Designing an Intelligent Control Philosophy in Reservoirs of Water Transfer Networks in Supervisory Control and Data Acquisition System Stations

Ali Dolatshahi Zand Kaveh Khalili-Damghani Sadigh Raissi

Citation: A. Dolatshahi Zand, K. Khalili-Damghani, S. Raissi. Designing an intelligent control philosophy in reservoirs of water transfer networks in supervisory control and data acquisition system stations. International Journal of Automation and Computing. http://doi.org/10.1007/s11633-021-1284-1 doi:  10.1007/s11633-021-1284-1
Citation: Citation: A. Dolatshahi Zand, K. Khalili-Damghani, S. Raissi. Designing an intelligent control philosophy in reservoirs of water transfer networks in supervisory control and data acquisition system stations. International Journal of Automation and Computing . http://doi.org/10.1007/s11633-021-1284-1 doi:  10.1007/s11633-021-1284-1

Designing an Intelligent Control Philosophy in Reservoirs of Water Transfer Networks in Supervisory Control and Data Acquisition System Stations

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    Author Bio:

    Ali Dolatshahi Zand received the B.Sc. degree in electrical engineering from Shahed University, Iran in 2003, and received the M. Sc. degree in industrial engineering from Islamic Azad University, South Tehran Branch, Iran in 2014. He is a Ph. D. degree candidate in industrial engineering at the Islamic Azad University, South Tehran Branch, Iran. He has been working in designing SCADA, system and industrial automation for more than 16 years. His research interests include SCADA systems, industrial automation, soft computing, meta-heuristic methods, artificial neural network, reliability engineering and demand forecasting. E-mail: adolatshahi@yahoo.com ORCID iD: 0000-0002-9095-0493

    Kaveh Khalili-Damghani received the M. Sc. degree from Islamic Azad University, South Tehran Branch, Iran in 2005, received the Ph. D. degree in industrial engineering from Islamic Azad University, South Tehran Branch, Iran in 2008, and received the Ph. D. degree in industrial management from Allameh Tabatabei University, Iran in 2012. He has published more than 200 papers in high quality journals such as Information Sciences, Quality and Reliability Engineering International, Annals of Operations Research, Expert Systems with Applications, Computers and Industrial Engineering, International Journal of Advanced Manufacturing Technology, Applied Soft Computing, Reliability Engineering and System Safety, Measurement, Journal of Industrial Engineering International, Journal of Industrial Engineering: Theory, Application, and Practice, Project Management Journal, TOP, and Applied Mathematics and Computations. He is associate editor of six international journals indexed by Scopus. His research interests include soft computing, fuzzy sets and systems, meta-heuristic methods, multi-criteria decision making, data envelopment analysis, reliability optimization, quantitative modelling of supply chain, and applied operations research. E-mail: k_khalili@azad.ac.ir (Corresponding author) ORCID iD: 0000-0002-2338-1673

    Sadigh Raissi received the B. Sc, M. Sc and Ph. D. degrees in industrial engineering from Islamic Azad University, Science and Research Branch, Iran in 2002. He is an associate professor at School of Industrial Engineering, Islamic Azad University, South Tehran Branch (IAU-STB), Iran. He has been engaged in industrial systems engineering technology development and the technical consultant from 1988 up to the present. He has worked in different management positions, both in the private and public sectors; the last one was deputy of research and planning at IAU-STB. By his attempts, more than 10 scientific journals initiated and research activities facilitated. Currently, he is also acts as Editor-in- Chief of the Journal of Industrial Engineering International. He has published more than 180 research papers. His research interests include quality & reliability engineering, system simulation, and statistical methods in engineering. E-mail: raissi@azad.ac.ir

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  • 收稿日期:  2020-06-26
  • 录用日期:  2021-01-28
  • 网络出版日期:  2021-03-24

Designing an Intelligent Control Philosophy in Reservoirs of Water Transfer Networks in Supervisory Control and Data Acquisition System Stations

doi: 10.1007/s11633-021-1284-1
    作者简介:

    Ali Dolatshahi Zand received the B.Sc. degree in electrical engineering from Shahed University, Iran in 2003, and received the M. Sc. degree in industrial engineering from Islamic Azad University, South Tehran Branch, Iran in 2014. He is a Ph. D. degree candidate in industrial engineering at the Islamic Azad University, South Tehran Branch, Iran. He has been working in designing SCADA, system and industrial automation for more than 16 years. His research interests include SCADA systems, industrial automation, soft computing, meta-heuristic methods, artificial neural network, reliability engineering and demand forecasting. E-mail: adolatshahi@yahoo.com ORCID iD: 0000-0002-9095-0493

    Kaveh Khalili-Damghani received the M. Sc. degree from Islamic Azad University, South Tehran Branch, Iran in 2005, received the Ph. D. degree in industrial engineering from Islamic Azad University, South Tehran Branch, Iran in 2008, and received the Ph. D. degree in industrial management from Allameh Tabatabei University, Iran in 2012. He has published more than 200 papers in high quality journals such as Information Sciences, Quality and Reliability Engineering International, Annals of Operations Research, Expert Systems with Applications, Computers and Industrial Engineering, International Journal of Advanced Manufacturing Technology, Applied Soft Computing, Reliability Engineering and System Safety, Measurement, Journal of Industrial Engineering International, Journal of Industrial Engineering: Theory, Application, and Practice, Project Management Journal, TOP, and Applied Mathematics and Computations. He is associate editor of six international journals indexed by Scopus. His research interests include soft computing, fuzzy sets and systems, meta-heuristic methods, multi-criteria decision making, data envelopment analysis, reliability optimization, quantitative modelling of supply chain, and applied operations research. E-mail: k_khalili@azad.ac.ir (Corresponding author) ORCID iD: 0000-0002-2338-1673

    Sadigh Raissi received the B. Sc, M. Sc and Ph. D. degrees in industrial engineering from Islamic Azad University, Science and Research Branch, Iran in 2002. He is an associate professor at School of Industrial Engineering, Islamic Azad University, South Tehran Branch (IAU-STB), Iran. He has been engaged in industrial systems engineering technology development and the technical consultant from 1988 up to the present. He has worked in different management positions, both in the private and public sectors; the last one was deputy of research and planning at IAU-STB. By his attempts, more than 10 scientific journals initiated and research activities facilitated. Currently, he is also acts as Editor-in- Chief of the Journal of Industrial Engineering International. He has published more than 180 research papers. His research interests include quality & reliability engineering, system simulation, and statistical methods in engineering. E-mail: raissi@azad.ac.ir

English Abstract

Citation: A. Dolatshahi Zand, K. Khalili-Damghani, S. Raissi. Designing an intelligent control philosophy in reservoirs of water transfer networks in supervisory control and data acquisition system stations. International Journal of Automation and Computing. http://doi.org/10.1007/s11633-021-1284-1 doi:  10.1007/s11633-021-1284-1
Citation: Citation: A. Dolatshahi Zand, K. Khalili-Damghani, S. Raissi. Designing an intelligent control philosophy in reservoirs of water transfer networks in supervisory control and data acquisition system stations. International Journal of Automation and Computing . http://doi.org/10.1007/s11633-021-1284-1 doi:  10.1007/s11633-021-1284-1
    • Supervisory control and data acquisition (SCADA) systems have several applications in water transfer networks. SCADA systems are used at all stages of the water flow, including treatment, transfer and distribution. It is practically impossible to maintain continuous flow of water without the usage of SCADA systems. An SCADA system includes a central control unit which is responsible for collecting data, archiving, and report generating, alarming, monitoring, and sending commands to work stations[1]. In Fig. 1, the schematic structure of the SCADA system and its stations are shown[2].

      Figure 1.  General structure of SCADA system

      In most water SCADA centers, there is no intelligent system for controlling valves or issuing commands, and only the operators in the control center, based on their experience, determine the openness percentage of the inlet valves of the tanks and issue the command through the SCADA system. This procedure may cause many human errors and low efficiency in the system. Another control tool used in SCADA system stations is the control philosophy that is implemented within programmable logic controllers (PLC). These types of control philosophies only work when the height of the tank is in the upper and lower conditions and the valves are opened or closed. So, the PLCs cannot make any decisions for a wide number of states. For instance, when the consumption is high or very low, the system is stressed and operators are not able to make optimal decisions. Therefore, a suitably designed control software and ultimately, an intelligently written control philosophy, can make a significant change in the management and performance of the water supply network in large cities.

      This paper attempts to present an approach to optimize the control philosophy at the local stations of the SCADA system. More formally, a hybrid neural-genetic fuzzy system is proposed to control the flow and height of water in the reservoirs of the water transfer networks. The proposed approach combines the artificial neural network, genetic algorithm, and fuzzy inference system to improve the performance of the SCADA stations through a new control philosophy for instruments and control valves in the reservoirs of the water transfer networks.

      Storage tanks are the main parts of the water transfer network. Tanks store and transfer the water from the treatment or other tanks. Fig. 2 presents the structure of a reservoir in which the lines above the tank present the input pipe and the lines under the tank present the output pipe and the moving operation valve are shown by the MOV.

      Figure 2.  Resevoir structure and valves

      The inlet-outlet valves and the height of a reservoir have always been the main concerns for the water transfer operators. An incorrect adjustment will cause a lack of water on the customer side or perhaps an overflow of the tank, both cases are undesirable. The first one makes the customers dissatisfied and in the second case, drinking water is wasted. In the studied case, the operator only regulates the input valves in an emergency situation, and the output valves are always open and not regulated.

      One of the necessary variables needed to properly adjust the inlet valve and maintain a proper reservoir height is the measurement of the output water, called the network demand, and forecasting its future changes. Estimation of the water demand function will help to efficiently manage the water transfer network. In this paper, first, the variables affecting the water demand are investigated and identified. Then a multi-core artificial neural network (ANN) is proposed to calculate Tehran's water demand. The parameters of the proposed multi-core neural network are optimized using a genetic algorithm (GA). In the next step, the water demand is estimated by a multi-core neural network, the height of the water in the tanks which are continuously measured, and the inflow of water to the tank are assumed as inputs of a fuzzy inference system (FIS). The proposed FIS takes the future estimation of the water demand in the network, the height of the water in the tank, and online inflow of the water to the tank as inputs and returns the positioning value of the valves for a safe and suitable water supply in which no preemption or overflow will occur. To evaluate the performance of the proposed system, two switches are used to monitor the top and bottom of the reservoir. The purpose of the controller is to maintain the height of the reservoir in the appropriate range.

      This paper is organized as follows. In Section 2, the literature is reviewed. Section 3 is dedicated to the proposed hybrid approach including, criteria and variable selection, multi-core neural networks, genetic algorithms, and fuzzy inference systems. In Section 4, the real case study and the results are presented and discussed, respectively. The concluding remarks and future research directions are presented in Section 5.

    • In this section, the literature of related past research is briefly reviewed. There has been study the main modules of proposed hybrid approach of this study. So, the application of artificial neural networks in forecasting as well as fuzzy inference systems as intelligent controller are investigated in the following sub-sections.

    • The use of ANNs is very popular in forecasting as they can recognize non-linear and complex relations among time series and historical data. Feed-forward neural networks are the most well-known ANNs in this field. However, neural networks usually require the setting of a large number of parameters and finding optimized configurations, which is reachable with a repetitive optimization process. In summary, in the short-term and long-term demand forecasting, a lot of successful research has been accomplished in recent years.

      Ediger and Akar[3] used autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models for demand forecasting of energy carriers in Turkey from 2005 to 2020. Jammazi and Aloui[4] forecasted the price of oil using wavelet and neural networks in 2012. Wu and Liu[5] used a recurrent neural network for forecasting the usage of fuel in 2015. Khwaja et al.[6] provided an improved model for short-term load forecasting using a bagged neural network (BNN). The bagging process for predicting consumption reduces the error compared to a single neural network[6]. Nizami and Al-Garni[7] used a two layered feed-forward neural network model to investigate the relation between the electric energy consumption of electric power in the Eastern province of Saudi Arabia with weather data, global radiation and population. Comparison with a regression model showed that the neural network model performs better for predictions[7]. Al-Saba and El-Amin[8] used a multi-layer perceptron (MLP) network and back-propagation algorithm to predict the electric energy consumption and compared the result with time series models and the results of the prediction with the neural network showed less error than the time series models[8]. Kermanshahi and Iwamiya[9] used neural networks to forecast the usage of electricity in Japan until 2020. They designed and tested a three-layered back-propagation and a recurrent neural network for the purpose of the forecasting. Network inputs included as gross national product, gross domestic product, population, households, air-conditioning, carbon dioxide emissions, industrial production index, oil prices, energy consumption and electricity prices[9]. Gonzalez-Romera et al.[10] used ANNs to predict the monthly electric energy demand for Spain and they trained two neural networks to forecast monthly electric consumption. Jaramillo-Moran et al.[11] used neural networks to forecast the monthly electric demand. Also, they believed multi-layer perceptron was well suited to act as a digital filter. They proved that an MLP was able to perform both filtering and forecasting at once if properly trained[11]. Szoplik[12] used ANN to predict natural gas consumption in Poland. The monthly temperature and calendar variables were considered as inputs of the neural network. The result of the study showed that MLP could predict gas consumption daily and hourly successfully[12]. Xie et al.[13] presented two comprehensive models for forecasting the reliability of the distribution network, which consisted of two separate sections. They proposed a three-layer ANN to predict the reliability of the distribution network using system failure data[13]. Aljanabi et al.[14] used an MLP model to forecast the daily ozone concentration. Their models′ variables used to predict the ozone concentration of the next day were the previous values of ozone, temperature, and humidity[14].

    • As mentioned, this paper presents a hybrid approach based on ANN and FIS. FIS is proposed to adjust the inlet valve position. In the following some applications of FIS and fuzzy controllers in the literature are reviewed.

      Moezi et al.[15] designed an fuzzy controller which worked based on the pulse width modulation technique to control three laboratory robots equipped with low-cost solenoids and fuzzy controller coefficients were determined by the Cuckoo optimization algorithm. Rajan and Sahadev[16] designed an FIS to control interconnected tanks. They used a fuzzy control instead of using mathematical modeling and classical control. They used a neural network to tune the fuzzy controller[16]. Sathiskumar and Parthasarathy[17] used a hybrid ANN and FIS method to control a three-phase induction motor. They tested the performance of their method under several real conditions. The results showed that the hybrid method performed suitably[17]. Sahu et al.[18] used an inference system including type-II fuzzy sets to normally set the frequency and tie-line power and they applied a meta-heuristic method to tune the parameter of the proposed FIS. Khater et al.[19] used a fuzzy controller to monitor nonlinear dynamic systems. They proposed an FIS on the basis of the Takagi-Sugeno (T-S) inference method. The parameters of the T-S were set using reinforcement learning. The performance of the proposed method was better than the gradient decent method[19]. Zaki et al.[20] used FIS to monitor the performance of a direct current motor speed. Their method really consisted of two hierarchies including a Mamdani inference engine in the lower level and an inverse model based on a T-S method in the higher level. The output of the T-S method was used to tune the parameters of the Mamdani method[20]. Priyanka et al.[21] applied an FIS to control the flow rate of the petroleum products in the concrete pipes. The performance of the proposed FIS was compared with a PLC based cascade proportional integral derivative (PID) controller. The outputs of the FIS were monitored using a SCADA screen. It was recognized that the proposed FIS outperformed the Cascade-PID controller[21]. Goswami and Joshi[22] reviewed the applications of FIS on direct current motors. Fernandes[23] used an FIS to control the continuously variable transmission (CVT) system in electric vehicles (EV). The proposed FIS was used to tune the maximum efficiency motor rotation speed[23]. Kang et al.[24] applied FIS to detect the degradation in feed-water heaters in power generation facilities and they recognized that the proposed FIS could efficiently manage the power generation plants[24]. Attia et al.[25] used an FIS to efficiently tune the air conditioning system of a building. The proposed FIS controlled the room temperature, the relative humidity, and the percentage of chilled and hot water flow rates at summer, and the percentage of hot water and steam flow rates at winter. Computer simulation was used to compare the performance of proposed FIS with the results of a conventional PID controller[25]. Algazar et al.[26] applied an FIS to a DC-DC converter device to control the maximum power point tracking (MPPT) of a photovoltaic (PV) system under variable temperature and isolation conditions. Suganthi et al.[27] reviewed the application of FIS on renewable energy systems. FISs were extensively used in recent years for site assessment, installation of photovoltaic/wind farms, the power point tracking in solar photovoltaic/wind optimization[27]. Eltamaly and Farh[28] applied FIS to control a wind energy conversion system (WECS). Koshiyama et al.[29] proposed a hybrid method called genetic programming fuzzy inference system for classification (GPFIS-CLASS) to tune a fuzzy inference system and they tested the performance of the GPFIS-CLASS using two sets of benchmark data. Caesarendra et al.[30] proposed an adaptive neuro-fuzzy inference system (ANFIS) to determine the surface finish quality from the deburring process and the results showed a decreasing trend in measured vibration signals during the deburring process. Another example is a fuzzy logic controller that controls the torque of an induction motor suggested by Errouha et al.[31] Al-Fetyani et al.[32] designed an ANFIS to control the position of a quadcopter. The performance of their proposed model was better than a classical proportional-derivative (PD) controller[32].

    • In this paper, a genetic algorithm, which is a meta-heuristic algorithm, is used to adjust the weights of neural networks and optimize the error function. For this purpose, the section examines meta-heuristic algorithms. Meta-heuristic methods have been proposed since the early 1980s in solving complex hybrid optimization problems. These methods are a set of approximate methods designed for compound optimization problems. Because heuristic methods for solving these problems are inefficient and ineffective. Meta-heuristic methods such as the genetic algorithm, particle swarm algorithm and tabu search can address the weaknesses of optimization methods. That is, they can produce acceptable and good answers in an acceptable time, but the main concern about these methods is not able to guarantee the optimal results obtained from them.

      In general, these types of algorithms, in addition to being used in solving mathematical models of single-objective and multi-objective optimization, also have many applications in control problems that can be adjusted by the PID controller and fuzzy controller parameters, improve the neural network learning process and determine the type of neural network structure. The following are some articles on meta-heuristic algorithms.

      Al-Janan et al.[33] designed an algorithm that they called UniNeuro to find out how to optimize the input setting in a double inverted pendulum (DIP). This algorithm combines neural networks and a uniform design (UD) in one integrated model. They used a hybrid UD multi objective genetic algorithm (HUDMOGA) to optimize the input parameters[33]. Li et al.[34] proposed a new method that combines the chaos algorithm with the GA to initialize the weights and thresholds of the neural network. Their method was used for recognizing the gesture. The proposed method has a better performance than back propagation[34]. Rajarathinam et al.[35] used GA to optimize the parameters of discrete-time PID controller. Long et al.[36] used a swarm optimization combined with a local search to optimize a fast-recurrent neural network. Dolatshahi-Zand and Khalili-Damghani[1] used dynamic multi objective particle swarm optimization (DMOPSO) for solving the bi-objective redundancy allocation problem. Their objectives were cost and reliability. Their proposed algorithm showed better performance than the mathematical method[1].

    • The results of the literature review indicate that demand forecasting in the literature is known as an important and well-known issue in all areas of water, electricity, energy, gas and fuel and has wide applications in the real world. So far, various methods such as neural networks, regression, time series, etc. have been used in designing prediction models. In past decades, time series methods were used, which over time, multiple regression methods have gradually replaced it and shown better performance. With the passage of time and the introduction of artificial neural networks, at first, they had a performance equal to regression, but with the development of training methods and changes in the structure of ANNs, they provided superior performance over other methods. More recent articles have examined the evolution of learning methods with meta-heuristic algorithms and the use of more complex structures for the subject of prediction. With this approach and the references mentioned in these articles, the issue of using hybrid methods to predict consumption is raised. Using hybrid methods with fuzzy variables includes topics that have not been addressed. On the other hand, combining calendars and placing occasions in different calendars cause some issues that this research tries to address. After the topic of demand forecasting, the amount of openness of the inlet valves of water tanks with fuzzy controller and the variables which are the output of a forecasting model will be among the issues that have not been addressed. By reviewing the literature in the field of fuzzy inference, it can be seen that the use of hybrid methods has shown better performance and also, the usage of a fuzzy controller in control topics has performed better than the control philosophy written based on the classical control in the PLC. These cases are investigated in this study on the water transmission network of Tehran and an attempt is made to develop a dynamic and intelligent control philosophy for the SCADA system.

    • In this section, the hybrid neural-genetic fuzzy system for SCADA stations is proposed. In this regard, first the problem of the research and the main stages of the proposed hybrid approach are described. Then, the details of the proposed hybrid method are discussed.

    • In Mega cities, most raw water sources are usually dams and wells. In this process, the raw water is taken from dams or wells and led to water treatments. After the treatment, it is changed into drinking water. Then, it is directed to reservoirs to satisfy the customers′ demand. Fig. 3 presents this process. Depending on the network structure, this process may be a time consuming and inefficient one. The position of input valves regarding the demand, inflow and level of the water in the tanks and reservoirs is so important. Incorrect setting of input valves may cause overflow of the tanks or flow preemption at the output valves.

      Figure 3.  Flow diagram of water in transfer and distribution networks

      In the case study of this article, the output valves are always open to maintain the proper pressure in the distribution network and improve the customer′s satisfaction, except for the emergency situations. Considering this point, a suitable tool for adjusting the input valve is going to be designed.

      One of the most important variables necessary to adjust the reservoir input valves, is to know the current and future demand of water. Therefore, in the first stage, the variables affecting consumption are identified. In the second stage, the real data associated with the selected variables are extracted from the historical databases. In the third stage, the collected data are pre-screened, summarized, and purified. In the fourth stage, a multi-core ANN approach is proposed to forecast the demand of a reservoir using the input variables. The parameters of the proposed ANN are configured using GA. In the fifth stage, an FIS is proposed in order to determine the inlet flow of a tank. The inputs of the FIS are outputs of the ANN as well as level variables. In the sixth stage, a transform mechanism is proposed. The task of the transform control unit (TCU) is to convert the flow rate obtained from the FIS to the inlet valve position, in order to provide the necessary flow. The whole methodology of the proposed hybrid approach has 6 stages. The main stages are shown in Fig. 4.

      Figure 4.  Stages of proposed hybrid neural-genetic fuzzy system for SCADA stations

    • In some cases, due to the high dimensions of existing variables, it is not possible to use all of them. For instance, when the number of available inputs is very high and the number of samples are small, it is not suitable to use all variables[3]. It should be noted that with the complexity of processes, by converting physical laws into chemical, biological, economic or even social relationships, the number of potential inputs of the model increases and as a result, the effectiveness of each variable will be reduced[37]. One solution is to select all inputs, all possible combinations of them, and finally select the most effective inputs. The choice of input variables for identifying a system is typically performed in the form of trial and error, or with the help of existing knowledge of dynamics.

      In mechanical processes, the relationship among variables is completely clear and the related inputs are selected using designer insights on process physics. In the prediction of consumption, the existence of unfit data, the existence of special events, sudden changes in the climate and some completely random variables reduce the prediction accuracy. To predict the demand of water in a region, there are a variety of factors that are divided into two general categories as follows:

      1) Socio-economic variables such as population, income, water prices, house numbers and inflation, which are mainly used to predict long-term demand for water.

      2) Past consumption, rainfall, temperature, humidity and cultural issues, which are mainly used for short-term or seasonal demand for water[38].

    • In this section, the variables affecting Tehran's water demand function are introduced. Regarding the literature review, short-term and long-term variables for prediction, and availability of information and data for variables in the historical databases, four main variables as depicted in Fig. 5 have been determined to be affecting Tehran's water demand function.

      Figure 5.  Effective variables on water demand

      What is planned in someone′s mind, whether it is work or free time, cannot be an absolute matter. The point to be addressed in this case study is that Friday is officially a day off in Iran, and in some organizations, Thursdays in addition to Fridays, are considered a holiday. Typically, with a look at the weekly consumption trends, it can be seen that water consumption is not decreasing on Thursdays and Fridays, and even sometimes it increases, but as it comes to the official holidays, the volume of travel increases and consumption decreases. In previous research, the holidays and the days between them were assigned a degree of membership according to the opinion of the experts[37]. In this paper, we use the fuzzy function to calculate the holiday value for a day. Therefore, depending on the nature of this variable, a fuzzy set is used to define it, and its membership degree will be used as an input variable to the model. Discrete fuzzy sets have been used in order to model the degree of membership of a day into holiday set. Two fuzzy sets as before holiday (BH) and after holiday (AH) are defined as relations (1) and (2), respectively. The membership values of three days and more, two days, one day, and the holiday have been determined in both BH and AH fuzzy sets.

      $$\begin{split} {BH}=&\left\{ \frac{\mathrm{three}\;\mathrm{days}\;\mathrm{before}\;\mathrm{and}\;\mathrm{more}}{0},\frac{\mathrm{two}\;\mathrm{days}\;\mathrm{before}}{0.125},\right.\\ &\left.\frac{\mathrm{one}\;\mathrm{day}\;\mathrm{before}}{0.5}\right.\left.,\frac{\mathrm{holiday}}{1}\right\} \end{split}$$ (1)
      $$\begin{split} {AH}=&\left\{\frac{\mathrm{three}\;\mathrm{days}\;\mathrm{after}\;\mathrm{and}\;\mathrm{more}}{0},\frac{\mathrm{two}\;\mathrm{days}\;\mathrm{after}}{0.125},\right.\\ &\left.\frac{\mathrm{one}\;\mathrm{day}\;\mathrm{after}}{0.5}\right.\left.,\frac{\mathrm{holiday}}{1}\right\}. \end{split}$$ (2)

      To calculate the membership degree of a day, the union of AH and BH fuzzy sets according to (3) is used.

      $$ {\mu }_{H}={\mu }_{(BH\cup AH)}={\rm{Max}}({\mu }_{BH},{\mu }_{AH}) $$ (3)

      $ {\mu }_{H} $: Degree of membership for the holidays

      $ {\mu }_{BH} $: Degree of membership for the days that are before the holiday

      $ {\mu }_{AH} $: Degree of membership for the days that are after the holiday.

    • As discussed in the input selection section, variables used as inputs in the short-term forecasting model of water demand are rainfall, air temperature, holidays and past consumption of water demand in the reservoirs of Tehran. The data of the input variables including daily output flow of water reservoirs in Tehran, daily rainfall, maximum, minimum and average air temperature in Tehran, and holidays were collected from the Tehran water SCADA as well as the site of the meteorological organization. These data are used as inputs to the multi-core ANN model. The proposed multi-core ANN model includes MLP and radial based function (RBF) for prediction. The structure of these two types of neural networks is discussed below.

    • Pre-processing and pre-screening of data will have a significant effect on the modeling and will increase the accuracy of the ANNs[39]. One of the most important pre-processing steps is scaling of data. The most important reason for scaling the data is to equalize the importance of the variables. On the other hand, when the incoming data are not in a similar scale, training of the ANN will not be an easy task. Another important point to note is that the range of input changes should be the same as the limits of the activation functions. Indeed, in this research, variables such as temperature and flow do not have the same range and should be adjusted. One of the techniques for “scaling the data” is the Min-Max normalization technique. In this study, (8) is used to scale the data[37].

      $$ {x}_{N}=\left(\frac{x-{\rm{Min}}\; {\rm{value}}\; {\rm{of}}\; x}{{\rm{Max}}\; {\rm{value}}\; {\rm{of}}\; x-{\rm{Min}}\; {\rm{value }}\;{\rm{of}}\; x}\times 2\right)-1 $$ (4)

      ${x}_{N}:\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}\;\;\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}$

      $ x $: Original data.

    • To predict the demand of the water which is picked from the reservoir, two main types of ANNs, called MLP and RBF, are proposed and used. Mathematical techniques as well as evolutionary algorithms (EAs) are used to train the proposed ANNs.

    • The number of neurons in the hidden layer has a crucial effect on the ANNs' performance. The large number of neurons in the hidden layer will extend the duration of the training process. Of course, the small number will reduce the generalization[40]. The task of identifying the number of neurons in the input and output layers is normally determined by the numbers of input and output variables. Identifying the number of neurons in the hidden layer is usually determined by trial and error. Of course, in some articles, genetic algorithms are also used to identify the number of neurons.

      The main purpose of creating an ANN is to establish a logical relationship between input and output with the number of specified layers. When the relationship between the involved variables is complicated, a simple neural network model may not be able to establish a relationship with good accuracy. Increasing the number of hidden layers for modeling physical processes is one of the ways to solve complex problems. On the other hand, the increase in the number of hidden layers will increase the number of connections and the total number of parameters in the ANN. Deciding on number of neurons in the hidden layers is an important part of deciding on the network′s general architecture. Although hidden layers are not directly in contact with the outside environment, they have a significant effect on the final output. Both the number of hidden layers and the number of neurons in each hidden layer should be carefully considered. Obviously, a compromise between the high amount and the low amount of the neurons in the hidden layer should be made. There are many rules of thumb to determine the correct number of neurons in the hidden layer[41]. In this study, for the preliminary estimation of the number of neurons in the hidden layer, the following rule is considered in which the minimum number of neurons can be approximately twice the number of inputs plus output variable[41]. The schematic structures of MLP and RBF for demand forecasting are shown in Figs. 6 and 7, respectively.

      Figure 6.  Schematic view of MLP

      Figure 7.  Schematic view of RBF

    • The learning process in ANN involves modifying the weights and biases of a network, also according to the learning algorithm, it forces the network to give a specific response to a particular input[40]. The learning process is created by a series of input and output data called training data to form the proper network behavior. In supervised learning methods, when the input is applied to the network, the network output is compared with the optimal response. Then the rule of learning is used to adjust the weights and biases to reach the desired response. The learning method tries to improve the current error of all the elements of the process. This global error reduction over time passes through a continuous weight correction process until the error reaches a specified limit for the target[40]. The overall training process consists of applying input and output data to the neural network. These data are often referred to as training sets. For each input set that is supposed to be applied to the network, an optimal output set is also provided[40].

      The parameters in Fig. 6 and Fig. 7 are defined as follows:

      Dt−1: Last day demand

      Tt: Current temperature

      Rt: Total rainfall

      Ht: Holiday.

      Most scholars have pointed out that the use of EAs is more common in support of ANNs[40]. In this paper, GAs and mathematical methods are used to regulate the parameters of the ANN. The main reasons for using GA in order to train the parameters of the ANN are listed as follows[40]:

      1) GA performs better than well-known classic non-linear optimization such as Levenberg Marquart.

      2) The computational efforts, i.e., required hardware such as RAM, and training CPU time for Levenberg Marquart is dramatically high for real case studies and big data.

      3) Classic training methods of ANNs such as Levenberg Marquart usually suffered from trapping in local optimum solutions while population-based optimization methods such as GA use crossover and mutation operators in order to diversify and intensify the searching processes.

      4) Classic training methods of ANNs use single start searching procedures in order to solve the problem, while multi-start mechanisms are used in population-based algorithms such as GA.

      5) GA is also the most well-known EA approach while it is easy to implement and straightforward to compare with other EAs.

      To evaluate the performance of a set of parameters, the neural network is trained by a certain number of iterations. During the training process, the neural network acquires different levels of performance for different categories of control parameters.

      To form such training mechanisms using EA, the weights should be stored in a matrix and updated at different time intervals. Therefore, an initial population of weights should be created, stored and updated in a matrix named chromosome[40].

    • According to the above, the EA should change the weights of the ANN. Hence, the formation of a chromosome, including weight and bias parameters, is necessary to achieve this. Fig. 8 shows how to form a chromosome for a given ANN with two inputs, one output, and one hidden layer including two neurons[40].

      Figure 8.  Formation of a chromosome associated with ANN

      The initial chromosome structure used in this research, based on the calculation of the number of hidden layers and the structure of the neural network layers is initially considered as (4-10-1). Considering the main problem of this study in the phase of forecasting the water demand, the structure of the proposed ANN is initially set as 4-10-1. This means the input layer has 4 neurons, the output layer has one neuron. The ANN has a hidden layer including 10 neurons. In the input layer 50 weights are required to be determined, i.e., each input to each neuron in the hidden layer (4 × 10) and one bias value for each neuron in the hidden layer (10). The output layer also has 10 weights which connect the hidden layer into the unique output of the ANN and one bias. So, the first structure of the chromosome of this study has 61 genes as presented in (5).

      $$\begin{split} {\rm{Chromosome}}=&[{w}_{\mathrm{1,1}},{w}_{\mathrm{1,2}},\cdots ,{w}_{\mathrm{1,40}},{w}_{\mathrm{2,1}},{w}_{\mathrm{2,2}},\cdots ,\\ &\;\;{w}_{\mathrm{2,10}},{b}_{\mathrm{1,1}},{b}_{\mathrm{1,2}},\cdots ,{b}_{\mathrm{1,10}},{b}_{\mathrm{2,1}}]. \end{split}$$ (5)

      The population of the chromosomes is formed in the shape of matrix. This conceptual matrix is shown in Fig. 9.

      Figure 9.  Schematic view of matrix of GA iterations for training of ANN

    • In each iteration, mean squared error (MSE) is calculated and it is used for performance evaluation of the ANN.

      $$ MSE=f\left(NN\right)=\frac{1}{P}\sum _{p}{e}^{2} $$ (6)

      where p is the number of data or patterns used for training and the error value is the difference between the output amount calculated by the ANN and the actual value of the output (e = YNetYreal). In this study, the data was divided into two categories of training and test, and the errors are calculated for each subset distinctively.

    • After the population is sorted by the cost function MSE, to form the next generation, the first 15% of the population is passed directly to the next generation, and 50% are passed on to the next generation by the crossover function and 15% by the mutation function.

      In the 50% crossover operation, after selecting the parents based on the selection methods, a random number between 1 and the number of chromosome gens is created to obtain the cut point and the crossover operation is performed as follows:

      Cut_point = randi (1, numel (Parent1));

      Off1 = Parent1;

      Off2 = Parent2;

      Off1(1: Cut_point) = Parent2(1: Cut_point);

      Off2(1: Cut_point) = Parent1(1: Cut_point);

    • As mentioned before, in the mutation operation 15% of the chromosomes (mutant number) are randomly selected and a random number between 1 and the number of chromosome genes is generated so that the relevant gene mutates with the following code:

      for i=1: Mutatant_Num

      b=randi ([1, population_Num]);

      MutatPop(i,b)= MutatPop(i,b) + 2×rand − 1;

      end

    • Steps of training ANN using GA are presented in Fig. 10.

      Figure 10.  Steps of training ANN using GA

    • Bagging is used to enforce the machine learning methods. Estimations of a trained ANN model can often lead to different results[6]. In the bagging technique, different models are trained using different data sets with replacement. Replacement means that each sample can be selected several times as a training set[6]. This ensures independence of training samples. For finding the results, different models are run. The final result is the average of the results achieved by all models[6].

      In this paper, a multi-core technique is used inspired by the bagging method, so that several groups of ANN, with different structures, will be responsible for prediction. Depending on the application, each core can be different in the type of feed forward network, the number of hidden layer neurons, and the use of activation functions.

    • As already mentioned, reservoir outlet valves are always open in the case study. Therefore, in order to maintain the continuous flow of water in the distribution network, the input valves of the tanks should be adjusted based on the customers′ demand. To achieve this, a fuzzy inference system is proposed in this subsection. In the previous section, a set of ANN was designed to estimate the demand rate as one of the inputs needed for the FIS. Considering the mechanical and electrical limitations of electric actuators and installing measuring instruments on the reservoir, the schematic configuration of the reservoir is presented in Fig. 11.

      Figure 11.  Schematic configuration of the reservoir including level meter and actuator

      Consider valve 2 is assumed to be in the standby mode and normally open (NO) position in Fig. 11, hence the main aim of the FIS is to determine the percentage of valve 1 openness. Therefore, the future flow (demand) as well as the current state of the reservoir height, which can be taken from level meters 1−4 sensors (average readings of sensors in the correct operation), can be used as input variables of the FIS which is used to determine the input flow of the reservoir. The estimated input flow will be used as the input of a transformer to determine the valve 1 position value (valve openness). It should be noted that the FIS output is the reservoir input flow which the tank inlet valve should be set to the appropriate position in order to achieve this flow. The task of the transform block is to convert the flow rate into the reservoir valve openness.

      With regard to the literature of the SCADA system, linguistic variables H, O and F are defined for height, demand and input flow of the reservoir as (7)−(9).

      $$ H\left(level\right)=\left\{{\rm{very}}\;{\rm{ low}},\; {\rm{low}},\; {\rm{high}},\;{\rm{very}} \;{\rm{high}}\}\right. $$ (7)
      $$ O\left(demand\right)=\left\{{\rm{very}}\;{\rm{low}}, \;{\rm{low}},\; {\rm{high}},\;{\rm{very}}\; {\rm{high}}\}\right. $$ (8)
      $$ F\left(inlet\right)=\left\{{\rm{very}} \;{\rm{low}}, \;{\rm{low}},\;{\rm{mid}},\; {\rm{high}},\;{\rm{very}}\; {\rm{high}}\}\right.. $$ (9)

      The associated fuzzy sets, i.e., granularity, of these linguistic variables are shown in Figs. 12-14, respectively.

      Figure 12.  Associated fuzzy sets for linguistic variable height

      Figure 13.  Associated fuzzy sets for linguistic variable demand

      Figure 14.  Associated fuzzy sets for linguistic variable input flow

    • Using the experience of the human operators as well as the definition of the fuzzy variables, the required fuzzy rules are defined to maintain continuous flow of water, adjusting the height of the reservoir, and satisfying the demand. Table 1 shows the tabular complete rule base considering different combinations of the inputs of the FIS, i.e., level of water in the tank and demand value, and the output of the FIS, i.e., input flow. As the level and demand have granulized using 4 linguistic variables, a complete rule base includes 16 fuzzy rules which are presented in Table 1.

      Table 1.  Tabular complete rule base

      Level demand Very low Low High Very high
      Very low Low Low Very low Very low
      Low Mid Mid Low Very low
      High High High Mid Low
      Very high Very high High Mid Low
    • The Mamdani inference system has been used in this paper[40]. In the Mamdani inference system, the crisp values of the level and demand are used as inputs and the inlet as output. First these values are fuzzified. In the Mamdani inference system, the rule of the min operator is used to calculate the correctness of the preceding proposition. Briefly, (10)−(12) are used to calculate the correctness of the rules.

      $$ r\left(k\right): {\rm{If}} \; {\rm{level}}\; {\rm{is}}\;{A}_{l}\;{\rm and}\; {\rm{demand}}\; {\rm{is}}\;{B}_{l}\;{\rm{then}}\; {\rm{inlet}}\; {\rm{is}}\;{C}_{l}\quad $$ (10)
      $$ {\alpha }_{k}={\rm{min}}\left\{{\mu }_{{A}_{l}}\left({{level}}\right),\right.\left.{\mu }_{{B}_{l}}\left({{demand}}\right)\right\}\quad\quad\quad\quad\quad $$ (11)
      $$ MM:{\mu }_{{r}_{k}}\left({{inlet}}\right)={\rm{min}}\left\{{\alpha }_{k},\left.{\mu }_{{C}_{l}}\left({{inlet}}\right)\right\}\right. \quad\quad\quad\quad $$ (12)

      where $ r $ is reserved for rule, k is reserved for number of rules, $ {A}_{l\;} $ is reserved for the l-th membership function of level variable, $ {B}_{l} $ is reserved for the l-th membership function of demand variable, $ {C}_{l\;} $ is reserved for the l-th membership function of the inlet flow variable, $ {\alpha }_{k} $ is reserved for the fuzzy value of the k-th rule, MM is reserved for the Mamdani Minimum, and $ {\mu }_{{r}_{k}} $ is reserved for membership function achieved for the inlet flow from rule k.

    • The max operator is used to aggregate the acquired membership functions ($ {\mu }_{{r}_{k}}\left(inlet\right) $)[40]. In order to observe safety tips and prevent overflow of the tank, a software variable is added to the system. Usually, there is a space above the concrete tanks for overflow. A point below this space is considered as the maximum reservoir capacity for watering. At level meters, a binary variable is defined as HH (high-high). If the height reaches this point and goes higher, this variable becomes 1, and if the level is lower than this point, its value is 0. The value of the membership function derived from the aggregation process is calculated by (13).

      $$ {\mu }_{{\rm{final}}}\left(inlet\right)={\rm{min}}\left\{{\mu }_{{\rm{aggrigated}}}\left(inlet\right),\left.\overline {HH}\right\}\right. $$ (13)

      where $ \overline {HH} $ is the complement of HH. Therefore, with respect to (13), if the height of a reservoir reaches to the critical point, the final value of the aggregated membership function is changed to zero. In order to prevent preemption of water flow, a binary variable called LL (low-low) is also defined for the bottom of the tank. If the water level reaches this point and falls below it, this variable becomes one, and if the water level is above this point, its value will be zero. Therefore, with respect to safety, the final formula for calculating the membership function is calculated from (14).

      $$ {\mu }_{{\rm{final}}}\left(inlet\right)={\rm{max}}\left\{{\rm{min}}\left\{{\mu }_{{\rm{aggrigated}}}\left(inlet\right),\left.\overline {HH}\right\}\right.,\left.LL\right\}\right. . $$ (14)

      Therefore, with respect to (14), if the height approaches the zero point, the final value of the aggregated membership function is changed to one.

    • In fuzzy control systems, the final decision should be made in certain situations. So, the defuzzification step involves determination of one crisp value as the output of the controller[42]. There are several defuzzification methods[40]. The most commonly used methods of defuzzification are Max-membership, center of gravity (COG) or centroid, weighted average, mean-max membership and center of sums[43]. In the defuzzification step, the simplicity of computations, continuity, and accuracy in the online controller systems are important[44]. In this paper, the COG defuzzifier has been used to calculate the crisp value of the tank input flow. The corresponding equations are shown as (15):

      $$ {inlet}^{*}=\frac{\displaystyle\int inlet.{\mu }_{{\rm{final}}}\left(inlet\right){\rm{d}}(inlet)}{\displaystyle\int {\mu }_{{\rm{final}}}\left(inlet\right){\rm{d}}(inlet)} $$ (15)

      where $ {inlet}^{\mathrm{*}} $ is the crisp value for inlet flow.

    • A TCU is proposed to convert the inlet flow rate obtained from the FIS to the inlet valve position. TCU adjusts the necessary flow to meet the HH and LL thresholds through determining the exact position of the inlet valve. The control valves have a linear function regarding the degree of openness[45]. On the other hand, the amount of flow of a control valve has a linear relation with the position of the valve[46]. Unfortunately, this linear relationship will change over time due to the amortization and other environmental factors. Therefore, the nonlinear autoregressive exogenous (NARX) neural network model has been used in the core of TCU to calculate the valve position value. This will decrease the effect of variations of the linear relation over time. The NARX model is a recurrent neural network that can identify and model complex systems[47]. Both offline and online data are gathered considering different settings of the valve position[48]. Both datasets are used to train the NARX model[49].

      The required flow rate is calculated by the fuzzy system and the amount of online input flow is measured by the flow meter 1 and flow meter 2 as shown in Fig. 11. The important point is that since the valve is placed in a series path with the flow meters, the flow through the flow meters is equal to the valve flow.

      Finally, the TCU uses the difference between the online value of the flow and the fuzzy system flow to determine the amount of change in the valve position, which is indicated by Δy. The TCU is depicted in Fig. 15.

      Figure 15.  Transform control unit (TCU)

      TCU adjusts the valve position until the online input flow reaches the proposed output of the FIS. In order to prevent repeated opening and closing of the reservoir valves, this setting will take place at specified and customizable intervals. Only in cases where the reservoir is in the HH position, in order to avoid overflowing, this delay is not considered for resetting the system and the input valve closes. Whenever the LL mode occurs, the inlet valve is completely open.

      Practically, these changes are applicable with the assumption that the main source of the reservoir is ideally suited. On the other hand, the proposed system can control the inlet flow if the upper tank is connected to the reservoir by gravity and its height should be in the appropriate range. If the height of the source, i.e., upper tank, does not meet, water pumps must be turned on to supply the required flow. Using the proposed hybrid approach the continuous flow of water in the water distribution network is guaranteed.

    • The proposed hybrid approach has three main modules, i.e., ANN, GA, and FIS. There are several parameters in each module which have been set due to several experimental experiences. The best-known parameters for ANN, GA and FIS have been reported in Table 2.

      Table 2.  Parameters of GA, NN and FIS

      GANNFIS
      ParametersTuning
      method
      ValuesParametersTuning methodValuesParametersTuning
      method
      Values
      Crossover rateDynamic,
      decrease with
      iteration
      0.5Total number
      of neurons
      Thumb rules40Number of membership
      functions in input
      Expert and
      error check
      4
      Mutation rateDynamic,
      increase with
      iteration
      0.15Weights
      and biases
      Genetic and
      Levenberg
      algorithm
      Dynamic in
      each run
      Number of membership
      functions in output
      Expert and
      error check
      5
      Pop sizeTry and error
      with MSE check
      100Number
      of layers
      Trial and error
      with MSE check
      2Number of rulesExpert16
    • The control of water transfer networks is so important. Human faults and errors may cause huge waste, inefficiencies, and damage in big cities. In this section, the results of the application of the proposed hybrid approach in a real case study are analyzed and discussed. It is notable that the proposed hybrid approach compares three methods for prediction of demand of water in Tehran, and chooses the best method for demand prediction using comparative analysis. In the second module of the proposed approach, an FIS with two inputs and one output is used to calculate the inlet flow based on predicted demand and the height of the water in the tank. In the third module, a transform control unit mechanism is proposed to relate the inlet flow achieved by FIS as an independent variable and the position of the valve of dependent variable using the NARX network. The results of the proposed approach are compared with those achieved by the traditional, i.e., manual system. First, the results of the forecasting model are presented. Then, the results of the FIS are described. The proposed approach is applied in the Tehran water transfer network.

      The transfer network in this study refers to treatment plants, pipes, wells, pumping stations and water storage reservoirs. This network includes 100 reservoirs and pumping stations, 500 wells and more than 1000 km of transmission lines. The network after the reservoir outlet pipe is called the distribution network, the length of it, is more than 10000 km. The main facilities of the distribution network are mainly pressure reducer valves. In the water transfer and distribution network of Tehran, water movement is mainly due to gravity. In this case study, water enters the reservoir by gravity and is sent to the customers in the same way. The following flowchart presents the schematic view of the water transfer network.

      Figure 16.  Schematic view of water transfer network

    • The ability of an independent variable added to improve the prediction of the dependent variable is related not only to its correlation with the dependent variable, but also to its correlation with the other independent variable. Collinearity is defined as a relation between two independent variables. Thus, the multi-collinearity refers to the relationship between several independent variables. Accordingly, for analyzing the proposed input variables to the ANN, the correlation coefficient and multi-collinearity are applied. Tables 3 and 4 present the results of the correlation and multi-collinearity tests, respectively.

      Table 3.  Correlation coefficients between independent and dependent variables

      HolidayPast demandAverage temperatureRain
      DemandPearson correlation− 0.239*0.955*0.811**− 0.272**
      Sig. (2-tailed)0.0000.0000.0000.000
      N1461146114611461
      * Correlation is significant at the 0.01 level (2-tailed).

      Table 4.  Multi-collinearity analysis of independent variables

      Coefficients*
      ModelUnstandardized coefficientsStandardized coefficientstSig.Collinearity statistics
      BStd. ErrorBetaToleranceVIF
      (Constant)444 541.25132 664.23813.6090.000
      Holiday− 41 658.6026 004.375− 0.055− 6.9380.0000.8791.138
      Past demand0.8180.0130.81861.2580.0000.3083.248
      Temp3876.806345.6490.14611.2160.0000.3263.068
      Rain− 518.623129.255− 0.031− 4.0120.0000.9331.072
      * Dependent variable: Demand

      It can be concluded from Table 3 that holiday and rain have an inverse effect on demand while past demand and average temperature have a direct effect on demand. The highest correlation is between demand and past demand. This means that a considerable amount of negative and positive deviations (i.e., variance) of dependent variables are by the independent variables.

      Table 4 shows that there is no serious collinearity between the dependent variables and that the variance inflation factor (VIF) value is smaller than the allowed limit (The value is 10.). Therefore, no dimension reduction is needed and the variables are suitable for entering the ANN.

    • Data are gathered from the data center of the Tehran water transfer network during 2014 to 2018. Holiday, past demand, average temperature and rainfall variables are selected as inputs and the amount of demand are selected as an output. Regarding the search in databases, the amounts of demand were extracted from the SCADA system in the Tehran water network and the rest of the variables were extracted from the meteorological databases. Considering the availability of data and their accuracy, daily records of data from the past 5 years starting from 2014 and ending in 2018 were used.

    • As mentioned before, after gathering data, scaling is necessary. Hence, all variables receive equal attention. Therefore, variables such as temperature, past demand, rainfall, and holiday which are not in the same range, are set in range [−1, 1] through (4). Then, the databases are formed again with normalized data and entered to ANN. The normalized database has a total number of 1825 of records as days and 5 fields. Although after deleting missing records, resolving the errors, and summarizing the data, a clean data base including 1500 records is achieved in order to be used by ANN.

    • Three well-known approaches have been used to predict the water demand in the Tehran water network on the basis of past historical data. The results of all prediction methods have been compared. More formally, the performance of two different ANNs, i.e., MLP and RBF, as well as the effect of using combination techniques to improve the performance of the prediction model, are examined. At the time of model development, the main goal is to achieve an optimal architecture for the neural network. With this goal, the experimental rules have been used to estimate the maximum number of neurons in the hidden layer. As mentioned before, there have been many rules of thumb to determine the initial number of neurons in the hidden layer. In this case, the initial value of neurons in the hidden layer is 10.

      It is notable that the initial number of neurons in the hidden layer in MLP and RBF was set equal to 10. GA was used to set the optimum parameters of the ANN. After running a loop, the number of neurons in the hidden layer was set equal to 40, and its further increase did not significantly affect the accuracy of the ANN. Suitable configurations of the ANNs are shown in Table 5.

      Table 5.  Suitable structure of neural network models

      Model MLP RBF
      Input layer variables Dt-1 AvgTemp Rt Ht Dt-1 AvgTemp Rt Ht
      Number of neurons in hidden layer 40 40
      Output layer variable Demand Demand
      Dt-1: Past demand; AvgTemp: Average temperature; Rt: Total rainfall; Ht: Holiday.
    • The metric used in this study to evaluate the performance of ANN is the MSE. Data are divided into train and test. The performance of MLP for all data, training data, and test data is shown in Figs. 17-19, respectively.

      Figure 17.  Overall performance of the MLP

      Figure 19.  Performance of MLP model for test data

      Fig. 17 which shows the performance of MLP for all data includes four graphs. The upper left graph in Fig. 17 presents the real time series of water demand, i.e., target of the ANN, versus the estimated water demand predicted by MLP, i.e., output. The graph validates the suitable estimation of proposed MLP. The upper right graph shows the correlation of output of the MLP and the target. This correlation is above 0.95 which demonstrates the quality of estimation. The lower left graph shows MSE for 1500 records of data. The MSE value is equal to 0.10543 which is an ideal value for 1500 records of data. The lower right graph in Fig. 17 presents the distribution of residuals versus the normal probability distribution function. It is clear the residuals of estimations by ANN follow a normal distribution behavior with a mean value close to zero and a very small standard deviation value. This indicates that the estimation of demand by ANN is not biased and is reliable. Figs. 18 and 19 which present the performance of MLP for train and test data demonstrate the validation of prediction.

      Figure 18.  Performance of MLP model for train data

    • The RBF model was also used to predict the demand of water. The RBF was trained and tested using 1500 records of historical data. The results of prediction using RBF are presented in Figs. 20-22 for all data, training data, and test data, respectively.

      Figure 20.  Overall performance of RBF model

      Figure 22.  Performance of RBF model for the test data

      It can be concluded from Figs. 21-23 that the performance of the proposed RBF is acceptable for test, train and all data. So, MLP and RBF are used as cores of a multi-core ANN mechanism for prediction of the water demand.

      Figure 21.  Performance of RBF model for the training data

      Figure 23.  Schematic view of complete rule base

    • As mentioned in the previous sections, using the bagging method in ANN will reduce the error. In this section, a dataset (bag) randomly sampled with replacement was used to form a quad-core model of ANN. The first two cores use the MLP and the second two cores use the RBF model for prediction. The output of the forecasting model using the multi-core mechanism is equal to the average of the cores output. The results of using the quad-core model for prediction are shown in Table 6. In general, if a large error is generated in one core, given that the real output is the average of all models; this will not meaningfully bias the final result of prediction.

      Table 6.  Results of quad-core mechanism in ANN

      ModelsRBFMLPAverage
      Performance indexMSEMSE
      Core 1Core 2Core 1Core 2
      Run 10.01052000.01012900.0154900.0076090.010937
      Run 20.01022000.01015800.0103570.0113270.010516
      Run 30.01001300.00990050.0120230.0137070.011411
      Run 40.01001500.01001100.0109800.0111580.010541
      Average0.0101920.010050.0122130.010950.010851

      Using the proposed quad-core ANN mechanism this has been run 4 times. As shown in Table 5, a large error is seen in core 1 of the MLP model in run 1, but the average of the error is reduced by using the multi-core technique. The proposed multi-core ANN mechanism improves the prediction of water demand. So, it is a candidate as the first module of the proposed hybrid approach to predict the demand of water.

    • As mentioned in previous sections, the FIS has two inputs and one output. The first input comes from the output of the multi-core ANN. i.e., the predicted demand of water in Tehran water network. Given that the output of the multi-core ANN is normalized, it must be re-scaled to enter the FIS. Equation (16) is used to re-scale the output of the multi-core ANN.

      $$ x=\frac{\left({x}_{N}+1\right)({\rm{Max}} \;x-{\rm{Min}}\; x)}{2}+{\rm{Min}}\;x $$ (16)

      The second input of the FIS is the height of the tank that is read from the SCADA system. Fig. 23 shows the inputs of the FIS with demand values of 2000 cubic meters per hour and height (level) of 2.5 m. The output is also 2150 cubic meters per hour. As mentioned before, according to the linguistic terms considered for the demand and height variables, the complete fuzzy rule base contains 16 fuzzy rules with two inputs and one output. The range of demand height are determined using historical data existing in the database.

    • Computational complexity of an algorithm is about the required resources, especially CPU time to run the algorithm. Although the proposed fuzzy inference system does not propose a classic algorithm, the performance of its inference engine depends on the following factors:

      1) Number of rules in rule set (RN)

      2) Number of inputs of a rule (IN)

      3) Number of linguistic terms in each input (LI)

      4) Number of patterns to be tested (NP).

      If computational resources for an FIS with RN rules including IN inputs in each rule and LI number of linguistic terms for each input have to be considered, so the following function for CPU time of a complete fuzzy rule base is used:

      F (CPU time) = (IN)LI ×RN.

      So, it is obvious that a complete rule base is not efficient anymore as the CPU time will dramatically increase as the LI, IN, and RN increases. Although in real case studies the optimum rule base and the practical rule base have a minimum required number of LI, IN and RN due to some rule mining metrics.

    • In this case study, the maximum flow that the valve can pass, is 4000 cubic meters per hour. This value is achieved when the valve is completely open. The corresponding valve has an almost linear characteristic and there is a linear relation between inlet flow as an independent variable and the position of the valve y(t). As mentioned earlier, this linear relation can change over time due to various factors. Therefore, NARX will be used to convert the amount of flow to the valve position. The designed structure for the TCU based on the NARX model is shown in Fig. 24.

      Figure 24.  Schematic view of NARX model

      To get started, the network is trained in offline mode with the Levenberg–Marquardt algorithm and the system starts up. After a few hours the system should be trained in online mode. The results of the NARX model are shown in Figs. 25 and 26. It should be noted that the number of delays in the input of the model is obtained by trial and error.

      Figure 25.  NARX model results

      Figure 26.  Comparison between actual output and model output

      When the y value is obtained, the Δy (the required change of the valve position) can be calculated. Several experiences revealed that the gap between required inlet flow which is determined by real demand of the water and the inlet flow which is estimated by the FIS and transformed into valve position is very small.

    • Given that the reservoir would overflow at a height of 5 m, the upper limit of the HH variable is set at 4.75 m, so for height greater than this, the HH signal will be one, and consequently the value of its NOT will be zero. The lower limits of the reservoir are set to 1 m and the value of the LL variable for a height lower than or equal to this limit, changes from 0 to 1. According to what is mentioned above, the membership value of inlet flow and IF-THEN control rules in TCU on the basis of two conditions of HH and LL are rewritten as follows:

      $$\begin{split} &{\mu }_{{\rm{final}}}\left(inlet\right)=\\ &\;\;\;{\rm{max}}\left\{{\rm{min}}\left\{{\mu }_{{\rm{aggrigated}}}\left(inlet\right),\left.\overline {HH}\right\}\right.,\left.LL\right\}\right. \end{split}$$ (17)
      $$\begin{split} &{\rm{If}}\; {\rm{state}} \;{\rm{of}} \;{\rm{the}}\; {\rm{level}}\; {\rm{is}}\; \bf{H}\bf{H} \; {\rm{then}} \; {{\mu }}_{{f}{i}{n}{a}{l}}\left({{i}{n}{l}{e}{t}}\right) = \\ &\;\;\;0 \; {\rm{and}}\; {\bf{inlet}} {\bf{flow}} ={\bf{0}}\; {\rm{and}} \;{{x}}_{1}=0 \end{split}$$ (18)
      $$\begin{split} &{\rm{If}}\; {\rm{state}}\; {\rm{of}}\; {\rm{the}}\; {\rm{level}}\; {\rm{is}}\; {\bf{L}}{\bf{L}} \;{\rm{then}} \; {{\mu }}_{{f}{i}{n}{a}{l}}\left({{i}{n}{l}{e}{t}}\right) = \\ &\;\;\;1\; {\rm{and}} \;{\bf{inlet\; flow}} ={\bf{4000}}\; {\rm{and}} \;{{x}}_{1}={\bf{100}}. \end{split}$$ (19)
    • The proposed hybrid neural-genetic fuzzy system was tested in a reservoir of the case study. The metric used to evaluate the performance of the proposed approach is the continuous status of the height of the water in the tank. So, if the height of the water in the reservoir is set between the two states LL and HH, the system has a good performance and if it deviates from these limits, a fault has occurred. To evaluate the performance of the proposed approach, it has been implemented on a pilot tank. The status of the water in the tank was monitored continuously for more than 35 consecutive days. Two experiments were run. In the first experiment, the tank was controlled by a human workforce trained for working with the SCADA system and in the second experiment; the control was carried out using the proposed approach. The numbers of system deviations are shown for both modes in Table 7.

      Table 7.  Safety limits state

      DaysHuman faultProposed approach faultDaysHuman faultProposed approach fault
      HH stateLL stateHH stateLL stateHH stateLL stateHH stateLL state
      12000190000
      21000200000
      30000210000
      40000221000
      52000230000
      60000240000
      70000250000
      81000260001
      90100270200
      100000280100
      110000291000
      120000301000
      130000310100
      141000320000
      151000330001
      160000340000
      170000350000
      180000361000

      It can be concluded from Table 7 that the total faults of the proposed hybrid approach are equal to 2 while the human operator imposes 17 faults on the water network. The proposed approach did not report the HH state while the performance of the human operator leads to 12 HH states. So, overflow of the reservoir which leads to waste of water resource has a very low probability when using the proposed hybrid approach. The probability of the overflow is equal to 0.27 when a human operator is handling the height of the water in the tank.

      The LL state has occurred 2 and 5 times when using the proposed hybrid approach and human operator, respectively. Although the contents of Table 6 reveal the outperformance of the proposed hybrid approach in comparison with the human operator control, the statistical analysis is proposed to demonstrate the meaningful superiority of the proposed hybrid approach. The following statistical hypothesis is tested:

      $$ \left\{\begin{aligned}&{H}_{0}: {\mu }_{{\rm{Total}}\; {\rm{Fault}}\; {\rm{of}} \;{\rm{Human}}\; {\rm{Control}}}=\\ &\;\;\;\;{\mu }_{{\rm{Total}} \;{\rm{Fault}}\; {\rm{of}} \;{\rm{Hybrid}} \;{\rm{Approach}}}\\ &{H}_{1}: {\mu }_{{\rm{Total}}\;{\rm{ Fault}} \;{\rm{of }}\;{\rm{Human}}\; {\rm{Control}}}\ne\\ &\;\;\;\;{\mu }_{{\rm{Total}}\; {\rm{Fault}}\; {\rm{of}}\; {\rm{Hybrid}}\; Approach}.\end{aligned}\right. $$ (20)

      To compare the difference between two means, T-test was used. The results of the test are shown in Table 8.

      Table 8.  Result of paired T-Test

      Paired differences
      MeanStd. deviationStd. error mean95% confidence interval
      of the difference
      tdfSig. (2-tailed)
      LowerUpper
      Pair 1Total fault of
      human − total
      fault of hybrid
      0.3060.5770.0960.1100.5013.179350.003

      According to a significant level presented in Table 7, the zero hypothesis is rejected. Therefore, the difference between the means of the two methods is statistically validated. This means that the number of the undesired states in the human control mode is greater than the number of the undesirable states in the proposed hybrid approach. The efficacy of a proposed hybrid system ensures that it can be used in an interconnected water supply system. The proposed hybrid approach of this study which was implemented as a pilot on one reservoir can be implemented simultaneously in all water supply network facilities including the dams, water treatments and all reservoirs.

    • As mentioned in the previous sections, the proposed intelligent system has performed better than the manual system. By reviewing the results as well as the performance of the system, the benefits of using it can briefly be discussed as follows.

      1) Preventing Reservoir Overflow. Overflow in large reservoirs located in metropolitan areas can be catastrophic and cause damages to houses and urban facilities. The proposed intelligent system prevents the reservoir overflow using and controlling the upper limit of the tank.

      2) Protecting distribution network. Reducing the height of the tanks allows air to enter the facilities and distribution network. In addition to damaging the facilities, this will cause a drop in the pressure of the distribution network and consequently results in customer dissatisfaction. The proposed intelligent system reduces the pressure drop in the network by controlling the lower limit of the tank.

      3) Production planning. The amount of water consumption in the future, especially in metropolitan areas, is always one of the main concerns of operation managers. Knowing the amount of the future consumption, informs managers the limits of water needed to purify and produce safe water. In a designed system, a quad-core neural network helps users to predict the future demand by considering the events of the week.

      4) Intelligent adjustment of the inlet valve of the tanks. According to the classic control philosophy written and loaded in the industrial controllers used for controlling the tanks, the inlet valves are always set in the open or close position or adjusted based on the experience of SCADA control center operators. In the proposed intelligent system, the inlet valves are adjusted according to the needs of the distribution network.

    • In this paper, a hybrid neural-genetic fuzzy inference system was proposed to design a new intelligent control philosophy of water level and flow rate of the reservoirs of water transfer networks using equipment used in SCADA systems, including instrumentation and control valves. In order to achieve this goal, first, the exploration and identification of the variables affecting the consumption of a reservoir were studied and the required data were extracted from the SCADA system and the meteorological organization. Then, a multi-core ANN model supported by a GA was used to predict the consumption of a reservoir. GA was used to optimize the parameters of the ANNs. The proposed multi-core ANN approach included two MLP and two RBF. Next, an FIS was designed to adjust the valve position in the tank. The output of the multi-core ANN model along with the reservoir height are used as input variables of the FIS. In the final step, for converting the output of the FIS, a TCU on the basis of the NARX model was used to convert the input flow of the reservoir to the valve position value. To evaluate the performance of the proposed system, two binary variables, HH and LL, which monitor the low and high levels of the reservoir, were used. The applicability and efficacy of the proposed approach were analyzed through a real case study in Tehran water's transfer network. The performance of the proposed system was compared with the human-based control mechanism. Statistical analysis revealed the outperformance of the proposed system. The main contributions and innovations of this research are summarized as follows:

      1) Hybridization of ANNs, GA, and FIS provides suitable features in order to model the complexities in the real case study.

      2) By testing the proposed approach in Tehran's water transfer network, it was observed that the use of the designed system significantly reduced the deviation of the reservoir's height from the desired levels, which would reduce waste and energy consumption in the network system.

      3) Combining ANN models supported by GA and creating a multi-core ANN model to predict the demand for water.

      4) Using a TCU on the basis of NARX with two-stage training to calculate the amount of the valve position, according to the conditions of the installed electric valves.

      5) Designing and implementing a flexible control philosophy to control the level of the water in the reservoirs on the basis of online demand, level of the water in the reservoir.

      6) Defining the floating holiday effect on consumption using fuzzy sets.

      Looking at the trend of population growth in the world and the limited availability of freshwater resources, the need for extensive research in the areas of water resource management, intelligent control in the water distribution network and fair distribution can be seen more than ever. Therefore, various suggestions can be made to develop and complete this research. Since in the process of transferring water into reservoirs, the transfer is not carried out only by gravity, usually, the pumping stations are used to transfer water to heights or upper reservoirs. Therefore, the design of the same system for pumping stations and the development of an intelligent control philosophy for switching on/off pumps for supplying the required flow at the inlet of an upstream reservoir, as well as reducing power consumption costs by considering peak shaving, are the first priorities of future research. On the other hand, in some water transfer networks, in addition to dams, some deep-water wells are used to provide water. Typically, the wells are connected individually or in groups to the inlet pipe of the tank. Therefore, the wells are added to the calculations as a source of supply at the inlet of the reservoirs and the way they add or drop regarding their amount of available flow should be added to the control philosophy. By calculating the delay time for transferring water from far off sources (like dams) to the entrance of the water treatments, and then to the tank entrance, providing a proper schedule program can be another interesting research field for supplying water at the inlet of the reservoirs. The proposed hybrid approach has a limit on its ANN module, as the consumer behavior, the rain patterns, the temperature changes, the proposed prediction phase may need to be updated. So, a tracking signal in order to check whether the ANN works suitably is important. Providing a dynamic ANN mechanism in order to extract the online pattern of the demand from a dynamic database supported by a set of intelligent sensors is another interesting research project.

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