Professor Technion - Israel Institute of Technology
Uncertainty is a common hurdle faced while solving any real-world problems. Water distribution system (WDS) problems are no exception. The optimal design and management problem of water distribution systems is always encountered with several uncertain parameters. Most of the past studies have ignored the uncertain parameters that explicitly effect the water quality in WDS like bulk and wall reaction rate, the temperature, PH, etc. In addition to these parameters, the assumption of instantaneous and complete mixing of water at cross junctions can also affect the water quality estimates in the WDS. The exact computation of level of mixing occurring at the junctions requires heavy computational modelling. This study focuses on obtaining the optimal treatment levels at the sources, considering the level of mixing at the cross junctions as uncertain/ unknown. A robust counterpart approach is proposed to reformulate the optimal treatment level problem to handle the uncertainty in mixing. The proposed methodology is explained using a grid-type illustrative example. An extended period simulation is considered to handle multiple loading conditions. The reformulation ensures the water quality constraint satisfaction for every time step considered. The objective of this problem is to obtain the water treatment levels at the sources to satisfy the water quality requirements at the demand nodes for all the time periods and be immune to variations in the level of mixing at cross junctions. The results showed a significant cost variation between complete and non-uniform mixing. The obtained treatment levels were verified through Monte-Carlo simulations.
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