Department of Civil and Environmental Engineering, Imperial College London, London SW7 2BB, United Kingdom.
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2BB, United Kingdom.
Water Res. 2023 Mar 1;231:119602. doi: 10.1016/j.watres.2023.119602. Epub 2023 Jan 18.
The provision of self-cleaning velocities has been shown to reduce the risk of discolouration in water distribution networks (WDNs). Despite these findings, control implementations continue to be focused primarily on pressure and leakage management. This paper considers the control of diurnal flow velocities to maximize the self-cleaning capacity (SCC) of WDNs. We formulate a new optimal design-for-control problem where locations and operational settings of pressure control and automatic flushing valves are jointly optimized. The problem formulation includes a nonconvex objective function, nonconvex hydraulic conservation law constraints, and binary variables for modelling valve placement, resulting in a nonconvex mixed integer nonlinear programming (MINLP) optimization problem. Considering the challenges with solving nonconvex MINLP problems, we propose a heuristic algorithm which combines convex relaxations (with domain reduction), a randomization technique, and a multi-start strategy to compute feasible solutions. We evaluate the proposed algorithm on case study networks with varying size and degrees of complexity, including a large-scale operational network in the UK. The convex multi-start algorithm is shown to be a more robust solution method compared to an off-the-shelf genetic algorithm, finding good-quality feasible solutions to all design-for-control numerical experiments. Moreover, we demonstrate the implemented multi-start strategy to be a fast and scalable method for computing feasible solutions to the nonlinear SCC control problem. The proposed method extends the control capabilities and benefits of dynamically adaptive networks to improve water quality in WDNs.
自清洗流速的设置已被证明可以降低供水管网（WDN）中变色的风险。尽管有这些发现，但控制实施仍然主要集中在压力和泄漏管理上。本文考虑控制日流量速度以最大化 WDN 的自清洁能力（SCC）。我们制定了一个新的最优设计控制问题，其中压力控制和自动冲洗阀的位置和操作设置被联合优化。问题公式化包括一个非凸目标函数、非凸水力守恒定律约束和用于建模阀位置的二进制变量，导致非凸混合整数非线性规划（MINLP）优化问题。考虑到解决非凸 MINLP 问题的挑战，我们提出了一种启发式算法，该算法结合了凸松弛（带域减少）、随机化技术和多启动策略来计算可行解。我们在具有不同大小和复杂程度的案例研究网络上评估了所提出的算法，包括英国的一个大型运行网络。与现成的遗传算法相比，凸多启动算法被证明是一种更稳健的求解方法，它为所有设计控制数值实验找到了高质量的可行解。此外，我们证明了所实现的多启动策略是计算非线性 SCC 控制问题可行解的快速和可扩展方法。该方法扩展了动态自适应网络的控制能力和优势，以改善 WDN 中的水质。
