# Application and Optimization of Algorithms for Pressure Wave Evaluation Based on Measurement Data
## 2 Related Work
With this large amount of data, the problem of detecting interesting parts of the datasets as automatically as possible arises. In [18], an algorithm for the online detection of anomalies in the measurements of a sensor system was proposed. This detection was evaluated on real datasets to demonstrate the reliability. The algorithm used piecewise linear models of time series that were representative and robust. This online detection allowed the computing of such models in near-real time, the building of them without prior knowledge of anomaly types, and the comparing of different time series of sensor data efficiently. As discussed in [19], decision makers from the petroleum industry should be able to quickly identify anomalies in order to take appropriate action. The correct detection of such anomalies serves to avoid, correct, or react to the associated situations. In this application context, heavy machines were monitored by hundreds of sensors each, which sent data at a high frequency for damage prevention. A segmentation algorithm was presented to efficiently detect anomalies on the machines. A benchmark was also made for comparison with other methods. The detection of road traffic anomalies is a very important aspect presented in [20]. Traffic anomalies can occur due to various reasons, such as the malfunctioning of sensors that collect traffic information. Therefore, a technique based on a statistical model was proposed for anomaly detection that identified temporal outliers in road traffic. A linear regression model and a z-score model were two statistical models that were used in combination to detect temporal outliers. The proposed technique could be used to detect sensor failures or unusual traffic incidents. One method to detect change-points in time series is kernel-based online change-point detection. The algorithm in [21] used a kernel-based method and showed reliable detection results for a variety of problems. Some aspects of the algorithm were modified to improve the detection performance. Theoretical analysis and numerical simulations were performed to confirm the improvement of the results and to be more efficient compared to a state-of-the-art method. Another method was presented in [22], where a Bayesian method was used to detect change-points. It determined whether there were changes in the mean or covariance at an unknown time in a sequence of independent multivariate normal observations. Different versions of the intrinsic Bayes factor were used to detect change-points. The results were tested and discussed on both simulated and real datasets. A holistic algorithm for localizing leakages in pipelines was presented in [23]. A method for detecting leakages in pipelines was proposed that was based on acoustic emission event characteristics and a Kolmogorov-Smirnov test (KS). To apply the method, a sliding window was used to examine the data. A pipeline leak indicator was also determined using the KS test. The experimental results showed that the developed indicator accurately distinguished the leakages without any prior information. Moreover, it was more suitable than traditional features such as mean, variance, and kurtosis. The literature review shows that there are some useful components in every presented publication, which are also taken up in this paper. The detection of PDTPs for localizing leakages in a DHN is the same as CPD in other contexts, such as those described in [12; 13; 14; 15]. The missing values and their handling in [14] were not available, but due to the parametrization of transmission technology, there were only non-uniform, time-discretesensor values available. In the case of leakage and the occurrence of a pressure wave, there is a similar main challenge to that in [15]. The machine learning approaches from [17] can also be used for leakage localization but will not be pursued in this paper. Furthermore, if the dynamics of a sensor response is equal, no pressure wave attenuation is available.