# Application and Optimization of Algorithms for Pressure Wave Evaluation Based on Measurement Data
## 5 Results and Discussion
The range of the PC values was 35.7 to 100.0%. Therefore, the evaluability of the events with the BCP algorithm was very different and correct localization was not always possible using the best overall time frame. The drop in the mean PC from 98.4 to 60.5% for the optimal and overall best evaluation time frames, respectively, indicated that practical application was difficult when judging the available measurement data for these 22 events. A detailed investigation should be performed to clarify reasons for that large drop and is out of the scope of this paper. Table 4 shows the maximum PC value for all the algorithms for each event, no matter what combination of \(T1\) and \(T2\) led to that result. The optimal time frames are not shown for reasons of simplicity. The algorithms in the table are sorted in descending order based \begin{table}
\begin{tabular}{c c c c c} \hline \hline \# & \(T1\) & \(T2\) & PC & PC [\(T1,\ T2\)] = [\(-100,\ 30\)] \\ \hline  
mean & \(-69\) & 53 & 98.4 & 77.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal time frame and maximum PC value of each event for the BCP algorithm and PC values for best overall time frame. on the mean maximum PC value in the last row. A PC value of 100.0% indicates a first place in the ranking. The KSS, CPD, and MAN algorithms had the highest PC values on average with 98.5%. The DFN algorithm was the worst with a PC value on average of 89.8%. This algorithm also had the worst maximum PC value of 39.3% for event 8. In general, the maximum PC value of 100.0% was reached 118 times. This means that an evaluation time frame \([T1,\ T2]\) existed for which the affected EAs were ranked in the first place in 60% of all cases. For each algorithm, the affected EA was in first place at least once for one event. For events 7, 17, and 20, no algorithm ranked the affected EA in the first place, yet. To find the overall best time frame for practical application for all the algorithms, a summary of the 198 (9 algorithms for 22 events) available heat maps was necessary to obtain a meaningful heat map (as in Figure 5) for each algorithm. All 22 heat maps of all the events for one algorithm were summarized. In Figure 6, the summarized PC values for each algorithm for all the events are also shown as a heat map. The heat map illustrates the summarized evaluability of all the events for each algorithm. All nine algorithms are presented row-wise (first row: BCP, CPD, DFN; second row KCP, KSS, LNR; third row MAN, MLR, PDN). The maximum summarized PC value is, again, dark green in a black box within each map. In contrast, the worst PC value is also red in a white box. Hence, the dark green PC value represents the maximum summarized PC value, and the overall best time frame could be determined directly. It was evident that each algorithm had an individual overall best time frame, which is shown in Table 5. Algorithms BCP, CPD, and MAN, benefitted from more data points before LDTP \(T1=\{-100,-100,-90\}\) and from fewer after LDTP \(T2=\{30,20,30\}\). For algorithms DFN, LNR, and PDN, the opposite was beneficial. Fewer data points before LDTP \(T1=\{-60,-30,-30\}\) and more data points after LDTP \(T2=\{120,120,110\}\) led to larger PC values. Fewer data points before and after the LDTP were good for algorithms KCP, KSS, and MLR with \(T1=\{-40,-20,-50\}\) and \(T2=\{30,20,40\}\). The heat maps had a relatively similar range between the max and min values for the summarized PCs of the DFN and LNR algorithms. This also applied to the BCP and CPD algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \# & **KSS** & **CPD** & **MAN** & **BCP** & **MLR** & **KCP** & **PDN** & **LNR** & **DFN** \\ \hline  
mean & 98.5 & 98.5 & 98.5 & 98.4 & 97.7 & 96.3 & 95.3 & 91.4 & 89.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum PC values of all algorithms for each event for arbitrary optimal \([T1,\ T2]\). Table 5 shows the mean PC of the summarized heat maps and the standard deviation, as well as the max and min PC values.