Prediction of Critical Submergence for Horizontal Intakes

Transcription

1 Proceengs of the Worl Congress on Engneerng Vol II WCE, July -,, Lonon,.K. Precton of Crtcal Submergence for Horzontal Intakes Arun Goel Abstract Accurate precton of the crtcal submergence for ntakes n open channels has been manly base on expermental stues an theoretcal equatons evelope are emprcal n nature. In the present stuy, estmaton of crtcal submergence for 9 o horzontal ntakes have been attempte by usng emprcal equatons, mult lnear regresson, back propagaton ANN an M moel tree base moelng. The horzontal ntakes have been teste expermentally for two fferent locatons of ntake from the channel be-one wth clearance from the bottom equal to zero (c = ) an the other havng half the ntake ameter (c = /). The ata set has ntake ppes of ameter equal to.,. an. mm for the crtcal submergence uner a we range of flow contons n a flume for 9 o horzontal ntakes. The stuy shows that the soft computng technque namely Back propagaton ANN an M moel tree have emerge as alternate to the analytcal equatons as suggeste by prevous nvestgators on the present ata. Keywors- Crtcal submergence, ntake, moelng, precton, ANN an M moel tree. F I. INTRODCTION LOW through hyraulc ntakes s one of the most complcate types of flow that occurs n nature an nustry. Vortces are forme at the ntakes when water s rawn from the reservors, rvers or sea. Vortces are forme at the ntakes when water s rawn from the reservors, rvers or sea. Thus causes atonal hea loss, rawown of floatng ebrs an reuce effcency of hyraulc machnery []. The vortex ncepton an precton of crtcal conton at ntakes s of nterest for engneerng applcatons n water qualty management [, ]. Intakes n the form of ppes are employe for wthrawng water from rver, lake, reservor for fferent purposes. Insuffcent epth of water above ntake coul result n the formaton of the ar entranng free surface vortces. Formaton of ar entranng vortces n front of ntake may cause operatonal problems, nose, corroson an ultmately reucton n the scharge. Ar entranng vortces have been observe frequently at many nstallatons such as Hrfanl Dam n Turkey, Harspranget Dam n Sween, Karba Dam n Zamba etc []. The vertcal stance between the water level an upper level of ntake s generally calle submergence. Due to nsuffcent submergence of the ntake, ar enters the ntake ppe an reucton n scharge takes place. The submergence epth at whch ncpent ar entranment takes place at the ppe ntake s calle crtcal submergence. The velocty of ntake ppe, ameter of ntake, poston of ntake (bottom clearance) an roughness of the bottom are some of the most effectve ar Arun Goel s wth Department of Cvl Engneerng at Natonal Insttute of Technology, Kurukshetra, Haryana, Ina. Emal: rarun_goel@yahoo.co.n, FAX: +9 ISBN: ISSN: -9 (Prnt); ISSN: -9 (Onlne) entranng problem. There are several methos of avong ar entranment.e. provng suffcent submergence at the ntake entrance by restorng to physcal stues. However, n some stuatons physcal moelng may not be economcal ue to tme an fnancal constrants. Hence n the present paper, an attempt has been mae to prect crtcal submergence of an ntake n water flow by usng soft computng technques ANN an M moel tree on the expermental ata taken from a stuy []. Several emprcal relatonshps an charts are avalable n lterature [, -] for the precton of crtcal submergence for ntakes. These relatonshps relate the crtcal submergence as a functon of Froue number, Reynols number, the vertcal heght of ntake, Weber number, crculaton an some more atonal parameters. Recently, authors n [] also propose the prectors for the crtcal submergence for both flat an bell mouth shape vertcal ntakes. They reporte that Froue number s the preomnant parameter whch affects the crtcal submergence. For the same Froue number, the values of crtcal submergence for flat an bell mouth vertcal ntakes are fferent. However, some nvestgators [, ] have apple soft computng technques lke RBF base ANN for precton of submergence ntake n water flow. In ref. [] authors nvestgate the crtcal submergence n stll water an open channel flow for permeable an mpermeable bottom by usng ANN an compare the results wth the lnear regresson. The present stuy, however, eals wth the etermnaton of crtcal submergence for a lateral (9 o ) horzontal ntake from an open channel flow by usng soft computng moelng technques lke mult lnear regresson, an Back propagaton ANN an M moel tree. II. DETERMINATION OF CRITICAL SBMERGENCE A. Analytcal Soluton An analytcal equaton for the crtcal submergence can be obtane by conserng the flow as potental flow wth ppe ntake as pont snk an superposton of pont snk an unform flow []. The Rankne half-boy of revoluton ves flow nto two regons namely flow area enterng an not enterng the ntake. ntl the upper bounary of the Rankne half boy of revoluton reaches the free surface, the surface water just above the centre of the ntake cannot enter the ntake. At crtcal conton, water surface level above the ntake s almost matchng the upper surface of the Rankne half-boy of revoluton whch s also calle crtcal sphercal snk surface (CSSS). Thus, the vertcal stance between any pont on the upper porton of the Rankne half-boy of revoluton an the ntake level may approxmately be taken as equal to the crtcal submergence. After analyss of the flow, the crtcal submergence n horzontal ntake may be calculate by usng the followng equaton: Sc r c c () Where Sc s crtcal submergence, r s raus of crtcal sphercal snk surface, c s bottom clearance, s ntake ppe ameter, s velocty of flow n ntake, s velocty of flow n flume. WCE

2 Proceengs of the Worl Congress on Engneerng Vol II WCE, July -,, Lonon,.K. B. Dmensonal Analyss [] Ths crtcal submergence can also be obtane by mensonal analyss of varables affectng t. Varous pertnent varables nfluencng the crtcal at a horzontal ntake ppe are,,, c, wth of the channel b, crculaton, mass ensty ρ, ynamc vscosty μ, surface tenson σ, an acceleraton ue to gravty g. The functonal relatonshp for the crtcal submergence S c can be wrtten as: S C f, b,,,,c,,,,g () Where, F = ntake Froue number; R = ntake Reynols number; an W = Weber number. Effect of wth of the channel may be neglecte for crtcal submergence S C < b. After mensonal analyss followng equatons as propose by [] are: (a) Prector for S C / for c = S c. g. (b) Prector for S C / for c = / S c.9 g.9 g.9 g () () moelle as the number of nput varables equals number of nput neurons an number of output varables equal number of output neurons. The etermnaton of optmal number of hen layers an hen neurons s usually cumbersome, as no general methoology s avalable for ther etermnaton. These networks learn from the tranng ata by ajustng the connecton weghts. There s a range of artfcal neural network archtectures esgne an use n varous fels of hyrology an hyraulcs. Most of the stues employng neural networks for water resource problems have use back propagaton & raal bass functon types of neural networks. In ths stuy, a fee-forwar neural network wth back propagaton learnng algorthm s apple. The basc element of a back-propagaton neural network s processng noe an structure of commonly use back propagaton neural network (Fgure ). A three layer fee forwar ANN has been shown n Fg, whch conssts of three layers known as nput, hen an output layers. Input layer neuron are calle as x, x, x ; hen layers neurons are h, h, h an output layers neurons are O,O,O. The output of a neuron s ece by an actvaton functon, whch can be step, sgmo, threshol an lnear etc. The propose relatonshps for S c /,.e., Equaton () an equaton () are valate for precton of S c / for c = an c = /. It was foun that for c = prectons s wthn + % error of observe values an for c = /, wthn + % error. The same equatons have been use n the present stuy n orer to make a comparson wth soft computng technques. The equatons namely Sc/ =. + F [] an Sc/ = + F [] are also use n the present stuy on the same ata set an the results are compare wth the soft computng technques. Fgure Three layer fee forwar neural network C. Precton Methos of Crtcal Submergence Here the author has use ata sets taken from the expermental stuy by [] for tranng an moel verfcaton to prect the crtcal submergence of horzontal ntake. The ANN, M moel tree an lnear regresson approaches are use to prect the crtcal submergence for the horzontal ntake at two fferent postons for c = an c = /. The results obtane are also compare wth analytcal equatons [,, ]. III. ARTIFICIAL NERAL NETWORKS A neural network s an artfcal ntellgence technque that mmcs a functon of the human bran. Neural networks are general-purpose computng tools that can solve complex non-lnear problems n the fel of pattern recognton, classfcaton, speech, vson an control systems. The network comprses a large number of smple processng elements lnke to each other by weghte connectons accorng to a specfe archtecture. A neuron conssts of multple nputs an a sngle output. The number of neurons n the nput an output layers are fxe by the problem beng In a back propagaton neural network, generally, there s an nput layer that acts as a strbuton structure for the ata beng presente to the network. Ths layer s not use for any type of processng. After ths layer, one or more processng layers follow, calle the hen layers. The fnal processng layer s calle the output layer n a network. Ths process s repeate untl the error rate s mnmze or reaches to an acceptable level, or untl a specfe number of teratons have been accomplshe. Graent escent metho can be use to ajust the nterconnectng weghts to acheve mnmal overall tranng error n mult-layer networks. The generalze elta rule, or back-propagaton s one of the most commonly use methos [] n whch the frst ervatve of the total error wth respect to a weght etermnes the extent to whch that weght s ajuste. A neural network base moellng approach requres settng up several user-efne parameters lke learnng rate, momentum, optmal number of noes n the hen layer an the number of hen layers so as to have a less complex network wth a better generalzaton capablty. ISBN: ISSN: -9 (Prnt); ISSN: -9 (Onlne) WCE

3 Proceengs of the Worl Congress on Engneerng Vol II WCE, July -,, Lonon,.K. IV. M MODEL TREE One of the popular ways of classfyng of a partcular nput s a ecson tree. It conssts of leaf or answer noes that ncate a class an ecson noes that contan an attrbute name an branches to other ecson tress. There are many effcent algorthms for bulng ecson trees such as ID an C. as propose n [9]. The structure of M moel tree follows the ecson trees an has multvarate regresson moel at leaf noes. Thus M s a combnaton of pecewse lnear moels, each of whch s sutable for a partcular oman of nput space as shown n Fg.. The algorthms of moel tree (MT) break the nput space of tranng ata through noes to assgn a lnear moel sutable to sub area of nput space. The contnuous splttng often results n a too complex tree that nees to be reuce to a smpler tree to mprove the generalze capacty. The value precte by moel at the leaf s ajuste by smoothng operaton to reflect the precte values at the noes along the path from root to that of leaf. The overall global moel s the collecton of these lnear moels, wheren optmal splttng of nput space s one automatcally. Moel tree can learn effcently an tackle tasks of hgh mensonalty wth hunre of attrbutes as mentone [,,, ]. Fgure Splttng the nput space X.X by M moel tree algorthm & each moel s lnear regresson moel. V. PERFORMANCE EVALATION CRITERION The ata sets mentone n the stuy by [] are use n the present stuy for moel bulng an valaton to assess the potental of the emprcal equatons, lnear regresson, Back propagaton ANN an M moellng technques n prectng the crtcal submergence for horzontal ntake. The correlaton coeffcent (CC) an Root Mean Square Error (RMSE) values are use as shown n equaton () an () manly for the performance evaluaton of moels an comparson of the results for precton of crtcal submergence. A hgher value of a correlaton coeffcent an a smaller value RMSE means a better performance of the moel. Further, measure values were plotte aganst the compute values of crtcal submergence obtane wth emprcal equatons, lnear regresson, Back propagaton ANN an M moel tree algorthms. To stuy the scatter of lne of perfect agreement (a lne at o ) was plotte for the ata set along wth % error lne. Error Measure Crtera:. Correlaton coeffcent (r) xy x r () y here x = X - X, y = Y - Y where X = observe crtcal submergence values; X = mean of X, Y = precte crtcal submergence values, Y = mean of Y.. Root mean square error. X Y RMSE () n VI. MATERIAL SED AND METHODS In ths paper moelng technques lke ANN, M moel tree an lnear regresson are beng apple to the problems n precton of crtcal submergence of the horzontal ntake. The ANN an M moel tree requre settng up of the optmum values of the parameters an the sze of the error-nsenstve zone nee to be etermne. To select user-efne parameters.e. ( no of teratons, learnng rate, hen layers, bases, weghts etc. ), a large number of trals were carre out by usng fferent combnaton of these parameters on each of the ata sets (Table ). To reach at a sutable choce of these parameters, the correlaton coeffcents (CC) an Root Mean Square Error (RMSE) were compare an a combnaton of parameters provng smallest value of RMSE an the hghest value of correlaton coeffcent was selecte for the fnal results. Smlarly, a number of trals were also carre out to fn a sutable value of (error-nsenstve zone) wth a fxe value of technque specfc parameters. Varaton n the error-nsenstve zone has no effect on the precte crtcal submergence, so a value of. was chosen for all the experments. Due to the avalablty of small ata sets, a cross valaton was use to tran an test the performance of the lnear, ANN an M moel tree base regresson technques usng WEKA software[]. The cross-valaton s a metho of estmatng the accuracy of a classfcaton or regresson moel. The nput ata set s ve nto several parts (a number efne by the user), wth each part n turn use to test a moel ftte to the remanng parts. In ths stuy, the ata sets of the laboratory were use for both creatng an testng the moels. For quanttatve comparson of results, an error measure, a correlaton coeffcent (r) an RMSE, whch presents the egree of lnear regresson assocaton between precte an true values has been consere, whch s preferre to, n many teratve precton an optmzaton scheme. VII. PREDICTION OF CRITICAL SBMERGENCE se of emprcal equatons n precton of crtcal submergence for horzontal ntake has been stue by []. The frst set of analyss was carre out by usng ata from the stuy [] prectng the crtcal submergence for horzontal ntake. Varous pertnent varables nfluencng the crtcal at a horzontal ntake ppe are ntake ppe ameter, velocty of flow n ntake, velocty of flow n flume, bottom clearance c, crtcal submergence Sc, ntake scharge Q, wth of the channel b, crculaton, mass ensty ρ, ynamc vscosty μ, surface tenson σ, an acceleraton ue to gravty g, Froue number F, Reynol Number, an weber number. However,, Q, were use to prect Sc/ for c = an, Q, D, were use to prect Sc/ for c = /. The values of Sc/ were calculate by analytcal equatons () an () as suggeste by []. A number of trals were carre out to reach at the maxmum correlaton coeffcent base on varous user-efne parameters requre for the ANN, M moel tree an lnear regresson base algorthms by usng WEKA software by a metho of cross valaton. Table proves the values of correlaton coeffcents an RMSE for the ata set. The results obtane for crtcal submergence by equatons () & () as suggeste by [] an soft computng technques lnear regresson, ANN an M moel tree are plotte shown n Fg. to Fg.. ISBN: ISSN: -9 (Prnt); ISSN: -9 (Onlne) WCE

4 Proceengs of the Worl Congress on Engneerng Vol II WCE, July -,, Lonon,.K. For c =, a correlaton coeffcent an RMSE for ANN (.9,.), M tree (.99,.), Ahma (.99,.) are obtane n comparson to a value of.9 (RMSE =.) by usng lnear regresson base moelng (Table ). Further, t s event from Fgure that more number of ponts are lyng on or close to the o lne when ANN an M moel tree an Ahma equaton base moels were use to prect the crtcal submergence n comparson to lnear regresson. For c = /, a correlaton coeffcent an RMSE for ANN (.999,.), M tree (.999,.), Ahma eq (.9,.) are obtane n comparson to a value of.99 (RMSE =.) by usng lnear regresson base moelng (Table ). Further, t can be seen from Fgure that more number of ponts are lyng on or closer to the o lne when ANN, M moel tree an Ahma equaton [] as compare to the lnear regresson. The varaton of actual crtcal submergence versus precte crtcal submergence for the values of c = an c = / by Ahma eq (), Swroop eq [] an Rey & Pckar equaton [] have been plotte n Fg. an Fg. respectvely. For c =, a correlaton coeffcent an RMSE by Swroop equaton [] (.,.), by Rey & Pckfor [] (.,.9) are obtane. For c = /, a correlaton coeffcent an RMSE by Swroop equaton [] (.,.), by Rey & Pckfor [] (.,.) are obtane. The results are better n case of c = / as ncate by the Table. The perusal of these two fgures ncates that the results are closer to the lne of perfect agreement by Ahma equaton [] as compare to Swroop equaton [] an Rey & Pckar equaton []. The prector by [, ] shows that precte values for c = an c = / are greater that the observe values. It may be ue to the fact that the prector by [, ] o not conser the approach velocty an relate crtcal submergence only wth Froue number of the ntake. However, a crtcal examnaton of Fg. to Fg. ncates that relatvely less use ANN an M moel tree technques have emerge as an alternate to the analytcal equatons suggeste by Ahma eq [] for the precton crtcal submergence of the horzontal ntake successfully. TABLE I VALES OF SPECIFIC PARAMETERS OF ANN MODELING S.No Intake poston Momen tum Type of parameter Learnng rate No of noes terato n c =.. c = /.. Precte Sc/ ANN M tree Lnear reg Ahma +% lne Observe Sc/ Ieal ft lne -% lne Fg. Varaton of actual crtcal submergence wth precte crtcal submergence for c = TABLE II COMPARISON OF RESLTS S No Intake poston Type of technque Correlaton coeffcent (r) Root mean square error (RMSE) c = ANN.9. c = M.99. c = Lnear.9. c = Ahma.99. c = Swroop.. c = Rey & Pckfor..9 c = / ANN.999. c = / M c = / Lnear.99. Precte Sc/ ANN M Lnear reg Ahma +% lne Observe Sc/ Ieal ft lne -% lne Fg. Varaton of actual crtcal submergence wth precte crtcal submergence for c = / c = / Ahma.9. c = / Swroop.. c = / Rey & Pckfor.. ISBN: ISSN: -9 (Prnt); ISSN: -9 (Onlne) WCE

5 Proceengs of the Worl Congress on Engneerng Vol II WCE, July -,, Lonon,.K. Precte Sc/ Observe Sc/ Ahma Sw aroop(9) Rey & Pckfor (9) Fg. Varaton of actual crtcal submergence wth precte crtcal submergence for c = by Ahma et al. (), Swroop (9 ) an Rey & Pckar (9 ). Precte Sc/ Observe Sc/ Ahma Sw aroop(9) Rey & Pckfor (9) Fg. Varaton of actual crtcal submergence wth precte crtcal submergence for c = / by Ahma et al. (), Swroop (9) an Rey & Pckar (9). VIII. +% lne Ieal ft lne CONCLSIONS -% lne +% lne Ieal ft lne -%lne Ths stuy was carre out to juge the potental an sutablty of soft computng technques lke Back propagaton ANN an M moel tree regresson base moellng n the precton of crtcal submergence for horzontal ntakes n comparson to emprcal equatons by Ahma et al. [] an the lnear regresson. The outcome of ths stuy encourages the applcaton of back propagaton ANN an M moel tree approach n prectng the crtcal submergence for horzontal ntakes as an alternatve approach to emprcal relatons an the lnear regresson. The stuy also conclues that the results obtane are parameter specfc an ata senstve. ACKNOWLEDGMENT Author wshes to acknowlege Ahma et al. () for ther expermental ata set collecte n laboratory whch has been utlze n ths paper. REFERENCES [] J. Knauss, J., Swrlng flow problems at ntakes. Hyraulc structures esgn manual, AA, Balkema, Rotteram, 9. [] L. Forbes an G. Hockng, Wthrawal from a two layer nvsc flu n a uct, Journal of Flu Mechancs, Vol., pp. -9, 99. [] Z. Ahma, K. V. Rao an M. K. Mttal, Crtcal submergence for horzontal ntakes n open channel flows, Internatonal Journal of Dam Engneerng, Vol XIX, Issue. pp -9,. [] A. K. Jan, K.G. Ranga Raju, an R.J.Gare, Vortex formaton at vertcal ppe ntakes, J of Hyraulc Engneerng, ASCE, Vol., No., pp.9-, 9. [] Ogaar, A. J., Free surface ar core vortex, J of Hyraulc Engneerng, (), 9. [] J.S.Gullver, an R.E.A.Arnt, Hyropower Engneerng Hanbook, McFGraw-Hll, Inc. N.Y. 99 [] ASCE. Guelnes for esgn of ntakes for hyroelectrc plants/ by the commttee on Hyropower ntakes of the Energy Dvson of the Amercan Socety of Cvl Engneers, 99. [] M. Jmng, L.Yuanbo an H. Jtang, Mnmum submergence before ouble-entrance pressure ntakes. Journal of Hyraulc Engneerng, ASCE, Vol., No., pp.-,. [9] F. Kocabas, an N.Ylrm, Effect of crculaton on crtcal submergence for an ntake. Journal of Hyraulc Research, IAHR, Vol., No., pp.-,. [] N.Ylrm, Crtcal Submergence for a Rectangular Intake. Journal of Engneerng Mechancs, ASCE, Vol., No., pp.9-,. [] E.S.R. Dura, Z. Ahma, an M.K. Mttal, "Crtcal submergence at vertcal ppe ntakes. Journal of Dam Engneerng, Vol XVIII, Issue, June, pp. -.. [] F. Kocabas an S.nal, Compare technques for crtcal submergence of an ntake n water flow: J of Avance Engg Software n press,. [] N. Eroglu an T. Baharl, Precton of crtcal submergence for rectangular ntake. J of Energy Engg. ():9-,. [] F. Kocabas, S. nal an B. nal, A neural network approach for precton of crtcal submergence of an ntake n stll water an open channel flow for permeable an mpermeable bottom Computers an Flus, (),pp. -,. [] N. Ylrm, an F.Kocabas, Crtcal Submergence for Intakes n open channel flow. Journal of Hyraulc Engneerng, ASCE, Vol., No., pp.9-9, 99. [] R. Swaroop, Vortex formaton at ntakes. ME ssertaton, CED, nversty of Roorkee, Ina, 9. [] Y.R. Rey an J.A. Pckfor, Vortces at ntakes n conventonal sump. Internatonal Water Power an Dam Constructon, Vol., No, 9 [] Rumelhart, D.E., Hnton, G.E. an Wllams, R.J. Learnng Internal Representaton by Error Propagaton, In: Parallel Dstrbute Processng: Exploratons, n Mcrostructures of Cognton, Cambrge, MIT Press, pp -, 99 [9] Qunlan J. R. Introucton to Decson Trees. Machne Learnng, Vol., pp. -, 9. [] Bhattacharya, B. an Solomatne, D. P., Applcaton of artfcal neural network n stage scharge relatonshp. Proceengs of th Internatonal Conference on Hyro nformatcs, Iowa,. [] Solomatne D P an Dulal K N, Moel tree as an alternatve to neural network n ranfall-runoff moelng. Hyrologcal Scence journal, Vol. (), pp. 99-,. [] Solomatne, P. an Mchael baskara L A Sek Flexble an optmal M moel trees wth applcatons to flow prectons. th nternatonal conference on Hyronformatcs Lonn, Phoon & babovc (es), worl scentfc company,. [] A.Goel, Precton of Maxmum Scour Downstream of Sk jump type Spllways usng M moel tree. Natonal conference on Rver Hyraulcs, MM Mullana, 9. [] Weka software verson.. ISBN: ISSN: -9 (Prnt); ISSN: -9 (Onlne) WCE