Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Correlation analysis between energy indices and source-to-node shortest pathway of water distribution network

상수도관망 수원-절점 최소거리와 에너지 지표 상관성 분석

  • Lee, Seungyub (Department of Civil and Environmental Engineering, University of Utah) ;
  • Jung, Donghwi (Department of Civil Engineering, Keimyung University)
  • 이승엽 (유타대학교 토목환경공학과) ;
  • 정동휘 (계명대학교 토목공학과)
  • Received : 2018.08.25
  • Accepted : 2018.09.13
  • Published : 2018.11.30
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Abstract

Connectivity between water source and demand node can be served as a critical system performance indicator of the degree of water distribution network (WDN)' failure severity under abnormal conditions. Graph theory-based approaches have been widely applied to quantify the connectivity due to WDN's graph-like topological feature. However, most previous studies used undirected-unweighted graph theory which is not proper to WDN. In this study, the directed-weighted graph theory was applied for WDN connectivity analyses. We also proposed novel connectivity indicators, Source-to-Node Shortest Pathway (SNSP) and SNSP-Degree (SNSP-D) which is an inverse of the SNSP value, that does not require complicate hydraulic simulation of a WDN of interest. The proposed SNSP-D index was demonstrated in total 42 networks in J City, South Korea in which Pearson Correlation Coefficient (PCC) between the proposed SNSP-D and four other system performance indicators was computed: three resilience indexes and an energy efficiency metric. It was confirmed that a system representative value of the SNSP-D has strong correlation with all resilience and energy efficiency indexes (PCC = 0.87 on average). Especially, PCC was higher than 0.93 with modified resilience index (MRI) and energy efficiency indicator. In addition, a multiple linear regression analysis was performed to identify the system hydraulic characteristic factors that affect the correlation between SNSP-D and other system performance indicators. The proposed SNSP is expected to be served as a useful surrogate measure of resilience and/or energy efficiency indexes in practice.

수원과 수용가 간 연결성은 비정상상황 시 상수도관망의 기능 유지 정도를 나타내는 시스템 특성 중 하나이다. 상수도관망은 점과 선으로 구성된 그래프로 간략화 될 수 있기 때문에, 연결성 평가를 위해 주로 그래프 이론이 적용되었다. 하지만, 대부분의 연구는 상수도관망에 적합하지 않은 무향-비가중 그래프 이론을 적용하였다. 본 연구에서는 유향-가중 그래프 이론을 상수도관망에 적용하였으며, 이를 기반으로 복잡한 수리해석 없이 상수도관망 연결성을 평가할 수 있는 지표인 SNSP (Source to Node Shortest Pathway)와 이의 역수인 SNSP-Degree (SNSP-D)를 제안하였다. 국내 J시 42개의 상수도관망을 이용하여 개발된 SNSP와 기존 상수도관망 성능평가지표 사이의 상관성 분석을 수행 및 검증하였다. 기존 상수도관망 성능평가지표는 수리해석 결과를 지표 계산에 이용하는 3개의 회복력(Resilience) 지표와 에너지 효율 지표이다. 분석 결과, SNSP의 역수인 SNSP-D의 합과 기존 상수도관망 성능지표 사이에 평균적으로 0.87 이상의 높은 피어슨 상관계수(Pearson Correlation Coefficient, PCC) 값이 도출되었다. 특히, 회복력 지표 중 하나인 Modified Resilience Index (MRI)와 에너지 효율 지표의 경우 PCC 0.93 이상의 높은 상관관계를 가지는 것으로 나타났다. 또한 다중 회귀 분석을 통해 SNSP-D와 회복력 및 에너지 효율 간의 상관성에 영향을 미치는 수리학적 변인을 확인하였다. 본 연구에서 제안한 SNSP 지표가 상수도관망의 대략적인 회복력 및 에너지 효율 수준을 알려줄 수 있는 지표로 실무에서 널리 활용될 것으로 기대된다.

Keywords

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