A diameter‐sensitive flow entropy method for reliability consideration in water distribution system design

2017

Water Resour Manage

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies.

Section: Introductionmentioning

confidence: 99%

Informational Entropy: a Failure Tolerance and Reliability Surrogate for Water Distribution Networks

2017

Water Resour Manage

“…Atkinson et al (2014) observed that an increase in entropy promotes an increase in capacity that is more globally distributed throughout the distribution network. Recently, Liu et al (2014) proposed an extension to the flow entropy function called diameter-sensitive flow entropy. Singh and Oh (2015) incorporated the Awumah et al (1991) entropy formulation in a variant known as Tsallis entropy (Tsallis 1988).…”

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confidence: 99%

“…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.…”

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confidence: 99%

“…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. Greco et al 2012;Atkinson et al 2014).…”

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confidence: 99%

“…Raad et al 2010) carried out comparisons on a consistent basis by optimizing each surrogate measure whereas other studies (e.g. Liu et al 2014) optimized some but not all.…”

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confidence: 99%

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

Siew

Saleh

et al. 2016

Water Resour Manage

An investigation into the effectiveness of surrogate measures for the hydraulic reliability and/or redundancy of water distribution systems is presented. The measures considered are statistical flow entropy, resilience index, network resilience and surplus power factor. Looped network designs that are maximally noncommittal to the surrogate reliability measures were considered. In other words, the networks were designed by multi-objective evolutionary optimization free of any influence from the surrogate measures. The designs were then assessed using each surrogate measure and two accurate but computationally intensive measures namely hydraulic reliability and pipe-failure tolerance. The results indicate that by utilising statistical flow entropy, the reliability of the network can be reasonably approximated, with substantial savings in computational effort. The results for the other surrogate measures were often inconsistent. Two networks in the literature were considered. One example involved a range of alternative network topologies. In the other example, based on wholelife cost accounting, alternative design and upgrading schemes for a 20-year design horizon were considered. Pressure-dependent hydraulic modelling was used to simulate pipe failures for the reliability calculations.

Entropy maximizing evolutionary design optimization of water distribution networks under multiple operating conditions

Czajkowska

2021

Environ Syst Decis

The informational entropy model for flow networks was formulated over 30 years ago by Tanyimboh and Templeman (University of Liverpool, UK) for a single discrete operating condition that typically comprises the maximum daily demands and was undefined for water distribution networks (WDNs) under multiple operating conditions. Its extension to include multiple discrete operating conditions was investigated experimentally herein considering the relationships between flow entropy and hydraulic capacity reliability and redundancy. A novel penalty-free multi-objective genetic algorithm was developed to minimize the initial construction cost and maximize the flow entropy subject to the design constraints.Furthermore, optimized designs derived from the maximum daily demands as a single discrete operating condition were compared to those derived from a combination of discrete operating conditions. Optimized designs from a combination of discrete operating conditions outperformed those from a single operating condition in terms of performance and initial construction cost. The best results overall were achieved by maximizing the sum of the flow entropies of the discrete operating conditions. The logical inference from the results is that the flow entropy of multiple discrete operating conditions is the sum of their respective entropies. Also, a crucial property of the resulting flow entropy model is that it is bias free with respect to the individual operating conditions; hitherto a fundamental weakness concerning the practical application of the flow entropy model to WDNs is thus addressed.