Robust optimization for water distribution systems least cost design

Abstract

[1] The objective of the least cost design problem of a water distribution system is to find its minimum cost with discrete diameters as decision variables and hydraulic controls as constraints. The goal of a robust least cost design is to find solutions which guarantee its feasibility independent of the data (i.e., under model uncertainty). A robust counterpart approach for linear uncertain problems is adopted in this study, which represents the uncertain stochastic problem as its deterministic equivalent. Robustness is controlled by a single parameter providing a trade-off between the probability of constraint violation and the objective cost. Two principal models are developed: uncorrelated uncertainty model with implicit design reliability, and correlated uncertainty model with explicit design reliability. The models are tested on three example applications and compared for uncertainty in consumers' demands. The main contribution of this study is the inclusion of the ability to explicitly account for different correlations between water distribution system demand nodes. In particular, it is shown that including correlation information in the design phase has a substantial advantage in seeking more efficient robust solutions.Citation: Perelman, L., M. Housh, and A. Ostfeld (2013), Robust optimization for water distribution systems least cost design, Water Resour. Res., 49,[6795][6796][6797][6798][6799][6800][6801][6802][6803][6804][6805][6806][6807][6808][6809]

A Spectral Approach to Uncertainty Quantification in Water Distribution Networks

“…Several applications have shown that taking parameter uncertainties into account may have significant influence on the results. For example Pasha and Lansey (2010) investigate the e ect of parameter uncertainties on water quality using the Monte Carlo method and Perelman et al (2013) investigate the influence of uncertainties in the context of least-cost design for water distribution networks.…”

Generating Scenarios of Cross-Correlated Demands for Modelling Water Distribution Networks

“…An approach to dealing with the uncertainty of demand consists in explicitly considering different possible realizations of its value at the nodes of a WDN, i.e., different loading scenarios and associating to each of them a measure of their probability. So, it is possible to find a feasible solution which is also as close as possible to the optimum for all the scenarios: this scenario-based approach is known as robust optimization [3]. In the same way it is possible also to derive WDN reliability [4] or to localize leakages [5] or to map pressure-heads for a real-time control [6], all under uncertain demand conditions.…”

Automated sub-zoning of water distribution systems

“…At regional scale, these include design and operation of water systems under future demand and water availability uncertainty (Chung et al, 2009;Housh et al, 2013), creation of new water resources by producing high quality water from saline or brackish water (Avni et al, 2013) and waste water reclamation (Zhang et al, 2013). At local scale, previous works focus on water distribution system design under demand (Babayan et al, 2005;Perelman et al, 2013) and hydraulic model uncertainty (Fu and Kapelan, 2011;Laucelli et al, 2012), operation for leakage control (Giustolisi et al, 2008;Ulanicki et al, 2008;Price and Ostfeld, 2014), and reduction of potable water demand by on-site graywater reuse (Penn et al, 2013).…”