Fuzzy probabilistic design of water distribution networks
Fuzzy probabilistic design of water distribution networks
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DOI：
10.1029/2010wr009739
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发表时间：
2011-05
影响因子：
5.4
通讯作者：
G. Fu;Z. Kapelan
中科院分区：
文献类型：
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作者：
G. Fu;Z. Kapelan
本文的主要目的是提出一种模糊概率方法，将任意不确定性和认知性不确定性结合在一个统一的框架内，用于给水管网的优化设计和修复。用模糊随机变量来刻画未来用水量的随机性和不精确性，其实现不是实数而是模糊数，节点水头需求用模糊集来表示，反映了用户需求的不精确性。以最小化总设计成本和最大化系统性能为目标，将优化设计问题描述为一个双目标优化问题。系统性能通过模糊随机可靠性来衡量，模糊随机可靠性定义为所有网络节点满足模糊头部要求的概率。在Dempster-Shafer证据理论意义上，满意度用必要性度量或信念度量来表示。提出了一种计算模糊随机系统可靠性的蒙特卡罗算法，并将其与非支配排序遗传算法II(NSGAII)有效地结合，得到了Pareto最优设计解。新提出的方法通过两个案例研究进行了演示：纽约隧道网络和河内网络。结果表明，该方法能有效地适应和处理设计过程中产生的各种随机性和认知性不确定源，并能提供既具有成本效益又具有较高可靠性的最优设计方案，以应对未来严重的不确定性。
The primary aim of this paper is to present a fuzzy probabilistic approach for optimal design and rehabilitation of water distribution systems, combining aleatoric and epistemic uncertainties in a unified framework. The randomness and imprecision in future water consumption are characterized using fuzzy random variables whose realizations are not real but fuzzy numbers, and the nodal head requirements are represented by fuzzy sets, reflecting the imprecision in customers' requirements. The optimal design problem is formulated as a two‐objective optimization problem, with minimization of total design cost and maximization of system performance as objectives. The system performance is measured by the fuzzy random reliability, defined as the probability that the fuzzy head requirements are satisfied across all network nodes. The satisfactory degree is represented by necessity measure or belief measure in the sense of the Dempster‐Shafer theory of evidence. An efficient algorithm is proposed, within a Monte Carlo procedure, to calculate the fuzzy random system reliability and is effectively combined with the nondominated sorting genetic algorithm II (NSGAII) to derive the Pareto optimal design solutions. The newly proposed methodology is demonstrated with two case studies: the New York tunnels network and Hanoi network. The results from both cases indicate that the new methodology can effectively accommodate and handle various aleatoric and epistemic uncertainty sources arising from the design process and can provide optimal design solutions that are not only cost‐effective but also have higher reliability to cope with severe future uncertainties.