Robustness-Based Design of Water Distribution Systems

Abstract

Robustness is generally defined as an ability of a system to maintain its function under a defined set of disturbances. To introduce robustness to the water distribution systems (WDSs) design, chance constrained, or so-called reliability-based models have been formulated. Under variations in system parameters, such as nodal demands and pipe roughness, system reliability is generally measured as the probability that the stochastic nodal pressures will be higher than an allowable minimum pressure limit. However, chance constraints may not be the best formulation to improve system robustness because it focuses on the likelihood of failure under a specified set of conditions rather than developing a solution that consistently provides adequate service. In addition, the reliability-based design requires defining the demand condition, its probability distribution and its statistics, which are not straight forward in practice. To address these difficulties, a robustness index that limits the range of the system function variability is posed here and incorporated in a two objective optimization problem. Resulting designs are compared with those from the reliability constraint formulation. The authors demonstrate that the robustness-based design improves resilience relative to the reliability-based design.