Coupling Decision Support Systems For The Optimization of The Management of Water Distribution Networks


 The analysis of the current situation of water distribution networks is based on all the alternatives that are technically feasible and implemented from the decision-maker's point of view. Taking the water distribution network of Tourville city as a case study, this paper combines a set of Decision Support Systems (DSS) including the Geographic Information Systems (GIS), multi-criteria analysis and hydraulic simulation models to establish a multi-criteria decision-making aid method for renovation and rehabilitation of water distribution networks. This combination creates an expert management system based on multi-criteria decision making that strengthens the optimization of the management of water distribution networks in terms of renovation and rehabilitation. After dividing the water distribution network into three emergency levels, it was concluded that 26% of the network is in urgent need of rehabilitation.


Background
A water distribution network is a complex hydraulic system because it consists of nodes liked by pipes with nonlinear hydraulic behavior. Decision making of this complex system requires data about the hydraulic state and many other variables (Duzinkiewicz & Ciminski 2006;Hajebi et al. 2014). Preventing pipeline renewal and diagnosing the malfunctions of the network are real challenges and require network managers with proper decision-making tools. Decision support tools and problem-solving are based on the use of models. Over time the Distribution Water System (DWS) ages and it is necessary to renew it when it reaches a threshold of obsolescence. This ageing generates dysfunctions that complicate the task of the manager. At this stage, managers start asking questions like: Should I renew the pipes? Which parts should I renew? When should I start?
Recently, decision making depends on mathematical science, software and models that can assess the situation of the system (Greco et al. 2016;Zyoud et al. 2016;Tarigan et al. 2018;Amorocho-Daza et al. 2019). Noted that the use of the Analytic Hierarchy Process (AHP) method is useful to water management in term of achieving a better understating of water management strategies. Blindu (2013) worked on adding the multi-criteria analysis to the Geographic Information Systems (GIS) to classify the behaviors rehabilitation programs in the short, medium, and long term. This paper creates an expert management system to make multi-criteria decisions by combines GIS, multi-criteria analysis and hydraulic simulation model, allowing the renovation and rehabilitation of water distribution network to have a strategic vision and prevent scenarios for optimizing the management of distribution networks.

Study area
This paper takes the water distribution network of Tourville city as a case study (Fig. 1), which is located 350 km west of Algiers with a population of 86,000 (ONS 2019). The region is characterized by rugged topography whose altitude ranges between 1 and 90 m. The Tourville sector is supplied by an elevated tank 40 m high. The length of the drinking water system (DWS) is about 35 km and it was made up of cast iron, steel and polyethylene high-density (PEHD) and the nominal diameters ranged between 63 and 300 mm.

Methodology
The developed methodology is divided into several steps in two main categories data collection and decision making using several tools and methods from: databases, GIS, hydraulic modeling of the network and multi-criteria studies, Fig. 2.
Data modeling is fundamental in the design of databases that will be used for the management of the water distribution network. Mike Urban software requires creating a diagram reflecting the physical characteristics of the components of the system: tanks, pipes, and junctions. Therefore, the characteristics of these components were collected (Abrunhosa 2015).
Mapping the results helps to identify and classify the sections by order of priority to generate real progress in managing the network.

Network behavior modeling
Mike Urban is one of the most efficient programs for modeling urban water as it covers all water networks in a city including water distribution, stormwater and sewer systems Mike Urban is a calculation model offers many advantages compared to traditional modeling tools such as standard data formats, the integrated interface under GIS and the calculation engine used for modeling is EPANET. Coupling Mike Urban with ArcGIS brings a number of new useful GIS functionalities oriented on topological data analysis (Metelka 2006).

Multi-criteria decision analysis (MCDA)
MCDA is a methodology designed for evaluating options considering decision-making objectives (Montibeller et al., 2006). Many methods have been developed, in their review, Velasquez and Hester (2013)  According to Tramarico et al. (2015), the Analytic Hierarchy Process (AHP) is the most applied method in technology and scientific research fields. AHP has been used for comparisons, weighting, and rankings alternatives in 4 steps to make a decision in an organized way (Saaty The pairwise comparisons of various criteria were organized into a square matrix.
where; A is the decision matrix, aij are comparisons between elements i and j for all i, j ∈ {1, 2,,, n}.
The comparison is made using a scale, Table 1, to indicate which element is important to another element with respect to which they are compared. The nine-point scale includes: [9, 8, 7, ..., 1/7, 1/8, 1/9], where 9 means extreme importance, 7 means very strong importance, 5 means strong importance, and so on down to 1, which means no preference (Şener et al. 2010). The weight of each of the dimensions, criteria and indicators is calculated by summing the columns of the matrix then dividing each of the values in the column by the sum of the columns.
The weight is obtained by calculating the average of each row (Boukhari et al., 2018).
To check the reliability of the pairwise comparisons, (CI) and (CR) allow us to know at what point the judgments are consistent and they are calculated by Equation (2) where: : the largest or the principal eigenvalue of the matrix.
n: the order of the matrix. Generally, the judgments are consistent if CR ≤ 10%. In case CR is larger than 10% the evaluation of criteria judgments must be reviewed. Once the weights of the elements per level are calculated, the final weight is computed by simply multiplying the weights of the lowest level (the indicators) by the weights of the higher levels (the corresponding criteria and dimensions).

The performance of the alternatives
Since the DWN is characterized by its complexity, the best way to understand this system is to break it down into hierarchical structure elements. The dimensions, criteria and indicators were used to define the emergency levels of pipes to rehabilitate the water distribution network. The hierarchy structure elements were determined by water supply managers and experts based on their experience and knowledge. In this paper, databases of the physical structure and the hydraulic behavior of the network are used.
To determine the performance of the alternatives and to identify the emergency level of the pipes concerning the rehabilitation of the water distribution network, five sub-criteria (SC) are used based on the sections of the network:1) the used materials; 2) the laying date; 3) the diameter of the pipe; 4) water pressure; and 5) water velocity.
Each of these sub-criteria has 3 indicators, which means 15 indicators in total. The evaluation of the indicators is used to measure the performance of the alternatives. The evaluation is performed by using indicators (categories) attributed to each sub-criteria related to each alternative, instead of evaluating the alternatives by pairwise comparisons (Silva et al., 2010).
The AHP enables the use of a hierarchical structure to display the preferences of alternatives relative to the objective (Amorocho-Daza et al., 2019).
The database contains many alternatives and related attributes, all these features are important for the decision-making process, therefore the rating approach is used when there are a large number of alternatives to be evaluated. The rating approach differs from the traditional AHP (relative measurement) because at the last level the alternatives are not found or there are many alternatives to be evaluated.

Pairwise comparisons and weighting
The results of the application of the AHP method show the classifying of dimensions, criteria and indicators and represented in matrices of weights (from table 3 to table 10) for example, the importance of the size of the diameter is less than the laying date because the age of the pipe is directly related to the condition of the pipe. For the pressure criterion: the comparison was made using the interpolation of the pressures at the node level and the extraction of the pipes situated at each pressure point.
To demonstrate how the pairwise comparisons of various criteria were calculated, the following steps illustrate the Comparison of indicator 1 in Table 6 for example: The elements of table 6 are regrouped in matrix A.

A=[
The weight of these elements is calculated by summing the columns of matrix A then dividing each of the values in the column by the sum of the columns. The weight is obtained by calculating the average of each row.
The sum of each column: [8 1.75 3.33] Dividing each of the values in the column by the sum of the columns: The weight is the average of each row: [ 0,122 0,558 0,320 ] (7)

Calculation of the emergency level of the sections
After calculating the weight of each indicator by the AHP model shown in Fig. 3, it is necessary to run the GIS integration step to classify and map out the sections in order of importance for the action of rehabilitation using the attribute table displayed in ArcGIS. The latter manages the physical entire water distribution network with its characteristic (diameter, materials, Pipe laying date) with the superposition of the base plan obtained by aerial photos of SEOR (Oran water and sanitation company).
To rank the alternatives, ArcGIS is used to select features that match the selection criteria. One of the selection methods used to select features in a layer is to select features using an attribute query.
Step 1: Selecting features (indicators) using an attribute query Step 2: In the table of contents, set the value of each weight in the corresponding column.
Step 3: Know that the lines represent the sections that are the alternatives so to get the priority of each section summing weights of each line is required.
Step 4: Defining levels by using the priorities obtained in step 3.
Displaying the results as shown in Fig. 4 helps us to identify the sections and rank them in order of priority to generate real progress in network management. The priority sections for maintenance action can be identified according to the order and the emergency category and the colors, it includes three classes: level 3 low in yellow color, level 2 medium in orange color and level 1 high priority for intervention in red color.  the short-, medium-and long-term to rehabilitate the water distribution network. The first level represents 26% of the length of the network which is the important one in term of criticality and it must be rehabilitated at first, so the focus was on this part.    (Barbeau et al. 2005). Suspended materials in the pipe start to settle when the flow velocity drops below a threshold that is around 0.06 m/s (Vreeburg & Boxall 2007). If a finite volume of water spends more time within a pipe indicates low flow conditions that may increase the precipitation and uptake of iron in metal pipes due to corrosion (Mutoti et al., 2007), residence time also leads to a rapid reduction of disinfectant residuals that allow microbial pathogens to regrow (Abokifa et al. 2016). The concentrations of particulate elements, between upstream and downstream of the pipe should increase, an analysis of the composition of suspended particles may detect aging pipes (Fujita et al. 2014).  The diameters that do not exceed 100 mm tend to present several stresses on the network, it is noted that more than 4.8 km of length is made of cast iron 2/3 of this length undergoes speeds lower than 0.5m/s it is due to the number of branches (dead-ends) on this part of the network, concerning the pressure, Fig. 9 shows that 84% of the network has pressure standards between 2 and 4.5 bar it is also noted that the minimal pressure in a network is generally set at 2 bar at the connexon point of a house or dwelling. Each of these indicators affects directly or indirectly the other one in a complex way which means the velocity can affect the aging of pipe and material, the diameter affects the velocity and so on.

CONCLUSIONS:
This paper leads to the establishment of a multi-criteria decision-making aid method for the adequate renovation and rehabilitation of distribution water networks. The combination of a set of decision support tools such as geographic information systems (GIS), multi-criteria analysis and hydraulic simulation model, help us to facilitate the complexity of the studied system because the difficulty is the determination of the specific sections to be renewed. The results of the application of the AHP method show the classifying of dimensions, criteria and indicators.
The selection of criteria was made by taking into consideration the physical characteristics of pipes as the diameter, materials and the laying date of the pipe, the hydraulic structure of the network as the velocity and the pressure of water. The priority sections for maintenance action can be identified according to the emergency levels category and the colors, it includes three classes: level 3 low, level 2 medium and level 1 high priority for intervention in red color. The result showed that the critical part represents 26% of the network that should be rehabilitated as soon as possible.

Declarations
Ethical Approval: Not applicable Consent to Participate: All the authors of this article have agreed to participate in this research study.

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