A real-time and eco-layout platform for optimization of supply/costs for water distribution systems management Open Access

In line with climate change, the quality, quantity, and access to water resources will potentially decrease in some places. This phenomenon, in turn, leads to expending more energy for water purification or pumping from more profound depths or remoter distances and consequently provides a road to the release of excess greenhouse gases (Maas 2009). Water transfer from sources to sink via pressurized distribution systems is associated with significant energy consumption. While considering the economic and environmental adverse effects, it is strictly required to reduce energy losses as much as possible. Energy loss in water distribution systems (WDS) is principally classified into operational and structural types. The most crucial contributing factor to operating loss are pumping inefficiencies and leakage. Meanwhile, structural energy loss deals with the WDS's topology and towards descending just if the topology is modified (Cabrera et al. 2019).

In general, the water supply and distribution-correlated research can be arranged into four categories. The first batch of operational optimization research is carried out to optimize pump efficiency and cost amount as the scheduling problem of off-line pumps with no direct relation to remote stations (Pohjankukka et al. 2017). Such optimizations chiefly use population-based random linear programming, like genetic algorithms (GA), simulated refrigeration algorithms, and ant colony optimization (ACO). Conversely, these optimization types do not react dynamically to operational conversions because they do not follow the supervisory control and data acquisition (SCADA) principle and habitually fixate on single-objective issues such as energy efficiency and minimizing design costs. Moreover, compared to multi-objective optimization, single-objective optimization reveals meaningful circumscription. Overall, these kinds of research manifested that, in terms of operational optimization, the offline multi-objective formulation approach exposes rather efficacious conclusions (Cherchi et al. 2015; Sowby 2018; Housh & Salomons 2019).

The second operational optimization studies class triggers two-objective approaches. Majorly, most of them regard minimizing energy costs as the leading goal and pump maintenance as the second target (Cherchi et al. 2015; Piano et al. 2021). Meanwhile, some local WDSds surveys weigh the greenhouse gas emissions amounts as the second objective (Siew & Tanyimboh 2012). Accordingly, single or multiple objective differential evolution (DE) algorithms coupled with artificial neural networks are engaged to pursue operational strategies. From a control system point of view, this kind of performed formulation has no sufficient flexibility against demand fluctuations and ever-changing operating conditions. Since the pump scheduling formulates in this method as single correlated or unchanging strategies, the system cannot dynamically adapt to nonlinear disturbances in the urban environment.

The third category relates to research that adjudges the meta-modeling approach instead of the fully calibrated hydraulic simulation of EPANET to reduce the computational load of operational optimization. The most prevalent elected strategy in mentioned research is replacing intricate and broad models with reduced-order models or artificial neural networks (ANNs) (Candelieri et al. 2020; Tran et al. 2020). In this model, the neurons of each layer connect to those in the other layers through nonlinear mathematical functions. As a result, the figured neural network can arrange a fully complex nonlinear system. In comparison with EPANET hydraulic models, alternative ANN models represent lower accuracy. Furthermore, in this modeling outline, the output state variable from the previous control stage will be considered as an input for the subsequent stage (Ali et al. 2018; Chen et al. 2020; Tran et al. 2020). Thus, the possible generated error along the control horizon abysmally affects the optimization target space. As a matter of course, a slight befallen error can potentially lead to feasibility departure.

The fourth research category introduces online optimization methods to eliminate the mentioned finitude. An automated linear controller can dynamically adapt to altering operating conditions. These controllers consist chiefly of a GA optimizer and an artificial neural network to simulate system hydraulic behavior more precisely (Abkenar et al. 2015; Ali et al. 2018; Taha et al. 2021). Although the GA enjoys considerable success in optimization, some limitations, especially in real-time systems, are still problematic. Applying a large number of evaluation functions for convergence gaining is the most severe disadvantage of this platform. Because each evaluation function needs an individual simulation period, the convergence of this optimizer establishes slowly. Additionally, since the GA finds the solutions randomly, there is the risk that impossible or irrational solutions include in the optimization. Metaheuristic algorithms are another valuable algorithm that acts as part of the real-time control optimization method in the water distribution system. The adaptive GA was for the first time implemented to optimize online WDS operations as a multi-objective problem (Alsaeedan & Menai 2015).

Altogether, such performance in the optimization development process indicates that further studies are still involved to improve supply and distribution system optimization. The proposed method, in turn, via addressing unexamined contributing factors and using available quantitative evidence, aims to develop a mathematical model named real-time dynamically dimensioned scheduler (RT-DDS) platforms in which, the conducting strategies is summarized in two ways. Firstly, the pressure reduction for energy saving, and secondly, purposeful design for supplying water by lower water pressure. In this approach, the state variables constraints are consolidated on the objective function using the penalty-free approach. The solution to the optimization problem is found by prospering a hydraulic and eco-layout simulation code, EPANet, with a nonlinear optimization code.

This paper is arranged as follows. The formulation of the pumping cost minimization problem along with developing an algorithm for solving this problem is outlined in section 2. Afterward, the results of numerical experiments following the elaborated model are described via a case study.

To minimize both the daily operating and topographic energy consumption (TEC) for equalizing the network pressure to the standard pressure, as much as possible, an advanced predictive control model (E-MPC) is formulated. To begin with, the obvious assumption is that initial storage water levels, demands and demand patterns, and peak and off-peak electricity tariffs are known. Then, both the objective function and constraints of the pumping cost minimization problem are formulated. Since supplying water at a pressure more than the required amount is an energy waste, this paper notices contributing factors to eliminate this effect. For this purpose in the first place, the system is considered an ideal one but, in the end, it has correlation with operational loss.

In this section, the optimization problem of both operating and structural cost is formulated considering a WDS composed of an unlimited water supply source connecting to pumps and distributing equipment. The objective function incorporates both continuous and discrete variables, neglecting any depreciation cost. Therefore, in this paper, the objective function deals with the pump's energy consumption and topographic energy.

One of the crucial service standards of viable storage management is to ensure the reliability of emergency scenarios as well as to regulate the pressures throughout the system. In this regard, by enforcing befitting restrictions on tank levels, the entire storage space in the system is controllable. Although the water level in all tanks or reservoirs may differ at the start and terminal of the scheduling period, this volume variation should not exceed a certain amount. This article wields notations for parameters in the pumping cost minimization problem. For convenience, an inventory including some of them is presented in Table 1.

To create a comprehensive operation cost function, the summation of the peak and off-peak duration has been propounded. Obviously, the energy cost at peak periods is more than the other one. Therefore, the cost function related to the off-peak period is gained by adding the entire day's cost to the difference between the peak and off-peak periods. The control horizon (T) should sufficiently stretch such that all the considered manipulating variables (v) import their effects on the control variable (cv).

In some planning objectives like irrigation of green spaces, where water supply reliability is not the main priority, the optimization schemes only focus on the economic cost reduction. However, energy-efficient and eco-friendly systems occupy a superior allotment in drinking water supply projects. Reliability of the structural system is commonly obtained by identifying system leading specifications such as average demands, the peak of consumption, and variability in usage concerning daytime and day in the year (Cabrera et al. 2019).

The quantitative study of RTC effect on labor costs is possible only in long-term evaluations; this criterion is eliminated from the objective function formula. In addition, direct downsizing of maintenance costs is problematic and, for this reason, an alternative measurement estimation approach has been applied to facilitate the process (Abdul Gaffoor 2017).

The EPANet simulator will hydraulically actualize the conservation of mass flow and energy. In every iteration, this simulation system is responsible for the hydraulic analysis of the input control matrix. This system offers several state variable matrices, including a pressure head matrix for all monitoring nodes and water level matrix in tanks as output. Terminally, the system's outputs are utilized to evaluate the constraints imposed on the optimization process. The present study has engaged basic parameters such as the total dynamic head, flow rate, and the total power to water conversion efficiency to calculate the hourly energy consumption of each operating pump. From a hydraulic point of view, the conversion efficiency of electricity to water is computed by the ratio of output power to motor input, which is determined by simulating the efficiency of pumps in a set of operating points and comparing them with each other (Sowby 2018).

In the case of structural energy, the ratio of E_U/E_S (η_ai), is the determining factor, such that the more this ratio closes to 1, the more the system is cost beneficial. Since there is no distinctive area for η_ai, just the exerted constraints on the operating phase are the sole constraints for limiting the present bi-objective problem. In the present WDS system, long-term hydraulic stability has warranted handling the terminal constraint on storage tanks. This constraint highlights conditions that remains applicable at any intentioned system horizon so that, at the end of that horizon, the system will be confined to a deterministic value (Abdul Gaffoor 2017; Elsisi et al. 2021).

In parallel to specific research targets, the presented method has designated parameters such as pressure control, storage management, and hydraulic stability as state variables. The control pressure not only asserts high-quality services for end users but also provides an opportunity to minimize leakage (Housh & Salomons 2019). Since the time interval between decision points should echo an actual period for long-term planning and short-term productivity, here the control horizon included 24 hours with one-hour time steps. Mathematical equations led the pump scheduling to improve the pump's performance in each control horizon. For fixed-speed pumps, the suggested program can demonstrate the number of pump switches all over the control horizon and, in the case of variable-speed pumps, the schedule plan achieves the operating speeds of the pumps. In this study, binary status control (BSC) scheduling programs accompanied with the time controlled triggers (TCT) are used for real-time control. In the BSC approach, the pump scheduling presumes a binary sequence in dimensions tantamount to the control horizon.

The dual-space feed-forward (FF) programs, commonly applied for model prediction, are formulized in such a way that maintains no memory about the number of pump switches that occurred beforehand. Therefore, the integral number of switches in a day may exceed the maximum allowable. To engender an accurate prediction engine, this study encompasses a novel feedback-control (FB), segmented into two supposed discrete horizons called planning and operating horizons (Abdul Gaffoor 2017). Counting elapsed switches within an appointed day to the current time step, the model calculates the remaining allowed switches for the current day to hold them as the upper limit of the maximum allowable switches in the operation horizon. The most contributing factor affecting the pump scheduling prediction presents structural and operational problems over the WDS, every so often the pumps endure some oscillations so that a qualified model is obligated to predict their effects accurately. Table 2 manifests the prediction correlated to structural and operational signals. Here, ‘oper’ and ‘plan’ refer to the abbreviations for operating and planning parts of the control horizon, and the related T and SW are their duration and the number of allowed switches, respectively.

Table 2

The communication between WDS and the prediction model (Behandish & Wu, 2014)

SIGNAL from water distributing system .			RESPONSE from model prediction engine .
Situation .	Boundary condition .	Violation .	If .	Then .
Upper-bound on nodes and storage pressure (structural factor)			and	and
End of the day, if any allowed switches are not used during the day (operating factor)
St the beginning and at the end of the calendar day (operating factor)			and	and

SIGNAL from water distributing system .			RESPONSE from model prediction engine .
Situation .	Boundary condition .	Violation .	If .	Then .
Upper-bound on nodes and storage pressure (structural factor)			and	and
End of the day, if any allowed switches are not used during the day (operating factor)
St the beginning and at the end of the calendar day (operating factor)			and	and

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In the debated process, the operating decision space is dynamically adjusted with daily pump switches, so that the integral number of allowed switches (Sw_max) on the control horizon equals the aggregate switches occurring on the operating and planning horizons. Therefore, the number of switches in a given calendar day never exceeds the allowed maximum. Furthermore, the order of sampling in the two horizons is independent of each other.

One situation typically occurring at the end of the calendar day, if the operation horizon has not used any of its allowable switches during the day, and now, at the end of the calendar day, it is at risk of occurring too many switches in a short period. In this situation, the controller sets the number of operating switches to zero to prevent them from occurring in the current operating horizon, and transmits these remains switches to the planning horizon, which is the next calendar day. Conversely, when the pumps request none of their allowed switches during the current calendar day, if the pump switches are blocked on the operating horizon, the controller encounters a constraint violation problem. Both described events will lead to oscillating behavior and temporary instabilities in the system (Rayner 1995; Abdul Gaffoor 2017).

The prediction process of the developed model abrogates in two categories containing the multi-layer perceptron (MLP) and the machine learning techniques. Because only one output value needs to be predicted, here, only a single neuron is allocated to the output layer. The learning algorithm manipulated is the Levenberg–Marquardt (LMA) algorithm, and two functions named mean squared error (MSE) and Pearson correlation coefficient are proposed for predictive behavior.

Compared to a single predictor, a set of them can make premier evaluations in the same reaction space because a set of predictors appreciably detracts the uncertainty of a single predictor and inhibits variance, bias, and prediction errors. Thus, each predictor in the set is tasked with playing a complementary role to the other. The bootstrap aggregation technique and boosting technique are two group-based learning methods that benefit this research, both of which are composed of multiple homogeneous estimators (Pohjankukka et al. 2017; Piano et al. 2021). In this research, random forests (RFs) carry out the learning process. Decision trees are changeable enough to handle both numerical and stratified feature spaces and do not need normalization of feature space. These features make it an ideal option for demand forecasting until it can predict continuous variables based on classified characteristics (Abdul Gaffoor 2017; Brentan et al. 2018).

In the real WDS systems, containing many pumps, the progressed optimizer must head broad decision spaces efficiently. Another wanted attribute is optimization algorithm flexibility with changes to model run time. The algorithm's computational efficiency hesitantly changes with the model run time, so the algorithm must achieve appropriate solutions quickly, skillfully, and by spending a minimum computational budget . On the one hand, the population-based algorithms impose a huge computation budget on the model for evaluating fitness function. On the other hand, instead of finding a transformative solution, these algorithms search a population of solutions; therefore, fitting the algorithm goes on leisurely. Thus, population-based algorithms do not reveal a compatible behavior with RTC (Abdul Gaffoor 2017; Taha et al. 2021). The simple and reasonable structure of DDS optimization algorithms, containing only one algorithmic parameter, accredits it to present a set of practical solutions instead of an optimal global one and handles a more drastic calibration on the computational scale requested by the operators. For this purpose, two types of DDS-derived algorithms are proposed as the design fundament.

The propRCVR module is mooted to initialize the WDS model state matrix and receives a set of decisions containing discrete decision variables (DDVs) from optimization engines to storing network properties and generates a set of decoding decisions and scheduling of the pattern-based pump to execute the simulation model in the second module, exeSIM. When the hydraulic simulation is performed, the completed state matrices are inserted into the third module or ecoLYT for checking the possibility of maximum equalization between the network's pressure and the pressure set by the standards. Afterward, data are uploaded to the forth module, ctrlBC, to ensure that the constraints in the optimization engine are fulfilled. If the constraints are satisfied, the objective functions are sent to the next module for calculation and confirmation, otherwise, the value of the objective function is no longer calculated and the program terminates prematurely. The module of guesstimating optimum solutions for objective function or optSoL, which is the fifth module, estimates the energy cost of the system performance indicators.

The coherent validation uses criteria such as scatter plots, quantile–quantile plots (Q–Q), histogram of residuals, and auto correlation function (ACF). The scatter plots indicate which response function areas the model has underestimated or overestimated, and Q–Q plots indicate any bias in the predicted model responses. A histogram of residuals is plotted to evaluate the Normal Distribution hypothesis and provides a succinct summary of the residual scale and symmetry. Ultimately, ACF measures, the successive correlation values of the residuals is a function of the delays and the Pearson correlation coefficient. If the value of ACF is close to zero, the residuals are considered to exhibit no automatic correlation. However, the non-zero values of the function indicate that the residuals consecutively correspond (Abdul Gaffoor 2017; Piano et al. 2021).

To maximize the coverage of the entrance space and prevent clustering, Sobol's quasi-random sampling method, which seems more uniform, has replaced pseudo-random sampling. Generally, in the quasi-random sampling method because the sample size tends to be infinite, the initial sets are attentively distributed and follows more effectively than the pseudo-random methods to prepare the desired system uniformity (Abdul Gaffoor 2017; Elsisi et al. 2021). The performance of the decision tree and MLP regressions for single family residential (SFRES) and multiple family residential (MFRES) datasets were evaluated implementing the three-step validation described previously.

To train and validate the estimators of this study an MLP, composed of six neurons in the hidden layer, as a single estimator, and a random decision forest, containing 1,500 decision trees, was selected as a combined estimator. Meanwhile, the cross-validation composed of ten layers (10-fold CV) was designed for replicative validation execution case study.

The modern city of Sadra is a planned satellite city located 15 km northwest of Shiraz. The urban population housed by water facilities in Sadra is 213,600. In this area, the combined length of transmission lines and urban water distribution network comprises 562 km (Bagheri & Tousi 2018). The purpose of this study was to develop and quantitatively evaluate the performance of predictive machine learning models for forecast hourly demand. In this way, the generalizability of the models to predict demand at both scales is evaluated. With the help of collected data on water consumption at different distances of the distribution network, at fixed one-hour intervals, consumers were divided into categories of single residential unit (SFRES), residential complex (MFRES), commercial, industrial, administrative, and gardening.

Depending on the size and type of municipal services, two regulated pricing programs (RPPs) are defined as input data in the hydraulic model. These programs include the monthly load demand of less than 50 kW and between 50 and 999 kW. A typical day of this study is October 28, 2019, with an average daily demand of 44 (ML/d). After storing the obtained data, in order to exert the constraints and direct the boundary conditions, the state variables were examined assigned to the outputs of the hydraulic model. Programs that violated operational constraints were excluded from the optimization process as non-executable programs. Boundary conditions were accustomed at the beginning of each time step, not based on SCADA reports of state variables but awarded to the output values of the previous time step simulation.

Studies on the tank level have also revealed that maintaining a volume equivalent to 32% of the tank capacity is sufficient to warrant compliance with the terminal constraints and the provision of emergency storage.

As networks represent dynamic systems, some of their hydraulic characteristics are subject to time and environment. As a result, reliability of the water supply is difficult to achieve. Therefore, in order to provide an appropriate pressure at any part of WDS, two fundamental parameters, pressure head and volume are more significant. The pressure head directly represents the energy but water body volume predominantly deals with the price because, in huge water bodies, pumping suffers from disruption (Cabrera et al. 2019).

Given the difference between the regional characteristics of each scenario or even the difference between the amount and type of consumption, in order to create an equilibrium relationship between the pressures required for each scenario, in other words, to develop the data more uniformly, the energy balance method is used.

Table 3 shows the outcomes of comparing the daily energy balance of seven various scenarios of which the pumps tested in the previous section constituted a part. These results indicate that the fourth scenario is the most qualified in terms of cost (US$0.984/day). The first and fifth scenarios represent the weaker configuration among other scenarios, as observed from the RTC modeling.

As mentioned previously, the costs incurred in any water distribution system depend on the structural and operational characteristics of that system, so the topographic energy affects the performance of the switches, for example when the water level in tanks or reservoirs is higher than the normal range, pumps will suffer from operation reduction. Conversely, when the pumps cannot perform their supply function well due to wear or failure, the required pressure of the nodes or a reliable level is not provided for the tanks. As follows, it seems logical that the results of the two functional and structural parts of the same system are in favor of each other.

On the one hand, the schedule of the pumps optimizes the number of switches and ensures that they are implemented at the right time, in order to construct a suitable platform for maximizing the operational phase of the water supply. On the other hand, the study of topological energy produces supply and demand more proportionate, in order to prevent the imposition of increased energy on the pumps. In a comprehensive and successful system, optimizing both structural and functional dimensions sustains a significant impact on the efficiency of the water distribution system. This dual-purpose optimization, along with zoning-focused management, provides a reliable water supply system.

Finally, the data from the model sensitivity analysis detected the degree of significance for each variable, including upper quality limits for drinking water, conveyance costs, network topology, leakage, precipitation and temperature. Additionally it calculates the supply capacity of the source and the cost of operations as a function of maximum supply from the source. Among the selected variables, the leakage accommodates the severest impact on optimum fronts with sensitivity indices (SI) of 1.49695. Pumping led to pressure distributions during intense use periods and consequently decreases the overall leakage related to pump scheduling. At the same time, Rainfall and temperature remain considerably in the second and third ranks, respectively.

This research discusses developing a bi-objective mathematical model nominated RTC–eco-layout model used to propose a utilizable decision-making approach that manipulates the present quantitative evidence reported from structural parts of a distributing system. To achieve this goal, a three-module plan, consisting of a prediction engine to estimate the system demand, a simulation engine to evaluate the effect of control settings on hydraulic parameters, and an optimization engine to make the crucial optimal decisions, was proposed.

The forecasting process of the developed model started by presenting the results of the structural part to the model for predicting the amount of water demand in the short term, and in the best way, by developing a data-driven machine. Afterward, some application programming interfaces (APIs) were introduced to integrate the simulation model and organize the simulation code into the Python environment. In the optimization engine, a DDS algorithm was embedded in such a way that it was based on the results of the simulation model and, with the help of exploratory validations, it was arranged to adapt the control strategy to the existing conditions. The optimization engine was embedded in such a way that it was based on the results of the simulation model and, with the help of exploratory validations, adapted the control strategy to the existing conditions. Ultimately, in order to ensure the efficiency of the developed model, a multi-stage validation was performed.

A prominent target of the eco-layout phase is to reduce the weights of the structural losses as much as possible, through which it would be possible to retain a durable and stable structure that makes it viable to achieve an eco-friendly and cost-effective WDS. This plan mainly was established to prevent the nodes experience surplus pressure and was implemented by dividing areas into smaller pressure zones. Through this approach, the natural energy head possesses the most portion of water transmission in elevated or hilly areas, like Sadra.

In general, presenting the results, it can be stated that

• The possible answers win the more superior objective function value as the predictions carried out by the composite estimators represent lesser variance than those made by single estimators and are more successful in generating a robust estimate in the test set.

• The RT-DDS algorithm intelligently applies the pumps such that those with more excellent yields or lesser energy consumption incorporate more quotas.

• Performing sensitivity analysis on the model characteristics and evaluating their relative effects on the model prediction capacity concluded that both operating and environmental variables contribute to the total uncertainty.

• Evaluating the F-TCT formulation, alone, on a typical day, with a perturbed demand profile, revealed that the algorithm preserves its hydraulic feasibility properties in the range of 19% energy cost savings. Besides, maintaining a volume equivalent to 30% of the tank capacity is sufficient to affirm the satisfaction of the terminal constraints and the provision of emergency reserves.

• The cost–benefits were increased up to about 25% by pursuing just the eco-layouts process and it is expected to be even more money-saving in the long term based on reducing the maintenance prices.

All in all, combining the R-TCT and eco-layout phase in a bi-objective optimization problem illustrates that considering both operating and structural contributing factors, it is possible for a qualified system to gain even 50% money-saving rewards. This matter seems vital for current systems repair and subsequent construction.

S.A. completed this study as part of her PhD thesis under the supervision of M.H.N. S.A. wrote the paper, while technical support and revisions were provided by M.H.N., during model development and validation as well as reviewing the paper final version. M.A.Z. assisted in revision and additionally reviewed and provided feedback.

The authors received no specific funding for this work.

All data are illustrated in the manuscript.

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

The authors declare there is no conflict.