3.1. Procedure
To verify the validity of the Monte Carlo anchor area detection model, simulation experiments are conducted following the specific steps outlined below, and
Figure 2 shows the model-solving logic.
Step 1: Construct a three-dimensional anchorage area of size 3n nautical miles by 3n nautical miles using MATLAB simulation software (version R2021a), where the water depth ranges from 20 to 40 m.
Step 2: Obtain obstacle information within the anchorage area and the two-dimensional coordinates of existing ships using information acquisition equipment such as Automatic Identification System (AIS) or radar equipment; denote the coordinates as , ……, mark the set of coordinates as , and import this information into an improved ship anchoring radius model to calculate the anchoring radius of existing ships.
Step 3: Using the two-dimensional coordinates of the anchorage obstacle from step 2 as the center of the circle, set a safe radius of the restricted water area with a set of coordinates .
Step 4: Input relevant information such as ship length and anchor chain length of existing ships into the safety spacing model as shown in Equation (2) or Equation (3) to calculate the anchoring radius and ship safety spacing value of existing ships.
Step 5: Use the Monte Carlo random plane anchor position detection algorithm to generate n sets of two-dimensional coordinates, which represent the choice of anchor points for ships awaiting anchor by the simulated ship to be moored, and the set of these coordinates is denoted as . The essence of the algorithm is to perform anchor position detection in the plane by random sampling in the horizontal plane to simulate the vessel position according to the characteristics of the Monte Carlo stochastic algorithm.
Step 6: Utilize the anchoring area detection model shown in Equation (4), the coordinate sets and are iteratively calculated to obtain the two-dimensional coordinates , ………… of the anchoring points of the ship to be anchored that satisfy the value of the ship’s safety spacing in Step 4, and the coordinate set of which is .
Step 7: Using
as the center and the anchoring radius as the radius, draw an anchor position circle. Within the anchor location circle, the anchor location circle was sampled using a Monte Carlo random sampling water depth detection. The principle of this method is to use the random function to set the angle and radius of the simulated sampling point, and subsequently use the polar coordinate formula to calculate the coordinates of the extracted point in the plane right-angled coordinate system to complete the random sampling of the anchor position circle, and then detect the water depth. After the first random sampling, add the water depth verification results of the sampled points as an additional data dimension, indicating whether the water depth meets the requirements.
stands for where the safety water depth limit is met, while
represents points where it is not met.
represents the sampling point, and the data of the water depth verification operation is incorporated into the collection
. When the second random sampling is conducted, the sampling point is compared with the data points in the collection
, and if there is such a data point, then the water depth verification data are taken directly. For the points with no data in
, then the data values are incorporated into the collection
after water depth verification. Compare the collection
with the draft depth values of vessels awaiting anchor to obtain anchoring points for vessels that satisfy both two-dimensional and three-dimensional depth requirements. The point collection is recorded as
, and judgment
within the coordinates of the point as the center of the circle within the anchoring circle is not within the point collection
. When the requirements of the point collection are met, this is recorded as
, and the following are subsequently marked:
,
……
……
. The data set relationship is shown in
Figure 3.
Step 8: Convert the three-dimensional anchoring point coordinates obtained in Step 7, which satisfy safety spacing and water depth restrictions, into anchoring points understood by ship position sensors, and transmit these coordinates to electronic charts or other relevant devices for ships awaiting anchor to select suitable positions for anchoring operations as practically needed.
3.2. Parameter Setting
In order to evaluate and compare the influence of different types of ships on anchor position selection, this study constructs an anchoring simulation system. In this system, using real data from the ship’s design-type scale and synthetic data obtained through Monte Carlo simulation, a three-dimensional intelligent anchor position detection algorithm combining the Monte Carlo random plane anchor position detection algorithm with Monte Carlo random sampling depth detection is experimentally applied to determine the anchor position selection for the ship to be anchored.
In this experiment, a three-dimensional anchorage sea area of 3 nautical miles ∗ 3 nautical miles is defined by MATLAB program. The depth of the anchorage is determined with reference to the anchorage depth data of Ningbo Zhoushan Port, which is one of the top three of the top ten ports in the world. Ningbo Zhoushan Port is known for its rich anchorage resources, with a wide range of depths, from shallow to deep, ranging from 3 to 51 m. Considering the anchoring needs and safety of large commercial vessels, a water depth between 20 m and 40 m is particularly suitable, which can ensure the stable anchoring of the vessels and avoid the inconvenience of operating in too deep water. Therefore, this study carefully constructs a three-dimensional simulation of the mooring area, focusing on the 20-to-40-m water depth section, based on the detailed anchorage depth data of Ningbo Zhoushan Port, to accurately match and meet the actual needs of most commercial vessels.
The ship types selected for the experiments of this thesis are closely based on the common ship types in the inter-provincial coastal freight ship capacity analysis report authoritatively released by the government. Meanwhile, in the current shipping market, bulk carriers and container ships have the largest transportation volume and a high demand for ships. By referring to the relevant data from government websites and the current market trends, we are able to ensure that the ship types selected in the experiment match the current development trends and actual needs of the shipping industry, which ensures the academic rigor of this study. Specifically, we chose chemical tankers, oil tankers, bulk carriers and container ships, and the specific ship type scales are shown in
Table 2.
The anchoring area detection is simulated using MATLAB based on the ship data in
Table 2 and the anchor position circle radius model and safe spacing model. Both existing ships in the anchorage and ships waiting to anchor belong to the four types mentioned above. The spacing between the existing ships in the anchorage adheres to the required safety distance standards for anchoring. In addition, under the two wind conditions of wind force ≤ 7 and wind force > 7, combined with the two water depth models of 20 m and 40 m, four types of ship safety spacings can be calculated.
Table 3 and
Table 4 present two groups of anchoring detection data with wind force ≤ 7, while
Table 5 and
Table 6 present two groups of anchoring detection data with wind force > 7.
According to maritime experience, when a ship is sailing in ballast condition, the minimum average draft should be at least 50% of the full load draft; during winter navigation, due to larger waves and winds, it should be between 55% and 60%. These reference data are summarized from the practical experience of ship drivers and are also provided as guidance parameters in the nautical literature [
32]. Therefore, in this study, 50% of the full load draft is taken as the calculated value for the draft in ballast condition. In accordance with the data in
Table 2 as well as the safety depth model, the demand for safe water depth during ship anchoring is calculated, as shown in
Table 7.
3.3. Results
The above-mentioned data are imported into the MATLAB simulation platform, and the simulation experiments are carried out according to the above steps. The Monte Carlo random simulation algorithm is utilized for simulation and arithmetic operation to detect the ship anchoring areas that meet the requirements for safe spacing and safe water depth. The PLOT function is used to project the areas satisfying the conditions for ship anchoring onto the seafloor in green shading and rendered into three-dimensional graphics. Additionally, 40 three-dimensional images of anchor position detection can be calculated from four sets of data in this experiment.
Figure 4,
Figure 5,
Figure 6 and
Figure 7 randomly provide eight anchor position detection images randomly extracted. Among them, the red dots in the figure simulate the existing ships, while the blue dots represent the drop anchor points that meet the two-dimensional conditions and satisfy the water depth restriction in the unloaded state. The pink dots represent the drop anchor points that further satisfy the water depth restriction in the full load state on the basis of the blue dots. The green dots indicate the drop anchor points that satisfy the conditions for both being generated within the anchoring circle and meeting the water depth requirements, based on the pink dots.
Figure 4 and
Figure 5 are the 3D detection images of different ship types in the case of a water depth of 20 m and wind force less than 7 and wind force more than 7, where a and b are the different sizes of the ship types. And between
Figure 4 and
Figure 5 are the different wind speeds, from which it can be seen that the larger the ship type, the fewer the points that meet the requirements, and similarly the larger the wind speed, the higher the requirements for the safety distance, and therefore the fewer the points that meet the requirements.
Figure 6 and
Figure 7 are different from
Figure 4 and
Figure 5 in that the ambient water depth is changed from 20 m to 40 m, and again, the larger the ship size and the higher the wind speed, the fewer the number of points that meet the requirements. However, compared to
Figure 4 and
Figure 5, a large number of green points can be clearly seen in
Figure 6 and
Figure 7, which indicates that there are a large number of drop anchor points that satisfy both the safety distance between planar anchor circles and the water depth requirements. This indicates that the ambient water depth becomes deeper and the number of points meeting the requirements increases.
Based on this experiment, it is possible to find out the effect of different boat sizes and load conditions on the anchoring position. The general conclusion is that the larger the boat size and the higher the wind speed, the higher the need for safe distance and water depth.