EVALUATION OF THE SUITABILITY OF GLOBAL GRADIENT ALGORITHM AND INVERSE MATRIX METHOD FOR STEADY-STATE ANALYSIS OF WATER DISTRIBUTION NETWORKS

Yıl 2018, Cilt: 7 Sayı: 1, 23 - 33, 31.01.2018

Selami Demir

https://doi.org/10.28948/ngumuh.383777

Öz

   Two methods
for steady-state analysis of water distribution networks (WDNs) were evaluated
in this paper: Global Gradient Algorithm (GGA) and inverse matrix method (IMM).
Both methodologies are based on the solution of nonlinear system of equations
formed by mass and energy balances within a WDN. A number of WDNs were solved
using both methods. Results showed that GGA solves the WDNs in around 70 to 75%
less number of iterations than IMM. Besides, single GGA solution of a WDN takes
less time compared to IMM solution (about 57% faster for a network of 31
elements). In contrast, single iteration takes 127 to 552 μs with IMM while it
takes 235 to 773 μs with GGA depending on the number of network elements.
Evaluations are based on the speed, the accuracy, and ease of handling the
iteration procedures and it was concluded that, although GGA provides faster
solutions, both methods are fast enough and IMM, with its simpler iteration
procedure, could be beneficial if employed for teaching WDNs in engineering
education.

Anahtar Kelimeler

Water distribution networks, systems of nonlinear equations, global gradient algorithm, inverse matrix method

İÇME SUYU ŞEBEKELERİNİN KARARLI DURUM ANALİZİ İÇİN KÜRESEL GRADYEN ALGORİTMASI VE TERS MATRİS YÖNTEMİNİN UYGUNLUĞUNUN DEĞERLENDİRİLMESİ

Öz

   Bu çalışmada içme suyu şebekelerinin kararlı
akım analizi için kullanılabilen iki yöntem değerlendirilmiştir: Küresel
Gradyen Algoritması (KGA) ve ters matris yöntemi (TMY). Her iki yöntem de
şebeke için yazılan kütle ve enerji korunum denklemlerinden oluşan, doğrusal
olmayan denklem sisteminin çözümüne dayanmaktadır. Bu çalışmada her iki yöntem
de kullanılarak bir dizi şebeke çözümü yapılmıştır. Sonuçlar, KGA’nın TMY’ye
göre yaklaşık %70 ile %75 oranında daha az iterasyonla sonuca ulaştığını
göstermiştir. Ayrıca, KGA ile tek şebeke çözümü, TMY’ye göre daha az zaman
almaktadır (31 elemanlı bir şebeke için yaklaşık %57 oranında daha hızlı). Buna
karşın, şebekedeki eleman sayısına bağlı olmak üzere TMY’de tek iterasyon 127
ile 552 µs’de tamamlanırken KGA’da 235 ile 773 µs sürmektedir. Değerlendirmeler
metotların hızı, doğruluğu ve iterasyon prosedürlerinin kolaylığına göre
yapılmış olup, KGA daha hızlı çözümler üretmesine karşın her iki yöntemin de
yeteri kadar hızlı olduğunu söylemek mümkündür ve iterasyon prosedürleri çok
daha kolay olduğu için TMY’nin mühendislik eğitiminde içme suyu şebekelerini
öğretmek için kullanılması KGA’ya göre daha avantajlı olabilir.

Anahtar Kelimeler

İçme suyu şebekeleri, doğrusal olmayan denklem sistemleri, küresel gradyen algoritması, ters matris yöntemi

Kaynakça

• [1] LIN, B.L., SHAN, H.M., HUANG, W.C., WU, R.S., LIAW, S.L., “The Enumeration Algorithm for the Practical Optimal Design of Pipe Network Systems”, Environmental Informatics Archives, 2, 87-98, 2004.
• [2] LOPES, A.M.G., “Implementation of the Hardy-Cross Method for the Solution of Piping Networks”, Computer Applications in Engineering Education, 12(2), 117-125, 2004.
• [3] KROPE, J., DOBERSEK, D., GORICANEC, D., “Flow Pressure Analysis of Pipe Networks with Linear Theory Method”, Proceedings of the 2006 WSEAS/IASME International Conference on Fluid Mechanics, 59-62, Florida, USA, 2006.
• [4] ZHANG, H., XU, J.L., CHENG, X., “Interactive Educational Software for Teaching Water Distribution Networks Design”, Computer Applications in Engineering Education, 24(4), 615-628, 2016.
• [5] SARBU, I., VALEA, E.S., “Nodal Analysis of Looped Water Supply Networks”, International Journal of Energy and Environment, 5(3), 452-460, 2011.
• [6] DEMİR, S., MANAV DEMİR, N., KARADENİZ, A., “An MS Excel Tool for Water Distribution Network Design in Environmental Engineering Education”, Computer Applications in Engineering Education, article in press, DOI: 10.1002/cae.21870, 2017.
• [7] ELHAY, S., SIMPSON, A.R., “Dealing with Zero Flows in Solving the Nonlinear Equations for Water Distribution Systems”, Journal of Hydraulic Engineering, 137(10), 1216-1224, 2011.
• [8] TODINI, E., A More Realistic Approach to the Extended Period Simulation of Water Distribution Networks. In MAKSIMOVIC, C., MEMON, F.A. BUTLER, D. (Eds.), Advances in Water Supply Management (pp. 173-184), Taylor & Francis, Holland, 2003.
• [9] ANG, W.K., JOWITT, P.W., “Solution for Water Distribution Systems Under Pressure-Deficient Conditions”, Journal of Water Resources Planning and Management – ASCE, 132(3), 175-182, 2006.
• [10] WU, Z.Y., CLARK, C., “Evolving Effective Hydraulic Model for Municipal Water Systems”, Water Resources Management, 23(1), 117-136, 2009.
• [11] GIUSTOLISI, O., LAUCELLI, D., “Water Distribution Network Pressure-Driven Analysis Using the Enhanced Global Gradient Algorithm (EGGA)”, Journal of Water Resources Planning and Management – ASCE, 137(6), 498-510, 2011.
• [12] ABDY SAYYED, M.A.H., GUPTA, R., “Predicting Deficient Condition Performance of Water Distribution Networks”, Civil Engineering Infrastructures Journal, 46(2), 161-173, 2013.
• [13] MOOSAVIAN, N., JAEFARZADEH, M.R., “Pressure-Driven Demand and Leakage Simulation for Pipe Networks Using Differential Evolution”, World Journal of Engineering and Technology, 1, 49-58, 2013.
• [14] MOOSAVIAN, N., JAEFARZADEH, M.R., “Hydraulic Analysis of Water Distribution Network Using Shuffled Complex Evolution”, Journal of Fluids, Article ID 979706, 2014.
• [15] MURANHO, J., FERREIRA, A., SOUSA, J., GOMES, A., SA MARQUES, A., “Convergence Issues in the EPANET Solver”, Procedia Engineering, 119, 700-709, 2015.
• [16] PUCCINI, G.D., BLASER, L.E., BONETTI, C.A., BUTARELLI, A., “Robustness-Based Design of Water Distribution Networks”, Water Utility Journal, 13, 13-28 2016.
• [17] ROSSMAN, L.A., EPANET2 Users’ Manual, Drinking Water Research Division, Risk Reduction Engineering Laboratory, Office of Research and Development, US Environmental Protection Agency, Cincinnati, 2000.
• [18] DEMİR, S., YETİLMEZSOY, K., MANAV, N., “Development of a Modified Hardy-Cross Algorithm for Time Dependent Simulations of Water Distribution Networks”, Fresenius Environmental Bulletin, 17(8a), 1045-1053, 2008.
• [19] NIAZKAR, M., AFAZLI, S.H., “Analysis of Water Distribution Networks Using MATLAB and Excel Spreadsheet: h-Based Methods”, Computer Applications in Engineering Education 25, 129-141, 2017.
• [20] NIAZKAR, M., AFAZLI, S.H., “Analysis of Water Distribution Networks Using MATLAB and Excel Spreadsheet: Q-Based Methods”, Computer Applications in Engineering Education 25, 277-289, 2017.
• [21] DEMIR, S., DUMAN, S., MANAV DEMİR, N., KARADENİZ, A., LUBURA, E., “An MS Excel Add-in for Teaching Hydraulics of Pipe Flow in Engineering Curricula”, Computer Applications in Engineering Education, article in press, DOI: 10.1002/cae.21898, 2017.