# 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
It can be seen that the results did not change much when \(\Delta t=10\) s. When \(\Delta t\) was set to be 2 s, the results above 8 kHz became slightly different, showing a difference of up to 6 dB. Compared to the \"10 s\" case, the source level was overestimated compared to that in Figure 20. This could be due to the randomness of the propeller cavitation, which could not be captured entirely by a short-term measurement. Apart from that, the agreement with the measured data is good in terms of trend and level. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Octave Band** & \multicolumn{3}{c}{\(\boldsymbol{SL_{\text{estimated}}}\)-\(\boldsymbol{SL_{\text{measured}}}\), **dB**} \\
**Center Frequency, Hz** & **C1** & **C2** & **C3** \\ \hline
31.5 & 24.8 & 24.4 & 25.1 \\
63 & 16.6 & 15.8 & 17.9 \\
125 & 7.1 & 6.0 & 7.4 \\
250 & \(-\)12.6 & \(-\)14.1 & \(-\)13.9 \\
500 & 1.8 & 1.6 & 2.0 \\
1000 & \(-\)1.3 & \(-\)1.6 & 0.1 \\
2000 & \(-\)1.2 & 1.4 & 4.3 \\
4000 & \(-\)5.0 & \(-\)3.3 & \(-\)1.3 \\
8000 & \(-\)3.5 & \(-\)2.3 & \(-\)1.1 \\
16,000 & \(-\)2.9 & \(-\)0.6 & \(-\)0.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Differences between measured and estimated source levels. Figure 23: Comparison of the source levels estimated for different recording times: (**a**) 10 s and (**b**) 2 s. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Range** \\ \hline Recording time (\(\Delta t\)), s & 60, 10, 2 \\ Frequency resolution (\(\Delta f\)), Hz & 4, 16, 64 \\ Number of sensors & 7, 5, 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters for the sensitivity analysis. The recording time may not be as important as the other parameters, provided that it guarantees a consistent result. The other two variables are, however, directly related to the computation time, and are thus very important in noise monitoring. For the variable ranges listed in Table 5, the corresponding results are plotted in Figure 24. For different frequency resolutions, three results showed very similar behaviors above 300 Hz. It should be noted that as \(\Delta f\) increases, the low-frequency data are lost in the one-third octave band spectrum conversion. The lack of data at low frequencies also resulted in differences between the estimated levels below 200 Hz. This would be improved if a logarithmic frequency range was used for the estimation. Overall, the result above 200 Hz did not change significantly, especially at high frequencies. As the frequency resolution is inversely proportional to the computation time, one might consider increasing \(\Delta f\) above 2 kHz, where the difference is less than 2 dB. For the number of sensors, locations \"P1\", \"C0\", \"S1\", \"S2\", and \"F1\" were selected for the five-sensor case and \"C0\", \"S2\", and \"F1\" for the three-sensor case (see Figure 18b). The reason for this is because the propeller rotates counter-clockwise in the propeller plane (looking upstream), and hence, the cavitation is stronger on the starboard side and near the propeller plane. Consequently, the signal-to-noise ratio is expected to be greater around this area. In Figure 24b, good agreement is seen above 1 kHz, where the cavitation noise is dominant. Below this frequency, the result deviates from the reference (seven sensors) by up to 10 dB. In all cases, except when \(\Delta t=2\) s, the high-frequency source level was estimated well, and hence, it can be said that the method has potential to be exploited in underwater radiated noise monitoring. Still, more work needs be done to ensure its robustness and accuracy. This includes optimization of the source region, number of sensors, and data processing.