An Information Entropy Based Event Boundary Detection Algorithm in Wireless Sensor Networks

Transcription

1 S S symmetry Artcle An Informaton Entropy Based Event Boundary Detecton Algorm n Wreless Sensor Networks Huafeng Wu, Qngshun Meng, Jangfeng Xan, *, Xaojun Me, Chrstophe Claramunt and Junkuo Cao 3, * Merchant Marne College, Shangha Martme Unversty, Shangha 0306, Chna; hfwu@shmtu.edu.cn (H.W.); mengqngshun@stu.shmtu.edu.cn (Q.M.); xjme94@63.com (X.M.) Naval Academy Research Insttute, Lanveoc-Poulmc, BP 600, 940 Brest Naval, France; chrstophe.claramunt@gmal.com 3 Network and Data Center, Hanan Normal Unversty, Hakou 5758, Chna * Correspondence: xanjangfeng030@63.com (J.X.); cjk@hannu.edu.cn (J.C.); Tel.: (J.X.) Receved: 6 March 09; Accepted: Aprl 09; Publshed: 5 Aprl 09 Abstract: Wreless Sensor Networks (WSNs) have been extensvely appled n ecologcal envronment montorng. Typcally, event boundary detecton s an effectve meod to determne e scope an event area n large-scale envronment montorng. Ths paper proposes a novel lghtweght Entropy based Event Boundary Detecton algorm (EEBD) n WSNs. We frst develop a statstc model usng nformaton entropy to fgure out e probablty at a sensor s a boundary sensor. The EEBD s ndependently executed on each wreless sensor n order to judge wheer t s a boundary sensor node, by comparng e values entropy aganst e reshold whch depends on e boundary wd. Smulaton results demonstrate at e EEBD s computable and fers valuable detecton accuracy boundary nodes w bo low and hgh network node densty. Ths study also ncludes experments at verfy e EEBD whch s applcable n a real ocean envronmental montorng scenaro usng WSNs. Keywords: event boundary detecton; nformaton entropy; wreless sensor networks; determnng rules; ecologcal envronment montorng. Introducton Wreless Sensor Networks (WSNs) are composed a consderable number low-cost, low-power and small-szed wreless sensors and have ganed partcular nterest for many envronment applcatons []. These sensor nodes are ten utlzed to montor and detect real-world events lke ol dffuson, fres, chemcal leaks by montorng varous physcal parameters such as humdty, concentraton, temperature, salnty and so on. In many montorng tasks, e core goal WSNs s to detect and track unexpected and abnormal events n real tme [,3]. Event boundary detecton s partcular mportance to determne e scope event occurrence and make preventve measures when unfortunate events happen n e envronment. In many cases, an event may spread over a network and sensor-based area an rregular shape. After a sudden ncdent such as ol spll polluton, tmely and accurate detecton e dffuson range events requres lots sensor nodes to work togeer and consumes large amounts energy. When compared w e analyss e entre event area, event boundary detecton s more effcent as t provdes a proper vew e sensors at wll be affected by broadcast messages [4]. Ths paper proposes a new lghtweght Event Boundary Detecton dstrbuted algorm (EEBD) to dentfy e real event boundary sensor nodes a montorng area usng WSNs. Two man prncples Informaton Entropy, at s, uncertanty and nformaton quantty [5], are appled to fgure out e Symmetry 09,, 537; do:0.3390/sym

2 Symmetry 09,, probablty a node beng a boundary node. We ntroduce an entropy based algorm at determnes e boundary nodes by comparng e values entropy amongst e neghbourng nodes. A seres smulatons show at e EEBD algorm provdes good precson when detectng event boundares.. Related Work Several studes have been presented to solve e problem event boundary detecton. A non-rangng event area detecton algorm to predct e event regon consdered as crcular has been ntroduced [6]. In Reference [7], e auors propose a graph eory based locaton-free event boundary detecton algorm at can adjust bo network parameters and e reshold dynamcally. In Reference [8], e auors propose a dstrbuted n-network event boundary detecton algorm usng e node s local nformaton to determne spatal and temporal evoluton event boundary. The auors n Reference [9] proposed an algorm for detectng boundary nodes based on a combnaton statstcs w model classfcaton and selecton. A maematcal statstcal meod for edge node detecton s presented n References [0,], where e am s to decde wheer a boundary canddate node s located on e real boundary an event regon rough nformaton nteracton w ts neghbourng nodes. In Reference [], e auors take nto account e spatal temporal correlaton sensors to detect boundary nodes. A decentralzed fault-tolerant event regon detecton meod s put forward n Reference [3]. It can accurately dentfy fault nodes and elmnate e abnormal sensed data to avert false detecton. At e expermental level, ey tuned every reshold to get hgher boundary fttng accuracy. In Reference [4], e auors presented a Secure Event Boundary Detecton (SEBD) meod utlzng local level nformaton. Ths approach s hghly reslent and provdes a good compromse between node detecton and random measurement fault. The man prncple behnd e SEBD approach s at a hghly relable determnaton rule and a system reshold are set for a node to recognze tself as a boundary node. In Reference [5], e hdden markov random feld model and teratve condtons are used to calculate e event coverage n e WSNs but e parameters e markov random model need to be traned by a large amount sample data. In Reference [6], a dstrbuted and locaton-free boundary detecton (DBD) algorm for determnng e event boundary s proposed n moble WSNs. DBD only needs e sensed data sngle node ree-hop neghbours. However, DBD only consders e scenaro a moble sensor node densty less an 0.6, so t s not applcable to WSNs where all sensor nodes move n real tme. In Reference [7], e auors utlzed e QUDG for event boundary area detecton and partton e event boundary area nto dsjont domnatng sets based on graph eory. Through perodc rotatng e dsjont domnatng sets event boundary area n WSNs can realze e lfespan maxmzaton boundary sensors. Two algorms are proposed for dentfyng faulty node and event boundary detecton n Reference [8]. The algorm can acheve accurate boundary node detecton for varous scalar sensed data values. The boundary wd s fxed equal to half e communcaton radus sensors. However, s s not sutable for low network denstes and scenaros w a small communcaton radus nodes because e number boundary nodes ncreases as e network densty and node radus ncrease. Then e communcaton cost e boundary node reports e message to e base staton ncreases. Conversely, f e number boundary nodes s too small, t wll affect e boundary node to ft e real boundary. To sum up, e exstng boundary node detecton algorm s hghly dependent on node sensng data and e bnary decson result a neghbour node w e calculaton error s used as nput data, whch results n cumulatve error. In addton, due to e hgh computatonal complexty and hgh energy consumpton, e meods proposed above are not sutable for event boundary detecton n moble WSNs, such as marne WSNs. 3. Network Model and Assumptons Let us consder a WSN w dense enough sensor nodes evenly deployed n a two-dmensonal sea area nterest called e sensor area at e ntal moment event occurrence. We use e topology

3 Symmetry 09,, x 3 7 Symmetry 09,, varyng sensng sgnal to ts neghbour regon. Normally, e ntensty e sgnal wll decrease w ncreasng dstance from e event centre. An event area s e doman around e actual boundary control scheme e proposed event where n a e prevous ntensty work [9]. sgnal When exceeds an event e gven occurs, reshold e relevant value envronmental Th. Then all sensors parameters n s n e sensor related sea area regon are lkely receve torado change, wave atsgnals s, e event from e reports event a tme-varyng area. The proposed sensng algorm sgnal to ts recommends neghbour a regon. meod Normally, for dentfyng e ntensty boundary nodes. e sgnal wll decrease w ncreasng dstance We from assume eat event sensor centre. nodes An event are area smlar s e n doman terms around er e computaton, actual boundary battery e lfe event and communcaton where e ntensty capablty. sgnal Each exceeds node e works gvenwell reshold and has value a loose Th. Then synchronzaton. all sensors nit s assumes sensorat sea e regon sensor s receve locaton rado wave nformaton sgnals from s correct e event snce area. we requre The proposed e rght algorm sensor s recommends locaton nformaton a meod for e dentfyng accurate boundary detecton nodes. boundary sensor nodes. A seres pror defntons are gven below: We assume at sensor nodes are smlar n terms er computaton, battery lfe and The term sensor area, denoted as, not only refers to e geographcal area covered by e communcaton capablty. Each node works well and has a loose synchronzaton. It assumes WSN but also to e set nodes n s area. We denote an event regon as, whch s e subregon covered by an event and s e remanng regon. Thus, = +. Hence, a at e sensor s locaton nformaton s correct snce we requre e rght sensor s locaton nformaton for e accurate detecton boundary sensor nodes. A seres pror defntons are gven below: sensor node S means t s an The term sensor area, denoted as affected node whle S means t s a normal node., not only refers to e geographcal area covered by e WSN A sensor node S w ts locaton nformaton, at s S( x, y), s consdered to be a but also to e set nodes n s area. We denote an event regon as ω, whch s e sub-regon boundary covered node by when an event t s and on e ϖ s actual e remanng boundary. regon. Let us consder Thus, = a boundary ω + ϖ. Hence, wd a sensor R defned node as S e ω communcaton means t s an affected radus node e whle sensor S S ϖ means accordng t s ato normal [3]. Let node. N( S ) denote e dsk centred A sensor at node S S w ts locaton nformaton, at s S (x, y), s consdered to be a boundary w e radus R. Therefore S s a boundary node f S, B r where node when t s on e actual boundary. Let us consder a boundary wd R defned as e S, B s e geographc dstance between S communcaton radus e sensor S accordng and B e actual boundary. Then e event to [3]. Let N(S ) denote e dsk centred at node boundary S w e Bradus ( S ) R. s Therefore e collecton S s a boundary such boundary node nodes. f S, B r where S, B s e geographc dstance between S and B e actual boundary. Then e event boundary B(S ) s e collecton Suppose at e sensor data nodes n e event area forms a gaussan dstrbuton such boundary nodes. N(, ) and e readngs oer sensors n form anoer dstrbuton N(, ), where Suppose at e sensor data nodes n e event area ω forms a gaussan dstrbuton N(µ, σ ) s small compared w and e readngs oer sensors n ϖ form anoer dstrbuton N(µ, σ ), where σ s small compared w. A sensor node s consdered to be an affected node when ts µ. µ A sensor node s consdered to be an affected node when ts sensng nformaton sensng nformaton exceeds e exceeds e reshold µ = µ reshold +µ, whle e oers are called normal nodes., whle e oers are called normal nodes. Let us suppose at Let eus event suppose boundary at e s aevent crcular boundary boundary s a crcular centredboundary on e event centred source. on e Theevent sensor source. area s The shown sensor n area Fgure s shown, e black n Fgure nodes, are e e black boundary nodes nodes. are e Fgure boundary on nodes. e rght Fgure shows e on e local rght areashows a sngle e local boundary area node. a sngle boundary node. Fgure. An llustraton a sensor area. Fgure. An llustraton a sensor area.

4 Symmetry 09,, x 4 7 Symmetry 09,, Proposed Algorm 4. Proposed Algorm 4.. The Statstcal Boundary Detecton Model 4.. The Our Statstcal goal s to Boundary desgn a dstrbuted Detecton Model algorm for a sngle node to decde wheer t s a boundary sensor Our by goal comparng s to desgn e asensng dstrbuted nformaton algormw for ats sngle neghbour node to decde sensor wheer nodes. Wout s a boundary loss sensor generalty by let comparng us maxmze e sensng e local nformaton boundary regon w ts a neghbour sngle boundary sensor nodes. n Wout Fgure, loss where generalty e actual boundary let us maxmze can be e consdered local boundary a straght regon lne. We a sngle use e boundary nearest boundary node n Fgure tangent, where e e boundary actual node boundary nstead can be e consdered actual boundary a straght a lne. sngle We node. use Because e nearest e boundary event regon tangent s generally e boundary much larger node an nstead e neghbour e actual area boundary a gven node, a sngle e neghbour node. Because area refers e event to e regon area s at generally a node much can cover larger wn an ts ecommuncaton neghbour area radus. a gven node, e neghbour area refers to e area at a node can cover As llustrated wn tsn communcaton Fgure, r s e radus. boundary wd and f an only f S les wn r, can t be consdered As llustrated as a boundary n Fgure sensor., r s Let e boundary denote e wd expected and f number an only f sensor S les nodes wn deployed r, can t per be consdered as a boundary sensor. Let ρ denote e expected number sensor nodes deployed per neghbour area S, called network node densty. Let S denote e neghbour nodes set neghbour area S, called network node densty. Let N S denote e neghbour nodes set sensor node sensor Snode. The S sensors. The sensors n e event n e event area are area denoted are denoted as affected as affected nodes nodes and and e e remanng remanng nodes nodes as normal as normal nodes. nodes. Fgure. An llustraton Boundary Detecton Model. If a node s located exactly on e actual boundary, ts ts neghbour nodes would have have half half nodes nodes as affected as nodes nodes whle whle e e oer oer half half as as normal nodes under e condton large-scale large scale dense sensor node deployment. In oer words, such a node has a hgh probablty beng a boundary node. However, ere s a need for a determnaton ruleto to fgure out wheera a node belongsto tobs B(S (,, r r). Thus, a proper range proporton s needed to measure how close a nodes sto e actual boundary. In order to to formulate formulate s s problem, problem, let uslet ntroduce us ntroduce an entropy an entropy functon functon H(p) to evaluate H() p to e evaluate probablty e probablty a sensor node a sensor s a boundary node s a sensor boundary node. sensor Thenode. entropy The sentropy used ass aused sort as probablty a sort probablty varable at varable evaluates at evaluates e dstrbuton e dstrbuton e sensors e n e sensors neghbourhood n e neghbourhood a gven sensor. a gven Accordng sensor. to Reference Accordng [0], to Reference H(p) s computed [0], Hp () ass computed as H(p) H ( p= ) pp log logp p () where p p denotes e categores nodes among e neghbour nodes w 0,. Let 0 denotes e categores nodes among e neghbour nodes w = 0,. Let = 0 represent e represent category e category normal nodes, normal whle nodes, whle = represents represents e affected e affected nodes, nodes, respectvely. respectvely. Then Then p s computed p s computed as as p = k /(ρ ) ()

5 Symmetry 09,, x 5 7 Symmetry 09,, p k /( ) () where where k k s e number status nodes and ρ s e network node densty. In our case, ere are s e number status nodes and s e network node densty. In our case, total two possbltes w p and q = p, where p denotes e rato affected nodes among total ere are total two possbltes w p and q p, where p denotes e rato affected nodes neghbour nodes, whle q denotes e normal ones. So H can be reduced by among total neghbour nodes, whle q denotes e normal ones. So H can be reduced by whch whch s s schematzed schematzed n n Fgure Fgure 3 3 as as a a functon functon p p.. H = H (p log ( p log p + pq log q log q) q) (3) (3) Fgure Fgure The The characterstcs e e H functon. functon. It appears at e derved values e entropy as denoted n (3) play an mportant role n It appears at e derved values e entropy as denoted n (3) play an mportant role n calculatng e probablty at a sensor node can be defned as a boundary node: calculatng e probablty at a sensor node can be defned as a boundary node:. H = 0 f and only f all e p. f and only f all e but p one are null. Ths means at all e neghbours S but one are null. Ths means at all e neghbours are entrely S are affected or absolutely normal. Oerwse, f H s postve, at s, node S has e probablty to be aentrely boundary affected node. or The absolutely hgher enormal. value Oerwse, H s, closer f H e s postve, node s toat e s, actual node boundary. S has e. When probablty all eto p are be a equal boundary (.e., p = node. q), ethe value hgher H e s e value largest and H s, se log closer. Thse also node ntutvely s to e e actual hgher boundary. probablty a node to be a boundary node. 3.. Any When change all e towards p are equalzaton (.e., p = e q), probabltes e value p, H qs ncreases e largest H. and s log. Ths s also ntutvely e hgher probablty a node to be a boundary node. Fgure 4 s a relatonshp dagram e value H and e number neghbour nodes. Fgure 4 3. Any change towards equalzaton e probabltes p, q ncreases H. shows at entropy H and e number neghbour nodes are postvely correlated. Fgure 4 s a relatonshp dagram e value H and e number neghbour nodes. Fgure 4 shows at entropy H and e number neghbour nodes are postvely correlated.

6 Symmetry 09,, x 6 7 Symmetry 09,, 537 x Entropy Entropy Number Neghbor Nodes Number Neghbor Nodes Fgure 4. Entropy vs. Number Neghbour Nodes. 4.. Determnng Rules Fgure Fgure Entropy Entropy vs. vs. Number Number Neghbour Neghbour Nodes. Nodes. 4.. Determnng Consder Fgure Rules5, where e actual boundary meets e dsk S at dots P and P whle 4.. Determnng Rules e event Consder boundary Fgurewd 5, where lne e meets actual e boundary dsk at dots meets P 3 e and dsk P 4. Therefore, S at dotse P and actual P boundary whle e Consder Fgure 5, where e actual boundary meets e dsk S ntersects event boundary e neghbourng wd lne meets area es dsk at dots P 3 and P 4. Therefore, actual at dots boundary P and ntersects P whle n two areas. Let A represent e left part S separated e neghbourng event boundary area wd S lne two meets areas. e dsk Let Aat represent dots P 3 and e left P 4. part Therefore, N S e separated actual boundary by actual by actual boundary. The remanng area S s represented by A boundary. The remanng area N ntersects e neghbourng area S S s represented. So we estmate e probablty by A n two areas. Let. So we estmate e probablty represent e left part node S separated dstrbuton node dstrbuton usng geometrc usng geometrc probablty. probablty. by actual boundary. The remanng area S s represented by A. So we estmate e probablty node dstrbuton usng geometrc probablty. Fgure Fgure An An llustraton llustraton crtcal crtcal node. node. As n Fgure 5, we consder a node S As n Fgure 5, we consder a Fgure node 5. at satsfes S, B = r as a crtcal node and ts entropy H as e determnng reshold H An at llustraton satsfes crtcal S, B node. r as a crtcal node and ts entropy. A has an area H as e determnng reshold H. A has an area As n Fgure 5, we consder a node A S = at satsfes S, B r as a crtcal node and ts entropy πr + S P P P 3 P 4 (4) H as e determnng reshold H. A A has an Rarea S P PPP (4) 3 4 where S P P P 3 P 4 means e area sector P P P 3 P 4, and where S PPPP means e area sector PPPP 3 4 A 3 4, and R S P PPP (4) 3 4 S P P P 3 P 4 = r R r + R arcsn r (5) rr where S PPPP means e area sector S PPPP , and PPPP r R r R arcsn (5) 3 4 so at we can estmate e probablty affected nodes n N S as R r so at we can estmate e probablty S affected PPPP r R nodes r Rn arcsn S as (5) 3 4 p = R + S P P P 3 P 4 πr (6) so at we can estmate e probablty affected nodes n as S

7 Symmetry 09,, x 7 7 Symmetry 09,, 537 SP 7 7 PPP 3 4 p (6) Meanwhle e probablty normal nodes s q p q = p (7) (7) Accordng to (3), e determnng reshold H s Accordng to (3), e determnng reshold H s H ( p log( p ) q log( q )) (8) H = (p log(p ) + q log(q )) (8) Here let us gve a bref descrpton e case f at f e H S beyond e H at S can be Here determned let us gveas a bref a boundary descrpton node. Consder e case ffgure at e 6, f Hnode S beyond S H at S can be s n e area BS (, r ), determned p as a boundary node. Consder Fgure 6, f node S s n e area B(S, r), p < p and p and q q. Then H H. If node S s outsde BS (, r ), p p and q q. Then q > q. Then H > H. If node S s outsde B(S, r), p > p and q < q. Then H < H. In oer H H. In oer words, nodes at fall nto e area BS (, r ) are more lkely to make p and q words, nodes at fall nto e area B(S, r) are more lkely to make p and q smlar, whch causes e entropy smlar, whch to be greater causes an e entropy H. to be greater an H. R Fgure Fgure An An llustraton llustraton boundary boundary node node and and non boundary non-boundary node. node. By applyng e proposed detecton model, we can set e boundary wd r convenently to By applyng e proposed detecton model, we can set e boundary wd convenently to acheve dfferent detecton goals. However, due to e geometrc probablty meod, e relatonshp acheve dfferent detecton goals. However, due to e geometrc probablty meod, e relatonshp between r and ρ has an mpact on e accuracy e evaluaton. If r s very small, H between r and has an mpact on e accuracy e evaluaton. If r s very can be extremely small, H can be hgh, at s, a few nodes can be detected as boundary nodes. If r s large, H extremely hgh, at s, a few nodes can be detected as boundary nodes. If r becomes very small n s large, H becomes some sataton H even be null as llustrated n Fgure 6. Thus an approprate r should be set to get an accurate very small event n some boundary. sataton H even be null as llustrated n Fgure 6. Thus an approprate r should Consder be set to at get nodes an accurate are deployed event boundary. utlzng e grd parttonng meod, en e area a square Consder grd δ equal at nodes to πr are deployed utlzng e grd parttonng meod, en e area a ρ where ρ s e network node densty. So e grd wd s δ = R πρ. Frstly, R square e grd boundary equal regon to w rwhere should contan s e at least network one square node densty. grd δ asso llustrated e grd nwd Fgure s 7. Secondly, e boundary wd r should not be greater an R δ n order not to make H too small. See R examples for e above stuaton n Fgures. Frstly, e boundary regon w r 7 and 8. To sum up, r should satsfy e should contan at least one square grd as followng nequalty, llustrated n Fgure 7. Secondly, e boundary δ r wd R r should δ not be greater an R n order (9) so not to make H too small. See examples for e above stuaton n Fgures 7 and 8. To sum up, r should satsfy e followng nequalty, π π R ρ r R R (0) ρ r R (9) As a result e nequalty, we get so π π R R R ρr R R () Rρ (0) smplfcaton leads to ρ 4π 3. As a result e nequalty, we get

8 Symmetry 09,, x 8 7 smplfcaton leads to 4 3. smplfcaton leads to 4 3. R R R R R R () () Symmetry 09,, Fgure 7. An llustraton extreme boundary wd. Fgure 7. An llustraton extreme boundary wd. Fgure 7. An llustraton extreme boundary wd. Fgure 8. An llustraton e range boundary wd. Fgure 8. An llustraton e range boundary wd. Fgure 8. An llustraton e range boundary wd. From e above dscusson, t can be seen at e formulaton H From e above dscusson, t can be seen at e formulaton s nfluenced by e s nfluenced by e relatonshp between r, R and ρ. By settng e boundary wd r n a certan range, we can get e relatonshp From e between above dscusson, r, R and t can. By be settng seen e at boundary e formulaton wd r H s nfluenced by e approprate reshold H n a certan range, we can get and en acheve e correspondng detecton results. Ths allows an outlne relatonshp between r, R and. By settng e boundary wd r n a certan range, we can get at e approprate fts e eventreshold boundaryh tobeand customzable. en acheve e correspondng detecton results. Ths allows an e outlne approprate Theat EEBD fts algorm reshold e event boundary conssts H and en to ree be acheve customzable. steps. e Frstly, correspondng each affected detecton node S results. Ths allows an collects nformaton outlne from The tsat neghbour EEBD fts e algorm nodes. event boundary Then conssts t computes to ree be customzable. steps. e value Frstly, Heach accordng affected to node (3), at S collects s nformaton The EEBD algorm conssts ree steps. Frstly, each affected node S collects nformaton from ts neghbour nodes. Then t computes H e value H accordng to (3), at s = (p log p + q log q) () from ts neghbour nodes. Then t computes e value H accordng to (3), at s H ( plog p qlog q) where () number H ( po flog a fpf ected qlog node q) () where p = (3) total neghbor number where number affected node p p = q (4) number total neghbor affected number node (3) Then, sensor node S p reports e value (3) total H and neghbor lstens number to ts neghbours node nformaton. In e rd step, gven boundary wd r and communcaton radus R to calculate e entropy reshold H whch s defned n (8). If H H, node S fnally marks tself as a boundary node. The steps EEBD algorm are as shown below.

9 Symmetry 09,, Algorm : Entropy based Event Boundary Detecton (EEBD) Algorm Input : Node S, boundary wd r, node densty ρ, communcaton radus R and M S = {} Output: broadcast e ID f t s e real event boundary senor node For each sensor node Intalze : compute H accordng to (8), H = 0; step ; Dscover e affected sensor nodes f sensng data > µ flag() else flag() 0 end Broadcast M S := { S, H, f lag() } to ts neghbour nodes f flag() == H (p log p + q log q) Update M S w new H end step ; Broadcast messagem S := { S, H, f lag() } Lsten to ts neghbour nodes step 3 f H H broadcast S as e fnal boundary node to e sn k, B(S, r) 5. Smulaton Results 5.. Smulaton Intalzaton In s smulaton, wreless sensors are unformly dstrbuted n a square area. Suppose at e square area s n e frst quadrant e plane coordnates. We suppose at e test event area s a crcle w a radus 50 and e centre e regon s located at (00, 00). Assume at normal node readngs satsfy e normal dstrbuton N(µ, σ ) whle sensor readngs are depcted form N(µ, σ ) n event area. Then e reshold µ = µ +µ. Mean and varance can be selected accordng to e actual stuaton, as long as e standard devaton s small compared w µ. µ In s smulaton, we set µ = 0, µ = 30, σ=. The communcaton radus s R = 0m. The boundary wd r = R/. The area δ a grd s computed by dvdng e area a crcle dsk N(S ), by e network node densty. The degree fttng (DF) s appled for estmaton accuracy as a performance measure. A(< r) A(d) DF = A(< r) (5) where A(<r) s e node group sgnfyng at e dstance to e boundary s no more an r, whle A(d) s e set boundary nodes whch are detected by proposed meod. False detecton rate (FR) s used to measure detecton error. A(> r) A(d) FR = A(> r) (6) where A(>r) s e set nodes at e dstance to e boundary s beyond r. The hgher DF and e lower FR mean e better performance an algorm does.

10 FR A( r) (6) where A(>r) s e set nodes at e dstance to e boundary s beyond r. The hgher DF and e lower FR mean e better performance an algorm does. Symmetry 09,, Smulaton Results 5.. The Smulaton results are Results averaged over 00 ndependently runs by NS (Network Smulator verson, NS). To The evaluate results e are averaged performance over 00EEBD, ndependently e selected runsbenchmark by NS (Network algorms Smulator are verson DBD [6], and LFEBD NS). [8]. To evaluate We also e suppose performance at nodes EEBD, are unformly e selecteddeployed benchmarkn algorms e montorng are DBD regon [6] and e locatons LFEBD [8]. all one We hop also suppose neghbour at sensors nodes are unformly avalable deployed to a sensor nnode. e montorng Snce s regon s one and e most prevalent locatons and smple all one hop moblty neghbour models, sensors sensor are avalable node moton to a sensor s smulated node. Snce usng se one random e most waypont moton prevalent model and []. smple Wout moblty loss models, generalty, sensor node we report motone s smulated results w usng boundary e random shapes waypont a crcle or a moton straght model lne. []. Fgure Wout 9a shows loss generalty, a vsualzed we result report e EEBD results w boundary network shapes node densty a crcle =0, or a straght lne. Fgure 9a shows a vsualzed result EEBD w network node densty ρ= 0, Fgure 9b presents a vsualzed result EEBD w network node densty Fgure 9b presents a vsualzed result EEBD w network node densty ρ= 0. =0. The small dots The small dots represent represent nodes nodes at at do donot not belong to e boundary sensor nodes nodes whle whle e e bold bold ones ones represent represent e e detected detected boundary sensor nodes. Ths shows at e detected event boundary by EEBD by EEBD gves gves a good a good approxmaton e event boundary as ntroduced n n defnton (a) Fgure 9. Cont.

11 Symmetry 09,, Symmetry 09,, x 7 Symmetry 09,, x (b) (b) Fgure Fgure Vsualzed smulaton result. (a) ρ= =0 (b) (b) ρ= 0. =0. Fgures 0 and show comparatve studes e DF and FR, as mentoned above. From Fgure 0, one Fgures can 0 observe and at show e comparatve proposed algorm studes has e a better DF and degree FR, as mentoned fttng an above. e DBD From and Fgures 0 and show comparatve studes e DF and FR, as mentoned above. From Fgure Fgure LFEBD 0, algorms one can observe when e atnode e proposed densty s algorm under 40. has Ths a better demonstrates degree at fttng e node an e densty DBDs 0, one can observe at e proposed algorm has a better degree fttng an e DBD and and proportonal LFEBD algorms to e DR when n bo e node boundary densty shapes. s under When 40. Ths e densty demonstrates s ncreased, at e e node number densty LFEBD s algorms when e node densty s under 40. Ths demonstrates at e node densty s sensors proportonal n NS ( to ) e wll DRncrease boaccordngly. boundary shapes. Thus, more Whensensors e densty are close s ncreased, to e boundary, e number at s, proportonal sensors n to N(Se ) wll DR ncrease n bo accordngly. boundary Thus, shapes. morewhen sensors e aredensty close to e s ncreased, boundary, at e s, number more more sensors are n e BS (, r ). So e geometrc probablty based on e area s more accurate. sensors sensors n are NS ( n ) e wll B(Sncrease, r). So e accordngly. geometrc probablty Thus, more based sensors on eare areaclose s more to e accurate. boundary, From e at s, From e Fgure 0, w e ncrease n node densty, especally when t s greater an 30, bo e more Fgure degree sensors 0, w are fttng n e ncrease e ncrease BS ( slghtly, n r ) node. So but e densty, our geometrc algorm especally probablty converges when t s earler based greater w on an a e densty 30, area bo s e about more degree 0. accurate. From fttng e Fgure ncrease 0, slghtly w e but our ncrease algorm n node converges densty, earler especally w a densty when t s about greater 0. an 30, bo e degree fttng ncrease slghtly but our algorm converges earler w a densty about 0. Degree fttng Fgure 9. Vsualzed smulaton result. (a) =0 (b) = Degree fttng EEBD for straght lne EEBD for ellpse DBD for straght lne DBD for ellpse LFEBD for straght lne EEBD for straght lne EEBD LFEBD for ellpse DBD for straght lne DBD for 40 ellpse Node densty LFEBD for straght lne 0.3 Fgure LFEBD for ellpse Degree fttng vs. vs. network densty. 0. Fgure Fgure shows shows aa comparatve comparatve study study FR. Node FR. The The EEBD densty EEBD algorm algorm false false detecton detecton rate rate gradually gradually decreased decreased w w e e ncrease ncrease node node densty densty but but e e FR FR e e proposed proposed algorm algorm s s slghtly slghtly hgher hgher an an e e LFEBD LFEBD and and DBD DBD algorm, Fgure algorm, 0. especally Degree especally n fttng n e e case vs. case network low low node node densty. densty densty but but stll stll n n aa very very small small range. Ths s owng to e small number neghbour sensors n e case low densty, whch Fgure causes e shows entropy a comparatve e node whch study s close FR. The to crtcal EEBD nodes algorm to fluctuate false detecton beyond e rate entropy gradually decreased w e ncrease node densty but e FR e proposed algorm s slghtly hgher an e LFEBD and DBD algorm, especally n e case low node densty but stll n a very small

12 Symmetry 09,, Symmetry 09,, x 7 range. Symmetry Ths 09, s owng, x to e small number neghbour sensors n e case low densty, whch causes 7 e entropy e node whch s close to crtcal nodes to fluctuate beyond e entropy reshold but reshold but s error decreases w e ncrease e node densty. Thus, even f e node beng s reshold error decreases but s w error e decreases ncrease w e node ncrease densty. e Thus, node even densty. f e Thus, nodeeven beng f e msjudged node beng s msjudged s stll near e boundary, s has lttle effect on fttng e event boundary. For practcal stll msjudged near e s boundary, stll near s e boundary, has lttle effect s on has fttng lttle effect e event on fttng boundary. e event For practcal boundary. applcatons, For practcal applcatons, ere s a certan error wn e acceptable range. ere applcatons, s a certanere error s wn certan eerror acceptable wn range. e acceptable range. False False detecton detecton rate rate Node densty Vs.FR 0.0 Node densty Vs.FR 0.0 EEBD for straght lne EEBD EEBD for for ellpse straght lne EEBD for ellpse DBD for straght lne DBD DBD for for ellpse straght lne LFEBD DBD for for ellpse straght lne LFEBD for for ellpse straght lne LFEBD for ellpse Node densty densty Fgure. False detecton rate vs. network densty. Fgure Fgure.. False False detecton rate rate vs. vs. network densty. Fgure Fgure Fgure shows shows shows at at at settng settng e e e dfferent dfferent boundary boundary wd wd wd has has has lttle lttle lttle effect effect effect on on on e e e accuracy accuracy e e e detecton detecton under under under e e e constrant constrant condtons. condtons. Ths Ths Ths permts permts us us us to to to try try try to to to choose choose few few few boundary boundary nodes, nodes, nodes, bo bo bo to to to ft ft ft e e e event event event boundary boundary but but but also also also save save save data data data fuson fuson fuson and and and communcaton communcaton costs. costs. costs. Fgure Fgure.. Degree Degree fttng fttng vs. vs. boundary boundary wd. wd. Fgure. Degree fttng vs. boundary wd. WSNs can be deployed on a large scale n target montorng sea areas and are ten utlzed WSNs can be deployed on large scale n target montorng sea areas and are ten utlzed to to montor WSNs ocean can be nformaton deployed on such a large as lght, scale ocean n target currents, montorng wnd sea drecton, areas and hydrology are ten and utlzed waterto montor ocean nformaton such as lght, ocean currents, wnd drecton, hydrology and water polluton. montor Aocean second nformaton seres smulatons such as lght, hasocean been made currents, n anwnd oceandrecton, montorng hydrology experment and usng water polluton. A second seres smulatons has been made n an ocean montorng experment usng WSNs. polluton. In e marne second envronment, seres smulatons e poston has been e node made and n an ts ocean relatve montorng poston toexperment e oer nodes usng WSNs. In e marne envronment, e poston e node and ts relatve poston to e oer nodes are WSNs. tme-varyng. In e marne We randomly envronment, select e 50 80% poston nodes e node as moble and ts nodes relatve andposton e remanng to e oer nodes nodes are are tme varyng. We randomly select 50 80% nodes as moble nodes and e remanng nodes are anchor are tme varyng. nodes. The smulaton We randomly set e select moble 50 80% node speed nodes from as moble 6 to 0 nodes m/s to and demonstrate e remanng more dfferent nodes are anchor nodes. The smulaton set e moble node speed from 6 to 0 m/s to demonstrate more performances anchor nodes. EEBD. The smulaton We use eset random e moble waypont node model speed to characterze from to 0 em/s movement to demonstrate e sensor more dfferent performances EEBD. We use e random waypont model to characterze e movement nodes. dfferent A marne performances sensor node EEBD. renews We tsuse own e one-hop random neghbourng waypont model nodeto data characterze at tme ntervals e movement 5 0 s. e sensor nodes. A marne sensor node renews ts own one hop neghbourng node data at tme The relatonshp e sensor nodes. between marne e detecton sensor rates node and renews nodets speed own are one hop dsplayed neghbourng n Fgure 3. node As e data densty at tme ntervals 5 0 s. The relatonshp between e detecton rates and node speed are dsplayed n Fgure ntervals 5 0 s. The relatonshp between e detecton rates and node speed are dsplayed n Fgure 3. As e densty e moble node ncreases, e value detecton rate decreases. As can be seen 3. As e densty e moble node ncreases, e value detecton rate decreases. As can be seen from Fgure 3, e updatng nterval greatly affects e event boundary detecton rate. The from Fgure 3, e updatng nterval greatly affects e event boundary detecton rate. The relatonshp between updatng nterval and boundary detecton rate s nversely proportonal. relatonshp between updatng nterval and boundary detecton rate s nversely proportonal.

13 Symmetry 09,, e moble node ncreases, e value detecton rate decreases. As can be seen from Fgure 3, e Symmetry updatng 09, nterval, x greatly affects e event boundary detecton rate. The relatonshp between 3 7 updatng nterval and boundary detecton rate s nversely proportonal. (a) (b) Fgure 3. Cont.

14 Symmetry Symmetry 09, 09,,, 537 x (c) (d) Fgure The The boundary detecton rates EEBD w dfferent denstes marne moble nodes. (a) (a) 50%. 50%. (b) (b) 60%. (c) (c) 70%. (d) (d) 80%. Fgure Fgure 4 4 presents presents e e computer computer smulaton smulaton dagram dagram marne marne event event boundary boundary detecton detecton usng usng 5 buoy 5 buoy nodes nodes at ntegrate at ntegrate multple multple marne marne sensors. sensors. Fgure Fgure 5 shows 5 e shows vsualzed e vsualzed smulaton smulaton result result boundary boundary detecton detecton obtaned obtaned by e EEBD by e algorm. EEBD algorm. As can be As seen can be from seen Fgure from 5, Fgure e EBBD 5, e algorm EBBD algorm acheves acheves accurate accurate event boundary event boundary detecton detecton at low buoy at low node buoy denstes. node denstes.

15 Symmetry 09,, 537 Symmetry Symmetry 09, 09,,, xx Fgure Fgure Marne Marne experment experment scenaro scenaro dagram. dagram. Fgure Fgure Vsualzed Vsualzed smulaton smulaton result result marne marne event event boundary. boundary Effcency Effcency Evaluaton Evaluaton 5.3. Overall, communcaton communcaton consumpton consumpton s s e e most most mportant mportant energy energy consumpton consumpton The Overall, WSNs. WSNs. The communcaton complexty complextyeach eachstage stage LFEBD O(d), because e EEBD only receves communcaton ee LFEBD s s O d, because e EEBD only receves e e nformaton report e neghbour node when e boundary detecton s carred out. In e nformaton report e neghbour node when e boundary detecton s carred out. In e mplementaton e LFEBD algorm, nodes and neghbours need to exchange data twce, frst e mplementaton e LFEBD algorm, nodes and neghbours need to exchange data twce, frst sensor data, secondly to evaluate e dfference between e calculated data. Moreover, data exchange e sensor data, secondly to evaluate e dfference between e calculated data. Moreover, data needs to choose a dfferent neghbourhood. So n e detecton, e proposed algorm saves at exchange needs to choose a dfferent neghbourhood. So n e detecton, e proposed algorm least half e communcaton consumpton. In terms computatonal complexty, e proposed saves at least half e communcaton consumpton. In terms computatonal complexty, e algorm only performs smple statstcs and comparsons. In e LFEBD algorm, each node needs proposed algorm only performs smple statstcs and comparsons. In e LFEBD algorm, each to dvde ts neghbourhood accordng to e geographc coordnates nto two or ree parts and en node needs to dvde ts neghbourhood accordng to e geographc coordnates nto two or ree update e dfference, so e computatonal complexty e LFEBD algorm s hgher compared parts and en update e dfference, so e computatonal complexty e LFEBD algorm s to EEBD. Because each node needng ts ree-hop neghbourng sensng data, e computatonal hgher compared to EEBD. Because each node needng ts ree hop neghbourng sensng data, e complexty DBD algorm s hgher compared to EEBD. computatonal complexty DBD algorm s hgher compared to EEBD. The proposed algorm can customze e settng e boundary wd n a certan range. Ths allows us to control e number boundary sensors whle ensurng e boundary detecton rate and

16 Symmetry 09,, The proposed algorm can customze e settng e boundary wd n a certan range. Ths allows us to control e number boundary sensors whle ensurng e boundary detecton rate and reduce e communcaton consumpton e boundary nodes to report sensng data to e snk node. It can be seen from e above dscusson at e EEBD algorm can acheve better detecton results w less traffc and lower computatonal complexty, especally n low densty, n e range reasonable false alarm rate. 6. Conclusons Ths expermental research ntroduced a dstrbuted boundary detecton algorm EEBD. Under e same boundary detecton probablty, e proposed algorm can reduce e number nodes to be deployed compared to e two benchmark algorms n montorng a sea area. The boundary wd can be customzed to not only reduce e communcaton consumpton reportng but also to satsfy e detecton accuracy. The smulaton results demonstrate at e EEBD performs better n terms accuracy w bo low and hgh node densty. The followng two-fold drectons are recommended for next study. () To furer decrease e sensor nodes energy consumpton and extend network lfespan under e condton ensurng e accuracy event boundary detecton, e energy consumpton model and e event reportng routng protocol need furer research. () A complete event dataset s necessary before e boundary detecton algorm s executed. Due to e adverse condtons e sea, e collected marne bg data always experence a serous data loss phenomenon n WSNs []. To furer mprove e accuracy event boundary detecton, e mssng data recovery WSNs s an mportant research topc. (3) Real marne event boundary detecton experments and event boundary dynamc trackng are also key research drectons for e future. Auor Contrbutons: All e auors have contrbuted equally to s research work. Fundng: Ths work was supported by e Natonal Natural Scence Foundaton Chna [Grant No , , 67099]; e Shangha Commttee Scence and Technology, Chna [Grant No ]; e Major Specal Scence and Technology Project Hanan Provnce [Grant No. ZDKJ070]; e Graduate Innovaton Foundaton Shangha Martme Unversty [Grant No. 06ycx04, 07ycx030]. Acknowledgments: The auors would lke to show er deepest grattude for e data and techncal support provded by Martme Stereo Search and Rescue Center Shangha Martme Unversty. Conflcts Interest: The auors declare no conflct nterest. References. Sheng, Z.; Mahapatra, C.; Zhu, C.; Leung, V.C. Recent Advances n Industral Wreless Sensor Networks Toward Effcent Management n IoT. IEEE Access 05, 3, [CrossRef]. Mnhas, U.I.; Naqv, I.H.; Qasar, S.; Al, K.; Shahd, S.; Aslam, M.A. A WSN for Montorng and Event Reportng n Underground Mne Envronments. IEEE Syst. J. 08,, [CrossRef] 3. Wang, T.Y.; Yang, M.H.; Wu, J.Y. Dstrbuted Detecton Dynamc Event Regons n Sensor Networks w a Gbbs Feld Dstrbuton and Gaussan Corrupted Measurements. IEEE Trans. Commun. 06, 64, [CrossRef] 4. Stanayah, L.; Datta, A.; Cardell-Olver, R. Heurstc algorm for fndng boundary cycles n locaton-free low densty wreless sensor networks. Comput. Netw. 00, 54, [CrossRef] 5. Aban, N.; Braun, T.; Gerla, M. Proactve cachng w moblty predcton under uncertanty n nformaton-centrc networks. In Proceedngs e 4 ACM Conference on Informaton-Centrc Networkng, Berln, Germany, 6 8 September07; pp Kundu, S.; Das, N. In-network area estmaton and localzaton n Wreless Sensor Networks. In Proceedngs e GC Workshop: The 7 IEEE Internatonal Workshop on Heterogeneous, Mult-Hop, Wreless and Moble Networks, Anahem, CA, USA, 3 7 December 0; pp

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