# Estimation of the Noise Source Level of a Commercial Ship Using On-Board Pressure Sensors
## 3 Source-Level Estimation at Full Scale
### Results and Discussion  
Using the simple beamforming method, the source level was estimated for each run, and the results were averaged. The source region was set as  
\[-2\,\mathrm{m} \leq x\leq 2\,\mathrm{m} \tag{19}\] \[-0.6D \leq y\leq 0.6D\] \[-0.6D \leq z\leq 0.6D,\]  
where \(D\) is the propeller diameter. The spacing was 0.1 m in all directions and the frequency resolution was 4 Hz. The estimated source level was compared with the measured source level in one-third octave bands. The results for operating condition C1 are plotted in Figure 20. It is seen that at low frequencies below 100 Hz, the estimated source level is about 20 dB larger than the measured one. The reasons for this discrepancy would mainly be the distance between the propeller (source) and the sensors (receiver), which was about 5 m. The corresponding wavelength from the relation \(\lambda/2=r\) is 10 m and the frequency is \(f_{\mathrm{min}}=c/\lambda=150\) Hz. This is the case when the source is placed at the center of the propeller. In reality, the source location varies within the propeller disc, depending on the cavitation pattern. In most cases, cavitation occurs when the propeller passes the upper part of the propeller plane, so that \(f_{\mathrm{min}}\) increases as the distance becomes shorter. The shortest distance corresponds to the 400 Hz band; hence, inaccuracy still exists between 150 and 400 Hz. Above this frequency, the agreement between the results is good, showing discrepancies within 6 dB. The Lloyd mirror effect due to the presence of free surface and the reflection from the sea bottom could also have played a role at low frequencies. As an example, the transmission loss (TL) due to the free-surface effect at hydrophone position (50 m depth) was calculated and plotted in Figure 21. A TL of less than 10 dB is seen below 100 Hz, which suggests that the measured URN could increase if this effect were to be considered. The reflection, however, is thought to be less significant, as inclusion of the reflection would have increased the measured URN. If the data measured from the deepest hydrophone (80 m depth) were considered, the measured URN would be less than the plotted value [7]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Position** & \(\boldsymbol{x(\mathrm{mm})}\) & \(\boldsymbol{y(\mathrm{mm})}\) \\ \hline P2 & \(-78\) & 1400 \\ P1 & \(-78\) & 600 \\ C0 & \(-78\) & \(-200\) \\ S1 & \(-78\) & \(-1000\) \\ S2 & \(-78\) & \(-1800\) \\ F1 & 848 & \(-200\) \\ F2 & 1648 & \(-200\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Positions of the pressure sensors; (0,0) = center of the propeller. As the data measured from individual hydrophones were not provided, comparisons could not be made. The results for conditions C2 and C3 are also plotted in Figure 22. The agreement is better at high frequencies, as the signal-to-noise ratio increases. Figure 21: Calculated transmission loss at the hydrophone position (50 m depth). Figure 22: Comparison of measured and estimated source levels for different conditions: (**a**) C2 and (**b**) C3. Figure 20: Comparison of measured and estimated source levels for condition C1. For a quantitative comparison, the differences between the measured and estimated source levels are listed in Table 4 for different octave band center frequencies. As seen in Figures 20 and 22, the differences are within 6 dB above 500 Hz. As the method was developed for noise monitoring, the source level should be obtained for a short recording time with a limited number of sensors. In addition, the number of frequencies for data processing should also be minimized in order to reduce the computation time. A sensitivity analysis was conducted to check these aspects for condition C1. The parameters are listed in Table 5.  
The source levels for two different recording times (10 s and 2 s) are shown in Figure 23. As the total measurement duration was 60 s, three different time ranges were chosen to check the consistency of the results.