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Research ArticleOptimized Design of Relay Node Placement forIndustrial Wireless Network

Heng Zhang Zeyu Zhang Fengxiang Zhang Li Li and Ying Wang

Faculty of Computer and Information Science Southwest University Chongqing 400700 China

Correspondence should be addressed to Heng Zhang dahaizhangheng163com and Zeyu Zhang 112883328qqcom

Received 31 July 2014 Revised 5 November 2014 Accepted 6 November 2014 Published 27 November 2014

Academic Editor Jiafu Wan

Copyright copy 2014 Heng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The industrial wireless network (IWN) is an important part of industrial CPS which must address the key issue of reliable andreal-time communication as well as the desired network lifetime The nodes of IWN are usually fixed on the devices for bettermonitoring of the state information of the equipment and environment while the relay node placement plays a significant role onnetwork performance guaranteeThis paper proposes an Integer Linear Program (ILP) placement strategy tomeet the fault toleranceand survivability requirement In addition an edge coloring algorithm is proposed to solve the conflict of TDMA communicationwhich improves paralleled and real-time communication performance Simulation results show that this placement strategy notonly meets the requirements of robust communication and survivability but also enhances real-time communication of IWN

1 Introduction

11 Introduction of CPS A cyber-physical system (CPS) is asystem of collaborating computational elements controllingphysical entities Today a precursor generation of cyber-physical systems can be found in areas as diverse as aerospaceautomotive chemical processes civil infrastructure energyhealthcare manufacturing transportation entertainmentand consumer appliances CPSwill play a great role especiallyin the industrial world This generation is often referred toas embedded systems In embedded systems the emphasistends to be more on the computational elements and lesson an intense link between the computational and physicalelementsTheCPS has been studied bymany foreign researchinstitutions The US National Science Foundation (NSF) hasidentified cyber-physical systems as a key area of research[1] Starting in late 2006 the NSF and other United Statesfederal agencies sponsored several workshops on cyber-physical systems [2ndash4] Some scholars have studied CPS inChina and the representative papers can be seen in [5ndash7]As the special WSN in the industry IWN can be used as animportant technology of CPS components It has attractedmore and more attention

12 Industrial Wireless Network IWN is specially designedfor harsh industrial environment application which hasbetter network performancewith respect to anti-interferencerobustness real-time and security through the use of meshnetwork spread spectrum frequency hopping and the mul-tihop techniqueThe concept of IWNwas firstly proposed bythe US Department of Energy (DOE) and it transformedother research which focuses of industrial automatic mea-surement and control field after the industrial field bus [8ndash10]ISA SP100 [11] WirelessHART [12ndash15] and WIA-PA [16] arethree IWN specifications which have some common featuressuch as short-rangemultihop wireless communication beingbattery-powered and a TDMA scheme [17] Although thereare some distinctions on node definition for these threespecifications all the nodes can be divided into sensor nodeand relay node logically Relay node must be scheduled inspecified time slots to fulfill correspondent communicationtask

In comparison to the random placement of a WSN senornode the positioning of an IWN node is relatively fixedAs usual the IWN node can be divided into sink noderelay node and sensor node There is little research on thesink node placement because it is usually fixed sensor node

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2014 Article ID 759826 12 pageshttpdxdoiorg1011552014759826

2 International Journal of Distributed Sensor Networks

placement primarily considers the probability-of-detectiondata fusion and accuracy [18 19] Tremendous attention hasbeen paid to address the issue of relay node placement onthe grounds that a relay node can be deployed flexibly therelay node acts as a bridge between the sensor node and sinknodes relay node placement strategy is distinct for differentapplication requirements Although we can use the AGVmobile robot or person with handheld devices to collect datathere is usually a limited number of mobile robots Peoplecannot use handheld mobile acquisition equipment to collectinformation in the harsh environment The AGV mobilerobot is not able to work in the limited space environment Inaddition the above two ways have a higher cost So we hopethat WSN can bear the bulk of the work only allowing manor AGV to carry out regular inspections and verifications Abetter node deployment strategy for the relay node can alsoprovide fine-grained navigation for the AGVormobile robotBy combining the two ways using IWN and AGV it can beeasier to complete the construction of an industrial intelligentenvironment Therefore we say that the deployment of therelay node is essential and important for research

13 Related Work on Relay Node Placement Hou et al [20]extended the network lifetime by designing an heuristic algo-rithm (SPINDS) to solve optimized RN placement problemexperiments validated the effectiveness of this algorithmChen et al [21] demonstrated that redundant fault-toleranttechniques improved query reliability and network lifetimeand it could be referred in RN placement While Hou et al[20] aimed to extend the network lifetime but this workdoes not consider the reliable communication issue in hashindustrial environments

Wang et al [22] tended to solve the issue of the minimumnetwork cost relay node placement under the constraint ofnetwork lifetime and connectivity This work firstly solvedthe minimum set cover problem without considering energyconsumption They also proposed three heuristic algorithmsto solve the energy consumption constraint Liu et al [23]aimed at network coverage and connectivity based on trans-portation industry and this work proposed a heuristic andnetwork flow algorithm to deal with the relay node placementproblem Wang et al [22] and Liu et al [23] were typicalrelayed node placement research under constraint of networkcoverage connectivity and lifetime but they did not considerfault tolerant issue in hash industry environment

Bredin et al [24] established 119896-connectivity network toimprove fault tolerance by RN

119904placement the greedy and

distributed algorithms were proposed and their performancehad been proven by simulations Han et al [25] focusedon adding additional RN

119904to improve fault tolerance and a

heuristic algorithm was proposed and validated by experi-ments Liu et al [26] and Liu et al [27] addressed the issueof the RN

119904placement for a two-tier sensor network under

a simply connected situation or a two-connected situationApproximation algorithms had been proposed for these twosituationsThe time complexitywas 6 + 120576 24 + 120576 or 6119879+ 12 +120576 Hao et al [28] proposed a fault tolerant placement solutionunder theminimumRN

119904constraints which could insure that

every sensor node can be connectedwith at least two RN119904and

two-connected among all the RN119904 and its time complexity

is 119874(119863log119899) where 119899 was the number of sensor nodes

and 119863 was the number of potential RN positions Kashyapet al [29] proposed an RN

119904placement algorithm targeting

two edges and the vertex connectivity in 119889-dimensionalEuclidean space and this work also considered the geometricdisorder The minimum spanning tree was deployed Tanget al [30] also proposed approximation algorithms for asimply connected network and a two-connected networkSimulations of Tang et al [30] showed similar results with Liuet al [26] and Liu et al [27] Zhang et al [31] concluded theexisting RN

119904placement algorithms and this work proposed

a fault tolerant placement algorithm based on the steinergraph This algorithm had a 119874(1) time complexity Zhanget al [32] addressed the nuclear power plant problem andit proposed a three-step application oriented solution theconstructing redundant connected graph the optimizationthrough genetic algorithm and the generating position ofrelay nodes Experimental results showed that this solutionhad a 3D obstacles avoidance with better network fault toler-ance and the optimized placement position feature Reference[24ndash31] aimed to establish fault tolerant sensor networkand they proposed profound theories and algorithms basedon Steiner and other graphic theories But these researchesdid not consider the industrial environment in practice forexample the influence of sink node position network delayand overall energy consumption was not considered

Bari et al [33] focused on 119896119904coverage and 119896

119903connectivity

of the RN119904placement problem It presented the integer linear

programming method and it also showed the effectivenessof the algorithm Sitanayah et al [34] gave a GRASTP-ARPcentralized placement algorithm which ensured 119896minus1 disjointpaths Bhuiyan et al [35] aimed at buildingmonitoring sensornetwork and analyzed its special issues such as communi-cation unstability unreachability and ambient noise Thenan RN

119904placement repairing algorithm called FTSHM was

proposed and it improved fault tolerance while consideringnetwork lifetime and connectivity Reference [33ndash35] soughtto construct a fault tolerant sensor network and all of themfocused on the practical testing experiments and techniqueswhich were very useful

Bari et al [36] presented the formal description of ILPand this work had improved the network fault tolerance byRN119904placementThis work also enhances the network lifetime

by routing load balance Z Wang and Q Wang [37] addedconstraints of irreversible communication path and commu-nication capacity into the existing RN

119904placement model

and this work proposed a new evaluation criterion-minimumnetwork distance factor Experimental results showed itsadvantage on the network energy consumption Wang et al[38] proposed an RN

119904placement algorithm to insure fault

tolerance under multiconstraints similar to Z Wang andQ Wang [37] this work also presented a new evaluationcriterion and its algorithm to improve the network energyconsumption Al-Turjman et al [39] constructed a simple3D cube model and this work proposed an integer linearprogramming under the constraints of fault tolerance andenergy consumption and it also proved that this algorithm

International Journal of Distributed Sensor Networks 3

can improve the network lifetime effectively Yang et al [40]and Chaudhry et al [41] proposed a network base stationplacement and a fault tolerant routing strategy This solutionmainly sought to improve the network robustness and life-time Comparing with the solution which only consideredconnectivity the experimental results of Yang et al [40] andChaudhry et al [41] showed that the lifetime of this solutiondid not be reduced significantlyMichael and Pinciu [42] con-cluded the techniques of sensor node coverage based on theartist gallery problem and the voronoi graphic and this workproposed an placement strategy which could ensure networkcoverage of several positions this result guaranteed networkfault tolerance and this work reduced overall network energyconsumption Reference [36ndash42] considered network faulttolerance routing load balance communication capacity andnetwork coverage these integrated research methods weremore practical Such fault tolerant and energy consumptionresearch methods were also applicable to IWN researchhowever there was no placement research of real timeperformance on IWN

Sun et al [43] addressed an RN119904placement issue of

IWN This work firstly analyzed the reason of industrialenvironment communication failure and explained that faulttolerance was a key issue in IWN applications In thiswork they proposed an integrated optimum strategy basedon genetic algorithm and simulated annealing algorithm torealize the goal of two-coverage of sensor nodes and two-connected among RN

119904 There could be a lot of future work

based on this paper as it did not considermany other practicalconstraints

14 Research Feature and Paper Arrangement Althoughspread spectrum frequency hopping and the TDMA tech-nique improves IWN reliability to some degree this networkstill has some deficiencies such as being battery powered andshort distance communication Moreover there are electro-magnetic interference multipath effects and other wirelesssignal interference all of which make it easier for commu-nication to fail Therefore this paper focuses on improvingthe fault tolerance ability and network lifetime of IWN Inaddition IWN also needs to focus on real time communi-cation because monitoring information should be deliveredwithin the required time [44 45] However when networkscale increases the communication resource utilization ofTDMA technique decreases greatly which will affect real-time communication This paper also seeks to enhance real-time communication through paralleled communication

The main contribution of this paper is (i) presentinga comprehensive constraint and formulation about faulttolerance energy consumption and real-time issues (ii)proposing a heuristic algorithm to calculate paralleled com-munication resources according to objective function (iii)simulation experiments to show the influence of otherparameters on real-time performance and validate thatthe proposed relay node placement strategy can improvereal time performance while guaranteeing fault toleranceand energy limitation which is firstly proposed in relatedresearch

2 Network Model and Formulation

21 Network Model This paper considers two-tiered IWNmodel in which lower-tiered is sensor nodes distributed insensing area or above sensing object to gather required data[18] It assumes the sensor nodes have been deployed inpredetermined position and the potential position of relaynode has also been determined using grid met 1 le 119894 le 119909 Let119878 be the set of sensor nodes and let 119877 be the set of potentialRN119904positions |119878| = 119909 and |119877| = 119910 For each sensor node 119894

1 le 119894 le 119909 for each potential RN119904position 119895 119909+1 le 119895 le 119909+119910

the label of base station is 119909 + 119910 + 1 119901119888-coverage means

that every senor node can transmit with at less 119901119888RN119904 119902119888-

connectivity means that every RN is connected with at least119902119888RN119904

The objective is to obtain the position of relay nodeto achieve minimum edge coloring under the followingrequirement (i) the relay node has fault tolerance coverageto sensor node and the communication among relay nodesis still fault tolerant (ii) meet the requirement of networklifetime and energy consumption (iii) the degree of node isbalanced to improve paralleled communication performance

Since there is data collection period of IWN (in oneperiod all the data collected from sensor node must betransmitted to base station) another two objectives of thispaper are to shorten the period time and to reduce thecommunication resource usage in one period

This RNrsquos placement strategy is specially designed forthe IWN of industrial application where the location ofnode does not change frequently and the network controlinformation is distributed by the network manager throughmessage advertisement thus this strategy is not suitable forsuch applicationwhose network topology changes frequently

22 Parameter Definition

(1) The following notation is the input constant in ILPformulation

(a) 119909 the number of sensor nodes and every sensornode has an index 119894 (1 le 119894 le 119909)

(b) 119910 the number of potential RN positions with aunique index for each position 119895 119909 + 1 le 119895 le

119909 + 119910(c) 119909 + 119910 + 1 the index of base station(d) 119903max the communication distance of sensor

node(e) 119889max the communication distance of RN

119904

(f) 119889119894119895 the Euclidean distance between node 119894 and

node 119895(g) 119901119888 theminimumnumber of RN

119904covering every

single sensor node(h) 119902119888 the minimum number of RN

119904which can be

reached by node 119895 (119889119895119899+119898+1

gt 119889max) to forwarddata to base station

(i) 1205721(1205722) energy coefficient for transmission

(reception)(j) 120573 energy coefficient for amplifiers


(k) 119904 path loss rate(l) 119887119894 the number of bits that need to sending by

node 119894(m) 119863 a large constant119863 ge sum

119909

119894=1119887119894

(n) the maximum allowable energy consumption ofeach RN in one period

(2) The following notation is the input variables

(o) 119860119894119895 binary variable If node 119894 chooses RN

119895as

back-up next hop 119860119894119895= 1 else 119860

119894119895= 0

(p) 119861119894119895 binary variable If node 119894 chooses RN

119895as

primary next hop 119861119894119895= 1 else 119861

119894119895= 0

(q) 119884119895 binary variable 119884

119895= 1 means that if RN is

placed in position 119895 it can be reached by sensornode or other RN

(r) 119862119895 the number of RN

119904which can be used by

RN119895to forward data to base station

(s) the number of bits forwarded by RN119895in one

period

23 ILP Formulation In this section ILP formulation is pro-posed which should guarantee that the RN

119904is 119901119888-coverage

to sensor nodes and 119902119888-connectivity among each other In

addition the level of conflict edge coloring in the networktopology should be as little as possible to improve the real-time performance under the constraints of fault toleranceenergy consumption and node degree

The objective function is as follows

Minimize 119862119905 (1)

subject to

(1) transmission range constraints

119889119895119896

gt 119889max 997904rArr 119890119895119896

= 0 forall119895 119896 119895 = 119909 + 119910 + 1 (2)

119861119894119895cup 119860119894119895= 1 997904rArr 119889

119894119895le 119903max forall119894 119894 isin 119878 forall119895 119895 isin 119877 (3)

(2) fault tolerance constraints

exist119861119894119895= 1 (119895 isin 119877) forall119894 119894 isin 119878 (4)

119909+119910

sum

119895=119909+1

119860119894119895+ 1 ge 119901

119888 forall119894 119894 isin 119878 (5)

119862119895= sum

119908(119908isin119877)cap(119889119895119908le119889max)cap(119889119908119909+119910+1lt119889119895119909+119910+1)

119884119908 (6)

119884119895= 1 997904rArr 119862

119895ge 119902119888

forall119895 119895 isin 119877 cap (119889119895119909+119910+1

ge 119889max) (7)

(3) energy consumption constraints

119908119895= sum

119894

119887119894119861119894119895

forall119894 119895 119894 isin 119877 119895 isin 119878 (8)

119909+119910+1

sum

119896=119909+1

119890119895119896minus

119909+119910

sum

119896=119909+1

119890119896119895

= 119908119895 forall119895 119895 isin 119878 (9)

119879119895=

119909+119910+1

sum

119896=119909+1

119890119895119896 forall119895 119895 isin 119878 (10)

119866119895= 120573

119909+119910+1

sum

119896=119909+1

119890119895119896(119889119895119896)119904

forall119895 119895 isin 119878 (11)

119877119895=

119909+119910

sum

119896=119909+1

119890119896119895 forall119895 119895 isin 119878 cup 119895 = 119909 + 119910 + 1 (12)

119864119895= 1205721119877119895+ 1205722119879119895+ 1205721119908119895+ 119866119895

le 119864max forall119895 119895 isin 119878 cup 119895 = 119909 + 119910 + 1

(13)

(4) real-time constraints

119886 le 119889119895le 119887 (14)

120590 = radic1

119873

119873

sum

119895=1

(119889119895minus 119906)2

le 119879 (15)

24 ILP Formal Specification Formula (1) is the objectivefunction which must achieve minimum conflict edge color-ing under certain constraints as followsThe transmission andcoverage constraints are in formulae (2) and (3) Formula (2)means that the transmission range is longer than Euclideandistance among RN

119904 which is the necessary condition of

connectivity There will be no data flow if the distancebetween the two RN

119904is longer than 119889max Formula (3) means

that if the sensor node chooses an RN as primary next hop orbackup next hop the distance between them is shorter thantheir Euclidean distance

Network coverage connectivity and fault tolerancebetween RN

119904are in formulae (4) (5) (6) and (7) Formula

(4) means there is one and only one RN to be primary nexthop for each sensor node Formula (5) means the numberof RN

119904for each sensor node to connect must be at least

119901119888minus 1 Formulae (6) and (7) mean the RN

119904used by node 119895

to forward data to the base station must meet transmissionrange direction and 119902

119888connectivity requirements

Energy consumption constraints are in formulae (8) (9)(10) (11) (12) and (13) which focus on limiting energy usein one period Formula (8) means the total number of bitsgenerated by sensorsrsquo nodes within the transmission range ofRN119895 Formula (9) shows the relation among data flow from

119895 to 119896 data flow from 119896 to 119895 and the data bits generated byrelated sensor nodes Formula (10) is the total number of bitsforwarded by RN

119895 Formula (11) means the amplifier energy

dissipated by RN119895 Formula (12) means the total number of

bits that RN119895received from other RN

119904 Formula (13) means


the total energy consumption of RN119895and its maximum

energy consumptionNode degree constraints are in formulae (14) and (15)

which seek to limit the number of neighbors to balancedlevel Parameter 119886 119887 and 119879 can be adjusted according to thepractical situation

3 Solution

31 Solution Explanation The solution is divided into twoparts The first part is to calculate all the topologies that meetfault-tolerance and energy consumption requirements thesecond part is to find a placement topology with the lowestlevel of conflict edge coloring from the result in the firstphase

The algorithm running time depends on the number ofbinary variables including119860

119894119895119861119894119895 and119884

119895 whose value does

not relay to the number of sensor nodes but relates to thepotential number of RN

119904 It can be inferred from the formula

that the potential number of RN119904is large which will make

the running time of the algorithm long while in practicalsituations most of the binary variables of RN

119904are zero due

to the limitation of transmission range Thus the calculationis simplified in the first phase In the second phase the coreidea is to conduct vertex coloring for several network topolo-gies To improve running efficiency a heuristic algorithmis used to avoid high time complexity in overall optimiza-tion

32 Calculating the Fewest Number of Conflict Edge ColoringThere are two sorts of communication conflicts in IWNwhich are direct conflict and indirect conflict For directconflict there are three kinds the first is that a node cannotreceive and send data simultaneously the second is that anode cannot receive data from twoneighbors simultaneouslythe third is that a node cannot send data to two neighborssimultaneously To avoid direct conflict the algorithm mustallocate different communication resources for such conflictlinks For indirect conflict due to channel sharing the solu-tionmust meet some interference constraint model the nodewill interfere with all its neighbors when it is sending dataand this situation must be considered in the communicationresource scheduling

In IWN the valid communication resources are res-tricted thus if using a traditional communication resourcesscheduling technique the above conflicts will make networkchannel utilization low which will reduce the networkthroughput increase transmission delay (real-time perfor-mance) and have a negative impact on large network scaleapplications Therefore if taking advantage of short distancewireless communication paralleled communication can beused to schedule same communication resources to suchlinks that do not conflict with each other Then the networkthroughput and real time performance can be improved

We transform the original graph into a link conflictgraph according to the communication conflict principleTheconflict edges in the original graph become vertexes in thelink conflict graph and then vertex coloring is conducted in

the link conflict graph to obtain the lowest coloring levelThere are many vertex coloring algorithms the backtrackbranch bounding method is accurate but high in timecomplexity the greedy algorithm is low in running time butthe results are normal the intelligent algorithms like neuralnetwork and genetic and ant-colony optimization the DNAalgorithm can obtain preferable results but the algorithmitself is very complex the running process is randomly andthe running time is long In this paper a maximum degreefirst heuristic algorithm is proposed on the basis of theWelshPowell algorithm The following are some explanations andalgorithm steps

For a graph (119866 = (119881 119864)) mapping (120587 119881 rarr 1 2

119896) is a 119896-vertex coloring and 1 2 119896 is the set of colorsfor any two neighbor nodes 120583 and 120592 if 120587(120583) = 120587(120592) thecoloring is normal The minimum value of normal 119896-vertexcoloring is called color number (120594(119866)) Δ(119866) which meansthe maximum degree of nodes 120594 and Δ are simple notation

Vertex coloring corresponds to vertex set partition If 120587is 119866119896-vertex coloring of 119866(120587(119881(119866)) = 1 2 119896) then120587minus1

(1) 120587minus1

(2) 120587minus1

(119896) is a partition of 119881(119866) If 120587 hasnormal coloring then every 120587

minus1

(119894) is vertex independentset of 119866 And if 119881

1 1198812 119881

119896 is a partition of 119881(119866) the

partition can derive a 119896-coloring 120587(119881119894= 120587minus1

(119894)) and wecalled 120587minus1(119894) to be an color group of 120587 If 119881

1 1198812 119881

119896 is

a partition of 119881(119866) and 119881119894are all independent set then this

partition is called color partition

Theorem 1 For any 119866 120594 le Δ + 1 is right

Demonstration Mathematical induction is used for vertexnumber 119899 of 119866 when 119899 = 1 120594 = 1 Δ ge 0 and 120594 le Δ + 1

is right For 119899 ge 2 119906 isin 119881(119866) suppose 1198661015840 = 119866 minus 119906 accordingto induction hypothesis 120594(1198661015840) le Δ(119866

1015840

) + 1 then there existsΔ(1198661015840

) + 1 color 120587 of 1198661015840 Because of Δ(1198661015840) le Δ(119866) 120587 is alsoΔ(1198661015840

) + 1 coloring of 1198661015840 Assuming 119889119866(119906) = 119896 the neighbor

vertex of 119906 is 1198811 1198812 119881

119896 due to |120587(V

1) 120587(V

119896)| le

119896 lt Δ(119866) + 1 there exit 119895 isin 1 2 Δ(119866) + 1 119895 notin

120587(V1) 120587(V

119896) let 120587(119906) = 119895 and then 120587 is a Δ(119866) + 1

coloring of 119866 thus the theorem is proved right and an upperbound is found which can be used as initial color set of ouralgorithm

Since the solution seeks to obtain the lowest level of vertexcolors firstly the heuristic algorithm uses one color for asmany vertexes as possible obviously these vertexes must notbemutual neighbors It is the samewith the following processThe algorithms first find the maximal independent set andthe entire vertex in this set is given the same color Thenthe second maximal independent set till the entire vertex isgiven a color Since there is no unique result for this methodwe must try to find a better result which is an NP completeproblem However we can infer that the degree of one vertexis larger its influence to other vertexes is greater Thus thisalgorithm gives higher priority for such a vertex with a largedegree which can reduce the influence This is the ideaof Welsh Powell algorithm Figure 1 outlines our algorithmsteps


Init transform TC sequence to

based on blacklist channels

Init sort the vertex set in descendorder based on degree as a result

i = i + 1

No

Yes

End

Assume k is the least positive integer

and j is a neighbor of i+1

i = n

120587(1) = 1 i = 1

d(1) ge d(2) middot middot middot ge d(n)V1 2 n

of CC(i+1) and then let 120587(i+1) = k

C(i+1) = 120587(j) jle i|

one-dimensional color set C1 2 Δ + 1

Figure 1 Coloring algorithm flow chart

4 Simulation Experiment and Result

In simulation 119903max = 40m and 119889max = 80m Assumethat the network communication is a cosmic model andenergy model is in Bari et al [36] 120572

1= 1205722= 50 nJbit 120573 =

100 pJbitm2 119904 = 2 and initial energy of every RN is 5 JIn order to focus on the key point the distribution of relay

nodes we do not conduct practical sensor placement like inZhang et al [18] but we use random placement strategy Thewhole network area includes 3 different sizes 80lowast80m2 90lowast90m2 and 100lowast100m2 and the gridmethod is used to obtainthe potential positions of RN

119904

The simulation programs run on a desktop with IntelCore i3 330GHzCPU and 4GRAM and the experimentenvironment is Matlab R2010B The main goal is to find thelowest level of edge coloring RN

119904placement topology in a

normal case execution time of the simulation is less than 20minutes when the value of main inputs reach maximum thewhole program will take over 35 minutes to finish

41 Network Performance without Real-Time Constraints orEnergy Constraints

(1) Single-Connected Topology (119901119888

= 119902119888

= 1) OnlyWhen considering connection only the network real-time

Chro

mat

ic n

umbe

r

Grid-64 Grid-81 Grid-100Relay nodes location scheme

4

6

8

10

Figure 2 Comparison of chromatic number of 40-sensor topologyunder different relay node schemes when 119901

119888= 119902119888= 1

Sensor-20 Sensor-40 Sensor-60Number of sensor nodes

Chro

mat

ic n

umbe

r

4

6

8

10

12

14

Figure 3 Comparison of chromatic number of different topologiesunder 81-Grid relay node scheme when 119901

119888= 119902119888= 1

performances are shown in Figures 2 and 3 Figure 2 illus-trates the relationship between real-time performance andnetwork area size under the same problem size (numberof sensors) According to the experiment results the real-time performance enhanceswith the gradual expansion of thenetwork area Figure 3 shows the effects of different numbersof sensors on the network real-time performance in the samearea As Figure 3 has shown the more the sensors exist in aunit area the worse the real-time performance of the networktopology is

(2) Multiple-Connected Topology (119901119888= 119902119888= 2) Only Fault-

tolerance constraints find a redundant backup pathwhich hasno intersections with the main path for both sensor nodesand relay nodes Thus the self-organizing topology gainsmultiple connections and the network robustness improvesIn Figure 4 the network real-time performance improveswhile the area size expands Figure 5 shows that real-timeperformance gets worse when more sensors are distributedin the same size area

Comparing Figure 2 with Figures 4 3 and 5 respec-tively the following conclusions are made (i) no matterif the topology is single-connected or multiple-connectedthe network real-time performances have almost similartrends of change under same effects (different number of



Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2


Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2

sensors or different size of network area) (ii) the real-time performance of a multiple-connected topology is muchworse than the performance of a single-connected topologysince there are no constraints to control the multitude ofadditional redundant backup paths therefore the probabilityof collisions in the network raises

42 Network Performance without Real-Time Constraints butEnergy Constraints The strategy of energy constraints is tolimit themaximum energy cost per round of nodes to preventthe early appearance of dead nodes In this experiment set-up three different levels of energy constraints are used RE-Level 1 (Restricted Energy Level 1) is the most relaxed with119864max = 26lowast10

minus4 nJ and Level 3 is the most constrained with119864max = 20 lowast 10

minus4 nJFigures 6 and 7 show the network real-time performances

of single-connected topology and multiple-connected topol-ogy respectively when energy constraints are includedContrast the chromatic numbers of topologies which have thesamenumber of sensors and the same size of network area butdifferent RE-Levels the real-time performances show almostno change This means that energy constraints alone cannotimprove the real-time performance of a network

Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3

Figure 6 Comparison of chromatic number of different topologieswith energy constraints under 81-Grid relay node schemewhen119901

119888=

119902119888= 1

Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 2

43 Network Performance with Both Real-Time Constraintsand Energy Constraints Real-time constraints will limit thedegree of each node and the standard deviation of thedegrees of all the nodes in a network Network topology candistribute all the data flows as equally as possible with real-time constraints so both lifetime and real-time performance

8 International Journal of Distributed Sensor NetworksCh

rom

atic

num

ber

6

4

2

0

8

10

12


No RDRD-Lv 1

RD-Lv 2RD-Lv 3

Figure 8 Comparison of chromatic number of different topologieswith energy constraints and real-time constraints under 81-Gridrelay node scheme when 119901

119888= 119902119888= 2

of the network will improve Here besides some real-timeconstraints fault-tolerance (119901

119888= 119902119888

= 1) and energyconstraints (119864max = 20 lowast 10

minus4 nJ) are included as well in thetopology

According to formulae (14) and (15) node degree 119889119895will

be constrained by both 119886 and 119887 and standard deviation ofnode degrees will be constrained by 119879 Three different levelsof real-time constraints are used in this experiment For 119889

119895

the point is to control the upper limit value 119887 RD-Level 1(Restricted Degree-Level 1) is the most relaxed with 119887 = 6and RD-Level 3 is themost constrainedwith 119887 = 4 the variale119886 which has a default value of 2 represents lower limit of119863

119895

for real-time altering in self-organizing proved difficult andineffient when default 119886 cannot satisfy the requirement theproposed algorithm will automatically alter the value of 119886 toadjust dynamic self-organizing topology The reference valueof 119879 is given in formula (15) and the actual 119879 value may havea slight deviation based on a given network

The effects of 119889119895on network real-time performance are

shown in Figures 8 and 9 From these two figures theresults indicate that the real-time performances obviouslyimprove through 119889

119895 and the improvements increase with

higher RD-Level Figures 10 and 11 show that using theproposed approach the network lifetimes can be significantlyimproved especially when 119879 (restricted 119879 indicated by ldquoRT-Levelrdquo in Figures 10 and 11) is more constrained

Figures 12 and 13 compare the number of relay nodesrequired by the proposed approach under different real-timeconstraint levels It can be seen from these two figures thaton the whole the number of relay nodes required is steadand increases very slightly when the real-time constraint levelraises Comparing Figures 8 to 13 comprehensively the results


Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

No RDRD-Lv 1

RD-Lv 2RD-Lv 3

Figure 9 Comparison of chromatic number of 40-sensor topologywith energy constraints and real-time constraints under differentrelay node schemes when 119901

119888= 119902119888= 2

S-20 S-40 S-60Number of sensor nodes

No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds

Figure 10 Comparison of lifetime of different topologies withenergy constraints and real-time constraints under 81-Grid relaynode scheme when 119901

119888= 119902119888= 2

indicate that the proposed approach improves the networkperformances significantly with very slight costs (number ofrelay nodes required)

Figures 14 and 15 show the performance comparisonsfor the following cases (i) ILP with no constraints (the left-most bar in each group indicated by ldquoILP-ALLrdquo [36]) (ii)



No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds

Figure 11 Comparison of lifetime of 40-sensor topology withenergy constraints and real-time constraints under different relaynode schemes when 119901

119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3

Sensor-20 Sensor-40 Sensor-60

70

60

50

40

30

20

10

0

Number of sensor nodes

Num

ber o

f rela

y no

des r

equi

red

Figure 12 Comparison of number of relay nodes required of dif-ferent topologies with energy constraints and real-time constraintsunder 81-Grid relay node schemes when 119901

119888= 119902119888= 2

ILP with fault-tolerance (the second bar from the left in eachgroup indicated by ldquoILP-REDrdquo [36]) (iii) ILP based approachwith fault-tolerance and some energy constraints (the thirdbar in each group indicated by ldquoILP-Barirdquo [36]) and (iv) anapproach with some real-time constraints based on (iii) (theright-most bar indicated by ldquoILP-ZHrdquo) Figure 14 compares


No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

Figure 13 Comparison of number of relay nodes required of 40-sensor topology with energy constraints and real-time constraintsunder different relay node schemes when 119901

119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH

Figure 14 Comparison of number of relay nodes required bydifferent approaches

the number of relay nodes required for different approachesand shows the results of real-time performance comparison

As shown in Figure 14 ILP-ALL requires the least numberof relay nodes for all networksThis is expected because ILP-ALL always generates a solution with the greedy algorithmILP-RED requires the most relay nodes since fault-tolerance


rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH

Figure 15 Comparison of chromatic number under differentapproaches

is considered but without other constraints and the numberof paths will simply be double in the network As energyconstraints are included the ILP-Bari requires more relaynodes than ILP-ALL and less nodes than ILP-RED

The main idea of the real-time constraint is to balancethe data flows and energy costs in the whole topologythereupon collisions and the lifetime of the network willbe improved In such cases the number of required relaynodes obtained by the proposed approach may be higherthan some other approaches (this is shown in Figure 14)However when incorporating Figure 15 with Figure 14 theresults illustrate that the number of required relay nodes isan inevitable cost to improve the whole performance of thenetwork The chromatic number of the proposed approachesis obviously less than other approaches (sometimes the ILP-ALL could also obtain the least chromatic number but thewhole performance cannot reach the proposed approach eglifetime) whichmeans collisions in the network are definitelycontrolled This proves that industrial WSN could achieve alink fault-tolerance node energy constraints and preferablereal-time performance within the proposed approach

5 Conclusion

In IWN except for fault tolerance and energy consumptionconstraints real time performance is also important but iseasily ignored Since the position of IWN nodes is usuallyfixed in reality the network real time performance is alsodetermined after topology placement Thus this paper con-siders fault tolerance energy consumption and real timeperformance of IWN and presents a formal description of theproblem of RN

119904placement For fault tolerance we consider

119901119888-coverage and 119902

119888-connectivity of RN

119904 for energy consump-

tion we consider maximum energy constraints in one periodfor every node and then a network conflict edge coloringalgorithm based on the Welsh-Power algorithm is proposedExperiment results show that this placement strategy canobtain better paralleled utilization of communication andit also meets fault tolerance and energy consumption con-straintsThus the network real time performance is improvedSince our current research needs to consider the applicationcompatibility of network topology wemainly seek to improvereal time performance In the future there are two aspectsto study further One is the realization of relay node optimaldeployment of the combination of the AGV and IWN withlimited numbers The other is the fine-grained navigation forAGV supported by the IWN monitoring the status of theequipment and environment

Conflict of Interests

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

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (Grant no 61202042) China-CanadaJoint Research Project (Grant no 2009DFA12100) the Fun-damental Research Funds for the Central Universities (Grantnos SWU113066 XDJK2015C023 and XDJK2012C019) andthe Scientific Research Foundation for the ReturnedOverseasChinese Scholars State Education Ministry of China

References

[1] W Wolf ldquoNews briefsrdquo IEEE Computer vol 40 no 11 pp 104ndash105 2007

[2] ldquoNew Research Directions for Future Cyber-Physical EnergySystemsrdquo 2009

[3] ldquoBridging the Cyber Physical and Social Worldsrdquo 2011[4] NIST Foundations for Innovation in Cyber-Physical Systems

Workshop 2012[5] J Wan H Yan H Suo and F Li ldquoAdvances in cyber-

physical systems researchrdquo KSII Transactions on Internet andInformation Systems vol 5 no 11 pp 1891ndash1908 2011

[6] J Wan H Yan Q Liu K Zhou R Lu and D Li ldquoEnablingcyber-physical systems with machine-to-machine technolo-giesrdquo International Journal of Ad Hoc and Ubiquitous Comput-ing vol 13 no 3-4 pp 187ndash196 2013

[7] J Wan M Chen F Xia D Li and K Zhou ldquoFrom machine-to-machine communications towards cyber-physical systemsrdquoComputer Science and Information Systems vol 10 no 3 pp1105ndash1128 2013

[8] C Alcaraz and J Lopez ldquoA security analysis for wireless sensormesh networks in highly critical systemsrdquo IEEE Transactions onSystems Man and Cybernetics Part C Applications and Reviewsvol 40 no 4 pp 419ndash428 2010

[9] V C Gungor and G P Hancke ldquoIndustrial wireless sensor net-works challenges design principles and technical approachesrdquoIEEE Transactions on Industrial Electronics vol 56 no 10 pp4258ndash4265 2009


[10] E Egea-Lopez A Martinez-Sala J Vales-Alonso J Garcia-Haro and J Malgosa-Sanahuja ldquoWireless communicationsdeployment in industry a review of issues options and tech-nologiesrdquo Computers in Industry vol 56 no 1 pp 29ndash53 2005

[11] ISA ldquoAn ISA StandardWireless Systems for Industrial Automa-tion Process Control and Related Applicationsrdquo ISA-10011a-2009 ISA 2009

[12] IEC ldquoIndustrial communication networksmdashfieldbus specifica-tionsmdashWirelessHART communication network and communi-cation profilerdquo IECPAS 62591 edition 10 IEC 2009

[13] D J Chen NMark andM AloysiusWirelessHART Real-TimeMesh Network for Industrial Automation Springer 2010

[14] J Song S Han A K Mok et al ldquoWirelessHART applyingwireless technology in real-time industrial process controlrdquo inProceedings of the IEEE Real-Time and Embedded Technologyand Applications Symposium (RTAS rsquo08) pp 377ndash386 St LouisMo USA April 2008

[15] P Ferrari A Flammini D Marioli S Rinaldi and E SisinnildquoOn the implementation and performance assessment of awirelessHART distributed packet analyzerrdquo IEEE Transactionson Instrumentation and Measurement vol 59 no 5 pp 1342ndash1352 2010

[16] Industrial Communication Networks ldquoCFieldbus specifica-tionsrdquo Tech Rep IECIECPAS 62601 CWIA-PA Communica-tion Network and Communication Profile 2009

[17] W L Lee A Datta and R Cardell-Oliver ldquoFlexiTP a flexible-schedule-based TDMA protocol for fault-tolerant and energy-efficient wireless sensor networksrdquo IEEE Transactions on Paral-lel and Distributed Systems vol 19 no 6 pp 851ndash864 2008

[18] H Zhang D Y Chen S Liu et al ldquoA WSN vibration sensornodes optimization placement strategy in nuclear power plantequipment monitoring applicationrdquo Journal of ConvergenceInformation Technology vol 8 no 2 pp 348ndash355 2013

[19] X Chang R Tan G Xing et al ldquoSensor placement algorithmsfor fusion-based surveillance networksrdquo IEEE Transactions onParallel and Distributed Systems vol 22 no 8 pp 1407ndash14142011

[20] Y T Hou Y Shi H D Sherali and S F Midkiff ldquoOn energyprovisioning and relay node placement for wireless sensornetworksrdquo IEEE Transactions on Wireless Communications vol4 no 5 pp 2579ndash2590 2005

[21] I-R Chen A P Speer and M Eltoweissy ldquoAdaptive fault-tolerant QoS control algorithms formaximizing system lifetimeof query-based wireless sensor networksrdquo IEEE Transactions onDependable and Secure Computing vol 8 no 2 pp 161ndash1762011

[22] QWang K Xu G Takahara and H Hassanein ldquoDevice place-ment for heterogeneous wireless sensor networks minimumcost with lifetime constraintsrdquo IEEE Transactions on WirelessCommunications vol 6 no 7 pp 2444ndash2453 2007

[23] L Liu B Hu and L Li ldquoEnergy conservation algorithmsfor maintaining coverage and connectivity in wireless sensornetworksrdquo IETCommunications vol 4 no 7 pp 786ndash800 2010

[24] J L Bredin E D Demaine M T Hajiaghayi and D RusldquoDeploying sensor networks with guaranteed fault tolerancerdquoIEEEACM Transactions on Networking vol 18 no 1 pp 216ndash228 2010

[25] XHan X Cao E L Lloyd andC-C Shen ldquoFault-tolerant relaynode placement in heterogeneous wireless sensor networksrdquoIEEE Transactions on Mobile Computing vol 9 no 5 pp 643ndash656 2010

[26] H Liu PWan and X Jia ldquoOn optimal placement of relay nodesfor reliable connectivity in wireless sensor networksrdquo Journal ofCombinatorial Optimization vol 11 no 2 pp 249ndash260 2006

[27] H Liu P J Wan and X H Jia ldquoFault-tolerant relay node place-ment in wireless sensor networksrdquo in Proceedings of the 26thIEEE International Conference on Computer Communications(INFOCOM rsquo07) vol 3595 pp 230ndash239 2005

[28] B Hao J Tang and G Xue ldquoFault-tolerant relay node place-ment in wireless sensor networks formulation and approxi-mationrdquo in Proceedings of the Workshop on High PerfomanceSwitching and Routing (HPSR rsquo04) pp 246ndash250 April 2004

[29] A Kashyap S Khuller and M Shayman ldquoRelay placementfor fault tolerance in wireless networks in higher dimensionsrdquoComputational Geometry Theory and Applications vol 44 no4 pp 206ndash215 2011

[30] J Tang B Hao andA Sen ldquoRelay node placement in large scalewireless sensor networksrdquo Computer Communications vol 29no 4 pp 490ndash501 2006

[31] W Y Zhang G Xue and S Misra ldquoFault-tolerant relay nodeplacement in wireless sensor networks problems and algo-rithmsrdquo inProceedings of the 26th IEEE International Conferenceon Computer Communications (INFOCOM rsquo07) pp 1649ndash1657May 2007

[32] H Zhang L Li D Chen Y Wu and J Ling ldquoA novel wsnrelay nodes placement strategy in NPP equipment monitoringapplicationrdquo in Proceedings of the 8th International Conferenceon Wireless Communications Networking and Mobile Comput-ing (WiCOM rsquo12) Shanghai China September 2012

[33] A Bari A Jaekel and S Bandyopadhyay ldquoOptimal placementof relay nodes in two-tiered fault tolerant sensor networksrdquoin Proceedings of the 12th IEEE International Symposium onComputers and Communications (ISCC rsquo07) pp 159ndash164 July2007

[34] L Sitanayah K N Brown and C J Sreenan ldquoFault-tolerantrelay deployment for k node-disjoint paths in wireless sensornetworksrdquo in Proceedings of the IFIPWireless Days (WD rsquo11) pp1ndash6 Niagara Falls Canada October 2011

[35] M Z A Bhuiyan J Cao and G Wang ldquoDeploying wirelesssensor networks with fault tolerance for structural health mon-itoringrdquo in Proceedings of the 8th IEEE International Conferenceon Distributed Computing in Sensor Systems (DCOSS rsquo12) pp194ndash202 May 2012

[36] A Bari A Jaekel J Jiang and Y Xu ldquoDesign of fault tolerantwireless sensor networks satisfying survivability and lifetimerequirementsrdquo Computer Communications vol 35 no 3 pp320ndash333 2012

[37] Z Wang and Q Wang ldquoResearch on multi-restricted fault-tolerant relay node placement algorithm in wireless sensornetworksrdquo Acta Electronica Sinica vol 39 no 3A pp 115ndash1202011

[38] Z Wang Q Wang D-B Wei and L Wang ldquoRelay node place-ment and addition algorithms inwireless sensor networksrdquoActaPhysica Sinica vol 61 no 12 Article ID 120505 pp 1ndash10 2012

[39] F M Al-Turjman A E Al-Fagih H S Hassanein and M AIbnkahla ldquoDeploying fault-tolerant grid-based wireless sensornetworks for environmental applicationsrdquo in Proceedings of theIEEE 35th Conference on Local Computer Networks (LCN rsquo10)pp 715ndash722 Denver Colo USA October 2010

[40] D Yang S Misra and G Xue ldquoJoint base station placementand fault-tolerant routing in wireless sensor networksrdquo inProceedings of the IEEE Global Telecommunications Conferencepp 1ndash6 December 2009


[41] S Chaudhry V Hung and R Guha ldquoOptimal placementof wireless sensor nodes with fault tolerance and minimalenergy consumptionrdquo in Proceedings of the IEEE InternationalConference on Mobile Ad Hoc and Sensor Sysetems pp 610ndash615October 2006

[42] T S Michael and V Pinciu ldquoArt gallery theorems for guardedguardsrdquo Computational Geometry vol 26 no 3 pp 247ndash2582003

[43] P Sun J Ma and N A Kai ldquoA genetic simulated annealinghybrid algorithm for relay nodes deployment optimizationin industrial wireless sensor networksrdquo in Proceedings of theIEEE International Conference on Computational Intelligence forMeasurement Systems and Applications (CIMSA rsquo12) pp 24ndash282012

[44] A Saifullah Y Xu C Lu and Y Chen ldquoReal-time schedulingfor WirelessHART networksrdquo in Proceedings of the 31st IEEEReal-Time Systems Symposium (RTSS rsquo10) pp 150ndash159 Decem-ber 2010

[45] S-E Yoo P K Chong D Kim et al ldquoGuaranteeing real-time services for industrial wireless sensor networks with IEEE802154rdquo IEEE Transactions on Industrial Electronics vol 57 no11 pp 3868ndash3876 2010

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



placement primarily considers the probability-of-detectiondata fusion and accuracy [18 19] Tremendous attention hasbeen paid to address the issue of relay node placement onthe grounds that a relay node can be deployed flexibly therelay node acts as a bridge between the sensor node and sinknodes relay node placement strategy is distinct for differentapplication requirements Although we can use the AGVmobile robot or person with handheld devices to collect datathere is usually a limited number of mobile robots Peoplecannot use handheld mobile acquisition equipment to collectinformation in the harsh environment The AGV mobilerobot is not able to work in the limited space environment Inaddition the above two ways have a higher cost So we hopethat WSN can bear the bulk of the work only allowing manor AGV to carry out regular inspections and verifications Abetter node deployment strategy for the relay node can alsoprovide fine-grained navigation for the AGVormobile robotBy combining the two ways using IWN and AGV it can beeasier to complete the construction of an industrial intelligentenvironment Therefore we say that the deployment of therelay node is essential and important for research

13 Related Work on Relay Node Placement Hou et al [20]extended the network lifetime by designing an heuristic algo-rithm (SPINDS) to solve optimized RN placement problemexperiments validated the effectiveness of this algorithmChen et al [21] demonstrated that redundant fault-toleranttechniques improved query reliability and network lifetimeand it could be referred in RN placement While Hou et al[20] aimed to extend the network lifetime but this workdoes not consider the reliable communication issue in hashindustrial environments

Wang et al [22] tended to solve the issue of the minimumnetwork cost relay node placement under the constraint ofnetwork lifetime and connectivity This work firstly solvedthe minimum set cover problem without considering energyconsumption They also proposed three heuristic algorithmsto solve the energy consumption constraint Liu et al [23]aimed at network coverage and connectivity based on trans-portation industry and this work proposed a heuristic andnetwork flow algorithm to deal with the relay node placementproblem Wang et al [22] and Liu et al [23] were typicalrelayed node placement research under constraint of networkcoverage connectivity and lifetime but they did not considerfault tolerant issue in hash industry environment

Bredin et al [24] established 119896-connectivity network toimprove fault tolerance by RN

119904placement the greedy and

distributed algorithms were proposed and their performancehad been proven by simulations Han et al [25] focusedon adding additional RN

119904to improve fault tolerance and a

heuristic algorithm was proposed and validated by experi-ments Liu et al [26] and Liu et al [27] addressed the issueof the RN

119904placement for a two-tier sensor network under

a simply connected situation or a two-connected situationApproximation algorithms had been proposed for these twosituationsThe time complexitywas 6 + 120576 24 + 120576 or 6119879+ 12 +120576 Hao et al [28] proposed a fault tolerant placement solutionunder theminimumRN

119904constraints which could insure that

every sensor node can be connectedwith at least two RN119904and

two-connected among all the RN119904 and its time complexity

is 119874(119863log119899) where 119899 was the number of sensor nodes

and 119863 was the number of potential RN positions Kashyapet al [29] proposed an RN

119904placement algorithm targeting

two edges and the vertex connectivity in 119889-dimensionalEuclidean space and this work also considered the geometricdisorder The minimum spanning tree was deployed Tanget al [30] also proposed approximation algorithms for asimply connected network and a two-connected networkSimulations of Tang et al [30] showed similar results with Liuet al [26] and Liu et al [27] Zhang et al [31] concluded theexisting RN

119904placement algorithms and this work proposed

a fault tolerant placement algorithm based on the steinergraph This algorithm had a 119874(1) time complexity Zhanget al [32] addressed the nuclear power plant problem andit proposed a three-step application oriented solution theconstructing redundant connected graph the optimizationthrough genetic algorithm and the generating position ofrelay nodes Experimental results showed that this solutionhad a 3D obstacles avoidance with better network fault toler-ance and the optimized placement position feature Reference[24ndash31] aimed to establish fault tolerant sensor networkand they proposed profound theories and algorithms basedon Steiner and other graphic theories But these researchesdid not consider the industrial environment in practice forexample the influence of sink node position network delayand overall energy consumption was not considered

Bari et al [33] focused on 119896119904coverage and 119896

119903connectivity

of the RN119904placement problem It presented the integer linear

programming method and it also showed the effectivenessof the algorithm Sitanayah et al [34] gave a GRASTP-ARPcentralized placement algorithm which ensured 119896minus1 disjointpaths Bhuiyan et al [35] aimed at buildingmonitoring sensornetwork and analyzed its special issues such as communi-cation unstability unreachability and ambient noise Thenan RN

119904placement repairing algorithm called FTSHM was

proposed and it improved fault tolerance while consideringnetwork lifetime and connectivity Reference [33ndash35] soughtto construct a fault tolerant sensor network and all of themfocused on the practical testing experiments and techniqueswhich were very useful

Bari et al [36] presented the formal description of ILPand this work had improved the network fault tolerance byRN119904placementThis work also enhances the network lifetime

by routing load balance Z Wang and Q Wang [37] addedconstraints of irreversible communication path and commu-nication capacity into the existing RN

119904placement model

and this work proposed a new evaluation criterion-minimumnetwork distance factor Experimental results showed itsadvantage on the network energy consumption Wang et al[38] proposed an RN

119904placement algorithm to insure fault

tolerance under multiconstraints similar to Z Wang andQ Wang [37] this work also presented a new evaluationcriterion and its algorithm to improve the network energyconsumption Al-Turjman et al [39] constructed a simple3D cube model and this work proposed an integer linearprogramming under the constraints of fault tolerance andenergy consumption and it also proved that this algorithm
























119904





119904which can be

reached by node 119895 (119889119895119899+119898+1







119909

119894=1119887119894




119895as


119894119895= 0


119895as


119894119895= 0








period


119904is 119901119888-coverage




Minimize 119862119905 (1)

subject to


119889119895119896

gt 119889max 997904rArr 119890119895119896

= 0 forall119895 119896 119895 = 119909 + 119910 + 1 (2)

119861119894119895cup 119860119894119895= 1 997904rArr 119889




119909+119910

sum

119895=119909+1

119860119894119895+ 1 ge 119901

119888 forall119894 119894 isin 119878 (5)

119862119895= sum


119884119908 (6)

119884119895= 1 997904rArr 119862

119895ge 119902119888

forall119895 119895 isin 119877 cap (119889119895119909+119910+1

ge 119889max) (7)


119908119895= sum

119894

119887119894119861119894119895

forall119894 119895 119894 isin 119877 119895 isin 119878 (8)

119909+119910+1

sum

119896=119909+1

119890119895119896minus

119909+119910

sum

119896=119909+1

119890119896119895

= 119908119895 forall119895 119895 isin 119878 (9)

119879119895=

119909+119910+1

sum

119896=119909+1

119890119895119896 forall119895 119895 isin 119878 (10)

119866119895= 120573

119909+119910+1

sum

119896=119909+1

119890119895119896(119889119895119896)119904

forall119895 119895 isin 119878 (11)

119877119895=

119909+119910

sum

119896=119909+1

119890119896119895 forall119895 119895 isin 119878 cup 119895 = 119909 + 119910 + 1 (12)

119864119895= 1205721119877119895+ 1205722119879119895+ 1205721119908119895+ 119866119895


(13)


119886 le 119889119895le 119887 (14)

120590 = radic1

119873

119873

sum

119895=1

(119889119895minus 119906)2

le 119879 (15)
























3 Solution



119894119895119861119894119895 and119884






119904are zero due









(1) 120587minus1

(2) 120587minus1


minus1


1 1198812 119881




1 1198812 119881

119896 is






1015840




vertex of 119906 is 1198811 1198812 119881

119896 due to |120587(V

1) 120587(V

119896)| le


120587(V1) 120587(V

119896) let 120587(119906) = 119895 and then 120587 is a Δ(119866) + 1







i = i + 1

No

Yes

End



i = n

120587(1) = 1 i = 1



C(i+1) = 120587(j) jle i|





1= 1205722= 50 nJbit 120573 =



119904






= 119902119888


Chro

mat

ic n

umbe

r


4

6

8

10


119888= 119902119888= 1


Chro

mat

ic n

umbe

r

4

6

8

10

12

14


119888= 119902119888= 1







Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2


Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2






Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 1

Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 2



rom

atic

num

ber

6

4

2

0

8

10

12


No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


119888= 119902119888





119895


119895








Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2





No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


70

60

50

40

30

20

10

0


Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2



No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH





rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
































119904





119904which can be

reached by node 119895 (119889119895119899+119898+1







119909

119894=1119887119894




119895as


119894119895= 0


119895as


119894119895= 0








period


119904is 119901119888-coverage




Minimize 119862119905 (1)

subject to


119889119895119896

gt 119889max 997904rArr 119890119895119896

= 0 forall119895 119896 119895 = 119909 + 119910 + 1 (2)

119861119894119895cup 119860119894119895= 1 997904rArr 119889




119909+119910

sum

119895=119909+1

119860119894119895+ 1 ge 119901

119888 forall119894 119894 isin 119878 (5)

119862119895= sum


119884119908 (6)

119884119895= 1 997904rArr 119862

119895ge 119902119888

forall119895 119895 isin 119877 cap (119889119895119909+119910+1

ge 119889max) (7)


119908119895= sum

119894

119887119894119861119894119895

forall119894 119895 119894 isin 119877 119895 isin 119878 (8)

119909+119910+1

sum

119896=119909+1

119890119895119896minus

119909+119910

sum

119896=119909+1

119890119896119895

= 119908119895 forall119895 119895 isin 119878 (9)

119879119895=

119909+119910+1

sum

119896=119909+1

119890119895119896 forall119895 119895 isin 119878 (10)

119866119895= 120573

119909+119910+1

sum

119896=119909+1

119890119895119896(119889119895119896)119904

forall119895 119895 isin 119878 (11)

119877119895=

119909+119910

sum

119896=119909+1

119890119896119895 forall119895 119895 isin 119878 cup 119895 = 119909 + 119910 + 1 (12)

119864119895= 1205721119877119895+ 1205722119879119895+ 1205721119908119895+ 119866119895


(13)


119886 le 119889119895le 119887 (14)

120590 = radic1

119873

119873

sum

119895=1

(119889119895minus 119906)2

le 119879 (15)
























3 Solution



119894119895119861119894119895 and119884






119904are zero due









(1) 120587minus1

(2) 120587minus1


minus1


1 1198812 119881




1 1198812 119881

119896 is






1015840




vertex of 119906 is 1198811 1198812 119881

119896 due to |120587(V

1) 120587(V

119896)| le


120587(V1) 120587(V

119896) let 120587(119906) = 119895 and then 120587 is a Δ(119866) + 1







i = i + 1

No

Yes

End



i = n

120587(1) = 1 i = 1



C(i+1) = 120587(j) jle i|





1= 1205722= 50 nJbit 120573 =



119904






= 119902119888


Chro

mat

ic n

umbe

r


4

6

8

10


119888= 119902119888= 1


Chro

mat

ic n

umbe

r

4

6

8

10

12

14


119888= 119902119888= 1







Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2


Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2






Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 1

Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 2



rom

atic

num

ber

6

4

2

0

8

10

12


No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


119888= 119902119888





119895


119895








Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2





No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


70

60

50

40

30

20

10

0


Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2



No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH





rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119909

119894=1119887119894




119895as


119894119895= 0


119895as


119894119895= 0








period


119904is 119901119888-coverage




Minimize 119862119905 (1)

subject to


119889119895119896

gt 119889max 997904rArr 119890119895119896

= 0 forall119895 119896 119895 = 119909 + 119910 + 1 (2)

119861119894119895cup 119860119894119895= 1 997904rArr 119889




119909+119910

sum

119895=119909+1

119860119894119895+ 1 ge 119901

119888 forall119894 119894 isin 119878 (5)

119862119895= sum


119884119908 (6)

119884119895= 1 997904rArr 119862

119895ge 119902119888

forall119895 119895 isin 119877 cap (119889119895119909+119910+1

ge 119889max) (7)


119908119895= sum

119894

119887119894119861119894119895

forall119894 119895 119894 isin 119877 119895 isin 119878 (8)

119909+119910+1

sum

119896=119909+1

119890119895119896minus

119909+119910

sum

119896=119909+1

119890119896119895

= 119908119895 forall119895 119895 isin 119878 (9)

119879119895=

119909+119910+1

sum

119896=119909+1

119890119895119896 forall119895 119895 isin 119878 (10)

119866119895= 120573

119909+119910+1

sum

119896=119909+1

119890119895119896(119889119895119896)119904

forall119895 119895 isin 119878 (11)

119877119895=

119909+119910

sum

119896=119909+1

119890119896119895 forall119895 119895 isin 119878 cup 119895 = 119909 + 119910 + 1 (12)

119864119895= 1205721119877119895+ 1205722119879119895+ 1205721119908119895+ 119866119895


(13)


119886 le 119889119895le 119887 (14)

120590 = radic1

119873

119873

sum

119895=1

(119889119895minus 119906)2

le 119879 (15)
























3 Solution



119894119895119861119894119895 and119884






119904are zero due









(1) 120587minus1

(2) 120587minus1


minus1


1 1198812 119881




1 1198812 119881

119896 is






1015840




vertex of 119906 is 1198811 1198812 119881

119896 due to |120587(V

1) 120587(V

119896)| le


120587(V1) 120587(V

119896) let 120587(119906) = 119895 and then 120587 is a Δ(119866) + 1







i = i + 1

No

Yes

End



i = n

120587(1) = 1 i = 1



C(i+1) = 120587(j) jle i|





1= 1205722= 50 nJbit 120573 =



119904






= 119902119888


Chro

mat

ic n

umbe

r


4

6

8

10


119888= 119902119888= 1


Chro

mat

ic n

umbe

r

4

6

8

10

12

14


119888= 119902119888= 1







Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2


Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2






Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 1

Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 2



rom

atic

num

ber

6

4

2

0

8

10

12


No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


119888= 119902119888





119895


119895








Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2





No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


70

60

50

40

30

20

10

0


Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2



No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH





rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













3 Solution



119894119895119861119894119895 and119884






119904are zero due









(1) 120587minus1

(2) 120587minus1


minus1


1 1198812 119881




1 1198812 119881

119896 is






1015840




vertex of 119906 is 1198811 1198812 119881

119896 due to |120587(V

1) 120587(V

119896)| le


120587(V1) 120587(V

119896) let 120587(119906) = 119895 and then 120587 is a Δ(119866) + 1







i = i + 1

No

Yes

End



i = n

120587(1) = 1 i = 1



C(i+1) = 120587(j) jle i|





1= 1205722= 50 nJbit 120573 =



119904






= 119902119888


Chro

mat

ic n

umbe

r


4

6

8

10


119888= 119902119888= 1


Chro

mat

ic n

umbe

r

4

6

8

10

12

14


119888= 119902119888= 1







Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2


Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2






Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 1

Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 2



rom

atic

num

ber

6

4

2

0

8

10

12


No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


119888= 119902119888





119895


119895








Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2





No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


70

60

50

40

30

20

10

0


Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2



No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH





rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













i = i + 1

No

Yes

End



i = n

120587(1) = 1 i = 1



C(i+1) = 120587(j) jle i|





1= 1205722= 50 nJbit 120573 =



119904






= 119902119888


Chro

mat

ic n

umbe

r


4

6

8

10


119888= 119902119888= 1


Chro

mat

ic n

umbe

r

4

6

8

10

12

14


119888= 119902119888= 1







Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2


Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2






Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 1

Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 2



rom

atic

num

ber

6

4

2

0

8

10

12


No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


119888= 119902119888





119895


119895








Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2





No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


70

60

50

40

30

20

10

0


Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2



No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH





rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2


Chro

mat

ic n

umbe

r

6

8

10

12

14


119888= 119902119888= 2






Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 1

Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

14


No RERE-Lv 1

RE-Lv 2RE-Lv 3


119888=

119902119888= 2



rom

atic

num

ber

6

4

2

0

8

10

12


No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


119888= 119902119888





119895


119895








Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2





No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


70

60

50

40

30

20

10

0


Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2



No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH





rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










rom

atic

num

ber

6

4

2

0

8

10

12


No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


119888= 119902119888





119895


119895








Chro

mat

ic n

umbe

r

6

4

2

0

8

10

12

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


119888= 119902119888= 2


No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2





No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


70

60

50

40

30

20

10

0


Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2



No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH





rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











No RTRT-Lv 1

RT-Lv 2RT-Lv 3

30E + 40

25E + 40

20E + 40

15E + 40

10E + 40

50E + 30

00E + 00

Life

time i

n ro

unds


119888= 119902119888= 2

No RDRD-Lv 1

RD-Lv 2RD-Lv 3


70

60

50

40

30

20

10

0


Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2



No RDRD-Lv 1

RD-Lv 2RD-Lv 3

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red


119888= 119902119888= 2


70

60

50

40

30

20

10

0

Num

ber o

f rela

y no

des r

equi

red

ILP-AllILP-RED

ILP-BariILP-ZH





rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










rom

atic

num

ber

6

4

2

0

8

10

12


ILP-AllILP-RED

ILP-BariILP-ZH




5 Conclusion



119901119888-coverage and 119902






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

















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









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