# Application and Optimization of Algorithms for Pressure Wave Evaluation Based on Measurement Data
## 4 Algorithms
This is an advantage over many conventional change-point algorithms, as they can only detect changes within marginal distributions [27]. The algorithm used an algorithm for multiple change-point analysis that used dynamic programming and pruning for segmentation. The method used approximate nonparametric estimation of multiple change-points. The cp3o framework (Change-Point Procedure via Pruned Objectives) was developed for this purpose [26]. This procedure applied a pruning routine to reduce the search space and computational cost. Therefore, existing goodness-of-fit methods were directly utilized. For the goodness-of-fit measure, the Kolmogorov-Smirnov statistic was applied. The algorithm found the location of the change-point, which was the PDTP in the present case. The seventh algorithm was the kernel-based change-point detection algorithm (KCP algorithm) [28]. The KCP algorithm was also implemented in the mentioned R package \"ecp\" and is an algorithm for multiple change-point analysis that uses the 'kernel trick' and dynamic programming for segmentation. The assumption of the multiple change-point problem is that the data belonging to a set are equipped with a positive semidefinite kernel. With a model-selection penalty, the selection of a number of change-points is allowed by using the kernel-based detection method of [PERSON] and [PERSON] [28]. For univariate data, the change-in-mean procedure was applied. The method found the location of the PDTP as a change-point within a single time series of each dataset. The eighth algorithm was the change-point detection in mean (CPD algorithm) [29]. This algorithm used the package \"changepoint\" in R. With this package, different change-point search methods can be selected and applied. The function we used from this package identified changes in mean and variance, calculating the optimal positioning and, if necessary, the number of change-points for data using the specified method. It was assumed that the data were normally distributed. The used parameter 'AMOC' stands for at most one change-point, which matched with the present data because only one change-point, the PDTP, should be found [29]. With changes in the mean and variance of a dataset, the change-point was found where the change was at its maximum. The same applied to variance because the method detected simultaneous changes in mean and variance [30]. With this combination, it was possible to detect the change-point that was the PDTP. The last algorithm was the Bayesian single change-point (BCP algorithm). For this algorithm, the package \"bcp\" in R was used. In this package, a Bayesian analysis for change-point problems is proposed, and the given methods from [PERSON] and [PERSON] are implemented [31]. A specific case was defined by the product partition model for the normal-error change-points. For univariate (or multivariate) Bayesian change-point analysis, it was assumed that the unknown partition of a time series into blocks existed and the mean was kept constant within each block [31]. The time series was divided into blocks where Bayesian methods were used to estimate the change-points or block boundaries of the unknown partitions. The method also supported multivariate change point problems [32]. The result was the estimated posterior probabilities of changes at each location, where the location with the highest probability was the PDTP. The pressure data were examined in a period of time of five minutes available. Around the LDTP described in Section 3, pressure data 150 s before and after the time point were evaluated. It was possible that each algorithm needed another time frame for application. Therefore, the applied time frame could be optimized in retrospect for the most suitable time frame. The selection of the time frame was conducted in such a way that the affected EA was in the highest-possible place in the ranking. The time frame needed time borders \(T1\) (left side of the LDTP) and \(T2\) (right side of the LDTP) that could be defined and then optimized.