Fisher Information of Mine Collapse Hole Detection Based on Sensor Nodes Connectivity

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1 Sensos & Tansduces, Vol. 3, Special Issue, July 3, pp Sensos & Tansduces 3 by IFSA Fishe Infomation of Mine Collapse Hole Detection Based on Senso Nodes Connectivity, Shengbo Hu, 3 Bi Si,, Heng Su Institute of Intelligent Pocessing, Guizhou Nomal Univesity, 55, China Centes fo RFID and WSN Engineeing, Guizhou Depatment of Education, 55, China 3 Institute of New Technology, Guizhou Academy of Sciences, 55, China shengbohu@63.com Received: 5 Apil 3 /Accepted: July 3 /Published: 3 July 3 Abstact: It is vey impotant to detect a collapse hole fo coal mine wokes. The possibility of detecting e collapse hole using WSN is pesented, because e tunnel in coal mine is naow and e poo woking condition. Compaing ee types of e hole detection meods, it is seen at e connectivity based meods ae used to detect coal mine collapse bette an oe meods. By establishing a -D model of e collapse hole in coal mine, a class of algoims fo detecting e collapse hole in coal mine is descibed. Based on log-nomal shadowing channel model, e accuacy of detecting e collapse hole in coal mine using Fishe Infomation is analyzed. Numeical calculation shows at connectivity based localization schemes ae used to detect collapse hole of coal mine bette. Copyight 3 IFSA. Keywods: Fishe infomation, Collapse, Hole detection, Mine, Undegound.. Intoduction Coal mine collapse is one of e main easons esult in coal mine fatalities in e past yeas in e wold []. Hence, it is vey impotant to detect a collapse hole and accuately povide location efeences fo coal mine wokes. Since e coal mine collapse may destoy some coal safety monitoing devices, detecting e collapse hole in coal mine becomes a geat challenge. The utilization of wie sensos to monito coal mine is e pimay meods at pesent. Howeve, e wied meod makes e monitoing systems less scalable and vulneable because of e poo woking conditions in a tunnel of coal mine. Once coal mine collapse occus, all wied sensos may be destoyed, and it is impossible to detect e collapse hole. Wieless senso netwok (WSN) is an event based self-oganized wieless netwok at elies on deploying spatially dense senso nodes obseving a physical phenomenon [-5]. Compaed wi taditional wie sensing, WSN can achieve lage coveage aea, geate accuacy, and moe flexible deployment. The utilization of a WSN to monito coal mine is benefit. Once coal mine collapse occus, not all senso nodes of a WSN ae destoyed. So, it is possible to detect e collapse hole in coal mine collapse hole. Fo example, Li and Liu pesent a meod based on a egula beacon stategy to detect e collapse hole in coal mine by egulating a mesh senso netwok deployment []. When a collapse occus, e goup of destoyed senso nodes in e coal mine wieless senso netwok ceates a hole [6]. The collapse hole bounday sepaates all e faulty senso nodes fom e woking nodes. Geneally, ee can be ee types of e hole detection meods. The appoaches based on geometic location meods [7, 8] ely on Aticle numbe P_SI_47 8

2 Sensos & Tansduces, Vol. 3, Special Issue, July 3, pp e nodes having geogaphical locations, and can find moe accuate bounday nodes an oe two meods, but each node has to equip exta device such as GPS to obtain e geogaphical locations. Unlike e meods, e statistical meods [9, ] wiout having location infomation usually assume e senso nodes ae unifomly distibuted on e sensing field. The majo weakness of e statistical meods is at e citeia fo detecting hole acquies fom e statistical chaacteistics cannot guaantee to find hole pecisely. The connectivity based meods [6,, ] use e infomation of neighboing senso nodes connectivity to detect e hole. Nomally, e meod has highe packet contol ovehead an pevious two meods due to having to collect infomation fom neighboing senso nodes; howeve, it does not need location infomation and has bette accuacy of finding bounday nodes an statistical meod. The senso nodes neie can be equipped any additional devices such as GPS, no ae unifomly distibuted because of e naow tunnel and e poo woking conditions in e tunnel in coal mine. So, e connectivity based meods ae used to detect coal mine collapse bette. Connectivity is just a binay vaiable detemined by whee o not a senso node can demodulate and decode a packet tansmitted by anoe senso node. Connectivity measuements can be obtained by compaing e Received Signal Steng () value between e two nodes against a powe eshold. The can be used to implement ange-based localization [3]. The localization meods ae popula because no additional hadwae is equied on e senso nodes. Howeve, e ange estimates using ae inaccuate and can lead to lage localization eo, because e value is affected by unpedictable shadowing and fading in e tunnel in coal mine. Yet connectivity is e binay vaiable caying infomation egading senso nodes location, and is often discussed wiout consideing at it is affected by shadowing and fading channel. So, e connectivity based meods fo localization have been actively eseached in hole detection and ad hoc outing in WSN [4-6]. Connectivity measuements ae actually just a binay quantization of e measuements against a powe eshold. Because measuements ae affected by unpedictable shadowing and fading in e tunnel in coal mine, it is vey impotant to analyze accuacy of detecting e coal mine collapse hole using e connectivity based meods. The est of is pape is oganized as follows. Section discusses e system models including -D model of e coal mine collapse hole and a class of algoims fo detecting e coal mine collapse hole using e connectivity based meods. Section 3 analyzes e accuacy of detecting collapse hole using Fishe Infomation. Section 4 descibes numeical calculation and discussion. Section 5 concludes is pape.. System Model.. -D Model of Coal Mine Collapse Hole Geneally, e tunnel of coal mine can be classified as ach-shaped, ectangle, tapezium, and semicicle tunnel. Fo convenience, we conside ectangle tunnel in is pape. A cluste of senso nodes ae deployed on e walls and oofs of e tunnel, as shown in Fig. (a). To facilitate collapse hole detection, Fig. (a) can be unfolded a -D epesentation as depicted in Fig. (b). (a) wall oof (b) A B C Fig.. A cluste of senso nodes deployment. wall In Fig., e elationships between e neighboing senso nodes in Fig. (b) ae e same as in Fig. (a). Howeve, e distance between any two nodes in Fig. (b) is geate an o equal to e distance between e pai in Fig. (a). Thus, e eal connectivity of e WSN is no less an shown in e -D epesentation in Fig. (b), and e accuacy of e collapse holes detection in Fig. (b) is peseved in Fig. (a). So, a cluste of senso nodes ae modeled as a -D gaph, G = (V, E), whee each vetex epesents a senso node, V is e set of a cluste senso nodes, and two vetices ae connected by an edge in E if and only if ei distance is at most e guaanteed communication adius. Once a mine collapse occus, some senso nodes n, n,, nk V ae destoyed. The extent of ese damaged nodes ceates a collapse hole wi convex hulls, which is suounded by alive senso nodes at contain all e damaged senso nodes in Fig.. Fig.. A collapse hole ceated by damaged senso nodes. 8

3 Sensos & Tansduces, Vol. 3, Special Issue, July 3, pp Algoim fo Detecting Collapse Hole Using Connectivity Connectivity simple epot whee o not a senso node can demodulate and decode a packet tansmitted by anoe senso node. Connectivity measuements can be obtained by compaing e Received Signal Steng () value between e two nodes against a powe eshold. Because e measuements ae affected by unpedictable shadowing and fading in e tunnel in coal mine, e connectivity can be descibed by a andom binay vaiable Q : Q i,,, P P P P () whee P is e measuement eceived at senso node i tansmitted by senso node j, P is e powe eshold of senso node. Eq. () shows at senso node i can demodulate and decode a packet tansmitted by senso node j if P P, and Q ; senso node i can not demodulate and decode a packet tansmitted by senso node j if P P, and Q. The connectivity based meods will use e assumption at two senso nodes ae connected if Q, and disconnected if Q. The advantage of ese meods is at location can be discussed wiout knowing e popagation model s paametes. So, a class of algoims fo detecting e collapse hole in coal mine can be descibed as follows [, 7]: Step (initialization): Each senso node boadcasts a ping equesting infomation to neighboing senso nodes. If P P, senso nodes ely wi ei ID, and e pinging node can ceate a list of its neighboing senso nodes. Step (integity checking): If a coal mine collapse occus, each senso node pings its neighboing senso nodes, keeps tack of e esponses and compaes e list of neighboing senso nodes. If P P, senso node eceives e ID (Identification Numbe) of senso node j, and maks senso node j as alive. If P P, senso node i can not eceive ID of senso node j, and maks e senso node as missed. If e node s numbe of missed neighboing nodes exceeds a eshold, senso node i maks itself as belonging to e collapse peimete. Step 3 (collapse hole scanning): Accoding to e list of senso nodes maked as on e collapse peimete, e classical Gaham algoim [8] is used to detect e collapse hole wi convex hulls. 3. Accuacy of Detecting Collapse Hole As shown in Section, analyzing e accuacy of detecting collapse hole using connectivity is to analyze e accuacy of estimating distance d between neighboing senso nodes equivalently using Q. So, we conside e topic of estimate distance d between neighboing senso nodes fom connectivity measuements using Fishe Infomation. 3.. Channel Model Because e tunnel is naow and poo envionment in coal mine, e is attenuated by pa losses, fading and shadowing losses [9]. Pa loss is e deteministic eduction function of distance d between neighboing senso nodes. Fading is e effect of multipa popagation. Because many wieless senso nodes use spead-spectum techniques, e fading can be educed mostly and its impact on e attenuated is not significant. Shadowing is e loss incued as a signal passes ough pemanent obstuctions (e.g. walls, buildings). Fo mostly senso nodes in e tunnel, shadowing losses can not be counteed. When a collapse occus, shadowing losses ae geate. So, e values follow e log-nomal shadowing model, a channel model widely used in WSN [], []. Let P () is e eceived signal powe at senso node wi e efeence distance d (Typically d ), and is e pa loss exponent, a paamete at depends on e envionment whee communication occus (typical values ae and 4 []). Unde log-nomal shadowing model, e eceived powe when e two senso nodes ae at a distance d can be witten as: ln P( d) ln P() ln d w, () whee w is e zeo-mean andom vaiable wi N,. nomal distibution 3.. Fishe Infomation In is pape, we focus on estimating distance d between neighboing senso nodes fom connectivity measuements, which cay infomation egading senso nodes location. As is well known, e Fishe Infomation measues e amount of infomation at a andom vaiable caies about an unknown paamete. And e invese of e Fishe Infomation, known as e Came-Rao Bound, is e minimum vaiance fo any unbiased estimato. Hee, e andom vaiable Q defined by Eq. () is used to estimate d. So, Va{ d ˆ}, e vaiance of estimating d is: 83

4 Sensos & Tansduces, Vol. 3, Special Issue, July 3, pp Va{ dˆ } I( d), (3) whee I( d ) is e Fishe Infomation of estimating distance d using e andom vaiable Q Fishe Infomation of Measuements Fo notational convenience, we define, z P() P( d). Then Eq. () can be witten as: z w d e (4) So, e undelying estimation poblem is to estimate d fom e measuements z satisfying Eq. (5), given e knowledge of and. Taking e logaim of Eq. (5), we obtain ln z ln d w (5) Let l ln z, l is a andom vaiable wi nomal distibution Nln d,. The log-likelihood functions given by ply l d (6) ln, ln ln Hence, e Fishe Infomation of measuements is given by I ( d) E ln p l, y d = k d whee k Fishe Infomation of Connectivity Measuements, (7) As shown in Section 3, e undelying estimation poblem is to estimate d fom e connectivity measuements. Then e Fishe Infomation of connectivity measuements depend not only e d between neighboing senso nodes, but also e value of e powe eshold P in Eq. (). Fo convenience, P need to be conveted into e distance eshold d. Fom Eq. (4), it can be obseved at l has a non-affine dependence on d and an affine dependence on w. Hence, no efficient estimato exists fo is poblem [3]. This leads us to choice e Maximum Likelihood Estimato (MLE) dˆ of e distance eshold d. The d ˆ is given by P( d) P ˆ ag max ln (, ) () d d p l y P P (8) Fom [4], conside e case of -level quantized. The Fishe Infomation of connectivity measuements is given by I ( dd. ) k h( d, d ) d, (9) CON whee e tem h( d, d ) depends on e ation between d and d : exp k ln( d / d ) h( d, d) ef k ln( d / d ) ] whee ef () is e eo function., () 4. Numeical Calculation and Discussion 4.. Numeical Calculation In is subsection, we investigate e Fishe Infomation I ( d) and ICON ) using numeical calculation The Pa Loss Exponent s Effects on I ( d ) Fig. 3 shows at e I ( d ) as a function of d fo diffeent values ( =4, 3,.5) and fixed value ( ). Fig. 3 descibes at amount of e I ( d ) available to estimate d deceases fo inceasing values of e distance d, and incease fo inceasing values of e values. This shows at e estimates become moe accuate because e attenuation caused by e pa loss cleas e measuement. Fishe Infomation I(d) k=4/ k=3/ k=.5/ distance d (m) Fig. 3. Fishe Infomation fo measuements at =. 84

5 Sensos & Tansduces, Vol. 3, Special Issue, July 3, pp The Values Effects on I ( d ) Fig. 4 shows at e I ( d ) as a function of d fo diffeent values ( =, 3, 4) and fixed value ( 3 ).Fig.4 descibes at amount of I ( d ) available to estimate d deceases fo inceasing values of e distance d and inceasing values of e values. This shows at e estimates become less accuate because e vaiability caused by e RF shadowing blus e measuement. Fig. 5 and Fig. 6 descibe at e ICON ) always peaks when d. In oe wods, d connectivity measuements each e maximum infomation if e distance eshold equals to e tue distance between neighboing senso nodes. Fom Eq. (), e maximum Fishe Infomation of connectivity measuements ICON ).63 I ( d) if d d. So, ICON ) is always lowe an I ( d ). Fishe Infomation I(d) k=3/ k=3/3 k=3/4 Fishe Infomation ICON(d,d) d= d=3 d= Fig. 4. Fishe Infomation fo measuements at = The k Values Effects on e Fishe Infomation I ) CON Fig. 5 shows at e ICON ) as a function of d when d=5m fo diffeent k values (k=3/4, 3/3, /3), and Fig. 6 shows at e ICON ) as a function of d when k=4/ fo diffeent d values (d=, 3, 4)..5 Fishe Infomation ICON(d,d) distance d (m) Fig. 5. Fishe Infomation fo connectivity measuements at diffeent k values. eshold d (m) k=4/3 k=3/3 k=/ eshold d (m) Fig. 6. Fishe Infomation fo connectivity measuements at diffeent d values. 4.. Discussion about Accuacy of Detecting Collapse Hole As shown in Section 4., measuements cay geate Fishe Infomation an connectivity ones. Howeve, is is only tue as long as e neighboing senso nodes ae wiin e adio coveage of each oe. When senso nodes ae wiin each oe s adio coveage, ey ae able to communication and successfully exchange adio message. Depending on e choice of P, two neighboing senso nodes at ae wiin each oe s adio ange can be consideed connected o disconnected. When e neighboing senso nodes ae fa fom adio coveage, ey will not be able to communication. So, no infomation can be collected, and I ( d). Instead, e senso nodes fa fom adio coveage can be associated to e value Q, and ICON ( d, d ). As shown above, ange-based localization schemes ae moe accuate when e neighboing senso nodes ae in e adio coveage of each oe, but connectivity based localization schemes ae is natually suited to localize nodes at ae fa fom adio coveage. Hence, connectivity based 85

6 Sensos & Tansduces, Vol. 3, Special Issue, July 3, pp localization schemes ae used to detect collapse hole of coal mine bette. 5. Conclusions It is vey impotant to detect a collapse hole fo coal mine wokes. This pape pesents e possibility of detecting e collapse hole using WSN, because e tunnel in coal mine is naow and e poo woking condition. Compaing ee types of e hole detection meods, we ink at e connectivity based meods ae used to detect coal mine collapse bette. By establishing a -D model of e collapse hole in coal mine, we descibe a class of algoims fo detecting e collapse hole in coal mine. Based on log-nomal shadowing channel model, we analyzes e accuacy of detecting e collapse hole in coal mine using Fishe Infomation, and make numeical calculation. Finally, we make e conclusion as follows: The lage e pa loss exponent, e geate Fishe Infomation. The lage e vaiability caused by e RF shadowing, e less Fishe Infomation. When senso nodes ae wiin each oe s adio coveage, e accuacy of detecting e collapse hole using measuements is highe an connectivity ones; When e neighboing senso nodes ae fa fom adio coveage, no infomation can be collected, and I ( d). Instead, e senso nodes fa fom adio coveage can be associated to e value Q, and ICON ( d, d ). Hence, connectivity based localization schemes ae used to detect collapse hole of coal mine bette. Acknowledgements The auos wish to ank e edito and eviewes fo ei valuable comments, coections, and suggestions, which led to an impoved vesion of e oiginal pape. This eseach is a poject patially suppoted by e National Natual Science Foundation of China (Gant No ) and Guizhou Science and Technology Innovation Goup fo RFID & WSN. Refeences []. M. Li, Y. Liu, Undegound coal mine monitoing wi wieless senso netwoks, ACM Tansactions on Senso Netwoks, Vol. 5, Issue, 9, pp. -9. []. K. Kavi, P. Rajiv and M. Avinash, A wieless senso netwok ai pollution monitoing system, Intenational Jounal of Wieless and Mobile Netwoks, Vol., Issue,, pp [3]. W. U. Bajwa, A. Sayeed and R. Nowak, Matched souce-channel communication fo field estimation in wieless senso netwoks, in Poceedings of e 4 Intenational Symposium on Infomation Pocessing in Senso Netwoks (IPSN 5), Los Angeles, Califonia, USA, 5 Apil 5, pp [4]. A. Modikhazeni, N. Inin, O. Ibahim, Empiical study on secue outing potocols in wieless senso netwoks, Intenational Jounal of Advancements in Computing Technology, Vol., Issue 5,, pp [5]. Lakhlef, A. Bomgni et J. F. Myoupo, An efficient pemutation outing potocol in multi-hop wieless senso netwoks, Intenational Jounal of Advancements in Computing Technology, Vol. 3, Issue 6,, pp [6]. Y. Wang, J. Gao and Joseph S. B. Mitchell, Bounday ecognition in senso netwoks by topological meods, in Poceedings of e Annual Intenational Confeence on Mobile Computing and Netwoking, Los Angeles, Califonia, Septembe 6, pp.-33. [7]. Q. Fang, J. Gao and L. J. Guibas, Locating and bypassing outing holes in senso netwoks, Jounal of Mobile Netwoks and Applications, Vol., Issue, 6, pp [8]. P. K. Sahoo, Y. Hsieh and P. Sheu, Bounday node selection and taget detection in wieless senso Netwok, in Poceedings of e IFIP Intenational Confeence on Wieless and Optical Communications Netwoks, Singapoe, July 7, pp. -5. [9]. S. P. Fekete, M. Kaufmann, A. Kolle and N. Lehmann, A New appoach fo bounday ecognition in geometic senso netwoks, in Poceedings of e 7 Canadian Confeence on Computational Geomety, Canada, August, 5, pp []. S. P. Fekete, A. Kölle, D. Pfistee, S. Fische and C. Buschmann, Neighbohood-based topology ecognition in senso netwoks, in Poceedings of e st Intenational Wokshop on Algoimic Aspects of Wieless Senso Netwoks, Finland, July 4, pp []. S. Funke and C. Klein, Hole Detection o: How much geomety hides in connectivity, in Poceedings of e ACM Annual Symposium on Computational Geomety, USA, June 6, pp []. O. Saukh, R. Saute, M. Gauge, P. J. Maón and K. Roemel, On bounday ecognition wiout location infomation in wieless senso netwoks, in Poceedings of e 7 Intenational Symposium on Infomation Pocessing in Senso Netwoks, USA, Apil 8, pp [3]. A. Savvides, C. Han and M. Shivastava, Dynamic fine-gained localization in Ad-Hoc netwoks of sensos, in Poceedings of e 7 Annual Intenational Confeence on Mobile Computing and Netwoking, Rom, Italy,, pp [4]. S. Babaie, S. S. Piahesh, Hole detection fo inceasing coveage in wieless senso netwok using tiangula stuctue, Intenational Jounal of Compute Science Issues, Vol. 9, Issue,, pp [5]. C. F. Huang, Y. C. Tseng, A suvey of solutions to e coveage poblems in wieless senso netwoks, Jounal of Intenet Technology, Vol. 6, Issue, 5, pp. -8. [6]. R. Nagpal, H. Shobe and J. Bachach, Oganizing a global coodinate system fom local infomation on an ad hoc senso netwok, in Poceedings of e nd 86

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