Advanced modeling and efficient optimization methods for real-time response in water networks
In response to a contamination incident in water distribution networks, effective mitigation procedures must be planned. Disinfectant booster stations can be used to neutralize a variety of contaminant and protect the public. In this thesis, two methods are proposed for the optimal placement of booster stations. Since the contaminant species is unknown a priori, these two methods differ in how they model the unknown reaction between the contaminant and the disinfectant. Both methods employ Mixed-Integer Linear Programming to minimize the expected impact over a large set of potential contamination scenarios that consider the uncertainty in the location and time of the incident. To make the optimal booster placement problem tractable for realistic large-scale networks, we exploit the symmetry in the problem structure to drastically reduce the problem size. The results highlight the effectiveness of booster stations in reducing the overall impact on the population, which is measured using two different metrics — mass of contaminant consumed, and population dosed above a cumulative mass threshold. Additionally, we also study the importance of various factors that influence the performance of disinfectant booster stations (e.g., sensor placement, contaminant reactivity and toxicity, etc.). ^ The booster station placement is performed at the planning stage. Once a contamination incident has taken place, knowledge of the contamination source location is important to inform the control and cleanup operations. Since this source identification problem needs to be solved in real time, computational speed on large-scale networks is of utmost importance. With this in mind, we propose a Bayesian probability-based method for source identification and a greedy algorithm for selecting manual grab sample locations. Measurements obtained from the selected manual sampling location can be used by the source identification method to further narrow the possible set of source locations. Indeed, the case study performed on a large-scale network (with over 12,000 nodes) highlights the computational speed of the proposed techniques, where both the source identification and sampling location calculations can be performed within seconds. ^ Various source identification strategies that have been developed by researchers differ in their underlying assumptions and solution techniques. In this work, we present a systematic procedure for testing and evaluating source identification methods. The performance of these source identification methods is affected by various factors including: size of water distribution network model, measurement error, modeling error, time and number of contaminant injections, and time and number of measurements. This work includes test cases that vary these factors and evaluates the proposed Bayesian probability-based source identification method along with two other methods from the literature. The tests are used to review and compare these different source identification methods, highlighting their strengths in handling various identification scenarios. ^
Carl D. Laird, Purdue University.
Chemical engineering|Operations research