Discrete Distribution Model of Ship Noise Source in Shipping Channel

Ship noise plays an important role in low-frequency ocean ambient noise. With the increasingly busy sea traffic, the randomness of the spatiotemporal distribution characteristics of ship noise is also increasing. However, most ships sail in a relatively fixed range in different sea areas. Most of the previous studies assumed that the ship noise sources in shipping channel satisfy a uniformly distribution, actually all kinds of large ships are not uniformly distributed in the shipping channel, and there are also many small boats distributed on the channel that contribute significantly to low-frequency ocean ambient noise. The channel within a certain sea area will be divided into different regions, and ship information (AIS) in different regions will be analyzed statistically in this paper. It is assumed that the ship noise sources in different channel regions are discrete point noise sources that obey a certain spatiotemporal statistical distribution, combined with the noise source level models of different types of ships to form a discrete source model of ship noise in shipping channel. Using the ray propagation theory considering the horizontal refraction of sound energy, the vertical distribution of the ship noise level in this sea area is calculated, and compared with the vertical noise level distribution of ship noise source uniform distribution model, the variation range of noise level vertical distribution of two models is close calculated noise level (such as maximum and minimum values) is consistent with the measured data. The discrete source model of ship noise established in this paper may provide a technical support for predicting low-frequency ambient noise characteristics near the channel.


Introduction
During World War II, studies on ship noise were first conducted.These studies focused primarily on the effects of frequency, speed, tonnage, and other parameters on the ship noise level.Since then, more indepth study has been done on ship noise since it has been discovered that different ship types have varied noise radiation characteristics, noise generating methods, and even different major frequency ranges of noise excitation.One of the studies on ship noise source level models that is now available is based on the statistical analysis of the observed ship noise data to generate a fitted noise source level formula connected to characteristics like ship speed, tonnage, frequency, etc.The other type is based on a ship's noise-generating mechanism, such as a propeller cavitation and mechanical noise.
Through the statistical analysis of low-frequency ocean ambient noise data, Ross [1] proposed that the low-frequency ocean ambient noise presents an annual growth trend of 0.5 dB, and then analyzed the influence of factors such as speed and frequency on the ship noise source level, summarized the relationship between the sound level and the speed of several types of ships, the speed range is 8 kn~24 kn, and the applicable frequency is above 100 Hz.The obtained ship noise level fitting formula is: In the above formula,   is the speed, the unit is kn, and f(Hz)is the frequency.The above fitting formula of ship noise level is the relationship between frequency and noise level.Ross In the above formula, DT is displacement, and the unit is ton (t).Whether the noise source level formula takes frequency or tonnage as a parameter, the applicable frequency range is above 100 Hz, but the Wenz [2] points out that the main frequency band of ship noise is below 100 Hz.Moreover, as ship technology has advanced and research has gone deeper, ships' speed and displacement have increased significantly.As a result, the Ross noise source level model's applicability has decreased significantly.
Wales and Heitmeyer [3] measured and fitted the ship noise in the Mediterranean Sea, obtained the average noise source level fitting of ships that is only related to the frequency f(Hz), and the applicable frequency band is 30 Hz~1200 Hz : ̅ () = 230 − 35.9 log 10  + 9.17 log 10 (1 In the 1980s, Urick [4] obtained the following noise source level fitting formula based on the measured data of cargo ships, oil tankers and large warships:  = 51  10  + 15  10  − 20  10   + 20  10  − 13.5 In the formula above, V stands for the propeller blade's rotational speed in feet per second, T for displacement,   for frequency, and D for distance in yards.Since obtaining the propeller's speed is typically challenging, Urick transformed the propeller's speed into the ship's speed and then found the formula for fitting using speed as the parameter:  = 60  10  + 9  10  − 20  10   + 20  10  + 35 The unit of speed K is knot.
Researchers in our nation have also put out numerous ship noise source level models in recent years.
Wang Bin [5] et al. analyzed the noise source levels of merchant ships in different China sea areas in recent years, and proposed a formula for ship noise source levels applicable to China sea areas.Peng Zilong [6] used the long-term measured noise data and ship information near the Zhoushan Archipelago to conduct a modeling study on the ship noise in the Zhoushan Archipelago sea area, on the basis of the Ross model and the RANDI-3 model, applicable to the merchant ship sound source level model based on statistical data in the East China Sea.
The ship noise source level model has different empirical formulas according to the distribution types of ship noise sources on the sea surface.Renner [7] divided ships into five categories: fishing boats, merchant ships, oil tankers, large oil tankers and supertankers.The noise source level of different ships are all related to frequency.A model of uniformly distribution of ship noise sources is created under the assumption that the radiated noise from each ship is spread evenly throughout the unit area.However, most studies consider ship noise sources to be randomly distributed point noise sources on the sea surface due to the unpredictability and discreteness of the dispersion of ships.
The U.S. Naval Laboratory [8] proposed the RANDI-2 and RANDI-3 models.The RANDI-3 model is an upgrade over the RANDI-2 model, it classifies ships into five types consistent with the ANDES model, and it can be used to predict the length and speed of each ship using a random uniform distribution function.
When there are shipping channels in concerned sea area, the low-frequency ocean ambient noise model often simplifies the ship noise sources in the channel to the noise sources uniformly distributed in certain area on the sea surface, but in the actual shipping channel, all kinds of large ships on the sea surface are not evenly distributed.The distribution of different small ships in the channel is also random, so the ship noise generated by those ships will also affect the low frequency ocean ambient noise.This is because in the sound propagation research, it is typically assumed that each ship is a non-uniformly distributed discrete point sound source.
It can be seen from the above description that the uniform distribution model of ship noise sources ignores the fact that the actual ship noise sources are similar to discrete point sources.Therefore, this study builds a ship noise sources discrete distribution model in the channel that fulfills certain statistical features based on the statistical analysis of the AIS data of all ships in shipping channels combined with the ship noise source level model.

Ship Noise Sources Discrete Distribution Model
The trajectory map of ships within 10 days during the noise measurement experiment in the South China Sea is shown in Fig. 1.Point A is the location of the receiving array.It can be seen that within 10 days, there are not only two shipping channels that are relatively close to the receiving array, but also a relatively obvious shipping channel within 400km south of the receiving array.The distribution of ship trajectories is used to separate the three shipping channels mentioned above into areas.According to Fig. 2, there are four areas: Areas 1, 2, 3, and 4. The sound speed profile is shown in Fig. 3. ) ， 20 ≤  ≤ 120 211.5 − 10  10 ( 2.9 ) ， 120 ≤  ≤ 1 3. AIS data analysis AIS (ship-borne automatic identification system) usually includes static information such as the MMSI number of the ship, ship type, ship length, and ship width, as well as dynamic information such as speed, course, latitude and longitude, and draft at different times.
When the AIS data is saved simultaneously, there may be omissions due to the information of different small fishing boats, moored or anchored ships, and ships that are in the region under consideration but are not the source of the ship noise.In order to determine the number of two different types of ships in the shipping channel region, ship length, ship draft, and ship speed, it is first essential to preprocess the gathered AIS data of each ship using techniques like sorting, screening, and interpolation.Fig. 4 depicts the precise AIS data processing path.Fig. 4 AIS data processing process (1) Remove AIS data that lacks MMSI numbers.Each ship's "identity information" is represented by its MMSI number.Because many non-ship floating items, including buoys in the water, are also located by AIS equipment, it is hard to tell whether it is a ship or not if the MMSI number is missing.
(2) Using longitude and latitude, filter out the ships that are only present in areas 1 to 4 since these areas already include the majority of the ships sailing in this sea region, and because the occasional ships outside of these areas are not in shipping channels, they are not relevant to statistics.
(3) Eliminate ships with a speed of zero during the initial time of AIS recording, because during the recording process, the speed is always zero, indicating that the ship is in a moored or anchored state.It mostly targets sailing ships, according to earlier investigations.However, when the speed is zero, the engine, propeller, and other components that mostly cause ship noise do not function, thus it is required to eliminate ships with a speed of zero.Although in certain circumstances, the ship is still consuming electricity to function even though it is not moving.
(4) According to the starting time of the same ship in the saved AIS data, the dynamic information of the ship (including time, latitude and longitude, speed, draft) is linearly interpolated at an interval of 1 hour.240 groups information on the number of ships, their captains, their speeds, and their drafts per hour were collected in Area 1~Area 4.
(5) The ships in each area are divided into two classes according on their length: first class ships are those with a length between 0 and 200 meters, while second class ships are those with a length between 201 and 999 meters.Compile information on the quantity, length, speed, and draft of two types of ships in each location on an hourly basis.
(6) The probability density functions of the four major characteristics impacting the noise of the two types of ships in various places are derived by averaging the four types of AIS information acquired for the two types of ships over a period of 10*24 hours.The ship length, number of ships, draft, and speed histograms for Class I ships in Areas 1 to 4 are shown in Fig. 5 (a)-(d).= 1).As a result, the "pseudo-random number" of ship parameters that follow the discrete distribution may be calculated.Each set of "pseudo-random numbers" created comprises the number of ships in the vicinity, the captain, draft, and speed of each specific type of ship.The "pseudo-random number" is inserted into the sound field calculation model and the ship noise source level model, and the distribution of ship noise levels with depth at the receiving array position is computed.
The modeling process of the ship noise source discrete distribution model is shown in Fig. 7.The examination of AIS data reveals that the number of ships of the two categories in various locations is more likely to be zero.The reason for this is that omissions will occur throughout the AIS data collection procedure.The number of ships in each location is zero, implying that there are now no ships in the waterway, which contradicts the realities.To make the calculation results more accurate and reduce the error caused by the omission of AIS data, add 1 to the number of ships generated by the probability distribution in each area during the calculation process, so that the total number of ships in all areas does not equal zero.

Statistical
In the simulation calculation, adopted Bellhop3D to calculate which considered horizontal refraction, the seabed terrain is based on the measured seabed topography of a specific island and reef sea area, and the sea depth is 2400m; the seabed is based on a single-layer seabed substrate model with a constant level, the sound velocity is 1650m/s, and the density is 1.8   3 ⁄ , the attenuation coefficient is 0.517 × ( 1000 ⁄ ) 1.07 , and the unit of f is Hz; the seawater density is 1  3 ⁄ excluding seawater absorption.The sound velocity profile is the Munk profile, and the receiving array is located within a depth range of 265m~885m.
Fig. 8 depicts the simulation results of the 50Hz ocean ambient noise level distribution with depth induced by the ship noise sources discrete distribution model in the channel region.

Fig.8 Simulation results of noise level depth distribution of 50Hz ship noise source discrete distribution model
The noise level distribution with depth is shown in Fig. 8 to be in the range of 65dB~74dB, with an intensity span of 9dB.The values of the fifth and twelfth array elements are rather big, yet the noise level does not appear to rise with depth.
Assuming that the number of ships, captain, speed, and draft are all generated at random using the ship information probability distribution, and that the random values of each variable are then used to calculate the receiving array ship noise level distribution with depth using the ship noise source level model and sound propagation model.The Fig. 8 is only the noise level depth distribution curve calculated by using one random result, so try to perform multiple calculations and take the average method to reduce the intensity span caused by random results, the result after multiple calculations and averaging is shown in the Fig. 9 below: Fig. 9 Ocean ambient noise level distribution with depth after multiple calculations and averaging Fig. 9 are the calculation results of 50 times average, 75 times average and 100 times average of the noise level calculated by using random ship information, and the noise level is still distributed in the range of 62 dB~72 dB , the intensity span after 100 averages is indeed reduced from 9 dB to 8 dB, but relatively speaking, multiple averages have little effect on the calculation results, the noise level at the 5th and 12th array elements is the largest, and there is still a gap of about 9 dB between the maximum and minimum values after multiple averages.Fig. 10 Simulation results of noise level depth distribution of 50Hz ship noise source uniform distribution model within 72 hours Assuming that the ship noise sources are uniformly distributed over the region depicted in Fig. 2, the simulation result of the noise level depth distribution is presented in Fig. 10.Different curves correspond to different numbers of ships within 72 hours.As noted in Fig. 10, there is a 5dB difference between the maximum and lowest curves, the average curve of the simulation results varies between 70 and 72 dB, and the noise level tends to rise as depth increases.
Compared with the ship noise sources uniform distribution model in waterways of islands and reefs, the ship noise point source model only changes the ship noise distribution area and the ship noise source level model in the area, but still uses the reciprocity principle.
In the shipping channel region, it is assumed that there is a point noise source in the unit area derived by dividing the distance step and angle step when utilizing the ship noise sources uniform distribution model for computation.After the noise reaches the receiving array, the sound pressure received by the receiving array elements at different depths is the superposition contribution of all point noise source, and the superposition of point noise source reduces the error caused by factors such as the sound rays horizontal refraction, so the intensity span of the noise level versus depth distribution curve calculated by the ship noise sources uniform distribution model is small.
Although the ship noise source is also taken into account as a point source when using the discrete distribution model for calculation, not all point sources exist in a unit area.Instead, the number of point sources in the area is determined based on the number of ships randomly generated by using the probability distribution, which in turn necessitates knowing where point sources are located.According to the probability distribution of the ship numbers of various types in Areas 1 to 4, it can be deduced that the probability that the ship numbers appear with probability of 1 is high.This is because in the simulation calculation, it is assumed that the point sources are evenly distributed in each area.The location of the sound source is established when there is just one point source of noise in the vicinity.The sound propagation process is also determined when the sound rays released from this location enter the receiving array, therefore each calculation's output looks remarkably similar and covers a wide range of intensities.
Comparing the calculation results of the ambient noise level distribution with depth between the ship noise source discrete distribution model and the ship noise source uniform distribution model, it can be seen that the noise level difference between different array elements calculated by the ship noise source discrete distribution model is larger, however, both of them use the three-dimensional ray algorithm in the calculation and the waveguide environment is the same, so it can be considered that the calculation error is caused by the ship noise source discrete distribution model.

Conclusion
The noise level distribution with depth calculated by discrete distribution model of ship noise source model has a relatively large intensity span, but taking the calculation result of 50 Hz as an example, the noise level depth distribution curve calculated by the ship noise uniform distribution model is distributed in In the range of 64 dB~71 dB, the depth distribution curve of the noise level calculated by the ship noise source point source model is 63 dB~71 dB after 100 averages, which is close to the distribution range of the calculation result of the uniform distribution model.The depth distribution of low-frequency ocean ambient noise level caused by ships in complex terrain sea areas can be estimated.
The reason for the large difference in noise levels between different array elements calculated by using the discrete distribution model of ship noise sources may be that the statistical data samples are insufficient, resulting in the probability density of ship information not fully reflecting the number of ships in the channel and the probability of ship information.Perform statistical analysis on a large amount of AIS data and conduct in-depth research to reduce calculation errors.

Fig. 5 Fig. 6
Fig.5 Histogram of Frequency Distribution of AIS Ship Information for Class I Ships Fig. 6 (a)~(d) are the frequency distribution histograms of ship length, number of ships, draft and speed of Class Ⅱ ships in Areas 1 to Area 4.