Water Demand as Fuzzy Random Variable in the Analysis of Water Distribution Networks

The analysis of water distribution networks (WDNs) involves number of parameters, some of which are uncertain and may affect the system performance. The deterministic approach considers such uncertain parameters as precisely known in the crisp value analysis. Among the various uncertain parameters, water demand at nodes which shows the major variation over the design life due to various factors including increase in population, improved way of living, fire demand, thefts, and leakages. The variation is due to combined effect of its random nature and imprecise knowledge at its values which is taken fuzzy. The various approaches in the literature consider water demand as either random or fuzzy. The present study aims to incorporate water demand as a fuzzy random variable (FRV) in the analysis of WDNs. The water demand at each node is assumed to be normally distributed with a fuzzy mean and standard deviation of ±10%. The water demand uncertainty is represented by a triangular membership function having random demand at its kernel and ±5% variation as its support. The methodology is illustrated through an example network from literature. The results obtained using fuzzy random approach are compared with those obtained by fuzzy approach.