We calculate the

# Optimal Sensor Placement for Leak Detection

Solutions determine where to place sensors for better detecting leaks and also the total number of sensors that should be placed all over the network

## Model Preparation and Sensitivity Matrix Calculation

For this kind of project, it is necessary to have (or create) a hydraulic model of the water network.

## Hydraulic Model

Used to evaluate the sensitivity (normally a function of the variation of the pressure) at each of the nodes of the network with respect to the occurrence of leaks at other nodes.

## Sensitivity Matrix

Values obtained are summarized in a sensitivity matrix.

## Decision Criteria for Placing Sensors

Sensors should be placed in the nodes with bigger sensitivity in order to gather the most relevant information regarding occurrency of leaks. However the use of this criteria alone may conduce to have all sensors concentrated in nodes relative close among them. It is also convenient to spread sensors over the network rather than concentrating them in a small region. As it is unknown where the leaks would be happening, the sensors should be covering the whole network. From this perspective a second criteria is normally added to evaluate how much spread are sensors in the solution obtained.

## Optimization-based Solution Process

Once the criteria for placing sensors has been established, an optimization algorithm will search the best placement solutions. The algorithms we have developed are using a multiobjective approach and rather than a single solution it provides a set of solution belonging to the Pareto front and representing the best compromise among the criteria we used for evaluating the placement of sensors

## Selecting Number of Sensors

Beyond the evaluation criteria, the cost also plays an important role in the selection of the final solution and it is directly associated with the number of sensors. This is the reason why a new component is incorporated to the Pareto front representing precisely the number of sensors. A 2D representation of the Pareto front with the same color only for solutions with the same number of sensors is used as a basis for comparing solutions. This representation helps to identify the convenience of increasing the number of sensors or not depending on how much the other criteria are improved when the number of sensors increases.

## The Final Solution

Both the selection of the number of sensors and the final solution to be adopted are obtained after a manual process of reviewing solution.

Several individual solutions belonging to the Pareto front are visualized on the network map and compared. Additional information from the utility and engineers criteria can be used at this time to select the final solution. For example, facilities (or difficulties) to install sensors at the selected places, real budget limitations, sensor characteristics, among others.

Having a reduced number of solutions to choose from is already a good but the necessary final step depend on the direct eye of engineers with experience and the additional information from the utility.

Sensor Placement for Leak Detection

# Project Report and Solution Transfer

After all these steps final report is written with details about the final solution and the different steps leading to it. Additionally, the software used for running calculations, is delivered to the utility in order to review / reevaluate results. The software is prepared to load the hydraulic model of the water network and the corresponding sensitivity matrix generated in the first steps. After a report is delivered it is perfectly possible to have rounds of questions and an additional presentation if necessary. You will have a solution and ready report in a maximum of 15 days for the optimal location of sensors for leak detection in your water network.

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