Keywords: entropy, reliability, water distribution systems, pressure-dependent analysis, demand-driven analysis.

Entropy as a surrogate measure for the reliability of water distribution systems (WDS) has been investigated for some time. It has the computational advantages of being easy to calculate, minimal data requirements and ease of incorporation into optimisation procedures. Reliability, on the other hand, is very computationally demanding. Based on this argument, the possible use of entropy as an indicator of reliability is very desirable.

To analyse the hydraulic behaviour of water distribution systems, most of the previous studies used demand-driven simulation models. The simulation assumes that demands in the network are fully satisfied regardless of the pressure in the system. The models give acceptable results when the systems are subject to normal operating conditions. However, WDSs are subject to component failures or very large demands, which may result in a reduction of the pressure in the system. When this happens, demand-driven analysis often gives results that indicate that the system is still supplying the full demand at lower, and sometimes, negative pressures. The validity of such results is obviously questionable. This study, however, uses head- dependent analysis (HDA) as well as demand-driven analysis (DDA). The pressure- dependent simulation approach has been suggested to provide more realistic results when WDSs operate under subnormal pressure conditions [1].

In addition to the use of pressure-dependent modelling, this is the biggest study of the relationship between entropy and reliability. The analyses involved the possible influence of redundancy or insufficient capacity, in the form of a small surplus or deficit in head at the critical node, on the relationship between entropy and reliability. This was done by comparing the performance of network designs with a small excess or shortfall in capacity with the same designs adjusted to satisfy the demands exactly. The possible effect of the cost objective function was also investigated. Different cost functions will produce different designs. These differences may have an effect on the entropy-reliability relationship. Another aspect was the influence of layouts on the relationship between entropy and reliability. Since the entropy of a WDS is a function of pipe flow rates, different layouts of the distribution system may have a significant impact on the relationship between entropy and reliability.

Overall, the results from the present study appear to strengthen the notion that the relationship between entropy and reliability is strong, with HDA generally yielding much better correlation than DDA.

1

Tahar, B., Tanyimboh, T.T., Templeman, A.B., "Pressure-dependent Modelling of Water Distribution Systems", in "Proceedings of the Third International Conference on Decision Making in Urban and Civil Engineering", Khosrowshahi, F., (Editor), London, 2002.

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