A Hybrid Graph–Hydraulic Approach for Identifying Critical Elements in Water Distribution Networks ^†

Abstract

Water distribution networks (WDNs) are susceptible to vulnerabilities that necessitate proactive management to ensure efficient incident management. When dealing with a sequence of failures triggered, for example, by hydraulic redistributions under failure conditions, the computational burden often becomes the limiting factor for exploring scenarios. Therefore, this study proposes a hybrid method combining a graph-based approach for prescreening critical pipes with a hydraulic assessment to rapidly identify critical nodes. Tested on an Austrian WDN, this approach effectively pinpoints primary failures (pipe failures) while reducing computational time. By integrating the hydraulic approach, the method successfully identified the most critical elements due to the failures. This method empowers operators to mitigate the impact of potential failures and enhance disaster robustness.

1. Introduction

Water distribution networks (WDNs) are complex critical infrastructure systems comprising sources (tanks, reservoirs and groundwater wells) and network elements (e.g., pipes and pumps) to supply drinking water from sources to consumers. Within a WDN, pipes serve as the principal components connecting different points within the system. These pipes are susceptible to various forms of failures, including pipe breakage. A failed pipe leads to a reduction in network functionality likely leading to an undersupply of water [1].

The severity of pipe failure scenarios in WDNs can be assessed by the amount of water not supplied in demand nodes. Therefore, identifying crucial pipes in large WDNs poses a complex combinatorial challenge. Hydraulic-based approaches are commonly utilized to determine the criticality of pipes in the event of failures [2]. These methods typically involve significant computational time and data for analysis. Alternative methods like graph-based mathematical approaches have been a faster and less data-intensive technique employed to find vulnerable pipes [3]. The technique depends on the connectivity of WDNs, which is depicted using a hydraulically informed graph-based method [4]. The hydraulically informed graph-based approach produces a criticality analysis ranking with more than 90% accuracy compared to hydraulic approaches but fails to provide a robust result to predict the extent of the impact caused by failures [5]. In this research, a novel hybrid graph–hydraulic approach is proposed to integrate both methodologies within a hybrid framework for rapidly identifying critical elements. This study aims to determine the 1st level of criticality (single element failures) using a specific graph-based measure, and subsequently, the list of critical pipes is utilized to assess the 2nd level of failure (hydraulically triggered failure of another element), identifying nodes with significant pressure changes in the network through hydraulic analysis.

2. Materials and Methods

The hybrid methodology consists of two parts, combining graph and hydraulic-based approaches, and is applied on a medium scale Alpine WDN in Austria with more than 8000 pipes and 9000 junctions as part of the RESIST research project. The methodology is coded in Python using the NetworkX [6] package for the graph-based assessment and the WNTR package [7] for the hydraulic-based assessment.

2.1. Graph-Based Approach (1st-Level Criticality)

A WDN graph comprises vertices representing nodes and sources and edges representing pipes, pumps, and valves. In the graph-based approach, a graph metric, demand edge betweenness centrality (EBC^Q), which is a modification of EBC (edge betweenness centrality) [8] specifically tailored for WDNs [9], is applied. In the context of EBC^Q (normal EBC^Q), the metric assigns weights Qi (demand on node i $\in$ n) to the shortest path along the SPLs,i, where i is the demand node and s is the source node:

$${EBC}^Q(p)=\sum _{i\in n}{SPL}_{s,i}\left(p\right)·Q_i$$

(1)

The graph-based approach for assessing the impact of pipe (p) failure is determined using graph pipe failure magnitude (GPFM). GPFM is computed by aggregating the capacity overload (Δc_o) values of all remaining edges (e_r) in the WDN (connected edges to the source) resulting from the failure of a specific pipe (p) [4]. In WDNs without disconnected nodes, Δc_o is the aggregation of the difference between the change in the flow capacity (Δc_k) and maximum capacity (c_max(i)) (determined by multiplying the maximum acceptable velocity v_max (m/s) and cross-section area of the pipe) of each pipe (Formula (2)), where Δc_k is the difference between the failure ${EBC}^Q\left(p\right)$ (EBC^Q recalculated after pipe failure) and normal ${EBC}^Q\left(p\right)$ of a pipe. Moreover, for WDNs with disconnected nodes, GPFM considers the demand (Dj) of disconnected nodes (j $\in$ n_k) arising from the failure scenario [5]. By summing up the Δc_o values for the remaining edges (connected edges) and the demands of disconnected nodes (n_k), GPFM quantifies the overall impact of edge failures on the network’s performance, offering insights into the criticality of various failure combinations. Thus, the graph-based approach is utilized to identify the most critical (5%) pipes in the WDN.

$$GPFM(p)=\left\{\begin{array}{ll}{\displaystyle \sum _{j\in n_k}}{D}_j+{\displaystyle \sum _{i\in e_r}}{\Delta c}_{o\left(i\right)}={∆c\left(i\right)}_k-c_{\mathit{max}}\left(i\right)& ,\hspace{1em}{{∆c\left(i\right)}_k>c}_{max}\left(i\right)\\ {\displaystyle \sum _{j\in n_k}}{D}_j& ,\hspace{1em}{{∆c\left(i\right)}_k\le c}_{max}\left(i\right)\end{array}\right.$$

(2)

2.2. Hydraulic-Based Approach (2nd-Level Criticality)

The hydraulic-based node failure approach is determined using the hydraulic pipe failure magnitude of a node (HPFM), reflecting the nodes lacking the required supply. EPANET2.2 [10] conducts pressure-driven analysis, simulating failures by closing affected pipes. HPFM values for nodal demand failures are calculated by comparing the difference between the required demand and supplied demand under failure conditions.

3. Results and Discussions

The graph-based approach (GPFM values) facilitated the rapid identification of the most critical pipes within the WDN. This approach demonstrated remarkable efficiency, completing the analysis in 98 min, with a notable computational gain factor of 68 compared to the hydraulic-based approaches utilizing EPANET 2.2 for pipe failures. The identified critical pipes (most critical 5% of pipes) were subsequently subject to further analysis using the hydraulic-based approach to determine the most impacted nodes within the network.

For example, Figure 1 shows the results for a failure of the most critical pipe within the WDN. The demand nodes shaded in orange are impacted (under-supplied—more than 30% of the demand) due to the failure of the pipe (highlighted in red) in this particular scenario. The displayed result illustrates one of the most critical pipe failures in the WDN. The graphical representation depicted in Figure 1 is also illustrated for each pipe failure among the top 5% of failed pipes.

The findings of this research could hold significant importance, particularly in scenarios requiring rapid analysis such as crises involving pipe bursts or zonal failures. This methodology also proves valuable for WDNs characterized by a large number of pipes, where conventional hydraulic-based approaches utilizing tools like EPANET 2.2 may necessitate a considerable amount of time. The efficiency of this methodology in swiftly identifying critical pipes enhances operators’ ability to pinpoint the most crucial demand nodes affected by pipe failures in WDNs. Consequently, operators can identify zones or nodes experiencing water supply deficiencies during an abnormal situation. Moreover, this methodology offers additional advantages for WDNs lacking comprehensive data or sufficient manpower. By solely employing graph-based approaches, critical pipes within the network can be identified without a reliance on specific software or data specifications. Furthermore, the method will be further developed to incorporate land classifications and pipe segment classification. Consequently, users could pinpoint the most critical land zones and segments in the network quickly in a crisis situation (1st- or 2nd-level failures), thereby improving the resilience of the WDN.

4. Conclusions

The hybrid framework proposed in this study effectively combines graph-based and hydraulic approaches to assess the criticality of pipes and nodes within water distribution networks (WDNs). By combining the strengths of both methodologies, our approach offers a rapid and efficient means of identifying critical components, particularly in large-scale networks. This method enhances operators’ ability to respond to crisis scenarios such as pipe bursts or failures, thereby improving overall network resilience and reliability.