# Estimation of the Noise Source Level of a Commercial Ship Using On-Board Pressure Sensors
## 1 Introduction  
The increase in commercial shipping has led to the development of ships with higher speeds and higher capacities, and the ambient noise of the sea has increased as a result [1, 2]. Now, the noise pollution from commercial ships is considered to be one of the major issues in the ocean environment [3, 4], and the International Maritime Organization (IMO) has set guidelines to mitigate it. In response to this, various research projects have been carried out, especially in Europe, to identify the radiated noise level as well as to reduce it. It is well known that the dominant underwater noise source of commercial ships is propeller cavitation. Due to its impulsive characteristics, the cavitation affects the tonal noise at blade-passing frequencies (BPFs) as well as the broadband noise. The radiated noise can be measured by a procedure based on ISO 17208-1 [5], which exploits an external noise measurement system located away from the target vessel [6, 7, 8]. However, this has several disadvantages in cost and time, and the measured noise is affected by the sea state. In addition, the test cannot be conducted for all operating conditions, so only a limited set of data can be obtained. More importantly, the noise level cannot be monitored after the measurement, which makes it difficult to know how much the noise is radiated during actual operations. This may not be a problem for noise monitoring close to shore, but the system can only cover a limited area [9, 10, 11, 12]. In terms of experimental approaches, model-scale tests have helped greatly in understanding cavitation behavior and radiated noise. Many studies have been carried out to predict the full-scale noise spectrum based on the scaling law recommended by International Towing Tank Conference [13]. Although the scaling exponents may be different fromthe recommended values, it was shown that the model-scale measurements could give reasonable estimations of the radiated noise at full scale with the scaling law [14; 15; 16; 17]. Still, there is room for improvement in the accuracy of these tests. This includes the viscous scaling effects, wake at the propeller plane, nucleus distribution, etc. In addition, the inconsistency in the results between different test facilities is still in question [18]. Numerical methods could also be used to predict the radiated noise as well as to analyze the noise-generating mechanism. These include the boundary element method (BEM) [19], potential flow theory, or computational fluid dynamics (CFD) with an acoustic analogy [20; 21; 22; 23]. Although these are being rapidly developed, gaps still exist between measurements and predictions. As model-scale measurements and numerical predictions can only be used for certain conditions, the need to make use of on-board sensors for noise monitoring is inevitable. An early attempt was made by [PERSON] and [PERSON] [24], who measured the source strength of a ship propeller using the principle of reciprocity. They developed a method using the transfer function between the cavitating propeller and the sound and vibration inside a ship. The method showed consistent volume acceleration at the propeller, which was calculated using the transfer functions from various locations where the other noise sources were not dominant. The fact that the cavitation and the hull pressure fluctuation are related led to the development of source strength estimation methods using measurements of hull pressure. For example, [PERSON] [25] formulated an inversion equation for estimating the source strength distribution using the BEM. An example of a single screw ship case was shown, in which a single monopole source was assumed. An initial source location was defined and the discrepancy between the measured and calculated hull pressures was calculated. By changing the source location, the point where the discrepancy was at its minimum was found. A similar approach can be found in the study by [PERSON] et al. [26].