3D criteria to improve real-time pressure control in water distribution network system architecture Open Access

SYMBOLS ROMAN

A

cross-sectional pipe area (m²)

a

celerity or elastic wave speed (m/s)

C

steady and unsteady constants (–)

D

pipe diameter (m)

g

gravitational acceleration (m/s²)

H

head loss (m)

L

pipe length (m)

P

pressure head (m)

Q

flow rate, leakage (m³/s)

Re

Reynolds number (–)

Sl

the slope of the pipeline (–)

t

time (s)

v

absolute velocity of the fluid (m/s)

x

coordinate along the pipe axis (m)

GREEK SYMBOLS

β

model parameter (–)

ε

strain (–)

v

mean roughness of the pipe wall

SUPERSCRIPTS

leaks

leakage output

α

model parameter

SUBSCRIPTS

d

day

f

loss friction

i

input or initial points

j

final points

k

pipe number

mean

average pipe pressure

n

reverse characteristic line

p

forward characteristic line

q

quasi-steady

r

retarded

The global water data estimated a non-revenue water (NRW) volume of 128 billion m³ and an NRW cost of 40 billion USD in 2020. It should be mentioned that the real numbers of water loss volume are higher as only 54% of the global population uses tap water. Developing countries account for almost 74% of the water loss. Data measurements mostly estimated a global NRW rate of 20–40%, with an average of 32% (AL-Washali 2021).

The advantages of service pressure control in water distribution networks (WDNs) have been frequently mentioned in the literature in recent years, including preventive measures for reducing background leakage (Negharchi & Shafaghat 2022), diminishing pipe leakage and burst, the possibility of lengthening the service life of the infrastructure, decreasing the hidden leakage rate (Ebadati et al. 2021), and reducing customer complaints (Creaco et al. 2018). The effectiveness of the pressure control approach and its promising outcomes have been frequently mentioned in several studies. A 20–25% saving in operation and maintenance costs (Burn et al. 2002), a 25% leakage reduction in Mutare, Zimbabwe (Marunga et al. 2006), a saving of up to 35% in the WDN of Tehran, Iran (Nazif et al. 2010), an 80% leakage decrease through the combination of pressure management and infrastructure renovation/improvement in C-Town, Canada (Roshani & Filion 2014), an 46% average flow reduction in a DMA of a WDN of Beijing, China (Xu et al. 2014), Alexandria, Egypt (Samir et al. 2017), 50% reduction potential of NRW in about 38 Indian cities (Bandari & Sadhukhan 2023), and determination of economic loss levels in WDN with an optimization algorithm, Türkiye (Yilmaz et al. 2023), suggest that pressure control is an efficient decision-making approach to find the optimal solution to the performance improvement of a WDN.

Based on traditional operation frameworks, WDNs are typically expected to be efficient in most operational scenarios and ensure acceptable standards for customer satisfaction, including proper pressure, flow rate, quality, and reliability (Creaco et al. 2019). Remote real-time control (RTC) and fixed-output pressure-reducing valves (FO-PRVs) have been of increasing interest for pressure control in WDNs. FO-PRVs are mechanical-hydraulic devices that automatically reduce the input pressure to a constant lower output pressure regardless of the flow rate or input pressure variations (Ulanicki & Skworcow 2014). Although FO-PRVs provide a high level of reliability, they are set to achieve a local regulation point for the output pressure. Therefore, FO-PRVs cannot ensure a higher or equal pressure head in a given node or an expected minimum pressure for a given demand in the WDN (Creaco et al. 2018). In contrast, the RTC system controls nodes at the lowest pressure level during the day in the WDN and can remotely activate valves. Thus, service pressure regulation through RTC not only tackles the aforementioned challenge but also allows for exploding remote sensing and measurement (Campisano et al. 2016; Creaco et al. 2018). The tendency to create fluctuations at low flow rates is another disadvantage of FO-PRVs (Ulanicki & Skworcow 2014). The problems of this type of control valve include deviation from the set control point, hydraulic instabilities, and cavitation (Changklom & Stoianov 2017). On the other hand, when the operating conditions approach an unsteady state such as a water hammer, the performance of the model diverges (Janus & Ulanicki 2017). The FO-PRV will only function properly at flow rates greater than or equal to 0.7 L/s and maintain the downstream pressure around the set value (Marsili et al. 2020).

The term pressure fluctuation is used to describe any change in pressure level within pipelines, whether the change is gradual as in daily pressure profiles, or sudden changes as in pressure transient events. In practice, most pipes throughout a distribution network are exposed to different pressures during daily and seasonal changes in water consumption, as well as due to changes in system performance (KILIC et al. 2011). The design of the water pipes takes into account the working pressures, and as such, the maximum water pressure throughout the network is not sufficient to cause failure. Due to the cyclical nature of pressure fluctuations, fatigue mechanisms may be a major factor in asset deterioration and eventual failure (Rezaei et al. 2015). In the research (Meniconi et al. 2022a, 2022b), experimental tests and transient flow analysis were investigated under the influence of network topology and the position of the transient generation point (end-user consumption). The results showed that the most reflected waves appear in two positions and then weaken: (1) at the junction of the service line (due to the trapping and shock of the water hammer effect at this point). This case is less effective in the current study. Because the purpose of the current research was to investigate the effects on the entire network, and on the one hand, based on the results of Meniconi et al. (2022b), the wave resulting from the water hammer in plastic pipes with viscoelastic properties is weaker than other materials such as metal. Here, all the studied network pipes are made of PE. (2) The pressure waves applied to the network are gathered in the parts with the smallest diameter of the pipe.

Pressure RTC systems typically consist of control programs and loops. To implement these control loops in the case-study area, data were collected using equipment such as pressure sensors, motorized valves, controllers, and telemetry systems. Then, to obtain the pressure settings in the target node(s), opening degree instructions were sent to the valves. Other devices, such as flow meters, could be used in sites, depending on the strategy, to enhance data processing in RTC and improve pressure control performance (Creaco & Franchini 2013). In addition, to efficiently set RTC systems for pressure control, a number of control aspects should be considered from simulation to field implementation. It is also required to take into account controller calibration, communication protocols, and pressure signal noise aspects to reflect their effects on control performance (Campisano et al. 2016).

In an RTC system, the pressure at critical node(s) is monitored through sensor(s). Then, a programmable logic controller (PLC) can effectively adjust the valve(s) through the signals to maintain the minimum required pressure in the remote critical node(s). Although RTC has a higher initial cost than PRVs, RTC-based valves have a greater return on capital (ROC) in the long run, particularly in areas with high leakage and water price per unit (Creaco & Walski 2017).

The RTC simulation assumes that each target node in the WDN is regularly controlled at a time step of Δt, and the hydraulic analysis and control of the WDN are simultaneously performed. Furthermore, based on the recommendation of valve providers, the valve shutters are assumed to have the same opening and closing rates. The shutter displacement of the valve begins at control time t at a very small mechanical rate (<1 mm/s) so that the hydraulic effects of the transient pressures caused by shutter displacement are eliminated (Campisano et al. 2010, 2016).

A review of previous studies indicates at least three valid reasons for the implementation of RTC in WDNs, including (Creaco et al. 2019):

• (1) Today, supervisory control and data acquisition (SCADA) and Internet of Things (IoT) technologies have facilitated supervision,

• (2) Case-study studies have proved that RTC has a significant potential to improve the performance of WDNs, and

• (3) RTC allows for saving water and energy.

To implement the RTC strategy on each positioned control valve, it is required to simulate the following stages for time t (Campisano et al. 2010):

• (I) Obtaining the pressures of all the sensitive nodes in the WDN;

• (II) Regulating the valve to achieve the desired pressure in the setpoint.

The selection of the target node (control node) is important in the establishment of an RTC architecture. Many studies proposed the node at the lowest pressure as the target node in the WDN. However, Campisano et al. (2010) suggested that nodes with a pressure change above 5% after the valve is fully closed (for example, a group of nodes that are affected by the action of the valve) are selected as target nodes. Moreover, the selection of appropriate control nodes is important from several aspects. First, the greatest leakage reduction results from the greatest removal of excess pressure at network nodes. On the other hand, the aim is to keep the pressure constant in the control node. Therefore, by choosing a control node outside the initial and end area of the distribution network, the greatest reduction in the signal of positive and negative pressure fluctuations is provided. As a result, by adjusting the service pressure, while increasing customer satisfaction, the possibility of pipe burst decreases (Campisano et al. 2016; Negharchi & Shafaghat 2022).

The selection of RTC architecture is an important step to maximize system performance. To select an effective and efficient architecture for the RTC system, detailed network design knowledge is required in order to identify PRV-sensitive nodes. In general, no architecture can be recommended as the most optimal alternative to adapt an RTC pressure program to WDNs since control systems encounter implementation challenges in sites (Campisano et al. 2016). However, local, remote, and single- or multi-control RTC architecture could be employed, depending on the WDN topology, connection patterns, and complexities (Creaco et al. 2019). Hence, different candidate architectures may be adopted.

For real-time PRV adjustment, the simplest architecture that can be adopted in the system is to use only one measuring (flow or pressure) sensor. In this architecture, the valve sensor and actuator are installed in the same location as the pumping station. The valve hydraulically pressurizes the flow and reduces the downstream service pressure.

The second architecture is implemented on relatively large systems, all of which are based on the remote control. A sensor performs remote measurements to set one (single-control) or more (multi-control) actuators (Berardi et al. 2018).

The third architecture, which is the most commonly used alternative for large WDNs, typically consists of multiple sensors and actuators, and the measurements performed in all the sites are sent to a central control room that operates different actuators in a coordinated manner at a comprehensive level. In some cases, sensors and actuators can communicate directly; however, they can be canceled by the control room.

Furthermore, depending on the RTC objectives, one can describe architectures that are controlled by an actuator based on measurements received by multiple distributed remote sensors in the network. Network control can consist of different degrees of automation, e.g., manual, supervised, and automatic. In manual control, actuators are set through instructions of human operators who compare the controlled variables to the setpoints. In supervised control, automatic controllers recommend modifications to supervision operators, and the operators apply the modifications based on their expertise. In the last case, fully automatized control is applied, even though it is possible to implement manual override under emergency conditions (Creaco et al. 2019).

The theoretical and practical advantages of pressure management have been analyzed in the literature, demonstrating the superiority of the RTC approach over FO control. In the RTC policy, the target node(s) are selected. Then, the most optimal regulatory head is identified through the dynamic modeling of network hydraulics. Finally, the effectiveness of the approach is evaluated using characteristics such as leakage reduction and customer complaint reduction. However, gaps remain yet to be filled in knowledge and technology development. First, no comprehensive criteria have been proposed for the selection of target nodes. The selection of the node with the lowest head as the target node in U-shaped¹ WDNs with pressure lack and excess pressure at the network level at the same time would yield unreliable results due to a lack of an effective pressure balance. Moreover, research has shown that control algorithms are very effective; however, their effectiveness is more dependent on field conditions and RTC system architecture (Creaco & Franchini 2013; Campisano et al. 2016; Creaco et al. 2019; Bosco et al. 2020). To select the target node from candidate nodes, the present study evaluates pressure fluctuation reduction and valve cavitation as criteria in addition to the existing criteria in the literature. Modeling of WDNs under unsteady flow conditions considering water consumption effects has been presented in previous studies (Huang et al. 2017; Bohorquez et al. 2020; Marsili et al. 2022). Here, to enhance the dynamic regulation capabilities, the unsteady flow based on the transient nature of the demand pulses was tested in the laboratory environment and then modeled using the method of characteristics (MOC). Furthermore, the present study sought to conveniently implement RTC architecture in terms of the number of sensors and the number of actuators using ANN results. The WDN of the Gavankola village in northern Iran was discussed as a case study as it had a diverse topography, a U-shaped structure, and a large number of private storage tanks. The measurements of the input flow rate (using an ultrasonic flow meter) and the pressure at the critical point were performed through remote sensing at 10- and 5-min intervals, respectively. It is worth noting the issue of understanding the pressure waves caused by water hammer or pulse demand was investigated in the context of the laboratory test of the authors' previous research. Then the solution method was implemented for a real network. It is worth mentioning that in field conditions, most of the transient flows are caused by the phenomenon of pulsed demand, which has much milder pressure wave effects than the impact of a water hammer.

The RTC architectures could be classified into two groups based on the network type:

• (I) Single-control architecture is recommended when the PRVs are positioned in the inlet of a branched network (with no loops). The target node is selected among nodes that are directly influenced by each PRV. This implies that the nodes which are sensitive to a given PRV are not sensitive to other PRVs. Fig. 1 of Campisano et al. (2016) depicts single-control architectures. Figure 1(a) shows a network in which all the nodes are sensitive to PRV 1, while Figure 1(b) indicates that PRV 2 enables the selection of another group of PRVs for these two PRVs.

• (II) Multi-control architecture is recommended when PRVs positioned in a looped network have shared sensitive nodes, as shown in Fig. 2 of Campisano et al. (2016). Figure 2(a) illustrates such a network. PRVs 1 and 2 mutually affect each other. Thus, the coordinated RTC of the two PRVs is necessary to avoid control system destabilization. Figure 2(b) shows a control architecture where the two PRVs share no sensitive node. As mentioned, single-control architecture is the only alternative recommended. The methods described in architectures I and II can be used for combined branched-looped networks.

This study used a real WDN in the Gavankola village, Mazandaran Province, northern Iran, as a case study to improve RTC architecture to reduce leakage and burst. The Gavankola WDN has features that have rarely been discussed in previous research. The selected rural area has various pressure services that involve two consumption patterns (Negharchi & Shafaghat 2022), and approximately half of the customers use private storage tanks to store water. Also, the tourist attraction of this village has caused a significant increase in water consumption on weekends. The WDN implements a gravitational distribution of water through polyethylene pipes and meets the national standards of Iran – i.e., the pipes have larger diameters than the required diameter for typical consumers. The WDN has been increased by nearly 1.4 km in length by experts to improve water distribution management in the past 12 months. The WDN was structured using nodes and 129 main branches. Table 1 summarizes the major characteristics of the WDN. It has a reservoir, a pumping station with a single pump, and nine commercial pipe sizes (32–125 mm). The maximum elevation difference between the reservoir and consumption points is 91 m. The WDN experiences high-pressure fluctuations during the day due to its U-shaped structure. It should be noted that bursts and leakage are much more likely to occur in variable-pressure water distribution systems (KILIC et al. 2011; Rezaei et al. 2015). High leakage was directly associated with the high pressure of the Gavankola WDN.

Pressure and flow rate data were collected at 5- and 10-min intervals for a 3-month period, respectively. An ultrasonic flow meter (SonixMeter SL300) with a data logger was installed on the inlet main pipe of the WDN (Soleyman.Co 2024). The flow velocity was measured via the time difference method (by measuring the time difference between ultrasonic signals transmitted between the sensors).

Consumption curves are used to determine the nodal demand. Two different approaches can be adopted to present the consumption curve. In the first approach, the amount of water entering the network is measured at different time intervals. Then the consumption multiplier is created based on the average consumption. Finally, considering this correction factor, the nodal demand is obtained at any time (Creaco et al. 2015). The second approach, known as the bottom-up approach, creates a consumption pattern or demand time series based on the aggregation of the nodal demand process of individual customers' demands. This approach is called demand pulses. In recent years, hydraulic analysis of unsteady flows using the concept of demand pulses has received more attention (Creaco et al. 2017). In the demand pulses approach, the amount of common demand is called pulse intensity and the demand withdrawal time is called pulse duration.

Here, a combination of three approaches of water demand time series, consumption accumulation pattern of each component, and leakage pattern has been used to create the demand pulse pattern in nodes. Based on the first approach, by measuring the inlet flow rate of the network, the pattern of the demand factor of the whole network can be determined. Then, based on the required flow of each pipe, the demand of each node is assigned.

The inlet flow rate of the network was collected over 3 months (Negharchi & Shafaghat 2020). Here, most customers use water storage tanks to store water at night within the specified limits.

A pressure sensor was installed in the critical node of the network, where the least service pressure to customers. Since this pressure is service pressure or discharge pressure, the trend of the pressure pattern (unlike the pressure and flow behavior at the network input) will indicate the pattern of demand pulses for customers with private storage tanks (Group B). The demand pulse pattern of Group A would be calculated as the difference between the total consumption pattern and the demand pattern of Group B, as shown in Figure 3. This study used remote data transmission without computers. The authors described the technical characteristics of the equipment in earlier works (Negharchi & Shafaghat 2020, 2021).

The coefficients are defined in Soares et al. (2008). The boundary conditions and equations of PRVs to solve the unsteady flow model in Table 1 are provided in Janus & Ulanicki (2018).

The numerical definition of each coefficient is available in earlier works (Soares et al. 2008). The boundary conditions and relationships of PRVs to solve the unsteady flow model are presented in Table 1 (Janus & Ulanicki 2018).

Furthermore, the additional equations that describe the boundary conditions at the two ends of the pipe should be determined.

The experimental WDN model at the Babol Noshirvani University of Technology was used to validate and calibrate the simulation model since it had the same pipe material (i.e., polyethylene) and density as the Gavankola WDN. Since it had a slope, this WDN could provide a realistic representation of WDNs. First, the system was simulated without the effects of drops for a steady-state flow. Then, the WDN was simulated for the same initial conditions in the computer code using the MOC. It was found that acceptable results could be obtained even by one division; however, more realistic results could be derived by increasing N_s. The evaluation of the effect of the space step (⁠⁠) on MOC accuracy indicated that the use of 20 divisions for each pipe in the WDN could yield the most rapid solution with an error below 1%. The unknown numerical parameters, including the coefficients of the longitudinal frictional pressure loss and local pressure losses in the steady-state flow, were obtained using experimental testing after the influential unsteady flow coefficients had been determined.

Artificial neural networks (ANNs) have been employed in WDNs since the late 1980s. They incorporate variables such as flow rate, pressure, district metered area (DMA) demand, reservoir water level, valve and pump settings, and pipe characteristics for leakage/burst detection, operational control settings, and the prediction of the pressure distribution and demand (O'Reilly et al. 2018; Kizilöz 2022; Rashid & Kumari 2023). Since it is impossible to install pressure sensors in all or a large number of nodes, it is not possible to permanently supervise and predict parameters, particularly leakage (Meirelles et al. 2017). Moreover, it may be time-consuming and costly to measure and analyze sensor data (Meirelles et al. 2017). Hence, ANNs could be utilized for process prediction.

Considering the complexity of WDNs, the present study adopted an ANN as an efficient approach for PRV setting prediction. A controller sets and controls the pressure adjustment screw on the valve pilot. The proposed ANN has a feedforward multi-layer perceptron (MLP) architecture (Wei et al. 2021). MLPs are popular predictive algorithms in water distribution systems. A review reported that nearly 40% of the papers in the literature had adopted MLPs for prediction (O'Reilly et al. 2018). The present study utilizes a hyperbolic tangent sigmoid activation function for neurons in the hidden layer (Rumelhart et al. 1985) and employs the Levenberg–Marquardt method to train the ANN.

The weights and bias are adjusted to minimize the mean square error (MSE) and maximize ANN performance. The input and output simulated data are randomly divided into training, validation, and testing datasets. The present study uses 70% of the simulated data as the training dataset, 15% of the data as the validation dataset, and the remaining 15% as the testing dataset.

The proposed ANN involved one hidden layer; however, the optimal number of neurons is dependent on the predicted error by the simulation. To select an effective ANN to predict the PRV opening degree, the number of neurons in the hidden layer was investigated using trial and error, evaluating performance and correlation coefficient. Finally, the optimal number of hidden neurons was selected.

The present study adopted the BP learning methodology, including dynamic learning. An iterative configuration enables the ANN to recover its previous results from the feedback of the produced opening degree settings. The adopted architecture is known as the element network, in which the outputs are compared to the inputs, utilizing BP to gradually set the PRV opening degree. This ANN was employed as it was an efficient behavior estimator in control systems. The development of an MLP can be summarized as (Barros Filho et al. 2018):

• (1) Defining the hidden layer number;

• (2) Defining the number of neurons in the hidden layer;

• (3) Generating random data for ANN weighting;

• (4) Implementing the regulation algorithm with real-time learning;

• (5) Confirming the PRV opening degree regulation.

The proposed ANN model consists of an input layer, a hidden layer, and an output layer. As the MLP was intended to control pressures in a WDN, the input signals included variables influencing pressure control. Furthermore, the supervision system consisted of a minimum of one and a maximum of three inputs and a single output. The inputs would receive signals from two pressure transducers, a flow meter, and PRV position feedback. The outputs were employed to change the pressure adjustment screw position. The ANN controller was aimed at maintaining the output pressure of the valves at a level near the setpoint in all the tests.

The control time step of Δt = 10 min was found to be effective for the analysis of the WDN. It was long enough to allow for neglecting instabilities arising from the valve reaction. In addition, it was short enough to enable a pressure deviation from the setpoint between two consecutive operation times. Indeed, the selection of the control time step was specific to the case study WDN. The present study sought to minimize the pressures of the pipes and ensure that the customer demands would be completely met. To this end, the estimated leakage was used as the evaluation criterion. For control conditions, the pressure of the control node was required to remain unchanged, while the pressure throughout the WDN was required to remain above 5 m (Campisano et al. 2010, 2016) and below 50 m, based on Iranian national regulations (Guideline 556 of Iran MOE 2017).

The simulations were aimed at:

• (1) Determining the proper target node for regulation in the control algorithm and

• (2) Determining the main parameter to implement the control algorithm.

An analysis of the pressure reduction potential indicated that RTC implementation in the main pipeline (including sub-branches that were not regulated by pressure management areas (PRVs)) while keeping PRVs installable at the primary of some PMAs could provide numerous benefits.

The node with the minimum pressure has been recommended to be considered as the control node in the literature; meeting the minimum allowable pressure in the control node minimizes the pressure levels throughout the WDN for a period of 24 h, diminishing the leakage. Furthermore, constant service pressure would satisfy customers. However, this scenario is not practical in the case study WDN due to its topography and U-shaped structure. The excess pressure begins at the end of Pipe 6. Thus, the control of this point enables the effective control of all the zones. As a result, the main PRV (RTC-PRV) was positioned at the end of Pipe 6.

If the node with the minimum pressure (selected as the control node) is kept at the minimum allowable head (i.e., 5 m), a large fraction of the WDN will still have a higher head than the maximum allowable level (i.e., 50 m).

Furthermore, the idea of selecting the node with the maximum pressure may be applied. However, the implementation of the control algorithm based on the maximum absolute head would keep a significant portion of the WDN below the minimum allowable head. Thus, the constraints can be handled only by eliminating all the excess pressures and using small pumps. To this end, the control node is selected from the nodes with low-pressure levels in the WDN. The present study utilizes two filters. First, the minimum daily pressure is considered as a criterion at the critical maximum pressure node. This level was simulated as 83 m in the WDN. Thus, the pipes whose minimum simulation pressures were below 38 m were filtered as the candidate target nodes, as shown in Figure 6 – this criterion was implemented based on the difference between the minimum and maximum allowable pressure levels (83 − 50 + 5 = 38 m). A total of 14 nodes were found to be candidate target nodes using this filter. Second, the worst node in each branch was selected, and the remaining nodes were excluded. Finally, the end nodes of pipes 62, 82, 91, and 60 were selected for analysis. The regulation of the pressure in the control nodes to the minimum pressure (i.e., 5 m) changed the initial pressure pattern (Figure 6) into a new pressure distribution, as shown in Table 2.

The end node of pipe 62 is the first candidate control node among four candidates, based on the literature. Under RTC implemented, when this node is kept at the minimum level (5 m), all the nodes in the WDN meet the minimum pressure constraint; however, 12% of the WDN exceeds the maximum allowable head (due to the high elevation differences in the case-study WDN). The implementation of RTC in the second candidate control node (the end of pipe 82) leads to slight violations of the two constraints. RTC in the third candidate control node (i.e., the end of pipe 91) would eliminate all the excess pressures; however, a pressure shortage appears in two sub-branches, which could be handled using two low-energy pumps.

The pressure fluctuation in these control nodes is of great importance. Although it led to the most optimal pressure levels and average WDN pressure, candidate control node 91 maximized the pressure fluctuation (up to 12.7 m). This would result in bursts. In other words, this node has both a positive and a negative effect on leakage reduction at the same time.

It was found that the positioning of the target node closer to the geographical center of the WDN reduces the pressure fluctuations. Therefore, node 60 was evaluated as the fourth candidate control node with different regulation conditions from the other candidates. It was regulated at 12 m. According to Table 2, node 60 not only provided the same benefits as node 91 but also reduced the pressure fluctuations.

Also, as mentioned earlier, in components of the network that have the smallest diameter, the most reflected waves appear. In this study, the RTC valve was selected based on the valve selection criteria of the manufacturer's catalog (as flow rate), with a size of two inches, while based on the RTC architecture, the pipe diameter at that position was 110 mm. Therefore, in addition to the considerations related to the cavitation index of the valve catalog, it is also evaluated as the potential point to create vulnerability indices.

Furthermore, the modification of the WDN (FO-PRV effect in the inlet of zone D) changed the leakage to 0.894 L/s in the non-RTC approach, while the use of RTC saves only 0.06 L/s of water, as shown in Figure 9(b). It should be noted that FO-PRV leakage reduction in the inlet of zone D was estimated to be larger for other control nodes. Thus, WDN modification can be expected to result in a 5–20% reduction in leakage.

Additionally, the results indicated that small pumps and VSPs would not be different in water loss reduction since the pump operation time and demand are low, and Mazandaran Water and Wastewater Company would not require additional pumps if sufficient water was stored in private storage tanks, with the approval of the customers.

An ANN with a hidden layer is employed. However, the optimal number of neurons is dependent on the predicted error. Hence, to develop an efficient ANN to predict the RTC-PRV control algorithm, different numbers of hidden neurons were evaluated using trial and error. Then, performance and correlation coefficient were evaluated to find the optimal number of neurons in the hidden layer. Table 3 represents the ANN input and output data ranges and the corresponding results.

This study applied RTC to a real-life WDN to evaluate whether it could be a field-oriented approach. Control node selection, RTC architecture, and control algorithm are known as the three main factors in the development and implementation of RTC methods. The first two factors were developed in a rural WDN in northern Iran. The dynamic hydraulic modeling of the field WDN was performed by developing a computer code using the MOC. Furthermore, the calibration results of the frictional pressure loss coefficients of steady and unsteady flows and the local pressure loss coefficients of the hydraulic model at the Babol Noshirvani University of Technology have been employed for field WDN simulations. To extract input data for the computer code, field measurements were used, including target node pressure measurements at 5-min intervals and WDN input flow rate measurements at 10-min intervals. Finally, the RTC architecture was simplified using an ANN and a control function. The results can be summarized as:

• (1) The total inflow rate was measured to be 4.18 L/s and the initial leakage was 1.105 L/s. Regardless of the effect of RTC, two pipeline modification and FO-PRVs approaches were investigated, which showed that the initial leakage was reduced to 0.894 and 0.873 L/s, respectively.

• (2) The control node with the minimum pressure would maximize the leakage but not necessarily the pressure fluctuations. Therefore, the burst rate and leakage would be likely to increase.

• (3) Since the conventional control node selection criteria (the node with the minimum pressure during the day) could not meet the pressure constraints, new criteria, including the cavitation index and head fluctuation, along with leakage reduction, play key roles in the selection of the control node.

• (4) In this study, the suggestion of past research (i.e., choosing the node with the lowest pressure in the WDN as the target node) was not applied, because in this case, one of the three selection criteria (i.e., cavitation index) was not met. Therefore, the node where the base working pressure was equal to 12 m instead of the minimum head (5 m) was chosen as the target node.

• (5) The ANN (MLP) indicated that the flow rate was the key parameter for remote sensing, and the RTC architecture was further simplified.

Considering the existence of lows and highs in real WDNs, it is suggested to analyze and investigate the process of air trapping and its unsteady flow modeling in future works.

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

The authors declare there is no conflict.