This paper investigates the efficacy of crossentropy and square-error objective functions used in training feed-forward neural networks to estimate posterior probabilities. Previous research has found no appreciable difference between neural network classifiers trained using cross-entropy or squared-error. The approach employed here, though, shows cross-entropy has significant, practical advantages over squared-error.

The economic and social costs of pipe failures in water and wastewater systems are increasing, putting pressure on utility managers to develop annual replacement plans for critical pipes that balance investment with expected benefits in a risk-based management context. In addition to the need for a strategy for solving such a multi-objective problem, analysts and water system managers need reliable and robust failure models for assessing network performance.In particular, they are interested in assessing a conduit's propensity to fail and how to assign criticality to an individual pipe segment. In this paper, pipe deterioration is modelled using Evolutionary Polynomial Regression. This data-driven technique yields symbolic formulae that are intuitive and easily understandable by practitioners. The case study involves a water quality zone within a distribution system and entails the collection of historical data to develop network performance indicators. Finally, an approach for incorporating such indicators into a decision support system for pipe rehabilitation/replacement planning is introduced and articulated.

The Colebrook-White formulation of the friction factor is implicit and requires some iterations to be solved given a correct initial search value and a target accuracy. Some new explicit formulations to efficiently calculate the Colebrook-White friction factor are presented herein. The aim of this investigation is twofold: (i) to preserve the accuracy of estimates while (ii) reducing the computational burden (i.e. speed). On the one hand, the computational effectiveness is important when the intensive calculation of the friction factor (e.g. large-size water distribution networks (WDN) in optimization problems, flooding software, etc.) is required together with its derivative. On the other hand, the accuracy of the developing formula should be realistically chosen considering the remaining uncertainties surrounding the model where the friction factor is used. In the following, three strategies for friction factor mapping are proposed which were achieved by using the Evolutionary Polynomial Regression (EPR). The result is the encapsulation of some pieces of the friction factor implicit formulae within pseudo-polynomial structures.Key words 9 9 9 9 Colebrook-White formula, computational speed, evolutionary polynomial regression, friction factor, pipe flow

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