## 2 Methodologies
### Water Quality Sensor Location Decision  
The constitution of the decision-making method of the emergency water sensor location proposed in this study is shown in Figure 2. First, the network information of the target region is obtained and normal and abnormal scenarios are established. The normal situation scenario utilizes the normal demand pattern of the target region over a 24-h period. For the abnormal situation, it assumes that there is a problem with the supply tank and that the water has to be supplied by operating an emergency connection pipe connected to a nearby regional reservoir. Next, the network information and established scenarios are applied to EPANET2 and hydraulic analysis is carried out. The direction of the flow calculated through the hydraulic analysis is calculated for each scenario, and each direction is visualized through a directed adjacency matrix. The mixed adjacency matrix is formed by adding all of the directed adjacency matrices of each derived scenarios. If there are directed adjacency matrices for 10 scenarios, the minimum value for the mixed adjacency matrix is 0 and the maximum value is 10. The mixed adjacency matrix signifies the directionality between nodes and needs to be converted into pipeline sensitivity, as in Equation (1):  
Figure 1: Pipeline distinction by flow directional sensitivity.  
\[FPS(i,j)=\frac{M(i,j)}{M(i,j)+M(j,i)} \tag{1}\]  
where _FPS(i, j)_ indicates the flow rate (sensitivity) in the direction from node \(i\) to node \(j\), and _M(i, j)_ indicates the mixed adjacency matrix from node _i (row)_ to the node _j (column)_. The sensitivity calculated in this way has two values per pipeline so the final sensitivity by pipeline for the normal and abnormal situations needs to be calculated using Equation (2):  
\[PS(X)=1-ABS(FPS(i,j)-FPS(j,i)) \tag{2}\]  
where _PS(X)_ represents the sensitivity of pipeline X. The calculated sensitivity is plotted on the X-axis (abnormal pipeline sensitivity) and Y-axis (normal pipeline sensitivity). In this case, the number of pipelines corresponding to the area where pipeline 4 is located (Figure 1), which was defined above as an important point, may have a greater number of water quality measuring devices than can be installed by the operator. Therefore, this study applies the Utopian Approach [31], a distance scaling method, to determine the priorities for installation. The Utopian Approach is a multi-criteria decision-making method based on a distance scale. It shows the standard values for each alternative in a normalized space, as shown in Figure 3, and determines the priority according to the distance from the Utopian Point (UP). In this study, the sensitivities to the flow direction change in the pipelines under normal and abnormal conditions, which were calculated above, are shown on the coordinate plane. They are arranged in the order of closeness to the UP and this order is used as the improvement priority. In order to meet the objective introduced above, the UP was set as (1,0) which is the point for high sensitivity in abnormal situations and low sensitivity in normal situations. The Utopian Approach distance equation applied for prioritization is shown in Equation (3):  
\[\textit{Euclidean Distance}(E.D)=\sqrt{\left(1-\textit{Abnormal PS}(X)\right)^{2}+\left(\textit{Normal PS}(X)\right)^{2}} \tag{3}\]  
Figure 2: Measuring instrument location and prioritization flowchart.