Shortest path criterion for sampling design of water distribution networks

Sampling design is often required for an appropriate assessment of monitoring points in water distribution networks to increase the effectiveness of measured data in calibrating the hydraulic model. Although many methods are available in the literature, they may be inadequate for reliable network calibration. This paper proposes a new method for the optimal collocation of monitoring points using a shortest path based approach. The monitoring points are identified by minimizing the sum of node distances from the closest sensor-node. Node distances were taken to be a weighted sum of the dimensionless arc length and the absolute head loss along arc. To ensure robustness with respect to the presence of outliers among pipe lengths and/or pressure drops, adequate reference measures were chosen for normalization. The optimization problem was solved using Mixed Integer Programming and a variant of the K-Means algorithm. Alternative formulations considering different path blending and distance norms were also analyzed. Numerical experiments carried out on both theoretical and real water distribution networks showed the reliability of the proposed approach and a greater effectiveness compared to similar methods available in the literature.