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ABSTRACT To maintain a sufficient chlorine residual in water distribution systems (WDSs), chlorine dosage needs to be regulated. The majority of previous studies that aimed to optimize chlorine dosage in WDSs considered single-species water quality (WQ) models featuring chlorine decay with simple reaction kinetics. Recent efforts have proposed using multi-species water quality (MS-WQ) models to account for chlorine interactions with various chemical and microbiological species, thus providing a comprehensive and accurate evaluation of the WQ within WDSs. Nevertheless, the key challenge of implementing MS-WQ models within optimization frameworks is their high computational cost and poor scalability for larger WDSs. Furthermore, previous optimization studies generally relied on evolutionary algorithms (EAs), which require conducting a significant number of WQ simulations. Bayesian optimization (BO) has been recently suggested as an efficient alternative to EAs for the optimization of computationally expensive functions. This study aims to present a systematic comparison between BO and other widely used EAs for the optimization of MS-WQ in WDSs. A case study featuring a real-life, midsized benchmark WDS was implemented to comprehensively evaluate all three optimization techniques. The results revealed that BO is notably more computationally efficient and less sensitive to changes in the constraints than EAs. 

Abstract A state‐space representation of water quality (WQ) dynamics describing disinfectant (e.g., chlorine) transport dynamics in drinking water distribution networks has been recently proposed. Such representation is a byproduct of space‐ and time‐discretization of the partial differential equations modeling transport dynamics. This results in a large state‐space dimension even for small networks with tens of nodes. Although such a state‐space model provides a model‐driven approach to predict WQ dynamics, incorporating it into model‐based control algorithms or state estimators for large networks is challenging and at times intractable. To that end, this paper investigates model order reduction (MOR) methods for WQ dynamics with the objective of performing post‐reduction feedback control. The presented investigation focuses on reducing state‐dimension by orders of magnitude, the stability of the MOR methods, and the application of these methods to model predictive control. 

Abstract Real‐time water quality control (WQC) in water distribution networks (WDN), the problem of regulating disinfectant levels, is challenging due to lack of (i) a proper control‐oriented modeling considering complicated components (junctions, reservoirs, tanks, pipes, pumps, and valves) for water quality modeling in WDN and (ii) a corresponding scalable control algorithm that performs real‐time water quality regulation. In this paper, we solve the WQC problem by (a) proposing a novel state‐space representation of the WQC problem that provides an explicit relationship between inputs (chlorine dosage at booster stations) and states/outputs (chlorine concentrations in the entire network) and (b) designing a highly scalable model predictive control (MPC) algorithm that showcases fast response time and resilience against some sources of uncertainty. 

In the wake of the terrorist attacks of 11 September 2001, extensive research efforts have been dedicated to the development of computational algorithms for identifying contamination sources in water distribution systems (WDSs). Previous studies have extensively relied on evolutionary optimization techniques, which require the simulation of numerous contamination scenarios in order to solve the inverse-modeling contamination source identification (CSI) problem. This study presents a novel framework for CSI in WDSs using Bayesian optimization (BO) techniques. By constructing an explicit acquisition function to balance exploration with exploitation, BO requires only a few evaluations of the objective function to converge to near-optimal solutions, enabling CSI in real-time. The presented framework couples BO with EPANET to reveal the most likely contaminant injection/intrusion scenarios by minimizing the error between simulated and measured concentrations at a given number of water quality monitoring locations. The framework was tested on two benchmark WDSs under different contamination injection scenarios, and the algorithm successfully revealed the characteristics of the contamination source(s), i.e., the location, pattern, and concentration, for all scenarios. A sensitivity analysis was conducted to evaluate the performance of the framework using various BO techniques, including two different surrogate models, Gaussian Processes (GPs) and Random Forest (RF), and three different acquisition functions, namely expected improvement (EI), probability of improvement (PI), and upper confident bound (UCB). The results revealed that BO with the RF surrogate model and UCB acquisition function produced the most efficient and reliable CSI performance.