Research ArticleA New Energy-Efficient Coverage Control with MultinodesRedundancy Verification in Wireless Sensor Networks

Zeyu Sun12 Chuanfeng Li13 Xiaofei Xing4 and Huihui Wang5

1School of Computer and Information Engineering Luoyang Institute of Science and Technology Henan 471023 China2School of Electronics and Information Engineering Xirsquoan Jiaotong University Shaanxi 710049 China3School of Electronics Electrical Engineering and Computer Science Queenrsquos University Belfast Belfast BT95AH UK4School of Computer Science and Educational Software Guangzhou University Guangdong 510006 China5Department of Engineering Jacksonville University 2800 University Blvd N Jacksonville FL 32211 USA

Correspondence should be addressed to Huihui Wang hwang1juedu

Received 5 September 2016 Accepted 27 October 2016

Academic Editor Jesus Corres

Copyright copy 2016 Zeyu Sun et alThis is an open access article distributed under theCreative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The target nodes are 119896-covered by the sensor nodes there will be a lot of redundant data forcing the phenomenon of congestionwhich lowers the network communication capability and coverage and accelerates network energy consumption Therefore thispaper proposes an energy-efficient coverage control with multinodes redundancy verification (ECMRV)The algorithm constructsthe coverage network model by using the positional relationship among the sensor nodes and the proof procedure of the sectorcoverage expected value of the monitoring area also has been provided On the aspect of the energy consumption this paper givesthe proportion of energy conversion functions between the working sensor nodes and the neighboring sensor nodes And by usingthe function proportional to schedule the sensor nodes with low energy we achieve the energy balance of the whole network andthe optimization of the network resources Finally the simulation experiments indicate that this algorithm can not only improvethe quality of network coverage but completely inhibit the rapid energy consumption of the sensor nodes as well as a result thenetwork lifetime extends which has verified availability and stability of the algorithm in the paper

1 Introduction

Wireless Sensor Network is a new type of network architec-ture which is formed by thousands of sensor nodes [1ndash3]Each sensor node has the abilities of sensing computingcommunicating and storing and the behavioral character-istic is to complete the communication transmission by themultihop method in the information world which makesdata acquisition data storage data computing and commu-nication transmission link network service system come intobeing [4 5]

The coverage quality and energy consumption are twoimportant indices of evaluating the performance of WirelessSensor Networks system Coverage quality can be directlyreflected in the deployment of the sensor nodes in themonitoring area And the network lifetime directly affectsthe quality of the entire network service which is mainlyreflected in the energy consumption of the sensor nodes

deployment Generally because of the restriction of thetopography environmental factors and many other con-straints the selection of the sensor node deployment israndom In the random deployment process due to theunpredictable sensor node location information in advanceit is possible to make a monitoring target node multiplycovered namely 119896-coverage Take the military battlefield asexample as shown in Figure 1 And there is another situationdue to the randomness it is possible to make a monitoringarea a blind one The only way to achieve complete coverageis to add more sensor nodes Although the two ways abovecan achieve complete coverage of the target to a certainextent there are still some shortcomings First becauseof the existence of the 119896-coverage in the process of datacollection and calculation and in the data transmission ofthe communication linkage there will be a large amount ofredundant data which cause larger error and uncertaintySecond the real meaning of the coverage is not the complete

Hindawi Publishing CorporationJournal of SensorsVolume 2016 Article ID 2347267 11 pageshttpdxdoiorg10115520162347267

2 Journal of Sensors

Figure 1 The topological structure of the coverage in the militarybattlefield

coverage of the entire monitoring area but the completecoverage of the certain target nodes in the process of coveringthe entire monitoring area completely to take no accountof the existence of the target nodes will consume a lot ofsensor node energy which will accelerate the speed of thecollapse of the whole network systemThird when deployingthe sensor nodes the existence of the randomness willinevitably cause excessive density in a certain coverage areaof the monitoring area resulting in the bottlenecking whicheventually generates information redundancy verification inthe channel but reduces the network expansibility

Aiming at the above shortages this paper proposed theenergy-efficient coverage control with multinodes redun-dancy verification (ECMRV) In this paper the coverageprobability and covering expected value of sensor nodesare solved by using the sector domains of the coveragearea when the moving target nodes are passing through themonitoring area as for the energy consumption this papergives the solution ofmultipoint transmission and single pointtransmission For the working sensor nodes having met thecertain coverage ratio when the moving target nodes arepassing across the 119896-coverage area it will close the sensornodes within or higher the threshold value or it will placethe sensor nodes in the sleeping state by the sensor nodeadaptive transformation mechanism and the other sensornodes will use the sensor node energy schedulingmechanismto compete the conversion of the energy of the sensor nodesso that the network lifetime can be extended

2 Related Knowledge

The technique of coverage control in WSNs is a veryimportant fundamental research and also one of the hotspotproblems right now in WSN The coverage quality willaffect the lifetime of the network In recent years manyexperts and scholars at home and broad have carried outplenty of researches thoroughly and carefully Literature [6]brings in the partial coverage optimization and constitutesthe partial 120572 coverage and after a series of calculation andoptimization of the 120572 the complete coverage optimization

is finally achieved All the above-mentioned algorithms haveachieved the effective coverage of the monitoring area tosome extent however they have the mutual problem thatthe algorithms have more calculations and they are morecomplex and the scalability of the Wireless Sensor Networkis worse Literature [7] provides a constructive methodof connected coverage protocol The protocol provides theproportional relation between the network coverage qualityand the network and the performance indexes of all theparameters in the network system and creates the schedulingcontrol algorithm (SCA) the purpose of which is to usethe least sensor nodes to guarantee the connection of thewhole network system Literature [8] introduces the artifi-cial intelligence algorithms that is the swarm intelligencealgorithm and the granule algorithm to complete the sensornodes deployment of the whole networkmonitoring area andin the stage of the coverage optimization the whole coverageis optimized by the two artificial intelligence algorithms andfinally realizes the complete coverage of the monitoring areaas for the energy consumption it completes the schedulingconversion of the sensor nodes energy by the heuristic sensornodes Scheduling which extends the lifetime of the networkLiterature [9] proposes the optimization strategy on coveragealgorithm based on Voronoi Satisfying the condition ofa certain coverage quality the algorithm adds some worksensor nodes to the coverage hole so as to improve thecurrent coverage ratio meanwhile it will search reasonableinformation of repairing site to guarantee the connection ofthe whole network Literature [10] also takes the Voronoi asthe research object and solves the information of wire rod sitethat formed by the geometry variation in the Voronoi andthe sensor nodes and finally completes the coverage of themonitoring area Literature [11] and literature [12] computethe goal sensor nodes effectively utilizing the different anglesof the sector composed by the sensor nodes and the targetnodes and give the method of computing the coverage prob-ability of differentmonitoring area All algorithmsmentionedabove have the better feasibility the higher reliability and thelarger network scalability However in the research processof the four algorithms their network models are much tooidealized From literature [9] to literature [11] they all takethe static target nodes as the research objective and literature[12] does not consider the situation when the moving targetnodes are the concerned target nodes which result in the 119896-barrier coverage Literature [13] proposes the polytypic targetcoverage algorithm based on the linear programming Thealgorithm utilizes the clustering structure to solve the poly-typic target coverage problem By computing the coverageability and the residual energy of the sensor it completesthe polytypic target optimization coverage in the way ofthe linear programming Literature [14] proposes the eventprobability driven mechanism algorithm This algorithmcalculated the coverage probability and the expected value ofthe sensor nodes with the probability model then optimizedthe result and finally achieved the optimal coverage Theabove two algorithms achieve the purposes of the optimalcoverage and the extension of the network lifetime but thecoverage condition is a little hasher and the calculations ofthe algorithms are much more complex

Journal of Sensors 3

In order to make the effective coverage of the monitoringarea better on the basis of literature [11] and literature [12]this paper proposes the energy-efficient coverage control withmultinodes redundancy verification (ECMRV) Taking useof sectorial the 119896-degree coverage the algorithm calculatesthe coverage expected value between the sensor nodes andthe moving target nodes And then the algorithm providesthe solving procedure of the coverage expected value whena certain sensor node finishes the coverage of the targetnodes In terms of the energy on the basis of the analysisof all the sensor nodesrsquo energy in the whole network thealgorithm provides the process of the energy comparisonunder the multilateral and unilateral connection that is theenergy consumption of the data in multicast is less thanthat of the unilateral sensor nodes In terms of the energyconversion the algorithm completes the energy conversionamong the sensor nodes through the self-scheduling mecha-nism extending the lifetime of the network Finally throughthe simulation experiments and the comparison with otheralgorithms the effectiveness and the stability of the ECMRValgorithm have been verified

3 The Network Model andthe Coverage Quality

31 Basic Concepts and BasicTheories For the sake of the bet-ter explanation and research of the WSNs coverage problemsand the convenience of the problems the ECMRV algorithmis based on the following four hypothesizes [10 15 16]

(1) All of the sensor nodes are all in the homogeneousform and the perceived range and the communica-tion range are both disc-shaped

(2) All of the sensor nodes can get their own positioninformation through the GPS technology

(3) The initial energy of all the sensor nodes is the sameand has the same sensing range and the speed is thesame as that of the clock

(4) The sensor nodes are deployed randomly in thesquare monitoring area with the length 119897 and theperceived range must be guaranteed to be less thanthe length 119897 and the boundary effect can be ignored

(5) The sensor nodes are randomly deployed in themonitoring areas with high density and the sensornodes are independent of each other

Definition 1 (the complete coverage) In the monitoring areaany target nodes must be covered by at least one sensornode that is the Euclidean distance of the sensor nodes andthe target nodes are smaller than the perceived range of thesensor nodes 119889(119894 119905) le 119877119894 which is called complete coverage

Definition 2 (the 119896-coverage) In the monitoring area anytarget nodesmust be covered by at least 119896 sensor nodesThusthe monitoring area is called 119896-degree coverage areaDefinition 3 (the coverage quality) In the monitoring areathe coverage quality is the specific value of the sum of the

sensed area of all the sensor nodes and the area of themonitoring area In a way it reflects the coverage degree ofthe target nodes

Definition 4 (the multilevel coverage) The coverage rate ofeach sensor node is 119901 then the coverage rate at any point ina two-dimensional plane is

119901119899 = 1 minus (1 minus 119901)119899 (1)

In (1) 119901119899 is themultilevel coverage ratio 119901 is the coverageprobability of any one of the sensor nodes 119899 is the number ofthe sensor nodes [10 17 18]

Theorem 5 When the moving target nodes enter the moni-toring area for the first time the first coverage expected value is119864(119883) = [1minus(1minus119901)119873]119901minus1 and119873 is the biggest number of timesthat the moving target nodes can complete the transmissionand 119901 is the coverage probability of the sensor nodes

Proof According to the probability theory suppose that 119883represents how many times the moving target nodes moveand the value range of119883 is possible to be119883 isin [1 2 3 119873]When 119883 = 119898 as well as meeting the condition of 1 le 119898 le119873minus1 that is when the first119873minus1moving target nodes are notcovered by the sensor nodes the distribution density functionof119883 will be

119875 (119883 = 119896) = 119901 (1 minus 119901)119896minus1 119896 = 1 2 3 119873 minus 1(1 minus 119901)119873minus1 119896 = 119873 (2)

According to the equation of the coverage thus

119864 (119883) = 119873minus1sum119896=1

119896119901 (1 minus 119901)119896minus1 + 119873 (1 minus 119901)119873minus1 (3)

Make 119902 = 1 minus 119901 and 119878 = sum119873minus1119896=1 119896(1 minus 119901)119896minus1 that is 119878 =sum119873minus1119896=1 119896119902119896minus1 is multiplied by 119902 in both sides of the equationthus 119902119878 = sum119873minus1119896=1 119896119902119896 that is

119878 = 1 minus 119902119873minus1(1 minus 119902)2 minus

(119873 minus 1) 119902119873minus11 minus 119902= 1 minus (1 minus 119901)119873minus1

1199012 minus (119873 minus 1) (1 minus 119901)119873minus1119901

(4)

Put (4) into (3) thus

119864 (119883) = 119901(1 minus (1 minus 119901)119873minus11199012 minus (119873 minus 1) (1 minus 119901)119873minus1119901 )

+ 119873(1 minus 119901)119873minus1 = [1 minus (1 minus 119901)119873] 119901minus1(5)

In the square monitoring area after a period of 119905 theenergy of the working sensor nodes must have been con-sumed by themselves which make the coverage area changecorrespond In order to suppress the energy consumption ofthe sensor nodes and extend the lifetime of the network as

4 Journal of Sensors

A

B

C

D

120573

120572

Figure 2 Multilateral and unilateral node connection

long as possible this paper adopts the sensor node energymodel to analyze the sensor node-energy that is consumed inthe process of unilateral and multilateral data transmissionmeanwhile the energy of the sensor node is consumed byits own work of calculation [19ndash22] storage and control Theenergy consumption model of the sensor node transmitter is

119864Tx (119897 119889) = 119897119864119879-elec + 119864amp (119897 119889)=

119897119864119879-elec + 1198971205761198911199041198892 119889 lt 1198890119897119864119879-elec + 119897120576amp1198894 119889 ge 1198890

(6)

And the energy consumption model of the receiver is

119864Rx (119897) = 119864119877-elec (119897) = 119897119864elec (7)

And 119897 is the bit of the data transmission 119889 is the Euclideandistance between the sensor nodes and the neighboringnodes and 1198890 is the threshold value of the distance ofthe communication sensor node When the distance ofthe communication sensor node is smaller than 1198890 theenergy damping index is 2 whereas the energy dampingindex will be 4 119864elec represents the energy consumptionof communication sensor nodes receiving and transmittingmodules [23 24]

Theorem 6 Less energy of the data is consumed in multicastthan the unilateral sensor nodes The mathematical inductionwhen 119899 rarr infin is shown in Figure 2

In 1st case according to formula (6) the formula of energydissipations directly from source node 119860 to target node 119863 ispresented as below

119864Tx 119860119863 (119897 119889119860119863) = 119897119864119879-elec + 1198971205761198911199041198892119860119863 119889119860119863 lt 1198890119897119864119879-elec + 119897120576amp1198894119860119863 119889119860119863 ge 1198890 (8)

In the 2nd case data are sent from node 119860 to 119861 andthen to 119863 From 119860 to 119861 when 119896 = 3 the model of energyconsumption when transmitting module in node 119860 can beinducted as follows

119864Tx 119860119861 (119897 119889119860119861) = 119897119864119879-elec + 1198971205761198911199041198892119860119861 119889119860119861 lt 1198890119897119864119879-elec + 119897120576amp1198894119860119861 119889119860119861 ge 1198890

119864Rx 119861 (119897) = 119897119864elec(9)

The energy consumption of node 119861 receiving the infor-mation is represented as below

119864Tx 119861119863 (119897 119889119861119863) = 119897119864119879-elec + 1198971205761198911199041198892119861119863 119889119861119863 lt 1198890119897119864119879-elec + 119897120576amp1198894119861119863 119889119861119863 ge 1198890 (10)

Then the total energy consumption fromnode119860 to119861 andthen to119863 is represented as below

119864Total = 119864Tx 119860119861 + 119864Rx 119861 + 119864Tx 119861119862 (11)

In their initial state the nodesworkwith the same amountof energy and are independent of each other The basicproperties of triangle are shown

At the beginning each node is independent of eachother and is working with equal energy This basic feature offorming triangles can be represented as below

119864Total = 119864Tx 119860119861 + 119864Rx 119861 + 119864Tx 119861119863 lt 119864Tx 119860119863 (12)

That is to say when 119896 = 3 less energy is consumed inmultilateral data transmission than in unilateral one Sowhen119896 = 3 formula (12) is justified

The data transmitting path is from 119860 to 119861 to 119862 and thento 119863 When 119899 rarr infin because ang120572 is an obtuse angle ang120572 gt1205872 cosang120572 lt 0 According to CosineTheorem 1198611198622 +1198621198632 lt1198611198632The triangle of connecting119861119862 and119863 is obtuse triangleHence formula (13) is obtained as below

119864Tx 119860119861 + 119864Rx 119861 + sdot sdot sdot + 119864Rx119899minus1 + 119864Tx119899minus1119899 lt sdot sdot sdotlt 119864Tx119860119861 + 119864Rx119861 + 119864Tx119861119863 lt 119864Tx119860119863 (13)

32 Cover Quality

Theorem 7 Randomly select 119896 sensor nodes within 119872 andthen the expectation of the coverage quality is

119864 (120578119896) = 1 minus 1 minus 120587 (11987720 + 1205822)area (119872)

119896

(14)

Proof The sensor node subject to the random uniformdistribution in119872 so the probability a sensor node is locatedin any position in119872 is 1area(119872) If any point 119902 is coveredby a sensor node 119886 (the perception radius is denoted with119877119886)then sensor node 119886must be locate in a circle of centered on q(the circle is denoted as119874(119902 119877119886) of radius 119877119886) Therefore theprobability that 119902 is covered by sensor node 119886 is

119875119886 = area (119874 (119902 119877119886))area (119872) (15)

Because the perception radius of sensor node 119886 is normaldistribution and 1198770 ge 33120582 the probability that any point iscovered by a work sensor node is

119875 = int211987700

119875119886 1(2120587)12 120582 exp(minus(119877119886 minus 1198770)21205822 ) d1198770 (16)

Journal of Sensors 5

Let 119909 = (119877119886 minus 1198770)120582 then119875 = (1205872 )

12 1area (119872) (int

1198770120582

minus119877012058212058221199092 exp(minus11990922 ) d119909

+ int1198770120582minus1198770120582

21205821199091198770 exp(minus11990922 ) d119909+ int1198770120582minus1198770120582

11987720 exp(minus11990922 ) d119909) (17)

Calculation is as follows

119875 = (1205872 )12 1

area (119872) (minus1205822 exp(minus1199092

2 )1003816100381610038161003816100381610038161003816100381610038161198770120582

minus1198770120582

+ (2120587)12 120582 + (2120587)12 11987720) asymp 120587 (11987720 + 1205822)area (119872)

(18)

The positions of all sensor nodes in119872 are independent ofeach other according to formula (1) the probability that anysensor node in119872 is at least covered by 119896 work sensor node is

119875119870 = 1 minus (1 minus 120587 (11987720 + 1205822)area (119872) )

119896

(19)

Assume the area covered by at least 119896 sensor nodes is1198721015840and then the expectation of the area for1198721015840 is

119864 (area (1198721015840)) = 119875119896area (119872) (20)

Therefore

119864 (120578119896) = 119864 (area (1198721015840))area (1198721015840) = 1 minus (1 minus 120587 (11987720 + 1205822)

area (119872) )119896

(21)

With Theorem 5 we can get the expectation of theminimum number of required work sensor nodes satisfyingdemanded coverage quality 120578119889 of applications namely

119864 (119896) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (22)

Theorem 8 After the redundant sensor nodes are powered offrandomlywithout causing any conflict if the rest working nodescan provide the coverage quality 119899119889 required by the applicationthe expectation for the number of redundant sensor nodesrsquoneighbors satisfies

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (23)

Proof Assuming the number of the remaining work sensornodes is 119873 after the redundant nods are powered off thenthe 119899 work sensor nodes still follow random and uniformdistribution Because the remaining work sensor nodes canstill accurately provide the coverage quality required inapplications by formula (22) we get

119864 (119873) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (24)

Denote the perception radius of sensor node as 119877119886 119877119887which represents the perception radius of sensor node 119887 If 119887is the coverage neighbor of 119886 then 119887must be located in a circlecentered on the radius 119877119886 +119877119887 (denote the circle as119874(119886 119877119886 +119877119887)) Therefore the probability that 119887 is a coverage neighborof 119886 is

119875119887minus119886 = area (119874 (119886 119877119886 + 119877119887))area (119872) (25)

Because the perception radius of all sensor nodes obeysnormal distribution 119873(1198770 1205822) as well as 1198770 ge 33120582 theprobability that a sensor node is the coverage neighbor ofanother sensor node is

119875 = int211987700

int211987700

119875119887minus119886sdot 121205871205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887(26)

Calculation is

119875 = 1area (119872) [int

21198770

0int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887+ int211987700

int211987700

119877119886119877119887sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887]

(27)

According to the computation process in formula (27) wehave

int211987700

int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887asymp 120587 (11987720 + 1205822)

(28)

Because

int211987700

119877119886 1(2120587)12 120582 exp(minus(1198770 minus 119877119886)221205822 ) d119877119886

= int1198770120582minus1198770120582

(1198770 + 120582119909) 1(2120587)12 exp (minus

1199092) d119909 = 1198770(29)

6 Journal of Sensors

int211987700

int211987700

2120587119877119886119877119887sdot 121205871205822 exp(minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ) d119877119886 d119877119887= 212058711987720

(30)

Then we have

119875 = 412058711987720 + 21205871205822area (119872) (31)

The expectation of the number of coverage neighborsensor nodes for each of the remaining119873 work sensor nodesis

119864 (119899) = (119864 (119873) minus 1) 119875= ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (32)

Therefore the expectations of the number of redundantcoverage neighboring sensor nodes satisfy

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (33)

33 Algorithm Description As to the redundancy of sensornodes the connection graph of sensor nodes gatheringredundancy is constructed that is the redundancy infor-mation calculated by a positioning algorithm (eg centroidpositioning and ranging location) of all the nodes in theprocess of gathering and the neighbor nodes The datacollected in this cluster are sent to the sink node throughcommunication links After the sink nodes receive theredundancy information it is calculated and analyzed Theconnection graph 119866 of redundancy relation is constructedaccording to the results of calculation and analysis Thedegree of connection graph 119866 is the number of limitedsides related to vertex It corresponds to the redundancydegree of sensor node When the number of sensor nodesincreases the redundancy degree increases correspondinglyIn the connection graph 119866 when the redundancy degreeof sensor node surpasses the preset threshold value thenode transferred to the state of sleeping At the same timethere exist several (119899 gt 2) high redundancy rate nodes Ifenergy is taken as choosing condition node with the mostenergy is chosen as the sleeping nodes by sort algorithm Andthis node together with the corresponding neighbor nodesis cancelled in connection graph 119866 Iteration algorithm isused to iterate Next node with most energy is found one

Table 1 The tabulation of the simulation parameters

Parameter ValueArea Ι 100 lowast 100Area ΙΙ 200 lowast 200Area ΙΙΙ 300 lowast 300119877119904 5mEnergy 5 JTime 800 s119877119888 10m119864119877-elec 50 Jb119864119879-elec 50 Jb120576119891119904 10 (Jb)m2

120576amp 100 (Jb)m2

119890min 0005 J

by one until the redundancy degree of all sensor nodes issmaller than the threshold value in the connection graph119866 As to energy consumption of sensor nodes clusteringalgorithm is used to control the administrator nodes andmember nodes respectively In the initial state of networkthe member node transmits the datum of ldquoinf coveragrdquo togathering node ldquoinf coveragrdquo includes the information oflocation ID and energy After one or several cycles thegathering node receives the information of sensor nodesTheinformation is calculated The node energy is stored in thechained list (CL) successively from the highest to the lowestone according to the rest node energy The top nodes possessthe covering ability of higher weight Nodes are controlledaccording to the positioning information The sensor nodethat satisfies the condition in the CL is sorted out and themessage ldquoinf noticerdquo is sent out to start the effective coverageThe rest nodes are in the state of sleeping to save the networkenergy expenses (see Algorithm 1)

4 System Evaluations

In order to verify the effectiveness and stability of the energy-efficient coverage control with multinodes redundancy veri-fication ECMRV algorithm this paper selects theMATLAB7as the simulation platform And the ECMRV algorithm iscompared with the four algorithms of the literature [13](the energy-efficient target coverage algorithm (ETCA)) andthe literature [16] (energy-efficient 119896-coverage algorithm(EEKCA)) the literature [14] (event probability drivenmech-anism EPDM) and the literature [17] (optimization strategycoverage control (OSCC)) And the simulation parametersare shown in Table 1

Experiment 1 In terms of prolonging the network lifetimethe ECMRV algorithm is compared with the ETCA and theEEKCA and the experimental data is the mean value of the200 simulation data as shown in Figures 3ndash5

Experiment 1 is a contrast experiment of the ECMRValgorithm and the ETCA and the EEKCA in terms of the

Journal of Sensors 7

(1) Procedure(2) Begin(3) nlarrNull Parameter Initializing(4) CLilarrNull(5) While (119894 lt= 119899)(6) (7) (8) 119904[119894]informationrarrs[i]bata Calculating and restoring the node information(9) 119904[119894]coverage-raterarrs[i]information according to the formula (18) calculate coverage

rate of sensor node(10) 119904[119894]neighborinformationrarrs[i]neighborbata(11) 119904[119894]broadcastrarrGn Send the nodes to the Gathering Nodes(12) 119894++(13) (14) ConstuctGraph() Construct Connecting Graph(15) while(119904[119894]energy gt= minenergy)(16) if(redundancynodes lt= 119868th) Nodesrsquo energy is not less than the threshold(17) Network working(18) else(19) (20) sorting(119904[119894]energy) sort according to nodesrsquo energy(21) 119904[119894]maxenergyrarrdormancy make the nodes of max-energy dormant(22) (23) if(Gnlarrs[i]inf covergae) (24) (25) CL[i]larrs[i]inf coverage Restore the received information in the linked list(26) 119894++ direct to the next sensor nodes(27) (28) if(119904[119894]energy gt= 119904[119894 + 1]energy)(29) (30) Gninf noticerarrs[i]data Gathering node information sent(31) 119904[119894]coveragerarrtargetnodes cover the target nodes with present nodes(32) (33)

Algorithm 1 ECMRV algorithm description

network lifetime in different monitoring areas In the exper-iment the values of 119896 are selected differently the networkscale can be changed by changing the number of the sensornodes deployed randomly in the monitoring area For themonitoring area of the smaller scale the initial value of thenumber of the sensor nodes deployed randomly is 30 basedon which the number of the sensor nodes increases step bystep From the simulation it can be seen that the lifetime ofthe Wireless Sensor Network is a linear rising trend with theincrease of the number of the sensor nodes The main reasonis that themember sensor nodes in the sensor nodes set coverthe target nodes by the scheduling mechanism of the sensornode In the same network environment compared with theETCA and the EEKCA the lifetime of the ECMRV algorithmhas been prolonged by 1129 on average as for the largerscale of the monitoring area the initial number of the sensornodes is 50 based on which the number of the sensor nodesincreases step by step The lifetime of the Wireless SensorNetwork is also a linear rising trend with the increase of thenumber of the sensor nodes The rise is more than that of thesmaller monitoring area and compared with the ETCA and

the EEKCA the network lifetime is increased by 1612 and1596

Experiment 2 The contrast experiment is taken between theECMRV algorithm and the EPDM algorithm of the literature[14] and the OSCC algorithm of the literature [17] in termsof the coverage ratio and multitargets cycle control coveragepreservation protocol [25] (MTCPP) in network runningtime Taking the monitoring area of 200lowast200m2 as examplethe experimental data is themean value of the 200 simulationdata as shown from Figures 6 to 8

In Figure 6 with the increase of the number of the sensornodes the coverage probabilities of the three algorithms arealso increasingWhen the coverage probability is 9999 and120582 = 2 the number of the sensor node is 237 when 120582 = 3 thenumber of the sensor nodes is 157 and when 120582 = 4 and thenumber of the sensor nodes is 132 the algorithm in this paperhas reached 9999 coverage however the EPDM algorithmand the OSCC algorithm have not reached 100 coveragewhich shows that the coverage ratio of the ECMRV algorithmis higher than that of the EPDM algorithm and the OSCC

8 Journal of SensorsN

etw

ork

lifet

ime (

s)

Number of nodes30 60 90 120 150

0

30

60

90

120

150

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 3 100 lowast 100m2 network lifetime

Number of nodes50 100 150 200 250 300

Net

wor

k lif

etim

e (s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 4 200 lowast 200m2 network lifetime

algorithm Thus the effectiveness of the ECMRV algorithmin this paper has been verified In Figure 7 at the initialtime of the program execution the coverage probabilities ofthe two algorithms are almost the same however as timepasses by the coverage probabilities of the two contractalgorithms are the declining trance The main reason is thatthe EPDM algorithm and the OSCC algorithm adopt theuninterrupted coverage to complete the coverage during therun time that is the target nodes in the monitoring areasare covered constantly until the energies of the target nodesare consumed up When 119905 = 150 the coverage probabilitiesof the three algorithms decline more obviously When 120582 =2 3 4 CPECMRV2 = 7656 CPECMRV3 = 9553 CPEPDM =7886 CPOSCC = 8402 and CPECMRV4 = 9771 When120582 = 4 the coverage probability in this paper is higherthan that of the EPDM algorithm and the OSCC algorithm

Number of nodes50 150 250 350 450

Net

wor

k lif

etim

e (s)

80

120

160

200

240

280

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 5 300 lowast 300m2 network lifetime

Coverage rate ()20 40 60 80 100

Num

ber o

f nod

es

40

80

120

160

200

240

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 6 200 lowast 200m2 network coverage rate

which shows that with the function of the same sensornodes the coverage probability of the ECMRV algorithmis higher than that of the other two algorithms which hasverified the effectiveness of the algorithm in this paper AndFigure 8 gives the curves of the working sensor nodes andthe sensor nodes contrast of the ECMRV algorithm andthe EPDM algorithm and the OSCC algorithm when thecoverage probabilities are the same ones When the numberof sensor nodes is maintained from 260 to 290 the numbersof sensor nodes of the three algorithms basically tend to bestable When 120582 = 2 3 4 the number of sensor nodes of theECMRV algorithm is maintained at 245 223 and 211 whilethe numbers of the sensor nodes in EPDM algorithm and theOSCC algorithm are maintained from 231 to 237 Thereforethemean value of the number of sensor nodes of the ECMRV

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Propagation

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DistributedSensor Networks

International Journal of

2 Journal of Sensors

Figure 1 The topological structure of the coverage in the militarybattlefield

coverage of the entire monitoring area but the completecoverage of the certain target nodes in the process of coveringthe entire monitoring area completely to take no accountof the existence of the target nodes will consume a lot ofsensor node energy which will accelerate the speed of thecollapse of the whole network systemThird when deployingthe sensor nodes the existence of the randomness willinevitably cause excessive density in a certain coverage areaof the monitoring area resulting in the bottlenecking whicheventually generates information redundancy verification inthe channel but reduces the network expansibility

Aiming at the above shortages this paper proposed theenergy-efficient coverage control with multinodes redun-dancy verification (ECMRV) In this paper the coverageprobability and covering expected value of sensor nodesare solved by using the sector domains of the coveragearea when the moving target nodes are passing through themonitoring area as for the energy consumption this papergives the solution ofmultipoint transmission and single pointtransmission For the working sensor nodes having met thecertain coverage ratio when the moving target nodes arepassing across the 119896-coverage area it will close the sensornodes within or higher the threshold value or it will placethe sensor nodes in the sleeping state by the sensor nodeadaptive transformation mechanism and the other sensornodes will use the sensor node energy schedulingmechanismto compete the conversion of the energy of the sensor nodesso that the network lifetime can be extended

2 Related Knowledge

The technique of coverage control in WSNs is a veryimportant fundamental research and also one of the hotspotproblems right now in WSN The coverage quality willaffect the lifetime of the network In recent years manyexperts and scholars at home and broad have carried outplenty of researches thoroughly and carefully Literature [6]brings in the partial coverage optimization and constitutesthe partial 120572 coverage and after a series of calculation andoptimization of the 120572 the complete coverage optimization

is finally achieved All the above-mentioned algorithms haveachieved the effective coverage of the monitoring area tosome extent however they have the mutual problem thatthe algorithms have more calculations and they are morecomplex and the scalability of the Wireless Sensor Networkis worse Literature [7] provides a constructive methodof connected coverage protocol The protocol provides theproportional relation between the network coverage qualityand the network and the performance indexes of all theparameters in the network system and creates the schedulingcontrol algorithm (SCA) the purpose of which is to usethe least sensor nodes to guarantee the connection of thewhole network system Literature [8] introduces the artifi-cial intelligence algorithms that is the swarm intelligencealgorithm and the granule algorithm to complete the sensornodes deployment of the whole networkmonitoring area andin the stage of the coverage optimization the whole coverageis optimized by the two artificial intelligence algorithms andfinally realizes the complete coverage of the monitoring areaas for the energy consumption it completes the schedulingconversion of the sensor nodes energy by the heuristic sensornodes Scheduling which extends the lifetime of the networkLiterature [9] proposes the optimization strategy on coveragealgorithm based on Voronoi Satisfying the condition ofa certain coverage quality the algorithm adds some worksensor nodes to the coverage hole so as to improve thecurrent coverage ratio meanwhile it will search reasonableinformation of repairing site to guarantee the connection ofthe whole network Literature [10] also takes the Voronoi asthe research object and solves the information of wire rod sitethat formed by the geometry variation in the Voronoi andthe sensor nodes and finally completes the coverage of themonitoring area Literature [11] and literature [12] computethe goal sensor nodes effectively utilizing the different anglesof the sector composed by the sensor nodes and the targetnodes and give the method of computing the coverage prob-ability of differentmonitoring area All algorithmsmentionedabove have the better feasibility the higher reliability and thelarger network scalability However in the research processof the four algorithms their network models are much tooidealized From literature [9] to literature [11] they all takethe static target nodes as the research objective and literature[12] does not consider the situation when the moving targetnodes are the concerned target nodes which result in the 119896-barrier coverage Literature [13] proposes the polytypic targetcoverage algorithm based on the linear programming Thealgorithm utilizes the clustering structure to solve the poly-typic target coverage problem By computing the coverageability and the residual energy of the sensor it completesthe polytypic target optimization coverage in the way ofthe linear programming Literature [14] proposes the eventprobability driven mechanism algorithm This algorithmcalculated the coverage probability and the expected value ofthe sensor nodes with the probability model then optimizedthe result and finally achieved the optimal coverage Theabove two algorithms achieve the purposes of the optimalcoverage and the extension of the network lifetime but thecoverage condition is a little hasher and the calculations ofthe algorithms are much more complex

Journal of Sensors 3

In order to make the effective coverage of the monitoringarea better on the basis of literature [11] and literature [12]this paper proposes the energy-efficient coverage control withmultinodes redundancy verification (ECMRV) Taking useof sectorial the 119896-degree coverage the algorithm calculatesthe coverage expected value between the sensor nodes andthe moving target nodes And then the algorithm providesthe solving procedure of the coverage expected value whena certain sensor node finishes the coverage of the targetnodes In terms of the energy on the basis of the analysisof all the sensor nodesrsquo energy in the whole network thealgorithm provides the process of the energy comparisonunder the multilateral and unilateral connection that is theenergy consumption of the data in multicast is less thanthat of the unilateral sensor nodes In terms of the energyconversion the algorithm completes the energy conversionamong the sensor nodes through the self-scheduling mecha-nism extending the lifetime of the network Finally throughthe simulation experiments and the comparison with otheralgorithms the effectiveness and the stability of the ECMRValgorithm have been verified

3 The Network Model andthe Coverage Quality

31 Basic Concepts and BasicTheories For the sake of the bet-ter explanation and research of the WSNs coverage problemsand the convenience of the problems the ECMRV algorithmis based on the following four hypothesizes [10 15 16]

(1) All of the sensor nodes are all in the homogeneousform and the perceived range and the communica-tion range are both disc-shaped

(2) All of the sensor nodes can get their own positioninformation through the GPS technology

(3) The initial energy of all the sensor nodes is the sameand has the same sensing range and the speed is thesame as that of the clock

(4) The sensor nodes are deployed randomly in thesquare monitoring area with the length 119897 and theperceived range must be guaranteed to be less thanthe length 119897 and the boundary effect can be ignored

(5) The sensor nodes are randomly deployed in themonitoring areas with high density and the sensornodes are independent of each other

Definition 1 (the complete coverage) In the monitoring areaany target nodes must be covered by at least one sensornode that is the Euclidean distance of the sensor nodes andthe target nodes are smaller than the perceived range of thesensor nodes 119889(119894 119905) le 119877119894 which is called complete coverage

Definition 2 (the 119896-coverage) In the monitoring area anytarget nodesmust be covered by at least 119896 sensor nodesThusthe monitoring area is called 119896-degree coverage areaDefinition 3 (the coverage quality) In the monitoring areathe coverage quality is the specific value of the sum of the

sensed area of all the sensor nodes and the area of themonitoring area In a way it reflects the coverage degree ofthe target nodes

Definition 4 (the multilevel coverage) The coverage rate ofeach sensor node is 119901 then the coverage rate at any point ina two-dimensional plane is

119901119899 = 1 minus (1 minus 119901)119899 (1)

In (1) 119901119899 is themultilevel coverage ratio 119901 is the coverageprobability of any one of the sensor nodes 119899 is the number ofthe sensor nodes [10 17 18]

Theorem 5 When the moving target nodes enter the moni-toring area for the first time the first coverage expected value is119864(119883) = [1minus(1minus119901)119873]119901minus1 and119873 is the biggest number of timesthat the moving target nodes can complete the transmissionand 119901 is the coverage probability of the sensor nodes

Proof According to the probability theory suppose that 119883represents how many times the moving target nodes moveand the value range of119883 is possible to be119883 isin [1 2 3 119873]When 119883 = 119898 as well as meeting the condition of 1 le 119898 le119873minus1 that is when the first119873minus1moving target nodes are notcovered by the sensor nodes the distribution density functionof119883 will be

119875 (119883 = 119896) = 119901 (1 minus 119901)119896minus1 119896 = 1 2 3 119873 minus 1(1 minus 119901)119873minus1 119896 = 119873 (2)

According to the equation of the coverage thus

119864 (119883) = 119873minus1sum119896=1

119896119901 (1 minus 119901)119896minus1 + 119873 (1 minus 119901)119873minus1 (3)

Make 119902 = 1 minus 119901 and 119878 = sum119873minus1119896=1 119896(1 minus 119901)119896minus1 that is 119878 =sum119873minus1119896=1 119896119902119896minus1 is multiplied by 119902 in both sides of the equationthus 119902119878 = sum119873minus1119896=1 119896119902119896 that is

119878 = 1 minus 119902119873minus1(1 minus 119902)2 minus

(119873 minus 1) 119902119873minus11 minus 119902= 1 minus (1 minus 119901)119873minus1

1199012 minus (119873 minus 1) (1 minus 119901)119873minus1119901

(4)

Put (4) into (3) thus

119864 (119883) = 119901(1 minus (1 minus 119901)119873minus11199012 minus (119873 minus 1) (1 minus 119901)119873minus1119901 )

+ 119873(1 minus 119901)119873minus1 = [1 minus (1 minus 119901)119873] 119901minus1(5)

In the square monitoring area after a period of 119905 theenergy of the working sensor nodes must have been con-sumed by themselves which make the coverage area changecorrespond In order to suppress the energy consumption ofthe sensor nodes and extend the lifetime of the network as

4 Journal of Sensors

A

B

C

D

120573

120572

Figure 2 Multilateral and unilateral node connection

long as possible this paper adopts the sensor node energymodel to analyze the sensor node-energy that is consumed inthe process of unilateral and multilateral data transmissionmeanwhile the energy of the sensor node is consumed byits own work of calculation [19ndash22] storage and control Theenergy consumption model of the sensor node transmitter is

119864Tx (119897 119889) = 119897119864119879-elec + 119864amp (119897 119889)=

119897119864119879-elec + 1198971205761198911199041198892 119889 lt 1198890119897119864119879-elec + 119897120576amp1198894 119889 ge 1198890

(6)

And the energy consumption model of the receiver is

119864Rx (119897) = 119864119877-elec (119897) = 119897119864elec (7)

And 119897 is the bit of the data transmission 119889 is the Euclideandistance between the sensor nodes and the neighboringnodes and 1198890 is the threshold value of the distance ofthe communication sensor node When the distance ofthe communication sensor node is smaller than 1198890 theenergy damping index is 2 whereas the energy dampingindex will be 4 119864elec represents the energy consumptionof communication sensor nodes receiving and transmittingmodules [23 24]

Theorem 6 Less energy of the data is consumed in multicastthan the unilateral sensor nodes The mathematical inductionwhen 119899 rarr infin is shown in Figure 2

In 1st case according to formula (6) the formula of energydissipations directly from source node 119860 to target node 119863 ispresented as below

119864Tx 119860119863 (119897 119889119860119863) = 119897119864119879-elec + 1198971205761198911199041198892119860119863 119889119860119863 lt 1198890119897119864119879-elec + 119897120576amp1198894119860119863 119889119860119863 ge 1198890 (8)

In the 2nd case data are sent from node 119860 to 119861 andthen to 119863 From 119860 to 119861 when 119896 = 3 the model of energyconsumption when transmitting module in node 119860 can beinducted as follows

119864Tx 119860119861 (119897 119889119860119861) = 119897119864119879-elec + 1198971205761198911199041198892119860119861 119889119860119861 lt 1198890119897119864119879-elec + 119897120576amp1198894119860119861 119889119860119861 ge 1198890

119864Rx 119861 (119897) = 119897119864elec(9)

The energy consumption of node 119861 receiving the infor-mation is represented as below

119864Tx 119861119863 (119897 119889119861119863) = 119897119864119879-elec + 1198971205761198911199041198892119861119863 119889119861119863 lt 1198890119897119864119879-elec + 119897120576amp1198894119861119863 119889119861119863 ge 1198890 (10)

Then the total energy consumption fromnode119860 to119861 andthen to119863 is represented as below

119864Total = 119864Tx 119860119861 + 119864Rx 119861 + 119864Tx 119861119862 (11)

In their initial state the nodesworkwith the same amountof energy and are independent of each other The basicproperties of triangle are shown

At the beginning each node is independent of eachother and is working with equal energy This basic feature offorming triangles can be represented as below

119864Total = 119864Tx 119860119861 + 119864Rx 119861 + 119864Tx 119861119863 lt 119864Tx 119860119863 (12)

That is to say when 119896 = 3 less energy is consumed inmultilateral data transmission than in unilateral one Sowhen119896 = 3 formula (12) is justified

The data transmitting path is from 119860 to 119861 to 119862 and thento 119863 When 119899 rarr infin because ang120572 is an obtuse angle ang120572 gt1205872 cosang120572 lt 0 According to CosineTheorem 1198611198622 +1198621198632 lt1198611198632The triangle of connecting119861119862 and119863 is obtuse triangleHence formula (13) is obtained as below

119864Tx 119860119861 + 119864Rx 119861 + sdot sdot sdot + 119864Rx119899minus1 + 119864Tx119899minus1119899 lt sdot sdot sdotlt 119864Tx119860119861 + 119864Rx119861 + 119864Tx119861119863 lt 119864Tx119860119863 (13)

32 Cover Quality

Theorem 7 Randomly select 119896 sensor nodes within 119872 andthen the expectation of the coverage quality is

119864 (120578119896) = 1 minus 1 minus 120587 (11987720 + 1205822)area (119872)

119896

(14)

Proof The sensor node subject to the random uniformdistribution in119872 so the probability a sensor node is locatedin any position in119872 is 1area(119872) If any point 119902 is coveredby a sensor node 119886 (the perception radius is denoted with119877119886)then sensor node 119886must be locate in a circle of centered on q(the circle is denoted as119874(119902 119877119886) of radius 119877119886) Therefore theprobability that 119902 is covered by sensor node 119886 is

119875119886 = area (119874 (119902 119877119886))area (119872) (15)

Because the perception radius of sensor node 119886 is normaldistribution and 1198770 ge 33120582 the probability that any point iscovered by a work sensor node is

119875 = int211987700

119875119886 1(2120587)12 120582 exp(minus(119877119886 minus 1198770)21205822 ) d1198770 (16)

Journal of Sensors 5

Let 119909 = (119877119886 minus 1198770)120582 then119875 = (1205872 )

12 1area (119872) (int

1198770120582

minus119877012058212058221199092 exp(minus11990922 ) d119909

+ int1198770120582minus1198770120582

21205821199091198770 exp(minus11990922 ) d119909+ int1198770120582minus1198770120582

11987720 exp(minus11990922 ) d119909) (17)

Calculation is as follows

119875 = (1205872 )12 1

area (119872) (minus1205822 exp(minus1199092

2 )1003816100381610038161003816100381610038161003816100381610038161198770120582

minus1198770120582

+ (2120587)12 120582 + (2120587)12 11987720) asymp 120587 (11987720 + 1205822)area (119872)

(18)

The positions of all sensor nodes in119872 are independent ofeach other according to formula (1) the probability that anysensor node in119872 is at least covered by 119896 work sensor node is

119875119870 = 1 minus (1 minus 120587 (11987720 + 1205822)area (119872) )

119896

(19)

Assume the area covered by at least 119896 sensor nodes is1198721015840and then the expectation of the area for1198721015840 is

119864 (area (1198721015840)) = 119875119896area (119872) (20)

Therefore

119864 (120578119896) = 119864 (area (1198721015840))area (1198721015840) = 1 minus (1 minus 120587 (11987720 + 1205822)

area (119872) )119896

(21)

With Theorem 5 we can get the expectation of theminimum number of required work sensor nodes satisfyingdemanded coverage quality 120578119889 of applications namely

119864 (119896) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (22)

Theorem 8 After the redundant sensor nodes are powered offrandomlywithout causing any conflict if the rest working nodescan provide the coverage quality 119899119889 required by the applicationthe expectation for the number of redundant sensor nodesrsquoneighbors satisfies

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (23)

Proof Assuming the number of the remaining work sensornodes is 119873 after the redundant nods are powered off thenthe 119899 work sensor nodes still follow random and uniformdistribution Because the remaining work sensor nodes canstill accurately provide the coverage quality required inapplications by formula (22) we get

119864 (119873) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (24)

Denote the perception radius of sensor node as 119877119886 119877119887which represents the perception radius of sensor node 119887 If 119887is the coverage neighbor of 119886 then 119887must be located in a circlecentered on the radius 119877119886 +119877119887 (denote the circle as119874(119886 119877119886 +119877119887)) Therefore the probability that 119887 is a coverage neighborof 119886 is

119875119887minus119886 = area (119874 (119886 119877119886 + 119877119887))area (119872) (25)

Because the perception radius of all sensor nodes obeysnormal distribution 119873(1198770 1205822) as well as 1198770 ge 33120582 theprobability that a sensor node is the coverage neighbor ofanother sensor node is

119875 = int211987700

int211987700

119875119887minus119886sdot 121205871205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887(26)

Calculation is

119875 = 1area (119872) [int

21198770

0int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887+ int211987700

int211987700

119877119886119877119887sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887]

(27)

According to the computation process in formula (27) wehave

int211987700

int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887asymp 120587 (11987720 + 1205822)

(28)

Because

int211987700

119877119886 1(2120587)12 120582 exp(minus(1198770 minus 119877119886)221205822 ) d119877119886

= int1198770120582minus1198770120582

(1198770 + 120582119909) 1(2120587)12 exp (minus

1199092) d119909 = 1198770(29)

6 Journal of Sensors

int211987700

int211987700

2120587119877119886119877119887sdot 121205871205822 exp(minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ) d119877119886 d119877119887= 212058711987720

(30)

Then we have

119875 = 412058711987720 + 21205871205822area (119872) (31)

The expectation of the number of coverage neighborsensor nodes for each of the remaining119873 work sensor nodesis

119864 (119899) = (119864 (119873) minus 1) 119875= ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (32)

Therefore the expectations of the number of redundantcoverage neighboring sensor nodes satisfy

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (33)

33 Algorithm Description As to the redundancy of sensornodes the connection graph of sensor nodes gatheringredundancy is constructed that is the redundancy infor-mation calculated by a positioning algorithm (eg centroidpositioning and ranging location) of all the nodes in theprocess of gathering and the neighbor nodes The datacollected in this cluster are sent to the sink node throughcommunication links After the sink nodes receive theredundancy information it is calculated and analyzed Theconnection graph 119866 of redundancy relation is constructedaccording to the results of calculation and analysis Thedegree of connection graph 119866 is the number of limitedsides related to vertex It corresponds to the redundancydegree of sensor node When the number of sensor nodesincreases the redundancy degree increases correspondinglyIn the connection graph 119866 when the redundancy degreeof sensor node surpasses the preset threshold value thenode transferred to the state of sleeping At the same timethere exist several (119899 gt 2) high redundancy rate nodes Ifenergy is taken as choosing condition node with the mostenergy is chosen as the sleeping nodes by sort algorithm Andthis node together with the corresponding neighbor nodesis cancelled in connection graph 119866 Iteration algorithm isused to iterate Next node with most energy is found one

Table 1 The tabulation of the simulation parameters

Parameter ValueArea Ι 100 lowast 100Area ΙΙ 200 lowast 200Area ΙΙΙ 300 lowast 300119877119904 5mEnergy 5 JTime 800 s119877119888 10m119864119877-elec 50 Jb119864119879-elec 50 Jb120576119891119904 10 (Jb)m2

120576amp 100 (Jb)m2

119890min 0005 J

by one until the redundancy degree of all sensor nodes issmaller than the threshold value in the connection graph119866 As to energy consumption of sensor nodes clusteringalgorithm is used to control the administrator nodes andmember nodes respectively In the initial state of networkthe member node transmits the datum of ldquoinf coveragrdquo togathering node ldquoinf coveragrdquo includes the information oflocation ID and energy After one or several cycles thegathering node receives the information of sensor nodesTheinformation is calculated The node energy is stored in thechained list (CL) successively from the highest to the lowestone according to the rest node energy The top nodes possessthe covering ability of higher weight Nodes are controlledaccording to the positioning information The sensor nodethat satisfies the condition in the CL is sorted out and themessage ldquoinf noticerdquo is sent out to start the effective coverageThe rest nodes are in the state of sleeping to save the networkenergy expenses (see Algorithm 1)

4 System Evaluations

In order to verify the effectiveness and stability of the energy-efficient coverage control with multinodes redundancy veri-fication ECMRV algorithm this paper selects theMATLAB7as the simulation platform And the ECMRV algorithm iscompared with the four algorithms of the literature [13](the energy-efficient target coverage algorithm (ETCA)) andthe literature [16] (energy-efficient 119896-coverage algorithm(EEKCA)) the literature [14] (event probability drivenmech-anism EPDM) and the literature [17] (optimization strategycoverage control (OSCC)) And the simulation parametersare shown in Table 1

Experiment 1 In terms of prolonging the network lifetimethe ECMRV algorithm is compared with the ETCA and theEEKCA and the experimental data is the mean value of the200 simulation data as shown in Figures 3ndash5

Experiment 1 is a contrast experiment of the ECMRValgorithm and the ETCA and the EEKCA in terms of the

Journal of Sensors 7

(1) Procedure(2) Begin(3) nlarrNull Parameter Initializing(4) CLilarrNull(5) While (119894 lt= 119899)(6) (7) (8) 119904[119894]informationrarrs[i]bata Calculating and restoring the node information(9) 119904[119894]coverage-raterarrs[i]information according to the formula (18) calculate coverage

rate of sensor node(10) 119904[119894]neighborinformationrarrs[i]neighborbata(11) 119904[119894]broadcastrarrGn Send the nodes to the Gathering Nodes(12) 119894++(13) (14) ConstuctGraph() Construct Connecting Graph(15) while(119904[119894]energy gt= minenergy)(16) if(redundancynodes lt= 119868th) Nodesrsquo energy is not less than the threshold(17) Network working(18) else(19) (20) sorting(119904[119894]energy) sort according to nodesrsquo energy(21) 119904[119894]maxenergyrarrdormancy make the nodes of max-energy dormant(22) (23) if(Gnlarrs[i]inf covergae) (24) (25) CL[i]larrs[i]inf coverage Restore the received information in the linked list(26) 119894++ direct to the next sensor nodes(27) (28) if(119904[119894]energy gt= 119904[119894 + 1]energy)(29) (30) Gninf noticerarrs[i]data Gathering node information sent(31) 119904[119894]coveragerarrtargetnodes cover the target nodes with present nodes(32) (33)

Algorithm 1 ECMRV algorithm description

network lifetime in different monitoring areas In the exper-iment the values of 119896 are selected differently the networkscale can be changed by changing the number of the sensornodes deployed randomly in the monitoring area For themonitoring area of the smaller scale the initial value of thenumber of the sensor nodes deployed randomly is 30 basedon which the number of the sensor nodes increases step bystep From the simulation it can be seen that the lifetime ofthe Wireless Sensor Network is a linear rising trend with theincrease of the number of the sensor nodes The main reasonis that themember sensor nodes in the sensor nodes set coverthe target nodes by the scheduling mechanism of the sensornode In the same network environment compared with theETCA and the EEKCA the lifetime of the ECMRV algorithmhas been prolonged by 1129 on average as for the largerscale of the monitoring area the initial number of the sensornodes is 50 based on which the number of the sensor nodesincreases step by step The lifetime of the Wireless SensorNetwork is also a linear rising trend with the increase of thenumber of the sensor nodes The rise is more than that of thesmaller monitoring area and compared with the ETCA and

the EEKCA the network lifetime is increased by 1612 and1596

Experiment 2 The contrast experiment is taken between theECMRV algorithm and the EPDM algorithm of the literature[14] and the OSCC algorithm of the literature [17] in termsof the coverage ratio and multitargets cycle control coveragepreservation protocol [25] (MTCPP) in network runningtime Taking the monitoring area of 200lowast200m2 as examplethe experimental data is themean value of the 200 simulationdata as shown from Figures 6 to 8

In Figure 6 with the increase of the number of the sensornodes the coverage probabilities of the three algorithms arealso increasingWhen the coverage probability is 9999 and120582 = 2 the number of the sensor node is 237 when 120582 = 3 thenumber of the sensor nodes is 157 and when 120582 = 4 and thenumber of the sensor nodes is 132 the algorithm in this paperhas reached 9999 coverage however the EPDM algorithmand the OSCC algorithm have not reached 100 coveragewhich shows that the coverage ratio of the ECMRV algorithmis higher than that of the EPDM algorithm and the OSCC

8 Journal of SensorsN

etw

ork

lifet

ime (

s)

Number of nodes30 60 90 120 150

0

30

60

90

120

150

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 3 100 lowast 100m2 network lifetime

Number of nodes50 100 150 200 250 300

Net

wor

k lif

etim

e (s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 4 200 lowast 200m2 network lifetime

algorithm Thus the effectiveness of the ECMRV algorithmin this paper has been verified In Figure 7 at the initialtime of the program execution the coverage probabilities ofthe two algorithms are almost the same however as timepasses by the coverage probabilities of the two contractalgorithms are the declining trance The main reason is thatthe EPDM algorithm and the OSCC algorithm adopt theuninterrupted coverage to complete the coverage during therun time that is the target nodes in the monitoring areasare covered constantly until the energies of the target nodesare consumed up When 119905 = 150 the coverage probabilitiesof the three algorithms decline more obviously When 120582 =2 3 4 CPECMRV2 = 7656 CPECMRV3 = 9553 CPEPDM =7886 CPOSCC = 8402 and CPECMRV4 = 9771 When120582 = 4 the coverage probability in this paper is higherthan that of the EPDM algorithm and the OSCC algorithm

Number of nodes50 150 250 350 450

Net

wor

k lif

etim

e (s)

80

120

160

200

240

280

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 5 300 lowast 300m2 network lifetime

Coverage rate ()20 40 60 80 100

Num

ber o

f nod

es

40

80

120

160

200

240

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 6 200 lowast 200m2 network coverage rate

which shows that with the function of the same sensornodes the coverage probability of the ECMRV algorithmis higher than that of the other two algorithms which hasverified the effectiveness of the algorithm in this paper AndFigure 8 gives the curves of the working sensor nodes andthe sensor nodes contrast of the ECMRV algorithm andthe EPDM algorithm and the OSCC algorithm when thecoverage probabilities are the same ones When the numberof sensor nodes is maintained from 260 to 290 the numbersof sensor nodes of the three algorithms basically tend to bestable When 120582 = 2 3 4 the number of sensor nodes of theECMRV algorithm is maintained at 245 223 and 211 whilethe numbers of the sensor nodes in EPDM algorithm and theOSCC algorithm are maintained from 231 to 237 Thereforethemean value of the number of sensor nodes of the ECMRV

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

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DistributedSensor Networks

International Journal of

Journal of Sensors 3

In order to make the effective coverage of the monitoringarea better on the basis of literature [11] and literature [12]this paper proposes the energy-efficient coverage control withmultinodes redundancy verification (ECMRV) Taking useof sectorial the 119896-degree coverage the algorithm calculatesthe coverage expected value between the sensor nodes andthe moving target nodes And then the algorithm providesthe solving procedure of the coverage expected value whena certain sensor node finishes the coverage of the targetnodes In terms of the energy on the basis of the analysisof all the sensor nodesrsquo energy in the whole network thealgorithm provides the process of the energy comparisonunder the multilateral and unilateral connection that is theenergy consumption of the data in multicast is less thanthat of the unilateral sensor nodes In terms of the energyconversion the algorithm completes the energy conversionamong the sensor nodes through the self-scheduling mecha-nism extending the lifetime of the network Finally throughthe simulation experiments and the comparison with otheralgorithms the effectiveness and the stability of the ECMRValgorithm have been verified

3 The Network Model andthe Coverage Quality

31 Basic Concepts and BasicTheories For the sake of the bet-ter explanation and research of the WSNs coverage problemsand the convenience of the problems the ECMRV algorithmis based on the following four hypothesizes [10 15 16]

(1) All of the sensor nodes are all in the homogeneousform and the perceived range and the communica-tion range are both disc-shaped

(2) All of the sensor nodes can get their own positioninformation through the GPS technology

(3) The initial energy of all the sensor nodes is the sameand has the same sensing range and the speed is thesame as that of the clock

(4) The sensor nodes are deployed randomly in thesquare monitoring area with the length 119897 and theperceived range must be guaranteed to be less thanthe length 119897 and the boundary effect can be ignored

(5) The sensor nodes are randomly deployed in themonitoring areas with high density and the sensornodes are independent of each other

Definition 1 (the complete coverage) In the monitoring areaany target nodes must be covered by at least one sensornode that is the Euclidean distance of the sensor nodes andthe target nodes are smaller than the perceived range of thesensor nodes 119889(119894 119905) le 119877119894 which is called complete coverage

Definition 2 (the 119896-coverage) In the monitoring area anytarget nodesmust be covered by at least 119896 sensor nodesThusthe monitoring area is called 119896-degree coverage areaDefinition 3 (the coverage quality) In the monitoring areathe coverage quality is the specific value of the sum of the

sensed area of all the sensor nodes and the area of themonitoring area In a way it reflects the coverage degree ofthe target nodes

Definition 4 (the multilevel coverage) The coverage rate ofeach sensor node is 119901 then the coverage rate at any point ina two-dimensional plane is

119901119899 = 1 minus (1 minus 119901)119899 (1)

In (1) 119901119899 is themultilevel coverage ratio 119901 is the coverageprobability of any one of the sensor nodes 119899 is the number ofthe sensor nodes [10 17 18]

Theorem 5 When the moving target nodes enter the moni-toring area for the first time the first coverage expected value is119864(119883) = [1minus(1minus119901)119873]119901minus1 and119873 is the biggest number of timesthat the moving target nodes can complete the transmissionand 119901 is the coverage probability of the sensor nodes

Proof According to the probability theory suppose that 119883represents how many times the moving target nodes moveand the value range of119883 is possible to be119883 isin [1 2 3 119873]When 119883 = 119898 as well as meeting the condition of 1 le 119898 le119873minus1 that is when the first119873minus1moving target nodes are notcovered by the sensor nodes the distribution density functionof119883 will be

119875 (119883 = 119896) = 119901 (1 minus 119901)119896minus1 119896 = 1 2 3 119873 minus 1(1 minus 119901)119873minus1 119896 = 119873 (2)

According to the equation of the coverage thus

119864 (119883) = 119873minus1sum119896=1

119896119901 (1 minus 119901)119896minus1 + 119873 (1 minus 119901)119873minus1 (3)

Make 119902 = 1 minus 119901 and 119878 = sum119873minus1119896=1 119896(1 minus 119901)119896minus1 that is 119878 =sum119873minus1119896=1 119896119902119896minus1 is multiplied by 119902 in both sides of the equationthus 119902119878 = sum119873minus1119896=1 119896119902119896 that is

119878 = 1 minus 119902119873minus1(1 minus 119902)2 minus

(119873 minus 1) 119902119873minus11 minus 119902= 1 minus (1 minus 119901)119873minus1

1199012 minus (119873 minus 1) (1 minus 119901)119873minus1119901

(4)

Put (4) into (3) thus

119864 (119883) = 119901(1 minus (1 minus 119901)119873minus11199012 minus (119873 minus 1) (1 minus 119901)119873minus1119901 )

+ 119873(1 minus 119901)119873minus1 = [1 minus (1 minus 119901)119873] 119901minus1(5)

In the square monitoring area after a period of 119905 theenergy of the working sensor nodes must have been con-sumed by themselves which make the coverage area changecorrespond In order to suppress the energy consumption ofthe sensor nodes and extend the lifetime of the network as

4 Journal of Sensors

A

B

C

D

120573

120572

Figure 2 Multilateral and unilateral node connection

long as possible this paper adopts the sensor node energymodel to analyze the sensor node-energy that is consumed inthe process of unilateral and multilateral data transmissionmeanwhile the energy of the sensor node is consumed byits own work of calculation [19ndash22] storage and control Theenergy consumption model of the sensor node transmitter is

119864Tx (119897 119889) = 119897119864119879-elec + 119864amp (119897 119889)=

119897119864119879-elec + 1198971205761198911199041198892 119889 lt 1198890119897119864119879-elec + 119897120576amp1198894 119889 ge 1198890

(6)

And the energy consumption model of the receiver is

119864Rx (119897) = 119864119877-elec (119897) = 119897119864elec (7)

And 119897 is the bit of the data transmission 119889 is the Euclideandistance between the sensor nodes and the neighboringnodes and 1198890 is the threshold value of the distance ofthe communication sensor node When the distance ofthe communication sensor node is smaller than 1198890 theenergy damping index is 2 whereas the energy dampingindex will be 4 119864elec represents the energy consumptionof communication sensor nodes receiving and transmittingmodules [23 24]

Theorem 6 Less energy of the data is consumed in multicastthan the unilateral sensor nodes The mathematical inductionwhen 119899 rarr infin is shown in Figure 2

In 1st case according to formula (6) the formula of energydissipations directly from source node 119860 to target node 119863 ispresented as below

119864Tx 119860119863 (119897 119889119860119863) = 119897119864119879-elec + 1198971205761198911199041198892119860119863 119889119860119863 lt 1198890119897119864119879-elec + 119897120576amp1198894119860119863 119889119860119863 ge 1198890 (8)

In the 2nd case data are sent from node 119860 to 119861 andthen to 119863 From 119860 to 119861 when 119896 = 3 the model of energyconsumption when transmitting module in node 119860 can beinducted as follows

119864Tx 119860119861 (119897 119889119860119861) = 119897119864119879-elec + 1198971205761198911199041198892119860119861 119889119860119861 lt 1198890119897119864119879-elec + 119897120576amp1198894119860119861 119889119860119861 ge 1198890

119864Rx 119861 (119897) = 119897119864elec(9)

The energy consumption of node 119861 receiving the infor-mation is represented as below

119864Tx 119861119863 (119897 119889119861119863) = 119897119864119879-elec + 1198971205761198911199041198892119861119863 119889119861119863 lt 1198890119897119864119879-elec + 119897120576amp1198894119861119863 119889119861119863 ge 1198890 (10)

Then the total energy consumption fromnode119860 to119861 andthen to119863 is represented as below

119864Total = 119864Tx 119860119861 + 119864Rx 119861 + 119864Tx 119861119862 (11)

In their initial state the nodesworkwith the same amountof energy and are independent of each other The basicproperties of triangle are shown

At the beginning each node is independent of eachother and is working with equal energy This basic feature offorming triangles can be represented as below

119864Total = 119864Tx 119860119861 + 119864Rx 119861 + 119864Tx 119861119863 lt 119864Tx 119860119863 (12)

That is to say when 119896 = 3 less energy is consumed inmultilateral data transmission than in unilateral one Sowhen119896 = 3 formula (12) is justified

The data transmitting path is from 119860 to 119861 to 119862 and thento 119863 When 119899 rarr infin because ang120572 is an obtuse angle ang120572 gt1205872 cosang120572 lt 0 According to CosineTheorem 1198611198622 +1198621198632 lt1198611198632The triangle of connecting119861119862 and119863 is obtuse triangleHence formula (13) is obtained as below

119864Tx 119860119861 + 119864Rx 119861 + sdot sdot sdot + 119864Rx119899minus1 + 119864Tx119899minus1119899 lt sdot sdot sdotlt 119864Tx119860119861 + 119864Rx119861 + 119864Tx119861119863 lt 119864Tx119860119863 (13)

32 Cover Quality

Theorem 7 Randomly select 119896 sensor nodes within 119872 andthen the expectation of the coverage quality is

119864 (120578119896) = 1 minus 1 minus 120587 (11987720 + 1205822)area (119872)

119896

(14)

Proof The sensor node subject to the random uniformdistribution in119872 so the probability a sensor node is locatedin any position in119872 is 1area(119872) If any point 119902 is coveredby a sensor node 119886 (the perception radius is denoted with119877119886)then sensor node 119886must be locate in a circle of centered on q(the circle is denoted as119874(119902 119877119886) of radius 119877119886) Therefore theprobability that 119902 is covered by sensor node 119886 is

119875119886 = area (119874 (119902 119877119886))area (119872) (15)

Because the perception radius of sensor node 119886 is normaldistribution and 1198770 ge 33120582 the probability that any point iscovered by a work sensor node is

119875 = int211987700

119875119886 1(2120587)12 120582 exp(minus(119877119886 minus 1198770)21205822 ) d1198770 (16)

Journal of Sensors 5

Let 119909 = (119877119886 minus 1198770)120582 then119875 = (1205872 )

12 1area (119872) (int

1198770120582

minus119877012058212058221199092 exp(minus11990922 ) d119909

+ int1198770120582minus1198770120582

21205821199091198770 exp(minus11990922 ) d119909+ int1198770120582minus1198770120582

11987720 exp(minus11990922 ) d119909) (17)

Calculation is as follows

119875 = (1205872 )12 1

area (119872) (minus1205822 exp(minus1199092

2 )1003816100381610038161003816100381610038161003816100381610038161198770120582

minus1198770120582

+ (2120587)12 120582 + (2120587)12 11987720) asymp 120587 (11987720 + 1205822)area (119872)

(18)

The positions of all sensor nodes in119872 are independent ofeach other according to formula (1) the probability that anysensor node in119872 is at least covered by 119896 work sensor node is

119875119870 = 1 minus (1 minus 120587 (11987720 + 1205822)area (119872) )

119896

(19)

Assume the area covered by at least 119896 sensor nodes is1198721015840and then the expectation of the area for1198721015840 is

119864 (area (1198721015840)) = 119875119896area (119872) (20)

Therefore

119864 (120578119896) = 119864 (area (1198721015840))area (1198721015840) = 1 minus (1 minus 120587 (11987720 + 1205822)

area (119872) )119896

(21)

With Theorem 5 we can get the expectation of theminimum number of required work sensor nodes satisfyingdemanded coverage quality 120578119889 of applications namely

119864 (119896) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (22)

Theorem 8 After the redundant sensor nodes are powered offrandomlywithout causing any conflict if the rest working nodescan provide the coverage quality 119899119889 required by the applicationthe expectation for the number of redundant sensor nodesrsquoneighbors satisfies

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (23)

Proof Assuming the number of the remaining work sensornodes is 119873 after the redundant nods are powered off thenthe 119899 work sensor nodes still follow random and uniformdistribution Because the remaining work sensor nodes canstill accurately provide the coverage quality required inapplications by formula (22) we get

119864 (119873) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (24)

Denote the perception radius of sensor node as 119877119886 119877119887which represents the perception radius of sensor node 119887 If 119887is the coverage neighbor of 119886 then 119887must be located in a circlecentered on the radius 119877119886 +119877119887 (denote the circle as119874(119886 119877119886 +119877119887)) Therefore the probability that 119887 is a coverage neighborof 119886 is

119875119887minus119886 = area (119874 (119886 119877119886 + 119877119887))area (119872) (25)

Because the perception radius of all sensor nodes obeysnormal distribution 119873(1198770 1205822) as well as 1198770 ge 33120582 theprobability that a sensor node is the coverage neighbor ofanother sensor node is

119875 = int211987700

int211987700

119875119887minus119886sdot 121205871205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887(26)

Calculation is

119875 = 1area (119872) [int

21198770

0int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887+ int211987700

int211987700

119877119886119877119887sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887]

(27)

According to the computation process in formula (27) wehave

int211987700

int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887asymp 120587 (11987720 + 1205822)

(28)

Because

int211987700

119877119886 1(2120587)12 120582 exp(minus(1198770 minus 119877119886)221205822 ) d119877119886

= int1198770120582minus1198770120582

(1198770 + 120582119909) 1(2120587)12 exp (minus

1199092) d119909 = 1198770(29)

6 Journal of Sensors

int211987700

int211987700

2120587119877119886119877119887sdot 121205871205822 exp(minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ) d119877119886 d119877119887= 212058711987720

(30)

Then we have

119875 = 412058711987720 + 21205871205822area (119872) (31)

The expectation of the number of coverage neighborsensor nodes for each of the remaining119873 work sensor nodesis

119864 (119899) = (119864 (119873) minus 1) 119875= ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (32)

Therefore the expectations of the number of redundantcoverage neighboring sensor nodes satisfy

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (33)

33 Algorithm Description As to the redundancy of sensornodes the connection graph of sensor nodes gatheringredundancy is constructed that is the redundancy infor-mation calculated by a positioning algorithm (eg centroidpositioning and ranging location) of all the nodes in theprocess of gathering and the neighbor nodes The datacollected in this cluster are sent to the sink node throughcommunication links After the sink nodes receive theredundancy information it is calculated and analyzed Theconnection graph 119866 of redundancy relation is constructedaccording to the results of calculation and analysis Thedegree of connection graph 119866 is the number of limitedsides related to vertex It corresponds to the redundancydegree of sensor node When the number of sensor nodesincreases the redundancy degree increases correspondinglyIn the connection graph 119866 when the redundancy degreeof sensor node surpasses the preset threshold value thenode transferred to the state of sleeping At the same timethere exist several (119899 gt 2) high redundancy rate nodes Ifenergy is taken as choosing condition node with the mostenergy is chosen as the sleeping nodes by sort algorithm Andthis node together with the corresponding neighbor nodesis cancelled in connection graph 119866 Iteration algorithm isused to iterate Next node with most energy is found one

Table 1 The tabulation of the simulation parameters

Parameter ValueArea Ι 100 lowast 100Area ΙΙ 200 lowast 200Area ΙΙΙ 300 lowast 300119877119904 5mEnergy 5 JTime 800 s119877119888 10m119864119877-elec 50 Jb119864119879-elec 50 Jb120576119891119904 10 (Jb)m2

120576amp 100 (Jb)m2

119890min 0005 J

by one until the redundancy degree of all sensor nodes issmaller than the threshold value in the connection graph119866 As to energy consumption of sensor nodes clusteringalgorithm is used to control the administrator nodes andmember nodes respectively In the initial state of networkthe member node transmits the datum of ldquoinf coveragrdquo togathering node ldquoinf coveragrdquo includes the information oflocation ID and energy After one or several cycles thegathering node receives the information of sensor nodesTheinformation is calculated The node energy is stored in thechained list (CL) successively from the highest to the lowestone according to the rest node energy The top nodes possessthe covering ability of higher weight Nodes are controlledaccording to the positioning information The sensor nodethat satisfies the condition in the CL is sorted out and themessage ldquoinf noticerdquo is sent out to start the effective coverageThe rest nodes are in the state of sleeping to save the networkenergy expenses (see Algorithm 1)

4 System Evaluations

In order to verify the effectiveness and stability of the energy-efficient coverage control with multinodes redundancy veri-fication ECMRV algorithm this paper selects theMATLAB7as the simulation platform And the ECMRV algorithm iscompared with the four algorithms of the literature [13](the energy-efficient target coverage algorithm (ETCA)) andthe literature [16] (energy-efficient 119896-coverage algorithm(EEKCA)) the literature [14] (event probability drivenmech-anism EPDM) and the literature [17] (optimization strategycoverage control (OSCC)) And the simulation parametersare shown in Table 1

Experiment 1 In terms of prolonging the network lifetimethe ECMRV algorithm is compared with the ETCA and theEEKCA and the experimental data is the mean value of the200 simulation data as shown in Figures 3ndash5

Experiment 1 is a contrast experiment of the ECMRValgorithm and the ETCA and the EEKCA in terms of the

Journal of Sensors 7

(1) Procedure(2) Begin(3) nlarrNull Parameter Initializing(4) CLilarrNull(5) While (119894 lt= 119899)(6) (7) (8) 119904[119894]informationrarrs[i]bata Calculating and restoring the node information(9) 119904[119894]coverage-raterarrs[i]information according to the formula (18) calculate coverage

rate of sensor node(10) 119904[119894]neighborinformationrarrs[i]neighborbata(11) 119904[119894]broadcastrarrGn Send the nodes to the Gathering Nodes(12) 119894++(13) (14) ConstuctGraph() Construct Connecting Graph(15) while(119904[119894]energy gt= minenergy)(16) if(redundancynodes lt= 119868th) Nodesrsquo energy is not less than the threshold(17) Network working(18) else(19) (20) sorting(119904[119894]energy) sort according to nodesrsquo energy(21) 119904[119894]maxenergyrarrdormancy make the nodes of max-energy dormant(22) (23) if(Gnlarrs[i]inf covergae) (24) (25) CL[i]larrs[i]inf coverage Restore the received information in the linked list(26) 119894++ direct to the next sensor nodes(27) (28) if(119904[119894]energy gt= 119904[119894 + 1]energy)(29) (30) Gninf noticerarrs[i]data Gathering node information sent(31) 119904[119894]coveragerarrtargetnodes cover the target nodes with present nodes(32) (33)

Algorithm 1 ECMRV algorithm description

network lifetime in different monitoring areas In the exper-iment the values of 119896 are selected differently the networkscale can be changed by changing the number of the sensornodes deployed randomly in the monitoring area For themonitoring area of the smaller scale the initial value of thenumber of the sensor nodes deployed randomly is 30 basedon which the number of the sensor nodes increases step bystep From the simulation it can be seen that the lifetime ofthe Wireless Sensor Network is a linear rising trend with theincrease of the number of the sensor nodes The main reasonis that themember sensor nodes in the sensor nodes set coverthe target nodes by the scheduling mechanism of the sensornode In the same network environment compared with theETCA and the EEKCA the lifetime of the ECMRV algorithmhas been prolonged by 1129 on average as for the largerscale of the monitoring area the initial number of the sensornodes is 50 based on which the number of the sensor nodesincreases step by step The lifetime of the Wireless SensorNetwork is also a linear rising trend with the increase of thenumber of the sensor nodes The rise is more than that of thesmaller monitoring area and compared with the ETCA and

the EEKCA the network lifetime is increased by 1612 and1596

Experiment 2 The contrast experiment is taken between theECMRV algorithm and the EPDM algorithm of the literature[14] and the OSCC algorithm of the literature [17] in termsof the coverage ratio and multitargets cycle control coveragepreservation protocol [25] (MTCPP) in network runningtime Taking the monitoring area of 200lowast200m2 as examplethe experimental data is themean value of the 200 simulationdata as shown from Figures 6 to 8

In Figure 6 with the increase of the number of the sensornodes the coverage probabilities of the three algorithms arealso increasingWhen the coverage probability is 9999 and120582 = 2 the number of the sensor node is 237 when 120582 = 3 thenumber of the sensor nodes is 157 and when 120582 = 4 and thenumber of the sensor nodes is 132 the algorithm in this paperhas reached 9999 coverage however the EPDM algorithmand the OSCC algorithm have not reached 100 coveragewhich shows that the coverage ratio of the ECMRV algorithmis higher than that of the EPDM algorithm and the OSCC

8 Journal of SensorsN

etw

ork

lifet

ime (

s)

Number of nodes30 60 90 120 150

0

30

60

90

120

150

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 3 100 lowast 100m2 network lifetime

Number of nodes50 100 150 200 250 300

Net

wor

k lif

etim

e (s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 4 200 lowast 200m2 network lifetime

algorithm Thus the effectiveness of the ECMRV algorithmin this paper has been verified In Figure 7 at the initialtime of the program execution the coverage probabilities ofthe two algorithms are almost the same however as timepasses by the coverage probabilities of the two contractalgorithms are the declining trance The main reason is thatthe EPDM algorithm and the OSCC algorithm adopt theuninterrupted coverage to complete the coverage during therun time that is the target nodes in the monitoring areasare covered constantly until the energies of the target nodesare consumed up When 119905 = 150 the coverage probabilitiesof the three algorithms decline more obviously When 120582 =2 3 4 CPECMRV2 = 7656 CPECMRV3 = 9553 CPEPDM =7886 CPOSCC = 8402 and CPECMRV4 = 9771 When120582 = 4 the coverage probability in this paper is higherthan that of the EPDM algorithm and the OSCC algorithm

Number of nodes50 150 250 350 450

Net

wor

k lif

etim

e (s)

80

120

160

200

240

280

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 5 300 lowast 300m2 network lifetime

Coverage rate ()20 40 60 80 100

Num

ber o

f nod

es

40

80

120

160

200

240

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 6 200 lowast 200m2 network coverage rate

which shows that with the function of the same sensornodes the coverage probability of the ECMRV algorithmis higher than that of the other two algorithms which hasverified the effectiveness of the algorithm in this paper AndFigure 8 gives the curves of the working sensor nodes andthe sensor nodes contrast of the ECMRV algorithm andthe EPDM algorithm and the OSCC algorithm when thecoverage probabilities are the same ones When the numberof sensor nodes is maintained from 260 to 290 the numbersof sensor nodes of the three algorithms basically tend to bestable When 120582 = 2 3 4 the number of sensor nodes of theECMRV algorithm is maintained at 245 223 and 211 whilethe numbers of the sensor nodes in EPDM algorithm and theOSCC algorithm are maintained from 231 to 237 Thereforethemean value of the number of sensor nodes of the ECMRV

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

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DistributedSensor Networks

International Journal of

4 Journal of Sensors

A

B

C

D

120573

120572

Figure 2 Multilateral and unilateral node connection

long as possible this paper adopts the sensor node energymodel to analyze the sensor node-energy that is consumed inthe process of unilateral and multilateral data transmissionmeanwhile the energy of the sensor node is consumed byits own work of calculation [19ndash22] storage and control Theenergy consumption model of the sensor node transmitter is

119864Tx (119897 119889) = 119897119864119879-elec + 119864amp (119897 119889)=

119897119864119879-elec + 1198971205761198911199041198892 119889 lt 1198890119897119864119879-elec + 119897120576amp1198894 119889 ge 1198890

(6)

And the energy consumption model of the receiver is

119864Rx (119897) = 119864119877-elec (119897) = 119897119864elec (7)

And 119897 is the bit of the data transmission 119889 is the Euclideandistance between the sensor nodes and the neighboringnodes and 1198890 is the threshold value of the distance ofthe communication sensor node When the distance ofthe communication sensor node is smaller than 1198890 theenergy damping index is 2 whereas the energy dampingindex will be 4 119864elec represents the energy consumptionof communication sensor nodes receiving and transmittingmodules [23 24]

Theorem 6 Less energy of the data is consumed in multicastthan the unilateral sensor nodes The mathematical inductionwhen 119899 rarr infin is shown in Figure 2

In 1st case according to formula (6) the formula of energydissipations directly from source node 119860 to target node 119863 ispresented as below

119864Tx 119860119863 (119897 119889119860119863) = 119897119864119879-elec + 1198971205761198911199041198892119860119863 119889119860119863 lt 1198890119897119864119879-elec + 119897120576amp1198894119860119863 119889119860119863 ge 1198890 (8)

In the 2nd case data are sent from node 119860 to 119861 andthen to 119863 From 119860 to 119861 when 119896 = 3 the model of energyconsumption when transmitting module in node 119860 can beinducted as follows

119864Tx 119860119861 (119897 119889119860119861) = 119897119864119879-elec + 1198971205761198911199041198892119860119861 119889119860119861 lt 1198890119897119864119879-elec + 119897120576amp1198894119860119861 119889119860119861 ge 1198890

119864Rx 119861 (119897) = 119897119864elec(9)

The energy consumption of node 119861 receiving the infor-mation is represented as below

119864Tx 119861119863 (119897 119889119861119863) = 119897119864119879-elec + 1198971205761198911199041198892119861119863 119889119861119863 lt 1198890119897119864119879-elec + 119897120576amp1198894119861119863 119889119861119863 ge 1198890 (10)

Then the total energy consumption fromnode119860 to119861 andthen to119863 is represented as below

119864Total = 119864Tx 119860119861 + 119864Rx 119861 + 119864Tx 119861119862 (11)

In their initial state the nodesworkwith the same amountof energy and are independent of each other The basicproperties of triangle are shown

At the beginning each node is independent of eachother and is working with equal energy This basic feature offorming triangles can be represented as below

119864Total = 119864Tx 119860119861 + 119864Rx 119861 + 119864Tx 119861119863 lt 119864Tx 119860119863 (12)

That is to say when 119896 = 3 less energy is consumed inmultilateral data transmission than in unilateral one Sowhen119896 = 3 formula (12) is justified

The data transmitting path is from 119860 to 119861 to 119862 and thento 119863 When 119899 rarr infin because ang120572 is an obtuse angle ang120572 gt1205872 cosang120572 lt 0 According to CosineTheorem 1198611198622 +1198621198632 lt1198611198632The triangle of connecting119861119862 and119863 is obtuse triangleHence formula (13) is obtained as below

119864Tx 119860119861 + 119864Rx 119861 + sdot sdot sdot + 119864Rx119899minus1 + 119864Tx119899minus1119899 lt sdot sdot sdotlt 119864Tx119860119861 + 119864Rx119861 + 119864Tx119861119863 lt 119864Tx119860119863 (13)

32 Cover Quality

Theorem 7 Randomly select 119896 sensor nodes within 119872 andthen the expectation of the coverage quality is

119864 (120578119896) = 1 minus 1 minus 120587 (11987720 + 1205822)area (119872)

119896

(14)

Proof The sensor node subject to the random uniformdistribution in119872 so the probability a sensor node is locatedin any position in119872 is 1area(119872) If any point 119902 is coveredby a sensor node 119886 (the perception radius is denoted with119877119886)then sensor node 119886must be locate in a circle of centered on q(the circle is denoted as119874(119902 119877119886) of radius 119877119886) Therefore theprobability that 119902 is covered by sensor node 119886 is

119875119886 = area (119874 (119902 119877119886))area (119872) (15)

Because the perception radius of sensor node 119886 is normaldistribution and 1198770 ge 33120582 the probability that any point iscovered by a work sensor node is

119875 = int211987700

119875119886 1(2120587)12 120582 exp(minus(119877119886 minus 1198770)21205822 ) d1198770 (16)

Journal of Sensors 5

Let 119909 = (119877119886 minus 1198770)120582 then119875 = (1205872 )

12 1area (119872) (int

1198770120582

minus119877012058212058221199092 exp(minus11990922 ) d119909

+ int1198770120582minus1198770120582

21205821199091198770 exp(minus11990922 ) d119909+ int1198770120582minus1198770120582

11987720 exp(minus11990922 ) d119909) (17)

Calculation is as follows

119875 = (1205872 )12 1

area (119872) (minus1205822 exp(minus1199092

2 )1003816100381610038161003816100381610038161003816100381610038161198770120582

minus1198770120582

+ (2120587)12 120582 + (2120587)12 11987720) asymp 120587 (11987720 + 1205822)area (119872)

(18)

The positions of all sensor nodes in119872 are independent ofeach other according to formula (1) the probability that anysensor node in119872 is at least covered by 119896 work sensor node is

119875119870 = 1 minus (1 minus 120587 (11987720 + 1205822)area (119872) )

119896

(19)

Assume the area covered by at least 119896 sensor nodes is1198721015840and then the expectation of the area for1198721015840 is

119864 (area (1198721015840)) = 119875119896area (119872) (20)

Therefore

119864 (120578119896) = 119864 (area (1198721015840))area (1198721015840) = 1 minus (1 minus 120587 (11987720 + 1205822)

area (119872) )119896

(21)

With Theorem 5 we can get the expectation of theminimum number of required work sensor nodes satisfyingdemanded coverage quality 120578119889 of applications namely

119864 (119896) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (22)

Theorem 8 After the redundant sensor nodes are powered offrandomlywithout causing any conflict if the rest working nodescan provide the coverage quality 119899119889 required by the applicationthe expectation for the number of redundant sensor nodesrsquoneighbors satisfies

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (23)

Proof Assuming the number of the remaining work sensornodes is 119873 after the redundant nods are powered off thenthe 119899 work sensor nodes still follow random and uniformdistribution Because the remaining work sensor nodes canstill accurately provide the coverage quality required inapplications by formula (22) we get

119864 (119873) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (24)

Denote the perception radius of sensor node as 119877119886 119877119887which represents the perception radius of sensor node 119887 If 119887is the coverage neighbor of 119886 then 119887must be located in a circlecentered on the radius 119877119886 +119877119887 (denote the circle as119874(119886 119877119886 +119877119887)) Therefore the probability that 119887 is a coverage neighborof 119886 is

119875119887minus119886 = area (119874 (119886 119877119886 + 119877119887))area (119872) (25)

Because the perception radius of all sensor nodes obeysnormal distribution 119873(1198770 1205822) as well as 1198770 ge 33120582 theprobability that a sensor node is the coverage neighbor ofanother sensor node is

119875 = int211987700

int211987700

119875119887minus119886sdot 121205871205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887(26)

Calculation is

119875 = 1area (119872) [int

21198770

0int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887+ int211987700

int211987700

119877119886119877119887sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887]

(27)

According to the computation process in formula (27) wehave

int211987700

int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887asymp 120587 (11987720 + 1205822)

(28)

Because

int211987700

119877119886 1(2120587)12 120582 exp(minus(1198770 minus 119877119886)221205822 ) d119877119886

= int1198770120582minus1198770120582

(1198770 + 120582119909) 1(2120587)12 exp (minus

1199092) d119909 = 1198770(29)

6 Journal of Sensors

int211987700

int211987700

2120587119877119886119877119887sdot 121205871205822 exp(minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ) d119877119886 d119877119887= 212058711987720

(30)

Then we have

119875 = 412058711987720 + 21205871205822area (119872) (31)

The expectation of the number of coverage neighborsensor nodes for each of the remaining119873 work sensor nodesis

119864 (119899) = (119864 (119873) minus 1) 119875= ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (32)

Therefore the expectations of the number of redundantcoverage neighboring sensor nodes satisfy

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (33)

33 Algorithm Description As to the redundancy of sensornodes the connection graph of sensor nodes gatheringredundancy is constructed that is the redundancy infor-mation calculated by a positioning algorithm (eg centroidpositioning and ranging location) of all the nodes in theprocess of gathering and the neighbor nodes The datacollected in this cluster are sent to the sink node throughcommunication links After the sink nodes receive theredundancy information it is calculated and analyzed Theconnection graph 119866 of redundancy relation is constructedaccording to the results of calculation and analysis Thedegree of connection graph 119866 is the number of limitedsides related to vertex It corresponds to the redundancydegree of sensor node When the number of sensor nodesincreases the redundancy degree increases correspondinglyIn the connection graph 119866 when the redundancy degreeof sensor node surpasses the preset threshold value thenode transferred to the state of sleeping At the same timethere exist several (119899 gt 2) high redundancy rate nodes Ifenergy is taken as choosing condition node with the mostenergy is chosen as the sleeping nodes by sort algorithm Andthis node together with the corresponding neighbor nodesis cancelled in connection graph 119866 Iteration algorithm isused to iterate Next node with most energy is found one

Table 1 The tabulation of the simulation parameters

Parameter ValueArea Ι 100 lowast 100Area ΙΙ 200 lowast 200Area ΙΙΙ 300 lowast 300119877119904 5mEnergy 5 JTime 800 s119877119888 10m119864119877-elec 50 Jb119864119879-elec 50 Jb120576119891119904 10 (Jb)m2

120576amp 100 (Jb)m2

119890min 0005 J

by one until the redundancy degree of all sensor nodes issmaller than the threshold value in the connection graph119866 As to energy consumption of sensor nodes clusteringalgorithm is used to control the administrator nodes andmember nodes respectively In the initial state of networkthe member node transmits the datum of ldquoinf coveragrdquo togathering node ldquoinf coveragrdquo includes the information oflocation ID and energy After one or several cycles thegathering node receives the information of sensor nodesTheinformation is calculated The node energy is stored in thechained list (CL) successively from the highest to the lowestone according to the rest node energy The top nodes possessthe covering ability of higher weight Nodes are controlledaccording to the positioning information The sensor nodethat satisfies the condition in the CL is sorted out and themessage ldquoinf noticerdquo is sent out to start the effective coverageThe rest nodes are in the state of sleeping to save the networkenergy expenses (see Algorithm 1)

4 System Evaluations

In order to verify the effectiveness and stability of the energy-efficient coverage control with multinodes redundancy veri-fication ECMRV algorithm this paper selects theMATLAB7as the simulation platform And the ECMRV algorithm iscompared with the four algorithms of the literature [13](the energy-efficient target coverage algorithm (ETCA)) andthe literature [16] (energy-efficient 119896-coverage algorithm(EEKCA)) the literature [14] (event probability drivenmech-anism EPDM) and the literature [17] (optimization strategycoverage control (OSCC)) And the simulation parametersare shown in Table 1

Experiment 1 In terms of prolonging the network lifetimethe ECMRV algorithm is compared with the ETCA and theEEKCA and the experimental data is the mean value of the200 simulation data as shown in Figures 3ndash5

Experiment 1 is a contrast experiment of the ECMRValgorithm and the ETCA and the EEKCA in terms of the

Journal of Sensors 7

(1) Procedure(2) Begin(3) nlarrNull Parameter Initializing(4) CLilarrNull(5) While (119894 lt= 119899)(6) (7) (8) 119904[119894]informationrarrs[i]bata Calculating and restoring the node information(9) 119904[119894]coverage-raterarrs[i]information according to the formula (18) calculate coverage

rate of sensor node(10) 119904[119894]neighborinformationrarrs[i]neighborbata(11) 119904[119894]broadcastrarrGn Send the nodes to the Gathering Nodes(12) 119894++(13) (14) ConstuctGraph() Construct Connecting Graph(15) while(119904[119894]energy gt= minenergy)(16) if(redundancynodes lt= 119868th) Nodesrsquo energy is not less than the threshold(17) Network working(18) else(19) (20) sorting(119904[119894]energy) sort according to nodesrsquo energy(21) 119904[119894]maxenergyrarrdormancy make the nodes of max-energy dormant(22) (23) if(Gnlarrs[i]inf covergae) (24) (25) CL[i]larrs[i]inf coverage Restore the received information in the linked list(26) 119894++ direct to the next sensor nodes(27) (28) if(119904[119894]energy gt= 119904[119894 + 1]energy)(29) (30) Gninf noticerarrs[i]data Gathering node information sent(31) 119904[119894]coveragerarrtargetnodes cover the target nodes with present nodes(32) (33)

Algorithm 1 ECMRV algorithm description

network lifetime in different monitoring areas In the exper-iment the values of 119896 are selected differently the networkscale can be changed by changing the number of the sensornodes deployed randomly in the monitoring area For themonitoring area of the smaller scale the initial value of thenumber of the sensor nodes deployed randomly is 30 basedon which the number of the sensor nodes increases step bystep From the simulation it can be seen that the lifetime ofthe Wireless Sensor Network is a linear rising trend with theincrease of the number of the sensor nodes The main reasonis that themember sensor nodes in the sensor nodes set coverthe target nodes by the scheduling mechanism of the sensornode In the same network environment compared with theETCA and the EEKCA the lifetime of the ECMRV algorithmhas been prolonged by 1129 on average as for the largerscale of the monitoring area the initial number of the sensornodes is 50 based on which the number of the sensor nodesincreases step by step The lifetime of the Wireless SensorNetwork is also a linear rising trend with the increase of thenumber of the sensor nodes The rise is more than that of thesmaller monitoring area and compared with the ETCA and

the EEKCA the network lifetime is increased by 1612 and1596

Experiment 2 The contrast experiment is taken between theECMRV algorithm and the EPDM algorithm of the literature[14] and the OSCC algorithm of the literature [17] in termsof the coverage ratio and multitargets cycle control coveragepreservation protocol [25] (MTCPP) in network runningtime Taking the monitoring area of 200lowast200m2 as examplethe experimental data is themean value of the 200 simulationdata as shown from Figures 6 to 8

In Figure 6 with the increase of the number of the sensornodes the coverage probabilities of the three algorithms arealso increasingWhen the coverage probability is 9999 and120582 = 2 the number of the sensor node is 237 when 120582 = 3 thenumber of the sensor nodes is 157 and when 120582 = 4 and thenumber of the sensor nodes is 132 the algorithm in this paperhas reached 9999 coverage however the EPDM algorithmand the OSCC algorithm have not reached 100 coveragewhich shows that the coverage ratio of the ECMRV algorithmis higher than that of the EPDM algorithm and the OSCC

8 Journal of SensorsN

etw

ork

lifet

ime (

s)

Number of nodes30 60 90 120 150

0

30

60

90

120

150

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 3 100 lowast 100m2 network lifetime

Number of nodes50 100 150 200 250 300

Net

wor

k lif

etim

e (s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 4 200 lowast 200m2 network lifetime

algorithm Thus the effectiveness of the ECMRV algorithmin this paper has been verified In Figure 7 at the initialtime of the program execution the coverage probabilities ofthe two algorithms are almost the same however as timepasses by the coverage probabilities of the two contractalgorithms are the declining trance The main reason is thatthe EPDM algorithm and the OSCC algorithm adopt theuninterrupted coverage to complete the coverage during therun time that is the target nodes in the monitoring areasare covered constantly until the energies of the target nodesare consumed up When 119905 = 150 the coverage probabilitiesof the three algorithms decline more obviously When 120582 =2 3 4 CPECMRV2 = 7656 CPECMRV3 = 9553 CPEPDM =7886 CPOSCC = 8402 and CPECMRV4 = 9771 When120582 = 4 the coverage probability in this paper is higherthan that of the EPDM algorithm and the OSCC algorithm

Number of nodes50 150 250 350 450

Net

wor

k lif

etim

e (s)

80

120

160

200

240

280

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 5 300 lowast 300m2 network lifetime

Coverage rate ()20 40 60 80 100

Num

ber o

f nod

es

40

80

120

160

200

240

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 6 200 lowast 200m2 network coverage rate

which shows that with the function of the same sensornodes the coverage probability of the ECMRV algorithmis higher than that of the other two algorithms which hasverified the effectiveness of the algorithm in this paper AndFigure 8 gives the curves of the working sensor nodes andthe sensor nodes contrast of the ECMRV algorithm andthe EPDM algorithm and the OSCC algorithm when thecoverage probabilities are the same ones When the numberof sensor nodes is maintained from 260 to 290 the numbersof sensor nodes of the three algorithms basically tend to bestable When 120582 = 2 3 4 the number of sensor nodes of theECMRV algorithm is maintained at 245 223 and 211 whilethe numbers of the sensor nodes in EPDM algorithm and theOSCC algorithm are maintained from 231 to 237 Thereforethemean value of the number of sensor nodes of the ECMRV

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Journal of Sensors 5

Let 119909 = (119877119886 minus 1198770)120582 then119875 = (1205872 )

12 1area (119872) (int

1198770120582

minus119877012058212058221199092 exp(minus11990922 ) d119909

+ int1198770120582minus1198770120582

21205821199091198770 exp(minus11990922 ) d119909+ int1198770120582minus1198770120582

11987720 exp(minus11990922 ) d119909) (17)

Calculation is as follows

119875 = (1205872 )12 1

area (119872) (minus1205822 exp(minus1199092

2 )1003816100381610038161003816100381610038161003816100381610038161198770120582

minus1198770120582

+ (2120587)12 120582 + (2120587)12 11987720) asymp 120587 (11987720 + 1205822)area (119872)

(18)

The positions of all sensor nodes in119872 are independent ofeach other according to formula (1) the probability that anysensor node in119872 is at least covered by 119896 work sensor node is

119875119870 = 1 minus (1 minus 120587 (11987720 + 1205822)area (119872) )

119896

(19)

Assume the area covered by at least 119896 sensor nodes is1198721015840and then the expectation of the area for1198721015840 is

119864 (area (1198721015840)) = 119875119896area (119872) (20)

Therefore

119864 (120578119896) = 119864 (area (1198721015840))area (1198721015840) = 1 minus (1 minus 120587 (11987720 + 1205822)

area (119872) )119896

(21)

With Theorem 5 we can get the expectation of theminimum number of required work sensor nodes satisfyingdemanded coverage quality 120578119889 of applications namely

119864 (119896) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (22)

Theorem 8 After the redundant sensor nodes are powered offrandomlywithout causing any conflict if the rest working nodescan provide the coverage quality 119899119889 required by the applicationthe expectation for the number of redundant sensor nodesrsquoneighbors satisfies

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (23)

Proof Assuming the number of the remaining work sensornodes is 119873 after the redundant nods are powered off thenthe 119899 work sensor nodes still follow random and uniformdistribution Because the remaining work sensor nodes canstill accurately provide the coverage quality required inapplications by formula (22) we get

119864 (119873) = ln (1 minus 120578119889)ln (1 minus 120587 (11987720 + 1205822) area (119872)) (24)

Denote the perception radius of sensor node as 119877119886 119877119887which represents the perception radius of sensor node 119887 If 119887is the coverage neighbor of 119886 then 119887must be located in a circlecentered on the radius 119877119886 +119877119887 (denote the circle as119874(119886 119877119886 +119877119887)) Therefore the probability that 119887 is a coverage neighborof 119886 is

119875119887minus119886 = area (119874 (119886 119877119886 + 119877119887))area (119872) (25)

Because the perception radius of all sensor nodes obeysnormal distribution 119873(1198770 1205822) as well as 1198770 ge 33120582 theprobability that a sensor node is the coverage neighbor ofanother sensor node is

119875 = int211987700

int211987700

119875119887minus119886sdot 121205871205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887(26)

Calculation is

119875 = 1area (119872) [int

21198770

0int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887+ int211987700

int211987700

119877119886119877119887sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887]

(27)

According to the computation process in formula (27) wehave

int211987700

int211987700

1198772119886sdot 11205822 exp[minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ] d119877119886 d119877119887asymp 120587 (11987720 + 1205822)

(28)

Because

int211987700

119877119886 1(2120587)12 120582 exp(minus(1198770 minus 119877119886)221205822 ) d119877119886

= int1198770120582minus1198770120582

(1198770 + 120582119909) 1(2120587)12 exp (minus

1199092) d119909 = 1198770(29)

6 Journal of Sensors

int211987700

int211987700

2120587119877119886119877119887sdot 121205871205822 exp(minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ) d119877119886 d119877119887= 212058711987720

(30)

Then we have

119875 = 412058711987720 + 21205871205822area (119872) (31)

The expectation of the number of coverage neighborsensor nodes for each of the remaining119873 work sensor nodesis

119864 (119899) = (119864 (119873) minus 1) 119875= ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (32)

Therefore the expectations of the number of redundantcoverage neighboring sensor nodes satisfy

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (33)

33 Algorithm Description As to the redundancy of sensornodes the connection graph of sensor nodes gatheringredundancy is constructed that is the redundancy infor-mation calculated by a positioning algorithm (eg centroidpositioning and ranging location) of all the nodes in theprocess of gathering and the neighbor nodes The datacollected in this cluster are sent to the sink node throughcommunication links After the sink nodes receive theredundancy information it is calculated and analyzed Theconnection graph 119866 of redundancy relation is constructedaccording to the results of calculation and analysis Thedegree of connection graph 119866 is the number of limitedsides related to vertex It corresponds to the redundancydegree of sensor node When the number of sensor nodesincreases the redundancy degree increases correspondinglyIn the connection graph 119866 when the redundancy degreeof sensor node surpasses the preset threshold value thenode transferred to the state of sleeping At the same timethere exist several (119899 gt 2) high redundancy rate nodes Ifenergy is taken as choosing condition node with the mostenergy is chosen as the sleeping nodes by sort algorithm Andthis node together with the corresponding neighbor nodesis cancelled in connection graph 119866 Iteration algorithm isused to iterate Next node with most energy is found one

Table 1 The tabulation of the simulation parameters

Parameter ValueArea Ι 100 lowast 100Area ΙΙ 200 lowast 200Area ΙΙΙ 300 lowast 300119877119904 5mEnergy 5 JTime 800 s119877119888 10m119864119877-elec 50 Jb119864119879-elec 50 Jb120576119891119904 10 (Jb)m2

120576amp 100 (Jb)m2

119890min 0005 J

by one until the redundancy degree of all sensor nodes issmaller than the threshold value in the connection graph119866 As to energy consumption of sensor nodes clusteringalgorithm is used to control the administrator nodes andmember nodes respectively In the initial state of networkthe member node transmits the datum of ldquoinf coveragrdquo togathering node ldquoinf coveragrdquo includes the information oflocation ID and energy After one or several cycles thegathering node receives the information of sensor nodesTheinformation is calculated The node energy is stored in thechained list (CL) successively from the highest to the lowestone according to the rest node energy The top nodes possessthe covering ability of higher weight Nodes are controlledaccording to the positioning information The sensor nodethat satisfies the condition in the CL is sorted out and themessage ldquoinf noticerdquo is sent out to start the effective coverageThe rest nodes are in the state of sleeping to save the networkenergy expenses (see Algorithm 1)

4 System Evaluations

In order to verify the effectiveness and stability of the energy-efficient coverage control with multinodes redundancy veri-fication ECMRV algorithm this paper selects theMATLAB7as the simulation platform And the ECMRV algorithm iscompared with the four algorithms of the literature [13](the energy-efficient target coverage algorithm (ETCA)) andthe literature [16] (energy-efficient 119896-coverage algorithm(EEKCA)) the literature [14] (event probability drivenmech-anism EPDM) and the literature [17] (optimization strategycoverage control (OSCC)) And the simulation parametersare shown in Table 1

Experiment 1 In terms of prolonging the network lifetimethe ECMRV algorithm is compared with the ETCA and theEEKCA and the experimental data is the mean value of the200 simulation data as shown in Figures 3ndash5

Experiment 1 is a contrast experiment of the ECMRValgorithm and the ETCA and the EEKCA in terms of the

Journal of Sensors 7

(1) Procedure(2) Begin(3) nlarrNull Parameter Initializing(4) CLilarrNull(5) While (119894 lt= 119899)(6) (7) (8) 119904[119894]informationrarrs[i]bata Calculating and restoring the node information(9) 119904[119894]coverage-raterarrs[i]information according to the formula (18) calculate coverage

rate of sensor node(10) 119904[119894]neighborinformationrarrs[i]neighborbata(11) 119904[119894]broadcastrarrGn Send the nodes to the Gathering Nodes(12) 119894++(13) (14) ConstuctGraph() Construct Connecting Graph(15) while(119904[119894]energy gt= minenergy)(16) if(redundancynodes lt= 119868th) Nodesrsquo energy is not less than the threshold(17) Network working(18) else(19) (20) sorting(119904[119894]energy) sort according to nodesrsquo energy(21) 119904[119894]maxenergyrarrdormancy make the nodes of max-energy dormant(22) (23) if(Gnlarrs[i]inf covergae) (24) (25) CL[i]larrs[i]inf coverage Restore the received information in the linked list(26) 119894++ direct to the next sensor nodes(27) (28) if(119904[119894]energy gt= 119904[119894 + 1]energy)(29) (30) Gninf noticerarrs[i]data Gathering node information sent(31) 119904[119894]coveragerarrtargetnodes cover the target nodes with present nodes(32) (33)

Algorithm 1 ECMRV algorithm description

network lifetime in different monitoring areas In the exper-iment the values of 119896 are selected differently the networkscale can be changed by changing the number of the sensornodes deployed randomly in the monitoring area For themonitoring area of the smaller scale the initial value of thenumber of the sensor nodes deployed randomly is 30 basedon which the number of the sensor nodes increases step bystep From the simulation it can be seen that the lifetime ofthe Wireless Sensor Network is a linear rising trend with theincrease of the number of the sensor nodes The main reasonis that themember sensor nodes in the sensor nodes set coverthe target nodes by the scheduling mechanism of the sensornode In the same network environment compared with theETCA and the EEKCA the lifetime of the ECMRV algorithmhas been prolonged by 1129 on average as for the largerscale of the monitoring area the initial number of the sensornodes is 50 based on which the number of the sensor nodesincreases step by step The lifetime of the Wireless SensorNetwork is also a linear rising trend with the increase of thenumber of the sensor nodes The rise is more than that of thesmaller monitoring area and compared with the ETCA and

the EEKCA the network lifetime is increased by 1612 and1596

Experiment 2 The contrast experiment is taken between theECMRV algorithm and the EPDM algorithm of the literature[14] and the OSCC algorithm of the literature [17] in termsof the coverage ratio and multitargets cycle control coveragepreservation protocol [25] (MTCPP) in network runningtime Taking the monitoring area of 200lowast200m2 as examplethe experimental data is themean value of the 200 simulationdata as shown from Figures 6 to 8

In Figure 6 with the increase of the number of the sensornodes the coverage probabilities of the three algorithms arealso increasingWhen the coverage probability is 9999 and120582 = 2 the number of the sensor node is 237 when 120582 = 3 thenumber of the sensor nodes is 157 and when 120582 = 4 and thenumber of the sensor nodes is 132 the algorithm in this paperhas reached 9999 coverage however the EPDM algorithmand the OSCC algorithm have not reached 100 coveragewhich shows that the coverage ratio of the ECMRV algorithmis higher than that of the EPDM algorithm and the OSCC

8 Journal of SensorsN

etw

ork

lifet

ime (

s)

Number of nodes30 60 90 120 150

0

30

60

90

120

150

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 3 100 lowast 100m2 network lifetime

Number of nodes50 100 150 200 250 300

Net

wor

k lif

etim

e (s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 4 200 lowast 200m2 network lifetime

algorithm Thus the effectiveness of the ECMRV algorithmin this paper has been verified In Figure 7 at the initialtime of the program execution the coverage probabilities ofthe two algorithms are almost the same however as timepasses by the coverage probabilities of the two contractalgorithms are the declining trance The main reason is thatthe EPDM algorithm and the OSCC algorithm adopt theuninterrupted coverage to complete the coverage during therun time that is the target nodes in the monitoring areasare covered constantly until the energies of the target nodesare consumed up When 119905 = 150 the coverage probabilitiesof the three algorithms decline more obviously When 120582 =2 3 4 CPECMRV2 = 7656 CPECMRV3 = 9553 CPEPDM =7886 CPOSCC = 8402 and CPECMRV4 = 9771 When120582 = 4 the coverage probability in this paper is higherthan that of the EPDM algorithm and the OSCC algorithm

Number of nodes50 150 250 350 450

Net

wor

k lif

etim

e (s)

80

120

160

200

240

280

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 5 300 lowast 300m2 network lifetime

Coverage rate ()20 40 60 80 100

Num

ber o

f nod

es

40

80

120

160

200

240

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 6 200 lowast 200m2 network coverage rate

which shows that with the function of the same sensornodes the coverage probability of the ECMRV algorithmis higher than that of the other two algorithms which hasverified the effectiveness of the algorithm in this paper AndFigure 8 gives the curves of the working sensor nodes andthe sensor nodes contrast of the ECMRV algorithm andthe EPDM algorithm and the OSCC algorithm when thecoverage probabilities are the same ones When the numberof sensor nodes is maintained from 260 to 290 the numbersof sensor nodes of the three algorithms basically tend to bestable When 120582 = 2 3 4 the number of sensor nodes of theECMRV algorithm is maintained at 245 223 and 211 whilethe numbers of the sensor nodes in EPDM algorithm and theOSCC algorithm are maintained from 231 to 237 Thereforethemean value of the number of sensor nodes of the ECMRV

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Journal of Sensors

int211987700

int211987700

2120587119877119886119877119887sdot 121205871205822 exp(minus

(119877119886 minus 119877119887)2 + (119877119887 minus 1198770)221205822 ) d119877119886 d119877119887= 212058711987720

(30)

Then we have

119875 = 412058711987720 + 21205871205822area (119872) (31)

The expectation of the number of coverage neighborsensor nodes for each of the remaining119873 work sensor nodesis

119864 (119899) = (119864 (119873) minus 1) 119875= ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (32)

Therefore the expectations of the number of redundantcoverage neighboring sensor nodes satisfy

119864 (119899) gt ln (1 minus 120578119889)ln ((1 minus 120587 (11987720 + 1205822) area (119872)) minus 1)sdot 412058711987720 + 21205871205822

area (119872) (33)

33 Algorithm Description As to the redundancy of sensornodes the connection graph of sensor nodes gatheringredundancy is constructed that is the redundancy infor-mation calculated by a positioning algorithm (eg centroidpositioning and ranging location) of all the nodes in theprocess of gathering and the neighbor nodes The datacollected in this cluster are sent to the sink node throughcommunication links After the sink nodes receive theredundancy information it is calculated and analyzed Theconnection graph 119866 of redundancy relation is constructedaccording to the results of calculation and analysis Thedegree of connection graph 119866 is the number of limitedsides related to vertex It corresponds to the redundancydegree of sensor node When the number of sensor nodesincreases the redundancy degree increases correspondinglyIn the connection graph 119866 when the redundancy degreeof sensor node surpasses the preset threshold value thenode transferred to the state of sleeping At the same timethere exist several (119899 gt 2) high redundancy rate nodes Ifenergy is taken as choosing condition node with the mostenergy is chosen as the sleeping nodes by sort algorithm Andthis node together with the corresponding neighbor nodesis cancelled in connection graph 119866 Iteration algorithm isused to iterate Next node with most energy is found one

Table 1 The tabulation of the simulation parameters

Parameter ValueArea Ι 100 lowast 100Area ΙΙ 200 lowast 200Area ΙΙΙ 300 lowast 300119877119904 5mEnergy 5 JTime 800 s119877119888 10m119864119877-elec 50 Jb119864119879-elec 50 Jb120576119891119904 10 (Jb)m2

120576amp 100 (Jb)m2

119890min 0005 J

by one until the redundancy degree of all sensor nodes issmaller than the threshold value in the connection graph119866 As to energy consumption of sensor nodes clusteringalgorithm is used to control the administrator nodes andmember nodes respectively In the initial state of networkthe member node transmits the datum of ldquoinf coveragrdquo togathering node ldquoinf coveragrdquo includes the information oflocation ID and energy After one or several cycles thegathering node receives the information of sensor nodesTheinformation is calculated The node energy is stored in thechained list (CL) successively from the highest to the lowestone according to the rest node energy The top nodes possessthe covering ability of higher weight Nodes are controlledaccording to the positioning information The sensor nodethat satisfies the condition in the CL is sorted out and themessage ldquoinf noticerdquo is sent out to start the effective coverageThe rest nodes are in the state of sleeping to save the networkenergy expenses (see Algorithm 1)

4 System Evaluations

In order to verify the effectiveness and stability of the energy-efficient coverage control with multinodes redundancy veri-fication ECMRV algorithm this paper selects theMATLAB7as the simulation platform And the ECMRV algorithm iscompared with the four algorithms of the literature [13](the energy-efficient target coverage algorithm (ETCA)) andthe literature [16] (energy-efficient 119896-coverage algorithm(EEKCA)) the literature [14] (event probability drivenmech-anism EPDM) and the literature [17] (optimization strategycoverage control (OSCC)) And the simulation parametersare shown in Table 1

Experiment 1 In terms of prolonging the network lifetimethe ECMRV algorithm is compared with the ETCA and theEEKCA and the experimental data is the mean value of the200 simulation data as shown in Figures 3ndash5

Experiment 1 is a contrast experiment of the ECMRValgorithm and the ETCA and the EEKCA in terms of the

Journal of Sensors 7

(1) Procedure(2) Begin(3) nlarrNull Parameter Initializing(4) CLilarrNull(5) While (119894 lt= 119899)(6) (7) (8) 119904[119894]informationrarrs[i]bata Calculating and restoring the node information(9) 119904[119894]coverage-raterarrs[i]information according to the formula (18) calculate coverage

rate of sensor node(10) 119904[119894]neighborinformationrarrs[i]neighborbata(11) 119904[119894]broadcastrarrGn Send the nodes to the Gathering Nodes(12) 119894++(13) (14) ConstuctGraph() Construct Connecting Graph(15) while(119904[119894]energy gt= minenergy)(16) if(redundancynodes lt= 119868th) Nodesrsquo energy is not less than the threshold(17) Network working(18) else(19) (20) sorting(119904[119894]energy) sort according to nodesrsquo energy(21) 119904[119894]maxenergyrarrdormancy make the nodes of max-energy dormant(22) (23) if(Gnlarrs[i]inf covergae) (24) (25) CL[i]larrs[i]inf coverage Restore the received information in the linked list(26) 119894++ direct to the next sensor nodes(27) (28) if(119904[119894]energy gt= 119904[119894 + 1]energy)(29) (30) Gninf noticerarrs[i]data Gathering node information sent(31) 119904[119894]coveragerarrtargetnodes cover the target nodes with present nodes(32) (33)

Algorithm 1 ECMRV algorithm description

network lifetime in different monitoring areas In the exper-iment the values of 119896 are selected differently the networkscale can be changed by changing the number of the sensornodes deployed randomly in the monitoring area For themonitoring area of the smaller scale the initial value of thenumber of the sensor nodes deployed randomly is 30 basedon which the number of the sensor nodes increases step bystep From the simulation it can be seen that the lifetime ofthe Wireless Sensor Network is a linear rising trend with theincrease of the number of the sensor nodes The main reasonis that themember sensor nodes in the sensor nodes set coverthe target nodes by the scheduling mechanism of the sensornode In the same network environment compared with theETCA and the EEKCA the lifetime of the ECMRV algorithmhas been prolonged by 1129 on average as for the largerscale of the monitoring area the initial number of the sensornodes is 50 based on which the number of the sensor nodesincreases step by step The lifetime of the Wireless SensorNetwork is also a linear rising trend with the increase of thenumber of the sensor nodes The rise is more than that of thesmaller monitoring area and compared with the ETCA and

the EEKCA the network lifetime is increased by 1612 and1596

Experiment 2 The contrast experiment is taken between theECMRV algorithm and the EPDM algorithm of the literature[14] and the OSCC algorithm of the literature [17] in termsof the coverage ratio and multitargets cycle control coveragepreservation protocol [25] (MTCPP) in network runningtime Taking the monitoring area of 200lowast200m2 as examplethe experimental data is themean value of the 200 simulationdata as shown from Figures 6 to 8

In Figure 6 with the increase of the number of the sensornodes the coverage probabilities of the three algorithms arealso increasingWhen the coverage probability is 9999 and120582 = 2 the number of the sensor node is 237 when 120582 = 3 thenumber of the sensor nodes is 157 and when 120582 = 4 and thenumber of the sensor nodes is 132 the algorithm in this paperhas reached 9999 coverage however the EPDM algorithmand the OSCC algorithm have not reached 100 coveragewhich shows that the coverage ratio of the ECMRV algorithmis higher than that of the EPDM algorithm and the OSCC

8 Journal of SensorsN

etw

ork

lifet

ime (

s)

Number of nodes30 60 90 120 150

0

30

60

90

120

150

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 3 100 lowast 100m2 network lifetime

Number of nodes50 100 150 200 250 300

Net

wor

k lif

etim

e (s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 4 200 lowast 200m2 network lifetime

algorithm Thus the effectiveness of the ECMRV algorithmin this paper has been verified In Figure 7 at the initialtime of the program execution the coverage probabilities ofthe two algorithms are almost the same however as timepasses by the coverage probabilities of the two contractalgorithms are the declining trance The main reason is thatthe EPDM algorithm and the OSCC algorithm adopt theuninterrupted coverage to complete the coverage during therun time that is the target nodes in the monitoring areasare covered constantly until the energies of the target nodesare consumed up When 119905 = 150 the coverage probabilitiesof the three algorithms decline more obviously When 120582 =2 3 4 CPECMRV2 = 7656 CPECMRV3 = 9553 CPEPDM =7886 CPOSCC = 8402 and CPECMRV4 = 9771 When120582 = 4 the coverage probability in this paper is higherthan that of the EPDM algorithm and the OSCC algorithm

Number of nodes50 150 250 350 450

Net

wor

k lif

etim

e (s)

80

120

160

200

240

280

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 5 300 lowast 300m2 network lifetime

Coverage rate ()20 40 60 80 100

Num

ber o

f nod

es

40

80

120

160

200

240

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 6 200 lowast 200m2 network coverage rate

which shows that with the function of the same sensornodes the coverage probability of the ECMRV algorithmis higher than that of the other two algorithms which hasverified the effectiveness of the algorithm in this paper AndFigure 8 gives the curves of the working sensor nodes andthe sensor nodes contrast of the ECMRV algorithm andthe EPDM algorithm and the OSCC algorithm when thecoverage probabilities are the same ones When the numberof sensor nodes is maintained from 260 to 290 the numbersof sensor nodes of the three algorithms basically tend to bestable When 120582 = 2 3 4 the number of sensor nodes of theECMRV algorithm is maintained at 245 223 and 211 whilethe numbers of the sensor nodes in EPDM algorithm and theOSCC algorithm are maintained from 231 to 237 Thereforethemean value of the number of sensor nodes of the ECMRV

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 7

(1) Procedure(2) Begin(3) nlarrNull Parameter Initializing(4) CLilarrNull(5) While (119894 lt= 119899)(6) (7) (8) 119904[119894]informationrarrs[i]bata Calculating and restoring the node information(9) 119904[119894]coverage-raterarrs[i]information according to the formula (18) calculate coverage

rate of sensor node(10) 119904[119894]neighborinformationrarrs[i]neighborbata(11) 119904[119894]broadcastrarrGn Send the nodes to the Gathering Nodes(12) 119894++(13) (14) ConstuctGraph() Construct Connecting Graph(15) while(119904[119894]energy gt= minenergy)(16) if(redundancynodes lt= 119868th) Nodesrsquo energy is not less than the threshold(17) Network working(18) else(19) (20) sorting(119904[119894]energy) sort according to nodesrsquo energy(21) 119904[119894]maxenergyrarrdormancy make the nodes of max-energy dormant(22) (23) if(Gnlarrs[i]inf covergae) (24) (25) CL[i]larrs[i]inf coverage Restore the received information in the linked list(26) 119894++ direct to the next sensor nodes(27) (28) if(119904[119894]energy gt= 119904[119894 + 1]energy)(29) (30) Gninf noticerarrs[i]data Gathering node information sent(31) 119904[119894]coveragerarrtargetnodes cover the target nodes with present nodes(32) (33)

Algorithm 1 ECMRV algorithm description

network lifetime in different monitoring areas In the exper-iment the values of 119896 are selected differently the networkscale can be changed by changing the number of the sensornodes deployed randomly in the monitoring area For themonitoring area of the smaller scale the initial value of thenumber of the sensor nodes deployed randomly is 30 basedon which the number of the sensor nodes increases step bystep From the simulation it can be seen that the lifetime ofthe Wireless Sensor Network is a linear rising trend with theincrease of the number of the sensor nodes The main reasonis that themember sensor nodes in the sensor nodes set coverthe target nodes by the scheduling mechanism of the sensornode In the same network environment compared with theETCA and the EEKCA the lifetime of the ECMRV algorithmhas been prolonged by 1129 on average as for the largerscale of the monitoring area the initial number of the sensornodes is 50 based on which the number of the sensor nodesincreases step by step The lifetime of the Wireless SensorNetwork is also a linear rising trend with the increase of thenumber of the sensor nodes The rise is more than that of thesmaller monitoring area and compared with the ETCA and

the EEKCA the network lifetime is increased by 1612 and1596

Experiment 2 The contrast experiment is taken between theECMRV algorithm and the EPDM algorithm of the literature[14] and the OSCC algorithm of the literature [17] in termsof the coverage ratio and multitargets cycle control coveragepreservation protocol [25] (MTCPP) in network runningtime Taking the monitoring area of 200lowast200m2 as examplethe experimental data is themean value of the 200 simulationdata as shown from Figures 6 to 8

In Figure 6 with the increase of the number of the sensornodes the coverage probabilities of the three algorithms arealso increasingWhen the coverage probability is 9999 and120582 = 2 the number of the sensor node is 237 when 120582 = 3 thenumber of the sensor nodes is 157 and when 120582 = 4 and thenumber of the sensor nodes is 132 the algorithm in this paperhas reached 9999 coverage however the EPDM algorithmand the OSCC algorithm have not reached 100 coveragewhich shows that the coverage ratio of the ECMRV algorithmis higher than that of the EPDM algorithm and the OSCC

8 Journal of SensorsN

etw

ork

lifet

ime (

s)

Number of nodes30 60 90 120 150

0

30

60

90

120

150

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 3 100 lowast 100m2 network lifetime

Number of nodes50 100 150 200 250 300

Net

wor

k lif

etim

e (s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 4 200 lowast 200m2 network lifetime

algorithm Thus the effectiveness of the ECMRV algorithmin this paper has been verified In Figure 7 at the initialtime of the program execution the coverage probabilities ofthe two algorithms are almost the same however as timepasses by the coverage probabilities of the two contractalgorithms are the declining trance The main reason is thatthe EPDM algorithm and the OSCC algorithm adopt theuninterrupted coverage to complete the coverage during therun time that is the target nodes in the monitoring areasare covered constantly until the energies of the target nodesare consumed up When 119905 = 150 the coverage probabilitiesof the three algorithms decline more obviously When 120582 =2 3 4 CPECMRV2 = 7656 CPECMRV3 = 9553 CPEPDM =7886 CPOSCC = 8402 and CPECMRV4 = 9771 When120582 = 4 the coverage probability in this paper is higherthan that of the EPDM algorithm and the OSCC algorithm

Number of nodes50 150 250 350 450

Net

wor

k lif

etim

e (s)

80

120

160

200

240

280

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 5 300 lowast 300m2 network lifetime

Coverage rate ()20 40 60 80 100

Num

ber o

f nod

es

40

80

120

160

200

240

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 6 200 lowast 200m2 network coverage rate

which shows that with the function of the same sensornodes the coverage probability of the ECMRV algorithmis higher than that of the other two algorithms which hasverified the effectiveness of the algorithm in this paper AndFigure 8 gives the curves of the working sensor nodes andthe sensor nodes contrast of the ECMRV algorithm andthe EPDM algorithm and the OSCC algorithm when thecoverage probabilities are the same ones When the numberof sensor nodes is maintained from 260 to 290 the numbersof sensor nodes of the three algorithms basically tend to bestable When 120582 = 2 3 4 the number of sensor nodes of theECMRV algorithm is maintained at 245 223 and 211 whilethe numbers of the sensor nodes in EPDM algorithm and theOSCC algorithm are maintained from 231 to 237 Thereforethemean value of the number of sensor nodes of the ECMRV

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Journal of SensorsN

etw

ork

lifet

ime (

s)

Number of nodes30 60 90 120 150

0

30

60

90

120

150

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 3 100 lowast 100m2 network lifetime

Number of nodes50 100 150 200 250 300

Net

wor

k lif

etim

e (s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 4 200 lowast 200m2 network lifetime

algorithm Thus the effectiveness of the ECMRV algorithmin this paper has been verified In Figure 7 at the initialtime of the program execution the coverage probabilities ofthe two algorithms are almost the same however as timepasses by the coverage probabilities of the two contractalgorithms are the declining trance The main reason is thatthe EPDM algorithm and the OSCC algorithm adopt theuninterrupted coverage to complete the coverage during therun time that is the target nodes in the monitoring areasare covered constantly until the energies of the target nodesare consumed up When 119905 = 150 the coverage probabilitiesof the three algorithms decline more obviously When 120582 =2 3 4 CPECMRV2 = 7656 CPECMRV3 = 9553 CPEPDM =7886 CPOSCC = 8402 and CPECMRV4 = 9771 When120582 = 4 the coverage probability in this paper is higherthan that of the EPDM algorithm and the OSCC algorithm

Number of nodes50 150 250 350 450

Net

wor

k lif

etim

e (s)

80

120

160

200

240

280

120582 = 2 ECMRVETCAEEKCA

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 5 300 lowast 300m2 network lifetime

Coverage rate ()20 40 60 80 100

Num

ber o

f nod

es

40

80

120

160

200

240

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 6 200 lowast 200m2 network coverage rate

which shows that with the function of the same sensornodes the coverage probability of the ECMRV algorithmis higher than that of the other two algorithms which hasverified the effectiveness of the algorithm in this paper AndFigure 8 gives the curves of the working sensor nodes andthe sensor nodes contrast of the ECMRV algorithm andthe EPDM algorithm and the OSCC algorithm when thecoverage probabilities are the same ones When the numberof sensor nodes is maintained from 260 to 290 the numbersof sensor nodes of the three algorithms basically tend to bestable When 120582 = 2 3 4 the number of sensor nodes of theECMRV algorithm is maintained at 245 223 and 211 whilethe numbers of the sensor nodes in EPDM algorithm and theOSCC algorithm are maintained from 231 to 237 Thereforethemean value of the number of sensor nodes of the ECMRV

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 9C

over

age r

ate (

)

Running time (s)100 200 300 400 500 600

40

60

80

100

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 7 200 lowast 200m2 network running time

Number of nodes250 260 270 280 290 300

Wor

king

nod

es

210

220

230

240

250

120582 = 2 ECMRVEPDMOSCC

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 8 Number of sensor nodes and working sensor nodes

algorithm is less than that of the other algorithms the numberof sensor nodes is reduced by 1349

Figure 9 provides the different network energy consump-tion in different monitoring area and the contracted algo-rithms are the algorithms in the literature [13] and literature[25] At the initial time of the three algorithms the networklifetime is increasing with the increase of the sensor nodesHowever the parameter range limitation in this paper andthe closing statement of the redundant sensor node makethe network lifetime of the algorithm in this paper smallerthan that of the other two algorithms when the networkenergy reaches the balancing statement Figure 10 providesthe network lifetime and the target node When the targetnodes are being covered the network energy of this paperis also smaller than that of the other two algorithms andthe reason is the same as the above situation In Figure 11

Number of nodes30 60 90 120 150

Net

wor

k lif

etim

e (s)

0

30

60

90

120

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 9 100 lowast 100m2 network lifetime and sensor nodes

Number of targets5 10 15 20 25

Net

wor

k lif

etim

e (s)

20

40

60

80

100

120

140

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 10 100 lowast 100m2 network lifetime and target nodes

the expansion of the monitoring area makes some of theredundant sensor nodes in the working state which hasprolonged the network lifetime When the parameter 120582 = 3the network lifetime of the algorithm in this paper is largerthan that of the ETCA when the parameter 120582 = 4 thenetwork lifetime is larger than that of the other algorithmsand Figure 12 provides the change of the network lifetimein the process of the coverage of the target node With theincreasing of the number of the target nodes the networklifetime of the three algorithms has been the declining tranceand finally provide the energy balance statement But duringthe declining process the average speed of the algorithmin this paper is smaller than that of the other algorithmsthe main reasons are as follows The coverage expectation ofintensively deployed sensor nodes in the monitoring area isquite largeMeantime some redundant nodes are waken up toworking nodes Hence the coverage probability is enhanced

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Sensors

Number of nodes50 100 150 200 250 300

40

80

120

160

200

240

Net

wor

k lif

etim

e (s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 11 200 lowast 200m2 network lifetime and sensor nodes

Number of targets10 20 30 40 50

Net

wor

k lif

etim

e (s)

0

50

100

150

200

250

300

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 12 200 lowast 200m2 network lifetime and target nodes

and the network lifetime is prolonged It is also applicablefor 300 lowast 300m2 According to the analysis from Figures 8ndash12 the algorithm in this paper has more energy during therunning time the reason is that in the coverage process thealgorithm in this paper closes some of the redundant sensornodes which greatly prolongs the network lifetime Thus inthe condition of the same sensor nodes numbers the runningtime of the algorithm in this paper is a little higher than thatof the other algorithms as shown in Figures 13 and 14

5 Conclusion

Based on the analysis of the coverage in the WirelessSensor Network this paper proposes an energy-efficientcoverage algorithm with multinode redundancy verification(ECMRV) The algorithm provides the calculation method

Number of nodes50 100 150 200 250 300

40

80

120

160

200

Runn

ing

time (

s)

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 13 200 lowast 200m2 running time and sensor nodes

Number of targets10 20 30 40 50

Runn

ing

time (

s)

40

80

120

160

200

240

120582 = 2 ECMRVETCAMTCPP

120582 = 3 ECMRV120582 = 4 ECMRV

Figure 14 200 lowast 200m2 running time and target nodes

with the expected value of the monitoring area and on thisbasis it proves the solving process which uses the least sensornodes to calculate the expected value of the monitoringarea meanwhile the first coverage expected value of themoving target node is calculated and deduced In terms ofthe energy this paper has provided a detailed process torestrict the energy consumption and with the correspondingcalculation it has proved that the energy consumption of themultilateral transmission is less than that of the unilateraltransmission Finally in the aspect of the different valueranges of 120582 the network lifetime and the network coveragethe simulation experiments are taken and the results arecompared with that of the ETCA the EEKCA the EPDMAlgorithm the OSCC algorithmand MTCPP Algorithmwhich finally verifies the effectiveness and the stability of thealgorithm in this paper

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 11

The futurework is to focus on how to realize the nonlinearprogramming for the effectiveness coverage of the multipletarget nodes and how to improve the effective coverage of theboundary of the monitoring area

Competing Interests

The authors declare no competing interests

Acknowledgments

The study is supported by Projects U1304603 and 61503174supported by the National Natural Science Foundation ofChina Projects 15A413016 16A520063 and 17A520044 sup-ported by Henan Province Education Department NaturalScience Foundation Projects 152300410115 152102410053162102210113 162102210276 and 162102410051 supported byNatural Science and Technology Research of FoundationProject of Henan Province Department of Science Project1201430560 supported by Guangzhou Education BureauScience Foundation Project 2016A030313540 supported byGuangdongNatural Science Foundation of ChinaThis paperis also supported by the National Scholarship Fund

References

[1] J-H Seok J-Y Lee W Kim and J-J Lee ldquoA bipopulation-based evolutionary algorithm for solving full area coverageproblemsrdquo IEEE Sensors Journal vol 13 no 12 pp 4796ndash48072013

[2] K Derr andMManic ldquoWireless sensor network configuration-part II adaptive coverage for decentralized algorithmsrdquo IEEETransactions on Industrial Informatics vol 9 no 3 pp 1728ndash1738 2013

[3] Z BWang J L Liao Q Cao H R Qi and ZWang ldquoAchievingk-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[4] C Yang and K-W Chin ldquoNovel algorithms for complete targetscoverage in energy harvesting wireless sensor networksrdquo IEEECommunications Letters vol 18 no 1 pp 118ndash121 2014

[5] M R Senouci A Mellouk L Oukhellou and A Aissani ldquoAnevidence-based sensor coverage modelrdquo IEEE CommunicationsLetters vol 16 no 9 pp 1462ndash1465 2012

[6] Y Li C Vu C Ai G Chen and Y Zhao ldquoTransformingcomplete coverage algorithms to partial coverage algorithms forwireless sensor networksrdquo IEEE Transactions on Parallel andDistributed Systems vol 22 no 4 pp 695ndash703 2011

[7] F-Z Meng H-Z Wang and H He ldquoConnected coverageprotocol using cooperative sensing model for wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 4 pp 772ndash7792011

[8] S Mini S K Udgata and S L Sabat ldquoSensor deploymentand scheduling for target coverage problem in wireless sensornetworksrdquo IEEE Sensors Journal vol 14 no 3 pp 636ndash6442014

[9] D W Gong and Y Y Yang ldquoLow-latency SINR-based datagathering in wireless sensor networksrdquo IEEE Transactions onWireless Communications vol 13 no 6 pp 3207ndash3221 2014

[10] HMahboubi KMoezzi A G Aghdam K Sayrafian-Pour andV Marbukh ldquoDistributed deployment algorithms for improvedcoverage in a network of wireless mobile sensorsrdquo IEEE Trans-actions on Industrial Informatics vol 10 no 1 pp 163ndash175 2014

[11] Y-C Tseng P-Y Chen and W-T Chen ldquok-angle objectcoverage problem in a wireless sensor networkrdquo IEEE SensorsJournal vol 12 no 12 pp 3408ndash3416 2012

[12] Z Wang J Liao Q Cao H Qi and Z Weng ldquoAchieving k-barrier coverage in hybrid directional sensor networksrdquo IEEETransactions on Mobile Computing vol 13 no 7 pp 1443ndash14552014

[13] X Xing G Wang and J Li ldquoPolytype target coverage schemefor heterogeneous wireless sensor networks using linear pro-grammingrdquo Wireless Communications and Mobile Computingvol 14 no 14 pp 1397ndash1408 2014

[14] Z Y Sun W G Wu H Z Wang H Chen and X F XingldquoA novel coverage algorithm based on eventprobability-drivenmechanism in wireless sensor networkrdquo Eurasip Journal onWireless Communications and Networking vol 2014 article 582014

[15] C-H Wu K-C Lee and Y-C Chung ldquoA Delaunay Triangu-lation based method for wireless sensor network deploymentrdquoComputer Communications vol 30 no 14-15 pp 2744ndash27522007

[16] C Li Z SunHWang andH Song ldquoA novel energy-efficient k-Coverage algorithm based on probability driven mechanism ofwireless sensor networksrdquo International Journal of DistributedSensor Networks vol 2016 Article ID 7474926 9 pages 2016

[17] Z Y Sun W G Wu H Z Wang H Chen and W WeildquoAn optimized strategy coverage control algorithm for WSNrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 976307 12 pages 2014

[18] C J Zhao H R Wu Q Liu and L Zhu ldquoOptimizationstrategy on coverage control in wireless sensor network basedon Voronoirdquo Journal of Communications vol 28 no 1 pp 36ndash43 2013

[19] Z Y Sun X F Xing C F Li Y L Nie and Y J CaoldquoA novel nonlinear multitarget 120581-degree coverage preservationprotocol in wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 3434961 13 pages 2016

[20] Z Lu WW Li andM Pan ldquoMaximum lifetime scheduling fortarget coverage and data collection in wireless sensor networksrdquoIEEE Transactions on Vehicular Technology vol 64 no 2 pp714ndash727 2015

[21] C-T Cheng H Leung and P Maupin ldquoA delay-aware networkstructure for wireless sensor networks with in-network datafusionrdquo IEEE Sensors Journal vol 13 no 5 pp 1622ndash1631 2013

[22] S Zairi B Zouari E Niel and E Dumitrescu ldquoNodes self-scheduling approach for maximising wireless sensor networklifetime based on remaining energyrdquo IET Wireless Sensor Sys-tems vol 2 no 1 pp 52ndash62 2012

[23] C Menegazzo and L C P Albini ldquoUnadvertised energy savingmethod for static and homogeneous wireless sensor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 105ndash111 2014

[24] L H Kong M C Zhao X-Y Liu et al ldquoSurface coverage insensor networksrdquo IEEE Transactions on Parallel and DistributedSystems vol 25 no 1 pp 234ndash243 2014

[25] Y P Li and Y L Yun ldquoA novel multi-targets cycle controlcoverage preservation protocol in wireless sensor networkrdquoInternational Journal of Future Generation Communication andNetworking vol 9 no 6 pp 17ndash28 2016

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of