Reliability assessment of water distribution systems with statistical entropy and other surrogate measures

Abstract

There is ever increasing commercial and regulatory pressure to minimise the cost of water distribution networks even as the demand for them keeps on growing. But cost minimizing is only one of the demands placed on the network design. Satisfactory networks are required to operate above a minimum level even if they experience failure of components. Reliable hydraulic performance can be achieved if sufficient redundancy is built in the network. This has given rise to various water distribution system optimization methods including genetic algorithms and other evolutionary computing methods. Evolutionary computing approaches frequently assess the suitability of enormous numbers of potential solutions for which the calculation of accurate reliability measures could be computationally prohibitive. Therefore, surrogate reliability measures are frequently used to ease the computational burden. The aim of this paper is to assess the correlation of surrogate reliability measures in relation to more accurate measures. The surrogate measures studied are statistical entropy, network resilience, resilience index and modified resilience index. The networks were simulated with prototype software PRAAWDS that produces more realistic results for pressuredeficient water distribution systems. Statistical entropy outperformed resilience index in this study. The results also demonstrate there is a strong correlation between entropy and failure tolerance.Keywords: Failure tolerance; pressure-deficient water distribution networks; pressure-dependent modelling; redundancy; resilience index; statistical entropy; reliability INTRODUCTIONOne of the major considerations in constructing water distribution networks is the capital cost of the project. To minimise cost of the network modellers endeavour to achieve a balance of smallest possible pipe sizes, tanks and pumps whilst still providing adequate amount of water to meet the demand. However, Walski (2001) questions the benefits of network optimization to achieve minimum cost at the expense of reduced system capacity, and consequently, reliability. He argues that due to uncertainty of future demands and loss in potential project net benefits following cost minimization, water distribution network (WDN) optimization based on cost alone is not viable. Hence another important factor in WDN design is reliability. To guarantee undisrupted water supply even during abnormal conditions, such as fire fighting or network component failure, a WDN has to have some redundancy built in it. But cost and reliability of a water distribution system are at least partly mutually conflicting constraints on design. Studies show that high cost is not always an indicator of high reliability, which means network optimization leading to minimum cost and maximum benefit and efficiency is desirable.

Penalty-Free Multi-Objective Evolutionary Approach to Optimization of Anytown Water Distribution Network

“…Farmani et al (2005Farmani et al ( , 2006 considered the resilience index (Todini 2000) and water age (Rossman 2002). Prasad and Tanyimboh (2008) investigated the statistical flow entropy (Tanyimboh and Templeman 2000;Tanyimboh et al 2011) and resilience index. More recently Atkinson et al (2014) maximized flow entropy and resilience index at once in an attempt to generate hybrid solutions with properties derived from the two measures.…”

Comparison of Surrogate Measures for the Reliability and Redundancy of Water Distribution Systems

“…Initially Tanyimboh and Sheahan (2002) and Tanyimboh and Setiadi (2008) generated the designs to investigate flow entropy. Subsequently Tanyimboh et al (2011) used the designs to investigate resilience index. The head at the supply node is 100 m; demand node elevations are 0 m; required residual head at demand nodes is 30 m; pipes are 1000 m long; Hazen-Williams roughness coefficient is 130; pipe diameters are continuous in the range 100 to 600 mm.…”

“…The available evidence suggests that higher entropy values increase the uniformity of the pipe diameters along with the reliability (Tanyimboh and Templeman 1993b;Tanyimboh and Setiadi 2008). Strong positive correlation between flow entropy and both hydraulic reliability and failure tolerance has been reported (Tanyimboh and Templeman 2000;Tanyimboh et al 2011;Gheisi and Naser 2015). Atkinson et al (2014) observed that an increase in entropy promotes an increase in capacity that is more globally distributed throughout the distribution network.…”

“…Thus statistical entropy may be considered a dependable surrogate reliability measure only if different designs with similar entropy values possess comparable characteristics. It was discovered previously that in general designs with the same maximum entropy value are very similar in terms of hydraulic reliability and construction cost (Tanyimboh and Sheahan 2002;Tanyimboh and Setiadi 2008;Tanyimboh et al 2011).…”

“…Comparisons of surrogate reliability measures include Prasad and Park (2004), Raad et al (2010), Baños et al (2011)), Tanyimboh et al (2011), Wu et al (2011), Greco et al (2012, Atkinson et al (2014), Liu et al (2014) and Gheisi and Naser (2015). While some of the studies simulated operating conditions with insufficient pressure realistically with pressuredependent modelling (Liu et al 2014;Gheisi and Naser 2015), others did not (e.g.…”