# Application and Optimization of Algorithms for Pressure Wave Evaluation Based on Measurement Data
## 2 Related Work  
The detection of a PDTP is comparable with the task of change-point detection (CPD). With CPD, in general, a special point within a time series should be found. For detecting such a point, several algorithms and methods are available, which are used for determining PDTPs. With respect to DHNs, to our knowledge no literature is present about the use of such detection methods. Nevertheless, we provided a brief overview on the literature that could be relevant within other contexts, and we applied some ideas from them and further algorithms to our problem. In [12], many CPD methods were proposed to detect change-points in time series. The examined methods included both supervised and unsupervised algorithms. Areas of application were medical condition monitoring, climate change detection, speech recognition, and image analysis. CPD defined the problem to find abrupt changes in data when a property of the time series changed. This could be different states within the data. The presented survey described different methods and introduced several criteria to compare the algorithms. Since a variety of CPD methods exist and they are mostly tested only on artificial data, these methods were applied to real datasets in [13]. The datasets consisted of different time series. Human experts assigned the appropriate change-point information to each dataset. Evaluation metrics were introduced to compare the different methods. A benchmark for the used algorithms was established and discussed. Within a time series, especially for sensor data, missing values are possible. In [14], a new algorithm for change-point detection was described for when the observed data may contain missing values. Missing data is particularly problematic for the application of conventional methods. The proposed method solved these problems by modelling dynamic distribution based on the underlying data as close to a time-varying, low-dimensional subset. Specifically, streaming data were used to track an approximation and measure deviations from those approximations. By computing various statistics on these deviations, the aim was to identify when the underlying manifold changed significantly or unexpectedly. Experiments and simulations demonstrated the robustness of the new method. Changes in the activity of gas sensors were addressed in [15]. The main challenge was the turbulent nature of gas dispersion and the sensor response dynamics. An algorithm to detect change-points was proposed and evaluated on individual gas sensors. In addition, a sensor selection algorithm was developed, and the detected change-points, with respect to sensor position, were evaluated. Besides change-point detection, anomaly detection methods can be used to detect special points in time series. In [16], an overview of methods to detect anomalies in sensor systems was given. In such systems with many sensors, anomaly detection is a particularly difficult problem since a trade-off between computational power and accuracy must be made within a limited framework. Ideally, such a change should be registered as quickly as possible. Various methods, from conventional techniques (statistical methods, time series analysis) to data-driven techniques (supervised learning, deep learning), were explored. The impacts of different architectural environments (e.g., cloud solution) on the sensor ecosystem were also shown. Leakage detection in DHNs can also be seen as anomaly detection. Therefore, opportunities for the application of machine learning models were presented in [17]. Leakages could be localized by using supervised ML methods that were trained with infrared images of the underground pipes. Different machine learning algorithms such as random forest, support vector machine, or logistic regression (LR) were applied. However, such approaches were not only used for leakage localization; they could also be applied to the extraction of heat load patterns or to assess the condition and quality of the installed valves. Wireless sensor systems collect a large amount of data.