamental

research issue in WSNs. It was considered to be the

measure of QoS for the sensing function of a sensor

network [1]. The sensors are in fixed and known

positions. So, we don’t have to process the SRs positions

which is also an issue of extensive research. The system

has to process its state and acquire possible problematic

areas of no-coverage to make relevant changes in order to

increase the detection performance rate, in case a new TR

enters its area of coverage. One of the changes that a

network has to execute is to find the optimal radius of

detection which will enable it to preserve a high

detection rate. That means that from an initial state 1

to a new state 2 etc, the network has to adapt to the

new circumstances and change its parameters. That

might also include additional groups of SRs to be used in

order to achieve TRs detection with triangulation. In this

paper, we'll also show how additional groups of SRs

activated close to a problematic area will increase the

network performance. We assume that the visualization

of changes in the network performance, plays a

significant role in order to tackle problematic areas of no

coverage.

2. Related work

The issue of network Area of Interest - AOI coverage is

of prime importance in order a FSN system of this type to

be able to perform localization with triangulation. The

deterioration of its performance based on coverage

problems due to possible obstacles in the AOI and

network is one of the main topics of this research. The

fact that every SR of the FSN system participate

individually on every single detection problem might

arise for a number of existing TRs in its surrounding area.

As shown in [1] SR blindness and Network blindness are

two strongly bonded concepts with TRs detection. In

WSNs systems used for positioning and localization,

there are several factors of uncertainty which influence

the Network detection performance, Communication

uncertainty, Sensing uncertainty and Data uncertainty

[2]. Among them the Sensing uncertainty is the category

that we consider as the main problem that the FSN

system of this type should focus aiming to a high

detection rate with triangulation. Current research which

implements Fuzzy logic theory for detection exists in

many sectors including warning systems. Among them

there is also the fire detection and warning systems. In

[4], a Fire Monitoring and Warning System (FMWS) is

presented based on Fuzzy Logic for the identification of a

true existent and dangerous fire event sending alerts to

the Fire Management System (FMS). Another important

problem which exist in WSNs is energy consumption that

has a direct effect on network operation and lifetime. In

[5], a novel energy-efficient method which uses fuzzy

logic applied on cluster heads (CH) of WSNs focusing

on cluster formation process was presented. The

proposed model, compared with the low-energy adaptive

clustering hierarchy protocol, demonstrated that the

proposed protocol improves network lifetime. In [6]

authors estimated WSNs sensor node positions using a

fuzzy logic algorithm. Although that a fuzzy controller

and a specific defuzzification method was used, it was

noted that there are still many fundamental problems

which has to be solved for the development of WSNs

technologies. In [7] a Fuzzy Logic Cluster Leach

Protocol (FUZZY-LEACH), was applied that used a

Fuzzy Logic Inference System (FIS) in the cluster

process. It was demonstrated that by using multiple

parameters in the cluster reduces energy consumption.

Fuzzy logic in WSNs, improves decision-making,

contributes to resource consumption and generally

increase network performance through efficient

deployment, localization, selection of cluster head,

security, etc.[8]. And it was proved in [9] that fuzzy

logic can provide more accurate event detection in a

WSN that monitor a fire event (fire and smoke).

By far, the most fuzzy-based reasoning incorporated into

fuzzy-based positioning systems is the Fuzzy inference.

The most commonly employed aggregation functions are

the Mamdani-type fuzzy inference system and weighted

average (based on membership grade) in Takagi–Sugeno

fuzzy inference system [12]. In [13] overlap functions

and overlap indices were used to introduce a specific

generalization of the Mamdani inference system. The

Fuzzy method offered based on overlap indices aims for

fire detection improvement through the use of a WSN

and analysis of fire lightness and distance. Likewise, two

Fuzzy techniques based on temporal properties are

proposed in [14] for this aim. Again through the use of a

WSN and the incorporation of Fuzzy logic in SR nodes

evidence of fire are analyzed. But this time previous and

present temperatures are evaluated and compared.

In [15] energy consumption of a WSN was explored by

using a Fuzzy Genetic Algorithm (GA) Clustering and

Ant Colony Optimization (ACO) routing. Fuzzy logic

implementation designed to form the clusters and for

clusters head selection. GA used for optimum fuzzy rules

generation and tuning the output value of fuzzy logic’s

memberships whilst the proposed ACO used to route the

information in the shortest path between the cluster heads

to the base station (BS). The results showed that the

energy level of single node was improved and the overall

network lifetime was enhanced.

3. Problem Statement

This paper investigates how Fuzzy logic theory can be

employed in this type of FSN system for localization with

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Lambros Frantzeskakis, Zisis Makris,

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triangulation, aiming to increase its detection

performance. In [1] it was shown that network saturation

due to the presence of multiple TRs decrease network

performance. Thus, we have to consider increasing

network detection coverage and maintain detection

performance in highly saturated environments due to

multiple TRs. In WSNs Network coverage definition

presupposes that each point in the Area of Interest AOI

to be covered by at least one SR, (k ≥1), were k is a

constant representing the minimum required value of

coverage [2]. In this particular type of FSN system the

value of k should remain as possible in a value of k were

k≥3 in the whole AOI, resulting in a high quality of

network coverage. In this work it is shown that Fuzzy

logic theory implementation is able to increase the FSN

system coverage performance.

4. Network model and Grid topology

During various tests, the basic parameter used was the SR

bearing which identifies a sensor (the bearing by which a

SR detects a TR), which is considered to have a detection

error DER for each SR. For this research many different

grids were used for tests. Among them the most

commonly used grids were: 1000 x 1000 m and 400 x

400 m grids. The m denotes a unit of length. The FSN

system needs to have a high detection performance and

deal with the phenomenon of saturation. The relevant

optimization techniques and the network grid

characteristics where presented in [10]. It was also shown

that with extra SRs the system might increase detection

rate thus enhancing performance. But it is vital for the

network to develop more flexible ways by combining its

adaptability with fuzzy logic theory to have a high

detection rate.

5. Fuzzy logic based localization to

minimize system saturation

As analyzed in [1], one of the fundamental issues the

system has to deal with is the saturation issue. The fuzzy

logic theory can enable the system to become more

flexible and adaptive, keeping its performance at a high

rate. As the system operates and its status changes from

state to state, depending on the number of TRs which

appear, the FSN need to examine automatically the

saturation level and intervene appropriately. Blindness of

SRs due to saturation needs to be processed continuously

and on a case by case basis, allowing for system

intervention. A Fuzzy logic method is then applied to the

system keeping its operational performance on a

satisfactory level.

5.1 Working Principle

In the FSN system for localization, sometimes we have to

face the high saturation rate. This concept is similar with

the problem of heat in a room. As with the case in which

a system is monitoring a room temperature and has to

deal with an increase in the room temperature, the FSN

system has to deal with area saturation and detection

degradation. That presupposes that the sensors network

will acquire enough data inputs in order to define the

relevant level of saturation.

The Fuzzy logic system consists of four main parts:

· Fuzzifier

· Rules

· Intelligence

· Defuzzifier

In the FSN system, a central hub calculates all data from

SRs continuously and applies the Fuzzification and

Defuzzification process in order to de-saturate the

system. The Fuzzy logic methodology dealing with

blindness issues is analyzed in this section. The general

architecture and the components of a Fuzzy logic system

are shown in Fig.5.1, [14].

Figure 5.1 - Fuzzy logic system [10]

5.2 FSN fuzzy logic Saturation Control

System

Fig.5.2 shows the FSN fuzzy logic Saturation

Control System. The FSN sets a saturation target as

an input and the fuzzy controller after comparing

that value with the current saturation level instructs

the FSN system about de-saturation or no change.

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Figure 5.2 - FSN fuzzy logic Saturation Control System

In Table 5.1 depicted below, we have the Fuzzy logic

algorithm that the system applies in order to perform de-

saturation.

Table 5.1 : Fuzzy logic algorithm

5.3 Fuzzy Set

In Fuzzy logic, a basic concept that needs to be

taken into consideration is the concept of Set.

Objects having one or more similar characteristics

can be collected and classified into a Set. In any

system the system designer evaluates the data and

its set membership till a satisfactory classification is

done. Objects belonging to a set are called members

of the set. In fuzzy, a set members have their own

membership grade associated with it [17].

Membership classification is shown in Table 5.2 for the

FSN system considered in this paper:

Table 5.2 - FSN system membership classification

5.4 Membership Functions

In Fig.5.3 it is depicted the membership for the FSN

system considered. The membership sets appear with

different colors and we can clearly see that the worst case

of a very high saturated area is shown with red color.

Figure 5.3 Membership Functions for S (Saturation) =

{Very Low Saturated - VLS, Low Saturated - LS,

Medium Saturated - MS, High Saturated - HS, Very High

Saturated - VHS}

5.5 Fuzzification of Input

As shown in Fig.5.1, a fuzzy logic system has the stages

of Fuzzification and Defuzzification. Fuzzification is the

process of making a crisp quantity fuzzy and it's done by

the Fuzzifier, whilst Defuzzification is done by a

decision-making algorithm that selects the best crisp

value based on a fuzzy set, and it's done by the

Defuzzifier. During the fuzzification process, the real

scalar values changes to fuzzy values. Arrangements of

Fuzzy variables ensure that real values get translated into

fuzzy values. The outcome after translating those real

values into fuzzy values, is called “linguistic terms”. The

input linguistic variables for Fuzzy Logic implemented in

the FSN system suggest two things: First, it shows

linguistically the difference between the set point and

second, express the measured and calculated saturation

level in one area. For fuzzified input, one triangular

function is used. To determine the range of fuzzy

variables according to the crisp inputs is the primary

requirement for proper running of the fuzzier program.

5.6 Fuzzy Membership Functions for

Outputs

The output linguistic variables express linguistically

applied values to the FSN central processing unit for

saturation control. In our case it is essential to attribute

fuzzy memberships to yield variable, which has to be

identical to the input variable. The fuzzy sets used for our

FSN system are shown below in table 5.3 and we can

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see that the range of 80 to 100 percentage corresponds to

a very high saturated VHS state.

Table 5.3 - Output linguistic variables.

5.7 Fuzzy Rules

In Fuzzy Logic, a rule base is constructed to control the

output variable. A fuzzy rule is a simple IF-THEN rule

with a condition and a conclusion. In Table 5.4, we have

a sample of the fuzzy rules for the FSN for localization

via TRN control system. Table 5.5, is a matrix

representation of the fuzzy rules for the said Fuzzy logic.

Row captions in the matrix, contain the values that the

current saturation levels. Column captions contain the

values for target saturation levels. Each cell (row,

column) is the resulting command when the input

variables take the values in that row and column. For

instance, the cell (4,3) in the matrix can be read as

follows: If the current saturation is MEDIUM and target

required is LOW then the command Decrease R (de-

saturate by decreasing the radius of coverage) is applied

to the system.

Table 5.4- Sample fuzzy rules for FSN saturation control system

Table 5.5 - Matrix representation for the FSN saturation Control System

5.8 Rule block

After the fuzzification of the current values of the input

variables, the system fuzzy controller continues with the

phase of “decision making,” or deciding what actions to

activate to bring the saturation level to the desired set

point value. For the action to be initiated, the measures

are minimal time of reaction as well as a minimal value

of saturation which might be achieved, combined with

best possible coverage. Except from the case that another

input order has been given to the system. The system

should execute de-saturation in an area or apply a

combination methodology for de-saturation in many sub-

areas in order to enable the system to keep its

performance high in the whole AOI.

5.9 Defuzzification

The Fuzzy Logic Controller forwards data information to

the Defuzzifier which performs initial processing of the

system status and afterwards feed with information the

central hub. As shown in Fig.5.4, the central hub initiates

the AOI de-saturation procedure if necessary. The system

gradually decreases the radius of coverage, R, of the

blinded SRs till their blindness is decreased resulting in

area de-saturation. Then the system applies the optimal

value of R for each SR in the saturated area in order to

achieve the best coverage combined with de-saturation.

The system applies the same methodology with the one

presented in [16] whilst in this case its application results

in de-saturation in combination with system coverage

performance maintenance. So the system, produces crisp

data as a result of the optimization methodology. Then,

the crisp data are forward backwards to the system and

the Fuzzy Logic Controller. At the end of this process,

the system re-calculates the overall saturation level and

finds the current system saturation level.

Figure 5.4 - FSN Defuzzication flow diagram

If current saturation level lies within the desired output

Fuzzy values, then the crisp blindness value is the crisp

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output value of the system. This methodology is named

as, Fuzzy Logic Saturation Control System FLSCS for

Fixed Sensors Network -. Fig.5.5 shows the FSN

Defuzzification Radius mode of operation for De-

saturation. The seven SRs for each square of the AOI are

depicted in Fig..5.5.

Figure 5.5 - FSN Defuzzification mode for De-Saturation

The radius R of the five SRs (four are placed in the

corners of the square depicted above in Fig.5.5 and the

fifth in the center of the square) is increased to a value till

the diagonal corner of the square. The other remaining

two of the seven SRs lies on the center of the two

opposite sides (upper and lower) of the square, increase

their radius R also till the opposite corner as it is depicted

in Fig.5.6 below.

Figure 5.6 - FSN Defuzzification mode for De-Saturation

5.10 Fixed Sensors Network - FSN AOI

partition

Fig.5.7 shows the FSN AOI divided in four main sub-

areas. In order to simplify the procedure, the FSN system

process each subareas individually and report the status to

the controller . The algorithm used for this process is

shown in Table 5.6.

Figure 5.7 - FSN division of AOI. System applies Fuzzy logic

algorithm for de-saturation in each main sub-area.

Table 5.6 - FSN Fuzzy logic de-saturation Algorithm

6. FSN Fuzzy logic De-Saturation

Methodology of adjacent areas

Fuzzy systems have the capability to operate as stand-

alone systems or be combined with other systems.

Additionally, they are able to supplement fully or

partially other systems or even more to be combined with

them (neural networks, evolutionary algorithms etc.)

resulting in hybrid systems [15]. Fuzzy systems already

have a significant participation in positioning systems. In

our case the FSN has a number of SRs which are shown

in Fig.5.8. Each of the four pre-mentioned sub-areas is

further divided to four cells, were there are participating

seven SRs for localization via triangulation in each cell of

these sub-areas. So, the whole AOI is divided further in

sixteen cells, The SRs mode of operation was analyzed in

section 5.10. Fig.5.9 below, shows the saturated sub-areas

of the AOI. The remaining sub-areas are LOW saturated.

All the depicted saturated sub-areas belong to area 3 of

the AOI.

\

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Figure 5.8 - FSN AOI divided in sixteen cells with SRs. Each cell

square has seven SRs for TR detection via TRN.

Figure 5.9 - FSN AOI saturated case. Area 3 is saturated with many

TRs as three of the four cells (3.1, 3.2 and 3.4) have many TRs.

6.1 Adjacent areas Algorithm

The Adjacent areas Algorithm as its name suggests is

related to the activation of adjacent SRs to a problematic

area. Meaning that the surrounding SRs close to a

problematic area might seek for any new TRs as the

existing SRs responsible for the saturated cells

monitoring might fail to detect a new TR. By that way the

system after applying fuzzification and defining the

saturated areas and cells in the AOI, activates more SRs

to seek in those areas aiming at reducing any existing

coverage problems.

6.1.1 Adjacent Areas Algorithm AAA

pseudo code

The following pseudo code represents how the system is

applying the AAA in order to face any saturation

problems.

Step 1

DO Seek and define adjacent SRs surrounding the

saturated cell.

Step 2

DO Count the number of the adjacent SRs.

Step 3

DO Activate these adjacent SRs for detection of any

new TRs in the problematic area.

Step 4

DO Calculate the new FSN coverage in the

particular problematic cell.

Step 5

THEN Inform the system for the new improved and

lowered saturation level.

Step 6

Seek for any further activation at another cell.

IF the answer is YES apply AAA to the new set of

adjacent SRs.

IF NO then apply AAA only for the previous

required cells.

Step 7

DO Continue applying the AAA for any saturated

cells.

DO Continue reporting to the system.

Concerning the previous case depicted in Fig.5.8, the

system in order to deal with the saturation problem

applies the adjacent areas methodology to decrease the

saturation problem which is shown below in Fig.5.10.

SRs apply the mode of operation which was described in

the de-fuzzification process in section 5.10 and the FSN

system achieves de-saturation in combination with better

coverage. This case of saturation is a case related with the

one fourth of the AOI.

Figure 5.10 - FSN AOI saturated case after applying Adjacent Areas

Algorithm AAA. Area 3 is saturated with many TRs.

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The system applies the methodology of adjacent areas to

decrease the coverage problem. In other cases where

there is saturation in a single cell of the AOI, the system

applies a different analogous approach to the adjacent

areas methodology. A different case where we have a

combination of two saturated cells is depicted in Fig.5.11.

The system calculates the number of the adjacent areas

and use them in order to enable the de-saturation process

to be executed. In this particular case it uses the adjacent

areas SRs in order to cover the saturated area. For the cell

2.2 it uses three adjacent cells (cells 2.1,2.3 and 2.4) and

for the cell 4.1 uses other three cells (cells 3.2,3.4 and

4.3). Those SRs extend their radius R till the diagonal

corner of the saturated area.

Figure 5.11 - FSN AOI saturated case. Two cells -cell

2.2 of area 2 and cell 4.1 of area 4 are saturated with

many TRs. The system applies the method of adjacent

areas to decrease the coverage problem.

6.2 Results of Fuzzy Logic implementation

on the System

Network Topology

Two network grids were employed to prove the Fuzzy

Logic concept on this particular FSN system., In the first

scenario the network grid has only seven SRs in a subarea

similar to Fig.5.8. The second is one fourth of the full

AOI of the network where 18 more SRs participate by

applying the adjacent areas algorithm on the saturated

area of Fig 5.11. The SRs of area 3 aren't counted in the

procedure of AAA. Fig. 5.12 shows the coverage of the

sub-area of the AOI with 7 SRs and 5 TRs.

Figure 5.12 Sub Area Coverage with 7 SRs - 5 TRs, Coverage -

Radius 350 m (no coverage is indicated in blue)

Fig 5.13 shows how system increases its performance of

coverage by activating the Adjacent areas Algorithm

AAA. These results clearly show the benefit of this

methodology and how the AAA algorithm can provide

positive results increasing the FSN system performance.

Figure 5.13 Sub Area Coverage with Adjacent Areas Algorithm with

19 SRs and 5 TRs, Coverage Radius 350 m (no coverage is indicated

with blue colour)

Fig. 5.14 below shows the coverage with two additional

TRs, (7SRs, 7TRs) These results illustrate that a number

of SRs in the sub-area have lost their detection capability

to a greater extend.

Figure 5.14 Sub Area Coverage with 7SRs-7TRs, Coverage Radius

350 m (no coverage is indicated with blue color)

The network coverage with different sensor coverage

radius R for different number of TRs are shown in

Figures 5.15,5.16 and 5.17. These results show, a

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coverage radius around 400 m provides better coverage

performance and depending on the number of TRs a

better coverage radius can be identified.

Figure 5.15 Area of Interest- AOI Coverage Plot 7SRs - 7TRs with

SRs Radius 350 units

Figure 5.16 Area of Interest- AOI Coverage Plot

7SRs - 12TRs SRs is Radius 350 units

Figure 5.17 Area of Interest- AOI Coverage Plot 7SRs -

20 TRs SRs is Radius 350 units

Figures 5.18 (a), (b) shows the effects of loosing sensors

in the sub - Area. These results show that the

combination of network saturation due to existing TRs

and the network performance degradation due to missing

SRs (SRs failure) can lead to a very low operational

performance . Fig. 5.18 (c) shows how how the network

coverage can be improved applying the adjacent areas

algorithm.

(a) (b) (c)

Figure 5.18 (a) Area of Interest - AOI Sub Area

Coverage 5SRs - 7TRs - Radius 350 units(no coverage

is indicated with blue colour)

(b) Area of Interest - AOI Sub Area

Coverage 6SRs - 7TRs - Radius 350 units (no coverage

is indicated with blue)

(c) Area of Interest - AOI Sub Area

Coverage with Adjacent Areas Algorithm 19SRs and

7TRs Radius - 350 units (no coverage is indicated with

blue colour)

Fig. 5.19 (a) and (b) shows the effects of network level

coverage with more TRs in the AOI(20 TRs) and how

the coverage is improved with adjacent areas algorithm

applied with an increased radius of coverage (450 m).

(a) (b)

Figure 5.19 (a) Area of Interest - AOI Sub Area

Coverage 7SRs and 20TRs SRs is Radius - 350 units

(no coverage is indicated with blue colour )

(b) Area of Interest - AOI Sub Area

Coverage after activation of the Adjacent Areas

Algorithm 19SRs and 20TRs Radius - 450 units (no

coverage is indicated with blue colour)

Fig. 5.20 and Fig. 5.21 shows the network level coverage

with more TRs in the AOI. We see that the coverage level

of the FSN system with 19 SRs, 7 TRs and with R=s 300

mis 98.8% while the same network with 12 TRs falls to

around 96%. After increasing the number of TRs to 20,

the network coverage further falls to 87.7% as shown in

Fig. 5.22. These results shows of the impact of sensor

blindness and saturation of the FSN system. In order to

overcome these challenges, techniques such as Adjacent

logic Algorithm and Fuzzy Logic methodology is

required.

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Figure 5.20 Area of Interest - AOI Coverage Plot 19 SRs - 7TRs

Radius 350 units

Figure 5.21 Area of Interest - AOI Coverage Plot 19 SRs - 20TRs

Radius 350 units

Figure 5.22 Area of Interest - AOI Coverage Plot 19 SRs - 20TRs

SRs Radius 350 units

In the following Fig. 5.23 we see that the optimal value

of radius R is far different from the previous graphs. It

reaches the value of 96.69% in about 300 units and the as

the R increases it decreases rapidly. This phenomenon

proves that the value of R has a significant role during the

operation of the FSN system and it also can affect

seriously the quality of coverage from state to state.

Figure 5.23 Area of Interest - AOI Sub Area Coverage after

activation of the Adjacent Areas Algorithm 19SRs and 20TRs Radius

- 450 units (no coverage is indicated with blue colour).

6.3 Outcome of FSN saturation control by

using fuzzy logic

The FSN system in order to perform the localization via

TRN of new TRs needs a high level of coverage in

combination with a low level of saturation in the AOI. If

one of these characteristics is deteriorated, then the

possibility of missing a new TR is increased. The Fuzzy

Logic theory implementation is enabling the FSN system

to react as the level of saturation is increased,

determining that coverage won't also decrease resulting in

a saturated system with low coverage performance. The

system by applying the adjacent area's methodology is

enabling the adjacent SRs to cover problematic

areas whilst continuously the system is measuring

the level of de-saturation in its sub-area. This Fuzzy

Logic implementation methodology plays a vital role in

the FSN system performance. In every state the system is

monitoring its state and from state to state. Also, and as

each sub-area of the AOI is processed, the FSN is able to

determine if additional SRs are needed to be activated or

the existed SRs are enough to keep the network's

performance on a satisfactory level.

7. Contributions

The contributions of this work is the development of a

methodology to evaluate and assess the performance of

this particular type of FSN, based on the problem

statement. Network Area Coverage problematic areas are

identified and areas of non coverage of three or more SRs

for triangulation are visualized for the system user. The

FSN system with implementation of the Fuzzy logic

theory evaluates the network status in any state and with

a certain number of existing TRs. Additionally, with the

novel algorithm of adjacent areas activation the system is

able to increase its detection performance in saturated

sub-areas of the AOI.

WSEAS TRANSACTIONS on SYSTEMS and CONTROL

DOI: 10.37394/23203.2022.17.39

Marios Sfendourakis, Alexios Staridas,

Iason Dimou, Alexia Dima, Theodore Papadoulis,

Lambros Frantzeskakis, Zisis Makris,

Rajagopal Nilavalan

E-ISSN: 2224-2856

356

Volume 17, 2022

8. Conclusions

This research presents significant work for a FSN system

for localization via triangulation. In previous research

papers [1], [10] it was shown that as the number of TRs

increase in the AOI issues of saturation and SRs

blindness appear in the network. In this paper it was

shown that the implementation of the Fuzzy logic theory

might enhance the capabilities of this particular type of

system. The system by applying the methodology

presented increases its detection performance and the

required coverage for performing triangulations in the

AOI or any sub-area. Additionally, it was shown that the

probability of detection differentiates from one topology

to another and as the TRs cause saturation to the system

more and more adjacent SRs might participate in the

process of detection and AOI coverage. The issues of

blindness and network saturation are strongly related with

the detection performance for this type of FSN. These

issues haven’t been researched up to now and forms a

new contribution to existing knowledge.

Author Contributions: Conceptualization, M.S.;

Methodology, Simulation and Optimization M.S..;

writing—original draft preparation; writing—review and

editing, M.S.; supervision, E.A. and N.R.; All

authors have read and agreed to the published

version of the manuscript.

Funding: This research received no external funding.

Acknownledgements

I would like to express my gratitude to Professor

Rajagopal and Professor Antonidakis, my research

supervisors, for their patient guidance, and useful

critiques of this research work. I would also like to thank

Professor Zakinthinaki for her valuable contribution in

producing the adequate Matlab software for the tests of

this research.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:

FSN Fixed Sensors Network

SRs Sensors

TRs Transmitters

ETRNs Existing Triangulations

QoS Quality of Service

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WSEAS TRANSACTIONS on SYSTEMS and CONTROL

DOI: 10.37394/23203.2022.17.39

Marios Sfendourakis, Alexios Staridas,

Iason Dimou, Alexia Dima, Theodore Papadoulis,

Lambros Frantzeskakis, Zisis Makris,

Rajagopal Nilavalan

E-ISSN: 2224-2856

357

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WSEAS TRANSACTIONS on SYSTEMS and CONTROL

DOI: 10.37394/23203.2022.17.39

Marios Sfendourakis, Alexios Staridas,

Iason Dimou, Alexia Dima, Theodore Papadoulis,

Lambros Frantzeskakis, Zisis Makris,

Rajagopal Nilavalan

E-ISSN: 2224-2856

358

Volume 17, 2022

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