# Application and Optimization of Algorithms for Pressure Wave Evaluation Based on Measurement Data
###### Abstract  
Leakages can occur in a district heating network, resulting in high economical damage. The propagating pressure wave resulting from large, spontaneous leakages reaches sensors at different locations in the network. This leads to pressure drops registered at each sensor at a different point in time. The time differences help to localize the leakage. Different algorithms are presented and applied in this paper to estimate the pressure drop time points based on non-uniform, time-discrete sensor signals. Five of the nine algorithms are self-developed with, e.g., parts of linear regression, whereas the other four algorithms have already been described in the literature, such as change-point detection. In this paper, several recorded events were investigated, and the algorithms were applied to real measurement data. After detection, leakage localization was performed to determine the affected exclusion area. A performance criterion was used as a measure to compare the algorithms. For practical application, the best-performing algorithm was identified. Furthermore, the events were classified according to how well they could be evaluated. d 202220 April 202222 April 202222 April 202222 April 2022222 April 202  
DHNs, as a special form of thermo-hydraulic network, are used to supply customers with energy. The whole system is closed, pressurized, and operated with deionized water (a special, treated form of water) as a medium. Supply pipes and mass flow are drawn in red and return in blue. With a heat exchanger, the consumers obtain the energy from the network. The pressure difference between supply and return drives the mass flow through the heat exchanger, and the supply temperature is reduced to the return temperature. To this end, the network operator has to ensure minimal pressure difference and supply temperature, and the customer has to cool down the medium to a maximal allowed return temperature. The pressure difference is regulated by the circulation pump. If it is too low, the circulation pump power is increased, and if it is too high, pump power is decreased. The pressure maintenance pump ensures a certain pressure level throughout the whole network. At the supply site, the cooled-down medium is heated up again by a heat exchanger. Several heat sources are possible. A power plant is depicted in Figure 1. When transporting the medium from the power plant to the consumer, no medium should be lost in order to ensure an uninterrupted supply. However, leakages can occur within the pipes. In the case of a large, spontaneous leakage, loss of the transport medium can be compensated for a certain period of time. The replenishment is performed via the refill mass flow (green), but the available quantity for this is limited. The refill is necessary to maintain the prevailing pressure in the entire network and to keep the medium liquid. Pressure sensors are installed in the network, and the data are permanently recorded [2]. With a monitoring program, the data can also be used to assist operator actions in the case of certain events [3]. If a leakage occurs, it is associated both with the loss of transport medium and with an initially local change in pressure conditions (a pressure drop). Immediately after the occurrence, the resulting pressure change spreads throughout the entire network. As soon as the pressure change is noticed by the pressure sensors distributed in the network, the pressurizer control reacts and feeds additional medium into the network. At each pressure sensor, the pressure wave is registered at a different point in time. A leak  
Figure 1: Schematic representation of a district heating network. age causes the pressure to decrease rapidly within a few seconds. Determining the correct pressure drop time point (PDTP) in order to localize the leakage is important because, if the loss is too large and lasts too long, the entire network must be shut down. Shutting down, repairing, and restarting the entire network has an influence on economy and reliability [4].