ACCEPTED VERSION. IWA Publishing 2006

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1 ACCEPTED VERSION D. sunas, J. Víkovský, G. Olsson,. Laber, and A. Spson Falure onorng n waer dsrbuon neworks Waer Scence and Technology, 006; 53(4-5): IWA Publshng 006 The defnve peer-revewed and eded verson of hs arcle s publshed n [Waer Scence and Technology, 53(4-5): , /ws ] and s avalable a PERISSIONS 1 ay, 015 hp://hdl.handle.ne/440/954

2 Falure onorng n waer dsrbuon neworks Dalus sunas*, John Víkovský**, Gusaf Olsson*, arn Laber***, and Angus Spson*** * Dep. of Indusral Elecrcal Engneerng and Auoaon, Lund Unversy, P.O. Box 118, 1 00 Lund, Sweden (E-al: Dalus.sunas@ea.lh.se, Gusaf.Olsson@ea.lh.se) ** Waer Assessen, Deparen of Naural Resources and nes, Queensland, Ausrala (E-al: jvkovsky@pg.co.au) *** School of Cvl and Envronenal Engneerng, Unversy of Adelade, Adelade SA 5005, Ausrala (E-al: aspson@cveng.adelade.edu.au, laber@cveng.adelade.edu.au ) Absrac An algorh for he burs deecon and locaon n waer dsrbuon neworks based on he connuous onorng of he flow rae a he enry pon of he nework and he pressure a a nuber of pons whn he nework s presened. The approach s desgned for edu o large burss wh openng es n he order of a few nues and s suable for neworks of relavely sall sze, such as dsrc eered areas (DAs). The burs-nduced ncrease n he nle flow rae s deeced usng he odfed cuulave su (CUSU) change deecon es. Based on paraeers obaned fro he CUSU es, he burs s sulaed a a nuber of burs canddae locaons. The calculaed changes n pressure a he pressure onorng pons are hen copared o he easured values and he locaon resulng n he bes f s seleced as he burs locaon. The EPANET seady-sae hydraulc solver s ulsed o sulae he flows and pressures n he nework. A sensvy-based saplng desgn procedure s nroduced o fnd he opal posons for pressure onorng pons. The proposed algorh s esed on a case sudy exaple nework and shows poenal for burs deecon and locaon n real waer dsrbuon syses. Keywords Ppe neworks; onorng; nsruenaon; burs deecon and locaon INTRODUCTION A ppe burs s a coon ype of falure n waer dsrbuon syses. I s an undesrable, expensve and, unforunaely, relavely frequen even. A ppe burs can be defned as he rupure of a ppe wall or oher eleen n he nework ha s usually followed by a sgnfcanly large dscharge of waer. Due o he hgh dscharge, burss can have draac consequences, ncludng daage o surroundng nfrasrucure, floodng of properes, nerruped supply, and consuer coplans. Snce any waer supply syses are old and n poor condon, s praccally possble o preven ppe falure. Neverheless, he daage and losses assocaed wh burss can be reduced by nsng he burs deecon and locaon e. Alhough os burss resul n he appearance of waer on he ground surface and are deeced by cusoers or waer copany personnel (passve burs deecon), he average locaon e can be sll que long. In orrson (004) he awareness and locaon of a 4 3 /hour burs s esaed o be 5 days. Obradovc (000) repored burs locaon es of around 18 hours. Experence fro he ol and gas ndusres shows ha he deernaon of a burs s locaon can be ade ore effcen and accurae by connuous onorng of he syse. Recen developens n nsruenaon and daa acquson have reduced he cos of onorng syses and ade connuous onorng of waer supply syses feasble. However, os burs (and leak) deecon echnques consder sngle ppelnes and canno be drecly appled o a nework suaon (Slva e al. 1996; Zhang 001; sunas e al. 003). In fac, he coplcaed opology found n waer dsrbuon neworks requres specal aenon for burs deecon and locaon ehods o be successfully appled.

3 The ajory of ppe nework onorng approaches found n he leraure focus on he assessen of leakage ha s presen n he syse. The os coon and sraghforward echnque s he concep of dsrc eerng area (DA) (WRc 1994). A dsrc s an area of he ppe nework ha s hydraulcally solaed fro he res of he nework by he peranen closure of valves. A DA ypcally coprses properes and has a eered ncong flow and pressure a he enry pon. The leakage level can be deerned by perforng a sple ass balance analyss of he flow ha s enerng he DA. anual echnques are hen used o locae he leak pon, such as lsenng devces and correlaors. Snce he DA concep was nroduced n he 1980s, a consderable aoun of research has been dreced owards fndng a ore effcen way o deec and locae leaks (Andersen and Powell 000; ounce e al. 003; Buchberger and Nadpall 004). os of leakage deecon and locaon echnques descrbed n he leraure arge he whole range of leak szes and ypes (.e. burs, background leakage) and usually do no deerne he exac leak locaon. THE SCOPE OF APPLICATION In hs paper, ppe burss of edu o large sze ha develop whn he perod of nues and have a subsanal nfluence on he pressure whn he nework are consdered. sunas e al. (004) presened a ehodology for he deecon and locaon of sudden burss n ppe neworks based on he connuous onorng of pressure a wo (or ore) pons whn he nework and hydraulc ransen heory. The approach s effcen for ppe falures ha nduce ransen waves no he syse. In soe cases, a ppe break can develop over a longer perod of e causng lle or no observable ransen behavour and herefore canno be locaed by he ransen-based echnque. Ths paper descrbes an approach ha can be referred o as an exenson of he echnque presened n sunas e al. (004) for slower burss. The flow rae and seady sae pressure readngs a a relavely low saplng rae are used o deec and locae he break. The proposed echnque s applcable on a scale of a DA. To splfy he descrpon of he ehod, wo basc assupons are ade: (1) here s only one flow enry pon n he DA analysed and () he deand whn he DA s purely resdenal and he oal deand s assued unforly dsrbued beween all nodes. ODELLING OF STEADY-STATE FLOW IN PIPE NETWORKS A waer dsrbuon nework bascally consss of se of nodes (juncons) ha are joned o each oher by lnks (ppes). The prncples of conservaon of ass a nodes and conservaon of energy beween nodes and n loops are used o odel pressure, flow and hydraulc eleens n he nework. Conservaon of ass dcaes ha he flud ass enerng any node wll be equal o he ass leavng he node: ppes j= 1 Q j D = 0 (1) where Q j s he nflow o node fro j h ppe and D s he deand a he node. The conservaon of ass equaon s appled o all nodes n a nework, resulng n one equaon for each node n he nework. Conservaon of energy dcaes ha he dfference n energy beween wo pons us be he sae regardless of he pah ha s aken (Bernoull 1738): P1 V1 P V Z ha = Z h f + h () γ g γ g

4 where: Z = elevaon; P = pressure; γ = flud specfc wegh; V = velocy; g = gravaonal acceleraon consan; h a = head added by pups; h f = head loss due o ppe frcon; h = head loss due o nor losses. When a seres of lnks and nodes consue a closed pah, hey for a loop. In a dsrbuon nework, he su of all energy losses n an ndependen closed pah or loop us equal zero. Addonally, energy us be conserved beween wo nodes of known energy. As a resul, one energy equaon us be developed for each ppe (or loop) dependng on he ehod used. In hs paper, he EPANET hydraulc solver (U.S. Envronenal Proecon Agency 000) s used o sulae he flows and pressures n a ppe nework. Fro Eqs. (1) and () can be seen ha change of deand a one node (.e. due o a burs) wll nfluence he flow raes and pressure a ha node and he dsrbuon of pressures and flow raes a oher nodes. Snce a nework wh easured nflow rae (DA) s consdered n hs sudy, he burs flow rae wll be fully realsed n he flow rae easureen a he enry pon of he syse. ONITORING OF SYSTE FLOW FOR A BURST EVENT In hs paper s proposed ha he burs even ay be deeced fro he connuous flow rae easureen a he enry pon of he nework. The burs dscharge wll ncrease he easured oal flow rae, Q, enerng he nework. The ncrease of Q ay be deeced usng a cuulave su (CUSU) change deecon es (Page 1954). The CUSU es has been exensvely appled for change deecon n dfferen e seres analyss probles (Bassevlle and Nkforov 1993). If he flow rae daa conans a hgh level of easureen nose pre-flerng s appled usng he adapve Recursve Leas Squares (RLS) fler. The fler esaes he sgnal θ fro he easureen Q (conanng nose) as θ ( 1 λ) Q = θ 1 + ( λ) ε = λθ (3) where ε = Q θ 1 s he predcon error and he paraeer λ [0,1) s he forgeng facor. The value of he forgeng facor deernes he soohng effec of he fler. The predcon error values ε are fed no he CUSU es o deerne wheher a change has occurred n he easured sgnal. aheacally, he CUSU es s forulaed as he followng e recurson G0 = 0 G = ax 1 f G > h hen ( G + ε ν, 0) ssue alar and se a =, G where G s he cuulave su value a a e, h and ν are hreshold and drf paraeers respecvely. For every saple of daa, he par of he change n sgnal ε ha exceeds he drf value (he expeced varaon) s added o he cuulave su G. When G reaches he hreshold value h, an alar s ssued and he e of change a s recorded. In he classcal for of he CUSU algorh G s hen rese o zero. A odfed CUSU es s presened n hs paper. Insead of reseng G drecly afer a (when G >h), he cuulave su s calculaed unl s value sars decreasng. The reason for such a odfcaon s due o he uncerany of he burs paraeers he burs sze and developen e (fro he burs even unl he axu burs flow s esablshed). Fgures 1a and 1b show he dealzed burs flow and oal flow rae races. The axu burs flow rae Q B,ax and he e f - s ha s aken for Q B o reach Q B,ax are unknown and can vary consderably for dfferen burss. As wll be shown laer n he paper, for he deernaon of he burs locaon s benefcal o regser he axu change n pressure nduced by he burs. To acheve ha, pressure easureens before he burs even (= s ) and afer he burs flow has reached s axu value (= f ) have o be deerned. As shown n Fgure 1c, s corresponds o he e when dg/d becoes posve and f corresponds o he e when dg/d becoes zero or negave. Based on hese observaons es s and f can be found. = 0 (4)

5 Q B () Q B,ax (a) Flow rae a burs pon (b) Syse s oal flow rae (c) Cuulave su Q () G() Q+Q B,ax 0 Q h 0 s f s f s a f Fgure 1. The generalsed races of (a) flow rae a burs pon, (b) oal flow rae an he enry pon and (c) cuulave su. The drf ν s chosen so ha s larger han ypcal operaonal flow rae oscllaons n he syse, whch can be deerned fro he hsorcal flow rae daa. Usually waer deand changes que rapdly durng ceran perods of he day and can be raher sagnan a oher es, especally durng he ngh hours. Thus, varable drf selecon can be nroduced o prove he perforance of he burs deecon and locaon echnque. The specfc drf se pons can be derved for every hour or peak/off-peak perods based on he observed flucuaons of flow rae n a parcular nework. Theorecally, hreshold h can have a sall posve value (resulng n a s ). However, n realy, he flucuaons n flow rae due o deand can exceed drf value whch would resul n G > 0. To preven false alars rggered by such suaons, h s se o be larger han drf,.e. h = ν. BURST LOCATION ALGORITH The scheac vew of he coplee burs deecon and locaon algorh s shown n Fgure. easure Q() CUSU Burs even? No Yes Fnd j =H j ( f )-H j ( s ) For all easureen pons Assgn unfor deand o nodes Q D, = Q( s )/N Trunk an Deand flucuaon Q() 3 DA Burs 1 Sulae burs a node wh ouflow Q D, = Q D, + Q B where Q B =ΔQ Calculae OF s k 1 k = j j OF s j= 1 p= p p Repea for all nodes = 1 o N Burs locaon seleced as node wh nu OF Fgure. The srucure of he connuous burs onorng algorh Once he presence of a burs s deeced n he flow rae easureen a he enry pon of he nework, he locaon of he burs s found by searchng for he burs node based on he observed changes of pressure a a nuber of easureen pons hroughou he nework. Usng he burs sar e s and he e when burs flow has reached s axu f, as denfed by he CUSU change deecon es, he oal change n flow rae due o he burs and he changes n pressure a he onorng pons can be calculaed:

6 ΔQ j = Q = H ( f j ) Q ( f ( ) H s ) j ( ) s (5) The deand value for an ndvdual node s assgned as a proporon of Q ( s ) based on hsorcal deand nforaon a ha node. If no deand nforaon s avalable, an average deand of Q D, =Q ( s )/N s assgned unforly o all nodes. The burs of sze Q B =ΔQ s sulaed by assgnng Q D, = Q D, + Q B o one burs canddae poson and calculang he pressure and flows n he nework. In hs sudy, all he nodes n he nework are nonaed as burs canddae locaons. Sulaed pressure values a he easureen pons are used for calculang he objecve funcon: s k 1 k = j j OF [ 1, N ] (6) s j= 1 p= p p where s he easured change n pressure, s s he sulaed change n pressure, k s a nuber of pressure easureen pons n he syse and 1,, k are he nodes where he easureen pons are locaed. The objecve funcon s calculaed for all burs canddae locaons and he node havng salles OF value s declared o be he burs poson. The burs sze s equal o he deeced change n he flow rae observed a he nle pon of he nework (Q B =ΔQ ). EASUREENT LOCATION ALGORITH The opal placeen of he pressure onorng pons s an poran facor ha nfluences he perforance of he proposed echnque. A large nuber of easureen posonng (also called saplng desgn) approaches are descrbed n he leraure (Lgge and Chen 1994; Bush and Uber 1998; De Schaezen e al. 000; Lansey e al. 001; Kapelan e al. 003; Víkovský e al. 003). os are based on sensvy analyss. The sensvy arx can be derved usng a perurbaon ehod (Bush and Uber 1998; De Schaezen e al. 000) where every eleen represens he change n a sae varable due o he change of a sngle paraeer: S, j * H j H j ( QD, ) H j ( QD, ) = [ 1, N ], j [1, N ] (7) Q Q Q D, D, * D, where H j (Q D, ) s he copued head a node j for he assued deand Q D, a node and H j (Q D, * ) s he copued head a node j afer alernang he assued deand Q D, a node o Q D, *. The value of Q D depends on he average deand n he syse ha can be deerned fro he hsorcal daa. The deand perurbaon Q D * s se dependng on he expeced sze of he burs. A saplng desgn can be defned as a se of onorng pons X=( 1,, k ) where j s he poson of j h onorng pon. The ask s o opally dsrbue k onorng pons aong N nodes. Two perforance ndcaors ay be used o easure he er of a parcular saplng desgn: (1) The su of sensves a all onorng pons n saplng desgn X for every possble burs locaon: N k η1, X = S, (8) = 1 j= 1 The upper l η 1,ax can be derved fro he sensvy arx by seng k=n. The lower l η 1,n s zero. j

7 () The probably ha a unque burs locaon wll be derved usng he objecve funcon fro Eq.(6) for every burs canddae locaon: η S, S j p, j = P > β S, S v p, v, X [ 1, N ], p [1, N ], j [1, k 1], v [, k] (8) where β depends on he resoluon of pressure easureens. The ls η,ax and η,n are assued o be 1 and 0 respecvely. To cobne he wo perforance ndcaors (Eq.(8) and (9)) no one objecve funcon a coprose prograng approach s used. Coprose prograng s a ul-creron dsance-based echnque desgned o denfy coprose soluons. The followng objecve funcon s used: ηn, X ηn,ax OF X = wn (9) n= 1 ηn,n ηn, ax where w 1 and w are he weghs for η 1 and η respecvely. The saplng desgn X ha has he salles value of OF X s seleced as opal saplng desgn. CASE STUDY The exaple nework odel shown n Fgure 3 s used o verfy he proposed ehod for burs deecon and locaon. The nework has 108 ppes and 79 nodes. Ppes have daeers beween 100 and 00, lenghs beween 70 and 10 and a roughness hegh of 0.. The node elevaons are n he range of 140 o 160. The nework s fed fro a fxed head (56 ) reservor. Fgure 3. The layou of he ppe nework used for he case sudy. The 4-hour ncong flow rae easureen (Fgure 4a) s arfcally generaed a 1 nue nervals based on he daa presened n Guerco e al. (001) assung ha 300 households are conneced o he nework. Nose s added o he flow rae paern as shown n Fgure 4b o represen dscree deand changes correspondng o household applance use as descrbed by Buchberger and Nadpall (004).

8 (a) (b) Fgure 4. (a) 4-hour deand curve and (b) zoo n on he deand curve o show nose characerscs. 1 nue saplng e. The burs was sulaed as an ncrease n he easured flow rae (Fgure 1a,b) wh sze correspondng o he acual sze of he burs and he slope beng proporonal o he burs openng e. The pressure was onored a nodes 8, 57 and 79 (1, and 3 n Fgure 3) whch were seleced usng he saplng desgn procedure descrbed earler n he paper (wh w 1 =0.8 and w =0.). The easured pressure changes a onorng pons were obaned by sulang he burs of he acual sze a he acual locaon and subracng pressure values before and afer he burs even: j=h j (afer burs)-h j (before burs) for all easureen ses j [1,k]. The varable drf value for CUSU es s obaned by dvdng a 4-hour perod no wo pars ngh (:00-06:00 hours) and day (6:00-:00 hours). The drf was chosen o be larger han he axu changes n flow rae durng he ngh and day e nervals as and L/s. The hreshold has been se o wce he drf value,.e and 3.56 L/s for ngh and day pars respecvely. Three ses of ess were perfored o evaluae he perforance of he proposed echnque: (1) Deecon of burss ha occur a dfferen es of he day, wh dfferen szes and openng es (see Table 1). Fve dfferen burss wh szes beween 5 and 0 L/s and openng es n he range of 1 o 8 nues were successfully deeced. Errors n he esaed sze of he burs were less han.5%. Table 1. Burs deecon ess and resuls. Acual burs paraeers Deeced burs paraeers Burs No. Te of burs Openng, n Sze, L/s Te of burs Openng, n Sze, L/s 1 4: : : : : : : : : : () Locaon of burss ha occur a burs canddae locaons. The acual burs was placed a he node of he nework (all nodes were esed, one es for each locaon) and he search for he burs locaon was perfored usng he proposed echnque. The fve dfferen burss fro he frs se of ess were esed and resuls are suarsed n Table. Around 70% of all esed burs locaons

9 were denfed unquely and n oher cases, wo or ore nodes (ncludng he acual burs locaon) clearly denfed he par of he nework where he falure has occurred. Table. Burs locaon ess and resuls when burss occur a nework nodes. Tes No. Acual burs Burs locaon ore han one locaon had Burs No. locaon found (ess) sae OF value (ess) 1-79 Nodes 1-79* Nodes 1-79* Nodes 1-79* Nodes 1-79* Nodes 1-79* *79 ess were perfored wh one burs node per es. (3) Locaon of burss ha occur a pons ha were no seleced as burs canddae locaons,.e. along he ppe lengh. The acual locaon of he burs was no o one of he canddae burs locaons. Alhough unable o deerne he rue burs locaon, he echnque denfed he adjacen node o he burs ppe as he burs locaon, as shown n Table 3. Table 3. Burs locaon ess and resuls when burss occur along ppes. Tes No. Burs No. Acual burs locaon Esaed burs node Beween nodes 3 and Beween nodes 63 and Beween nodes 17 and 4, Beween nodes 39 and CONCLUSIONS The proposed burs deecon and locaon echnque has been deonsraed o be exreely prosng. As shown n he case sudy, a range of burss ha occur a dfferen es of he day wh dfferen szes and openng es and a dfferen locaons whn he nework were successfully deeced and locaed. One flow rae and only hree pressure onorng pons are enough o fnd he unque locaon of he burs ha occurs a (or n beween) for up o 70% of nodes n he nework ha has 79 nodes and 108 ppes. The echnque s based on he real-e connuous onorng of nework nflow and pressure, hus, he burs s deeced and locaed drecly afer occurs and he solaon e can be nzed prevenng he large losses assocaed wh he ppe falure. Furher research, ncludng feld valdaon n real ppe neworks, s requred o ake a ore specfc evaluaon of he nfluence of burs paraeers, nework opology and easureen accuracy on he perforance of he ehod. The proposed echnque s suable for applcaons on he DA level, whch would ake s pleenaon n he real waer dsrbuon neworks que sraghforward. If pleened, he proposed echnque could ncrease he effcency and relably of he waer supply. The cos of nsallaon s relavely low and he nvesen reurn e s expeced o be shor. REFERENCES Andersen, J. H., and Powell, R. S. (000). "Iplc Sae-Esaon Technque for Waer Neworks onorng." Urban Waer, (), Bassevlle,., and Nkforov, I. V. (1993). Deecon of Abrup Changes: Theory and Applcaons, Prence-Hall, Englewood Clffs, New Jersey, USA. Bernoull, D. (1738). Hydrodynaca, Argenora.

10 Buchberger, S. G., and Nadpall, G. (004). "Leak Esaon n Waer Dsrbuon Syses by Sascal Analyss of Flow Readngs." Journal of Waer Resources Plannng and anageen, ASCE, 130(4), Bush, C. A., and Uber, J. G. (1998). "Saplng Desgn ehods for Waer Dsrbuon odel Calbraon." Journal of Waer Resources Plannng and anageen, ASCE, 14(6, Noveber/Deceber), De Schaezen, W., Walers, G. A., and Savc, D. A. (000). "Opal Saplng Desgn for odel Calbraon Usng Shores Pah, Genec and Enropy Algorhs." Urban Waer, (), Guerco, R., agn, R., and Pallavcn, I. (001). "Insananeous Resdenal Waer Deand as Sochasc Pon Process." Waer Resources anageen. Ecology and he Envronen, 48. Kapelan, Z. S., Savc, D. A., and Walers, G. A. (003). "ulobjecve Saplng Desgn for Waer Dsrbuon odel Calbraon." Journal of Waer Resources Plannng and anageen, ASCE, 19(6, Noveber/Deceber), Lansey, K. E., El-Shorbagy, W., Ahed, I., Araujo, J., and Haan, C. T. (001). "Calbraon Assessen and Daa Collecon for Waer Dsrbuon Neworks." Journal of Hydraulc Engneerng, ASCE, 17(4), Lgge, J. A., and Chen, L.-C. (1994). "Inverse Transen Analyss n Ppe Neworks." Journal of Hydraulc Engneerng, ASCE, 10(8), sunas, D., Víkovský, J. P., Olsson, G., Spson, A. R., and Laber,. F. (003). "Ppelne Burs Deecon and Locaon Usng a Connuous onorng Technque." Inernaonal Conference on Advances n Waer Supply anageen, CCWI, Iperal College London, UK. sunas, D., Víkovský, J. P., Olsson, G., Spson, A. R., and Laber,. F. (004). "Burs Deecon and Locaon n Ppe Neworks Usng a Connuous onorng Technque." 9 h Inernaonal Conference on Pressure Surges, BHR Group, Cheser, UK. orrson, J. (004). "anagng Leakage by Dsrc eered Areas: A Praccal Approach." Waer 1, ounce, S. R., Khan, A., Wood, A. S., Day, A. J., Wddop, P. D., and achell, J. (003). "Sensor- Fuson of Hydraulc Daa for Burs Deecon and Locaon n a Treaed Waer Dsrbuon Syse." Inforaon Fuson, (4), Obradovc, D. (000). "odellng of Deand and Losses n Real-Lfe Waer Dsrbuon Syses." Urban Waer, (), Page, E. S. (1954). "Connuous Inspecon Schees." Boerka, 41, Slva, R. A., Bua, C.., Cruz, S. L., and Perera, J. A. F. R. (1996). "Pressure Wave Behavour and Leak Deecon n Ppelnes." Copuers & Checal Engneerng, 0(Suppleen 6. Par A), S491-S496. U.S. Envronenal Proecon Agency. (000). "Epane Verson.0." U.S. Envronenal Proecon Agency. Víkovský, J. P., Lgge, J. A., Spson, A. R., and Laber,. F. (003). "Opal easureen Se Locaons for Inverse Transen Analyss n Ppe Neworks." Journal of Waer Resources Plannng and anageen, ASCE, 19(6, Noveber/Deceber), WRc. (1994). "anagng Leakage Repors." WRc, UK. Zhang, J. (001). "Sascal Ppelne Leak Deecon for All Operang Condons." Ppelne & Gas Journal, 4-45.

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