# Application and Optimization of Algorithms for Pressure Wave Evaluation Based on Measurement Data
###### Abstract
For localization, hardware- or software-based approaches are available, such as image processing with infrared sensors or different data-driven methods with machine learning methods [5]. Another application for image analysis is the detection of oil spills with the usage of remote sensing methods [6]. Figure 2 shows exemplarily one exclusion area (EA) and the topology of the investigated network. On the left side, the blue area belongs to EA 3. Each EA can be separated from the rest of the network by remote control. Ideally, only the EA affected by the leakage is separated [7]. The blue EA 3 is adjacent to the blue EAs 2, 4, and 7. Hence, three different shafts are visible with remote-controlled, motor-driven valves and pressure sensors. On the right side, a simplified network topology is shown, which is considered in this work. There is one supplier feeding in three different lines, which are connected directly or with linking lines. Altogether, \(N_{EA}=28\) EAs are present including the supplier. The topology yields six meshes and should describe the connections between the EAs. The aim of this paper is the application and evaluation of nine different algorithms to detect the PDTPs in pressure data of 22 real events. Five algorithms are self-developed, and four have already been presented in the literature. After the application of the algorithms and the determination of the PDTPs, these time points are used to localize the leakage. For further real events, leakage localization is performed, as well as other methods such as those described in [8] and [9]. The PDTPs are used in an established framework presented in [10] to generate a ranking of the EAs. Ideally, the EA affected by the leakage is ranked first, but how well this works depends on the PDTPs determined by the algorithms. A performance criterion (PC) presented in [10,11] is used to compare the algorithms. It can be calculated for any number of results. In the case of a single ranking, the following holds: if the EA affected by the leakage is ranked first, the PC value is 100.0%; otherwise, if it is ranked last, the PC value is 3.6% (\(=\frac{1}{N_{EA}}=\frac{1}{28}\)). The goal is to find the best-performing algorithm over all the events and to classify which events are better evaluable. The performance of algorithms can depend on the parameters chosen for evaluation. In this paper, the focus  
Figure 2: Exemplary exclusion area (blue 3) and simplified network topology. lies on the evaluation time frame that is selected. For all other parameters, standard or best-known values are selected and kept constant, if there are any. The evaluation time frame can be optimized for historical events, as the EA affected by the leakage is known. An evaluation time frame is selected where the affected EA is ranked highest. However, for application in the case of a future real event, an evaluation time frame has to be set before the affected EA is known. Finally, for each algorithm, a recommendation is given for the best evaluation time frame and the application of the most suitable algorithm. The paper is divided into six sections. After the introduction, Section 2 presents some related work. In Section 3, the background and motivation are given. The algorithms are described in detail in Section 4. Then, the results of the estimated PDTPs are used to localize the leakage with a specific framework for several real events in Section 5 before Section 6 briefly concludes.