research article energy-balanced uneven clustering...

Research ArticleEnergy-Balanced Uneven Clustering Protocol Based onRegional Division for Sensor Networks

Chao Sha1234 Tian-cheng Shen1 Jin-yu Chen15 Yao Zhang15 and Ru-chuan Wang123

1College of Computer Nanjing University of Posts and Telecommunications Nanjing Jiangsu 210003 China2Provincial Key Laboratory for Computer Information Processing Technology Soochow University Suzhou Jiangsu China3Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks Nanjing Jiangsu 210003 China4Institute of Computer Technology Nanjing University of Posts and Telecommunications China5School of Engineering and Computation New York Institute of Technology New York City NY USA

Correspondence should be addressed to Chao Sha shacnjupteducn

Received 4 February 2015 Revised 25 May 2015 Accepted 30 May 2015

Academic Editor Neil Y Yen

Copyright copy 2015 Chao Sha 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

In view of the unbalanced energy consumption of traditional cluster-based sensor networks this paper proposes a type of unevenclustering protocol in data collectionThe network is divided into inner and outer regions according to the distance between nodesand the base stationThe inner region is consisted of several layers and nodes in outer region are deployed in grids of different sizesSensor data is collected by nodes in outer region and then is be transmitted to the inner region Nodes in the inner region do datafusion and forward data from the lower layer to the higher one Simulation results show that compared with MTP and CDFUDthe proposed algorithm performs well in balance of energy consumption and could effectively prolong the network lifetime

1 Introduction

Due to the dense deployment of sensor networks sensorydata tended to have larger redundancy in time and spacewhich not only increase the cost of transmission and pro-cessing but also affect the expansion of its application [1 2]In the age of big data and ubiquitous network it has beenone of the key technologies to further improve the executionefficiency aswell as the quality of sensory datawith the help ofdata fusion and data aggregation in wireless sensor networks(WSNs for short)

On the other hand energy consumption problem is alsoone of the hotspots inWSNs How to achieve efficient energymanagement and optimization on the sensor nodes withweak computation and communication capabilities as wellas limited power reserve is also a key problem which couldgreatly improve the network performance

For most of the existing data fusion algorithms theyalways focus on the optimization of energy consumption incommunication between nodes but ignore the cost of energyconsumption in data fusion in the dense deployment wireless

sensor networks [3] In addition the large amount and vari-ous types of sensor data have greatly increase the overhead ofcalculating and processing of the nodeTherefore calculatingbecome another source of energy consumption [4]

Based on the regional cluster network structure thispaper analyzes the energy consumption during data trans-mission and fusion process and put forward a type of energy-balanced data fusion method which is efficiently decreasingthe energy consumption of the whole network

The rest of the paper is organized as follows The relatedworks and the network model are described in Sections2 and 3 respectively In Section 4 we analyse the energyconsumption of nodes in inner region and outer regionExperimental results are shown in the fifth section and theconclusion is provided in the last section

2 Related Works

There are two types of data gathering methods in WSNsthe routing-driven method and the fusion-driven one [5] Inrouting-drivenmethod sensor data is transmitted hopbyhop

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 647570 11 pageshttpdxdoiorg1011552015647570

2 International Journal of Distributed Sensor Networks

through the shortest path and data from different sources willbe fused However the fusion process depends only on thedata dependency in fusion-driven method and the efficiencyof data gathering of this method has nothing to do with nodedeployment [6] In this paper a type of routing-driven datagathering method based on uneven clustering and regionaldivision is proposed

LEACH [7] is the first data gathering architecture forwireless sensor networks that achieves low energy dissipationand latency without sacrificing application-specific quality[8] It uses a clustering architecture where each node in thecluster sends its data to a local cluster head However thismode is responsible for collecting data from all sensors inthe cluster and sends them to the receiving end without datafusion which not only reduces the bandwidth utilization butalso increases energy consumption

PEGASIS is an enhancement over LEACH [9] Nodes areorganized to form a chain so that they need to communicateonly with their closest neighbors PEGASIS avoids clusterformation and only uses one node in a chain to transmit tothe sink node instead of using multiple nodes It reduces theenergy consumption on transmission per round as the powerdraining is spread uniformly over all nodes NeverthelessPEGASIS presents a big delay for the most distant node inthe chain even if the clustering overhead is avoided

Another kind of typical energy aware data gatheringprotocol is MTP (Multi-Tier Trace-Back Protocol) [10] Itselects one node with the most sufficient energy as well asthe shortest distance to the base station (BS for short) as therelay node which could communicate with the BS directlyOther nodes could only transmit and fuse their data to theparent node in the upper layer If the cluster head in MTPis far away from the BS it will consume more energy duringdata gathering fusing and transmitting On the other handaccording to MTP nodes in the upper layer will also forwardits data to their parent node even if the parent node is just inthe lower layer It not only increases the transmission cost butalso reduces the reliability of the whole network

Yue et al proposed an uneven clustering algorithm basedon grid namely CDFUD [11 12] (Clustering Data FusionAlgorithm Based on Uneven Division) Sizes of the grids aredifferent from each other according to their distance to the BSand the node with the maximal residual energy in each gridis chosen as the cluster head Similar to LEACH the clusterhead in each gird transmit the data of its members as well asitself to BS with one hop The main disadvantage of CDFUDis that the cluster head consumes energy rapidly which causesunbalance energy consumption in the network119870-Means [13] Data Relay Clustering algorithm is devel-

oped to group the sensor nodes for energy efficient datacommunication 119870 arbitrary points are picked as the clusterhead by the sink node Cluster members are obtained foreach CH based on distance metric Then in each CH dataaggregation process is done for limiting the energy spentin transmission Although it reduces the communicationoverhead it also reduces the number of nodes transmittingdata to sink node and unable to collect enough informationwhich we need

Es(J d)

Node Node

Sending module

Eelec times J

Eelec times J

120583amp times J times dn

Signal amplifier

d

Receiving module

ER(J)

Figure 1 Energy consumption model for one node

TMMDF [14] eliminates negligent errors by Dixonmethod to obtain a valid observation data and uses thetriangle module operator to assign weights of each sensordata Finally it gets the fusion estimate values Although datadelay of this method is greatly increased it is not an efficientmethod for large-scale data processing

Based on the study above an energy-balanced unevenclustering protocol (EUCP) is proposed in this paper Accord-ing to the distance between nodes and BS it divides regionsinto clusters with different sizes And the size of each clusteras well as the number of nodes is related to the energyconsumption of each grid Simulation results show thatEUCP could effectively prolong the network lifetime andbalance the whole network energy consumption

3 Method Description

31 Network Model As we know in two-dimensional spacethe communication and sensing area of one node is a circularwhose center is the node itself [15] Therefore in EUCPwe assume that the shape of the network is also a circularMoreover it has been proved that clustered structure issuitable for data fusion in WSNs [16] so it is still be adoptedin EUCP However in cluster-based WSNs nodes which arefar from BS undertake minor data fusion mission (the nodeson boundary of the network even do not need to fuse data)while nodes which are close to BS often receive and processmore data So in EUCPwe adopt the hierarchical structure todesign the whole network for data transmission and fusion

The attenuation model of wireless signal can be dividedinto free-space model and multipath fading model [17] asshown in Figure 1 A sensor node consumes energy when it isgenerating local data receiving data transmitting data or instandby mode [18] The energy for generating one bit of dataand the standby energy consumed by one node are assumedto be the same for all nodes which can always be ignoredFor energy used in receiving and transmitting we adoptthe first order radio model described in [19] We assumethat 119864

119878(119869 119889) and 119864

119877(119869) represent the energy consumption

of sending module and receiving module while 119864elec is theunit energy consumption of sending and receiving circuitsThe energy consumption of circuit is in direct proportion tothe data package size 119869 120583amp is the constant parameter ofsignal amplifier and 119889

0is assumed as the unit of transmission

distance In general 1198890is equal to the communication radius

119877 of nodesWe assume that each node send 119888 bit data package

International Journal of Distributed Sensor Networks 3

Sector 1

Boundary of the inner region

Sector 2

Sector 3

Base node

Boundary of the outer region

Sensor node

d0

d1 d2

dkD

middot middot middot

Laye

r kLa

yer 2

Laye

r 1

Figure 2 Network structure

in its slot time and the distance of transmitting is 119889 Thus theenergy consumption of sending module is [18]

119864119904 (119869 119889) =

119888119864elec + 1198881205831198911199041198892 119889 lt 1198890

119888119864elec + 119888120583amp1198894 119889 ge 1198890

(1)

and to receive this message the radio expends

119864119877 (119869) = 119888119864elec (2)

In EUCP all the nodes are distributed uniformly in acircle area with radius 119863 (119863 gt 1198890) and the BS is inthe network center Based on the analysis above signalattenuation will be more serious when the nodes spacing isgreater than 119889

0 So we divide the network into inner region

and outer region by the boundary of 1198890 as shown in Figure 2

The gray area in this graph is inner region and the white oneis the outer region Points in Figure 2 are the sensing nodes

As shown in Figure 2 in the inner region the distancebetween nodes and BS is smaller than 119889

0 According to (1)

energy consumption of sending data is proportional to 1198892As we know nodes in outer region is a little far from BS Sothe multihop transmission method is used [20] to relay datathrough nodes in inner region which will certainly increasethe energy assumption and traffic load of nodes Thereforewe further divide the inner region into 119896 annular regionscalled ldquoinner ringsrdquo We assume that nodes in 119894th inner ringonly need to transmit data to nodes in 119894minus1th inner ring Afterdata fusion data will eventually be transmitted to BS hop byhop The widths of each inner ring are 1198891 1198892 119889119896

In wireless network signal quality is determined mainlyby base station antennas In general we divide the circleregion into three sector regions with covering angle 21205873As shown in Figure 2 considering the similarity of the threesector regions we only take one of them as an example

A

CB

D

EF

H

G

120579

r

Figure 3 Distribution of nodes with maximum density

32 Circular Division in Inner Region In EUCP 119877119878is defined

as the sensing radius as shown in Figures 3 and 4The distri-bution density of nodes is defined as 120588 According to [21]to realize completely coverage in omnidirectional sensornetworks the maximum and minimum distribution density120588max and 120588min are

120588max =2

radic31198772119904

120588min =2

3radic31198772119904

(3)

Obviously when the density of nodes is higher than 120588maxredundant nodes will exist While when the density is lowerthan 120588min the hole will appear

Without loss of generality we assume 120588 = (120588max+120588min)2Therefore in the inner region showed in Figure 5 the width1198891of innermost ring satisfies the following

120588times120587119889

21

3= 1198991 (4)

1198991 is the total number of nodes in the innermost ring In

addition to promote the efficiency of data fusion and reducethe workload of nodes around base station we construct asimilar structure of binary tree by connecting the nodes ininner region Thus in Figure 5 for the second layer of innerregion its width 119889

2satisfies the following

120588

3times [120587 (1198891 +1198892)

2minus120587119889

21] = 21198991 (5)

Similarly the width of 119896th layer of inner region satisfies

120588

3times[

[

120587(

119896

sum

119894=1119889119894)

2

minus120587(

119896minus1sum

119894=1119889119894)

2

]

]

= 2119896minus1 times 1198991 (6)


A O

B

E

C

D

F

120579r

Figure 4 Distribution of nodes with minimum density

Base noded1

d2dkminus1

dk

d0

Number of nodes is n1

Number of nodes is nk

Figure 5 A similar structure of binary tree in the inner region

Widths of all inner rings satisfy

119896

sum

119894=1119889119894 = 1198890 (7)

In inner region we group every two nodes in 119894th layertogether and they choose one node in the 119894 minus 1th layer as aparent node Therefore the binary tree is constructed fromthe 119896th layer to the innermost layer which is named as ldquodatafusion binary treerdquo To insure that two nodes in adjacent ringscould communicate with each other the communicationradius 119877

119905of one node should be greater than the longest

distance of two nodes in adjacent inner ring In Figure 6 weassume the maximum distance is 1198891015840

119877119905gt 1198891015840= radic119889

20 + (1198890 minus 119889119896)

2minus 21198890 (1198890 minus 119889119896) cos

21205873

= radic311988920 minus 31198890119889119896 + 1198892119896

(8)

33 Division of Outer Region Based on Uneven ClusteringIn EUCP nodes in outer region are far from BS and thedistance between them is longer than 119889

0 Therefore multiple

d1d2

dkminus1dk

d0

d998400(d998400 lt Rt)A B

2120587

3

O

Figure 6 The longest distance in adjacent ring

dk+1 d

k+2dk+1

d0

d998400998400

D

Inner regionBase node

Outer region

Figure 7 Subregions in outer region

hop transmission should be used Moreover the area of theouter region is much bigger than inner one So we dividethe outer region into a number of uneven-sized subsectorregions and each region is defined as a cluster referring tothe thought of GAF methods [22]

First we divide the outer region into 119897 annular regionscalled ldquoouter ringsrdquo and number them as layer 119896 + 1 layer119896 + 2 layer 119896 + 119897 Then each ldquoouter ringrdquo is dividedinto a number of small regions with angel 120579 We call thesesmall regions ldquosubregionsrdquo In EUCP we divide each layer ofthe outer ring into 119908 subregions as shown in Figure 7 InFigure 7 120579 = 21205873119908 and 119908 is equivalent to the number ofnodes 119899119896 in the outermost layer of the inner regionAccordingto this way outer regions are divided into 119897times119908 subregionsThecluster head collect data from each node in a subregion andtransmit it to the upper cluster heads hop by hop to nodes ininner regions

From the analysis above it is obvious that in EUCP eachnode in the subregion should communicate with each otherin one hop Taking the outermost subregion for example themaximumdistance of any two nodes is just the length of diag-onals of this subregion We assume the length of diagonalsis 11988910158401015840 Therefore as shown in Figure 7 the communicationradius 119877

119905needs to satisfy

119877119905gt 11988910158401015840= radic1198632 + (119863 minus 119889

119896+1)2minus 2119863(119863 minus 119889

119896+119897) cos 120579

= radic21198632 + 2119863119889119896+1 + 119889

2119896+119897minus 2119863(119863 minus 119889

119896+119897) cos 2120587

3119899119896

(9)


Similar to LEACH in the initial stage of clustering nodesin subregion need to broadcast packets containing their IDnumber residual energy and coordinates (119883

119894 119884119894) The node

with the maximum residual energy is selected as the clusterhead If there are two ormore standards-compliant nodes thenearest one is selected as the cluster head by comparing theEuclidean distance between them and the subregion centerwhich balances the energy consumption of all nodes in thesubregion

After the first round of data fusion and transmission thecluster heads will be reselected The priority of node 119894 insubregion is defined as 119901 as shown in the following

119901 = 120572times119864119894+120573

119889119894119900

+120574

120594119888

(10)

119889119894119900

is the distance between node 119894 and the subregioncenter 120594

119888is the number of times that node 119894 is selected as

a cluster head 120572 120573 120574 are the constant parameters The nodewith themaximum value 119901will be selected as the cluster headin the next round and the new cluster head needs to broadcastits identity to its neighbors in the subregion

4 Analysis of Energy Consumption

41 Energy Consumption of Nodes in Inner Region As men-tioned above a similar structure of binary tree is built in innerregion whose root is the base station Each node (except theleaf nodes) needs to fuse data collected by itself and its twochild nodes before uploading while leaf nodes collect thedata from the corresponding cluster heads in outer region andtransmit them to their parent nodes in 119896 minus 1th layer The datafusion rate is 120578

For a node in 119894th layer of the inner region 119885119894is defined

as the amount of its data needed to be uploaded in one roundtime Thus if 119894 lt 119896 119885

119894is just the sum of the amount of data

collected by itself (defined as119866) and uploaded by its two childnodes While for a node in 119896th layer 119885

119896is just the sum of the

amount of data collected by itself and data uploaded by itscorresponding cluster head in outer region (defined as119876

119896+1)

119885119896= 119866+119876

119896+1

119885119896minus1 = 119866+ 2 (119866+119876119896+1)

119885119896minus2 = 119866+ 2 (119866+ 2 (119866+119876119896+1)) 120578

(11)

By using mathematic induction we obtain

119885119896minus119886=

119886minus1sum

119894=02119894119866120578119894 + 2119886 (119866+119876

119896+1) 120578119886minus1

119896 minus 1 ge 119886 ge 1

(12)

Thus for each node in 119896 minus 119886th layer its energy consump-tion 119864

119896minus119886during one round time is

119864119896minus119886= 119864 (119879

119896minus119886) + 119864 (119877

119896minus119886) + 119864 (119865

119896minus119886)

119864 (119879119896minus119886) = 119885119896minus119886(119864elec +120583fs119889

2(119896minus119886119896minus119886minus1))

119864 (119877119896minus119886) = 2119885

119896minus119886+1119864elec

119864 (119865119896minus119886) = 119891times119885119896minus119886

(13)

119891 is defined as the energy consumption of data fusion perbit and 119889(119896minus119886119896minus119886minus1) is the distance between a node in 119896 minus 119886thlayer and its parent in 119896minus119886minus1th layerTherefore this distanceapproximately satisfies

119889(119896minus119886119896minus119886minus1) = 05 (119889119896minus119886 +119889119896minus119886minus1) (14)

For nodes in 119896th layer there is no need to do data fusionSo the energy consumption 119864119896 can be expressed as

119864119896= 119864 (119879

119896) + 119864 (119877

119896)

= (119866+119876119896+1) (119864elec +120583fs119889

2(119896119896minus1)) +119876119896+1119864elec

= (119866+ 2119876119896+1) 119864elec + (119866+119876119896+1) 120583fs119889

2(119896119896minus1)

(15)

since the number of nodes in each layer of the inner regionsatisfies geometric progression whose common ratio is 2Based on the above analysis the total energy consumption119864in of all nodes in inner region in one round time is

119864in =119896minus1sum

119886=12119896minus119886minus1 times 1198991 times119864119896minus119886 +119864119896 (16)

42 Energy Consumption of Nodes in Outer Region

421 Energy Consumption of Data Fusion for the ClusterHead We take a subregion in 119896+119895th layer of the outer regionas an example to analyze the energy consumption of nodesIt is assumed that data fusion is finished by the cluster headof each subregion and the data fusion rate is still 120578 Thus foreach cluster head in the 119896 + 119895th layer (119895 lt 119897) the amount ofdata 119876

119896+119895after one round of data fusion is

119876119896+119895 = (120588 times 119878119896+119895 times119866+119876119896+119895+1) times 120578 (17)

And the energy consumption on data fusion 119864(119865119896+119895) for

each cluster head is

119864 (119865119896+119895) = (120588 times 119878

119896+119895times119866+119876

119896+119895+1) times119891 (18)

Therefore for the cluster head in the 119896 + 119897th layer weobtain

119876119896+119897= 120588times 119878

119896+119897times119866times 120578

119864 (119865119896+119897) = 120588 times 119878

119896+119897times119866times119891

(19)


119878119896+119895

and 119878119896+119897

are defined as area of the subregion in 119896+119895thand 119896+119897th layers respectively By the analysis above we obtain

119878119896+119895 =21205873119908times120587[

[

(

119896+119895

sum

119894=1119889119894)

2

minus(

119896+119895minus1

sum

119894=1119889119894)

2

]

]

119878119896+119897=

21205873119908times120587[

[

1198632minus(

119896+119897minus1sum

119894=1119889119894)

2

]

]

(20)

422 Energy Consumption of Transmission for the ClusterHead and Its Members Since nodes are uniformly dis-tributed for each subregion in the 119896 + 119895th layer it is assumedthat the average distance between cluster members and thecluster head is one-half length of its diagonal (defined as11988910158401015840

119896+119895) Therefore the total energy consumption of transmis-

sion for all cluster members in this subregion (defined as1198641(119879119896+119895)) is

1198641 (119879119896+119895)

= [119866times119864elec +119866times120583fs times (0511988910158401015840

119896+119895)

2] (120588 times 119878119896+119895 minus 1)

(21)

In the equation

11988910158401015840

119896+119895

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus1

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus1

sum

119894=1119889119894cos 2120587

3119899119896

(22)

In addition each cluster head needs to transmit the fuseddata to the upper cluster head These data are collected bycluster head itself as well as its members and uploaded by thecluster head in the lower layer So the energy consumption oftransmission for a cluster head in the 119896+119895th layer (defined as1198642(119879119896+119895)) is

1198642 (119879119896+119895)

= (119866times119864elec +119866times120583fs times1198632(119896+119895119896+119895minus1))119876119896+119895

(23)

119863(119896+119895119896+119895minus1) is the distance between the two neighboringcluster heads in 119896 + 119895th layer and the 119896 + 119895 minus 1th layer In theworst case 119863(119896+119895119896+119895minus1) is the length of diagonal of the sectorcombined by two neighboring subregions in 119896+119895th layer and119896 + 119895 minus 1th layer as follows

MAX (119863(119896+119895119896+119895minus1))

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus2

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus2

sum

119894=1119889119894cos 2120587

3119899119896

(24)

For simplicity we define

119863(119896+119895119896+119895minus1) = 05 (119889

119896+119895+119889119896+119895minus1) (25)

423 Energy Consumption of Receiving for the Cluster HeadFor the cluster head in the 119896 + 119895th layer its energy con-sumption on data receiving (defined as 119864(119877

119896+119895)) is mainly on

receiving data of its members as well as the data upload by thelower cluster heads So

119864 (119877119896+119895) = [(120588 times 119878

119896+119895minus 1) times119866+119876

119896+119895minus1] times 119864elec (26)

While for the cluster head in 119896 + 119895th layer its energyconsumption on data receiving (defined as 119864(119877

119896+119897)) is

119864 (119877119896+119897) = (120588 times 119878

119896+119897minus 1) times119866times119864elec (27)

Therefore in one round time of data collection andfusion the total energy consumption of nodes in outer region(defined as 119864out) is expressed as

119864out

=

119897minus1sum

119895=1[119864 (119865119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895)]

+119864 (119865119896+119897) + 1198641 (119879119896+119897) + 1198642 (119879119896+119897) + 119864 (119877119896+119897)

(28)

That is

119864out =119897minus1sum

119895=1(120588119878119896+119895119866+119876

119896+119895+1) 119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

+ [(120588119878119896+119895 minus 1)119866+119876119896+119895minus1] 119864elec + 120588119878119896+119897119866119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119897)2] (120588119878119896+119897minus 1) + (119866119864elec

+119866120583fs1198632(119896+119897119896+119897minus1))119876119896+119897 + (120588119878119896+119897 minus 1) 119866119864elec

(29)

To balance energy consumption it is assumed that theenergy consumption of nodes in each subregion of outerregion is approximately equal as follows

119864119896+1 asymp 119864119896+2 asymp sdot sdot sdot asymp 119864119896+119895 asymp sdot sdot sdot asymp 119864119896+119897 (30)

In (30) we have

119864119896+119895= 119864 (119865

119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895) (31)

As for the multihop wireless sensor networks it is wellknown that clusters near the center could receive more datathan the clusters which are away from the center Thereforewe have

119864 (119865119896+119895) gt 119864 (119865

119896+ℎ) 119895 lt ℎ

119864 (119877119896+119895) gt 119864 (119877119896+ℎ) 119895 lt ℎ

(32)


Table 1 Parameter values of the inner region

Parameter Symbol Value UnitWidth of layer 1 119889

1315 m

Width of layer 2 1198892

23 mWidth of layer 3 119889

3288 m


3869 mEnergy consumption ofwireless sending and receivingcircuit

119864elec 50 nJtimesbminus1

Energy consumption ofamplifier in free-space model 120583fs 10 pJtimes(bm2)minus1

Energy consumption ofamplifier in multipath fadingmodel

120583amp 00013 pJtimes(bm4)minus1

Energy consumption of fusionfor one bit 119865 167 times 10

minus11 Jtimesbminus1

To satisfy (30) we need

1198641 (119879119896+119895) +1198642 (119879119896+119895) lt 1198641 (119879119896+ℎ) + 1198642 (119879119896+ℎ)

119895 lt ℎ

(33)

That is

[119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

lt [119866119864elec +119866120583fs (0511988910158401015840

119896+ℎ)2] (120588119878119896+ℎminus 1)

+ (119866119864elec +119866120583fs1198632(119896+ℎ119896+ℎminus1))119876119896+ℎ 119895 lt ℎ

(34)

Through analysis of (34) we obtain 119889119896+119895

lt 119889119896+ℎ

Therefore the area of subregions in outer region is not of thesame size That is to say subregion which is close to the edgeof networks has bigger area At last the outer region is presentas an uneven clustering structure

5 Experimental Results and Analysis

To analyze the balance of energy consumption as well as thenetwork lifetime during data collection process we use thejava language to build the data collection model and thenput the initial values for each parameter into the programto calculate the values of energy consumption and theirvarianceThis paper compares EUCPwithMTP andCDFUDalgorithm respectively

51 Performance of Data Collection in Inner Region Thewidth 1198890 of the inner region is 122m and it is divided into fourlayers Data generated by each node is 1 bit in an unit of timeand the number of nodes in the first layer 119899

1is 2 similarly

1198992= 4 119899

3= 8 and 119899

4= 16 Parameters values of the inner

region are shown in Table 1We set the fusion rate 120578 to be 025 05 075 and 10

respectively to analyze energy consumption on EUCP and

000

150

300

450

600

750

900

1050

EUCP

Ener

gy (J

)

MTP1 MTP2 MTP3 MTP4

times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1

Figure 8 Energy consumption of EUCP and MTP in one round ofdata fusion and transmission

MTP (including MTP1 MTP2 MTP3 and MTP4) MTPirepresent the running of MTP in the 119894th round

According to MTP during the 119894th round nodes which isnot in the 119894th layer need to fuse and transmit data to nodes inthe 119894th layer hop by hop while nodes in the 119894th layer transmitall of the data to a node with the maximal residual energy ofthis layer which will then directly transmits these data to BS

As shown in Figure 8 for the same data fusion rate 120578energy consumption of MTP

1is a little more than EUCP

However with the increasing of rounds energy consumptionof MTP is significantly higher than EUCP In MTP

2 a node

which has maximal residual energy in layer 2 communicateswith BS directly But before this nodes in layer 1 shouldtransmit data to the nodes in layer 2 which is far fromBSThismodewill obviously cause thewaste of energy while in EUCPnodes in layer 1 transmit data to BS after having collected allthe data from other layers which could keep equal energyconsumption in each round of data fusion as well as dataforwarding and could prolong network lifetime

The inner region is divided into 4 layers and the energyconsumption of each layer is 1198641 1198642 1198643 and 1198644 respectivelyFigures 9 10 11 and 12 are the energy consumption of EUCPand MTP in different layers

It is easy to know that for different values of 120578 energyconsumption ofMTP4 is always the highest one And the rela-tionship between energy consumption of these algorithmsis EUCP lt MTP1 lt MTP2 lt MTP3 lt MTP4 Withthe increasing of rounds energy consumption of MTP alsoincreases But for EUCP energy consumption of each roundis stable which could effectively save energy of nodes

As shown in Figures 9ndash12 the differences in energy con-sumption between each layer are small in EUCP However


00

10

20

30

40

50

60

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4

Layer1 Layer2 Layer3 Layer4 Layers1ndash4

times10minus5

Figure 9 Energy consumption in each layer ofMTP andEUCP (120578 =025)

00

10

20

30

40

50

60

70

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4

Layer1 Layer2 Layer3 Layer4

times10minus5

Layers1ndash4

Figure 10 Energy consumption in each layer of MTP and EUCP(120578 = 05)

for MTP with the increasing of rounds differences in energyconsumption between each layer become larger and larger

Figure 13 shows that variances of energy consumption aresmall in EUCP MTP

1 and MTP

2 While with the increasing

of rounds variance of energy consumption of MTP becomelarger than that of EUCP

00

10

20

30

40

50

60

70

80

90

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


00

20

40

60

80

100

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


52 Performance of Data Collection in Outer Region Wecompare the energy consumption in outer region of EUCPand CDFUD algorithmThe outer region is also divided into4 layers whose widths are 119889

5 1198896 1198897 and 119889

8 respectively As

shown in Figure 7 the number of subregions of each layeris equal to the number of leaf nodes in the inner region and


00

10

20

30

40

50

60

70

80

Varia

nce

EUCP MTP1 MTP2 MTP3 MTP4

times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1

Figure 13 Variance of energy consumption of EUCP and MTP

Table 2 Parameter values of the outer region


540 m



760 m


70 mNumber of nodes in each clusterof layer 5 119899

55

Number of nodes in each clusterof layer 6 119899

610


715


820

Number of subregions 119908 16

nodes in each subregion form a clusterThe number of nodesin any subregion of layer 119896 is defined as 119899

119896 and value of the

parameters in outer region are shown in Table 2As shown in Figure 14 EL119894 and CL119894 are defined as the

energy consumption of a cluster in the 119894th layer of EUCPand CDFUD respectively For different value of 120578 energyconsumption of EUCP is low and well-balanced while inCDFUD it is unbalanced Specifically energy consumptionof layer 8 is 150 times larger than that of layer 5 in CDFUD

As shown in Figure 15 for EUCP the differences of energyconsumption between two adjacent layers are around zeroWhile for CDFUD the value is about 920 times of EUCPwhich verifies well-balanced energy consumption of EUCPin outer region

As shown in Figure 16 for different value of 120578 thetotal energy consumption of EUCP is always far less than

00

20

40

60

80

100

120

Ener

gy (J

)

EL5 EL6 EL7 EL8 CL5 CL6 CL8CL7

times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1

Figure 14 Energy consumption of EUCP and CDFUD in outerregion

00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5

EL8-EL7EL7-EL6EL6-EL5

CL8-EC7CL7-CL6CL6-CL5

Figure 15 Differences of energy consumption of EUCP andCDFUD in outer region

CDFUD For transmitting the same amount of data energyconsumption of EUCP is only 6 of CDFUD

As shown in Table 3 energy consumption variances ofEUCP are less than 27 with different 120578 On the contrarythe value of EUCP is 92961 Because in CDFUD no matterhow far is the node from BS the cluster head will directlytransmit data to base station without data fusion this willinevitably generate mass of redundant data and increase theenergy consumption on sending and receiving


Table 3 Variances of energy consumption

Algorithm 120578 Variance

EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD

Figure 16 Total energy consumption of EUCP and CDFUD

6 Conclusion

A type of energy-balanced uneven clustering protocol isproposed in this paper Sensor network is divided into tworegions and the inner is further divided into clusters withdifferent sizes Simulation results show that EUCP could notonly prolong the network lifetime but also balance the wholenetwork energy consumption

In the future the expansion of clustering in the outerregion will be analyzed And the residual energy should notbe the only criterion for selecting the cluster header in ourfuture work Moreover the cluster head rotation strategy alsoneeds to be considered

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The subject is sponsored by the National Natural ScienceFoundation of China (61202355) Research Fund forthe Doctoral Program of Higher Education of China(20123223120006) China Postdoctoral Science Foundation

(2013M531394) Natural Science Foundation of JiangsuProvince (BK2012436) Jiangsu Provincial Research Schemeof Natural Science for Higher Education Institutions(14KJB520029) Postdoctoral Foundation of Jiangsu Province(1202034C) Open Project of Provincial Key Laboratoryfor Computer Information Processing Technology ofSoochow University (KJS1327) and the Project funded byPriority Academic Program Development of Jiangsu HigherEducation Institutions (Information and CommunicationYX002001)

References

[1] O M Al-Kofahi and A E Kamal ldquoScalable redundancy forsensors-to-sink communicationrdquo IEEEACM Transactions onNetworking vol 21 no 6 pp 1774ndash1784 2013

[2] 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

[3] F Castanedo ldquoA review of data fusion techniquesrdquoThe ScientificWorld Journal vol 2013 Article ID 704504 19 pages 2013

[4] L Li andW-J Li ldquoThe analysis of data fusion energy consump-tion in WSNrdquo in Proceedings of the International Conference onSystem Science Engineering Design andManufacturing Informa-tization (ICSEM rsquo11) vol 1 pp 310ndash313 IEEE October 2011

[5] M M Almasri and K M Elleithy ldquoData fusion models inWSNs comparison and analysisrdquo in Proceedings of the Zone 1Conference of the American Society for Engineering Education(ASEE Zone 1) pp 1ndash6 IEEE Bridgeport Conn USA April2014

[6] R Tan G Xing B Liu J Wang and X Jia ldquoExploiting datafusion to improve the coverage of wireless sensor networksrdquoIEEEACM Transactions on Networking vol 20 no 2 pp 450ndash462 2012

[7] A Ihsan K Saghar and T Fatima ldquoAnalysis of LEACHprotocol(s) using formal verificationrdquo in Proceedings of the12th International Bhurban Conference on Applied Sciences andTechnology (IBCAST rsquo15) pp 254ndash262 Islamabad PakistanJanuary 2015

[8] M Shurman N Awad M F Al-Mistarihi and K A DarabkhldquoLEACH enhancements for wireless sensor networks based onenergy modelrdquo in Proceedings of the 11th IEEE InternationalMulti-Conference on Systems Signals and Devices (SSD rsquo14) pp1ndash4 February 2014

[9] M Gupta and L Saraswat ldquoEnergy aware data collection inwireless sensor network using chain based PEGASISrdquo in Pro-ceedings of the Recent Advances and Innovations in Engineering(ICRAIE rsquo14) pp 1ndash5 IEEE Jaipur India May 2014

[10] X Liu Q Wang and X Jin ldquoAn energy-aware data gatheringand routing protocol for WSNrdquo Journal of Computer Researchand Development vol 45 no 1 pp 83ndash89 2008

[11] J Yue W Zhang W Xiao D Tang and J Tang ldquoA clusteringdata fusion algorithm based on unequal division for wirelesssensor networksrdquo Journal of Computer Research and Develop-ment vol 48 no 1 pp 247ndash254 2011

[12] J Yue W Zhang W Xiao and D Tang ldquoA novel unequalcluster-based data aggregation protocol for wireless sensornetworksrdquo Przegląd Elektrotechniczny vol 89 no 1 pp 20ndash242013


[13] S Nithyakalyani and S S Kumar ldquoData relay clustering algo-rithm for wireless sensor networks a data mining approachrdquoJournal of Computer Science vol 8 no 8 pp 1281ndash1284 2012

[14] Y Yu X Feng and J Hu ldquoMulti-sensor data fusion algorithmof triangle module operator in WSNrdquo in Proceedings of the10th International Conference on Mobile Ad-Hoc and SensorNetworks (MSN rsquo14) pp 105ndash111 IEEE Maui Hawaii USADecember 2014

[15] D Kim E Noel and K W Tang ldquoWSN communication topol-ogy construction with collision avoidance and energy savingrdquoin Proceedings of the IEEE 11th Consumer Communications andNetworking Conference (CCNC rsquo14) pp 398ndash404 IEEE LasVegas NV USA January 2014

[16] R Kumar and U Kumar ldquoA hierarchal cluster framework forwireless sensor networkrdquo in Proceedings of the InternationalConference on Advances in Computing and Communications(ICACC rsquo12) pp 46ndash50 August 2012

[17] K M Yusof J Woods and S Fitz ldquoShort-range and nearground propagation model for wireless sensor networksrdquo inProceedings of the IEEE Student Conference on Research andDevelopment (SCOReD rsquo12) pp 124ndash128 IEEE Pulau PinangMalaysia December 2012

[18] C Hua and T-S P Yum ldquoMaximum lifetime routing and dataaggregation for wireless sensor networksrdquo in NETWORKING2006 Networking Technologies Services and Protocols Perfor-mance of Computer and Communication Networks Mobile andWireless Communications Systems vol 3976 of Lecture Notesin Computer Science pp 840ndash855 Springer Berlin Germany2006

[19] W R Heinzelman A Chandrakasan and H Balakrish-nan ldquoEnergy-efficient communication protocol for wirelessmicrosensor networksrdquo in Proceedings of the 33rd AnnualHawaii International Conference on System Siences vol 2 p 10January 2000

[20] M Kubo K Nakanishi K Yanagihara and S Hara ldquoA multiplecooperative node selection method for reliable wireless multi-hop data transmissionrdquo IEICE Transactions on Communica-tions vol 97 no 8 pp 1717ndash1727 2014

[21] J Ai and A A Abouzeid ldquoCoverage by directional sensorsin randomly deployed wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 1 pp 21ndash41 2006

[22] J Grover and M Sharma ldquoOptimized GAF in wireless sensornetworkrdquo in Proceedings of the 3rd International Conference onReliability InfocomTechnologies andOptimization (ICRITO rsquo14)pp 1ndash6 IEEE Noida India October 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



through the shortest path and data from different sources willbe fused However the fusion process depends only on thedata dependency in fusion-driven method and the efficiencyof data gathering of this method has nothing to do with nodedeployment [6] In this paper a type of routing-driven datagathering method based on uneven clustering and regionaldivision is proposed

LEACH [7] is the first data gathering architecture forwireless sensor networks that achieves low energy dissipationand latency without sacrificing application-specific quality[8] It uses a clustering architecture where each node in thecluster sends its data to a local cluster head However thismode is responsible for collecting data from all sensors inthe cluster and sends them to the receiving end without datafusion which not only reduces the bandwidth utilization butalso increases energy consumption

PEGASIS is an enhancement over LEACH [9] Nodes areorganized to form a chain so that they need to communicateonly with their closest neighbors PEGASIS avoids clusterformation and only uses one node in a chain to transmit tothe sink node instead of using multiple nodes It reduces theenergy consumption on transmission per round as the powerdraining is spread uniformly over all nodes NeverthelessPEGASIS presents a big delay for the most distant node inthe chain even if the clustering overhead is avoided

Another kind of typical energy aware data gatheringprotocol is MTP (Multi-Tier Trace-Back Protocol) [10] Itselects one node with the most sufficient energy as well asthe shortest distance to the base station (BS for short) as therelay node which could communicate with the BS directlyOther nodes could only transmit and fuse their data to theparent node in the upper layer If the cluster head in MTPis far away from the BS it will consume more energy duringdata gathering fusing and transmitting On the other handaccording to MTP nodes in the upper layer will also forwardits data to their parent node even if the parent node is just inthe lower layer It not only increases the transmission cost butalso reduces the reliability of the whole network

Yue et al proposed an uneven clustering algorithm basedon grid namely CDFUD [11 12] (Clustering Data FusionAlgorithm Based on Uneven Division) Sizes of the grids aredifferent from each other according to their distance to the BSand the node with the maximal residual energy in each gridis chosen as the cluster head Similar to LEACH the clusterhead in each gird transmit the data of its members as well asitself to BS with one hop The main disadvantage of CDFUDis that the cluster head consumes energy rapidly which causesunbalance energy consumption in the network119870-Means [13] Data Relay Clustering algorithm is devel-

oped to group the sensor nodes for energy efficient datacommunication 119870 arbitrary points are picked as the clusterhead by the sink node Cluster members are obtained foreach CH based on distance metric Then in each CH dataaggregation process is done for limiting the energy spentin transmission Although it reduces the communicationoverhead it also reduces the number of nodes transmittingdata to sink node and unable to collect enough informationwhich we need

Es(J d)

Node Node

Sending module

Eelec times J

Eelec times J

120583amp times J times dn

Signal amplifier

d

Receiving module

ER(J)

Figure 1 Energy consumption model for one node

TMMDF [14] eliminates negligent errors by Dixonmethod to obtain a valid observation data and uses thetriangle module operator to assign weights of each sensordata Finally it gets the fusion estimate values Although datadelay of this method is greatly increased it is not an efficientmethod for large-scale data processing

Based on the study above an energy-balanced unevenclustering protocol (EUCP) is proposed in this paper Accord-ing to the distance between nodes and BS it divides regionsinto clusters with different sizes And the size of each clusteras well as the number of nodes is related to the energyconsumption of each grid Simulation results show thatEUCP could effectively prolong the network lifetime andbalance the whole network energy consumption

3 Method Description

31 Network Model As we know in two-dimensional spacethe communication and sensing area of one node is a circularwhose center is the node itself [15] Therefore in EUCPwe assume that the shape of the network is also a circularMoreover it has been proved that clustered structure issuitable for data fusion in WSNs [16] so it is still be adoptedin EUCP However in cluster-based WSNs nodes which arefar from BS undertake minor data fusion mission (the nodeson boundary of the network even do not need to fuse data)while nodes which are close to BS often receive and processmore data So in EUCPwe adopt the hierarchical structure todesign the whole network for data transmission and fusion

The attenuation model of wireless signal can be dividedinto free-space model and multipath fading model [17] asshown in Figure 1 A sensor node consumes energy when it isgenerating local data receiving data transmitting data or instandby mode [18] The energy for generating one bit of dataand the standby energy consumed by one node are assumedto be the same for all nodes which can always be ignoredFor energy used in receiving and transmitting we adoptthe first order radio model described in [19] We assumethat 119864

119878(119869 119889) and 119864

119877(119869) represent the energy consumption

of sending module and receiving module while 119864elec is theunit energy consumption of sending and receiving circuitsThe energy consumption of circuit is in direct proportion tothe data package size 119869 120583amp is the constant parameter ofsignal amplifier and 119889

0is assumed as the unit of transmission

distance In general 1198890is equal to the communication radius

119877 of nodesWe assume that each node send 119888 bit data package


Sector 1


Sector 2

Sector 3

Base node


Sensor node

d0

d1 d2

dkD


Laye

r kLa

yer 2

Laye

r 1



119864119904 (119869 119889) =

119888119864elec + 1198881205831198911199041198892 119889 lt 1198890

119888119864elec + 119888120583amp1198894 119889 ge 1198890

(1)


119864119877 (119869) = 119888119864elec (2)






0 According to (1)



A

CB

D

EF

H

G

120579

r




120588max =2

radic31198772119904

120588min =2

3radic31198772119904

(3)



120588times120587119889

21

3= 1198991 (4)




120588

3times [120587 (1198891 +1198892)

2minus120587119889

21] = 21198991 (5)


120588

3times[

[

120587(

119896

sum

119894=1119889119894)

2

minus120587(

119896minus1sum

119894=1119889119894)

2

]

]

= 2119896minus1 times 1198991 (6)


A O

B

E

C

D

F

120579r


Base noded1

d2dkminus1

dk

d0





119896

sum

119894=1119889119894 = 1198890 (7)




119877119905gt 1198891015840= radic119889

20 + (1198890 minus 119889119896)

2minus 21198890 (1198890 minus 119889119896) cos

21205873

= radic311988920 minus 31198890119889119896 + 1198892119896

(8)



d1d2

dkminus1dk

d0

d998400(d998400 lt Rt)A B

2120587

3

O


dk+1 d

k+2dk+1

d0

d998400998400

D


Outer region






119877119905gt 11988910158401015840= radic1198632 + (119863 minus 119889

119896+1)2minus 2119863(119863 minus 119889

119896+119897) cos 120579

= radic21198632 + 2119863119889119896+1 + 119889

2119896+119897minus 2119863(119863 minus 119889

119896+119897) cos 2120587

3119899119896

(9)



119894 119884119894) The node



119901 = 120572times119864119894+120573

119889119894119900

+120574

120594119888

(10)

119889119894119900












119896+1)

119885119896= 119866+119876

119896+1

119885119896minus1 = 119866+ 2 (119866+119876119896+1)

119885119896minus2 = 119866+ 2 (119866+ 2 (119866+119876119896+1)) 120578

(11)


119885119896minus119886=

119886minus1sum

119894=02119894119866120578119894 + 2119886 (119866+119876

119896+1) 120578119886minus1

119896 minus 1 ge 119886 ge 1

(12)



119864119896minus119886= 119864 (119879

119896minus119886) + 119864 (119877

119896minus119886) + 119864 (119865

119896minus119886)



119864 (119877119896minus119886) = 2119885

119896minus119886+1119864elec


(13)




119864119896= 119864 (119879

119896) + 119864 (119877

119896)

= (119866+119876119896+1) (119864elec +120583fs119889

2(119896119896minus1)) +119876119896+1119864elec

= (119866+ 2119876119896+1) 119864elec + (119866+119876119896+1) 120583fs119889

2(119896119896minus1)

(15)










119864 (119865119896+119895) = (120588 times 119878

119896+119895times119866+119876

119896+119895+1) times119891 (18)


119876119896+119897= 120588times 119878

119896+119897times119866times 120578

119864 (119865119896+119897) = 120588 times 119878

119896+119897times119866times119891

(19)


119878119896+119895

and 119878119896+119897


119878119896+119895 =21205873119908times120587[

[

(

119896+119895

sum

119894=1119889119894)

2

minus(

119896+119895minus1

sum

119894=1119889119894)

2

]

]

119878119896+119897=

21205873119908times120587[

[

1198632minus(

119896+119897minus1sum

119894=1119889119894)

2

]

]

(20)




1198641 (119879119896+119895)


119896+119895)

2] (120588 times 119878119896+119895 minus 1)

(21)

In the equation

11988910158401015840

119896+119895

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus1

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus1

sum

119894=1119889119894cos 2120587

3119899119896

(22)


1198642 (119879119896+119895)


(23)


MAX (119863(119896+119895119896+119895minus1))

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus2

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus2

sum

119894=1119889119894cos 2120587

3119899119896

(24)


119863(119896+119895119896+119895minus1) = 05 (119889

119896+119895+119889119896+119895minus1) (25)


119896+119895)) is mainly on


119864 (119877119896+119895) = [(120588 times 119878

119896+119895minus 1) times119866+119876

119896+119895minus1] times 119864elec (26)


119896+119897)) is

119864 (119877119896+119897) = (120588 times 119878



119864out

=

119897minus1sum

119895=1[119864 (119865119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895)]

+119864 (119865119896+119897) + 1198641 (119879119896+119897) + 1198642 (119879119896+119897) + 119864 (119877119896+119897)

(28)

That is


119895=1(120588119878119896+119895119866+119876

119896+119895+1) 119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

+ [(120588119878119896+119895 minus 1)119866+119876119896+119895minus1] 119864elec + 120588119878119896+119897119866119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119897)2] (120588119878119896+119897minus 1) + (119866119864elec


(29)



In (30) we have

119864119896+119895= 119864 (119865

119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895) (31)


119864 (119865119896+119895) gt 119864 (119865

119896+ℎ) 119895 lt ℎ

119864 (119877119896+119895) gt 119864 (119877119896+ℎ) 119895 lt ℎ

(32)




1315 m



3288 m










1198641 (119879119896+119895) +1198642 (119879119896+119895) lt 1198641 (119879119896+ℎ) + 1198642 (119879119896+ℎ)

119895 lt ℎ

(33)

That is

[119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

lt [119866119864elec +119866120583fs (0511988910158401015840

119896+ℎ)2] (120588119878119896+ℎminus 1)


(34)


lt 119889119896+ℎ





1is 2 similarly

1198992= 4 119899

3= 8 and 119899




000

150

300

450

600

750

900

1050

EUCP

Ener

gy (J

)

MTP1 MTP2 MTP3 MTP4

times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1







2 a node






00

10

20

30

40

50

60

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5


00

10

20

30

40

50

60

70

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4




1 and MTP



00

10

20

30

40

50

60

70

80

90

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


00

20

40

60

80

100

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4



5 1198896 1198897 and 119889

8 respectively As



00

10

20

30

40

50

60

70

80

Varia

nce


times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1




540 m



760 m



55


610


715


820








00

20

40

60

80

100

120

Ener

gy (J

)


times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1


00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5









EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Sector 1


Sector 2

Sector 3

Base node


Sensor node

d0

d1 d2

dkD


Laye

r kLa

yer 2

Laye

r 1



119864119904 (119869 119889) =

119888119864elec + 1198881205831198911199041198892 119889 lt 1198890

119888119864elec + 119888120583amp1198894 119889 ge 1198890

(1)


119864119877 (119869) = 119888119864elec (2)






0 According to (1)



A

CB

D

EF

H

G

120579

r




120588max =2

radic31198772119904

120588min =2

3radic31198772119904

(3)



120588times120587119889

21

3= 1198991 (4)




120588

3times [120587 (1198891 +1198892)

2minus120587119889

21] = 21198991 (5)


120588

3times[

[

120587(

119896

sum

119894=1119889119894)

2

minus120587(

119896minus1sum

119894=1119889119894)

2

]

]

= 2119896minus1 times 1198991 (6)


A O

B

E

C

D

F

120579r


Base noded1

d2dkminus1

dk

d0





119896

sum

119894=1119889119894 = 1198890 (7)




119877119905gt 1198891015840= radic119889

20 + (1198890 minus 119889119896)

2minus 21198890 (1198890 minus 119889119896) cos

21205873

= radic311988920 minus 31198890119889119896 + 1198892119896

(8)



d1d2

dkminus1dk

d0

d998400(d998400 lt Rt)A B

2120587

3

O


dk+1 d

k+2dk+1

d0

d998400998400

D


Outer region






119877119905gt 11988910158401015840= radic1198632 + (119863 minus 119889

119896+1)2minus 2119863(119863 minus 119889

119896+119897) cos 120579

= radic21198632 + 2119863119889119896+1 + 119889

2119896+119897minus 2119863(119863 minus 119889

119896+119897) cos 2120587

3119899119896

(9)



119894 119884119894) The node



119901 = 120572times119864119894+120573

119889119894119900

+120574

120594119888

(10)

119889119894119900












119896+1)

119885119896= 119866+119876

119896+1

119885119896minus1 = 119866+ 2 (119866+119876119896+1)

119885119896minus2 = 119866+ 2 (119866+ 2 (119866+119876119896+1)) 120578

(11)


119885119896minus119886=

119886minus1sum

119894=02119894119866120578119894 + 2119886 (119866+119876

119896+1) 120578119886minus1

119896 minus 1 ge 119886 ge 1

(12)



119864119896minus119886= 119864 (119879

119896minus119886) + 119864 (119877

119896minus119886) + 119864 (119865

119896minus119886)



119864 (119877119896minus119886) = 2119885

119896minus119886+1119864elec


(13)




119864119896= 119864 (119879

119896) + 119864 (119877

119896)

= (119866+119876119896+1) (119864elec +120583fs119889

2(119896119896minus1)) +119876119896+1119864elec

= (119866+ 2119876119896+1) 119864elec + (119866+119876119896+1) 120583fs119889

2(119896119896minus1)

(15)










119864 (119865119896+119895) = (120588 times 119878

119896+119895times119866+119876

119896+119895+1) times119891 (18)


119876119896+119897= 120588times 119878

119896+119897times119866times 120578

119864 (119865119896+119897) = 120588 times 119878

119896+119897times119866times119891

(19)


119878119896+119895

and 119878119896+119897


119878119896+119895 =21205873119908times120587[

[

(

119896+119895

sum

119894=1119889119894)

2

minus(

119896+119895minus1

sum

119894=1119889119894)

2

]

]

119878119896+119897=

21205873119908times120587[

[

1198632minus(

119896+119897minus1sum

119894=1119889119894)

2

]

]

(20)




1198641 (119879119896+119895)


119896+119895)

2] (120588 times 119878119896+119895 minus 1)

(21)

In the equation

11988910158401015840

119896+119895

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus1

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus1

sum

119894=1119889119894cos 2120587

3119899119896

(22)


1198642 (119879119896+119895)


(23)


MAX (119863(119896+119895119896+119895minus1))

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus2

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus2

sum

119894=1119889119894cos 2120587

3119899119896

(24)


119863(119896+119895119896+119895minus1) = 05 (119889

119896+119895+119889119896+119895minus1) (25)


119896+119895)) is mainly on


119864 (119877119896+119895) = [(120588 times 119878

119896+119895minus 1) times119866+119876

119896+119895minus1] times 119864elec (26)


119896+119897)) is

119864 (119877119896+119897) = (120588 times 119878



119864out

=

119897minus1sum

119895=1[119864 (119865119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895)]

+119864 (119865119896+119897) + 1198641 (119879119896+119897) + 1198642 (119879119896+119897) + 119864 (119877119896+119897)

(28)

That is


119895=1(120588119878119896+119895119866+119876

119896+119895+1) 119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

+ [(120588119878119896+119895 minus 1)119866+119876119896+119895minus1] 119864elec + 120588119878119896+119897119866119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119897)2] (120588119878119896+119897minus 1) + (119866119864elec


(29)



In (30) we have

119864119896+119895= 119864 (119865

119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895) (31)


119864 (119865119896+119895) gt 119864 (119865

119896+ℎ) 119895 lt ℎ

119864 (119877119896+119895) gt 119864 (119877119896+ℎ) 119895 lt ℎ

(32)




1315 m



3288 m










1198641 (119879119896+119895) +1198642 (119879119896+119895) lt 1198641 (119879119896+ℎ) + 1198642 (119879119896+ℎ)

119895 lt ℎ

(33)

That is

[119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

lt [119866119864elec +119866120583fs (0511988910158401015840

119896+ℎ)2] (120588119878119896+ℎminus 1)


(34)


lt 119889119896+ℎ





1is 2 similarly

1198992= 4 119899

3= 8 and 119899




000

150

300

450

600

750

900

1050

EUCP

Ener

gy (J

)

MTP1 MTP2 MTP3 MTP4

times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1







2 a node






00

10

20

30

40

50

60

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5


00

10

20

30

40

50

60

70

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4




1 and MTP



00

10

20

30

40

50

60

70

80

90

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


00

20

40

60

80

100

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4



5 1198896 1198897 and 119889

8 respectively As



00

10

20

30

40

50

60

70

80

Varia

nce


times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1




540 m



760 m



55


610


715


820








00

20

40

60

80

100

120

Ener

gy (J

)


times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1


00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5









EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










A O

B

E

C

D

F

120579r


Base noded1

d2dkminus1

dk

d0





119896

sum

119894=1119889119894 = 1198890 (7)




119877119905gt 1198891015840= radic119889

20 + (1198890 minus 119889119896)

2minus 21198890 (1198890 minus 119889119896) cos

21205873

= radic311988920 minus 31198890119889119896 + 1198892119896

(8)



d1d2

dkminus1dk

d0

d998400(d998400 lt Rt)A B

2120587

3

O


dk+1 d

k+2dk+1

d0

d998400998400

D


Outer region






119877119905gt 11988910158401015840= radic1198632 + (119863 minus 119889

119896+1)2minus 2119863(119863 minus 119889

119896+119897) cos 120579

= radic21198632 + 2119863119889119896+1 + 119889

2119896+119897minus 2119863(119863 minus 119889

119896+119897) cos 2120587

3119899119896

(9)



119894 119884119894) The node



119901 = 120572times119864119894+120573

119889119894119900

+120574

120594119888

(10)

119889119894119900












119896+1)

119885119896= 119866+119876

119896+1

119885119896minus1 = 119866+ 2 (119866+119876119896+1)

119885119896minus2 = 119866+ 2 (119866+ 2 (119866+119876119896+1)) 120578

(11)


119885119896minus119886=

119886minus1sum

119894=02119894119866120578119894 + 2119886 (119866+119876

119896+1) 120578119886minus1

119896 minus 1 ge 119886 ge 1

(12)



119864119896minus119886= 119864 (119879

119896minus119886) + 119864 (119877

119896minus119886) + 119864 (119865

119896minus119886)



119864 (119877119896minus119886) = 2119885

119896minus119886+1119864elec


(13)




119864119896= 119864 (119879

119896) + 119864 (119877

119896)

= (119866+119876119896+1) (119864elec +120583fs119889

2(119896119896minus1)) +119876119896+1119864elec

= (119866+ 2119876119896+1) 119864elec + (119866+119876119896+1) 120583fs119889

2(119896119896minus1)

(15)










119864 (119865119896+119895) = (120588 times 119878

119896+119895times119866+119876

119896+119895+1) times119891 (18)


119876119896+119897= 120588times 119878

119896+119897times119866times 120578

119864 (119865119896+119897) = 120588 times 119878

119896+119897times119866times119891

(19)


119878119896+119895

and 119878119896+119897


119878119896+119895 =21205873119908times120587[

[

(

119896+119895

sum

119894=1119889119894)

2

minus(

119896+119895minus1

sum

119894=1119889119894)

2

]

]

119878119896+119897=

21205873119908times120587[

[

1198632minus(

119896+119897minus1sum

119894=1119889119894)

2

]

]

(20)




1198641 (119879119896+119895)


119896+119895)

2] (120588 times 119878119896+119895 minus 1)

(21)

In the equation

11988910158401015840

119896+119895

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus1

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus1

sum

119894=1119889119894cos 2120587

3119899119896

(22)


1198642 (119879119896+119895)


(23)


MAX (119863(119896+119895119896+119895minus1))

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus2

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus2

sum

119894=1119889119894cos 2120587

3119899119896

(24)


119863(119896+119895119896+119895minus1) = 05 (119889

119896+119895+119889119896+119895minus1) (25)


119896+119895)) is mainly on


119864 (119877119896+119895) = [(120588 times 119878

119896+119895minus 1) times119866+119876

119896+119895minus1] times 119864elec (26)


119896+119897)) is

119864 (119877119896+119897) = (120588 times 119878



119864out

=

119897minus1sum

119895=1[119864 (119865119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895)]

+119864 (119865119896+119897) + 1198641 (119879119896+119897) + 1198642 (119879119896+119897) + 119864 (119877119896+119897)

(28)

That is


119895=1(120588119878119896+119895119866+119876

119896+119895+1) 119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

+ [(120588119878119896+119895 minus 1)119866+119876119896+119895minus1] 119864elec + 120588119878119896+119897119866119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119897)2] (120588119878119896+119897minus 1) + (119866119864elec


(29)



In (30) we have

119864119896+119895= 119864 (119865

119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895) (31)


119864 (119865119896+119895) gt 119864 (119865

119896+ℎ) 119895 lt ℎ

119864 (119877119896+119895) gt 119864 (119877119896+ℎ) 119895 lt ℎ

(32)




1315 m



3288 m










1198641 (119879119896+119895) +1198642 (119879119896+119895) lt 1198641 (119879119896+ℎ) + 1198642 (119879119896+ℎ)

119895 lt ℎ

(33)

That is

[119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

lt [119866119864elec +119866120583fs (0511988910158401015840

119896+ℎ)2] (120588119878119896+ℎminus 1)


(34)


lt 119889119896+ℎ





1is 2 similarly

1198992= 4 119899

3= 8 and 119899




000

150

300

450

600

750

900

1050

EUCP

Ener

gy (J

)

MTP1 MTP2 MTP3 MTP4

times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1







2 a node






00

10

20

30

40

50

60

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5


00

10

20

30

40

50

60

70

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4




1 and MTP



00

10

20

30

40

50

60

70

80

90

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


00

20

40

60

80

100

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4



5 1198896 1198897 and 119889

8 respectively As



00

10

20

30

40

50

60

70

80

Varia

nce


times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1




540 m



760 m



55


610


715


820








00

20

40

60

80

100

120

Ener

gy (J

)


times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1


00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5









EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119894 119884119894) The node



119901 = 120572times119864119894+120573

119889119894119900

+120574

120594119888

(10)

119889119894119900












119896+1)

119885119896= 119866+119876

119896+1

119885119896minus1 = 119866+ 2 (119866+119876119896+1)

119885119896minus2 = 119866+ 2 (119866+ 2 (119866+119876119896+1)) 120578

(11)


119885119896minus119886=

119886minus1sum

119894=02119894119866120578119894 + 2119886 (119866+119876

119896+1) 120578119886minus1

119896 minus 1 ge 119886 ge 1

(12)



119864119896minus119886= 119864 (119879

119896minus119886) + 119864 (119877

119896minus119886) + 119864 (119865

119896minus119886)



119864 (119877119896minus119886) = 2119885

119896minus119886+1119864elec


(13)




119864119896= 119864 (119879

119896) + 119864 (119877

119896)

= (119866+119876119896+1) (119864elec +120583fs119889

2(119896119896minus1)) +119876119896+1119864elec

= (119866+ 2119876119896+1) 119864elec + (119866+119876119896+1) 120583fs119889

2(119896119896minus1)

(15)










119864 (119865119896+119895) = (120588 times 119878

119896+119895times119866+119876

119896+119895+1) times119891 (18)


119876119896+119897= 120588times 119878

119896+119897times119866times 120578

119864 (119865119896+119897) = 120588 times 119878

119896+119897times119866times119891

(19)


119878119896+119895

and 119878119896+119897


119878119896+119895 =21205873119908times120587[

[

(

119896+119895

sum

119894=1119889119894)

2

minus(

119896+119895minus1

sum

119894=1119889119894)

2

]

]

119878119896+119897=

21205873119908times120587[

[

1198632minus(

119896+119897minus1sum

119894=1119889119894)

2

]

]

(20)




1198641 (119879119896+119895)


119896+119895)

2] (120588 times 119878119896+119895 minus 1)

(21)

In the equation

11988910158401015840

119896+119895

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus1

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus1

sum

119894=1119889119894cos 2120587

3119899119896

(22)


1198642 (119879119896+119895)


(23)


MAX (119863(119896+119895119896+119895minus1))

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus2

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus2

sum

119894=1119889119894cos 2120587

3119899119896

(24)


119863(119896+119895119896+119895minus1) = 05 (119889

119896+119895+119889119896+119895minus1) (25)


119896+119895)) is mainly on


119864 (119877119896+119895) = [(120588 times 119878

119896+119895minus 1) times119866+119876

119896+119895minus1] times 119864elec (26)


119896+119897)) is

119864 (119877119896+119897) = (120588 times 119878



119864out

=

119897minus1sum

119895=1[119864 (119865119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895)]

+119864 (119865119896+119897) + 1198641 (119879119896+119897) + 1198642 (119879119896+119897) + 119864 (119877119896+119897)

(28)

That is


119895=1(120588119878119896+119895119866+119876

119896+119895+1) 119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

+ [(120588119878119896+119895 minus 1)119866+119876119896+119895minus1] 119864elec + 120588119878119896+119897119866119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119897)2] (120588119878119896+119897minus 1) + (119866119864elec


(29)



In (30) we have

119864119896+119895= 119864 (119865

119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895) (31)


119864 (119865119896+119895) gt 119864 (119865

119896+ℎ) 119895 lt ℎ

119864 (119877119896+119895) gt 119864 (119877119896+ℎ) 119895 lt ℎ

(32)




1315 m



3288 m










1198641 (119879119896+119895) +1198642 (119879119896+119895) lt 1198641 (119879119896+ℎ) + 1198642 (119879119896+ℎ)

119895 lt ℎ

(33)

That is

[119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

lt [119866119864elec +119866120583fs (0511988910158401015840

119896+ℎ)2] (120588119878119896+ℎminus 1)


(34)


lt 119889119896+ℎ





1is 2 similarly

1198992= 4 119899

3= 8 and 119899




000

150

300

450

600

750

900

1050

EUCP

Ener

gy (J

)

MTP1 MTP2 MTP3 MTP4

times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1







2 a node






00

10

20

30

40

50

60

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5


00

10

20

30

40

50

60

70

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4




1 and MTP



00

10

20

30

40

50

60

70

80

90

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


00

20

40

60

80

100

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4



5 1198896 1198897 and 119889

8 respectively As



00

10

20

30

40

50

60

70

80

Varia

nce


times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1




540 m



760 m



55


610


715


820








00

20

40

60

80

100

120

Ener

gy (J

)


times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1


00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5









EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119878119896+119895

and 119878119896+119897


119878119896+119895 =21205873119908times120587[

[

(

119896+119895

sum

119894=1119889119894)

2

minus(

119896+119895minus1

sum

119894=1119889119894)

2

]

]

119878119896+119897=

21205873119908times120587[

[

1198632minus(

119896+119897minus1sum

119894=1119889119894)

2

]

]

(20)




1198641 (119879119896+119895)


119896+119895)

2] (120588 times 119878119896+119895 minus 1)

(21)

In the equation

11988910158401015840

119896+119895

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus1

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus1

sum

119894=1119889119894cos 2120587

3119899119896

(22)


1198642 (119879119896+119895)


(23)


MAX (119863(119896+119895119896+119895minus1))

= radic(

119896+119895

sum

119894=1119889119894)

2

+ (

119896+119895minus2

sum

119894=1119889119894)

2

minus 2119896+119895

sum

119894=1119889119894

119896+119895minus2

sum

119894=1119889119894cos 2120587

3119899119896

(24)


119863(119896+119895119896+119895minus1) = 05 (119889

119896+119895+119889119896+119895minus1) (25)


119896+119895)) is mainly on


119864 (119877119896+119895) = [(120588 times 119878

119896+119895minus 1) times119866+119876

119896+119895minus1] times 119864elec (26)


119896+119897)) is

119864 (119877119896+119897) = (120588 times 119878



119864out

=

119897minus1sum

119895=1[119864 (119865119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895)]

+119864 (119865119896+119897) + 1198641 (119879119896+119897) + 1198642 (119879119896+119897) + 119864 (119877119896+119897)

(28)

That is


119895=1(120588119878119896+119895119866+119876

119896+119895+1) 119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

+ [(120588119878119896+119895 minus 1)119866+119876119896+119895minus1] 119864elec + 120588119878119896+119897119866119891

+ [119866119864elec +119866120583fs (0511988910158401015840

119896+119897)2] (120588119878119896+119897minus 1) + (119866119864elec


(29)



In (30) we have

119864119896+119895= 119864 (119865

119896+119895) +1198641 (119879119896+119895) +1198642 (119879119896+119895) +119864 (119877119896+119895) (31)


119864 (119865119896+119895) gt 119864 (119865

119896+ℎ) 119895 lt ℎ

119864 (119877119896+119895) gt 119864 (119877119896+ℎ) 119895 lt ℎ

(32)




1315 m



3288 m










1198641 (119879119896+119895) +1198642 (119879119896+119895) lt 1198641 (119879119896+ℎ) + 1198642 (119879119896+ℎ)

119895 lt ℎ

(33)

That is

[119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

lt [119866119864elec +119866120583fs (0511988910158401015840

119896+ℎ)2] (120588119878119896+ℎminus 1)


(34)


lt 119889119896+ℎ





1is 2 similarly

1198992= 4 119899

3= 8 and 119899




000

150

300

450

600

750

900

1050

EUCP

Ener

gy (J

)

MTP1 MTP2 MTP3 MTP4

times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1







2 a node






00

10

20

30

40

50

60

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5


00

10

20

30

40

50

60

70

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4




1 and MTP



00

10

20

30

40

50

60

70

80

90

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


00

20

40

60

80

100

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4



5 1198896 1198897 and 119889

8 respectively As



00

10

20

30

40

50

60

70

80

Varia

nce


times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1




540 m



760 m



55


610


715


820








00

20

40

60

80

100

120

Ener

gy (J

)


times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1


00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5









EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1315 m



3288 m










1198641 (119879119896+119895) +1198642 (119879119896+119895) lt 1198641 (119879119896+ℎ) + 1198642 (119879119896+ℎ)

119895 lt ℎ

(33)

That is

[119866119864elec +119866120583fs (0511988910158401015840

119896+119895)2] (120588119878119896+119895minus 1)

+ (119866119864elec +119866120583fs1198632(119896+119895119896+119895minus1))119876119896+119895

lt [119866119864elec +119866120583fs (0511988910158401015840

119896+ℎ)2] (120588119878119896+ℎminus 1)


(34)


lt 119889119896+ℎ





1is 2 similarly

1198992= 4 119899

3= 8 and 119899




000

150

300

450

600

750

900

1050

EUCP

Ener

gy (J

)

MTP1 MTP2 MTP3 MTP4

times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1







2 a node






00

10

20

30

40

50

60

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5


00

10

20

30

40

50

60

70

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4




1 and MTP



00

10

20

30

40

50

60

70

80

90

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


00

20

40

60

80

100

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4



5 1198896 1198897 and 119889

8 respectively As



00

10

20

30

40

50

60

70

80

Varia

nce


times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1




540 m



760 m



55


610


715


820








00

20

40

60

80

100

120

Ener

gy (J

)


times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1


00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5









EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00

10

20

30

40

50

60

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5


00

10

20

30

40

50

60

70

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4




1 and MTP



00

10

20

30

40

50

60

70

80

90

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4


00

20

40

60

80

100

Ener

gy (J

)

EUCPMTP1MTP2

MTP3MTP4


times10minus5

Layers1ndash4



5 1198896 1198897 and 119889

8 respectively As



00

10

20

30

40

50

60

70

80

Varia

nce


times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1




540 m



760 m



55


610


715


820








00

20

40

60

80

100

120

Ener

gy (J

)


times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1


00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5









EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00

10

20

30

40

50

60

70

80

Varia

nce


times10minus9

120578 = 025

120578 = 05

120578 = 075120578 = 1




540 m



760 m



55


610


715


820








00

20

40

60

80

100

120

Ener

gy (J

)


times10minus5

120578 = 025

120578 = 05120578 = 075120578 = 1


00

20

40

60

80

100

Diff

eren

ces (

J)

120578 = 025 120578 = 05 120578 = 075 120578 = 1

times10minus5









EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












EUCP

120578 = 025 12120578 = 05 15120578 = 075 057120578 = 1 27

CDFUD 120578 = 1 92961

00

20

40

60

80

100

120

140

160

Ener

gy (J

)

Algorithms

times10minus5

EUCP 120578 = 025

EUCP 120578 = 05

EUCP 120578 = 075

EUCP 120578 = 1

CDFUD


6 Conclusion





Acknowledgments



References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article energy-balanced uneven clustering...

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