Statistical analysis of measured underwater radiated noise from merchant ships using ship operational and design parameters

Shipping is a known source of underwater noise, and shipping may dominate underwater noise near sea lanes (Wenz, 1962). Powered ships unintentionally radiate underwater noises mainly due to propeller cavitation under usual operations (Ross, 1976; Urick, 1975). Moreover, offshore underwater noise increased potentially due to shipping activities (Andrew , 2011; Andrew , 2002). In 2014, the International Maritime Organization (IMO) agreed with the nonmandatory guidelines for the reduction of underwater radiated noise (URN) from merchant ships. In January 2022, in a subcommittee on Ship Design and Construction (SDC), the IMO started a review of the guidelines to identify the next step.

The effect of URN is evaluated by the source level, propagation loss, exposure duration, and the receiver's auditory characteristics. Measuring the source level of URN from a ship is not an easy task. The International Standard Organization (ISO) published ISO 17208-1:2016 “Underwater acoustics—Quantities and procedures for description and measurement of underwater sound from ships—Part 1: Requirements for precision measurements in deep water used for comparison purposes” (ISO, 2016). This standard requires testing special operations of the ship in deep water (>150 m in depth), which is costly and not be feasible in shallow water areas. Then, an ISO working group is developing a new standard, ISO 17208-3 (ISO, 2019), for URN measurements in shallow water.

The characteristics of URN from ships have been studied for a long time, and several simple estimation models have been proposed (Brown, 1976; Ross, 1976; Urick, 1975). In recent years, URN from many ships was measured by deploying hydrophones near a sea lane, and the URN levels were reported (MacGillivray , 2020; MacGillivray , 2019, MacGillivray , 2021; McKenna , 2013; Simard , 2016). Related to the uncertainty in the URN measurements, Humphrey (2015) reported that the URN levels measured by a single hydrophone deviate 1–2 dB in several runs. Also, Sponagle (1988) reported that the 95% confidence intervals for URN measurement were 4.77 dB with single data sets and 6.50 dB with combined data sets based on regression analysis of many measured URN by a single hydrophone. Here, the single data sets consist of measured URN from one ship in a few days, and the single data sets consist of measured URN from one ship over a period of several years. Since the measurements of the URN level from a ship showed an uncertainty of several decibels (Humphrey , 2015; Sponagle, 1988), estimating the source level for a specific merchant ship type requires many data sets measured in open water. To estimate the source level, the propagation loss of URN from ships needs to be validated (Bassett , 2012; Prins , 2016; Putland , 2022).

Related to reduction of the source level, URN reduction measures should not increase, preferably should reduce, Greenhouse Gas (GHG) emissions. Since URN due to propeller cavitation can be decreased by reducing the swept area of cavitation (Brown, 1976), there are two simple ideas to reduce URN: slow steaming and increasing propeller blade area. It is known that the former reduces URN and GHG emissions, and latter reduces URN but increases GHG emissions. Hasuike (2019) quantitatively estimated the URN reduction, GHG emission increase, and their relationship based on propeller cavitation estimation and URN estimation by Brown's formula (Brown, 1976). The estimated URN from a 10 000 TEU container ship, a 182 600 DWT bulk carrier, and a roll-on/roll-off ship showed that slow steaming from 75% maximum continuous ratio (MCR) to 30% MCR results in URN reduction of 13.8–16.8 dB and that URN reduction of 7–8 dB by increasing propeller blade area results in GHG emission increases of 6.7%–12.5%. The efficiency of the slow steaming is also verified by URN measurement of actual ships. Hasuike (2019) introduced the URN reduction of a bulk carrier by comparing the measured URN under 0%, 8%, 50%, and 85% MCR. Sakamoto and Kamiirisa (2018b) showed that slow steaming from Navigation-full engine output, which is usually set at 85%–90% MCR, to Half engine output, which is usually set at around 50% MCR, results in URN reduction of around 10 dB based on the URN measurement of two cargo liners and that the source level of the URN and its reduction can be estimated by CFD. Sakamoto and Kamiirisa (2018a) showed further validation of the URN estimation by CFD. MacGillivray (2019) measured URN in and outside of the slow down area for many merchant ships and showed the URN reduction of 1.21–3.43 dB per slow steaming of 1 kn. The effectiveness of slow steaming in URN reduction is clear as noted previously, and its reduction is being clarified both experimentally and computationally.

In the previous studies (MacGillivray and de Jong, 2021; Ross, 1976; Urick, 1975; Wittekind, 2014), models of the source level of URN from merchant ships showed the effects of ship parameters such as length, speed, and draft. However, these effects were separately considered despite the correlation between length, speed, and draft. MacGillivray (2022) consider the simultaneous effects of ship draft, ship speed, wind resistance, surface grazing angle, ship length, nominal main engine revolution number, total main engine power, design speed, and vessel age. In this study, underwater sound measurements were conducted, and regression analysis was applied to the source levels of the URN from many merchant ships. The regression analysis simultaneously determined the coefficients of the model with ship length, speed, and draft, to examine the effect of each parameter and discuss simplified URN estimation measures. Further, since propeller cavitation of a merchant ship under operational conditions is almost determined by the hull form and the design ship speed of the individual ship, the effect of ship speed and draft is considered as the ratio to service speed and maximum draft, respectively.

In this project, three hydrophones were deployed near the sea lane passing through the south of Izu-Oshima Island for about four months. Referring to the Automatic Identification System (AIS) data, regression analysis is applied to the source levels of the URN from different types of ships. Further, the noise level variation with ship length, ship speed ratio to service speed, and draft ratio to maximum draft (loading condition) is examined for each ship type and compared with previous studies.

Measurements of underwater sound were conducted in the water south of Izu-Oshima Island, Japan (Fig. 1). Table I shows the measurement period, the sinker points for the monitoring station with hydrophones (see Sec. II B), and the water depth at the sinker point. The position of the sinker was estimated by measuring the slant range from a work vessel to the disconnection device at several points using sound waves. The site was selected mainly from two perspectives: many merchant ships on international voyages should pass near the site, and the water depth is more than 300 m, which is required for URN measurement of a ship 200 m long in ISO 17208–1:2016 (ISO, 2016). The monitoring station with the hydrophones was deployed in the center of the sea lane. This sea lane is used for trans-Pacific voyages.

Three hydrophones were deployed with two pressure gauges (depth meter) and a current meter (Table II). The auxiliary instruments were mainly used for estimating hydrophone position underwater. The measurement conditions shown in Table II were determined to enable one-month recording given the battery capacity and data storage constraints. The frequency range of the hydrophone is wide enough to measure URN from merchant ships, which has dominant energy at around 100 Hz.

The hydrophones were deployed using a sinker and buoyant materials to form the monitoring station as vertically as possible from the sea floor (Fig. 2). The depths of the hydrophones were determined based on ISO 17208-1:2016 (ISO, 2016), assuming the closest horizontal distance between the ship and the hydrophones (CPA distance) is 200 m, which is required for URN measurement of a ship 200 m long. In this measurement site, the mean length of ships was estimated to be around 200 m. The depth below the sea surface of the three hydrophones were 53.6, 115.5, and 200 m, which correspond to the depression angles of 15°, 30°, and 45°, respectively. Here, the term “CPA” is an abbreviation for “closest point of approach” and indicates the point where the horizontal distance between the ship and the hydrophones reaches the minimum value.

The RL is obtained by calculating the power spectrum density (PSD) of the wav file data from the hydrophones using the fast Fourier transform (FFT), averaging the PSD over 10 s, and adding the calibration factor to the PSD. The number of the samples is set to 2¹⁵, which corresponds to about 0.683 s of sound data. During the FFT, the Hanning window is applied.

A U-shaped interference pattern appears in the spectrogram of underwater sound when a ship passes by, and the time the vertex of the U-shaped pattern appears is defined as the time that the ship is at the CPA (CPA time). The CPA distance is estimated from the time series of the ship and hydrophone positions. The ship positions at the CPA time are estimated by linearly interpolating the ship positions from the AIS with time. The hydrophone positions are estimated based on the two pressure gauges and the current meter installed in the monitoring station (Fig. 2); therefore, d_H and $CPA$ are estimated by considering the hydrophone positions at each time. Here, the monitoring station is assumed to be rigid and inclines at an angle θ to the azimuth measured by the current meter (Fig. 3). Based on this assumption, the inclination angles are calculated from the depth of the hydrophone 1 and 3 measured by the pressure gauge 1 and 2, respectively. Then, the value of θ is estimated as a mean value of the inclination angles, and the depth of each hydrophone is estimated using θ.

Since the URN from merchant ships under usual operations is governed by propeller cavitation noise, C should be organized by the parameters related to τ_c and $σ 0.7 R$⁠. However, the parameters are generally not available to the public. In this study, it is assumed that ships of the same type have a similar hull form and propeller geometry. τ_c and $σ 0.7 R$⁠, which are directly related to propeller cavitation and organized by the ship speed, the propeller size, and the propeller revolution number. Propeller size can be roughly represented by the ship length for the same ship type. Hence, C is modeled for each ship type with the ship length and speed. The propeller revolution number is not used for the regression analysis in this study because it is not generally accessible. In addition, since propeller cavitation is affected by p, the ship draft plays a key role. A shallow draft will lead to a low static pressure, and then, the propeller easily cavitates. Conversely, since a shallow draft will result in a low ship resistance, the propeller load will be reduced. This will mitigate propeller cavitation. Thus, C is also modeled with ship draft.

Propellers for merchant ships are designed to maximize propulsion efficiency to the extent that cavitation does not cause operational problems; thus, cavitation is allowed to a certain limit in the design stage (e.g., Suzuki , 2020). Assuming the cavitation limit is almost determined by the hull form and the design ship speed, the cavitation noise level is considered to be comparable for the same ship types if the size is the same. This is another reason for modeling the URN for each ship type using ship length.

There are two types of ship speed: speed over the ground and speed over the water. The former can be obtained through the AIS. The latter is directly related to propeller inflow speed. Subsequently, ship speed over the water is estimated from the speed over the ground and the water current speed measured by the current meter, and it is used as V. Note that since the current meter was deployed underwater (Fig. 2), the estimated speed over the water is considered to include a certain error.

In previous studies, URN was modeled by the ship speed ratio to a certain constant value defined based on ship type (e.g., MacGillivray and de Jong, 2021). Using such a constant value based on ship type only may not be optimal since the propeller cavitation of a merchant ship under operational conditions is almost determined by the hull form and the design ship speed of the individual ship. Therefore, we consider that using the design ship speed of the individual ship is more appropriate. In this study, the ship service speed (ship speed under normal service conditions) is used to represent the design ship speed (ship speed used for propeller design).

The values of the left-hand side of Eq. (12) for the regression analysis are obtained from the observed data during the $1 st$– $4 th$ periods (Table I). SLs that satisfied the following three conditions were used in the regression analysis: the cases in which the URN from the ship was dominant in the underwater sound recorded by all the three hydrophones in the frequency range of 300–10 00 Hz, the SLs of URN from ships on international voyages, and the cases in which the CPA distance was less than double the water depth. By checking the spectrograms around the CPA time for each passage, we confirmed that the URN from the ship was dominant.

SL variations by CPA distance is validated by SLs of a ship that passed near the monitoring station several times. The one-third octave band SLs (center frequency of 400, 500, 630, and 800 Hz) of the ship are shown in Fig. 5 only in the cases where the operational condition of the ship is almost the same. In the range where the PL used in this study is valid, SL for the same frequency should be almost the same level. From this point of view, the PL seems to be valid when the CPA distance is less than 1400 m. Considering the paucity of the data for CPA distance between 900 and 1400 m and the safety margin, the analysis in this study was conducted using the cases in which the CPA distance was less than double the water depth. The operational condition data of the ship that are not included in the AIS data (e.g., propeller revolution number) were obtained from the operator).

Finally, the number of ships used for the regression analysis is shown in Table III. Here, “No. of ships” is the number of ships that passed near the monitoring station, and “No. of passes” is the total number of times ships passed, corresponding to N. Table III also shows the minimum, median, and maximum values of each variable. The regression analysis neglects the correlation between the values of C of the same ship on different voyages. For the other ship types, the number of ships that match the previously established criteria is not large enough for the regression analysis.

The comparison of the obtained C and the regression analysis with ship length and ship speed is shown in Fig. 6 as three-dimensional (3D) plots. In Fig. 6, the points indicate values of C, the planes indicate the regression equation, and the lines between the points and planes indicate the residuals. Note that extrapolation is not recommended although the planes are shown throughout the 3D plot. The residual plot for the regression analysis with ship length, ship speed, and ship draft is shown in Fig. 7. The residuals of the regression analysis are almost within ± 5 dB. Table IV shows the obtained coefficients for Eq. (12) with and without the ship draft effect for each ship type. Table IV also shows the 95% confidence intervals of the coefficients, the errors of the regression analysis, and the p-values. Related to the uncertainty in the measurement of URN from a ship, Humphrey (2015) reported that the standard deviation of URN from a ship recorded by a single hydrophone for several runs was 1–2 dB. Additionally, Sponagle (1988) reported that the 95% confidence interval for URN from a ship based on the measurement within a few days was 4.77 dB and that the 95% confidence interval for URN from a ship based on the measurement at different times over several years was 6.50 dB. Hence, the estimated URN from a ship includes an uncertainty of several decibels. The residuals of the regression analysis and the uncertainty of the URN measurement can be considered at a similar level. The p-values for the coefficients indicate the statistical significance of the relationships. Except when the 95% confidence interval includes zero, the p-values are enough small (p < 0.05), so that the coefficients are statistically significant.

The number of samples for container ships is the largest among all ship types (Table III). Furthermore, the container ships show a large variation in ship length and speed reduction ratio (Fig. 6). These factors lead to the large values of R² and the small values of the RMSE for container ships. Subsequently, it is confirmed that the values of $a L ratio$ and $a V ratio$ are positive for container ships.

The values of R² are smaller and the values of the RMSE are larger for general cargo ships than those of other ship types. Since the 95% confidence intervals are so large, we can not conclude that a negative coefficient for speed reduction indicates URN increase by ship speed, which is physically inconsistent.

The regression equations for bulk carriers and chemical tankers and oil tankers have smaller coefficients for both ship length and speed reduction ratio than that of container ships, and the 95% confidence intervals are large. Considering the draft change effect increases the value of R² and reduces the value of the RMSE. Generally, bulk carriers and tankers are engaged in transportation in one direction, while container ships are engaged in transportation in a two-way direction. Hence, the draft change is larger for bulk carriers and tankers than for container ships. This is considered to be one of the factors contributing to the improvements. Since the $a d ratio$ is positive for these ship types, the source levels of the URN are slightly lower under light load conditions than that of fully loaded conditions if the speed is the same. This tendency was also noted by MacGillivray (2020, 2021).

Car carriers show a significant variation in ship speed reduction ratio. This point leads to the positive value of $a V ratio$⁠. Conversely, the car carriers have almost the same ship length due to the size of the Panama Canal. This point leads to an insufficiently accurate estimation of URN variation with ship length.

MacGillivray (2019) reported URN reduction by slow steaming with the model $a v × 10 log 10 ( V low / V high )$⁠. Here, $V low$ is the ship speed in the slow down area, and $V high$ is the ship speed outside of the slow down area. The values of a_v, with their 90% confidence intervals in a similar frequency range (0.5 kHz–15 kHz) to our analysis, were reported as 3.35 ± 0.47 (⁠ $R 2 = 0.653$⁠) for all ship types, 3.97 ± 0.55 (⁠ $R 2 = 0.912$⁠) for container ships, 1.91 ± 0.89 (⁠ $R 2 = 0.232$⁠) for bulk carriers, and 1.65 ± 2.45 (⁠ $R 2 = 0.151$⁠) for tankers. The values are larger than our results, while the confidence intervals of the coefficients for bulk carriers and tankers are as large as our results. Since a_v by MacGillivray (2019) is based on the URN measurement with slow steaming (i.e., intentional slow down), the value of a_v can be considered to reflect the effect of slow steaming more significantly on the URN reduction than our results. Further, the values of R² are large for container ships and small for other ship types. The coefficient of determination R² is a measure of the goodness of fit of a regression model and indicates what percentage of the total observed variation in the dependent variable is explained by explanatory variables. Thus, the reason for the differences in the values of R² between ship types is that the variation of C is not considered sufficiently large compared to the uncertainty in the measurement of URN and ship speed.

Ship speed reduction and URN reduction may not be fully correlated. This is because ship speed reduction can include both intentional speed reduction (i.e., slow steaming) and unintentional speed reduction due to disturbances (i.e., speed loss). While the former can contribute to URN reduction, the latter does not contribute URN reduction. Factors that can change the ship speed include disturbances (such as waves, wind, and ocean currents), hull fouling, and slow steaming. Except for slow steaming, the propeller thrust does not decrease, or the cavitation number does not increase Eqs. (9)–(11), so even if the ship speed decreases, the cavitation does not decrease and then the URN is not reduced. Since the speed reduction ratio in this study includes the effects of all the factors that can change the ship speed, the speed reduction coefficients would underestimate URN reduction by slow steaming. This may be the reason why the speed reduction coefficients in this study are smaller than the coefficients by MacGillivray (2019), which is based on the URN measurement with intentional slow down. It is considered that the effect of slow steaming can be captured more accurately when propeller shaft horsepower, which is more directly related to propeller cavitation, is used rather than ship speed.

Three hydrophones were deployed near the shipping lane passing south of Izu-Oshima Island, Japan, for almost four months. The source levels of URN from merchant ships on international voyages that passed close to the monitoring station are reported for 265 ships as the mean value of source levels in the range of 300–1000 Hz estimated from the three hydrophones with the PLs of spherical propagation with the simplified correction factor of the Lloyd's mirror effect.

As a result of the regression analysis and the comparisons with previous studies, the following are shown:

1. the regression analysis shows the source level of the URN from merchant ships for each ship type and its variation with ship length, speed reduction ratio, and draft ratio;

2. the residuals of the regression analysis and the uncertainty of the URN measurement can be considered at a similar level;

3. the source levels of the URN from container ships strongly depend on ship length, while those of bulk carriers and tankers do not;

4. the coefficients for the speed reduction ratio underestimate the URN reduction by slow steaming; and

5. the source levels of the URN from container ships, bulk carriers, and tankers are slightly lower under light load conditions than under fully loaded conditions if the ship speed is the same.

It is because the speed reduction includes both intentional and unintentional slow down that the coefficients for the speed reduction ratio in this study underestimate the URN reduction by slow steaming shown in the previous studies. Therefore, it is considered that the effect of slow steaming can be captured more accurately when propeller shaft horsepower, which is more directly related to propeller cavitation, is used rather than ship speed. If the URN reduction by slow steaming is to be evaluated using ship speed as a direct parameter, URN measurements in and outside of an intentional slow steaming area are considered necessary, as was the case in the study of MacGillivray (2019).

We would like to express great appreciation to all members of the steering committee of the Underwater Radiated Noise by Shipping Project for constructive suggestions and discussions, particularly from Dr. Nobuhiro Hasuike and Dr. Yasuhiko Inukai. We would like to thank the technical staff of Nippon Marine Enterprises, Ltd. and Marine Works Japan Ltd. for designing and deploying the monitoring station. We would also like to thank Messrs. Soma Oizumi and Kengo Yasumoto for their help in the data analysis. This work is supported by the Underwater Radiated Noise by Shipping Project of Japan Ship Technology Research Association in the fiscal years 2020 and 2021 funded by the Nippon Foundation. Furthermore, this work is partially supported by the Fundamental Research Developing Association for Shipbuilding and Offshore (REDAS).