# Application and Optimization of Algorithms for Pressure Wave Evaluation Based on Measurement Data
## 5 Results and Discussion
For all the events, the mean PC value was calculated, which corresponds to the max PC value in Table 5. In addition, the mean for an arbitrary optimal time frame with the highest possible PC value for the algorithms is presented (cp. Table 4). The last row contains the difference between these two values. The algorithms in the table are sorted in descending order based on the mean PC value. For each algorithm, the affected EA was in the first place at least once for one event. As already mentioned, the first place in the ranking led to a PC value of 100.0% and the last place to a PC value of 3.6%. For each event, every algorithm performed differently. Therefore, different algorithms should have been applied to different events, but this was not applicable in practice as well. Based on the mean value of each algorithm, the BCP algorithm performed best within its overall best time frame with a mean PC of 77.3%. This was larger than the 70% suggested as a minimal value to be ready for practical use [10]. For events 5, 9, 11, and 13, the affected EAs were ranked in the first place. To be on the first three places, a PC value of \(\geq\)92.9% was necessary. The BCP algorithm ranked the affected EAs for \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \# & **BCP** & **KSS** & **CPD** & **PDN** & **MLR** & **KCP** & **MAN** & **LNR** & **DFN** & **Mean** \\ \hline  
Mean(cp. Table 5) & 77.3 & 71.6 & 71.3 & 70.6 & 68.0 & 66.9 & 66.7 & 60.9 & 60.1 \\ Mean(cp. Table 4) & 98.4 & 98.5 & 98.5 & 95.3 & 97.7 & 96.3 & 98.5 & 91.4 & 89.8 \\ Diff & \(-21.1\) & \(-26.9\) & \(-27.3\) & \(-24.7\) & \(-29.7\) & \(-29.4\) & \(-31.8\) & \(-30.5\) & \(-29.7\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: PC values of each algorithm for all events within the optimal time frame. nine events (5, 9, 11, 12, 13, 14, 19, 20, and 22) in the first three places. For this comparison, the KSS and CPD algorithms were better because they ranked for ten events the affected EAs in the first three places. Both also had the affected EA in the first place for four events like the BCP algorithm. The worst algorithm within its own overall best time frame was the DFN algorithm with a mean PC value of 60.1%. When the differences between the PCs for arbitrary optimal and overall best time frames were compared, the BCP algorithm had the smallest difference with a value of \(-21.1\%\). Therefore, this algorithm had high PC values within both the overall best time frame and an arbitrary time frame. The MAN algorithm had the highest difference with a value of \(-31.8\%\). Either all optimal time frames were similar to the overall best time frame or the BCP algorithm was the most robust against changes in the evaluation time frame. Based on its overall best time frame with more data points before LDTP (\(T1=-100\)) and only a few data points after LDTP (\(T2=30\)), a pressure curve with a strong drop was identified. Therefore, the most important drop within the time frame was detected. As described in Section 4, the division of the pressure curve into multiple blocks and the use of Bayesian methods to estimate change points was an advantage of this algorithm. Larger differences within the pressure curve could be better determined within these blocks. In contrast, the DFN algorithm showed the worst mean PC values for the overall best time frame. This was due to the fact that many differences within the pressure curve could be identified as a maximum difference with the location of the PDTP. However, these differences could also be normal noise differences between different data points. Therefore, this algorithm was not that robust, and the low PC values indicated a wrong detection of the PDTP. Overall, all the algorithms needed their own overall best time frame to evaluate the pressure curves and determine the PDTPs. The BCP algorithm had the highest best mean PC value and the lowest difference; this algorithm should be implemented in a practical setting and used for the determination of the PDTPs.