# Burst Detection in Water Distribution Systems:
## 1 Introduction
The classification methods need lacking labels data, which means time series consisting by normal and abnormal data with information on the bursts occurrence, for the algorithm training. On the contrary, only normal data without outliers are used by prediction methods. In addition, statistic methods, which are set up for identifying outliers, require both normal and abnormal data. In addition, lacking labels are compulsory for the evaluation of the performance of the all classes of methods and the uncertainty analysis of the alarms. In order to provide the massive amount of data required, three options are currently available. Firstly, burst events can be collected by opening fire hydrants or drain valves [22; 23]. This process allows for having reliable data with a full knowledge of leakages in terms of location, duration, and magnitude. However, it has the drawbacks that this procedure is time-consuming, economically expensive, and above all causes disservice. Secondly, real hydraulic data with historical bursts report can be used, as [19; 24]. Nevertheless, two important limitations affect real dataset: the knowledge of bursts time, amount of water losses, and the data uncertainty due to the sensors performance and the presence of missing data. Thirdly, another option for providing the data are the synthetic data generation as proposed by [25; 26]. In this case, the main issue is that the methods trained with such data are not reliable for real applications due to scarce variation in the provided dataset. Given that the large amount of data required is the main limitation of all categories of data-driven models [10], the authors deem that the only feasible way to provide the needed dataset is the synthetic data generation due to the difficulties in collecting accurate real data or in generating bursts by hydrants. However, no proper data generator methodology has already been proposed that is able to provide suitable data for the development of anomaly detection methods because of scarce variation of water demand representation and poor accuracy of bursts modeling. Thus, this work aims to lay the foundations in the synthetic generation of water consumption data in order to support the development of bursts detection in WDS. Therefore, a methodology for the generation of water consumption time series is presented, which comprises all its components, i.e., the water request, the background losses and the bursts, in terms of mean and variation. For the sake of clarity, the water request is defined in this paper as the water demand required by the aqueduct users. The term demand is used instead to indicate the water demand actually supplied by the water distribution system to the users. In addition, water consumption means the total amount of water delivered by the water supply system including both water demand and water losses along the distribution network. Summarizing, the contribution of this study is a reliable methodology that provides suitable water consumption data. The final scope is to support the development of data-driven techniques for the bursts detection, which need a large amount of accurate data. Specifically, the proposed methodology, hereafter refers as stochastic-hydraulic time series generator (SHtsG, hereafter), relies on two principal phases: the water request modeling and the hydraulic WDS simulation. The first stage is based on a superimposition approach that takes into account the daily, weekly, and seasonal deterministic patterns together with the random component of the variation. Its output is the water request time series of the different group of WDS districts. On the other hand, the second stage involves the production of hydraulic data on the base of a distributed fully pressure driven model (DFPDM, hereafter) able to properly simulate the water demand, the background leakages, and the busts.