research article a cluster-based fuzzy fusion algorithm...

Research ArticleA Cluster-Based Fuzzy Fusion Algorithm for Event Detection inHeterogeneous Wireless Sensor Networks

ZiQi Hao1 ZhenJiang Zhang1 and Han-Chieh Chao2

1Key Laboratory of Communication and Information Systems School of Electronic and Information EngineeringBeijing Municipal Commission of Education Beijing Jiaotong University Beijing 100044 China2Department of Electronic Engineering National Ilan University Yilan 26047 Taiwan

Correspondence should be addressed to ZhenJiang Zhang zhjzhang1bjtueducn

Received 2 November 2014 Accepted 22 December 2014

Academic Editor Qing-An Zeng

Copyright copy 2015 ZiQi Hao 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

As limited energy is one of the tough challenges in wireless sensor networks (WSN) energy saving becomes important in increasingthe lifecycle of the network Data fusion enables combining information from several sources thus to provide a unified scenariowhich can significantly save sensor energy and enhance sensing data accuracy In this paper we propose a cluster-based data fusionalgorithm for event detectionWe use 119896-means algorithm to form the nodes into clusters which can significantly reduce the energyconsumption of intracluster communication Distances between cluster heads and event and energy of clusters are fuzzified thus touse a fuzzy logic to select the clusters that will participate in data uploading and fusion Fuzzy logic method is also used by clusterheads for local decision and then the local decision results are sent to the base station Decision-level fusion for final decision ofevent is performed by base station according to the uploaded local decisions and fusion support degree of clusters calculated byfuzzy logic method The effectiveness of this algorithm is demonstrated by simulation results

1 Introduction

Recent advances of low-cost wireless sensor networks havebrought about many applications such as military environ-mental monitoring and intelligent transportation systemEvent detection has been widely studied as a typical applica-tion of WSN

Heterogeneous wireless sensor networks (HWSN) arenetworks composed of different kinds of sensors which aredifferent in some aspects such as energy computing powerand storage space In HWSN such as a cluster-based networkcluster heads are more powerful than cluster members in allthe resources like power storage communication and proce-ssing data this heterogeneity alleviates the overhead of clustermembers for the fact that all the expensive computationscan be performed by cluster headers [1] Therefore theload-balance and lifetime of network can be significantlyimproved

Data fusion is a technology that enables combining infor-mation from several sources in order to form a unified pic-ture and it is widely used in various areas such as sensor

networks robotics and video and image processing [2] Asan efficient method for collaborative decision making ofmultiple sensors data fusion has many advantages in WSNUsing multiple sensors to detect the same event can largelyeliminate data ambiguity which may be caused by only onesensor thus to enhance data reliability and ability of faulttolerance effectively Moreover as WSN is energy limitednetwork the sensors are generally battery powered and oncedeployed it is hard to be recharged therefore energy savingbecomes an important factor for expanding the lifetime ofWSN Concerning the fact that energy consumption causedby communication is considerably larger than that of dataprocessing when data fusion is performed sensor data arefused and only the result is forwarded thus the number ofmessages is reduced which can significantly avoid collisionsand save communication energy

Clustering is a frequently used physical architecture ofdata fusion it groups sensor nodes into several clusters inorder to achieve the network scalability objective [3] Everycluster has a cluster head (CH) for executing data fusion andserving as a relay as a consequence CH consumes more

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 641235 11 pageshttpdxdoiorg1011552015641235

2 Journal of Sensors

energy than ordinary sensor nodes therefore a more pow-erful sensor is more likely to be selected as a cluster head

Fuzzy reasoning is a theoretical reasoning scheme of datafusion it introduces the novel notion of membership degreewhich enables dealing with imperfect data appropriately [4]Generally the sensing data of a single sensor may be vagueand partial thus it is difficult to obtain the final fusion deci-sion result via precisely quantitative calculation of these imp-erfect data Fuzzy logic uses themembership degree to fuzzifythe partial data and then combines themwith fuzzy rules thusto produce fuzzy output which is an efficient solution to dealwith the uncertainty of data

Previous researchesmainly focus ondesigning or improv-ing the fusion or clustering algorithms independently fewworks have combined the two technologies together to per-formmonitoring taskThe authors of [5] have proposed a clu-ster based multisensor data fusion algorithm in WSN usingfuzzy logic for event detection the method adopted fuzzylogic approach to handle the uncertainty and vagueness pre-sent in the environment data in the local decision period ofcluster head However the proposed fuzzy logic fusionmeth-od only considers data level fusion of intracluster withoutdesigning the specific clustering algorithm and decision-levelfusion method

In this paper we proposed a cluster-based fusion methodfor event detection We consider a heterogeneous wirelesssensor networks deployment environment where two kindsof sensor nodes exist one is ordinary sensors which we assu-me to be same with nodes in [5] where each sensor node isequipped with diverse sensors (temperature humidity lightand Carbon Monoxide) thus data of different attributes canbe gained The other kind of sensor is mobile nodes whichhave the properties ofmobility andhigh energyMobile nodesserve as CHs which will move from random deployed initialposition to the corresponding destinations calculated by 119896-means algorithm The proposed 119896-means based clusteringalgorithm can achieveminimumenergy consumption of intr-acluster communication The function of CH is performingintracluster fusion and local decision and it also serves asdelay for sending the local decision results to the base stationIn order to enhance the accuracy of event detection wepropose a fusion support degree for each cluster which meansthe probability for a cluster to participate in the decision-level fusion for final decision of emergency eventThe clustersof which the value of fusion support degree is less than apredefined threshold will be rejected from the data fusionwhile the value serves as weight of local decisions whenperforming decision-level fusion The fusion support degreeis determined by distance between CH and event centre andremaining energy of CH and cluster members Finally thebase station will perform decision-level fusion according tolocal decisions and fusion support degrees uploaded by CHsof clusters will join the data fusion to make final decision andmake corresponding warning alarms

The rest of paper is organized as follows we present ourrelated work in Section 2 Section 3 is some preliminariesbefore we introduce our cluster based fuzzy decision fusionalgorithm (CFDF) Section 4 gives the CFDF overview and

detailed descriptions In Section 5 we evaluate the perfor-mance of the proposed algorithm We conclude this paper inSection 6

2 Related Work

Numerous researches have been done in the field of datafusion and clustering In this section we give some reviewof the related work

Khaleghi et al [2] give a critical review of data fusionstate-of-the-art methodologies a new data centric taxonomyof data fusion methodologies was introduced and the chal-lenging aspects and existing algorithms in each category arediscussed The date-related data fusion algorithms can bedivided into dealing with data imperfection data correla-tion data inconsistency and data disparateness Generallyresearches and algorithms about data fusion mainly focus onthree levels [6] The lowest level fusion is data-level fusionof which the processing is to merge the observed raw dataRaw sensor data can be directly combined if the sensor dataare commensurate Techniques for raw data fusion typicallyinvolve classic detection and estimation methods such asaveraging method However if the data are uncorrelated thefusion should be performed at a feature or a decision levelFeature-level fusion can be performed after data-level fusionor directly performed by a single sensor In feature-levelfusion features are extracted from multiple sensor observa-tions and combined into a single feature vector for decision-level fusion Decision-level fusion is the highest level fusionof which the main idea is fusion of local decisions of eachsensor the local decision is a preliminary determinationof an entityrsquos location attributes identity and so on Themost commonly used decision-level fusion methods includevoting techniques Bayesian inference andDempster-Shaferrsquosmethod [6]

Gok et al in [7] proposed a decision-level fusion algo-rithmbased on fuzzy logic used for single target classificationThe research adopts 119896NN to make local decisions whichmight cost a lot of time because it needs quite a few numberof training samples to train classifiers At each node a fusionchancewill be calculated according to the distance and energyof received information using a fuzzy method The proposeddecision-level fusion method achieves high efficiency on theoccasion that the number of sensors is quite small Howeverwhen a large number of sensor nodes are needed in a givensensing field using every sensor to conduct local decision anduploading decision results will result in massive extra infor-mation processing and communication energy consumptionGrouping the sensors into several clusters could be a goodway to solve the above problem in that the majority of dataprocessing and transmission could be done at CHs

Clustering algorithms in the literature vary in their objec-tives often the objective is related to application requirements[3] For example if the application is sensitive to data delaythe connectivity and length of data routing paths are usuallyconsidered as critical problems Some other popular prob-lems such as load balancing fault-tolerance minimal clustercount andmaximal network longevity are also concerned In

Journal of Sensors 3

the field of distributed clustering algorithms each sensor exe-cutes the algorithm independently and their states are basedon the cluster membership decisions on their own statesLow Energy Adaptive Clustering Hierarchy (LEACH) [8] isthemost popular distributed clustering algorithm a dynamicadaptive probability-based CH selecting mechanism wasproposed Unlike the LEACH of which the selection ofCHs is random hybrid energy-efficient distributed clustering(HEED) [9] proposes a CH selecting method considering ahybrid of energy and communication cost DWEHC in [10]proposed by Ding et al can achieve more aggressive goalsthan those of HEED the weight of CH is based on its residualenergy and distance to its neighbors and the largest weightnode in a neighborhoodmay become a CH Simulation resu-lts illustrated that DWEHC can do better in load-balance andhas 119874(1) time complexity

Manjunatha et al in [5] suggested a data fusion methodbased on clustering for environment monitoring In the pro-posed method each sensor is equipped with diverse sensorsand the processing and fusion of these diverse sensor signalsare carried out by CHs using proposed fuzzy rule based sys-tem The reliability and accuracy of environmental detectionare gained by multiple data fusion However this paper didnot give a complete data fusion processing for it only consid-ered fusion of intracluster and multiple sensing variables butthe decision-level fusion of intercluster was not mentioned

3 Preliminaries

In this section wewill give a brief introduction to somemath-ematical models used in our proposed cluster-based fusionmodel and also give some assumptions under the monitoringenvironment of this paper

31 A Brief Introduction to 119896-Means Algorithm 119896-means clus-tering [11] is one of the simplest unsupervised learning algo-rithms that solve the clustering problem The specific objec-tive of 119896-means is to classify a given data set into a certainnumber of clusters (assume 119896 clusters) The main idea is todefine 119896 centroids randomly or in a cunning way beforehandand then assign each data point to the closest centroid to bea member of the current cluster the first round is completedafter all the data points are assigned By now 119896 clusters areconstructed and next the second round will be performed byrecalculating 119896 new centroids as barycenters of the clustersresulting from the previous round and then a new bindinghas to be done between the same data set points and the near-est new centroids And then do this loop until centroids donot move any more

Finally this algorithm aims at minimizing an objectivefunction in this case a squared error function The objectivefunction

119869 =

119896

sum

119895=1

119899

sum

119894=1

100381710038171003817100381710038171003817119909(119895)

119894minus 119888119895

100381710038171003817100381710038171003817

2

(1)

where 119909(119895)119894minus 1198881198952 is a chosen distance measure between a

data point 119909(119895)119894

and the cluster centre 119888119895 is an indicator of

the distance of the 119899 data points from their respective clustercentresThe specific steps of 119896-means are described as follows[12]

(1) Place 119896 points into the space represented by the obje-cts that are being clustered These points representinitial group centroids

(2) Assign each object to the group that has the closestcentroid

(3) When all objects have been assigned recalculate thepositions of the 119896 centroids

(4) Repeat Steps (2) and (3) until the centroids no longermove This produces a separation of the objects intogroups fromwhich themetric to beminimized can becalculated

32 The Fuzzy Theory Introduction The concept of fuzzy setwas proposed by Zadeh in 1965 [4] and the introduction offuzzy theory is to deal with problems involving knowledgeexpressed in vague or linguistic terms especially when theboundary of the set contained in the universe is ambiguousvague or fuzzy [5] In general crisp set the relation betweenan element and a given set is that the element is either belong-ing to the set or not However in a fuzzy set the element is notdefinitely belonging to a set or not instead some ambiguity orvagueness may exist thus elements belong to a fuzzy set to acertain degree represented by a number in interval [0 1] Thenumber is called membership degree the larger the value ofmembership degree is the greater the degree of the elementbelonging to the set isWhen the values of all the elements areeither 0 or 1 the fuzzy set will degenerate into a crisp set

Considering a set 119883 whose element is represented by 119909the membership function 120583

119860(119909) is a function that associates

with each 119909 in119883 with a membership degree in [0 1] A fuzzyset 119860 in 119883 is a set of ordered pairs and is given as 119860 =

119909119894 120583119860(119909) 119909119894 isin 119883 where 119909119894 represents the element in a fuzzyset 119860

Fuzzy logic inference is a process using the fuzzy inputand fuzzy rules to obtain the fuzzy output of which the sub-stance is to map the input space into a given output spaceby fuzzy roles The fuzzy roles normally use the IFTHENstatement the format of which is IF 119909 is119860Then 119910 is 119861 where119909 119910 are the input linguistic variable and output linguisticvariable and 119860 119861 are the linguistic value of fuzzy set beforereasoning and after reasoning respectively Mamdani fuzzyinference system proposed by Ebrabim Mamdani in 1975 isa widely used fuzzy inference method which can implementthe reasoning computation from input to output effectivelythrough a serious of predefined fuzzy roles

33 Assumptions In this paper we consider a cluster-baseddata fusion algorithm for event detection our research isbased on the following assumptions

(1) To simplify the complexity of the problem we assumethe sensing field is a flat two-dimensional region nobarriers exist thus the mobile nodes can smoothlymove inside the sensing area And also the nodes are


uniformly deployed in the sensing filed and cannot berecharged after deployment

(2) In consideration of load-balance problem we adopt aheterogeneousWSN composed of two kinds of sensornodes general static nodes and mobile nodes themobile nodes will act as CHs and the energy of whichis preset higher than that of general nodes becauseCHs will consume more energy on data transmissionand processing

(3) Each sensor node can achieve its location by a GPSmodule or some other techniques such as the methodproposed in [13] The locations will be forwarded toBS only once and stored by BS for the subsequentclustering and fusion calculation

(4) Like LCA [14] a single-hop intracluster topology isestablished by our proposed 119896-means based clusteringalgorithm and TDMA is used for intracluster com-munication Intercluster uses multiple-hop routing toarrive at the sink node

4 Cluster Based Fuzzy FusionAlgorithm (CBFFA)

In this section we will introduce our proposed cluster-basedfuzzy fusion algorithm (CBFFA) Considering the time com-plexity of clusteringmay decline the efficiency of event detec-tion we proposed a centralized none-event driven clusteringmethod namely the clustering is performed before someevent occurs Algorithm 1 illustrated the pseudocode ofCBFFA

Our proposed CBFFA includes three phases the initialclustering phase event detection phase and finally the eventwarning phase In initial phase the sensor nodes (includingstatic nodes and mobile nodes) are randomly deployed inthe two-dimensional sensing filed and each sensor sends itsposition coordinate to the BS viamultihop routingTherewiththe 119896-means based clustering algorithm (119896BCA) will beconducted We assume that the number of mobile nodes willbe larger than that of clusters and the remaining mobilenodes which are not selected to be the CH will serve asspare nodes The detailed description of the proposed 119896-means based clustering algorithm (119896BCA) is introduced inSection 41 After dividing the nodes in sensing filed into 119896clusters the event detection will be performed When anemergency arises it will be detected by the sensors aroundimmediately In this paper we assume the location of theevent centre to be the position coordinates of the sensorwhich first detects the event

It is obvious that a considerable number of sensors in eachcluster can achieve the sensing data for event detection Inthis paper our objective is to select the clusters of which thesensing accuracy is relatively high to carry out data fusionthus to improve accuracy of event detection Meanwhile forprolonging the lifetime of the wholeWSN the clusters havingrelatively low energy are not recommended to join in the datafusion Instead they will switch into sleeping mode

The accuracy of the monitoring data may vary with thedistance between sensor and the event centre when the dista-nce increases the accuracy will decline In addition the rema-ining energy of sensors also has an influence to the accu-racy of the event detection considering both sending andreceiving information will consume energy of sensors whena sensor has little energy and cannot be recharged duringtransmitting the sensing data may fail to be sent thus thetransmission reliability is closely related to the remainingenergy of sensors We proposed a fuzzy theory based methodto decide the chance (fusion support degree) of a clusterto participate in the data fusion the fusion support degreeis calculated in the BS according to the uploaded distancevalue between CH and event centre and average remainingenergy value of a cluster The specific calculation process offusion support degree is described in Section 42 When thefusion support degree is less than a predefined thresholdwhich means the cluster is either quite far from the eventcentre or lower in energy as explained before the sensingdata accuracy of these clusters will be very low Thereforethese clusters will be rejected from data fusion and enter intosleeping mode The clusters of which fusion support degreeis larger than threshold will conduct data transmission andfusionHere the fusion support degree is a value that explainsthe credibility of a clusterrsquos local decision the higher the valueis the more contribution the local decision will bring to thefinal decision-level fusion result Finally the final decision-level fusion will be conducted at the BS and afterwards thecorresponding early warning information will be made

41 119896-Means Based Clustering In this section we will intro-duce the 119896-means based clustering algorithm (119896BCA) The119896-means clustering algorithm can be viewed as a greedyalgorithm for partitioning the 119899 samples into 119896 clusters so asto minimize the sum of the squared distances to the clustercenters And for sensor nodes the transmission energy con-sumption is closely dependent on transmission distancewhich is proportional to squared Euclidean distance or quad-ruplicate Euclidean distance [15] Therefore 119896BCA will havegood performance for decreasing intracluster energy con-sumption However the initialized centroids and the valueof 119896 are not specified in the algorithm Usually the initialcentroids are determined by random way and 119896 is a man-made value In this paper we adopt a cunning way to deter-mine the value of 119896 and the centroidsrsquo initial position thatis we selected the least possible value of 119896 to guarantee thenetwork connectivity and initial positions of centroids aresuggested to be uniformity distributed and far from eachother Algorithm 2 illustrated the pseudocode of 119896BCA

First we should determine the number of clusters accord-ing to size of a clusterWe adopt themean of numbers of staticnodes inside the circle centred by each of 119873119896 mobile nodesto be the size of a cluster In consideration of connectivityintercluster the radius of the circle is suggested to be 1198771198884In order to increase the convergence speed of 119896-means theinitial centroids should be far from each other thuswe appro-ximately divide the sensing field into 119896 number of squaresand let centres of them be initial centroids After running 119896-means algorithm the convergent centroids are achieved and


NotationsBS the base station119896119894 the number of static nodes in cluster 119894119864CM 119864CH initial energy of cluster members and CH respectively119864CM119894 average remaining energy of members in cluster 119894119901CM 119901CH weighting factors of cluster member and CH satisfying 119901CM + 119901CH = 1119864119862119894

average remaining energy of cluster 119894119875119894 a predefined threshold to determine a cluster will join fusion or not119896meansBasedClustering(nodes) the clustering algorithm based on 119896-means proposed in this paperFusionSupportDegree(CH119894) the chance of a cluster to participate in the final decision-level fusionLocalDecision(CH119894) intra-cluster fusion and local decision performed by CH119894DecisionLevelFusion(CHs) the process of decision-level fusion conducted by BSInitialization clustering phase(1) Deploy all the nodes (both the static nodes and mobile nodes) randomly in the sensing filed(2) For each static node do(3) Send its location (119909119894 119910119894) to BS via multi-hop routing(4) Vector staticNodes(119894)larr (119909119894 119910119894)

(5) End for(6) For each mobile node do(7) Send its location (119909119888119894 119910119888119894) to BS via multi-hop routing(8) Vector mobileNodes(119894)larr (119909119888119894 119910119888119894)

(9) End for(10) 119896meansBasedClustering(matrix nodes)Event detection phase(1) If an event occurs(2) Then the first node that detect the event sent its location (119909event 119910event) to BS var multi-hop routing(3) For each cluster head CH

119894

(4) 119889119888119894 larr radic(119909119888119894 minus 119909event)2 + (119910119888119894 minus 119910event)

2

(5) End for(6) For each CM119895 in 119862119894(7) Send its remaining energy 119864119895 to 119862119894(8) End for(9) For each 119862119894

(10) 119864CM119894 larr1

119896119894

119896119894

sum

119895=0

119864119895 119864119862119894larr 119901CM

119864CM119894

119864CM+ 119901CH

119864CHi

119864CH

(11) Send 119864119862119894 to BS(12) End for(13) For each cluster head CH

119894

(14) 119875119894 larr FusionSupportDegree(CH119894)(15) If 119875119894 gt 119875119904(16) Then(17) 119863119862119894

larr LocalDecision(CH119894)(18) 119863119862119894

is sent to BS(19) Else(20) 119862119894 turns on sleep mode(21) End If(22) End For(23) 119875final larr DecisionLevelFusion(CHs)(24) End IfEvent alert phase(1) BS makes the corresponding early warning information according to decision-level fusion result

Algorithm 1 Pseudocode of cluster based fuzzy fusion algorithm (CBFFA)

next the mobile nodes server as CHs should move to thesecentroids thus to ensureminimizing the energy consumptionof intracluster communication A variety of methods can beused to choose CHs and match them to the locations of

centroids the most common one is greedy method for eachof the 119896 centroids the nearest mobile node will be chosen as aCH and move to location of the current centroid To achieveglobal optimum Hungarian method can be used to obtain


Notations119877119888 communication range of the CH

119873119896 a selected number of mobile nodes to determine number of clusters 119896Static nodes number of static nodesInput Coordinates of static nodes Vector staticNodesDetermine value of 119896(1) For 119894 = 1 119873119896(2) For all static nodes (119909119895 119910119895) If

(3) radic(119909119895 minus 119909119888119894)2 + (119910119895 minus 119910119888119894)

2 le119877119888

2(4) Static Number(119894)(++)(5) End for(6) End for

(7) cluster sizelarr 1

119873119896

119873119896

sum

119894=1

Static Number(119894)

(8) 119896 larr static nodescluster size

(9) Divide the sensing field into 119896 squares and order the centres of squares to be initial positions of centroidsDetermine converged centroids using 119896-means(1) Let initial initial positions of centroids to be1198981 1198982 119898119896(2) Until there are no changes in any mean(3) Use the estimated means to classify the samples into clusters(4) For 119894 from 1 to 119896(5) Replace119898119894 with the mean of all of the samples for cluster 119894(6) End For(7) End UntilMotion period for CHs(1) Select 119896mobile nodes and dispatch them to locations of119898

1 1198982 119898

119896using greedy method or Hungarian method

Algorithm 2 Pseudocode of 119896-means based clustering algorithm (119896BCA)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 4

Cluster 3

Cluster 2

Figure 1 Clustering result of 119896BCA

the optimalmatchingwhich canminimize the overallmovingdistance of mobile sensors Figure 1 shows the clusteringresult of 119896BCA

42 The Fusion Support Degree The fusion support degree isa value that measures the reliability for the measured data of

a cluster As discussed before the accuracy of event detectionis closely related to distance between the sensor and eventand the remaining energy of a sensor thus this paper usesdistance and remaining energy to decide the fusion supportdegree Generally we use far or near to describe a distanceand use high or low to describe energyHowever the linguisticvariables suchlike far or highmay include some level of unce-rtainty and vagueness Therefore the final decision result ofevent may be imprecise if crisp sets of distance and energyare used to deal with data fusion As fuzzy logic can deal withthe knowledge of which the boundaries are not clear throughmembership function for this reason we adopt fuzzy logicmethod to calculate fusion support degreeWe adopt a similarmethod as proposed in [7] using distance and remainingenergy as two fuzzy input variables and fusion supportdegree as fuzzy output Figure 2 illustrated the structure offuzzy logic method where the distance and energy are crispinput variables and fusion support degree is crisp output afterdefuzzification

To simplify the analysis for problem trapezoidal andtriangular membership function is defined to describe fuzzyinput variables distance and energy The membership func-tions and corresponding linguistic states of distance andenergy are shown in Figures 3(a) and 3(b)

Figure 4 shows the membership functions and corre-sponding linguistic states of fuzzy output variable namelyfusion support degree We introduce the same membership


Distance

Energy

Mamdani fuzzy

inference system

Fuzzy rules

Fuzzification

Fuzzification

DefuzzificationFusion support degree

Fuzzy logic system

Figure 2 Structure of fuzzy logic method

functions used in [7] The fusion support degree is dividedinto nine levels namely LL (Low in Low) LM (Mediumin Low) LH (High in Low) ML (Low in Medium) MM(Medium in Medium) MH (Medium in High) HL (Low inHigh) HM (Medium in High) and HH (High in High) andthe fusion support degree they represent is successively larger

Table 1 illustrated fuzzy rules for our fuzzy algorithmIn research [7] the authors consider a sensing environmentwith obstacles thus even the sensor is relatively near fromthe target the sensing accuracy may be low due to obstaclesTherefore they give more weight on energy fuzzy variablethan distance when dealing with fuzzy output In this paperwe assume no obstacles exist so the accuracy is largely relatedto distance consequently in most cases we give fuzzy inputvariable distance more weight However under the circumst-ances that remaining energy of cluster is quite low to prolongthe lifetime of networks the cluster having low energy is notsuggested to join the fusion thus we give more weight onenergy when the remaining energy is low

After fuzzy variables and fuzzy rules are designed a fuzzyinference method should be used to achieve fuzzy outputthus to get the final system outputs (FusionSupportDe-gree(CHi) in Algorithm 1) through defuzzification In thispaper we use the most commonly used fuzzy inference sys-tem namely Mamdani method to obtain fuzzy output

43 Local Decision We take fire detection as an example ofevent detection In this scenario fire centre can be modeledas a fixed coordinate point in the sensing filed Each sensorhas an integrated multiple sensors module which can collectenvironmental information such as temperature humiditylight intensity and the amount ofCarbonMonoxide (CO) [5]thus the sensing data structure of a sensor can be describedas a multidimensional vector (V1 V2 V119899) where V119894 (1 le

119894 le 119899) stands for the value of 119894th environmental informationvariable

After fusion support degrees of each cluster are calculatedby BS the clusters whose fusion support degrees are lessthan the threshold will be eliminated from fusion processingwhich means they will not conduct data uploading and datafusion while the clusters whose fusion support degrees arelarger than the threshold will perform local decision andupload decision results thus to join the final decision-level

Table 1 Fuzzy rules for our fuzzy algorithm

Rulenumber Distance Energy Fusion support

degree1 Far High MM2 Far Medium ML3 Far Low LL4 Medium High HL5 Medium Medium MH6 Medium Low LM7 Near High HH8 Near Medium HM9 Near Low LH

fusion The local decision of a cluster includes two stepsFirstly all sensors inside a cluster send their sensing data toCH then intracluster fusion is performed by CH Secondlyaccording to the fusion results the CH will make the localdecision which reflects evaluation of emergency level for thecurrent cluster to event

When all sensors inside a cluster have sent their sensingdata to the CH intracluster data fusion is conducted Weuse the mean of sensing values of each dimension to beintracluster fusion result Considering that some sensorsmight have a possibility of being damaged during deployingwhich will reduce the accuracy of sensing data thus thesesingular sensors should be eliminated before data fusion

Note that the multidimensional vector of cluster 119894 afterfusion is represented by (V1198941 V1198942 V119894119899) The mean of these119899 variables will be used to conduct local decision howeverit is not easy to achieve a quantitative equation for localdecision result therefore we adopt the fuzzy logic methodsame as proposed in Section 42 to get local decision resultby fuzzifying each dimension of (V1198941 V1198942 V119894119899) to be fuzzyinput and defining decision result as fuzzy output variableThis paper did not design the specific fuzzy sets and rules forfuzzy input and output so that the designing of fuzzy sets isclosely dependant on the type of events when event changesfuzzy input and fuzzy rules will change as well

44 Decision-Level Fusion The result of local decision dis-cussed in Section 43 is a percentage value calculated by asingle cluster which illustrated the possibility an event willhappen or the degree of emergencyThe decision-level fusionmeans combining local decisions from several clusters to geta final evaluation of the event The fusion support degreeand local decision result introduced before are preparedfor decision-level fusion and (2) shows calculation of finaldecision-level fusion result

119875final =sum119901119894gt119901119904

119875119894119863119888119894

sum119901119894gt119901119904

119875119894

(2)

where 119875119894 denotes fusion support degree of cluster 119894 and 119863119888119894denotes local decision result of cluster 119894 If 119875final is larger thana threshold BS will make the corresponding early warninginformation according to fusion result


0 5 10 15 20 25 30 35 40 45 500

05

1

15

Distance between sensor node and event

Mem

bers

hip

degr

ee

NearMedium

Far

(a)

0 01 02 03 04 05 06 07 08 09 10

05

1

15

Normalized average remaining energy of cluster

Mem

bers

hip

degr

ee

HighLowMedium

(b)

Figure 3 (a) Fuzzy sets for distance between sensor and event (b) Fuzzy sets for remaining energy

0 10 20 30 40 50 60 70 80 90 1000

02

04

06

08

1

12

Fusion support degree ()

Mem

bers

hip

degr

ee

LLLMLH

MLMMMH

HLHMHH

Figure 4 Fuzzy sets for fuzzy output variable fusion support degree

5 Results and Discussion

In this section we will evaluate the performance of our pro-posed cluster-based fuzzy decision fusion algorithm (CFD-FA) The simulation is implemented in Matlab We assumethe sensing area to be a flat two-dimensional square region ofwhich the size is 50m times 50m 200 static sensor nodes and 15mobile nodes are randomly deployed on the sensing area andthe communication radius (sensors can communicate witheach other when their distance is less than communicationradius) is assumed to be 30m We take fire detection as anexample of event detection and the sensing data structure of asensor is defined as a multidimensional vector (temperaturelight intensity and CO density)

51 Analysis of 119896-Means Based Clustering Algorithm (119896BCA)Firstly we give a simulation of the initial clustering algorithm

119896BCA According to Algorithm 2 we order 119873119896 = 5 thenthe cluster size is estimated by (3) of which the value is 355The value means the maximum size a cluster could be soas to meet the connectivity of the network Consequentlythe number of clusters should be more than the value of200355 = 56

cluster sizelarr997888 1

119873119896

119873119896

sum

119894=1

Static Number (119894) (3)

Figure 5 shows the clustering results when the number ofcluster changes It is obvious that with the increasing ofcluster number the number of members in a cluster reducesconsequently Therefore the average communication energyconsumption of a cluster will reduce

In order to analyze lifetime of thewhole network Figure 6gives a quantitative analysis of overall communication dis-tance and variance of cluster size when number of clusterschangesWhen the cluster number changes from 5 to 15 thereis a declining trend of the overall distance which illustratesthat the larger the cluster number is themore energy-efficientthe network will be Generally the lifecycle of whole networkin a clustering environment is not only related to the overallcommunication consumption but also related to balance ofcluster size A balanced clustering means that clusters haveapproximate sizes thus to guarantee balance of energy con-sumption between different clusters As shown in Figure 6the variance of cluster sizes changes irregularly when the clus-ter number is less than 10 however when cluster number islarger than 10 the variance has a decline trend Above analysisconcludes that number of clusters will definitely influencethe lifecycle of whole network In some certain circumstancethe more the cluster number is the more energy-efficientand load-balanced the network will be However increasingof cluster number will cause a corresponding increasing of


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 4

Cluster 1

Cluster 2

Cluster 3

Cluster 6

Cluster 5

(a)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

(b)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(c)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(d)

Figure 5 Clustering results of 119896BCA when cluster number 119896 changes (a) 119896 = 6 (b) 119896 = 7 (c) 119896 = 8 (d) 119896 = 15

5 6 7 8 9 10 11 12 13 14 150

02

04

06

08

1

Cluster numbers

Ove

rall

dist

ance

of i

ntra

cluste

ran

d va

rianc

e for

clus

ter s

ize

Overall distanceVariance of cluster size

Figure 6 Overall distance of intracluster and variance of cluster sizewhen cluster number 119896 changes

mobile nodes generally mobile nodes are more expensivethan ordinary nodes thus with the increasing of cluster

number the cost of whole networkwill be increased either Sothere is a tradeoff between lifetime and cost of the networkthe number of cluster should be designed according to theactual situation

52 Simulation for Event Detection Tomake the compromisebetween the lifecycle and expense of network the clusternumber is proposed to be 12 Figure 7 shows the assumedevent detection scenario 12 clusters are formed by 119896BCAand a random event occurs with a location of (2818) Nextthe fusion support degree of each cluster is calculated byfuzzy method introduced in Section 42 We use the fuzzylogic toolbox on Matlab to simulate the fuzzy output Table 2illustrates the fusion support degree results of 12 clusters inwhich the distance means distance between fire centre andCH and energymeans the average residual energy of a clusterWe define the threshold of fusion support degree to be 40Therefore cluster 5 cluster 8 and cluster 10 will be rejectedfrom data fusion and enter into sleeping mode the data


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9

Figure 7 Event detection scenario when cluster number is 12

Table 2 Fusion support degree of clusters

Clusternumber Distance Energy () Fusion support

degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70

fusion and event detection processing are performed by theremaining 9 clusters

In the simulation of local decision we use the same fuzzysets of inputs and output variables as proposed in [5] 33 = 27rules are designed some of the example rules are as follows

IF Temperature is low and light intensity is low andCO is low THEN fire probability is vary lowIF Temperature is high and light intensity is high andCO is high THEN fire probability is vary highIF Temperature is medium and light intensity is highand CO is high THEN fire probability is high

Table 3 is the local decisions for clusters whichmeans the fireprobability evaluated by the current cluster

Finally the final decision-level fusion is calculated byformula (2) the result is 119875final = 605 meaning that thereis a probability of 605 that a fire disaster could happen

Table 3 Local decisions for clusters

Rulenumber

Fusion supportdegree

Intraclusterfusion result

Fire probability(119863119888119894) ()

1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75

The final result and corresponding early warning informationwill be sent to users for disaster prevention

53 Algorithm Complexity Analysis At last we will give thecomputation complexity evaluation of the proposed CFDFAIt has been calculated that the time complexity of 119896-meansis 119874(119905119896119889119899) where 119905 is number of iterations 119896 is number ofclusters 119899 is number of data objects and 119889 is the dimension(equals 2 in this paper) The time complexity of eventdetection is 119874(119899 + 4119896 + 2119898 + 1) where 119898 is number ofclusters taking part in data fusion Therefore the total timecomplexity is 119874(119899) which means the proposed algorithmis completed in linear time thus it is efficient and enablesscalability when dealing with large data sets Moreover as theclustering is performed once the sensors are deployed beforeevent occurs the time consumption of clustering can beignoredwhen analyzing the efficiency of event detection thusthe proposed algorithm is efficient enough for detecting andreporting sudden events

6 Conclusions

In order to enhance the accuracy of event detection thispaper proposed a cluster-based data fusion algorithm usingfuzzy logic method (CFDFA) for event detection in a het-erogeneous wireless sensor network In terms of the energy-efficient problem in WSN we suggested a 119896-means basedclustering algorithm (119896BCA) the clustering algorithm canefficiently reduce energy consumption of intracluster andsimulation results illustrated that when a proper cluster num-ber is chosen well load-balance of cluster size can also begained thus the lifetime of network can be prolonged A crispform of possibility of event occurrence can be achieved bybase station after CFDFA is performed we take fire detectionas an example to simulate our event detection algorithm andget crisp value of the fire probability

In the future we may consider more complicated scenar-ios where the event is no longer static thus an event-drivendynamic clustering algorithm will be designed Moreover wemay work onmore details about the efficient intracluster datafusion algorithms suitable for our event detection algorithmwhere singular point detectionmay be a key point to be consi-dered


Conflict of Interests

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

Acknowledgments

This research is supported by National Natural Science Foun-dation under Grant 61371071 Beijing Natural Science Foun-dation under Grant 4132057 and Academic Discipline andPostgraduate Education Project of Beijing Municipal Com-mission of Education

References

[1] B Premamayudu V Rao and S Varma ldquoA key managementamp establishment scheme in heterogeneous wireless sensor net-works (HWSN)rdquo International Journal of Applied EngineeringResearch vol 9 no 20 pp 6813ndash6821 2014

[2] B Khaleghi A Khamis F O Karray and S N Razavi ldquoMulti-sensor data fusion a review of the state-of-the-artrdquo InformationFusion vol 14 no 1 pp 28ndash44 2013

[3] A A Abbasi andM Younis ldquoA survey on clustering algorithmsfor wireless sensor networksrdquo Computer Communications vol30 no 14-15 pp 2826ndash2841 2007

[4] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[5] PManjunatha A KVerma andA Srividya ldquoMulti-sensor datafusion in cluster based wireless sensor networks using fuzzylogic methodrdquo in Proceedings of the IEEE Region 10 and the 3rdInternational Conference on Industrial and Information Systems(ICIIS rsquo08) pp 1ndash6 IEEE Kharagpur India December 2008

[6] D L Hall and J Llinas ldquoAn introduction to multisensor datafusionrdquo Proceedings of the IEEE vol 85 no 1 pp 6ndash23 1997

[7] S Gok A Yazici A Cosar and R George ldquoFuzzy decision fus-ion for single target classification in wireless sensor networksrdquoin Proceedings of the IEEE International Conference on FuzzySystems (FUZZ rsquo10) pp 1ndash8 Barcelona Spain July 2010

[8] W B Heinzelman A P Chandrakasan and H Balakrish-nan ldquoAn application-specific protocol architecture for wirelessmicrosensor networksrdquo IEEE Transactions onWireless Commu-nications vol 1 no 4 pp 660ndash670 2002

[9] O Younis and S Fahmy ldquoHEED a hybrid energy-efficientdistributed clustering approach for ad hoc sensor networksrdquoIEEE Transactions on Mobile Computing vol 3 no 4 pp 366ndash379 2004

[10] P Ding J A Holliday and A Celik ldquoDistributed energy-efficient hierarchical clustering for wireless sensor networksrdquoin Distributed Computing in Sensor Systems vol 3560 ofLectureNotes inComputer Science pp 322ndash339 Springer BerlinGermany 2005

[11] J B MacQueen ldquoSome methods for classification and analysisof multivariate observationsrdquo in Proceedings of 5th BerkeleySymposium on Mathematical Statistics and Probability vol 1pp 281ndash297 University of California Press Berkeley Calif USA1967

[12] httphomedeibpolimiitmatteuccClusteringtutorial htmlkmeanshtml

[13] D Niculescu and B Nath ldquoAd hoc positioning system (APS)using AOArdquo in Proceedings of the 22nd Annual Joint Conference

of the IEEE Computer and Communications (INFOCOM rsquo03)vol 3 pp 1734ndash1743 2003

[14] A Ephremides J E Wieselthier and D J Baker ldquoA designconcept for reliable mobile radio networks with frequencyhopping signalingrdquo Proceedings of the IEEE vol 75 no 1 pp56ndash73 1987

[15] P Ding J A Holliday and A Celik ldquoDistributed energy-efficient hierarchical clustering for wireless sensor networksrdquoin Distributed Computing in Sensor Systems Lecture Notes inComputer Science pp 322ndash339 Springer Berlin Germany2005

International Journal of

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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



energy than ordinary sensor nodes therefore a more pow-erful sensor is more likely to be selected as a cluster head

Fuzzy reasoning is a theoretical reasoning scheme of datafusion it introduces the novel notion of membership degreewhich enables dealing with imperfect data appropriately [4]Generally the sensing data of a single sensor may be vagueand partial thus it is difficult to obtain the final fusion deci-sion result via precisely quantitative calculation of these imp-erfect data Fuzzy logic uses themembership degree to fuzzifythe partial data and then combines themwith fuzzy rules thusto produce fuzzy output which is an efficient solution to dealwith the uncertainty of data

Previous researchesmainly focus ondesigning or improv-ing the fusion or clustering algorithms independently fewworks have combined the two technologies together to per-formmonitoring taskThe authors of [5] have proposed a clu-ster based multisensor data fusion algorithm in WSN usingfuzzy logic for event detection the method adopted fuzzylogic approach to handle the uncertainty and vagueness pre-sent in the environment data in the local decision period ofcluster head However the proposed fuzzy logic fusionmeth-od only considers data level fusion of intracluster withoutdesigning the specific clustering algorithm and decision-levelfusion method

In this paper we proposed a cluster-based fusion methodfor event detection We consider a heterogeneous wirelesssensor networks deployment environment where two kindsof sensor nodes exist one is ordinary sensors which we assu-me to be same with nodes in [5] where each sensor node isequipped with diverse sensors (temperature humidity lightand Carbon Monoxide) thus data of different attributes canbe gained The other kind of sensor is mobile nodes whichhave the properties ofmobility andhigh energyMobile nodesserve as CHs which will move from random deployed initialposition to the corresponding destinations calculated by 119896-means algorithm The proposed 119896-means based clusteringalgorithm can achieveminimumenergy consumption of intr-acluster communication The function of CH is performingintracluster fusion and local decision and it also serves asdelay for sending the local decision results to the base stationIn order to enhance the accuracy of event detection wepropose a fusion support degree for each cluster which meansthe probability for a cluster to participate in the decision-level fusion for final decision of emergency eventThe clustersof which the value of fusion support degree is less than apredefined threshold will be rejected from the data fusionwhile the value serves as weight of local decisions whenperforming decision-level fusion The fusion support degreeis determined by distance between CH and event centre andremaining energy of CH and cluster members Finally thebase station will perform decision-level fusion according tolocal decisions and fusion support degrees uploaded by CHsof clusters will join the data fusion to make final decision andmake corresponding warning alarms

The rest of paper is organized as follows we present ourrelated work in Section 2 Section 3 is some preliminariesbefore we introduce our cluster based fuzzy decision fusionalgorithm (CFDF) Section 4 gives the CFDF overview and

detailed descriptions In Section 5 we evaluate the perfor-mance of the proposed algorithm We conclude this paper inSection 6

2 Related Work

Numerous researches have been done in the field of datafusion and clustering In this section we give some reviewof the related work

Khaleghi et al [2] give a critical review of data fusionstate-of-the-art methodologies a new data centric taxonomyof data fusion methodologies was introduced and the chal-lenging aspects and existing algorithms in each category arediscussed The date-related data fusion algorithms can bedivided into dealing with data imperfection data correla-tion data inconsistency and data disparateness Generallyresearches and algorithms about data fusion mainly focus onthree levels [6] The lowest level fusion is data-level fusionof which the processing is to merge the observed raw dataRaw sensor data can be directly combined if the sensor dataare commensurate Techniques for raw data fusion typicallyinvolve classic detection and estimation methods such asaveraging method However if the data are uncorrelated thefusion should be performed at a feature or a decision levelFeature-level fusion can be performed after data-level fusionor directly performed by a single sensor In feature-levelfusion features are extracted from multiple sensor observa-tions and combined into a single feature vector for decision-level fusion Decision-level fusion is the highest level fusionof which the main idea is fusion of local decisions of eachsensor the local decision is a preliminary determinationof an entityrsquos location attributes identity and so on Themost commonly used decision-level fusion methods includevoting techniques Bayesian inference andDempster-Shaferrsquosmethod [6]

Gok et al in [7] proposed a decision-level fusion algo-rithmbased on fuzzy logic used for single target classificationThe research adopts 119896NN to make local decisions whichmight cost a lot of time because it needs quite a few numberof training samples to train classifiers At each node a fusionchancewill be calculated according to the distance and energyof received information using a fuzzy method The proposeddecision-level fusion method achieves high efficiency on theoccasion that the number of sensors is quite small Howeverwhen a large number of sensor nodes are needed in a givensensing field using every sensor to conduct local decision anduploading decision results will result in massive extra infor-mation processing and communication energy consumptionGrouping the sensors into several clusters could be a goodway to solve the above problem in that the majority of dataprocessing and transmission could be done at CHs

Clustering algorithms in the literature vary in their objec-tives often the objective is related to application requirements[3] For example if the application is sensitive to data delaythe connectivity and length of data routing paths are usuallyconsidered as critical problems Some other popular prob-lems such as load balancing fault-tolerance minimal clustercount andmaximal network longevity are also concerned In




3 Preliminaries




119869 =

119896

sum

119895=1

119899

sum

119894=1

100381710038171003817100381710038171003817119909(119895)

119894minus 119888119895

100381710038171003817100381710038171003817

2

(1)


data point 119909(119895)119894
































119894


2


(10) 119864CM119894 larr1

119896119894

119896119894

sum

119895=0

119864119895 119864119862119894larr 119901CM

119864CM119894

119864CM+ 119901CH

119864CHi

119864CH


119894











2 le119877119888



119873119896

119873119896

sum

119894=1




1 1198982 119898



0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 4

Cluster 3

Cluster 2








Distance

Energy

Mamdani fuzzy

inference system

Fuzzy rules

Fuzzification

Fuzzification


Fuzzy logic system















119875final =sum119901119894gt119901119904

119875119894119863119888119894

sum119901119894gt119901119904

119875119894

(2)



0 5 10 15 20 25 30 35 40 45 500

05

1

15


Mem

bers

hip

degr

ee

NearMedium

Far

(a)

0 01 02 03 04 05 06 07 08 09 10

05

1

15


Mem

bers

hip

degr

ee

HighLowMedium

(b)


0 10 20 30 40 50 60 70 80 90 1000

02

04

06

08

1

12


Mem

bers

hip

degr

ee

LLLMLH

MLMMMH

HLHMHH







119873119896

119873119896

sum

119894=1





0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 4

Cluster 1

Cluster 2

Cluster 3

Cluster 6

Cluster 5

(a)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

(b)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(c)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(d)


5 6 7 8 9 10 11 12 13 14 150

02

04

06

08

1

Cluster numbers

Ove

rall

dist

ance

of i

ntra

cluste

ran

d va

rianc

e for

clus

ter s

ize







0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9




degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70







Rulenumber




1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75



6 Conclusions






Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












3 Preliminaries




119869 =

119896

sum

119895=1

119899

sum

119894=1

100381710038171003817100381710038171003817119909(119895)

119894minus 119888119895

100381710038171003817100381710038171003817

2

(1)


data point 119909(119895)119894
































119894


2


(10) 119864CM119894 larr1

119896119894

119896119894

sum

119895=0

119864119895 119864119862119894larr 119901CM

119864CM119894

119864CM+ 119901CH

119864CHi

119864CH


119894











2 le119877119888



119873119896

119873119896

sum

119894=1




1 1198982 119898



0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 4

Cluster 3

Cluster 2








Distance

Energy

Mamdani fuzzy

inference system

Fuzzy rules

Fuzzification

Fuzzification


Fuzzy logic system















119875final =sum119901119894gt119901119904

119875119894119863119888119894

sum119901119894gt119901119904

119875119894

(2)



0 5 10 15 20 25 30 35 40 45 500

05

1

15


Mem

bers

hip

degr

ee

NearMedium

Far

(a)

0 01 02 03 04 05 06 07 08 09 10

05

1

15


Mem

bers

hip

degr

ee

HighLowMedium

(b)


0 10 20 30 40 50 60 70 80 90 1000

02

04

06

08

1

12


Mem

bers

hip

degr

ee

LLLMLH

MLMMMH

HLHMHH







119873119896

119873119896

sum

119894=1





0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 4

Cluster 1

Cluster 2

Cluster 3

Cluster 6

Cluster 5

(a)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

(b)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(c)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(d)


5 6 7 8 9 10 11 12 13 14 150

02

04

06

08

1

Cluster numbers

Ove

rall

dist

ance

of i

ntra

cluste

ran

d va

rianc

e for

clus

ter s

ize







0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9




degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70







Rulenumber




1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75



6 Conclusions






Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























119894


2


(10) 119864CM119894 larr1

119896119894

119896119894

sum

119895=0

119864119895 119864119862119894larr 119901CM

119864CM119894

119864CM+ 119901CH

119864CHi

119864CH


119894











2 le119877119888



119873119896

119873119896

sum

119894=1




1 1198982 119898



0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 4

Cluster 3

Cluster 2








Distance

Energy

Mamdani fuzzy

inference system

Fuzzy rules

Fuzzification

Fuzzification


Fuzzy logic system















119875final =sum119901119894gt119901119904

119875119894119863119888119894

sum119901119894gt119901119904

119875119894

(2)



0 5 10 15 20 25 30 35 40 45 500

05

1

15


Mem

bers

hip

degr

ee

NearMedium

Far

(a)

0 01 02 03 04 05 06 07 08 09 10

05

1

15


Mem

bers

hip

degr

ee

HighLowMedium

(b)


0 10 20 30 40 50 60 70 80 90 1000

02

04

06

08

1

12


Mem

bers

hip

degr

ee

LLLMLH

MLMMMH

HLHMHH







119873119896

119873119896

sum

119894=1





0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 4

Cluster 1

Cluster 2

Cluster 3

Cluster 6

Cluster 5

(a)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

(b)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(c)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(d)


5 6 7 8 9 10 11 12 13 14 150

02

04

06

08

1

Cluster numbers

Ove

rall

dist

ance

of i

ntra

cluste

ran

d va

rianc

e for

clus

ter s

ize







0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9




degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70







Rulenumber




1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75



6 Conclusions






Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













2 le119877119888



119873119896

119873119896

sum

119894=1




1 1198982 119898



0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 4

Cluster 3

Cluster 2








Distance

Energy

Mamdani fuzzy

inference system

Fuzzy rules

Fuzzification

Fuzzification


Fuzzy logic system















119875final =sum119901119894gt119901119904

119875119894119863119888119894

sum119901119894gt119901119904

119875119894

(2)



0 5 10 15 20 25 30 35 40 45 500

05

1

15


Mem

bers

hip

degr

ee

NearMedium

Far

(a)

0 01 02 03 04 05 06 07 08 09 10

05

1

15


Mem

bers

hip

degr

ee

HighLowMedium

(b)


0 10 20 30 40 50 60 70 80 90 1000

02

04

06

08

1

12


Mem

bers

hip

degr

ee

LLLMLH

MLMMMH

HLHMHH







119873119896

119873119896

sum

119894=1





0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 4

Cluster 1

Cluster 2

Cluster 3

Cluster 6

Cluster 5

(a)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

(b)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(c)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(d)


5 6 7 8 9 10 11 12 13 14 150

02

04

06

08

1

Cluster numbers

Ove

rall

dist

ance

of i

ntra

cluste

ran

d va

rianc

e for

clus

ter s

ize







0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9




degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70







Rulenumber




1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75



6 Conclusions






Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Distance

Energy

Mamdani fuzzy

inference system

Fuzzy rules

Fuzzification

Fuzzification


Fuzzy logic system















119875final =sum119901119894gt119901119904

119875119894119863119888119894

sum119901119894gt119901119904

119875119894

(2)



0 5 10 15 20 25 30 35 40 45 500

05

1

15


Mem

bers

hip

degr

ee

NearMedium

Far

(a)

0 01 02 03 04 05 06 07 08 09 10

05

1

15


Mem

bers

hip

degr

ee

HighLowMedium

(b)


0 10 20 30 40 50 60 70 80 90 1000

02

04

06

08

1

12


Mem

bers

hip

degr

ee

LLLMLH

MLMMMH

HLHMHH







119873119896

119873119896

sum

119894=1





0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 4

Cluster 1

Cluster 2

Cluster 3

Cluster 6

Cluster 5

(a)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

(b)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(c)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(d)


5 6 7 8 9 10 11 12 13 14 150

02

04

06

08

1

Cluster numbers

Ove

rall

dist

ance

of i

ntra

cluste

ran

d va

rianc

e for

clus

ter s

ize







0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9




degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70







Rulenumber




1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75



6 Conclusions






Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25 30 35 40 45 500

05

1

15


Mem

bers

hip

degr

ee

NearMedium

Far

(a)

0 01 02 03 04 05 06 07 08 09 10

05

1

15


Mem

bers

hip

degr

ee

HighLowMedium

(b)


0 10 20 30 40 50 60 70 80 90 1000

02

04

06

08

1

12


Mem

bers

hip

degr

ee

LLLMLH

MLMMMH

HLHMHH







119873119896

119873119896

sum

119894=1





0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 4

Cluster 1

Cluster 2

Cluster 3

Cluster 6

Cluster 5

(a)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

(b)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(c)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(d)


5 6 7 8 9 10 11 12 13 14 150

02

04

06

08

1

Cluster numbers

Ove

rall

dist

ance

of i

ntra

cluste

ran

d va

rianc

e for

clus

ter s

ize







0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9




degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70







Rulenumber




1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75



6 Conclusions






Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 4

Cluster 1

Cluster 2

Cluster 3

Cluster 6

Cluster 5

(a)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

(b)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(c)

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

(d)


5 6 7 8 9 10 11 12 13 14 150

02

04

06

08

1

Cluster numbers

Ove

rall

dist

ance

of i

ntra

cluste

ran

d va

rianc

e for

clus

ter s

ize







0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9




degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70







Rulenumber




1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75



6 Conclusions






Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

511

7

12

2 Event

31

4

6

8

10 9




degree (119875119894) ()1 2703 083 6162 317 035 6863 2772 073 5734 2124 066 6275 1576 013 206 1400 085 7497 1774 069 6528 3008 035 3279 1941 045 6010 1427 023 21411 2527 048 58712 1569 095 70







Rulenumber




1 616 (21 322 52) 3152 686 (80 875 85) 9223 573 (30 300 38) 4454 627 (23 225 41) 326 749 (60 810 80) 9167 652 (40 355 81) 759 60 (35 450 60) 62511 587 (20 268 50) 2512 70 (38 303 71) 75



6 Conclusions






Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












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 a cluster-based fuzzy fusion algorithm...

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