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

Tiku T. Tanyimboh

doi:10.1007/s11269-017-1684-8

Tiku T. Tanyimboh

Open Access

https://doi.org/10.1007/s11269-017-1684-8

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Abstract

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.

Highlights

Water distribution systems are part of the critical economic networks on which modern-day societies depend, and it is widely accepted that there is considerable uncertainty associated with their planning, design and operation
It is widely accepted that, ideally, explicit criteria for hydraulic capacity reliability and failure tolerance should be included in the design specifications for water distribution systems
It was observed that the ranges of the entropy values achieved by the various flow entropy options (Case I to III) were different

Summary

Introduction

Water distribution systems are part of the critical economic networks on which modern-day societies depend, and it is widely accepted that there is considerable uncertainty associated with their planning, design and operation. The uncertainty arises from many factors, for example, the deterioration in the structural integrity and hydraulic capacity, unpredictable demands for fire-fighting and random fluctuations in the demands in addition to the underlying temporal and spatial variations, to name but a few. It is widely accepted that, ideally, explicit criteria for hydraulic capacity reliability and failure tolerance should be included in the design specifications for water distribution systems. Quantified reliability measures for water distribution systems are difficult to define and evaluate (Wagner et al 1988). It is even more challenging to incorporate reliability in the procedures used to optimize the design of water distribution systems. Some surrogate reliability measures such as flow entropy and resilience index have been adopted as they are computationally less demanding (Templeman 1982; Yates et al 1984)

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