Dynamic Adjustment Optimisation Algorithm in 3D...

HindawiJournal of SensorsVolume 2019 Article ID 1018434 14 pageshttpsdoiorg10115520191018434

Research ArticleDynamic Adjustment Optimisation Algorithm in 3D DirectionalSensor Networks Based on Spherical Sector Coverage Models

Xiaochao Dang 12 Chenguang Shao 1 and Zhanjun Hao 12

1College of Computer Science and Engineering Northwest Normal University Lanzhou 730070 China2Gansu Province Internet of Things Engineering Research Center Lanzhou 730070 China

Correspondence should be addressed to Chenguang Shao 1796648742qqcom

Received 16 May 2019 Accepted 2 August 2019 Published 7 October 2019

Academic Editor Antonio Lazaro

Copyright copy 2019 Xiaochao Dang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In directional sensor networks research target event detection is currently an active research area with applications in underwatertarget monitoring forest fire warnings border areas and other important activities Previous studies have often discussed targetcoverage in two-dimensional sensor networks but these studies cannot be extensively applied to three-dimensional networksAdditionally most of the previous target coverage detection models are based on a circular or omnidirectional sensing modelMore importantly if the directional sensor network does not design a better coverage algorithm in the coverage-monitoringprocess its nodesrsquo energy consumption will increase and the network lifetime will be significantly shortened With the objectiveof addressing three-dimensional target coverage in applications this study proposes a dynamic adjustment optimisationalgorithm for three-dimensional directional sensor networks based on a spherical sector coverage model which improves thelifetime and coverage ratio of the network First we redefine the directional nodesrsquo sensing model and use the three-dimensionalVoronoi method to divide the regions where the nodes are located Then we introduce a correlation force between the targetand the sensor node to optimise the algorithmrsquos coverage mechanism so that the sensor node can accurately move to thespecified position for target coverage Finally by verifying the feasibility and accuracy of the proposed algorithm the simulationexperiments demonstrate that the proposed algorithm can effectively improve the network coverage and node utilisation

1 Introduction

A three-dimensional (3D) wireless sensor networks (WSNs)consists of several tiny battery-powered sensors that cancommunicate with each other to monitor a 3D field of inter-est (FOI) [1] for target events WSNs include sensor networks(ie omnidirectional sensor networks) and directional sensornetworks (DSNs) Research into WSN coverage is roughlyclassified into three branches area coverage barrier coverageand target coverage In recent years WSNs coverage has beenan active research area with a wide range of practical applica-tions target detection [2] healthcare applications [3] targetlocation [4] data transmission [5] etc In these real-worldapplications we can detect some target events in the regionof interest by deploying sensor nodes Therefore the use ofexisting methods and techniques to achieve effective eventdetection is now the current research focus At the same timeimproving multiple objectives (eg reducing the networkrsquos

overall energy consumption while ensuring a high coverageratio) is an indispensable consideration in research

In most of the previous studies the researchers have dis-cussed and presented solutions for 2D coordinate systemsunder realistic conditions to reduce the difficulty and theyhave made great progress [6ndash8] However modelling andstudying DSNs coverage are still less common in 3D systemsthan in 2D systems not only does the difficultly of researchincrease in 3D systems but deployed sensor nodes oftenencounter complex environmental influences (eg weatherand climate) In recent years some researchers have estab-lished models for 3D WSNs and proposed correspondingdistributed optimisation algorithms [9ndash11] However theWSN node coverage model is mainly based on the 2Domnidirectional sensing model and a large part of theresearch in 3D systems is based on the omnidirectional ballsensing model While the omnidirectional sensing modelcan provide better range and node utilisation for area

2 Journal of Sensors

coverage we only require modest energy and nodes with lim-ited directional detection to achieve target coverage for a setof targets or special events in practice Therefore 3D DSNscoverage research is more suitable for the above conditions

Of course the directional sensor not only needs to con-sider its own position and sensing range (as with the omnidi-rectional sensor) but must also consider the angle changeproblem Furthermore when nodes are randomly deployedcovered they cannot be accurate and some omissions willoccur Therefore in a specific environment we need adynamic algorithm to select the optimal number of activenodes to detect the target [12] At the same time we needto consider moving or rotating these active nodes within acertain period to adjust their own headings to achieve thebest coverage For example in [8] the use of unattendedsensor networks has been discussed for detecting targetsusing energy-efficient methods The authors are dedicatedto analysing the trade-offs between power consumption andquality of service in WSNs in terms of detection capabilitiesand latency In [13] the authors propose using the hybridmovement strategy (HMS) to solve the problem of highenergy consumption (resulting from mobility) and improvethe coverage ratio of DSNs Although the method proposedabove can reduce the energy consumption of the networkand improve the coverage ratio the rotation angle of the 3Ddirectional sensor node is difficult to determine increaseddimensionality brings further complications

Therefore we propose a network model suitable fordirectional sensors and related dynamic adjustment optimi-sation algorithms for 3D systems We first design a sensingmodel that is more suitable for 3D DSNs and allows us toquantify the rotation angle of the node Secondly to achieveaccurate coverage we extend traditional 2D Voronoi divisionand apply it to 3D DSNs We also use theory and experimen-tation to verify the algorithm to further reduce networkenergy consumption Finally we design experimental simula-tions and perform algorithm comparisons to further ana-lyse our algorithmrsquos effectiveness Our main contributionsare highlighted as follows

(i) We are the first to propose a spherical sector sensingmodel for 3D DSNs that quantifies the rotation anglein combination with using a 3D Voronoi method[14] to divide space using the sensorsrsquo positions

(ii) We design a synergistic priority coverage mecha-nism to reduce the moving distance of nodesthereby reducing excessive energy consumptionwhile guaranteeing a high coverage ratio for the sen-sor network

(iii) We optimise the traditional virtual force algorithmto suit practical conditions and we perform a fulltheoretical analysis and experimental comparativeanalysis of the algorithm proposed in this paper toverify its validity and accuracy

The remainder of this paper is organised as follows InSection 2 the research progress and related work on DSNsin recent years are summarised In Section 3 the DSNs

coverage model and sensing angle are described and the rel-evant definitions are provided After this we compare thedifferences between 2D and 3D Voronoi and give the 3DVoronoi partition theory in Section 4 We then show howwe have designed and improved the relevant algorithms andprovide its design steps in Section 5 In Section 6 we describethe simulations and experiments we performed on the algo-rithm and compare it with other algorithms for analysis Con-clusions and future works are discussed in the final section

2 Related Works

In recent years research on DSNs has been carried outmainly based on 2D planes For example in [15] the authorspropose a cluster head- (CH-) based distributed target cov-erage algorithm to solve a Maximum Coverage with Mini-mum Sensor (MCMS) problem The authors also designeddistributed clustering and target coverage algorithms toreduce network energy consumption Subsequently in [12]they designed a target coverage algorithm for DSNs in anenergy-saving manner based on [15] through the distrib-uted clustering mechanism The authors improved the dis-tributed algorithm in [15] to use the CH approach andensure that it is used appropriately to enhance DSNs tar-get coverage In [16] the authors propose a new method(based on particle swarm optimisation) to maximise cover-age for 2D regions This algorithm allows a directional sensornode to constantly adjust its sensing direction to provide thebest coverage However most of the above studies map 3Dsensor coverage problems into 2D for discussionmdashthey can-not be applied directly in three dimensions Therefore weneed to consider not only dimensionality but also a node-aware model that can be applied in the dimension of theactual environment

In addition the nodes are often distributed randomly inthe monitoring area Reducing the deployment costmdashwhileusing the limited node energy for efficient coveragemdashhasbecome an active research topic The authors point out thatmotility and mobility are essential for DSN nodes to mini-mise occlusion effects and coverage overlap in [17] At thesame time motility is superior tomobility in terms of networkcost and energy efficiency Therefore almost all research aimsto solve coverage problems through motility

In practice however there are still some coverage holesthat can only be addressed through mobility For examplethe authors in [18] use the directionality of the orienta-tion sensor to rotate it to locate periodic detection objectsTherefore the above authors developed an event monitoringsystem that proposed a maximum coverage deployment(MCD) heuristic iteration to deploy sensors to cover targetsBut we must not only consider the direction of the orienta-tion sensor (ie the change or rotation of its sensing angle)to enable efficient deployment we must also consider thatthe orientation sensor can move to fill coverage holes in themonitoring area (ie DSNs can be moved) Thereforethe literature [13] proposes HMS to solve the high energyconsumption of directional sensor movement The authorsuse the cascading method to adjust the coverage of the DSNseffectively reducing network energy consumption In [19]

x

z

Rso

y

M

B1A1

C1

F

120579

Figure 1 Spherical sector sensing model

Figure 2 Target detection model

3Journal of Sensors

the authors propose an algorithm based on learning autom-ata to address the orientation sensor networkrsquos coveragequality requirements and to maximise the network lifetime(ie priority-based target coverage) The algorithm dividesthe DSNs into several coverage sets so that each coverageset can meet the coverage quality requirements of all tar-gets Thus it effectively extends the network lifetime

In [13 18 19] the authors have better solved the problemof mobile energy consumption but these are based on 2Dplane verification and are not suitable for 3D environmentsTherefore the research of the literature [20ndash22] has succes-sively proposed the orientation sensor model and algorithmfor the 3D coordinate system For example the authors stud-ied the low-power green communication of 3D DSNs andproposed the space-time coverage optimisation scheduling(STCOS) algorithm to obtain the maximum network cover-age in [21] In [22] the authors propose a network coverageenhancement algorithm based on an artificial fish swarmalgorithm to improve the coverage rate However theauthors only optimised the angle of the sensor and did notsolve the mobility problem in the directional sensor In[23] the authors propose prescheduling-based k-coveragegroup scheduling (PSKGS) and self-organised k-coveragescheduling (SKS) algorithms to reduce the cost of the algo-rithm and ensure the effective monitoring of node qualityThe experimental results show that PSKGS improves moni-toring quality and the SKS algorithm reduces the nodersquoscomputation and communication costs

In addition the special geometric properties of the Voro-noi diagram are applied in many aspects of WSN coverage In[24] the authors propose Voronoi-based centralised approx-imation (VCA) and Voronoi-based distributed approxima-tion (VDA) for optimal coverage in DSNs The authorshave experimentally verified that the two algorithms canreduce the coverage overlap and achieve a higher coveragerate In [25] the authors combine the special set featuresof the 2D Voronoi graph with the real-time response ofdynamic environment changes and propose a distributedgreedy algorithm that can select and adjust the intracellularsensing direction based on coverage (IDSampIDA) Obviouslythe research on the 2D Voronoi algorithm has shown betterresults but it is rarely applied in three dimensions

Therefore based on the typical literature [14 25] thispaper improves and extends the Voronoi method making itsuitable for 3D DSNs target coverage In this paper we pro-pose a dynamic adjustment optimisation algorithm for 3DDSNs based on a spherical sector coverage model This algo-rithm can maximise coverage and improve network lifetimeby adjusting the direction and specific movements of nodesin the DSNs In the subsequent experimental verification sec-tion we discuss the proposed algorithm and compare it withother algorithms

3 Network Coverage Model and AngleQuantification Method

31 Network Coverage Model First we assume that the sens-ing model of the sensor node covers a sphere with its mid-point at the nodersquos position oiethxi yi ziTHORN and its sensing

range Rs is the maximum detection distance Initially it isassumed that sensor nodes si are randomly scattered inan L3 target area and the set of nodes is sifs1 s2⋯sngRc represents the communication radius of the node whenthe Euclidean distance between two nodes si and sj satisfiesdethsi sjTHORN lt Rc we call them neighbour nodes [26] In a tradi-tional 2D study most researchers transform the sensor nodesinto a 2D planar fan to achieve coverage optimisation Insome related 3D research fields the nodersquos sensing range isabstracted into a covering model of a rounded hammerHowever the coverage model of the 3D directional sensorshould be obtained by rotating a planar fan with radius Rsand central angle 2θ around its axis of symmetry as shownin Figure 1 Therefore we define the directional nodersquos sens-ing range as a spherical sector sensing model As shown inFigure 1 the spherical sector OmdashA1B1C1 represents the cov-erage model of the directional sensor When 2θ = 360deg itscoverage matches that of the omnidirectional sensor nodeTherefore the spherical sector network model redefined inthis paper is more suitable for modelling the coverage of 3Dsensor nodes

Initially sensor nodes are randomly scattered in thetarget monitoring area which may result in an uneven nodedistribution excessive node energy consumption and dupli-cate or missing coverage for some targets In Figure 2 thegrey dots indicate targets that need to be covered and thethree spherical sectors represent sensor coverage Some ofthe targets in Figure 2 are not completely covered Thereforethe sensor network may also have omission problems result-ing in lower node utilisation Before designing a 3D DSNscoverage algorithm based on the 3D Voronoi diagram parti-tion the following assumptions are made

x

z

y

P

Main direction

ro120595

120596

120579

120593

Figure 3 Node sensing direction


(i) The sensor nodes are isomorphic and each node hasaccess to its own location and that of its neighbournodes through some technical means

(ii) Each node has the same detection range but its sens-ing range can be different that is each sensor canselect different sensing angles 2θ where each si canselect its own sensing angle 2θi

(iii) Each node can rotate and move freely in anydirection

32 Model Angle Quantification In previous studies the ran-domly distributed target point p in space is covered by thedirectional node si and the basic conditions dethoi pTHORN le Rsand ∣φ le θ∣ need to be satisfied Most studies [27 28] usethe partitioning model shown in Figure 3 to specify anglesHowever it is difficult for this model to quantify the angle φbetween the target point p and the node si In particular it isdifficult to determine the necessary rotation amount when anode must rotate to cover a target Furthermore the sensingmodel and direction angle partitioning of Figure 3 is abstractand impractical for directional sensor nodes with differingθ and varying main direction angle ψ

Therefore we redefine the sensing model and propose anangle and direction division method using one octant of asphere to unify the rotation as shown in Figure 4 As long asthe spherical sector busbar is exactly tangent to the three edgesof OmdashABC (ie the spherical sector contains OmdashABC) cov-erage can be achieved by rotating the model to the coordinatesystem in which the target event is locatedmdashwhen the condi-tion dethsi pTHORN le Rs is satisfied The above assumptions canreduce omissions and node energy consumption In thisregard we subsequently respecified the conditions underwhich the target event can be covered by the directed node

As shown in Figure 4 we cut the sphere of radius r alongits axes of symmetry to divide it into eight parts that is theshaded portion in Figure 4(a) is the isolated polyhedronOmdashABC For a more intuitive understanding and for anal-ysis and quantification we separately extract the shaded partsremoved in Figure 4(a) and draw the perspective view shownin Figure 4(b) To quantify the angle θ in our model we needto solve for angCOOprime Therefore we project the point O onto a

plane containing Oprime that is perpendicular to the line passingthrough O and Oprime For a more intuitive understanding andanalysis we separately extract the triangle ABC inFigure 4(b) and draw the plane view shown in Figure 4(c)The line segments AO BO and CO are perpendicular andcongruent (ie AO = BO = CO = r) so we determine AB =AC = BC =

ffiffiffi2

pr In Figure 4(c) Oprime represents the projection

of point O which is located at the centre of the equilateral tri-angle ABC Note that CD = eth ffiffiffi

2p

2THORNr We now calculate COprime = CDcos 30∘ = etheth ffiffiffi

2p

2THORNrTHORNcos 30∘ = eth ffiffiffi6

p3THORNr The con-

necting line segments OprimeG and OG form the right triangleGOOprime as shown in Figures 4(b) and 4(d) In Figure 4(d)φ = angCOOprime is exactly on the direction angle we need to calcu-late that is φ = arcsin eth ffiffiffi

6p

3THORN asymp 5474∘ Note that φ is notrelated to the radius r Next we draw a plane view of thespherical sector projection on the plane as shown inFigure 4(e) We know that 2φ is not equal to the true angleat which the spherical sector OmdashABC is projected ontothe plane 2φ ne angCOG the inner angle of the calculatedangCOG = 90∘ Therefore we can get the minimum sensingangle θ when the condition θ = arcsin eth ffiffiffi

6p

3THORN is satisfiedas shown in Figure 4(e) At this time the regular triangu-lar pyramid OABC is surrounded by the spherical sectorOmdashA1B1C1 Meanwhile when the projected fanrsquos centralangle 2θ ge 2 arcsin eth ffiffiffi

6p

3THORN the spherical sector sensing areacontains the polyhedron OmdashABC

In summary we first assume that the nodersquos centralangle 2θ ge 2 arcsin eth ffiffiffi

6p

3THORN can meet the required coverageWe then specify that a target point pethx y zTHORN is to be cov-ered by the sensor node siethxi yi ziTHORN subject to the follow-ing conditions

(i) The Euclidean distance between points p and si mustbe less than or equal to the maximum sensing dis-tance of the node that is dethsi pTHORN le Rs

(ii) The angle φ formed between the vector from p to siand the nodersquos main sensing direction must be lessthan θ that is φ le arcsin eth ffiffiffi

6p

3THORN asymp 5474∘

(iii) The central angle of the directed sensing model sat-isfies 2θ ge 2 arcsin eth ffiffiffi

6p


33 Related Definitions For a more intuitive follow-up anal-ysis and discussion of this article we introduce the followingdefinitions to better describe the problem

Definition 1 (3D-directed node sensing model) A 3D-directed sensing model can be represented by the five-tupleltsiethx y zTHORNw Rs 2θ ψ gt where si w Rs 2θ (0 le θ le π)and ψ represent the vertex position coordinate the mainsensing direction vector the nodersquos sensing radius the nodersquossensing angle and the nodersquos sensing direction respectively

Definition 2 (neighbour node) Each node is unique withinthe Voronoi therefore according to reference [29] we canspecify that two sensor nodes that have the same neighbour-ing edge are neighbouring nodes

x

y

z

O r

A

B

C

(a)

2r

rOprime

O

A

C

B

radic

G

(b)

C

BA

60deg

120deg

r

Oprime

D

2rradic

22

radic997888

(c)

O

r

OprimeG C

120593

r63

radic997888

(d)

F

r

h

o

A1B1

C1

120579

r63

radic997888

(e)

Figure 4 Angle division of sensing model

5Journal of Sensors

Definition 3 (network coverage ratio) We refer to the sens-ing accuracy model in [27] to determine the probability thatany point p in space is monitored by node si Assuming thatthe sensing accuracy C decays as the distance increases thesensing accuracy Csi p is

Csi p =1

1 + αd si peth THORNeth THORNβ eth1THORN

where Csi p represents the sensing accuracy of sensor si atpoint p and dethsi pTHORN represents the Euclidean distance frompoint p to si which can be calculated as

d si peth THORN =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix minus xieth THORN2 + y minus yieth THORN2 + z minus zieth THORN2

q eth2THORN

Constants α and β reflect the device correlation coefficientfor the physical characteristics of the sensor Typically β has arange of (1~4) and α is used as an adjustment parameter

A target in the monitoring area can be covered simulta-neously by multiple sensor nodes and its coverage probabil-ity C can be expressed as

C = 1 minusYNi=1

1 minus Csi p

eth3THORN

which is equivalent to

C = 1 minusYNi=1

1 minus 11 + αd si peth THORNeth THORNβ

eth4THORN

4 Voronoi Partitioning Method

41 2D Voronoi Principle In the early research of two dimen-sional DSN coverage nodes are randomly distributed in theplane and divided into the 2D Voronoi method As shownin Figure 5 given a set of sensor nodes si = fs1 s2⋯sngthe bounded plane is divided into polygonal cells Ki = fK1K2⋯Kng such that each cell Ki contains exactly one ofthe sensor nodes si where si is called the Ki-divided gen-eration node [14 30] Furthermore according to the parti-tioning property of the Voronoi diagram the distanceDethsi TTHORN from any point T in cell Ki to si is shorter thanthe distance Dethsj TTHORN between the point T and the neigh-bour nodes of si

As shown in Figure 6 there are 70 sensor nodes in theplane and the grey area represents the coverage of each nodeAfter division eachVoronoi unit corresponds to a single node

42 3D Voronoi Partition Principle After reviewing therelated 2D Voronoi research in the previous section weextend it to divide three-dimensional volumes The volumeis divided into polyhedral Voronoi units called V-body unitseach is an irregular multifaceted closed convex bodyaccording to the literature [14] Meanwhile each unit Vi isinfV1 V2⋯Vng contains a unique node si Hence accordingto the property of 2D-Voronoi the 3D Voronoi partitioningdefinition satisfies

Q Vieth THORN = Vi isin L3 ∣ d T sieth THORN le d T sj

j

= 1 2⋯n minus 1f gforallj ne ig

eth5THORN

It can be concluded from the aforementioned results thatthe number of nodes Nsi

is equal to the number of Voronoi

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

5001

2

3

4

5

6

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8

9

10

11

12

13

14

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19

20 21

22

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24 25

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53 54

55

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57 58

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606162

63

64

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69

70

Figure 5 2D Voronoi diagram

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500

Figure 6 2D Voronoi node coverage


units NViafter division that is Nsi

=NVi i = eth1 2⋯nTHORN

Thus this paper first uses this important neighbouring prop-erty to divide and study the 3D coverage problem

5 VFA Analysis and 3D-DAOA

As discussed earlier directional sensor network nodes can beseparated into a unique set of nonoverlapping V-body unitsby the 3D Voronoi partitioning method after an initialrandom deployment We know a target may not be detectedby a given node and each target could be located in anyV-body unit Additionally according to the Voronoi parti-tioning property we will first consider nodes preferentially

covering targets in that nodersquos V-body unit for which weneed to design related node rotation and movement algo-rithms to achieve coverage

51 Definitions of VFA In sensor network coverage the VFA(virtual force algorithm) [31] algorithm has enabled nodesdeployed in the monitoring environment to be redeployedby different virtual field forces The concept of a virtual forcefirst came from physics that is when the distance betweentwo atoms is too small they are separated by the repulsionbetween them When the distance between two atoms is toolarge gravity is generated bringing them closer to each other[14 32] In this article we need to redesign an improved 3D-VFA to solve the following problems

(i) Redeploying a node in a 3D Voronoi partition toaccurately cover uncovered targets

(ii) Quantifying the nodersquos rotation angle and the unityof the nodersquos coordinate system

(iii) Defining the virtual forcesmdashthose generatedbetween nodes (eg mutual attraction and repul-sion) and obstacle repulsion between the forcesmdashtomove the directional nodes to complete the coverage

52 Improved 3D-VFA Analysis Through the above defini-tion of virtual forces we mainly address directional nodemobility During optimisation nodes move under a totalresultant force FA thereby achieving node balance and uni-form target coverage In the monitoring region we assumethat a sensor node is subject to a gravitational force Fa fromneighbouring nodes an interaction force Fij from nodesand a force Fo between the node and the boundary of the targetregion L The total force FA is therefore

FA = n

j=1jneiFij + Fa + Fo eth6THORN

We further constrain our virtual forces to prevent thenode from running out of energy prematurely due to exces-sive node movement We introduce two distance thresholdsrmin represents the minimum safe distance between nodesand rb represents the distance beyond which the interactionforce between the nodes is zero According to the literature[14 33] equation (7) defines the interaction force Fij

between the nodes as

Fij =

+infin 0 lt d si sj

le rmink1mimj

d si sj a1 rmin lt d si sj

lt rb

0 d si sj

= rbminusk2mimj

d si sj a2 rb lt d si sj

le Rc

0 d si sj

gt Rc

8gtgtgtgtgtgtgtgtgtgtgtgtgtgtltgtgtgtgtgtgtgtgtgtgtgtgtgtgt

eth7THORN

7Journal of Sensors

Here k1 k2 a1 and a2 represent gain coefficients and miandmjrepresent the node quality factor (typically with value of1) When the distance between two nodes dethsi sjTHORN satisfies thecondition rmin lt dethsi sjTHORN lt rb the nodes aremutually exclusive

To enable the node to perform motion detection on tar-gets that are far away we set the target Ti as the attractionsource for the node In addition we consider the problemof incompleteness of the node-aware signals as mentionedin [34] Therefore we establish the force between the sensingmodelrsquos centre of gravity and the target In this paper thecentre of gravity of the spherical fan is at Gi and the centreof gravity of the spherical sector is

Gi =38 2r minus heth THORN eth8THORN

where r represents the length of the spherical sector busbar(ie r = Rs) and h represents the length of the point F andthe vertex Cprime in the plane sector as shown in Figure 4(e)then h = FC1 = reth1 minus cos θTHORN Therefore we can calculatethe centre of gravity Gi for the node model (ie Gi = eth38THORNeth2r minus hTHORN = eth38THORNreth1 + cos θTHORN) The gravitational pull of thetarget on the nodersquos centre of gravity can be calculated as

Fa =minusk3mGi

mTi

d Gi Tieth THORNae j isinQ Teth THORN

0 otherwise

8gtltgt eth9THORN

where k3 and ae represent the gain coefficient and dethGi TiTHORNrepresents the Euclidean distance from the nodersquos centre ofgravity Gi to target Ti Additionally mTi

and mGirepresent

quality factors of target Ti and node model Gi respectivelyQethTTHORN represents the force generated by the target set T inthe region of action

Additionally to avoid collisions between nodes andobstacles during movement we must add a boundary repul-sion Fomdashthis ensures the distance between nodes is in theoptimal range According to [14] boundary repulsion is cal-culated as

Fo =k4mimj

d si sj ab 0 lt d si sj

le L

0 d si sj

gt L

8gtgtltgtgt eth10THORN

where k4 and ab are the gain coefficients and dethsi sjTHORN is thedistance between node si and the obstacle When the distancebetween the node and the obstacle is within L the node isrepelled by the obstacle

53 3D-DAOA We design related algorithms to solve twocore issues encountered with directional sensor nodes noderotation and mobility in [29] We now describe a dynamicadjustment optimisation algorithm for 3D DSNs based onspherical sector coverage models 3D-DAOA Meanwhileto address the issues encountered with the original VFAapproach we designed the dynamic coverage adjustment

strategy and combined it with 3D-VFA shown below If thedeployed sensor node can cover the target by rotating rota-tion takes priority and we reduce the activity of the nodersquosmobility coverage method Therefore we present the designsteps and pseudocode of the algorithm in this paper

Step 1 Deploy the number n of sensor nodes si in the moni-toring area L

Step 2 The 3D Voronoi method is used to divide the regionL where the sensor nodes si are located leaving each node isin its own Voronoi unit vi

Step 3 For each directional sensor we set its coordinatesystem origin to the sensorrsquos position and define the centralangle 2θ of the nodersquos sensing model where2θ ge 2 arcsineth ffiffiffi

6p


Step 4 Assuming that the position information of the targetpoint T j is known we test the conditions dethsi T jTHORN le Rs andφ le θ If both are true we store the number of targets thathave been covered NTk

and the number of nodes that are cov-ering the target NSk

and execute Step 5 otherwise we executeStep 13

Step 5 Evaluate dethsi T jTHORN le Rs again If it is true we calculatethe number of target points NTf

and proceed to Step 7 oth-

erwise we execute Step 12

Step 6 Calculate the set of angles σ between each target thathas been covered Tk and the main direction axis w and findthe smallest angle σmin among them

Step 7 Calculate the number NTsof remaining targets Ts

that isNTs=NTf

minusNTk

Step 8 Determine whether the angle ξ between Ts and w sat-isfies the conditions ξ lt θ + σmin or ξ lt θ minus σmin

Step 9 If one of the above conditions is satisfied the maindirection axis of the node is rotated by θ + σmin or ξ lt θ minusσmin toward the target point Ts Otherwise the target that isnot currently covered Ta is marked and we execute Step 10

Step 10 The remaining nodes are retained rotation isstopped and the number of nodes N2 is calculated

Step 11 The resultant force Fa of the idle neighbour nodeand Ta is introduced to move the idle neighbour node SIto cover Ta

Step 12 Calculate the total number of remaining nodes Nscand the number of targets that are not covered NTc

Step 13We use the resultant force FA to move the remainingnodes Sc to Tc

1 Input1 The total number n of sensor nodes si and the perceived radius of the nodes Rs2 Input2 Ti The area of the targets3 Randomly generate the number n of nodes si in the area L of 100m3 size4 L=Polyhedron ([0 0 01 0 01 1 00 1 00 0 11 0 11 1 10 1 1] lowast 100)5 si = galleryethprimeunf ormdataprime frac123 n 0THORN lowast 1006 Maxiter = 50 Set the maximum number of iterations7 Max_Step = 0~10 Set the maximum moving step size of the node8 θi = 2θ Set the initial angle of all directional nodes9 Pi = LocationethsiTHORN Get location information for all nodes siethx y zTHORN10 frac12vi L = VoronoiethPi R3THORN Divide V-body units isin vi vi = fv1 v2⋯vng11 if dethsi T jTHORN le Rs ampamp φ le θ

12 Tk = SizeethNTkTHORN ampamp Sk = SizeethNSk

THORN13 Calculate the number of targets that have been covered NTk

14 Calculate the number nodes that are covering the target NSk15 while i leNum do16 if dethsi T jTHORN le Rs then17 NTf

= SizeethT f THORN ampamp σi = SizeethθminTHORN18 Calculate the number of target points NTf

and the minimum angle σmin19 Calculate the number of target points covered by the same node NTs

20 else21 Select the free neighbour nodes NTs

ethNTs=NTf

minusNTkTHORN to move to cover Ta

22 if ξ lt θ + σminkξ lt θ minus σmin then

23 Rotate the main direction axis w by θ plusmn σmin24 else25 NTs

= SizeethTsTHORN26 Calculate the number of target points that are currently not covered NTs

27 FA = n

j=1jneiFa + Fij + Fo Calculate the total force FA

28 Move Sc rarr Tc29 end if30 Set the number of iterations and repeat lines 12-29 until coverage is complete31 end if32 end while

Algorithm 1 Dynamic adjustment optimisation algorithm (3D-DAOA)

Table 1 Parameter settings

Name Value

Simulation area size L 100m3

Total number of targets Noi 25

Number of nodes n 60100

Sensing radius Rs 10~60mNode communication radius Rc Rc = 2Rs

Initial residual energy E 30 J

rmin Rs times 3~7eth THORNα 05

β 05

Angle of view θ 10∘ le θ le 90∘


Step 14 Repeat Steps 4 5 6 7 8 9 10 11 12 and 13 a setnumber of iterations until all nodes move to the optimal posi-tion and complete the final coverage

In this paper the 3D Voronoi method is first used todivide the space in which the nodes are located allowing usto determine whether a target is located inside a Voronoiunitmdashthough a target might not be contained in any unitsAs the number of nodes increases so does the density ofthe increasingly compact V-body units therefore with alarge number of nodes and events our method can moreaccurately divide the space for target detection Howeverthis paper aims to use algorithms to improve network cov-erage ratios and increase average node residual energyOur main goal is to find a better balance between thenode utilisation and remaining energy to extend the net-work lifetime To achieve this we design the nodersquos cov-erage rotation mechanism priority coverage mechanismand movement mechanism We first design the discriminantcondition of the algorithm by combining the 3D Voronoi

partitioning method with an optimised core adjustmentmechanism The pseudocode of 3D-DAOA is shown inAlgorithm 1

0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X

TargetSensing rangeMoved sensor nodes

(c)

Figure 7 Simulation experiment diagrams (a) initial node deployment (b) experimental simulation process (c) experimentalsimulation result

9Journal of Sensors

6 Experiment Simulation and Discussion

61 Simulation Environment and Results In this section weuse MATLAB (2015b) to perform simulation experimentsto verify the performance of the proposed algorithm Ini-tially we randomly deploy the sensor nodes into a 100m3

cube to test the target points of the deployment Accordingto [35] when node deployment is low the optimal node dis-tance to ensure network connectivity is Rc = 2Rs When thenumber of nodes is large the optimal distance for networkconnectivity is Rc =

ffiffiffi3

pRs The simulation parameters are

listed in Table 1

We first deploy the nodes as shown in Figure 7(a)where the blue cone represents the directional nodes Inthe first set of experiments shown in Figure 7 60 direc-tional sensor nodes were randomly deployed in a 100m3

space During the algorithm the 3D Voronoi partitioningmethod is used to divide the space into 60 different V-body units using the number and positions of the nodessuch that each node si is located in the respective unit vias shown in Figure 7(b) As shown in Figure 7(c) a reddot represents a target to be covered and a blue cone rep-resents the node of the target covered by the algorithmmovement adjustment The black cone indicates the nodersquos

20 30 40 50 60Sensing radius (m)

0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60

Random algorithmImproved VFA

3D-DAOA

Figure 8 Coverage ratio with increasing sensing ratio

Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60

15 30 45 60 75Angle of view (degrees)

0

10

20

30

40

50

60

70


3D-DAOA

Figure 9 Coverage ratio with increasing field of view


change of the position toward a target that is not withinthe coverage range of the algorithm The simulation resultsshow that when the position coordinates of 25 targets areknown the number of targets covered by nodes is firstlycalculated under the adjustment of the algorithm Whenthe target is not within the nodersquos coverage the algorithmselects some of the nodes to move

62 Algorithm Analysis and Contrast Experiment To furtherverify the accuracy of the experiment we compared the3D-DAOA with the random algorithm (RA) and theimproved VFA algorithm [36] In Experiment 1 we setthe number of nodes N = 25 the nodersquos angle of viewAOV = 55∘ and the number of target points T = 60 to ver-ify the relationship between the nodersquos detection radiusand the coverage ratio As shown in Figure 8 as the detec-tion radius increases the coverage ratio of the three algo-rithms also increases However the coverage of theproposed algorithm is significantly higher than that ofthe other two algorithms It can also be seen fromFigure 8 that the coverage ratio of the algorithm firstreaches full coverage when the sensing radius is 60mbecause the algorithm can reasonably divide the node posi-tion from the beginning and it can achieve precise cover-age through rotation or movement by setting the priorityadjustment strategy Therefore the proposed algorithmcan reduce coverage redundancy and greatly improve thecoverage ratio of the overall network

In Experiment 2 we verified the effect on the coverageratio of changing the nodersquos viewing angle as shown inFigure 9 where we see that the coverage of the three algo-rithms increases as the viewing angle increases however thisincrease is less than that caused by increasing the detectionradius because different fields of view (FOV) of the samenode have different effects on the coverage ratio Thereforehaving a larger FOV achieves a larger coverage range thatis the probability of covering a target also increases The

advantage of the proposed algorithm is that it can betterdetermine the current location of nodes and targets and ituses the priority coverage mechanism or idle nodes to achievea higher coverage ratio

Sensor nodes typically carry a power source with limitedenergy and it is difficult to replenish this energy Thereforewe need to use energy reasonably In this experiment thenodersquos rotational and mobile energy consumption make upa large portion of its total energy consumption Accordingto [13 37] a single directional node rotating 180deg consumes152 J of energy this means a single node rotating 1 degreeconsumes 0009 J However each node consumes 36 J per1m of movement

In Experiment 3 we assume the number of nodes N = 25the angle of view θ = 55deg and that the initial energy of eachnode is 30 J to verify the relationship between the averageresidual energy and the coverage ratio in the three algo-rithms As shown in Figures 10 and 11 when the viewingangles of the nodes are the same in each algorithm the aver-age residual energy decreases as the angle increases while thecoverage ratio of the nodes increases as the angle increasesThe improved VFA algorithm has the lowest average residualenergy because it does not dynamically adjust the coveragemechanism which leads to too many mobile nodes There-fore the VFA algorithm has the largest average node energyconsumption 3D-DAOA reasonably reduces unnecessaryenergy consumption to achieve a better balance while ensur-ing a high coverage ratio

We now compare the residual energy of a single node inthe three algorithms with the total coverage ratio when theangles take different values as shown in Table 2 From thiswe conclude that the total value of the two index values forthe proposed algorithm is greatest when the angle of view is55deg because 3D-DAOA can appropriately balance the net-work coverage and energy consumption Furthermore itcomprehensively considers a variety of factors and indicatorsto achieve better detection results

2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA

Energy values (J)Total coverage ratio values ()

Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)

Figure 10 Index values of each algorithm when θ = 45∘

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)



Table 2 Average node residual energy and coverage ratio values for the three algorithms

Angle ofview θ

Random algorithm Improved VFA 3D-DAOAResidualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333

11Journal of Sensors

Combining the data in Figures 10 and 11 with Table 2 weconclude that the nodersquos residual energy after the randomalgorithm has almost no change and the coverage rate is the

lowest because this algorithm does not cause the node torotate or move based on the targetrsquos position Under the sameevaluation index conditions the proposed algorithm has

10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)

Figure 12 The effect of changes in the number of nodes on thecoverage ratio (when the number of the targets is small)

30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100

Random algorithmImproved VFA3D-DAOA

Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)

Figure 13 The effect of changes in the number of nodes on thecoverage ratio (when the number of the target points is large)


obvious advantages over the improved VFA algorithm thealgorithmrsquos priority coverage mechanism achieves accuratetarget coverage the dynamic adjustment mechanism avoidsinvalid node movement and the algorithmrsquos coverage strat-egy is better when the angle of view is 55deg

In Experiments 4 and 5 we verified the relationshipbetween the number of nodes and the coverage ratio InExperiment 4 we set N = 25 θ = 55deg T = 60 and Rs = 30mas shown in Figure 12 We conclude that as the number ofnodes increases the overall coverage ratio of the three algo-rithms increases Figure 12 also shows that when there arefewer nodes the coverage ratio of the three algorithms islower The coverage of the random algorithm and theimproved VFA algorithm is lower than that of 3D-DAOAespecially when the number of nodes exceeds 30

In Experiment 5 setting T = 100 does not changeother indicators as shown in Figure 13 Additionally whenthe number of target points is large the proposed algo-rithm has a higher coverage ratio Therefore under the sameconditions the proposed algorithm is more suitable forlarge-scale target detection because the adjustment mecha-nism of 3D-DAOA enables the node to accurately coverthe target

7 Conclusions

In this paper we studied target coverage in 3D DSNs Firstwe improved the traditional 3D directional sensing modeland proposed a spherical sector model that is more suitablefor 3D directional sensor nodes Next we unified the coordi-nate system of the nodes and rotated them to achieve cover-age using the spherical sector model We then quantified thesensing modelrsquos perspective to provide an effective detectionscheme for directional node coverage We proposed a corre-lation algorithm and combined node rotation and mobility toachieve priority coverage effectively enabling our algorithmto achieve a higher coverage ratio while reducing networkenergy consumption Finally we verified and compared3D-DAOA with other algorithms to prove its reliability andaccuracy In future efforts we will further study the algo-rithmrsquos actual test environment and target mobility

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (61762079 and 61662070) and KeyScience and Technology Support Program of Gansu Provinceunder Grant No 1604FKCA097 and No 17YF1GA015

References

[1] H P Gupta S V Rao and T Venkatesh ldquoAnalysis of stochas-tic coverage and connectivity in three-dimensional heteroge-neous directional wireless sensor networksrdquo Pervasive andMobile Computing vol 29 pp 38ndash56 2016

[2] T Wang Z Peng C Wang et al ldquoExtracting target detectionknowledge based on spatiotemporal information in wirelesssensor networksrdquo International Journal of Distributed SensorNetworks vol 12 no 2 Article ID 5831471 2016

[3] P Kumar and H J Lee ldquoSecurity issues in healthcare applica-tions using wireless medical sensor networks a surveyrdquo Sen-sors vol 12 no 1 pp 55ndash91 2012

[4] M R L F e Silva G H S de Carvalho D C Monteiro andL S Machado ldquoDistributed target location in wireless sensorsnetwork an approach using FPGA and artificial neural


networkrdquo Wireless Sensor Network vol 7 no 5 pp 35ndash422015

[5] O D Incel A Ghosh B Krishnamachari andK Chintalapudi ldquoFast data collection in tree-based wirelesssensor networksrdquo IEEE Transactions on Mobile Computingvol 11 no 1 pp 86ndash99 2012

[6] A Pananjady V K Bagaria and R Vaze ldquoOptimally approx-imating the coverage lifetime of wireless sensor networksrdquoIEEEACM Transactions on Networking vol 25 no 1pp 98ndash111 2017

[7] E Tuba M Tuba and M Beko ldquoMobile wireless sensornetworks coverage maximization by firefly algorithmrdquo in2017 27th International Conference Radioelektronika (RADIO-ELEKTRONIKA) pp 1ndash5 Brno Czech Republic April 2017

[8] P Medagliani J Leguay G Ferrari V Gay and M Lopez-Ramos ldquoEnergy-efficient mobile target detection in wirelesssensor networks with random node deployment and partialcoveragerdquo Pervasive and Mobile Computing vol 8 no 3pp 429ndash447 2012

[9] X Yang ldquoA collision-free self-deployment of mobile roboticsensors for three-dimensional distributed blanket coveragecontrolrdquo in 2017 IEEE International Conference on Roboticsand Biomimetics (ROBIO) pp 80ndash85 Macau China Decem-ber 2017

[10] S M N Alam and Z J Haas ldquoCoverage and connectivity inthree-dimensional networks with random node deploymentrdquoAd Hoc Networks vol 34 pp 157ndash169 2015

[11] V Nazarzehi and A V Savkin ldquoDistributed self-deploymentof mobile wireless 3D robotic sensor networks for completesensing coverage and forming specific shapesrdquo Roboticavol 36 no 1 pp 1ndash18 2018

[12] M M Islam M Ahasanuzzaman M A Razzaque M MHassan A Alelaiwi and Y Xiang ldquoTarget coverage throughdistributed clustering in directional sensor networksrdquo EUR-ASIP Journal on Wireless Communications and Networkingvol 2015 no 1 2015

[13] M A Guvensan and A G Yavuz ldquoHybrid movement strat-egy in self-orienting directional sensor networksrdquo Ad HocNetworks vol 11 no 3 pp 1075ndash1090 2013

[14] X Dang C Shao and Z Hao ldquoTarget detection coverage algo-rithm based on 3D-Voronoi partition for three-dimensionalwireless sensor networksrdquo Mobile Information Systemsvol 2019 Article ID 7542324 15 pages 2019

[15] M M Islam M Ahasanuzzaman M A Razzaque M MHassan and A Alamri ldquoA distributed clustering algorithmfor target coverage in directional sensor networksrdquo in 2014IEEE Asia Pacific Conference on Wireless and Mobile pp 42ndash47 Bali Indonesia August 2014

[16] S Peng Y Xiong M Wu and J She ldquoA new method ofdeploying nodes for area coverage rate maximization in direc-tional sensor networkrdquo in IECON 2017 - 43rd Annual Confer-ence of the IEEE Industrial Electronics Society pp 8452ndash8457Beijing China October 2017

[17] M A Guvensan and A Gokhan Yavuz ldquoOn coverage issues indirectional sensor networks a surveyrdquo Ad Hoc Networksvol 9 no 7 pp 1238ndash1255 2011

[18] Y C Wang Y F Chen and Y C Tseng ldquoUsing rotatableand directional (RampD) sensors to achieve temporal coverageof objects and its surveillance applicationrdquo IEEE Transac-tions on Mobile Computing vol 11 no 8 pp 1358ndash13712012

[19] H Mohamadi S Salleh and A S Ismail ldquoA learningautomata-based solution to the priority-based target coverageproblem in directional sensor networksrdquo Wireless PersonalCommunications vol 79 no 3 pp 2323ndash2338 2014

[20] B Cao X Kang J Zhao P Yang Z Lv and X Liu ldquoDifferen-tial evolution-based 3-D directional wireless sensor networkdeployment optimizationrdquo IEEE Internet of Things Journalvol 5 no 5 pp 3594ndash3605 2018

[21] C Han L Sun F Xiao and J Guo ldquoAn energy efficiency nodescheduling model for spatial-temporal coverage optimizationin 3D directional sensor networksrdquo IEEE Access vol 4pp 4408ndash4419 2016

[22] H Dong K Zhang and L Zhu ldquoAn algorithm of 3D direc-tional sensor network coverage enhancing based on artificialfish-swarm optimizationrdquo in The 2012 International Work-shop on Microwave and Millimeter Wave Circuits and SystemTechnology pp 1ndash4 Chengdu China April 2012

[23] P Sahoo H Thakkar and I S Hwang ldquoPre-scheduled and selforganized sleep-scheduling algorithms for efficient K-coveragein wireless sensor networksrdquo Sensors vol 17 no 12 p 29452017

[24] J Li R Wang H Huang and L Sun ldquoVoronoi-based coverageoptimization for directional sensor networksrdquo Wireless SensorNetwork vol 1 no 5 pp 417ndash424 2009

[25] T W Sung and C S Yang ldquoVoronoi-based coverage improve-ment approach for wireless directional sensor networksrdquo Jour-nal of Network and Computer Applications vol 39 pp 202ndash213 2014

[26] P Kumar Sahoo M J Chiang and S L Wu ldquoAn efficient dis-tributed coverage hole detection protocol for wireless sensornetworksrdquo Sensors vol 16 no 3 p 386 2016

[27] J Huang L Sun R Wang and H Huang ldquoImproved virtualpotential field algorithm based on probability model in three-dimensional directional sensor networksrdquo International Jour-nal of Distributed Sensor Networks vol 8 no 5 Article ID942080 2012

[28] H Topcuoglu M Ermis I Bekmezci and M Sifyan ldquoA newthree-dimensional wireless multimedia sensor network simu-lation environment for connected coverage problemsrdquo Simu-lation vol 88 no 1 pp 110ndash122 2012

[29] W Li C Huang C Xiao and S Han ldquoA heading adjustmentmethod in wireless directional sensor networksrdquo ComputerNetworks vol 133 pp 33ndash41 2018

[30] A Boukerche and X Fei ldquoA Voronoi approach for coverageprotocols in wireless sensor networksrdquo in IEEE GLOBECOM2007-2007 IEEE Global Telecommunications Conferencepp 5190ndash5194 Washington DC USA November 2007

[31] X Yu W Huang J Lan and X Qian ldquoA novel virtual forceapproach for node deployment in wireless sensor networkrdquoin 2012 IEEE 8th International Conference on DistributedComputing in Sensor Systems pp 359ndash363 Hangzhou ChinaMay 2012

[32] A Howard M J Matarić and G S Sukhatme ldquoMobile sensornetwork deployment using potential fields a distributed scal-able solution to the area coverage problemrdquo in DistributedAutonomous Robotic Systems 5 pp 299ndash308 Springer TokyoJapan 2002

[33] M R Senouci A Mellouk K Asnoune and F Y BouhidelldquoMovement-assisted sensor deployment algorithms a surveyand taxonomyrdquo IEEE Communications Surveys amp Tutorialsvol 17 no 4 pp 2493ndash2510 2015


[34] G Fusco and H Gupta ldquoPlacement and orientation of rotatingdirectional sensorsrdquo in 2010 7th Annual IEEE Communica-tions Society Conference on Sensor Mesh and Ad Hoc Commu-nications and Networks (SECON) pp 1ndash9 Boston MA USAJune 2010

[35] H Liu Z J Chai J Z Du and B Wu ldquoSensor redeploymentalgorithm based on combined virtual forces in three-dimensional spacerdquo Acta Automatica Sinica vol 37 no 6pp 713ndash723 2011

[36] X Li L Ci M Yang C Tian and X Li ldquoDeploying three-dimensional mobile sensor networks based on virtual forcesalgorithmrdquo in Advances in Wireless Sensor Networks CWSN2012 pp 204ndash216 Springer Berlin Heidelberg 2012

[37] D ORourke R Jurdak J Liu D Moore and T Wark ldquoOn thefeasibility of using servo-mechanisms in wireless multimediasensor network deploymentsrdquo in 2009 IEEE 34th Conferenceon Local Computer Networks pp 826ndash833 Zurich Switzer-land October 2009

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Submit your manuscripts atwwwhindawicom


coverage we only require modest energy and nodes with lim-ited directional detection to achieve target coverage for a setof targets or special events in practice Therefore 3D DSNscoverage research is more suitable for the above conditions

Of course the directional sensor not only needs to con-sider its own position and sensing range (as with the omnidi-rectional sensor) but must also consider the angle changeproblem Furthermore when nodes are randomly deployedcovered they cannot be accurate and some omissions willoccur Therefore in a specific environment we need adynamic algorithm to select the optimal number of activenodes to detect the target [12] At the same time we needto consider moving or rotating these active nodes within acertain period to adjust their own headings to achieve thebest coverage For example in [8] the use of unattendedsensor networks has been discussed for detecting targetsusing energy-efficient methods The authors are dedicatedto analysing the trade-offs between power consumption andquality of service in WSNs in terms of detection capabilitiesand latency In [13] the authors propose using the hybridmovement strategy (HMS) to solve the problem of highenergy consumption (resulting from mobility) and improvethe coverage ratio of DSNs Although the method proposedabove can reduce the energy consumption of the networkand improve the coverage ratio the rotation angle of the 3Ddirectional sensor node is difficult to determine increaseddimensionality brings further complications

Therefore we propose a network model suitable fordirectional sensors and related dynamic adjustment optimi-sation algorithms for 3D systems We first design a sensingmodel that is more suitable for 3D DSNs and allows us toquantify the rotation angle of the node Secondly to achieveaccurate coverage we extend traditional 2D Voronoi divisionand apply it to 3D DSNs We also use theory and experimen-tation to verify the algorithm to further reduce networkenergy consumption Finally we design experimental simula-tions and perform algorithm comparisons to further ana-lyse our algorithmrsquos effectiveness Our main contributionsare highlighted as follows

(i) We are the first to propose a spherical sector sensingmodel for 3D DSNs that quantifies the rotation anglein combination with using a 3D Voronoi method[14] to divide space using the sensorsrsquo positions

(ii) We design a synergistic priority coverage mecha-nism to reduce the moving distance of nodesthereby reducing excessive energy consumptionwhile guaranteeing a high coverage ratio for the sen-sor network

(iii) We optimise the traditional virtual force algorithmto suit practical conditions and we perform a fulltheoretical analysis and experimental comparativeanalysis of the algorithm proposed in this paper toverify its validity and accuracy

The remainder of this paper is organised as follows InSection 2 the research progress and related work on DSNsin recent years are summarised In Section 3 the DSNs

coverage model and sensing angle are described and the rel-evant definitions are provided After this we compare thedifferences between 2D and 3D Voronoi and give the 3DVoronoi partition theory in Section 4 We then show howwe have designed and improved the relevant algorithms andprovide its design steps in Section 5 In Section 6 we describethe simulations and experiments we performed on the algo-rithm and compare it with other algorithms for analysis Con-clusions and future works are discussed in the final section

2 Related Works

In recent years research on DSNs has been carried outmainly based on 2D planes For example in [15] the authorspropose a cluster head- (CH-) based distributed target cov-erage algorithm to solve a Maximum Coverage with Mini-mum Sensor (MCMS) problem The authors also designeddistributed clustering and target coverage algorithms toreduce network energy consumption Subsequently in [12]they designed a target coverage algorithm for DSNs in anenergy-saving manner based on [15] through the distrib-uted clustering mechanism The authors improved the dis-tributed algorithm in [15] to use the CH approach andensure that it is used appropriately to enhance DSNs tar-get coverage In [16] the authors propose a new method(based on particle swarm optimisation) to maximise cover-age for 2D regions This algorithm allows a directional sensornode to constantly adjust its sensing direction to provide thebest coverage However most of the above studies map 3Dsensor coverage problems into 2D for discussionmdashthey can-not be applied directly in three dimensions Therefore weneed to consider not only dimensionality but also a node-aware model that can be applied in the dimension of theactual environment

In addition the nodes are often distributed randomly inthe monitoring area Reducing the deployment costmdashwhileusing the limited node energy for efficient coveragemdashhasbecome an active research topic The authors point out thatmotility and mobility are essential for DSN nodes to mini-mise occlusion effects and coverage overlap in [17] At thesame time motility is superior tomobility in terms of networkcost and energy efficiency Therefore almost all research aimsto solve coverage problems through motility

In practice however there are still some coverage holesthat can only be addressed through mobility For examplethe authors in [18] use the directionality of the orienta-tion sensor to rotate it to locate periodic detection objectsTherefore the above authors developed an event monitoringsystem that proposed a maximum coverage deployment(MCD) heuristic iteration to deploy sensors to cover targetsBut we must not only consider the direction of the orienta-tion sensor (ie the change or rotation of its sensing angle)to enable efficient deployment we must also consider thatthe orientation sensor can move to fill coverage holes in themonitoring area (ie DSNs can be moved) Thereforethe literature [13] proposes HMS to solve the high energyconsumption of directional sensor movement The authorsuse the cascading method to adjust the coverage of the DSNseffectively reducing network energy consumption In [19]

x

z

Rso

y

M

B1A1

C1

F

120579



3Journal of Sensors









x

z

y

P

Main direction

ro120595

120596

120579

120593










ffiffiffi2



2p


2p


p3THORNr The con-


6p


6p


6p



6p




6p



6p





x

y

z

O r

A

B

C

(a)

2r

rOprime

O

A

C

B

radic

G

(b)

C

BA

60deg

120deg

r

Oprime

D

2rradic

22

radic997888

(c)

O

r

OprimeG C

120593

r63

radic997888

(d)

F

r

h

o

A1B1

C1

120579

r63

radic997888

(e)


5Journal of Sensors


Csi p =1




q eth2THORN



C = 1 minusYNi=1

1 minus Csi p

eth3THORN


C = 1 minusYNi=1


eth4THORN






j


eth5THORN



0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

5001

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20 21

22

23

24 25

26

27

28

29 30

31

32

33

34

35

36

37

38

39

40

41

42

43

44 45

46 47

48

49

50

51

52

53 54

55

56

57 58

59

606162

63

64

65

66

67

68

69

70


0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500














FA = n




Fij =

+infin 0 lt d si sj

le rmink1mimj


lt rb

0 d si sj

= rbminusk2mimj


le Rc

0 d si sj

gt Rc


eth7THORN

7Journal of Sensors





Fa =minusk3mGi

mTi


0 otherwise

8gtltgt eth9THORN


and mGirepresent



Fo =k4mimj


le L

0 d si sj

gt L








6p










that isNTs=NTf

minusNTk














ethNTs=NTf





27 FA = n





Name Value







β 05






0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X


(c)


9Journal of Sensors




ffiffiffi3


listed in Table 1




0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


x

z

Rso

y

M

B1A1

C1

F

120579



3Journal of Sensors









x

z

y

P

Main direction

ro120595

120596

120579

120593










ffiffiffi2



2p


2p


p3THORNr The con-


6p


6p


6p



6p




6p



6p





x

y

z

O r

A

B

C

(a)

2r

rOprime

O

A

C

B

radic

G

(b)

C

BA

60deg

120deg

r

Oprime

D

2rradic

22

radic997888

(c)

O

r

OprimeG C

120593

r63

radic997888

(d)

F

r

h

o

A1B1

C1

120579

r63

radic997888

(e)


5Journal of Sensors


Csi p =1




q eth2THORN



C = 1 minusYNi=1

1 minus Csi p

eth3THORN


C = 1 minusYNi=1


eth4THORN






j


eth5THORN



0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

5001

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20 21

22

23

24 25

26

27

28

29 30

31

32

33

34

35

36

37

38

39

40

41

42

43

44 45

46 47

48

49

50

51

52

53 54

55

56

57 58

59

606162

63

64

65

66

67

68

69

70


0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500














FA = n




Fij =

+infin 0 lt d si sj

le rmink1mimj


lt rb

0 d si sj

= rbminusk2mimj


le Rc

0 d si sj

gt Rc


eth7THORN

7Journal of Sensors





Fa =minusk3mGi

mTi


0 otherwise

8gtltgt eth9THORN


and mGirepresent



Fo =k4mimj


le L

0 d si sj

gt L








6p










that isNTs=NTf

minusNTk














ethNTs=NTf





27 FA = n





Name Value







β 05






0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X


(c)


9Journal of Sensors




ffiffiffi3


listed in Table 1




0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


x

z

y

P

Main direction

ro120595

120596

120579

120593










ffiffiffi2



2p


2p


p3THORNr The con-


6p


6p


6p



6p




6p



6p





x

y

z

O r

A

B

C

(a)

2r

rOprime

O

A

C

B

radic

G

(b)

C

BA

60deg

120deg

r

Oprime

D

2rradic

22

radic997888

(c)

O

r

OprimeG C

120593

r63

radic997888

(d)

F

r

h

o

A1B1

C1

120579

r63

radic997888

(e)


5Journal of Sensors


Csi p =1




q eth2THORN



C = 1 minusYNi=1

1 minus Csi p

eth3THORN


C = 1 minusYNi=1


eth4THORN






j


eth5THORN



0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

5001

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20 21

22

23

24 25

26

27

28

29 30

31

32

33

34

35

36

37

38

39

40

41

42

43

44 45

46 47

48

49

50

51

52

53 54

55

56

57 58

59

606162

63

64

65

66

67

68

69

70


0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500














FA = n




Fij =

+infin 0 lt d si sj

le rmink1mimj


lt rb

0 d si sj

= rbminusk2mimj


le Rc

0 d si sj

gt Rc


eth7THORN

7Journal of Sensors





Fa =minusk3mGi

mTi


0 otherwise

8gtltgt eth9THORN


and mGirepresent



Fo =k4mimj


le L

0 d si sj

gt L








6p










that isNTs=NTf

minusNTk














ethNTs=NTf





27 FA = n





Name Value







β 05






0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X


(c)


9Journal of Sensors




ffiffiffi3


listed in Table 1




0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


x

y

z

O r

A

B

C

(a)

2r

rOprime

O

A

C

B

radic

G

(b)

C

BA

60deg

120deg

r

Oprime

D

2rradic

22

radic997888

(c)

O

r

OprimeG C

120593

r63

radic997888

(d)

F

r

h

o

A1B1

C1

120579

r63

radic997888

(e)


5Journal of Sensors


Csi p =1




q eth2THORN



C = 1 minusYNi=1

1 minus Csi p

eth3THORN


C = 1 minusYNi=1


eth4THORN






j


eth5THORN



0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

5001

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20 21

22

23

24 25

26

27

28

29 30

31

32

33

34

35

36

37

38

39

40

41

42

43

44 45

46 47

48

49

50

51

52

53 54

55

56

57 58

59

606162

63

64

65

66

67

68

69

70


0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500














FA = n




Fij =

+infin 0 lt d si sj

le rmink1mimj


lt rb

0 d si sj

= rbminusk2mimj


le Rc

0 d si sj

gt Rc


eth7THORN

7Journal of Sensors





Fa =minusk3mGi

mTi


0 otherwise

8gtltgt eth9THORN


and mGirepresent



Fo =k4mimj


le L

0 d si sj

gt L








6p










that isNTs=NTf

minusNTk














ethNTs=NTf





27 FA = n





Name Value







β 05






0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X


(c)


9Journal of Sensors




ffiffiffi3


listed in Table 1




0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

5001

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20 21

22

23

24 25

26

27

28

29 30

31

32

33

34

35

36

37

38

39

40

41

42

43

44 45

46 47

48

49

50

51

52

53 54

55

56

57 58

59

606162

63

64

65

66

67

68

69

70


0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500














FA = n




Fij =

+infin 0 lt d si sj

le rmink1mimj


lt rb

0 d si sj

= rbminusk2mimj


le Rc

0 d si sj

gt Rc


eth7THORN

7Journal of Sensors





Fa =minusk3mGi

mTi


0 otherwise

8gtltgt eth9THORN


and mGirepresent



Fo =k4mimj


le L

0 d si sj

gt L








6p










that isNTs=NTf

minusNTk














ethNTs=NTf





27 FA = n





Name Value







β 05






0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X


(c)


9Journal of Sensors




ffiffiffi3


listed in Table 1




0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


7Journal of Sensors





Fa =minusk3mGi

mTi


0 otherwise

8gtltgt eth9THORN


and mGirepresent



Fo =k4mimj


le L

0 d si sj

gt L








6p










that isNTs=NTf

minusNTk














ethNTs=NTf





27 FA = n





Name Value







β 05






0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X


(c)


9Journal of Sensors




ffiffiffi3


listed in Table 1




0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









ethNTs=NTf





27 FA = n





Name Value







β 05






0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X


(c)


9Journal of Sensors




ffiffiffi3


listed in Table 1




0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0100

20

40

60

Z

100

80

100

80

Y

50 60

X

4020

0 0

(a)

100

80

60

40

20

0100

5050

100

0 0Y

Z

X

(b)

Y

100

80

60

40

20

5050

0

0 0

100100

Z

X


(c)


9Journal of Sensors




ffiffiffi3


listed in Table 1




0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

10

20

30

40

50

60

70

80

90

100

Tota

l cov

erag

e rat

io (

)

N = 25 120579 = 55deg T = 60


3D-DAOA


Tota

l cov

erag

e rat

io (

)

N = 25 Rs = 30 T = 60


0

10

20

30

40

50

60

70


3D-DAOA










2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


2971

1706

2451

034

043

052

0

01

02

03

04

05

06

0

5

10

15

20

25

30

35

Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA 3D-DAOA


Tota

l cov

erag

e rat

io (

)

Aver

age r

esid

ual e

nerg

y (J

)


Randomalgorithm

Randomalgorithm

ImprovedVFA

ImprovedVFA

3D-DAOA3D-DAOA

2935

1431

2246

037

048

061

0

01

02

03

04

05

06

07

Tota

l cov

erag

e rat

io (

)0

5

10

15

20

25

30

35

Aver

age r

esid

ual e

nerg

y (J

)




Angle ofview θ


Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

Residualenergy

Coverageratio ()

Totalvalue

45deg 2971 34 6371 1706 43 6006 2451 52 7651

55deg 2935 37 6635 1431 48 6231 2246 61 8346

60deg 2917 39 6817 1152 53 6452 2033 63 8333




10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


10 15 20 25 30 35 40 45 50Number of nodes

10

20

30

40

50

60

70

80

90

100

Random algorithm

Rs = 30 120579 = 55deg T = 60

Improved VFA3D-DAOA

Tota

l cov

erag

e rat

io (

)


30 35 40 45 50 55 60 65 70Number of nodes

20

30

40

50

60

70

80

90

100


Rs = 30 120579 = 55deg T = 100

Tota

l cov

erag

e rat

io (

)






7 Conclusions


Data Availability




Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Dynamic Adjustment Optimisation Algorithm in 3D...

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