Mobile Sensor Networks for Leak and Backflow Detection in Water Distribution Systems

Transcription

1 Moble Sensor Networks for Leak and Backflow Detecton n Water Dstrbuton Systems M. Agumbe Suresh, L. Smth, A. Rasekh, R. Stoleru, K. Banks, B. Shhada Department of Computer Scence and Engneerng, Texas A&M Unversty Department of Cvl Engneerng, Texas A&M Unversty Department of Computer Scence, Kng Abdullah Unversty of Scence and Technology Abstract Leak detecton and backflow detecton are essental aspects of Water Dstrbuton System (WDS) montorng. Most exstng solutons for leak detecton n water dstrbuton systems focus on the placement of expensve statc sensors located strategcally. In contrast to these, we propose a soluton whereby moble sensors, ther movement aded only by the nherent flow n the system (e.g., water flow n a WDS), detect leaks. Informaton about the leaks are collected from the sensors ether by physcally capturng them, or wth through wreless communcaton. Specfcally, we propose models to maxmze leak detecton, gven a cost constrant (a lmt on the number of sensors). We compare our results to the state of the art and also compare smulatons to mathematcal results to demonstrate the performance of our solutons. I. INTRODUCTION Water Dstrbuton Systems (WDS) play an essental role n our lves. About 9% of the populaton of U.S receves drnkng water from nearly 7, publc WDS. Spannng nearly one mllon mles, ths bured ppelne nfrastructure plays a major role n preservng publc health and ndustral growth n ever-growng urban envronments. The naton s water nfrastructure, however, s agng [8][][6][2]. Many urban water mans may easly date back to early 2th century and are hghly prone to breaks as they are reachng the end of ther servce lfe. Ths s evdenced by estmated 237,6 water man breaks per year n the U.S. leadng to nearly $2.8 bllon lost n yearly revenue [9]. Consequences of water man breaks are twofold: () water loss, dsruptons, and damages due to leakage and () publc health rsks due to backflow events. Water leakage n WDSs cause sgnfcant loss of water n WDSs that already stressed by growng water demand and recurrent droughts over the past decade. The World Bank estmates that worldwde 48.6 bllon cubc meters of water are lost every year, a large proporton of whch s due to water leakages n WDSs [24]. Severe water leakage may also cause ground nstabltes and subsequent secondary economc losses n the forms of damages to urban water, transportaton, and communcaton lnes. Backflow s an unwanted flow of non-potable water or other substances nto the drnkng WDS ppelnes. It occurs through cracks, breaks, or loose connectons when a reverse pressure gradent exsts at cross-connectons. A U.S. EPA complaton of backflow ncdents data ndcates that 459 ncdents caused an estmated 2,93 llnesses from 97 to 2 [8]. The Amercan Water Works Assocaton s report [] on the renvestment needs for the naton s agng drnkng water nfrastructure estmated that $25 bllon may be requred over the next 3 years to replace worn out systems. Such practces would not be effcently accomplshed unless they are well nformed of the condtons of ppelne systems at hgh spatal resolutons ncludng the locaton of cracks, breaks, or loose connectons. Collecton of ths nformaton for the ubqutous bured ppelne nfrastructure usng the exstng onlne statonary technologes (.e., statc sensors placed outsde the ppes), however, s extremely burdensome and costly, f not mpossble. Inlne free-swmmng sensor technologes (moble sensors that travel wth the water flow nsde the ppe and collect nformaton about leaks) [23] [6] [3] [2] [3] has been recently desgned and demonstrated for detectng and pnpontng leaks n ppelnes. When usng free-swmmng sensors to detect leaks, an mportant prmtve s to ensure that the leak s detected. Ths s possble only f the sensor traverses the ppe that has the leak (.e., sensng coverage), whch s the key focus of the paper. Most exstng n-ppe moble sensor solutons dsrupt the normal functonng of a WDS [3] [22], or are too large and nvolve tedous operatons [2]. The movement of a free swmmng moble sensor n a WDS wth branchng ppes s random n terms of the path taken by the sensor. Several exstng solutons gnore ths aspect and assume that they can ensure a determnstc path for the sensor [3] [23] [22] [2]. To reduce the cost of operaton and automate the process of montorng all ppes n a gven area, there s a need to ntellgently nsert suffcent number of sensors so as to ensure that sensors traverse all ppes. It s mportant to note that a utlty manager may suspect the presence of a leak wth the help of a statc sensor system, n whch case, a moble sensor network ads the statc sensor system n confrmng the presence and localzng the leak. A recent work tackles the optmzaton of number of sensors used when a utlty owner/user provdes a requred degree of coverage [2]. Degree of coverage refers to the mnmum probablty that a leak present on any of the ppes s detected. Throughout the paper, we refer to ths problem as the Maxmzaton of Number of Sensors problem (). Gven a constrant on the degree of coverage, the paper presents a greedy algorthm to select the best nserton ponts and number of sensors to nsert at those ponts so as to mnmze

2 2 the number of sensors requred. The paper also presents a mechansm to localze leaks usng statc devces, called beacons, placed outsde the ppelne. The performance of the soluton s evaluated usng a smulator called FlowSm. The metrc used n the evaluaton was sensng coverage, whch s the number of edges covered by sensors n each smulaton run. A more realstc constrant n desgnng a moble sensor network for WDS leak detecton s the number of avalable sensors, whereby we answer the queston - what s the best sensng coverage we can expect wth a gven number of sensors. We solve the problem of maxmzng the probablty of detectng a leak, gven a constrant on the number of moble sensors that may be used. Specfcally, we tackle two problems, namely, the Maxmzaton of the Lower Bound of Sensng Coverage (), and the Maxmzaton of the Average Sensng Coverage (),.e., we derve nserton ponts and number of sensors to nsert at those ponts so that the lower bound, or average sensng coverage s maxmzed whle keepng the number of sensors nserted constant. Typcally, we are nterested n montorng a part of a WDS where the leak s suspected to be present. The sensors have uncontrolled moblty and ther movement s aded by the flow of water n the ppes. We assume that there s a certan tme perod when the flows n the network do not change (tme-nvarant flow). Our solutons tend to perform better than, snce our problem s formulated to maxmze sensng coverage. To the best of our knowledge, ths paper s the frst attempt to maxmze the probablty of leak detecton usng moble sensors, wthout dsruptng the functon of the WDS, when there s a fxed number of sensors avalable. More formally, the contrbutons of ths paper are: We formulate two optmzaton problems wth a constrant on number of sensors, namely maxmzaton of lower bound of sensng coverage (), and maxmzaton of average sensng coverage () We present solutons usng standard technques,.e., nteger lnear programmng and greedy heurstcs to solve the and problems respectvely We compare our solutons to [2] problem and demonstrate an mprovement n both the lower bound and the average sensng coverage n a vrtual model cty, Mcropols [4] II. BACKGROUND AND RELATED WORK We look at the state of the art on Leakage and Backflow Detecton from two perspectves: water dstrbuton system montorng for leak detecton and wreless sensor networkng for WDS montorng. We also provde background on the terms used n ths paper. A. State of the Art n WDS Leak Detecton There exst several methods based on varous operatng prncples for detecton, localzaton, and pnpontng of leakages n muncpal water dstrbuton systems. Water audts based on meterng and water balance calculatons can be performed to quantfy water losses and provde an extremely crude approxmaton of the locaton of losses. A better estmaton s acheved through step-testng method whereby valves are systematcally closed to subdvde the area and localze the leakage. A comparatvely more recent leak localzaton method s acoustc loggng that s performed usng hydrophones or vbraton sensors []. Ground penetratng radar s employed to localze the leaks by vrtue of detectng underground vods caused by leakage water flow n the mmedate vcnty of ppes. More accurate leakage localzaton, whch s also referred to as leakage pnpontng, may be acheved usng leak nose correlaton, tracer gas, and pg-mounted acoustc technques. Detaled descrpton and comparson of these well-known methods for detecton and pnpontng of leaks may be found n [9] [7] [6]. The applcaton of nlne, moble sensors technology for leakage pnpontng has attracted a lot of attenton by both researchers and practtoners durng the recent years. They have been already appled to water utltes of several ctes around the world, ncludng Dallas, Montreal, and Manla. Ther ncreasng popularty s presumably assocated wth ther ablty to pnpont the leaks more accurately than other exstng methods wthout causng any dsrupton to regular water utlty servce. Table I contans most of the exstng practcal solutons that use moble sensors for leak detecton n WDS. It s clear from the table that there s no soluton that addresses the randomness of sensor movement at junctons of a WDS. Although nlne, moble sensors for pnpontng leakages have been already desgned and fabrcated, decson support models to facltate and enhance ther operaton through smulaton of ther movement n the ppelnes network and optmzaton of ther applcaton s stll underdeveloped. Development of such computatonal models s a major focus of ths study. B. State of the Art n WDS montorng usng Moble Sensors Several solutons to montor ppelne usng moble sensors are addressed by the research communty [2] [4] [9]. TropusNet [4] s a soluton for autonomous contnuous montorng of ppelnes. The soluton however assumes that the path of a sensor can be made determnstc by controllng the flow of water, whch s mpractcal wthout dsruptng the functon of the WDS. MISE-PIPE [9] s another smlar system based on magnetc nducton n underground ppes. Several theoretcal results n ppelne montorng usng moble sensors are also present. [27] performs a mathematcal analyss of sensor placement and presents analyss of complex networks usng graph theoretc concepts. [5] addresses the gallery guardng problem that requres every pont n the ppe to be montored by a robot. However, these problems are specfc to controlled moble devces. The problem of ensurng k-coverage n scenaros smlar to the one we consder s presented n [26]. However, the coverage requrement s dfferent,

3 3 Authors/Company Name Capabltes Sensng technology Free-swmmng or lne tethered Pure Technologes Sahara [22] Detectng leaks, pockets of trapped gas, Hydrophone; camera Lne tethered and vsual nspecton Pure Technologes SmartBall [23] Detectng leaks, pockets of trapped gas, Acoustc emtter and recever Free-swmmng and structural defects Pure Technologes PpeDver [2] Detectng leaks, pockets of trapped gas, Acoustc emtter and recever Free-swmmng and structural defects La et al. (2) PpeProbe [3] Mappng hdden ppelne Meterng pressure and angular Free-swmmng velocty Trnchero et al. (29) [25] Detectng leakage. Includes wreless Hydrophone Free-swmmng transmsson system Chatzgeorgou (2) [6] Detectng leakage Hydrophone Free-swmmng Purdue-TAMU sensor [3] Measurng water qualty parameters. Ion-selectve electrode based bochp Free-swmmng Includes energy harvest and wreless transmsson systems MIT MRL Lab PpeGuard [5] Detectng leakage Measurng pressure Free-swmmng Can be potentally used for backflow detecton TABLE I EXISTING TECHNOLOGIES THAT USE MOBILE SENSORS FOR WDS LEAK DETECTION and moblty s gnored. Despte all the exstng research n practcal as well as theoretcal aspects of ppelne montorng, there s very lttle focus on random, uncontrolled movement of sensors. C. Prelmnares In ths paper, we are nterested n detectng a leak usng a set of moble sensors. The movement of sensors n the ppes cannot be controlled. The movement of water n the ppes pushes the sensors and the sensors flow along the drecton of water flow. If a sensor flows along a ppe wth a leak, t detects the presence of a leak. The nformaton from the sensors s collected ether by communcatng wth the sensors through wreless access ponts placed outsde the ppes, or by physcally capturng the sensors. We model a WDS as a drected graph G(V, E) wth vertces V correspondng to junctons and edges E correspondng to the ppes. There are n vertces n the network, V = {v,..., v n }. The edges n the network are drected and denoted as e j, where the edge s drected from ntal vertex v to termnal vertex v j. The vertces are numbered so that f there s nonzero flow from v to v j then < j. The total number of avalable sensors s s. The sensors placement s determned usng a vector, s = {s, s 2,... s n } where s sensors are nserted n vertex v. The tme of nserton of the sensors s not of sgnfcance, as long as they are nserted before the flows n the ppes change due to varyng demands. We are usually nterested n montorng a certan part of the WDS, called a zone of nterest I. A zone of nterest s typcally the set of edges where the utlty owner/user suspects that the leak s present. III. PROBLEM FORMULATION Before we formulate the problem, we present the leak detecton model (.e., the sensng model), and the sensor moblty model. A. Leak Detecton Model We assume a bnary sensng model,.e., f a sensor passes by a leak, t detects the presence of a leak. Therefore, for leak detecton, we requre that at least one sensor traverses the edge contanng the leak. Typcal locaton accuracy of Sahara leak detecton technology [22], for nstance, s wthn.5 feet and t can locate very small leaks (as small as.5 gal/mn) as clamed by the manufacturer. Ths s consstent wth our model, snce the average length of a ppe n the model cty used n our evaluatons, Mcropols [4], s 3 feet. Throughout ths paper, f a sensor covers an edge, t s assumed that f a leak was present on that edge, t s detected. B. Sensor Moblty Model We assume that the flows n the ppes of the WDS are known, and fxed, for the perod of tme durng whch sensors are deployed. The movement of sensors through ppes s probablstc owng to the flud dynamcs at the junctons of the WDS. In ths paper, we assume that the probablty of a sensor movng through an edge s dependent on the dstrbuton of outgong flows at junctons. The probablty of movng from one vertex to another by traversng a sngle edge s represented n matrx M, where an element p j of matrx M: p j = probablty of movng from vertex v to vertex v j on a sngle edge (n one transton step) Snce G s a drected graph wth no cycles, the matrx M s an upper trangular matrx, as follows: p 2... p n... p 2n M = We model the movement of sensors through vertces as a bnomal dstrbuton. Each sensor represents a tral n the bnomal experment and the probablty that a sensors travels

4 4 through a certan edge s the probablty of success for the trals. We assume that the movement of a sensor s ndependent of the movement of any other sensor. Smlar to [2], we defne a traversal probablty matrx to represent the probablty of a sensor reachng another vertex traversng any path as: T = M k = I + M + M An element of matrx T, t j, s the probablty of reachng vertex v j wth a sensor startng at v. The probablty that a sensor startng at vertex v wll vst the edge s t e,jk = t,jk p jk As ndcated earler, we use a vector s to keep track of the confguraton of sensor deployment. In the vector s = [s, s 2,..., s n ], the entry s k represents the number of sensors deployed at node v k. Probablty of coverng an edge: Consder a scenaro where s sensors are nserted at vertex v. Here, the probablty at least one of these sensors reaches (vsts) edge s ( t e ) s,jk Ths s obtaned based on the probablty of the complement event n whch none of the s sensors, that travel ndependently, reaches. Now consder the cumulatve effect of all sensors nserted n a confguraton s = {s, s 2,... s n }, where s s the number of sensors nserted n vertex v. The probablty that at least one sensor reaches wth the confguraton s, represented as P V (s, ) s P V (s, ) = C. Problem formulaton n ( ) t e s,jk = We formulate two problems, namely, the problem of maxmzng the least probablty of coverng any edge, and the problem of maxmzng the average probablty of coverng any edge. Note that coverng an edge s synonymous to detectng a leak present on that edge. ) Maxmze Lower Bound Sensng Coverage (): We defne Lower Bound Sensng Coverage, LBSC as the mnmum probablty of coverng an edge,.e., Lower Bound Sensng Coverage s the largest number such that E, [P V (s, )] LBSC,.e., LBSC = mn [P V (s, )] As mentoned before, the problem of ensurng a certan LBSC whle mnmzng the number of sensors was formulated n [2] (). In ths paper, we compare our soluton wth. maxmze LBSC.e., maxmze mn such that s = c =...n [( s =... n ( t e,jk ) s )] 2) Maxmze Average Sensng Coverage (): We defne Average Sensng Coverage, ASC for edges as the expected number of edges to be vsted by at least one sensor of the confguraton dvded by total number of edges. For every edge, we ntroduce the ndcator random varable, χ s,ejk, that takes the value f the edge s vsted by the confguraton of sensors and the value otherwse. χ s,ejk = { wth probablty p = P V (s, ) wth probablty p [ Sensng coverage s therefore formally defned as ] E e χ jk s,, the expected number of edges vsted by sensors n the confguraton s. Due to the lnearty of expected value SC = E χ s,ejk = E [ ] χ s,ejk = P V (s, ) ejk ejk maxmze j such that s = c =...n maxmze ASC.e., [ s =... n IV. SOLUTIONS ( t e,jk) s ] For the optmzaton problems stated n the prevous secton, we use standard technques to solve them as descrbed n ths secton. A. Integer Lnear Programmng to solve the Problem The problem of maxmzng lower bound sensng coverage s a mn-max problem that can be reduced to an nteger lnear programmng problem as: [ max mn ] ( ) t e s,jk s whch reduces to mn s max ( ) t e s,jk Snce logarthm s a monotone ncreasng functon, () (2)

5 5 Algorthm Greedy for problem Requre: n, c, t e,jk : ntalze s as 2: for k = to c do 3: max =, nsertat = 4: for all v V do 5: ncrement s 6: f [ ] ( t e,jk )s > max then 7: max = ] [ ( t e,jk )s 8: nsertat = v 9: end f : decrement s : end for 2: ncrement nsertat element n s 3: end for Fg.. v Example network from EPANET v 2 [ ] ( ) ln t e s,jk = ln ( t e,jk) s ( ) where log t e,jk are constants. The problem therefore reduces to: v 3 v 4 v 5 v 8 v 7 v 6 v 9 v mnmze x such that s = c =...n ln ( t e,jk) s x =... n s =... n where x s a new varable ntroduced to convert a mn-max problem to a lnear program. The above problem s solved usng the CPLEX mxed nteger lnear programmng functon. B. Algorthms/Heurstcs to solve the problem The objectve n the problem of maxmzng average sensng coverage ASC s wrtten as mnmze j ( β s j whch s a non lnear convex programmng problem. We solve ths problem usng a heurstc as descrbed n Algorthm for the nteger optmzaton problems. The algorthm starts wth an ntal confguraton n whch no sensors are nserted (lne ) and nsert one sensor at a tme (lne 2), wth nserton done at the node that would generate the best value of the objectve functon gven the confguraton of sensors already n place (lnes 4-). ) C. Example v v 2 Fg. 2. Example network from EPANET To understand the optmzaton problems and ther solutons, we present a sample 2 node network generated from EPANET [7], as shown n fgure. Ths network can be smplfed and wrtten as a graph as shown n fgure 2. At each juncton, the flows are equally dstrbuted n all the outgong edges,.e., p 23 = p 24 = p 27 = 3, p 45 = p 46 = 2, etc. Here, the zone of nterest ncludes all the edges. The problems are solved wth the constrant s + s s 2 =. The soluton to the problem, solved usng CPLEX s {6,, 2, 2,,,,,,,, }, and the lower bound sensng coverage acheved s.995. The soluton to the problem, solved usng the greedy heurstc n Algorthm s {5,, 2, 2,,,,,,,, } and the average sensng coverage s.945. V. PERFORMANCE EVALUATION We use a vrtual cty network model (Mcropols [4]) n our smulatons. Mcropols s a complete model of a cty WDS that s modeled usng EPANET [7]. The performance of our algorthm was evaluated aganst [2]. The placement of sensors s determned usng Flowsm [2] for the prob-

6 Acheved ASC.9 Acheved ASC.9 Acheved ASC (a) (b) (c) Fg. 4. Comparson between and for acheved average sensng coverage n MATLAB for (a) Zone I, (b) Zone I 2, (c) Zone I 3 Acheved ASC (a) Acheved ASC (b) Acheved ASC Fg. 5. Comparson between and for acheved average sensng coverage over runs n FlowSm for (a) Zone I, (b) Zone I 2, (c) Zone I 3 (c) (a) (b) (c) Fg. 6. Comparson between and for acheved lower bound sensng coverage n MATLAB (a) Zone I, (b) Zone I 2, (c) Zone I (a) (b) (c) Fg. 7. Zone I 3 Comparson between and for acheved lower bound sensng coverage over runs n FlowSm for (a) Zone I, (b) Zone I 2, (c) lem, CPLEX n MATLAB for the problem, and a greedy heurstc mplementaton n MATLAB for the M ASC problem. The smulatons were also run on FlowSm [2], that smulates the movement of moble sensors n a WDS based on flows determned by EPANET. Moble sensors have a clear advantage over statc sensors n terms of locatng the leaks. However, to acheve ths end, we need to ensure that the moble sensors traverse through the ppe wth the leak. Ths paper addresses the ssue of coverng all the edges n a gven zone of nterest wth moble sensors, snce t s an essental prerequste for locatng leaks. Comparng the soluton aganst statc sensor networks wll therefore be unfar. On the other hand, other moble sensor solutons assume that the path followed by the sensors s determnstc. Therefore comparng aganst these solutons s also unfar. The parameters that we vared are: () Number of sensors; () zone of nterest - I, I 2, I 3. For comparson, the metrcs we use are: () average sensng coverage (ASC); () lower bound sensng coverage (LBSC). We set the total number of

7 7 Reservor Pumpstaton Ppe I3 V = 7 E = 84 I2 V = 65 E = 86 a greedy heurstc snce the problem s a non-lnear nteger programmng problem. s reduced to a lnear nteger problem that s solved usng CPLEX n MATLAB. Both these solutons are compared to a prevous paper that solves the problem of Mnmzaton of Number of Sensors (). Both the solutons are showed to perform better than n smulaton as well as mathematcally. R EFERENCES I V = 35 E = 44 Fg. 3. Mcropols [4] vrtual cty model showng the zones of nterest for valdaton sensors to 8 dfferent values based on 8 degrees of coverage nputs to M N S (.2,.3,....9) for 3 dfferent zones of nterest. The three zones of nterest are as shown n Fgure 3. All three zones of nterest have dfferent number of vertces, number of edges, and flow dstrbutons at junctons. The ASC and LBSC calculated mathematcally usng MATLAB are plotted n Fgure 5 and Fgure 6. The ASC and LBSC acheved n smulaton usng FlowSm s presented n Fgure 4 and Fgure 7. Here, each scenaro s smulated tmes, and the fgures plot the mean and one standard devaton (f applcable). As the number of sensors s ncreased, the acheved ASC unformly ncreases for both M ASC and M N S problems n both smulaton and mathematcally, as shown n Fgure 4 and Fgure 5. It s nterestng to observe n Fgure 4 that the acheved ASC wth the M ASC s usually hgher than that of M N S, except n one case (Zone I2, number of sensors 328). Ths s because the algorthm n M ASC s a greedy heurstc and does not always acheve the optmal soluton. However, n most cases, M ASC performs better than M N S. It s nterestng to observe Fgure 7 that as the number of sensors s ncreased, the acheved LBSC does not show any dscernable trend n smulatons. However, the LBSC shows an ncreasng trend n theory, as shown n Fgure 6. Ths s because of the random movement of sensors at junctons. The randomness has a lower effect on an average n the case of ASC, but when movement of sensors through ndvdual edges s consdered n calculatng the LBSC, the results become less predctable. In the mathematcal results n Fgure 6, t s clear that LBSC from M N S s lower than that of M LBSC, snce the M LBSC problem s desgned to maxmze LBSC, and the CPLEX solver s used to obtan the optmal soluton. VI. C ONCLUSION Ths paper deals wth leak detecton n Water Dstrbuton Systems. In ths paper, we present an optmzaton problem to maxmze the average, and lower bound probablty of detectng leaks n a WDS, namely Maxmzaton of Average Sensng Coverage (), and Maxmzaton of Lower Bound of Sensng Coverage (). s solved usng [] Amercan Water Works Assocaton. Renvestng n drnkng water nfrastructure. 2. [2] Amercan Water Works Assocaton. Bured no longer: confrontng amerca s water nfrastructure challenge. 23. [3] M. K. Banks, A. Brovont, S. Pekarek, M. Porterfeld, A. Salm, and R. Wu. 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