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Tracing disinfectant (e.g., chlorine) and contaminants evolution in water networks requires the solution of one-dimensional (1D) advection-reaction (AR) partial differential equations (PDEs). With the absence of analytical solutions in many scenarios, numerical solutions require high-resolution time and space discretizations, resulting in large model dimensions. This adds complexity to the water quality control problem. In addition, considering multispecies water quality dynamics rather than the single-species dynamics produces a more accurate description of the reaction dynamics under abnormal hazardous conditions (e.g., contamination events). Yet, these dynamics introduce a nonlinear reaction formulation to the model. To that end, solving nonlinear 1D AR PDEs in real time is critical to achieving monitoring and control goals for various scaled networks with a high computational burden. In this work, we propose a novel comprehensive framework to overcome the large-dimensionality issue by introducing different approaches for applying model order reduction (MOR) algorithms to the nonlinear system followed by applying a real-time water quality regulation algorithm that is based on an advanced model to maintain desirable disinfectant levels in water networks under multispecies dynamics. The performance of this framework is validated using rigorous numerical case studies under a wide range of scenarios demonstrating the challenges associated with regulating water quality under such conditions. [ABSTRACT FROM AUTHOR]

Chlorine is a widely used disinfectant and proxy for water quality (WQ) monitoring in water distribution networks (WDN). Chlorine-based WQ regulation and control aim to maintain pathogen-free water. Chlorine residual evolution within WDN is commonly modeled using the typical single-species decay and reaction dynamics that account for network-wide, spatiotemporal chlorine concentrations only. Prior studies have proposed more advanced and accurate descriptions via multi-species dynamics. This paper presents a host of novel state-space, control-theoretic representations of multi-species water quality dynamics. These representations describe decay, reaction, and transport of chlorine and a fictitious reactive substance to reflect realistic complex scenarios in WDN. Such dynamics are simulated over space- and time-discretized grids of the transport partial differential equation and the nonlinear reaction ordinary differential equation. To that end, this paper (i) provides a full description on how to formulate a high fidelity model-driven state-space representation of the multi-species water quality dynamics and (ii) investigates the applicability and performance of different Eulerian-based schemes (Lax–Wendroff, backward Euler, Crank–Nicolson, and Implicit Upwind) and Lagrangian-based schemes (Method of Characteristics) in contrast with EPANET and its EPANET-MSX extension. Numerical case studies reveal that the Implicit Upwind scheme, Method of Characteristics, and Lax–Wendroff scheme outperform other schemes with reliable results under reasonable assumptions and limitations. [ABSTRACT FROM AUTHOR]

• Bayesian optimization is applied for water quality control in distribution networks. • Coupling BO with EPANET to optimize the scheduling of multiple chlorine boosters. • Systematic testing of acquisition functions, covariance kernels, and BO parameters. • Results revealed substantial variability in the performance of different BO methods. • Choice of acquisition function more influential than choice of covariance kernel. Chlorine remains the most widely used disinfectant in drinking water treatment and distribution systems worldwide. To maintain a minimum residual throughout the distribution network, chlorine dosage needs to be regulated by optimizing the locations of chlorine boosters and their scheduling (i.e., chlorine injection rates). Such optimization can be computationally expensive since it requires numerous evaluations of water quality (WQ) simulation models. In recent years, Bayesian optimization (BO) has garnered considerable attention due to its efficiency in optimizing black-box functions in a wide range of applications. This study presents the first attempt to implement BO for the optimization of WQ in water distribution networks. The developed python-based framework couples BO with EPANET-MSX to optimize the scheduling of chlorine sources, while ensuring the delivery of water that satisfies water quality standards. Using Gaussian process regression to build the BO surrogate model, a comprehensive analysis was conducted to evaluate the performance of different BO methods. To that end, systematic testing of different acquisition functions, including the probability of improvement, expected improvement, upper confidence bound, and entropy search, in conjunction with different covariance kernels, including Matérn, squared-exponential, gamma-exponential, and rational quadratic, was conducted. Additionally, a thorough sensitivity analysis was performed to understand the influence of different BO parameters, including the number of initial points, covariance kernel length scale, and the level of exploration vs exploitation. The results revealed substantial variability in the performance of different BO methods and showed that the choice of the acquisition function has a more profound influence on the performance of BO than the covariance kernel. [ABSTRACT FROM AUTHOR]