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

Abstract

   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.

Keywords

• 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

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