Cty Unversty of New York (CUNY) CUNY Academc Works Internatonal Conference on Hydronformatcs 8-1-2014 Practcal Applcaton Of Pressure-Dependent EPANET Extenson Alemtsehay G. Seyoum Tku T. Tanymboh Follow ths and addtonal works at: http://academcworks.cuny.edu/cc_conf_hc Part of the Water Resource Management Commons Recommended Ctaton Seyoum, Alemtsehay G. and Tanymboh, Tku T., "Practcal Applcaton Of Pressure-Dependent EPANET Extenson" (2014). CUNY Academc Works. http://academcworks.cuny.edu/cc_conf_hc/380 Ths Presentaton s brought to you for free and open access by CUNY Academc Works. It has been accepted for ncluson n Internatonal Conference on Hydronformatcs by an authorzed admnstrator of CUNY Academc Works. For more nformaton, please contact AcademcWorks@cuny.edu.
11 th Internatonal Conference on Hydronformatcs HIC 2014, New York Cty, USA APPLICATION OF PRESSURE-DEPENDENT EPANET EXTENSION ALEMTSEHAY G SEYOUM AND TIKU T TANYIMBOH Cvl and Envronmental Engneerng, Unversty of Strathclyde, Glasgow, 107 Rottenrow, Glasgow, G4 0NG, Unted Kngdom Abstract Several hydraulc modellng approaches have been proposed prevously to smulate pressure defcent operatng condtons n water dstrbuton systems more realstcally ncludng the pressure dependent EPANET extenson model EPANET-PDX that has an embedded logstc nodal head-flow functon. The model has been extensvely tested prevously on benchmark as well as real lfe networks. In ths artcle, we demonstrate an alternatve mplementaton of the lne search and backtrackng procedure to enhance EPANET-PDX further. Ths has ncreased the robustness by enhancng greatly the computatonal propertes for low flow condtons and ncreasng the algorthm s consstency over a wder range of operatng condtons. We present results for extended perod smulatons of a real lfe network consderng ppe closures and varatons n the heads at the supply nodes. Keywords: Logstc pressure-dependent nodal head-flow functon, pressure defcent water dstrbuton system, lne mnmzaton, lne search and backtrackng, EPANET-PDX, penaltyfree constraned evolutonary multobjectve optmzaton INTRODUCTION Hydraulc models are used extensvely n the desgn and operaton of water dstrbuton systems to help predct potental changes under a wde range of operatng condtons. In abnormal operatng condtons, water dstrbuton systems may be pressure defcent and thus unable to satsfy demands n full (Gupta and Bhave [1]; Tanymboh and Templeman [9]). In such crcumstances, pressure dependent analyss models are sutable, to quantfy the shortfall n flow and pressure accurately for crucal decson-makng. Such scenaros cannot be smulated satsfactorly wth the conventonal demand drven analyss models as they do not consder the relatonshp between nodal flows and the avalable pressure. A revew of nodal head-flow functons can be found n Tanymboh and Templeman [9]. Recently, Sew and Tanymboh [6] developed a pressure dependent extenson of the EPANET hydraulc smulator to enable modellng of pressure defcent networks. The model has an ntegrated contnuous nodal head-flow functon (Tanymboh and Templeman [9]) coupled wth a lne search and backtrackng procedure to facltate convergence. Extensve testng conducted on the model wth benchmark and real lfe networks revealed good modellng
performance. Also, the model was combned wth a penalty-free mult-objectve genetc algorthm for optmzaton of water dstrbuton systems that generated superor results for benchmark as well as real lfe networks n terms of cost, hydraulc performance and computatonal effcency compared to prevous solutons (Sew and Tanymboh [7], Sew et al. [8]). It has also been utlsed for water qualty modellng of real lfe networks (Seyoum and Tanymboh [4]). Overall, the model has not experenced convergence problems whle executng mllons of smulatons. Havng demonstrated the robustness and benefts of the model prevously, ncludng seamless ntegraton n genetc algorthms, t seems benefcal to nvestgate ways of mprovng the algorthm further. In ths artcle, the lne search and backtrackng procedure of the algorthm has been mproved. Ths has ncreased the robustness further by enhancng greatly the computatonal propertes for low flow condtons and ncreasng the algorthm s consstency over a wder range of operatng condtons. Extended perod smulatons were executed, for a real lfe network that comprses multple supply sources and varous demand categores consderng a range of normal and pressure-defcent operatng condtons. Detals of the results and computatonal effcency of the mproved algorthm are ncluded heren. PRESSURE DEPENDENT EPANET EXTENSION The pressure-dependent extenson EPANET-PDX ntegrates the contnuous nodal head-flow functon that Tanymboh and Templeman [9] proposed n the global gradent algorthm (Todn and Plat [10]) that s the hydraulc analyss model of EPANET 2. Qn ( Hn ) = Qn req exp( α + β Hn ) 1 + exp( α + β Hn ) (1) where, for node, Qn and Hn are the flow and head respectvely; Qn req s the demand; α and β are parameters determned usng relevant feld data. The rato Qn /Qn req s the fracton of the demand satsfed and s called the demand satsfacton rato, wth values from 0 to 1. Preservng the full functonalty of EPANET 2, the pressure-dependent extenson model can perform hydraulc and water qualty modellng under normal and low-pressure condtons entrely seamlessly ncludng extended perod smulatons (Sew and Tanymboh [5, 6]; Seyoum and Tanymboh [4]). To ntegrate the nodal head-flow functons n the global gradent algorthm, the lne search and backtrackng procedure (Press et al. [2]) was utlzed n EPANET-PDX to help ensure global convergence. In each teraton of the global gradent algorthm, the lne search procedure checks the full Newton step frst. If the Newton step does not make progress towards convergence that s acceptable, backtrackng along the Newton drecton s carred out to obtan an acceptable step. The applcaton of the lne search and backtrackng procedure n the prevous mplementaton n Sew and Tanymboh [6] was somewhat lmted, n an attempt to preserve the excellent computatonal propertes of EPANET 2. We have developed an mproved mplementaton heren that allows more teratons of the lne search procedure. A sgnfcant mprovement has been acheved partcularly for operatng condtons that have extremely small flows n comparson to the demands. For smplcty the mproved algorthm s named herenafter as EPANET-PDX (0.2) whle the orgnal verson s named EPANET-PDX (0.1). EXAMPLE, RESULTS AND DISCUSSION The real lfe network ndcated n Fgure 1 s used here to demonstrate the accuracy, computatonal effcency and robustness of the enhanced pressure dependent model. The
network conssts of 251 ppes of varous lengths, 228 demand nodes, 29 fre hydrants and 5 supply nodes. The network s suppled n full from the neghbourng water supply zones va the supply nodes R1 to R5 n Fgure 1 that have a level of 155 m. The network comprses multple demand categores that nclude domestc demand, commercal demand, unaccounted for water and fre demands. We used the Darcy-Wesbach ppe frcton head loss formula (Rossman [3]). Further detals of the network can be found n Seyoum and Tanymboh [4]. The requred resdual head at all demand nodes s 20 m. For all three models consdered here namely EPANET 2 and both versons of EPANET-PDX, extended perod smulatons were carred out by varyng the supply node heads from 75 m to 130 m n equal steps of 1 m. Also, 10 addtonal extended perod smulatons were performed by closng varous combnatons of the supply ppes from the sources wth the three EPANET hydraulc smulator varants. Each extended perod smulaton covered a perod of 31 hours, based on a 1-hour hydraulc tme step. All smulatons were carred out on an Intel Xeon workstaton (2 processors of CPU 2.4 GHz and RAM of 16 GB). Fgure 1. Network layout Fgure 2 shows a comparson of EPANET-PDX (0.1) and (0.2), for the average hourly network demand satsfacton ratos. All the smulatons reported n ths artcle were extended perod smulatons as mentoned earler. Identcal results were obtaned for the hydraulc smulatons, for the entre range of demand satsfacton ratos.
Network demand satsfacton rato 1.0 0.8 0.6 EPANET-PDX (0.1) 0.4 EPANET-PDX (0.2) 0.2 0.0 75 85 95 105 115 125 135 Head at supply nodes R1-R5 (m) Fgure 2. Influence of varatons n supply node heads on the flow delvered Fgure 3 shows the number of teratons needed to solve the system of hydraulc equatons as a functon of the pressure n the network. The average numbers of teratons requred per smulaton were 6.96, 4.80 and 5.16 for EPANET-PDX (0.1), EPANET-PDX (0.2) and EPANET 2 respectvely. EPANET-PDX (0.2) acheved a sgnfcant mprovement for very low supply node heads and, overall, requred the smallest numbers of teratons. Fgure 4 compares the CPU tmes. It was noted that wth the excepton of extremely low flow condtons, EPANET-PDX (0.1) performs consstently well on the whole. However, t s qute varable n performance when the supply node heads are very low. Ths nconsstency has been addressed here n EPANET-PDX (0.2) wthout a sgnfcant reducton n the computatonal effcency for other flow condtons. However, EPANET 2 n general s more effcent and consstent. 8 Number of teratons 6 4 2 75 85 95 105 115 125 135 Head at supply nodes (R1-R5) (m) EPANET-PDX (0.1) EPANET-PDX (0.2) EPANET-2 Fgure 3. Number of teratons requred as a functon of the avalable pressure n the network On average EPANET-PDX (0.1) and (0.2) that use lne mnmzaton requred about 0.30 seconds and 0.29 seconds, respectvely, per extended perod smulaton compared to 0.16 seconds for EPANET 2. It s worth re-statng, however, that EPANET 2 s not entrely sutable for pressure-defcent operatng condtons. Also, EPANET 2 and EPANET-PDX apply convergence crtera that are not dentcal (Sew and Tanymboh [6]). Therefore, t s worth emphaszng that the EPANET 2 results here provde a rough gude rather than an absolute drect comparson.
0.8 0.6 CPU tme (s) 0.4 0.2 0.0 75 85 95 105 115 125 135 Head at supply nodes (R1-R5) (m) EPANET-PDX (0.1) EPANET-PDX (0.2) EPANET-2 Fgure 4. Comparson of CPU tmes for EPANET 2 and EPANET-PDX EPANET-PDX (0.2) was assessed also, n the context of smulated major supply mans falures by closng smultaneously the supply ppes from three supply nodes out of fve. A total of 10 such supply falures resultng from multple smultaneous supply mans falures were smulated. In these smulatons the network was suppled by only two supply nodes out of fve and the nodal demands were fully satsfed n each case (.e. all the network demand satsfacton ratos were 1.0). The average numbers of teratons requred per extended perod smulaton were 6.77, 5.22 and 4.90 for EPANET-PDX (0.1), EPANET-PDX (0.2) and EPANET 2, respectvely. The correspondng CPU tmes were 0.20 seconds, 0.21 seconds and 0.14 seconds, respectvely, for EPANET-PDX (0.1), EPANET-PDX (0.2) and EPANET 2. Even wth network demand satsfacton ratos of 1.0 for each ppe closure smulaton, the CPU tmes for the EPANET-PDX (0.1) and EPANET-PDX (0.2) models were about the same. Hence, the alternatve mplementaton of EPANET-PDX would appear to be successful. CONCLUSIONS An alternatve mplementaton of the lne search and backtrackng procedure for ntegratng the logstc nodal head-flow functon nto the system of hydraulc equatons n the global gradent algorthm has been demonstrated on a real lfe water dstrbuton network consderng 66 extended perod smulatons. A sgnfcant mprovement n the computatonal propertes has been acheved for extremely low flow condtons. ACKNOWLEDGEMENTS Ths project was carred out n collaboraton wth Veola Water UK (now Affnty Water) and funded n part by the UK Engneerng and Physcal Scences Research Councl (EPSRC grant reference EP/G055564/1), the Brtsh Government (Overseas Research Students Awards Scheme) and the Unversty of Strathclyde. The above-mentoned support s acknowledged wth thanks. The authors also thank Dr Lews Rossman of the Unted States Envronmental Protecton Agency, for assstance he provded on the EPANET source code.
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