Field validation of a pressure transient source localization method in a water distribution network Open Access

Rapid advancements in electronics is driving significant progress in the pressure monitoring of water distribution networks (WDNs). These innovations incorporate ultra-low-power hardware to support continuous high-frequency sampling and edge processing, utilize diverse radio technologies and communication protocols, capitalize on higher battery density and capacity with optimized energy usage, and benefit from lower manufacturing costs. Consequently, pressure sensors (loggers) have become more affordable, reliable, and capable of high-rate pressure sampling. This technology is particularly useful for pipe condition assessment offering detailed information on transient events and capturing dynamic water pressure behavior (Hoskins 2015; Jara-Arriagada & Stoianov 2022). Such high-resolution characterization of transient events enables correlation of increased dynamic activity with potential pipe failures and water quality concerns (Aisopou et al. 2014; Starczewska et al. 2015; Weston et al. 2021; Konstantinou et al. 2024).

In light of the increasing complexity of control strategies and operational interventions in water distribution networks, continuous, high-resolution pressure monitoring is important to ensure safe and reliable network performance. Pressure transients can originate from a variety of sources, including pumps and valves control, operational activities, and industrial consumer operations that are beyond the direct control of water network operators. Beyond facilitating assessments of network performance, continuous pressure monitoring provides valuable insights into the hydraulic conditions that may lead to failures. Consequently, high-resolution pressure monitoring is essential for detecting, interpreting, and mitigating hydraulic instabilities that can occur under normal water distribution operations.

To hydraulically calm water supply networks and thereby prolong their operational lifespan, it is crucial to detect and localize sources of pressure transients. The intensity, duration, and recurrence of these events depend on the network’s intrinsic properties as well as the mechanisms by which they are generated (Hoskins 2015; Jara-Arriagada & Stoianov 2022). This work focuses on medium to large magnitude transient events, which have the potential to compromise pipe integrity through fatigue and high-impact loads (Jara-Arriagada & Stoianov 2024). In addition, such transients can mobilize biofilms or allow pathogen intrusion under sub-atmospheric pressures, posing risks to water quality and public health (Weston et al. 2021; South West Water 2024).

Small-magnitude transient events, whose occurrence is not distinctly observable in the acquired time-series pressure data, are not considered here. Research indicates that certain industrial and residential consumers can trigger small, longer-lasting transient events (Marsili et al. 2021, 2022). Depending on both their magnitude and the pipe material, these smaller amplitude events may or may not cause fatigue-related damage (Jara-Arriagada & Stoianov 2024). Such small-amplitude transients may occur randomly throughout the network and can be treated as background transients.

Medium to large-magnitude transient events typically arise from a well-defined set of sources, including control valves, pumps, firefighting activities, sudden pipe bursts, and large consumer demands (Rathnayaka et al. 2015). However, these pressure transients propagate rapidly throughout the network, making it difficult to identify their exact source without first establishing a suitable search area (Starczewska et al. 2014). To address this need, various studies have focused on localizing pressure transient sources through both simulated and experimental approaches.

The primary method for source localization in water distribution systems relies on analyzing the arrival times of the initial pressure wavefront at multiple time-synchronized, high-resolution pressure sensors (Misiunas et al. 2005; Srirangarajan et al. 2013). This method has been documented with several successful implementations (Srirangarajan et al. 2013; Hampson 2014; Hampson et al. 2014), with some case studies showing that this method is feasible for real-world operational networks (Srirangarajan et al. 2013; Hampson 2014; Guibert et al. 2023).

In a recent study (Jara-Arriagada et al. 2024), we proposed an extension of this method within an optimization framework to address the impact of network connectivity uncertainty on transients source localization accuracy. Closed isolation valves or other connectivity issues, treated as blockages, can substantially increase estimation errors (Jara-Arriagada et al. 2024), since unknown obstacles (or unknown valve statuses) compromise the hydraulic connectivity model used to compute pressure wave propagation paths (Jara-Arriagada et al. 2024). To mitigate this challenge, the extended method employs a k-shortest (fastest) path routing algorithm, thus accounting for multiple plausible propagation paths (Jara-Arriagada et al. 2024). Although this method has been validated with simulated transient data, its effectiveness under real operational conditions has yet to be demonstrated.

In this study, we aim to validate the previously proposed pressure transient source localization method using a real-world case in the United Kingdom. The investigated network exhibits frequent transient events triggered by an industrial user, producing a unique dataset characterized by both high-magnitude and recurring pressure transients. Their consistent daily occurrence from a single source facilitates clear discrimination from other hydraulic instabilities and uncertainties, offering a valuable opportunity to assess the proposed algorithm. Over the course of one week, data collection enabled rigorous quantification of wave arrival time estimation errors. Building on this dataset, the following contributions are presented:

1. Evaluate the performance of the multi-path source localization method proposed in Jara-Arriagada et al. (2024) on a real operational network and derive insights from the results.

2. Examine the effect of transient wave arrival time determination accuracy on source localization errors.

3. Investigate how the number of pressure monitoring devices (sensors) affects the performance of the proposed source localization method in this real operational context.

This section outlines the methodology used to implement the transient source localization method proposed in Jara-Arriagada et al. (2024) on a dataset of time series of pressure transients collected from an operational water distribution network in the UK. First, we describe the case study setup. We then provide a concise overview of the transient source localization method introduced in Jara-Arriagada et al. (2024). Finally, we detail the procedure used to evaluate the performance of this localization approach and to investigate the impact of varying the number of pressure sensors.

Various algorithms for detecting transient onsets have been proposed (Hampson 2014), employing wavelet analysis, Hilbert transforms, gradient detection, and probabilistic methods (Hampson 2014; Hoskins 2015). Hampson (2014) demonstrated that a gradient-based detection strategy, relying on the maximum gradient change in the pressure signal, offers a favorable balance of accuracy and consistency. After preliminary trials, we opted for a slightly modified version of this gradient-based approach, given its simplicity and minimal computational requirements. This algorithm could also be embedded within the firmware of battery-operated pressure monitoring devices, thereby reducing the need to transmit high-resolution pressure data wirelessly.

Hundreds of transient events were available for analysis. Although small, a notable distinction emerged between rising and dropping transients at the front wave arrival; rising transients exhibited a more gradual increase in pressure, whereas dropping transients were typically sharper. This disparity likely results from the speed at which the industrial user opens or closes the valve. For simplicity, we have chosen to use dropping transients, since their wave arrival onset is more straightforward to detect. Moreover, the primary focus of this article is to assess the performance of the transient source localization method rather than the precision of the pressure transient onset detection method. Although the onset detection method may still exhibit some inaccuracies, our goal is to test the source localization method using the most accurate onset detection outcomes possible.

Additionally, to aid the identification of transient onsets in the pressure time series, a set of heuristics was developed. Essentially, the set of heuristics aids at identifying the most likely onset of pressure transient events from a set of onset candidates. The heuristics inspect the local vicinity of each transient onset candidate to confirm that no other transient event is forming beforehand, and that the transient wave continues to rise afterward (Figure 2(a)). A detailed illustration of the onset detection process is provided in Figure 2(b).

The primary objective and main contribution of this article is to experimentally validate the performance of the transient source localization method proposed in Jara-Arriagada et al. (2024). This method analyzes multiple wave propagation paths to identify the most likely route through which a pressure wave would first arrive at the pressure monitoring locations. Its fundamental premise is that network connectivity may be uncertain (e.g., isolation valves with unknown states can block specific flow paths). If these valves are not accurately represented in the hydraulic model, such connectivity gaps can compromise the performance of transient source localization methods that rely solely on the shortest path from the source to the pressure sensors.

A comprehensive discussion of the method’s implementation and problem formulation is provided in Jara-Arriagada et al. (2024). The approach also involves selecting a factor α, which slightly increases the calculated wave propagation time along the path identified by the algorithm, thereby aligning it with the measured wave propagation times. This factor functions as a compensator for potential measurement inaccuracies in pressure wave arrival times. Further details can be found in the Appendix section of Jara-Arriagada et al. (2024). In this study, following the recommendation in Jara-Arriagada et al. (2024), we adopt a value of 0.06 for α.

In this case study, the source of the transient events was known to be an industrial user located at a specific location. We assigned this site to a terminal node of a valve in the network and designated it as the true source location. The distance between the true source node in the network and the node identified by the transient source localization method was determined via the shortest path. This distance was taken as the error for the transient source localization method.

To evaluate the accuracy of the transient source localization method, we applied it to 93 transient events. The main objective was to characterize the distribution of localization errors, accounting for variations in wave arrival times identified by the transient onset detection method. For each event, the distance between the estimated and true source was recorded, and the resulting errors were aggregated into a histogram to visualize the overall error distribution. For this analysis, we used the discretized network from the initial test, since the true source location was known to be within the discretized area. The purpose of using this discretized area was to enable a more precise assessment of localization error by ensuring a uniform distribution of nodes around the true source.

We performed a preliminary evaluation for the influence of the number of sensors on the transient source localization by iteratively removing sensors from the original configuration. Examining the impact of the number of deployed pressure sensors includes 15 possible configurations, generated by successively removing one sensor at a time from the original set of six until only two remain. For simplicity, we opted to remove sensors one by one, starting with the ones that were farthest away from the source, ultimately reducing the set to two sensors. For each sensor subset, transient analyses were performed at different times of the day, and the resultant error distributions were plotted.

This section presents the results obtained from analyzing the high-resolution pressure data and applying the transient source localization method to the operational network under study. To align with the contributions outlined in the introduction, these results are organized into three subsections.

Using the gradient detection algorithm described in Section 2.2, we derived the wave arrival onset times for each sensor from the collected high-resolution water pressure time series. To conduct an initial evaluation of the transient source localization method proposed in Jara-Arriagada et al. (2024), we selected one transient event from the dataset. Particular care was taken to accurately determine the wave arrival onset times, thereby minimizing potential errors. The corresponding localization results are shown in Figure 3.

The transient source localization results for this scenario display a high degree of accuracy, with an estimated error of approximately 17 m. We attribute this accurate result to the relatively low noise level in the pressure signals recorded during the transient event. Notably, the algorithm selected the fourth-shortest path for sensor 6, suggesting a possible network blockage or, alternatively, an inaccurate estimate of the pipe wave speed along that particular route.

Based on Figure 4, the transient onset detection algorithm performed particularly well for sensor 2, whereas sensors 3 and 4 did not exhibit a well-defined distribution of arrival times. In Figure 4, we also include thick vertical lines representing the analytically determined arrival times derived from the shortest-path distance between sensor 1 and each of the remaining sensors. These calculated travel times correspond reasonably well to the observed wave arrival time distributions, except for the path to sensor 6. As outlined in Section 3.1, the transient source localization algorithm identified the path to sensor 6 as potentially having a blockage or being subject to larger errors in the estimated pipe wave speed.

The proposed pressure-transient source localization method uses a k-shortest path routing algorithm to generate a set of candidate routes that a pressure wave may travel to reach the monitoring sensors. Under the assumption that pressure transients propagate along the network’s shortest path, any discrepancies in network connectivity (e.g., a closed valve) can cause the true propagation route to deviate from the one specified in the hydraulic model. Therefore, if the algorithm identifies a higher-order path, it suggests a potential misrepresentation of the network in the model.

In this study, the algorithm generally selected the primary shortest path for all sensors, except for sensor 6. Closer inspection of Figure 4 reveals that the predicted wave travel time for sensor 6 differs markedly from the measured travel time. Multiple sources of uncertainty can affect transient source localization; however, depending on the travel time along any alternative route, certain uncertainties that might have led the algorithm to favor the alternate path can be eliminated.

One key source of uncertainty arises from the transient onset detection, which in this case is limited by a sampling frequency of 64 S/s. This sampling rate implies a maximum possible error of approximately 0.0156 s, corresponding to a distance of about 20 m at a wave speed of 1,300 m/s. Further complications can emerge from gradual pressure changes, which may introduce up to 0.1 s (approximately 130 m) of error in arrival-time detection for sensor 6, as shown in Figure 4. Sensor location inaccuracies could also contribute, either compounding existing errors or acting as an independent source of error. In this specific network, the pipeline segment leading to sensor 6 is just over 100 m (or roughly 0.077 s of wave travel in cast iron), so it is unlikely that the alternative path was chosen solely due to mislocation of the sensor within the pipeline segment.

Figure 4 also shows a 0.175 s discrepancy between the analytically determined wave travel time along the primary path to sensor 6 and the average of the measured travel times. While the maximum expected errors discussed earlier can partially account for this offset (0.77 + 0.1 + 0.156 = 1.026), the measured travel time used in Section 3.1 aligns well with the average value, indicating that measurement error alone likely does not explain the divergence between measured travel times and analytical travel time.

Two principal sources of uncertainty may thus explain why the algorithm selected an alternative path. First, the wave speed assigned to the pipes near sensor 6 could be incorrect. In particular, the 270 m path is designated as cast iron (estimated wave speed of 1,314 m/s), which implies a travel time of 0.205 s; if, however, these pipes were actually plastic with a wave speed of 265 m/s, the travel time would be around 1.018 s, resulting in a substantial 0.813 s discrepancy. Such a large difference could prompt the algorithm to select another path if some pipes are, in fact, plastic. Second, a closed valve along the main route would force the wave to detour via an alternative path. Although valve records for this network were not available, the emergence of a higher-order path solution suggests that inaccuracies in pipe materials or valve statuses may exist in the current hydraulic model.

This study validates the pressure-transient source localization method proposed in Jara-Arriagada et al. (2024) using a unique dataset from an operational water distribution network. The results show that this method reliably identifies the source of transient events in close proximity to the actual initiation point. Multiple real transient events were analyzed, confirming consistent performance and indicating that, despite uncertainties in wave arrival times, localization errors remain within acceptable distances from the true source. An initial assessment of sensor quantity revealed that five sensors maintain robust accuracy; while configurations with four or three sensors remain usable, they exhibit broader error distributions.

The current method yields a single candidate for the transient source. An extension of the method would integrate the k-shortest path information generated by the algorithm with a suitable scoring framework (e.g., Srirangarajan et al. 2013) to delineate a broader search region for source localization. Reliable, current information on pipe materials is vital to ensure robust performance, as the localization methodology accommodates different pipe materials and their corresponding wave velocities. Nonetheless, plastic pipes may introduce additional uncertainty during transient onset detection and wave speed estimation, underscoring the need for further investigation of material-related impacts. Future efforts should also consider embedding the proposed method into a holistic network monitoring and asset management system. Additionally, further developments in theoretical underpinnings and computational efficiency are desirable, for example, by incorporating prior knowledge to constrain the search area and reduce computational effort. Ultimately, the transient source localization method discussed here enables the use of advanced pressure and pump control strategies in water supply networks, which generally operate under near–steady-state conditions but can be adversely affected by pressure transients.

This work was funded by the National Agency for Research and Development (ANID)/Scholarship Program/DOCTORADO BECAS CHILE/2020–72210314 (for C. J.-A.), and the Royal Academy of Engineering Senior Research Fellowship in Dynamically Adaptive Water Supply Networks [Reference no: RCSRF2324-17-41] (for I.S.).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.