Intelligent Detection of 3D Anchor Position Based on Monte Carlo Algorithm (2024)

1.1. Background

In recent years, the world shipping market has witnessed rapid development, with an increase in the volume of oil, bulk cargo, and container shipment year by year. This growth is accompanied by noticeable trends toward largescale, deepwater, and intelligent ships. The flourishing maritime industry has led to continuous growth in port throughput, accompanied by improvements in both the speed and quality of port development. Anchorage, as a fundamental requirement and vital infrastructure for maritime development, plays a crucial role in enhancing port efficiency, ensuring that navigational channels remain clear, and promoting safe navigation. With the escalating demand for maritime transportation in commercial trade, the efficient and secure operation of anchorages has become an essential task.

As a major maritime nation, China is actively promoting the development of intelligent ship technology. The China Classification Society (CCS) has outlined the “Specifications for Intelligent Ships”, which define intelligent ship technology as the automatic perception and acquisition of data and information about the ship, the maritime environment, logistics and ports through the use of sensors, communication and Internet of Things (IoT). On the basis of computer technology [1], auto-control technology [2], and big data mining and analytics [3,4], intelligent ships are capable of achieving intelligent operations in ship navigation [5], management [6], maintenance [7], and cargo transportation [8]. These advancements aim to enhance ship safety, environmental friendliness, cost-effectiveness, and reliability. Consequently, research on intelligent ship technology plays a crucial role in facilitating the digital transformation and smart development of the maritime industry.

1.2. Literature Review

The study of various resources in the port systems, such as anchorages, waterways, berths, sizes of loading and unloading equipment and transportation equipment, has received considerable attention by researchers. The existing literature related to anchorage is usually based on optimization algorithms or models for anchorage allocation and planning, anchorage capacity design, and so on.

Regarding the allocation of ship anchorages, Malekipirbazari et al. [9] optimized the algorithm and introduced a heuristic algorithm to modify the maximum null priority algorithm to optimize space utilization. The study of Madadi, Bahman et al. [10] further considered the temporal dynamics by taking into account ship arrivals and departures and dynamically placing them in the polygonal anchorage and proposed a spatiotemporal approach to solve this multi-objective anchorage planning problem. Huang et al. [11] focused on the nature of anchorage utilization capacity and argued that the utilization capacity of an anchorage depended on the selection of the actual anchorage position of a ship. Oz et al. [12] built on Huang’s work and for the first time, considered a ship’s anchorage safety while studying the anchorage allocation problem. Their algorithm significantly improved the safety of anchor position allocation while mainly maintaining a similar level of utilization. In addition, a few researchers have also studied anchorage construction and mooring planning from the perspectives of marine space planning [13] and mooring system [14] as a way to further optimize ship anchorage allocation. In recent years, Cao et al. [15] introduced an innovative intelligent detection algorithm specifically designed for the anchorage areas of maritime autonomous surface ships (MASSs) that are single-moored. They enhanced both the mooring radius model and the safety distance model for moored vessels, significantly advancing the intelligent development of anchorage allocation technology. Zhao et al. [16] proposed a dynamic multi-objective optimization model for anchor position allocation, which not only considered the dynamic change of anchorage occupancy, but also took into account the dual objectives of safety and capacity maximization, and realized the efficient and safe use of anchorage resources by optimizing the arrangement of vessel positions.

In terms of anchorage capacity design, Park et al. [17] calculated the anchorage operation rate of the port through the Anchorage Operation Rate model (AOR model) and evaluated the available anchorage capacity. Kwon et al. [18] proposed the concept of “anchorage capacity index”, which provides a more scientific and accurate method for planning the number of terminals in the port, through the refined calculation of the berthing demand of the incoming ships according to the tonnage. This index provides a more scientific and reasonable basis for the planning of the number of port terminals, and solves the problem of only studying the adequacy of designated berths without considering the expansion of berthing capacity. Guo et al. [19] proposed a new multi-objective optimization model of maximum anchorage capacity reliability and minimum anchorage redundancy area from the uncertainty of inbound and outbound ship sizes and arrival times, which solved the problem of the fact that the actual capacity that can accommodate ships is lower than the designed capacity.

Researchers have studied anchorage allocation from different perspectives, and the core objective is to optimize the utilization efficiency of anchorage resources so as to improve the smoothness of ship operations and economic benefits. However, the key to achieve this goal not only lies in the spatial allocation of anchorage, but also involves the design of anchorage capacity. A reasonable design of anchorage capacity can ensure that ships can be safely and stably anchored under various sea conditions, which in turn can support an efficient and orderly anchorage allocation system, forming a virtuous circle and jointly promoting the overall effectiveness of port operation.

1.3. Discussion of Previous Methods

In summary, the existing studies on ship anchorage mainly focuses on two aspects: (1) the problem of anchor position allocation on how to maximize the utilization rate and reduce the risk of ship collision in the limited anchorage space and (2) the problem of how to maximize the capacity of anchorage and improve the operation rate of anchorage. So far, only a few studies have considered the problem of anchorage detection, and there are fewer studies on the anchorage area of ships and intelligent anchor position detection, and even fewer works on anchor position detection in three-dimensional space considering the influence of water depth conditions. In addition, the available studies are unable to address the demands of the development of intelligent ship technology; furthermore, the anchor position selection of ship anchoring needs to be supported by accurate detection methods.

In practical maritime operations, ships must possess the capability to detect suitable anchor positions at the starting and destination ports, as well as along the navigation route, to meet various needs such as emergencies, cargo handling, embarkation and disembarkation of personnel, and anchoring. Currently, traditional methods for selecting ship anchor positions rely on limited factors, such as empirical judgments based on ship distribution, water depth, seabed conditions, and weather conditions, leading to low accuracy and poor real-time performance. Consequently, these methods fail to meet the requirements of modern maritime practices. In practice, to ensure the safety of ship anchoring, larger anchorage radii are often chosen, resulting in the inefficient use of anchorage resources. Conversely, selecting too small anchorage radii poses potential risks. At the same time, the limited availability of deepwater berths in many harbors has resulted in large vessels having to operate offshore at anchor, resulting in congested anchorages, as depicted in Figure 1. During periods of high wind speeds, the risk of dragging anchors due to tidal fluctuations increases, posing safety concerns for anchored vessels and necessitating emergency evasive maneuvers. Moreover, ships may encounter situations requiring anchoring in both shallow and deep waters during their operations, and from a seafarer’s perspective, “consideration should be made of the depth of water, the type of stranding site, and the removal of submerged obstructions”. A poorer holding ground increases the risk of anchor-dragging [20]. However, existing anchor position detection methods often overlook water depth conditions, leading to a reduced detection accuracy or failure in complex underwater environments, while some existing technologies can provide anchor position detection that accounts for both surface conditions and water depth, leading to practical issues such as low anchoring precision and significant safety hazards during operations. As a result, there is a lack of scientific and universally applicable anchor positioning techniques for different water depth conditions. The rational planning and selection of anchored locations by vessels to maintain safety during anchoring operations represent a significant challenge for ship intelligent detection technologies. This study aims to address these challenges and develop advanced anchor positioning techniques, incorporating judgments of anchorage water depth into consideration alongside ship size and distribution, which will enhance the accuracy of ship anchor position selection, aligning with practical navigation needs and playing a crucial role in maximizing anchorage resource utilization.

The emergence of 3D ship anchor position intelligent detection methods can effectively provide assistance to vessels in swiftly identifying suitable anchor positions during emergencies, mitigating the impacts and losses caused by upstream vessel drag-offs. It also improves the efficiency and safety of marine operations and plays a vital role in maximizing the use of anchorage resources.

2.1. Monte Carlo Stochastic Algorithm

Monte Carlo stochastic algorithm is a computational method based on probabilistic statistics, which is widely used in various engineering fields. The simulation method is realized by a large number of simple repeated sampling, which is less impacted by the limitations of the problem circ*mstances. It features simplicity and ease of programming, providing relatively accurate solutions. The Monte Carlo stochastic simulation method finds extensive application across various fields, such as the ship lock navigation condition restriction model [21], workspace analysis of robotic arms [22,23,24], reliability analysis in geotechnical engineering [25], risk analysis in hazardous material transportation [26], risk analysis in transportation systems [27], etc. The problem of ship anchorage area detection shares the same scientific principle as solving these engineering problems, which involves simulating multiple uncertain factors through random sampling under given input conditions to ultimately obtain comprehensive and reliable analytical results. Therefore, by drawing on the successful applications of the Monte Carlo method in other engineering fields, the rationality and feasibility of using this method for ship anchorage area detection can be justified.

In this study, the algorithm simulates various factors within the anchorage area, such as ship positions, by generating random numbers to obtain a range of possible outcomes. By repeating the simulation calculations multiple times, a stable anchor position can be obtained, which serves as a basis for accurately detecting suitable anchor positions in subsequent steps. In addition, the Monte Carlo stochastic algorithm is also used to randomly sample points within the area to calculate the feasibility of the ship anchoring at different positions. Through repeated simulation calculations, the optimal anchor position can be determined, thereby avoiding anchor accidents and vessel damage caused by insufficient or excessive water depths.

2.2. Anchor Position Circle Radius Model and Safe Spacing Model

Different countries and regions have different standards for outgoing chain length, and the outgoing chain length of Chinese moored ships is the largest under different water depths, which is the most conservative and safe, as shown in Table 1. Therefore, this study adopts a simplified model for anchoring radius based on the standard of outgoing chain length of Chinese anchored vessels.

2.3. Anchoring Area Detection Model

2.4. Safe Water Depth Model

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 $\left(x_1,y_1\right)$, $\left(x_2,y_2\right)$……$\left(x_n,y_n\right)$, mark the set of coordinates as $S_b$, 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 $R_d$ of the restricted water area with a set of coordinates $S_d$.

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 $D$ 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 $S_m$. 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 $S_b$ and $S_m$ are iteratively calculated to obtain the two-dimensional coordinates $\left(X_{e1},Y_{e1}\right)$, $\left(X_{e2},Y_{e2}\right)$……$\left(X_{ei},Y_{ei}\right)$……$\left(X_{en},Y_{en}\right)$ of the anchoring points of the ship to be anchored that satisfy the value $D$ of the ship’s safety spacing in Step 4, and the coordinate set of which is $S_e$.

Step 7: Using $S_e$ 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. $\left(x_r,y_r,h_r,1\right)$ stands for where the safety water depth limit is met, while $\left(x_r,y_r,h_r,0\right)$ represents points where it is not met. $\left(x_r,y_r,h_r\right)$ represents the sampling point, and the data of the water depth verification operation is incorporated into the collection $S_{S1}$. When the second random sampling is conducted, the sampling point is compared with the data points in the collection $S_{S1}$, and if there is such a data point, then the water depth verification data are taken directly. For the points with no data in $S_{S1}$, then the data values are incorporated into the collection $S_{S2}$ after water depth verification. Compare the collection $S_{S2}$ 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 $S_f$, and judgment $S_f$ within the coordinates of the point as the center of the circle within the anchoring circle is not within the point collection $S_d$. When the requirements of the point collection are met, this is recorded as $S_g$, and the following are subsequently marked: $\left({\phi }_1,{\lambda }_1,h_1\right)$, $\left({\phi }_2,{\lambda }_2,h_2\right)$……$\left({\phi }_i,{\lambda }_i,h_i\right)$……$\left({\phi }_m,{\lambda }_m,h_m\right)$. 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.