Distributed Fault Detection of Wireless Sensor Networks

Transcription

1 Dstrbuted Fault Detecton of Wreless Sensor Networs Jnran Chen, Shubha Kher, and Arun Soman Dependable Computng and Networng Lab Iowa State Unversty Ames, Iowa {jrchen, shubha, ABSTRACT Wreless Sensor Networs WSNs have become a new nformaton collecton and montorng soluton for a varety of applcatons. Faults occurrng to sensor nodes are common due to the sensor devce tself and the harsh envronment where the sensor nodes are deployed. In order to ensure the networ qualty of servce t s necessary for the WSN to be able to detect the faults and tae actons to avod further degradaton of the servce. The goal of ths paper s to locate the faulty sensors n the wreless sensor networs. We propose and evaluate a localzed fault detecton algorthm to dentfy the faulty sensors. The mplementaton complexty of the algorthm s low and the probablty of correct dagnoss s very hgh even n the exstence of large fault sets. Smulaton results show the algorthm can clearly dentfy the faulty sensors wth hgh accuracy. Categores and Subject Descrptors C.2.1 [Networ Archtecture and Desgn]: Communcaton General Terms Algorthm, Performance, Desgn Wreless Keywords Wreless sensor networs, Fault tolerance, Dstrbuted algorthm 1. INTRODUCTION The dramatc advances n wreless communcaton and electroncs have enabled the development of low cost, low power, and multfunctonal wreless sensor nodes whch consst of sensng, data processng, and communcaton components. These tny sensor nodes can easly be deployed nto a desgnated area to form a wreless networ and perform specfc functons. Wth recent ntensve research n ths area, wreless sensor networs have been appled n varous areas, such as envronment and habtat montorng, ecophysology, condton-based equpment mantenance, dsaster management, and emergency response. Due to the low cost and the deployment of a large number of sensor nodes n an uncontrolled or even harsh or hostle envronments, t s not uncommon for the sensor nodes to become faulty and unrelable. The networs must exclude the faulty sensors to ensure the networ qualty of servce. To dentfy the faulty sensor nodes s not trval at all because of the exstng challenges. Sensor nodes are powered by batteres, whch are consdered as lmted resources. It s very expensve for the base staton to collect nformaton from every sensor and dentfy faulty sensors n a centralzed manner. Dfferent applcatons may requre the fault detecton to be conducted n a real-tme mode wth low latency or hgh throughput. Therefore, a localzed and dstrbuted generc algorthm for each node s hghly preferred n wreless sensor networs. Tradtonal testng and fault detecton n computer systems are carred out n the form of bult-n self-test BIST subsystems or n the form of sgnature verfcaton subsystems. Bult-n self-repar BISR technques are often used to mprove the yeld n DRAM memores. Our approach adopted the mutual testng method at the processor level where each processng element s capable of testng ts neghbors [1]. A processng element tests another processng element and generates a test result based on the success of the test results. The test results may be arbtrary because the tester tself can be faulty. A processor s determned to be good or faulty by dagnosng the collecton of all such test results. The algorthm proposed n [1] s appled to regular connected multprocessor systems. However, the topology of wreless sensor networs s not regular. Therefore, each sensor must mantan a certan number of neghbors, that s the degree of the networ must be hgh. In a densely deployed sensor envronment, ths condton can be easly realzed. Our major contrbuton of ths paper s the development of a generc localzed fault detecton algorthm for wreless sensor networs. The paper s organzed as follows. We frst revew the lterature n the fault detecton area n Secton 2. Then, we defne the networ model and fault model n Secton 3. The dstrbuted algorthm for faulty sensor dentfcaton s proposed n Secton 4. A smple example s also llustrated n Secton 4. Performance analyss s presented n Secton 5. Smulaton results are reported n Secton 6. Fnally we conclude the paper and suggest future wor n Secton 7.

2 2. RELATED WORK In ths secton, we brefly revew the related wors n the area of fault detecton n wreless sensor networs. Fault tolerance n VLSI-based systems and fault tolerance n dstrbuted systems have been studed ntensvely n the past. In VLSI systems, fault tolerance has been addressed at all levels of abstracton, ncludng crcut level, logc level, regster transfer level, program level, and system level. In [2], a watchdog processor s used for concurrent systemlevel error detecton technques. A watchdog processor s a small and smple coprocessor that detects errors by montorng the behavor of a system. They showed that a large number of errors can be detected by montorng the control flow and memory-access behavor. In dstrbuted systems, fault detecton and dentfcaton has long been the subject of actve research. A large number of testng connectons among unts n multprocessor fault dagnoss, whch s too expensve and even not allowed n many applcatons. In [3], they proposed a general approach to fault dagnoss that s wdely applcable and only needs a lmted number of connectons among unts. The algorthm uses a majorty vote among the neghbors of a unt to determne the status of the unt. A dstrbuted dagnoss algorthm to locate faulty PE s n large-scale regular nterconnected structures based on the concepts of system-level dagnoss s developed n [1]. Ths algorthm can ether wor n a systolc manner or be executed on a supervsory processor to dentfy the faulty processor. They showed the probablty of correct dagnoss s very hgh even n the presence of a large faulty sets. Recently, fault tolerance and management n WSNs have drawn attenton from the researchers n the area. In [5], a falure detecton scheme usng a management archtecture for WSNs called MANNA, s proposed and evaluated. The scheme creates a manager located externally to the WSN. It has the global vson of the networ and can perform complex tass that would not be possble nsde the networ. Management actvtes tae place when sensor nodes are collectng and sendng temperature data. Every node wll chec ts energy level and send a message to the manager/agent whenever there s a state change. The manager can then obtan the coverage map and energy level of all sensors based upon the collected nformaton. To detect node falure, the manager sends GET operatons to retreve the node state. Wthout hearng from the nodes, the manager wll consult the energy map to chec ts resdual energy. In ths way, MANNA archtecture s able to locate faulty sensor nodes. However, ths approach requre an external manager to perform the centralzed dagnoss. And the communcaton between nodes and the manager s too expensve for WSNs. In [6], a taxonomy for classfcaton of faults n sensor networs and the frst on-lne model-based testng technque are ntroduce. The technque consders the mpact of readngs of a partcular sensor on the consstency of mult-sensors fuson. The sensor s most lely to be faulty f the elmnaton of t sgnfcantly mproves the consstency of the results. A way to dstngush a random nose s to run a maxmum lelhood or Bayesan approach on the mult-sensor fuson measurements.if the accuracy of fnal results of multsensor fuson mprove after runnng these procedure, a random nose should exst. To get a consstent mappng of the sensed phenomena, dfferent sensors measurements need to be combned n a model. Ths cross-valdaton-based technque can be appled to a broad set of fault models. It s generc and can be appled to an arbtrary system of sensors that use an arbtrary type of data fuson. However, ths technque s centralzed. Sensor node nformaton must be collected and sent to the base staton to conduct the on-lne fault detecton. An energy effcent fault-tolerant detecton scheme s proposed n [7] to ntroduce the sensor fault probablty nto the optmal event detecton process. The optmal detecton error was shown to decrease exponentally wth the ncrease of the neghborhood sze. They attempted to dsambguate events from both nose related measurement error and sensor fault and lmt the effects of faulty sensor on the event detecton accuracy. The measurement nose and sensor faults are lely to be stochastcally unrelated, whle event measurements are lely to be spatally correlated. The Bayesan detecton scheme n [7] selects the mnmum neghbors for a gven detecton error bound such that the communcaton volume s mnmzed durng the fault correcton. Luo et al. n [7] dd not explctly attempt to detect faulty sensors, nstead the algorthms they proposed mprove the event detecton accuracy n the presence of faulty sensors. In [8], a faulty sensor dentfcaton algorthm s developed and analyzed. The algorthm s purely localzed and requres low computatonal overhead, t can be easly scaled to large sensor networs. In the algorthm, the readng at a sensor s compared wth ts neghbors medan readng. If the dfference s large or large but negatve, the sensor s very lely to be faulty. Although ths algorthm wors for large sze of sensor networs, the probablty of sensor faults needs to be small. If half of the sensor neghbors are faulty and the number of neghbors s even, the algorthm cannot detect the faults as expected. The paper also mentoned the need of sensors physcal locaton, whch requre expensve GPS or other technques to realze. Our localzed faulty detecton algorthm does not need any physcal poston and wors for large sze of faulty sensors. Even when half neghbors fal, t can stll successfully dentfy the faulty sensors. 3. NETWORK MODEL AND FAULT MODEL We assume sensors are randomly deployed n the nterested area and all sensors have a common transmsson range. The area s assumed to be entrely covered by the sensors. As shown n Fgure 3, the dar crcles represent faulty sensors and the lght gray crcles are good sensors. There could be a falure occurrng n a certan area as llustrated n the fgure. All sensors n the area go out of servce. Snce we are dependng on majorty votng, we assume that each sensor has at least 3 neghborng nodes. Because a large amount of sensors are cast nto the nterested area to form a wreless networ, ths condton can be easly obtaned. Each sensor node s able to locate the neghbors wthn ts transmsson range through a broadcast/acnowledge protocol.

3 Random ndvdual falure t l = t l+1 t l ; d t l j : measurement dfference between S and S j from tme t l to t l+1, d t l x t l j ; j = d t l+1 j d t l j = xt l+1 x t l+1 j x t l c j: test between S and S j, c j {0, 1}, c j = c j; θ1 and θ2: two predfned threshold values; T : tendency value of a sensor, T {LG, LT, GD, FT}; Faulty node Area falure Worng node Maxd: an estmate of propagaton dstance from a set of dentfed good sensors n the frst round of the algorthm teratons. The worst case s n, the best case s log n, and we tae a reasonable n. Fgure 1: Sensor nodes randomly deployed over an area Faults may occur at dfferent levels of the sensor networ, such as physcal layer, hardware, system software, and mddleware [4]. In ths paper, we focus on hardware level faults by assumng all system software as well as the applcaton software are already fault tolerant. The frst of the two groups of components at hardware level conssts of a computaton engne, storage subsystem and power supply nfrastructure, whch are very relable. Another group of components are sensors and actuators whch are most prone to malfunctonng. Because n the frst group of components the heterogeneous BISR fault tolerant schemes wll provde the targeted level of fault tolerance [4], we only consder the sensor faults whch nclude three types of faults: calbraton systematc error, random nose error, and complete malfunctonng. Nodes are stll capable of recevng, sendng, and processng when they are faulty. 4. LOCALIZED FAULTY SENSOR DETECTION In ths secton, we frst gve some defntons for the varables. Then, we present the localzed fault detecton algorthm. 4.1 Defntons We lst the notatons used n our algorthm and analyss below, n: total number of sensors; p: probablty of falure of a sensor; : number of neghbor sensors; S: set of all the sensors; NS : set of the neghbors of S ; x : measurement of S ; d t j: measurement dfference between S and S j at tme t, d t j = x t x t j; Sensors are consdered as neghborng sensors f they are wthn the transmsson range of each other. Each node regularly sends ts measured value to all ts neghbors. We are nterested n the hstory data f more than half of the sensor s neghbors have a sgnfcantly dfferent value from t. We can use ths d t l j to fnd f the current measurement s dfferent from prevous measurement. If the measurements change over the tme sgnfcantly, t s more lely the sensor s faulty. A test result c j s generated by sensor S based on ts neghbor S j s measurements usng two varables, d j and d j, and two predefned threshold value θ1 and θ2. If a sensor s faulty, t can generate arbtrary measurements. If c j s 0, most lely ether both S and S j are good or both are faulty. Otherwse, f c j s 1, S and S j are most lely n dfferent status. Sensors can be ether LG or LF, determned by usng test value from ts neghborng sensors. Each sensor sends ts tendency value to all ts neghbors. The number of the LG sensors wth concdent test results determnes whether the sensors are GD or FT. That s S j NS and T j = LG, 1 cj c j = 1 2c j must be greater or equal to NS /2 to clam S s good. In other words, a good S wll be dagnosed as GD n the frst round f t has less than /4 bad neghbors. The probablty of a sensor beng dagnosed as GD n frst round of teraton s: = /4 =0 where s the bad neghborng sensors. p 1 p 1 If a GD sensor s found n the networ, ts test result can be used to dagnose other sensors status. The nformaton can be propagated through the whole networ to dagnose all other sensors as good or faulty. If the dagnoss s consstent wth the test results, the dagnoss s vald. If there s no sensor beng dagnosed, all ts neghbors are ether not dagnosed or are dagnosed as faulty.

4 4.2 Algorthm The localzed faulty sensor detecton algorthm s summarzed n the followng: Algorthm 1 Localzed Fault Detecton: Step 1: Each sensor S tests every member of S j NS to generate test c j{0, 1} usng the followng method: 1: Each sensor S, set c j = 0 and compute d t j; 2: IF d t j > θ1 THEN 3: Calculate d t l j ; 4: IF d t l j > θ2 THEN c j = 1; Step 2: S generates a tendency value T based upon ts neghborng sensors test value: 1: IF S j NS cj < NS /2, where NS s the number of the S s neghborng nodes THEN 2: T = LG; 3: ELSE T = LF; 4: Communcate T to neghbors; Step 3: Compare the number of S s LG neghborng nodes wth dfferent test results to determne ts status: 1: IF S j NS andt j =LG 1 2cj NS /2 THEN 2: T j = GD; 3: Communcate T to neghbors; Step 4: For the remanng undetermned sensors, do the followng steps n parallel for Maxd cycles: 1: FOR = 1 to n 2: IF T = LG or T = LF THEN 3: IF T j = GD S j NS, THEN 4: IF c j = 0 THEN 5: T = GD; 6: ELSE T = FT; 7: ELSE repeat 8: Communcate T to neghbors; Step 5: If ambguty occurs, then the sensor s own tendency value determne ts status: 1: FOR each S, IF T j = T = GD S j, S NS, where j, and IF c j c THEN 2: IF T = LG or LF THEN 3: T = GD or FT End Algorthm 1 Test results c depends on the threshold θ, whch can be defned accordng to varous applcatons at the deployment tme. In step 1, we can also set two θ1 and θ2 values to be dfferent as we desre. Step 5 s a valdaton chec to mae sure the dagnoss s consstent throughout the entre networ. 4.3 Example In ths secton, we present an example to llustrate our algorthm. Fg.2 shows a partal set of sensor nodes n a wreless sensor networ wth some faulty nodes. Nodes S 1 S 9 nsde the crcle area are the nodes we are nterested n. If the two nodes are neghbors, they are connected by dotted lne. Communcaton between nodes outsde the crcle are not shown n the fgure. Each node nsde the nterested area are tested by ts neghbors. Test results are ether 0 or 1 dependng upon the measurement dfference and threshold value θ. Tendency value T s fnalzed at the thrd teraton. Table 1 lsts the analyss results obtaned by applyng the Localzed Fault Detecton Algorthm. Four out of nne sensor nodes n the area are faulty. The other fve nodes are good and there s no ambguty occurrng n ths example. Each node s neghbors wth GD tendency value generate the same testng results when they determne the node s status Interested area 12 Unnown status sensor Communcaton among sensors Fgure 2: A partal set of sensor nodes n a wreless sensor networs wth faulty sensors Frst, each of S 1 S 9 generates c j test results for all ther neghbors n the way as specfed n step 1 of our algorthm. The results are shown under the 2nd and 3rd columns of Table 1. Secondly, S 1 S 9 decde ther own tendency value, T 1 T 9. If the summaton of test results s less than half of the number of ts neghbors, the sensor s lely good. Otherwse, t s lely faulty. For example, for S 1, s j NS 1 c1j = 1 < NS 1 /2 = 3 T 1 = LG. The same test s done for all other nodes. For S 2, s j NS 2 c2j = 3 > NS2 /2 = 2 T 2 = LF. We assume that sensors outsde the crcle can decde ther tendency value n the same way. Then, we need to fnd GD sensors from all the sensors. Loo at S 1, as specfed n step 3 of our localzed fault detecton algorthm, s j NS 1 andt j =LG 1 2c1j = 3 > NS1 /2 T 1 = GD. We obtaned all the values under the Iteraton 1 column n Table 1 from ths step. Fnally, by usng the GD sensors, we can test other non-gd sensors to fnd out ther status base upon the test results. The values under Iteraton 2 column n Table 1 are generated from ths step. The last step s to chec f there s any ambguty between any neghbors test results. All test results are consstent n ths example. From ths localzed fault detecton algorthm and the above example, we mae the followng observatons: 1. A sensor node S s tendency value can be LG f S s good and has NS /2 or more good neghbors. It can also be LG f S s faulty and has over NS /2 faulty neghbors.

5 Table 1: Analyss of Faults n Fg.2 S S j wth c j = 0 S j wth c j = 1 T n Iteratons ,5,11,12 10 LG GD GD 2 4 3,12,13 LF LF FT 3 1,7 2,6 LG GD GD 4 2 7,14,20 LF LF FT 5 1,15 6,8 LG GD GD 6 8 3,5,7,9 LF LF FT 7 3,9,14 4,6,16 LG GD GD 8 6,17 5,9,18 LF LF FT 9 7,18,19 6,8,16 LG GD GD 2. If no GD sensor s determned at step 3, the networ can not determne the sensor nodes status at all and the algorthm wll ext at ths step. Only at least one sensor node s dagnosed as GD n step 4, can ths algorthm contnue to execute and determne more sensors status. 3. A faulty sensor can only be dagnosed as good sensor n step 3 because the system wll not use any ncorrect nformaton n step A good sensor can be dagnosed as a faulty sensor only when some faulty sensors are dagnosed as good nodes n step 3. By usng these observatons, we can further analyze the algorthm. 5. ANALYSIS OF THE ALGORITHM We defne that the dagnoss of faulty sensors s correct f no good sensor s dagnosed as faulty and no faulty sensor s dagnosed as good. The dagnoss s complete f all sensor nodes are dentfed as faulty or good n a predefned tme. An ncorrect dagnoss happens when a good sensor s labeled as faulty or a faulty sensor s labeled as good. A dagnoss s ncomplete f any node s status cannot be dagnosed n the networ. A complete and correct dagnoss s desred. Generally, an ncorrect dagnoss s unacceptable because the error nformaton may be propagated to the base staton or users. However, an ncomplete dagnoss s acceptable under certan crcumstances. Our proposed algorthm mnmzes the lelhood of ncorrect dagnoss. The probablty of correct and complete faulty sensor dagnoss s computed and analyzed n the followng. Let p be the probablty of falure of node S. Let = NS. A sensor node wth tendency value LG can be ether good or faulty. A sensor node wth tendency value LF can also be ether good or faulty. The probablty of a good sensor node havng a lely good tendency value s: P glg = 1 p /2 1 =0 p 1 p 2 The probablty of a good sensor wth a lely faulty tendency value s: P glf = 1 p /2 1 =0 1 p p 3 The probablty that a sensor s faulty and has a lely good tendency value s: P flg = p /2 1 =0 =0 1 p p 4 The probablty that a sensor s faulty and has a lely faulty tendency value s: /2 1 P flf = p 1 p p 5 From the observatons n Secton 4, a faulty sensor s LG value s determned by ts neghborng nodes. Only when at least half of ts neghbors are faulty and have LG tendency value, the faulty sensor wll be dagnosed as good. The probablty of a faulty sensor beng dagnosed as good s: P FG = p a= 2 { a a 2 a b Pflg a [Pglg b P a b c flf b=0 c=0 P c glf]} 6 The probablty that none of the faulty sensors s dagnosed as good n the entre networ s: P NFG = n p 1 p n 1 P FG 7 =0 n A good sensor s not dagnosed as a good sensor only when the dfference between LG faulty sensors and LG good sensors s less than half of ts neghbors. The probablty of a good sensor not beng dagnosed as good node s: P GG = 1 p 2 1 a=0 { a a a b Pflg a [Pglg b P a b c flf b=0 c=0 P c glf]} 8 The probablty that no good sensor nodes are dagnosed as good n the entre networ s: P NGG = n =0 n p 1 p n P n GG 9 From Equaton 7 and Equaton 9, P NFG and P NGG approach 1 and 0 respectvely when networ sze goes to exponentally large. Snce the number of sensors n WSN can be hundreds and networ sze s relatvely large, the probablty that none of the faulty sensors s dagnosed as good approaches one. The probablty that all good sensors are not beng dagnosed as good s very small, whch s approachng 0. Table 2: Probablty of No Faulty Sensor Dagnosed as Good p Average Number of Sensors

6 Table 3: Probablty of No Good Sensor Dagnosed as Good p Average Number of Sensors E E E E E E E E E E Tables 2 and 3 show the probabltes P NFG and P NGG under dfferent probabltes of falure of sensors and wth dfferent average number of neghbors. The results demonstrate that wth large networ sze almost all the good and faulty sensors wll be dagnosed correctly. The probabltes calculated n the tables show that our algorthm performs well. However, n real stuaton, when sensors are deployed n the feld randomly, they may not have enough number of neghbors for the correct and complete analyss. Ths can cause the ncorrect dagnoss, resultng faulty sensors beng dagnosed as good or good sensor beng dagnosed as faulty. 6. SIMULATION RESULTS For smulaton we used C++ as the tool. An example smulaton scenaro composed of total 1024 sensor nodes are randomly deployed n a regon of sze unts as shown n Fgure 3. The measurement parameter x s consdered to be temperature. We set the values of x as good and faulty wth ranges as follows, Good = degrees and Faulty as degrees. Also transmsson range was chosen to ensure that sensors have the average number of neghbors n smulaton runs. In step 1 of the algorthm, a threshold value θ1 and θ2 are needed to determne the testng value. We set both θ1 and θ2 to be 15 for the smulaton. Detecton accuracy False alarm rate Average 7 Neghbors Average 10 Neghbors Average 15 Neghbors Average 20 Neghbors Sensor fault probablty Fgure 4: Faulty Sensor Detecton Accuracy Average 7 Neghbors Average 10 Neghbors Average 15 Neghbors Average 20 Neghbors Sensor fault probablty Fgure 5: False Alarm Rate n Faulty Sensor Detecton 30 y x Sensor Node Fgure 3: A regon wth 1024 sensor nodes randomly deployed n t Faulty sensor detecton accuracy FSDA and false alarm rate FAR are the two metrcs used to evaluate our algorthm performance. FSDA s defned as the rato of the number faulty sensor detected to the total number of faulty sensors n the feld. The FAR s the rato of the number of non-faulty sensor dagnosed as faulty to the total number of non-faulty sensors. In the smulaton, sensors are randomly chosen to be faulty wth the probabltes of 0.05, 0.10, 0.15, 0.20, and 0.25 respectvely under dfferent average number of neghbors for each sensor. Average number of neghbors/sensor s chosen to be 7, 10, 15, and 20 respectvely. Fgures 4 and 5 show the faulty sensor detecton accuracy and false alarm rate aganst the sensor fault probablty for dfferent average number of neghbors. In Fgure 4, the detecton accuracy for 7 neghbors and 10 neghbors decreases when the fault probablty becomes larger. But the fault detecton accuracy s stll about 97% when there are about 25% of the sensors beng faulty. There are several faulty sensors not beng dagnosed as faulty because the randomly deployment of the sensors n the networ results n very few neghbors for those sensors. When the average of number neghbors s greater than 15, the fault detecton s very hgh and almost all the faulty sensors can be detected even under a hgh faulty sensor probablty. Ths result s consstent wth our probablty analyss n Secton 5. In Fgure 5, for the 7 neghbors and 10 neghbors, the hgher the fault probablty, the hgher false alarm rate. Ths s be-

7 cause the large number of faulty sensor test good sensors to be Lely Faulty and these good sensors are then dagnosed as faulty sensors. For 15 and 20 neghbors, the false alarm rate s as low as 0. Agan, ths s consstent wth our probablty analyss. Overall, our algorthm outperforms prevous fault detecton algorthm proposed n [8] n terms of the faulty sensor detecton accuracy and false alarm rate. Our localzed fault detecton algorthm acheves hgh detecton accuracy and low false alarm rate even wth a large set of faulty sensors. 7. CONCLUSION We proposed a dstrbuted localzed faulty sensor DLFS detecton algorthm where each sensor dentfes ts own status to be ether good or faulty and the clam s then supported or reverted by ts neghbors as they also evaluate the node behavor. The proposed algorthm s analyzed usng a probablstc approach. In our probablstc analyss, the probabltes of faulty sensors beng dagnosed as good and good sensors not beng dagnosed as good n the entre sensor networ are very low. [5] L. B. Ruz, I.G.Squera, L. B. Olvera, H. C. Wong, J. M. S. Noguera, and A. A. F. Lourero. Fault management n event-drven wreless sensor networs. MSWM 04, October 4-6, 2004, Veneza, Italy. [6] F. Koushanfar, M. Potonja, and A. Sangovann-Vncentell. On-lne Fault Detecton of Sensor Measurements. Sensors, Proceedngs of IEEE Volume 2, 22-24, Oct. 2003, pp [7] X. Luo, M. Dong, and Y. Huang. On dstrbuted fault-tolerant detecton n wreless sensor networs. IEEE Transactons on Computers, Vol.55, No.1: 58-70, Jan [8] M. Dng, D. Chen, K. Xng, and X. Cheng. Localzed fault-tolerant event boundary detecton n sensor networs. Proceedngs of IEEE INFOCOM 2005, Mam, March Fnally, the algorthm s tested usng a smulaton for an example case under dfferent number of faulty sensors n the same area. Our smulaton results show that the FSDA s over 97% even when 25% nodes are faulty. The FAR s very accurate when the sensor fault probablty s low. Smulaton results support and demonstrate that our proposed algorthm can have a hgh fault detecton accuracy and low false alarm rate wth a large number of faulty sensors exstng n the networ. At ths tme there may be ssues related to scalablty and overhead due to exchange of nformaton between neghbors. However, the am of ths wor s to detect a faulty sensor as faulty n a dstrbuted envronment. The success of dong so s promsng and we would le to extend t to see how t behaves n extremely large deployments. We are further worng on developng an algorthm to fnd the event edge by partally usng the algorthm proposed n ths paper. Future wor should nclude the mplementaton of the algorthms on NS2 sensor networ smulators. 8. REFERENCES [1] A. K. Soman and V. K. Agarwal. Dstrbuted Dagnoss Algorthms for Regular Interconnected Structures. IEEE Transacton of Computers, Vol.41, No.7: , July [2] A. Mahmood and E. J. McClusey. Concurrent error detecton usng watchdog processors-a survey. IEEE Transactons on Computers, Vol.37, No.2: , Feb [3] D. Blough, S. Sullvan, and G. Masson. Fault dagnoss for sparsely nterconnected multporcessor systems. In Proc. of FTCS-19, 1989, pp [4] F. Koushanfar, M. Potonja, and A. Sangovann-Vncentell. Fault-Tolerance n Sensor Networs. Handboo of Sensor Networs, I. Mahgoub and M. Ilyas eds., CRC press, Secton VIII, no. 36, 2004.