Detection of multi-branching pipes using transients in a pilot-scale pipeline system with uncertainties

A

cross-sectional area of pipeline

a

isolated wave speed of the pipe

D

pipe diameter

f

Darcy–Weisbach friction factor

g

gravitational acceleration

H

pressure head

n₁, n₂, n₃, n₄

nonlinear transient constants in a specific transient injection

Q

flow rate

t

time

x

distance of the pipeline system

τ

dimensionless coefficient of the relative valve opening

A water transmission pipeline system, consisting of main underground pipelines, plays a critical role in the sustainability of urban life. There are several types of pipeline elements in urban water pipelines, including series, branched, and lopped elements (Che et al. 2021). Distribution of drinking water to domestic users is largely dependent on how branched pipeline elements are arranged.

Branching pipe systems can provide drinking water efficiently according to demand and protect continuous resource supply even if one element fails (Meniconi et al. 2021a). It is essential to understand the role and to check the functions of the branches for reliable management of urban water systems. It is suspected that uncountable branches of urban water systems are being used illegally. The branched elements are illegally connected to the main pipelines, resulting in unexpected pressure fluctuations and adversely affecting urban water systems (Ebrahimi et al. 2022).

This results in a mismatch between water bills and total water usage, which is one of the most pressing problems with water management (Lee 2005; Stephens 2008). Detecting and predicting leaks in urban water systems have been the keys to addressing the water loss issue (Yu et al. 2023; McMillan et al. 2024; Sostero et al. 2024). It is also crucial to pay attention to branching elements because they can contribute significantly to water loss (Meniconi et al. 2011).

Several issues relating to branched pipeline elements can be addressed by considering the actual flow characteristics of urban water systems. It is important to recognize that pipeline systems are fundamentally unsteady in nature, meaning that pressure and flowrate continuously change over time and space. Flow changes or stagnation within such a system result in unexpected pressure waves with abnormal fluctuations in head and flowrate. As fluctuation patterns converge to specific flow conditions, a hydraulic transient is defined as the transition from one equilibrium condition to another under certain flow conditions.

As field pipeline systems are always subject to transient flow due to valve operations in each household, conducting research under hydraulic transient flow conditions will enhance the practical applicability of pipeline studies (Marsili et al. 2023; Kim et al. 2024). Hence, many pipeline studies have been conducted using hydraulic transients, usually induced by fast valve closures to reduce costs (Castellani et al. 2024; Kim 2024; Maietta et al. 2024; Toumi & Sekiou 2024; Zhang et al. 2024).

An instant valve closure makes a high-pressure wave propagate into a pipeline system, inducing pressure variations that are both positive and negative. It can cause cavitation within the pipe, resulting in failure of pipe components such as pipes, valves, and fittings, making it difficult to apply to field pipeline systems (Yuce & Omer 2019). Several researchers have explored alternatives that induce minimal hydraulic transients in a pipeline system without valve closure to avoid the risks associated with instant valve closure. A portable pressure wave maker device, connected to a pipeline system via a connecting valve, injects high-pressure waves into a pipeline system (Brunone et al. 2008). Brunone et al. (2021) studied the optimal design procedure for a smart portable device and assessed the device's effectiveness in detecting leaks in water transmission systems. The leak detection process was facilitated with minimal pressure disturbance due to this enhanced portable performance. Using wavelet analysis of pressure measurements from regulated pressure injection, Lee et al. (2021) developed a leak detection method for a simple pipeline system. Analyzing injected pressure data with wavelet analysis, they can determine the leak location in a pilot-scale pipeline system using the pressure damping wave and pressure vibration wave. By injecting safe transient flow into an actual pipeline system with a portable pressure wave maker, Capponi et al. (2024) proposed a transient test-based method for detecting the open status of an in-line valve under inverse transient analysis and correctly capturing the transient response of a series junction.

A pressure injection method involves injecting pressurized water into a pipeline system, which propagates a smaller pressure wave rather than valve closure, reducing pipeline damage risk (Meniconi et al. 2021b). In order to improve its applicability in real-life pipeline systems, this study carried out numerical and experimental analyses not only under an instant valve closure but also using a transient pressure injection.

A transient-based method should also be considered for detecting branching pipes in urban water systems. Unknown branched pipe elements, such as leaks and blockages, are also treated as abnormalities in a pipeline system. The pressure signal fluctuates meaningfully when a transient pressure wave is generated in a pipeline system. It is possible to detect an abnormality in a pipeline system using this fluctuation by analyzing the direct pressure responses in transient signals and the characteristics of overall pressure reflection in frequency responses (Che et al. 2021; Castellani et al. 2024). Transient-based studies have mainly been conducted for the purpose of diagnosing such abnormalities in urban water systems, mostly focusing on research aimed at addressing leakage detection issues in a pipeline system (Kim 2020; Choura et al. 2021; Meniconi et al. 2021b; Brunone et al. 2022; Pan et al. 2022; Keramat et al. 2023). Leakage in a pipeline system can be detected using the frequency response method owing to the leak characteristic causing pressure oscillation without altering the system's boundary conditions (Stephens 2008; Kim 2020). It has also been successfully developed to detect single-branching pipes by using wavelet transforms and frequency response functions (Meniconi et al. 2011; Duan & Lee 2016).

Nevertheless, it is challenging to explain the frequency response of branching pipes because of the boundary conditions that exist both at the ends and sides. A pipeline system with branching pipes deforms the boundary conditions and complicates the frequency-based detection of branching pipes, which worsens as the number of branching elements increases (Kim 2023).

Therefore, branching pipes will be detected by analyzing the direct pressure response of transient signals. For detecting branching pipes, research had previously focused on single-branching pipes (Meniconi et al. 2011; Duan & Lee 2016; Meniconi et al. 2018; Ebrahimi et al. 2022); however, multi-branching pipeline system research focused on addressing issues such as multi-leak detection (Torres et al. 2021) and reliable skeletonization (Meniconi et al. 2021a; Kim 2023). Detecting multi-branching pipelines accurately was first proposed by Ko et al. (2024). Based on real valve action and interference effects between different branching pipes, this study demonstrated transient-based multi-branching pipes detection (TBMBD) in a numerical reservoir-pipe-valve system. However, real-life systems need to address issues related to unknown pipeline components in field systems, such as features of unknown sections of the pipeline that may alter pressure signals. In this paper, a direct pressure response analysis of an experimental pipeline system is performed to support the reliability of TBMBD for field systems.

This means that uncertainties within urban water supply systems should be properly considered for practical research on TBMBD. The uncertainty of unknown information affects pressure fluctuations in normal hydraulic responses and hampers the prediction of several water problems in real pipeline systems. Two broad categories of uncertainties had been identified and addressed: epistemic uncertainties and empirical uncertainties (Wang & Ghidaoui 2018; Alawadhi & Tartakovsky 2020; Wang et al. 2020a; Wang 2021; Duan & Keramat 2022; Tjuatja et al. 2023), as well as aleatoric uncertainties in repeated experimental attempts (Basse 2019; Wang et al. 2020b; Hu et al. 2023; Wang et al. 2023).

Many uncertainty studies have proposed advanced methods for identifying, analyzing, and quantifying them, but their practical application still suffers from limitations. In particular, most urban water systems are complicated networks with many unknown components and present a wide range of uncertainties, making it very challenging to determine which types exist and where they are located. These uncertainties introduce problems in both diagnosing and addressing the hydraulic issues caused by specific abnormalities or components. Therefore, this paper proposed TBMBD under the assumption that uncertainties of unknown states exist as boundary conditions within the pipeline system. With the developed TBMBD, uncertainty assessment will be quicker and easier in the real field, reducing labour-intensive processes.

To improve the field applicability of TBMBD methods, this study extends the development of Ko et al. (2024) for pipeline systems with unknown uncertainties. Identifying the hidden uncertainty signals for a pipeline system is the key element of this research. Using the polynomial transient model (PTM), experimental pressure signals from a rectilinear pipeline system with uncertainties are acquired and calculated. The original uncertainty signal can be recovered through signal processing techniques such as superimposition. This uncertainty signal is used to introduce advanced signal manipulation techniques. Following the isolation of uncertainty responses, two superimposing processes are applied to the signals from each of the three branched elements of the experimental system. Verifications were performed under two different transient generation conditions, valve closures and pressure injections, taking into account three different uncertainty factors.

This paper is organized as follows: Section 2.1 explains the systematic processing for uncertainty signal separation used in transient analysis. Section 2.2 presents a method for TBMBD using uncertainty signals. Section 2.3 introduces the experimental pipeline system, which includes multi-branching pipes and uncertainties. Based on signal processing and experiments, we present a multi-branching pipe detection system under rectilinear flange conditions in Section 3.1, small and large leak flange conditions in Section 3.2, and 0.25 m series flange conditions in Section 3.3. As a final step, Section 3.4 compares the method with previous studies to evaluate its performance in detecting multi-branching pipes.

Two distinct approaches address the difference between a real-life system and its mathematical approximation. These were expressed in terms of the acquisition of experimental data from transient events for a pipeline system having multiple unknown uncertainties and the analysis of the pressure signal from the numerical analysis of the corresponding intact system. The PTM was used for the accurate evaluation of the transient introduction condition (Ko et al. 2024), which solved the mass and momentum balance equation for pressurized pipeline systems.

The raw pressure signals can be normalized for signal processing between distinct signals. The Joukowsky pressure can be used for the normalization of experimental and numerical pressure signal responses from transient introduction, which provides an identical scale in signal reconstruction. Finally, the inherent uncertainty signal can be extracted by superimposing multiple normalized pressure signals. The signal processing procedure described here is a systematic method of identifying uncertainties in a system response arising from unknown boundary conditions without the process of physical implementation or mathematical description.

Using n-branching pipeline elements, we are able to obtain experimental raw pressure signals per one transient condition. Through proper signal superimposition, we can isolate the uncertainty and rectilinear pipeline signals in these normalized signals based on Joukowsky pressure responses in transient initiation. This results in the acquisition of signals for uncertainties-rectilinear-isolated signals (URIS).

As a result of separating the interference effect between n-branching pipes, this method can be used to identify a specific element from multi-branching pipeline elements.

In order to validate the performance of the TBMBD scheme in this system, three points should be pre-checked. First, the length of the branched pipe element closest to the downstream valve and the distance between the two branching pipes should be properly spaced. Due to interference effects between adjacent branching pipes, pressure responses for TBMBD can be disturbed (Ko et al. 2024). As a result, branching pipes were installed at points 26.5 and 39.7 m from the downstream valves, with a distance of 13.2 m between them, and their lengths of 3.0 and 6.3 m, respectively. Second, downstream control valves must be closed when pressure waves are injected into this system. The pressure injection device is attached to the connecting valve of the main pipe at 0.3 m from the downstream valve, allowing regulated pressure waves to be injected into the system when the connecting valve is opened. Lastly, various pipe fittings introduce unknown fluctuations into a pressure signal to create artificial uncertainties. A pipe flange is a component that connects pipeline elements, but it can also deteriorate the ability to detect abnormalities by changing acoustic waves to propagate acoustically in an unexpected manner (Li et al. 2018; Williams et al. 2020). Therefore, a stainless flange is installed 57.1 m from the downstream valve, and its length is 0.93 m. Three types of stainless flange were used to generate distinct pressure signals corresponding to different uncertainty levels: rectilinear flange, leak flange, and series flange. There is no difference in the pipe property of all flanges, except that the inner diameter of the series flanges is 0.25 m. A high-frequency pressure transducer was used to obtain transient signals at 0.6 m from the downstream valve (Lee et al. 2021).

The signal processing for characterizing the uncertainty signal uses raw pressure signals obtained by the transient experiment and those simulated by a transient model. As shown in Figure 3, the uncertainty is related to the arbitrary flange used in the experiment. The transient events are either caused by an instant valve closure at the downstream control valve or by pressure injection that rapidly opens the connecting valve between the main pipeline system and the pressure injection device. The simulated pressure signal was calculated using PTM based on Equations (1)–(4) in the intact pipeline system. These pressure signals were normalized using the Joukowsky pressure responses of transient initiation for processing the pressure signal.

These results are also shown in Figure 4(b), which presents the normalized head signals on transient conditions of pressure injection under identical boundary conditions. The overall decreasing pattern in the experiment signal was associated with the unsteady friction effect along the pipeline extension. The largest pressure damping in these signals was observed between 0.1 and 0.15 s due to the pressure wave reflected upstream of the reservoir, and the phase difference indicates the variation of the wave speed within the experimental pipeline system (Lee et al. 2021). In spite of these discrepancies between experiment signals, it is not necessary to consider them explicitly because multi-branch pipe detection only utilizes the initial pressure response before 0.1 s (Ko et al. 2024). Additionally, unexpected pressure fluctuations caused by uncertain parts, including rectilinear flanges, were generated before the pressure damping unlike the transient condition of instant valve closure, as depicted in Figure 4(a). For handling these unexpected pressure responses, this study introduced a systematic signal processing method for separating uncertainty signals (Figure 1). The uncertainty signal was isolated from Joukowsky-normalized head signals of all pipeline system layouts to perform TBMBD.

The field applicability of the developed TBMBD method can be enhanced with additional experiment validation using different uncertainty conditions. An experiment with different uncertainty conditions was conducted by converting the uncertainty zone of the pipeline system (Figure 3) into a leak flange made of the same materials as the rectilinear flange. Combining the flange and leak effects, the leak flange introduces complicated uncertainties that alter normal pressure responses, making them more unpredictable. Two distinct leak conditions can be produced by two flanges: a small leak flange with a leak flowrate of 20 mL/s, which represents 32.9% of the steady flowrate for a small leak flange, and a large leak flange with a 50 mL/s leak flowrate, which represents 67.3% of the steady flowrate for a large leak flange.

As shown in Figure 4, signals from the experiment under different leak flange conditions were recorded in the same format under the same transient conditions as in Section 3.1.

Compared to Figure 4(a), the experiment signal of the leaky flange included pressure responses of a pressure drop, greater pressure oscillations, and greater pressure attenuation in the overall experiment signal than the intact flange (Covas & Ramos 2010; Choura et al. 2021). Under transient conditions of pressure injection, the small leaky flange caused pressure oscillations in the experiment signal. Furthermore, this signal exhibited unexpected pressure fluctuations before pressure damping at 0.15 s, similar to Figure 4(b), making it difficult to identify the precise pressure response of the small leak flange.

Large leak flange conditions resulted in much greater responses than small leak flange conditions (Covas & Ramos 2010; Zhang et al. 2024). It was found that the experiment signal was more convergent under the large leak flange condition than in the rectilinear and small leak flange condition. This signal also showed unexpected pressure fluctuations prior to pressure damping at 0.15 s. Therefore, the leak effects cannot be clearly defined on the pressure injection condition, whereas they can be on the instant valve closing condition. This property enabled the characterization of the uncertainty signal and conducting TBMBD, as described in Section 3.1, under small and large leak flange conditions.

TBMBD was further validated in the pipeline system using a series flange as the uncertainty zone (Figure 3). This series pipeline flange has the same material as the main pipeline, but its inner diameter is 0.25 m, which is greater than that of the main pipeline. As a pipeline system undergoes transient events, the wall thicknesses, wave speed, and friction factor differ from those of the standard pipe system (Chaudhry 2014; Jha et al. 2018; Malesińska et al. 2021). Under the same transient conditions as in the previous sections, an experiment signal was obtained based on an unknown assumed uncertainty.

A series flange in the experiment signal of valve closure condition caused pressure damping without a pressure drop or an overall pressure attenuation after damping. There are unexpected pressure fluctuations that obscure a confirmation of a series flange pressure response in the experiment signal under the pressure injection condition. The experiment signal experienced more pressure damping with more complicated noise responses than those in rectilinear and leaky flanges. By separating uncertainty from the developed TBMBD method, signal acquisition for TBMBD can be facilitated, despite these pressure responses in the extended flange condition.

According to Table 1, each condition showed different timing of the pressure damping phases. These differences resulted from different injection times of transient flow and partially by nonlinear ball valves, as well as different pressure wave speeds in the main pipe. Based on distinct specific timings, Table 2 presents predicted distances for two branching pipes, A and B, from the pressure transducer. The prediction errors for Branches A and B were less than 10% compared to the real positions. The conditions of the leaky flange showed the largest prediction error among all flanged conditions. Two branching pipes, A and B, may be hampered in their position prediction by the leaky flange, which causes greater pressure oscillations. For several uncertainties in the pipeline system, hydraulic pressure damping can be observed for detecting two branching pipes. However, it has been demonstrated that there are limited errors in determining the accurate positions for the two branching pipes.

This study developed an abnormality detection scheme for multi-branching elements in a pilot-scale pipeline system with uncertainties using transient analysis and experiments. The key point is that even though uncertainties in the pipeline system were left in an unknown state, detecting multi-branching pipes can be achieved through the application of the developed systematic signal processing. This means that the uncertainty of a pipeline system can be properly treated without realistic configuration, such as characterization and quantification, which had been explored in most existing uncertainty studies (Duan & Keramat 2022; Hu et al. 2023; Tjuatja et al. 2023; Wang et al. 2023). Consequently, the method proposed in this study has the potential to expand to diagnose the other specific unknown components (e.g., blockage) as well as unknown branching elements for pipeline systems while the other uncertainties (e.g., wave speed and transient condition) were treated as the unknown components. We believe that the proposed method can substantially relax the limitations of pipeline diagnosis, which are associated with unknown uncertainty.

This paper proposed a method to enhance the field applicability of the TBMBD scheme as an extended study from the authors’ previous work. The key objective of the method is to identify multi-branching pipes in pilot-scale pipeline systems with several unknown uncertainty conditions. Systematic signal processing for the isolation of uncertainty signals was proposed. Uncertainty signals were separated by superimposing transient-based experimental signals with unknown uncertainty signals and numerical data without uncertainties from the PTM. Original uncertainty signals were utilized in the developed TBMBD method to acquire IURIS for detecting multi-branching pipes from experimental pressure signals. The developed TBMBD method was experimentally validated with a two-branching-pipes system with uncertainties of various pipe flanges under two transient conditions, instant valve closure and pressure injection.

The two branching pipes in the pilot-scale pipeline system with uncertainties can be detected under all conditions of various pipe flanges and transients. It was identified in two distinct phases of hydraulic pressure damping in IURIS for Branch AB. Even though there were limited errors (<10%) in determining the accurate positions for the two branching pipes, the distinct responses for detecting the two branching pipes can be achieved through systematic signal processing for separating uncertainty signals and the developed TBMBD method. It can be applicable to a rectilinear pipeline system regardless of the number of branches, the method of transient generation, the wave speed in the system, and the presence of complicated uncertainties.

However, it is only possible to detect multi-branching pipes in a rectilinear reservoir-pipe-valve system with reasonable distances between branching pipes. A multi-branching pipe that has pipes too close to each other makes it challenging to accurately identify its position due to interference between reflected waves from the branches. Nevertheless, this paper shows meaningful results that it enables the diagnosis of a pipeline system in terms of handling uncertainties in the system itself. A noteworthy contribution is the detection of multi-branching pipes without the use of unknown uncertainties. This approach can increase the revenue water ratio in urban water systems by reducing unexpected water use. It can be further improved for field applicability by considering more uncertainties in a pipeline system, such as the presence of looped pipes or outflow from branching pipes, which significantly affect steady flowrate. Further study needs to be carried out under conditions of more disturbances in various pipeline systems and elaboration of the developed signal processing method, which can be a promising direction simply because of the viewpoint of uncertainty itself, which can not only relax the existing understanding of uncertainty but also provide an effective isolation platform for distinct uncertainties in transient signals.

This work was supported by the Daegu Gyeongbuk Institute of Science and Technology (DGIST) Research and Development (R&D) of the Ministry of Science and Information & Communications Technology (ICT) (Grant number 2024010409), the Electronics and Telecommunications Research Institute (ETRI) grant funded by the Korean government (Grant number 24ZD1120, Regional Industry Information Technology (IT) Convergence Technology Development and Support Project), and the National Research Foundation of South Korea (Grant number 2022R1A4A5028840).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.