多属性分形分析在供水管网整体脆弱性量化与高风险预警中的应用

Application of Multi-Attribute Fractal Analysis in Quantifying the Overall Vulnerability of Water Supply Networks and Early Warning of High Risks

摘要: 供水管网作为城市关键基础设施，易因泄漏、爆管等扰动引发级联失效，导致严重供水中断与经济损失。现有方法多聚焦单点或静态失效，难以综合刻画多尺度异质性与整体稳健性。本研究提出基于多属性复合分形维数的脆弱性评估框架，将管道长度、高程差、节点需求及稳态压力四维度融入盒计数法计算，并通过Spearman敏感性加权聚合构建复合指标。对开源网络进行压力驱动级联失效蒙特卡罗模拟，结果显示复合分形维数与失效率强正相关，显著优于单一维数，其中压力维数贡献最高，需求与高程维数呈负相关，反映动态水力与地形缓冲作用。在高风险与非高风险二分类中，模型整体准确率高。该方法多尺度、数据驱动，通过与网络效率、介数中心性等传统图论指标的直接对比，突显了方法的预测精度，为供水管网风险分级、关键点识别及针对性干预提供高效量化工具，具有较好的泛化性与工程应用潜力。

Abstract: The water supply network, as a crucial infrastructure of the city, is prone to cascading failures due to leakage, pipe bursts, etc., resulting in severe water supply disruptions and economic losses. Existing methods mostly focus on single-point or static failures, and are difficult to comprehensively depict multi-scale heterogeneity and overall robustness. This study proposes a vulnerability assessment framework based on multi-attribute composite fractal dimension, integrating the four dimensions of pipe length, elevation difference, node demand, and steady-state pressure into the box-counting method calculation, and constructing a composite index through Spearman sensitivity weighted aggregation. Monte Carlo simulations of pressure-driven cascading failures in an open-source network were conducted, and the results showed that the composite fractal dimension was strongly positively correlated with failure rate, significantly outperforming a single dimension. Among them, the pressure dimension contributed the most, and the demand and elevation dimensions were negatively correlated, reflecting dynamic hydraulic and terrain buffering effects. In the binary classification of high-risk and non-high-risk, the overall accuracy of the model was high. This method is multi-scale and data-driven. By directly comparing with traditional graph theory indicators such as efficiency and betweenness centrality, it highlights the prediction accuracy of the method. It provides an efficient quantitative tool for risk classification, key point identification, and targeted intervention in water distribution networks, and has good generalization and engineering application potential.