A method for evaluating the importance of a port
By clustering and buffer analysis of ship trajectory point data, combined with information entropy and TF-IDF algorithms, the spatial scope and functions of the port area are identified, solving the problem of detailed internal operation of the port area in traditional evaluation methods, and realizing a detailed assessment of the importance of the port area.
Patent Information
- Application Number
- CN202210621542.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-01
- Publication Date
- 2026-02-10
- Estimated Expiration
- 2042-06-01
AI Technical Summary
Traditional port/port area evaluation methods treat ports/port areas as nodes in the transportation network, failing to reflect the specific operational status within ports/port areas and lacking detailed evaluation of the attributes within ports/port areas.
By acquiring ship activity trajectory data, cluster analysis and buffer analysis are used to identify the spatial range of the port area. Combined with information entropy and TF-IDF algorithms, the types and frequencies of ships within the port area are measured, and the functions and importance of the port area are identified.
This allows for a more detailed evaluation of the port area's internal operations, enabling a more accurate demonstration of the port area's actual functions and importance, and improving the comprehensiveness and accuracy of the port area's evaluation.
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Figure CN115062934B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of port area evaluation technology, specifically relating to a method for evaluating the importance of a port area. Background Technology
[0002] Traditional port / port area evaluation methods mainly treat the entire port / port area as a node, evaluating its importance from the perspective of the overall cargo transportation route based on factors such as the degree of concentration and routes of maritime transport. However, since the internal settings of each port / port area are different, evaluating only the overall role of the port / port area in the shipping route is not detailed enough and usually fails to show the specific operation of the port / port area.
[0003] For example, Chinese invention patent application publication number CN108985499A discloses a method for evaluating the importance of ports in a container shipping network based on comprehensive centrality. The method determines the importance of a port in the entire shipping network based on information such as port route information, the number of connection paths between the port and other ports, and path length.
[0004] Therefore, current evaluations of ports / port areas often treat them as transmission nodes in a transportation network, focusing on the extent to which they contribute to the network, while neglecting to study and evaluate the internal attributes of the ports / port areas themselves. Summary of the Invention
[0005] The purpose of this invention is to provide a method for evaluating the importance of a port area, which solves the problem that the existing evaluation method, which only regards the port / port area as a whole as a node in the transportation network, cannot reflect the specific operation of the port / port area.
[0006] To achieve the above objectives, the present invention provides a method for evaluating the importance of a port area, comprising the following steps:
[0007] (1) Obtain the trajectory point data of all ship activities and the navigation trajectory point data of each ship; perform cluster analysis on the trajectory point data of all ship activities, determine the port area based on the clustering results, convert the trajectory points in the port area into a plane, and thus determine the spatial range of each port area.
[0008] (2) Identify the vessel entry behavior based on the navigation trajectory point data of each vessel and the spatial range of each port area obtained in step (1); and statistically analyze the types of vessels that enter the port and the frequency of each type.
[0009] The entry into port refers to the act of causing the ship's navigation trajectory to intersect with the spatial range of the port area; if it is identified that the ship's own navigation trajectory point is within the spatial range of one of the port areas, it is determined that the ship has entered the port area, the ship is regarded as a ship docked in the port area, and the type of the ship is recorded.
[0010] (3) Calculate the information entropy of each port area based on the type of vessel that enters the port and the frequency of the type, and measure the importance of each port area by the value of the information entropy.
[0011] The beneficial effects are as follows: Based on the refined spatial range of different port areas according to the ship aggregation situation, this evaluation method introduces the concept of information entropy. According to the type and frequency of ships berthed in the port area, the richness of ship types berthed in the port area is represented by information entropy to measure the importance of each port area. It can evaluate the importance of port areas from the perspective of port area function, thereby better showing the actual operation of the port area and helping to achieve a comprehensive evaluation of the port area.
[0012] Furthermore, in order to transform the trajectory points after ship trajectory clustering into surfaces and determine the refined port area spatial range, buffer analysis is performed on the trajectory points in each cluster result. A circle with the trajectory point as the center and a set radius is used as the buffer. The buffers generated by the points in the same cluster are merged to form the spatial range of each port area.
[0013] Since the port area exists in a planar form, and the result obtained by trajectory point clustering is a point set, the buffer analysis method described above needs to be used to extract the planar port area from the point set.
[0014] Furthermore, to eliminate the influence of areas where ship navigation tracks converge and ship anchorages are located, and to more accurately identify port areas, after obtaining the spatial range of each port area, it is first determined whether the spatial range of each port area intersects with the coastline; if there is no intersection, the spatial range is determined not to be a port area, and subsequent steps are not continued; if there is an intersection, subsequent steps are continued.
[0015] Since ship routes often intersect during navigation, there may be many ship trajectory points in sea areas with dense routes. These may be misidentified as port areas where ships gather and dock during clustering. Similarly, there may be many ship trajectory points in ship anchorage areas, which may also be misidentified as port areas. Therefore, by taking advantage of the characteristic that port areas usually include wharves on the coastline, we can exclude ship trajectory clusters and ship anchorage areas to improve the accuracy of port area identification.
[0016] Furthermore, to obtain more accurate clustering results, the density-based clustering algorithm DBSCAN was used to perform clustering analysis on the ship activity trajectory point data.
[0017] Furthermore, in order to reflect the internal functional attributes of the port area itself, the port areas are classified according to their main functions, and the functions of the port areas are also identified to determine the most important functions of each port area; the most important functions of the port area are related to the types of ships berthed in the port area and their corresponding entry frequencies.
[0018] Furthermore, to remove interference from unknown types of ship trajectory data and differences in position report frequencies among different types of ships on port area function identification, and to ensure that the main functions of the port area can be inferred from the ship type, the TF-IDF algorithm is used to identify port area functions. The calculation steps for identifying port area functions are as follows:
[0019] Let there be m types of ships T1, T2, T3, …, T m n port areas P1, P2, P3, …, P n So, Hong Kong P i The formula for calculating the TF value of a ship of type j is:
[0020]
[0021] In the formula, The type is T j Ships docked in port area P i The quantity in For Hong Kong area P i The total number of ships docked in China;
[0022] Port Area P i The formula for calculating the IDF value of a ship of type j is:
[0023]
[0024] In the formula, n represents the total number of port areas. For ships including type T j The number of port areas, if none of the port areas contain this type of vessel, then =0;
[0025] Based on the above formula, we can obtain P for the port area. i The formulas for calculating the TF-IDF values of different types of ships are as follows:
[0026]
[0027] After calculating the TF-IDF value of each type of vessel, the function corresponding to the vessel type with the highest TF-IDF value is taken as the most important function of the port area.
[0028] Because different types of ships report their positions at varying frequencies when acquiring navigation data, the port entry frequency of a ship type with a high position reporting frequency will inevitably be higher than that of a ship type with a low position reporting frequency. Therefore, it is not possible to determine the main ship types berthing in a port area by comparing the port entry frequency of one ship type relative to other ship types within the same port area. Instead, it is necessary to compare the frequency of a certain type of ship in a certain port area with its frequency in other port areas. If a ship appears more frequently in a port area and less frequently in other port areas, then that type of ship can be considered to represent the function of that port area.
[0029] Furthermore, the formula for calculating the information entropy of a port area is:
[0030]
[0031] Where n is the number of ship types berthed in the port area, p i The probability of vessel type i docking in this port area is calculated using the following formula:
[0032]
[0033] in n is the number of ship types berthed in the port area; m i Let M be the number of times vessel type i calls at this port area, and M be the total number of times all types of vessels call at this port area.
[0034] The higher the information entropy value, the more diverse the types of ships docked in the port area, and the greater the importance of the port area to the entire port.
[0035] The more types of vessels berthed in a port area, and the more services it can provide to various vessels, the more important that port area is compared to others. Since information entropy can measure the overall probability of various vessel types appearing in a port area and can represent the richness of vessel types in the area, the magnitude of the information entropy value is used to reflect the importance of a port area. Attached Figure Description
[0036] Figure 1 This is a flowchart of the method for evaluating the importance of a port area in an embodiment of the present invention. Detailed Implementation
[0037] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.
[0038] Method Implementation Examples
[0039] This embodiment provides a method for evaluating the importance of a port area, referring to... Figure 1The specific steps are as follows:
[0040] (1) Obtain the trajectory point data of all ship activities and the navigation trajectory point data of each ship.
[0041] One approach is to use an Automatic Identification System (AIS) to record vessel activity trajectories and identify the unique navigation paths of each vessel. Therefore, using AIS to acquire vessel activity trajectory points and corresponding navigation trajectory point data for each vessel provides detailed information about vessel navigation, offering more accurate data for subsequent steps of determining the port area and identifying vessels within it. In other embodiments, GPS positioning or similar methods can also be used to acquire vessel activity trajectory point data and the individual vessel's navigation trajectory point data.
[0042] (2) Perform cluster analysis on the trajectory point data of all ship activities, and determine the port area based on the clustering results.
[0043] After obtaining the trajectory point data of ship activities, since there will inevitably be a large number of docked ships in the port area, this characteristic is used to conduct preliminary identification of the port area.
[0044] In this embodiment, the DBSCAN algorithm is used to extract point clusters of trajectory points generated by ships gathering in the port area from a large number of trajectory points. These point clusters can represent the existence and approximate location of the port area.
[0045] The DBSCAN algorithm is a density-based clustering algorithm that can discover clusters of various shapes and sizes in noisy data. Its specific clustering process works as follows:
[0046] ① Select a trajectory point as a sample from the low-speed ship activity trajectory point data, take this selected trajectory point as the center, draw a circle with radius r as the neighborhood, if the number of trajectory points in the circle is greater than the set density threshold, then all trajectory points in the circle are classified into the same cluster.
[0047] ② Using each trajectory point within the circle as a new center, continue drawing circles with radius r. Calculate the situation of other unclassified trajectory points in these new circles. When the number of trajectory points in a new circle exceeds the set density threshold, add all trajectory points in the new circle to the above cluster. Then, using each trajectory point in the new circle as a new center, repeat the above operation in this step until no new trajectory points are added, thus completing the division of a cluster.
[0048] ③ Continue to select samples from the remaining unclassified trajectory points and repeat steps ①-② above until all trajectory points with sufficiently high cluster density are divided into different clusters. These point clusters are the trajectory point clustering results.
[0049] Density-based clustering algorithms can accurately identify clustered areas of ship trajectory points, discard loosely distributed trajectory points, and avoid the impact of trajectory points outside the port area on port area identification.
[0050] In other embodiments, other clustering algorithms can also be used to obtain clustering results to identify the existence of the port area and preliminarily determine its location.
[0051] (3) Convert the trajectory points in the port area into a plane to determine the spatial range of each port area.
[0052] After clustering, the ship trajectory points are divided into various clusters, revealing the aggregation of ship activities in the port. However, the port area, as a region, has a certain spatial extent and exists in a planar form. Therefore, it is necessary to transform the clustered points into planar areas, and use the obtained planar areas as the port area boundaries.
[0053] In this embodiment, buffer analysis is mainly used to transform the point clusters obtained by clustering the ship's trajectory points into planar regions. Buffer analysis specifically refers to automatically creating a buffer polygon layer within a certain width around point, line, and surface entities. It is an important spatial analysis function, often used for boundary delimitation. In this embodiment, after clustering the ship's trajectory points, the trajectory points in each cluster are used as buffer objects. A circle with a certain radius is drawn with the trajectory points in the cluster as the center to form a buffer. Then, the buffers generated by the trajectory points within the same cluster are merged. By combining these buffers, each point cluster can form a complete planar region, which is considered the spatial range of a port area.
[0054] In this embodiment, after obtaining the set of trajectory points clustered in the port area through a clustering algorithm to preliminarily determine the approximate location of the port area, the spatial range of the port area is extracted based on buffer analysis to complete the extraction of the spatial range of the port area.
[0055] Since ship routes often intersect, potentially generating a dense cluster of intersection points, and ships also create numerous clustered trajectory points in anchorage areas, the port area obtained using the aforementioned clustering extraction method will include both anchorage areas and route clustering areas. Therefore, after obtaining the port area spatial range, the characteristic that a port area inevitably includes wharves located on the coast can be utilized to remove anchorage areas by determining whether the obtained port area spatial range intersects with the coastline. That is, after obtaining the spatial range of each port area, first determine whether the spatial range of each port area intersects with the coastline; if there is no intersection, the spatial range is determined not to be a port area, and subsequent steps are not continued; if there is an intersection, subsequent steps are continued.
[0056] (4) Based on the spatial range of each port area obtained from the ship activity trajectory point data, identify the ship entry behavior, and statistically analyze the types of ships that enter the port and the frequency of the types.
[0057] Having already acquired the navigation trajectory data of each vessel, if a vessel enters the port, its navigation trajectory will inevitably intersect with the spatial range of the port area, and a portion of the vessel's navigation trajectory points will inevitably appear within the port area. Therefore, by statistically analyzing the frequency of vessels entering a port area within a certain time period, we can characterize the berthing situation of vessels in that port area during that time period. Similarly, when recording frequencies, we can categorize and statistically analyze them according to vessel type, that is, statistically analyze the entry frequency of various types of vessels in each port area, thereby obtaining the berthing situation of different types of vessels in each port area during that time period. When a vessel's navigation trajectory point is identified as falling within the spatial range of one of the port areas, it is determined that the vessel has entered the corresponding port area, and the vessel is considered to be berthed in the port area, and its type is recorded.
[0058] Based on the frequency of port entry for various types of vessels in each port area as statistically analyzed in the above process, the functions of the port areas can be evaluated and identified, thereby reflecting the internal functional attributes of the port areas and classifying them from the perspective of their main functions. Since different types of vessels will berth in port areas with different functions, such as commercial ports berthing more cargo ships and industrial ports berthing more oil tankers, statistical analysis of the vessels berthed in a port area can determine the functional type of the port area.
[0059] Traditional statistical methods derive port area functions based on the number of trajectory points of different types of vessels berthed within the port area. However, in practical applications, the acquired vessel trajectory point data may contain many data points where the vessel type cannot be determined. Furthermore, different types of vessels have significantly different position reporting frequencies; for example, oil tankers report positions more frequently than fishing vessels. Vessels with higher position reporting frequencies will inevitably be counted as having more port entry times than those with lower frequency. This can lead to situations where the number of port entry times for vessels with high position reporting frequencies but few actual entries is similar to the number of times they actually enter the port, making it difficult to represent the true number of port entry times. Therefore, this embodiment employs the TF-IDF (Term Frequency-Inverse Document Frequency) algorithm to statistically analyze the types of vessels active within the port area.
[0060] The TF-IDF algorithm can accurately filter known ship types for function identification analysis, eliminating the influence of unknown ship types. It compares the frequency of a certain type of ship in a specific port area with its frequency in other port areas. If a ship appears more frequently in the port area than in other port areas, then the function corresponding to that type of ship can be considered the primary function of that port area, eliminating the influence of different ship position reporting frequencies. The calculation steps of the port function identification method based on the TF-IDF algorithm are as follows:
[0061] Let there be m types of ships T1, T2, T3, …, T m n port areas P1, P2, P3, …, P n So, Hong Kong P i The formula for calculating the TF value of a ship of type j is:
[0062] (1)
[0063] In the formula, The type is T j Ships docked in port area P i The quantity in For Hong Kong area P i The total number of ships docked in China;
[0064] Port Area P i The formula for calculating the IDF value of a ship of type j is:
[0065] (2)
[0066] In the formula, n represents the total number of port areas. For ships including type T jThe number of port areas, if none of the port areas contain this type of vessel, then =0;
[0067] Based on the above formula, we can obtain P for the port area. i The formulas for calculating the TF-IDF values of different types of ships are as follows:
[0068] (3)
[0069] After calculating the TF-IDF value of each type of vessel, the function corresponding to the vessel type with the highest TF-IDF value is taken as the most important function of the port area.
[0070] (5) Calculate the information entropy of each port area based on the type of vessel that enters the port and the frequency of the type, and measure the importance of each port area by the value of the information entropy.
[0071] The formula for calculating the information entropy of a port area is as follows:
[0072] (4)
[0073] Where n is the number of ship types berthed in the port area, p i The probability of vessel type i docking in this port area is calculated using the following formula:
[0074] (5)
[0075] in n is the number of ship types berthed in the port area; m i Let M be the number of times vessel type i calls at this port area, and M be the total number of times all types of vessels call at this port area.
[0076] When the types of ships berthed in a port area are relatively homogeneous, the entropy value will be relatively small, and the port area will have a relatively singular function. For example, the ships berthed in a certain fishing port are usually fishing boats. Conversely, a comprehensive port area has diverse functions and can provide services for different types of ships. That is, the types of ships berthed in the port area are relatively diverse, and the entropy value will be relatively large.
[0077] Therefore, the higher the information entropy value, the more diverse the types of ships berthed in the port area, and the greater the importance of that port area to the entire port. The more types of ships berthed in a port area, the more services that port area can provide to various types of ships, and the more important that port area is compared to other port areas. Since information entropy measures the overall probability of various ship types appearing in a port area and represents the richness of ship types within the region, the magnitude of the information entropy value reflects the importance of a port area.
[0078] The following uses the port areas of Quanzhou Port and Kaohsiung Port as examples. Using the AIS datasets from September to October 2017 for the Kaohsiung Port waters (118.5°E~119.1°E, 24.6°N~25.1°N) and the Quanzhou Port waters (117.25°E~119.05°E, 24.30°N~25.56°N) as vessel berthing data for Kaohsiung and Quanzhou Ports, the above method is applied for functional identification and importance evaluation analysis.
[0079] Since ships are basically stationary when anchored in the port area and their sailing speed is low, this paper only selects ship trajectory points with a speed of less than 1 knot / h for port area extraction. A large number of trajectory points are clustered near the coastline, showing obvious spatial clustering distribution characteristics.
[0080] After acquiring vessel trajectory data, a port area extraction experiment was conducted on Quanzhou Port and Kaohsiung Port using a port area extraction method combining the DBSCAN algorithm and buffer analysis. Since vessels also generate numerous low-speed trajectory points in anchorage areas, the vector range obtained by the port area extraction method includes the anchorage area. After obtaining the vector range, the anchorage area can be removed by checking if the vector range intersects with the coastline. The port area extraction results for Kaohsiung Port constitute one port area range. The port area extraction results for Quanzhou Port contain a total of 22 port area ranges.
[0081] After obtaining the spatial range of each port area in Quanzhou Port and Kaohsiung Port, the ship entry activity identification method is used to identify ships entering the port area, and the ship entry activities are counted. Then, TF-IDF is used to identify the spatial functions of the port area, and information entropy is used to evaluate the importance of the port area.
[0082] From September to October 2017, a total of 16 types of vessels entered Kaohsiung Port for operations, totaling 5,182 voyages. The types of vessels operating in Kaohsiung Port are shown in Table 1. Cargo ships and oil tankers are the main vessels operating in Kaohsiung Port, accounting for more than 55% of the total. The information entropy of Kaohsiung Port is calculated to be 0.564, indicating that it is a complex commercial port.
[0083] Table 1 Types of Vessels Entering Kaohsiung Port
[0084]
[0085] Based on port entry activities, between September and October 2017, a total of 19 types of vessels operated in 22 port areas of Quanzhou Port, making a total of 7,995 voyages.
[0086] After identifying vessel entry activities, the types of vessels operating within the 22 port areas were statistically analyzed, using voyages as the unit. Port areas 11, 12, and 19 showed a high number of cargo ship activities, indicating they are commercial ports. Port areas 2 and 4 showed a high number of oil tanker activities; oil tankers, as important industrial goods transport vessels, indicate these two port areas are key industrial ports in Quanzhou. Port areas 16 and 17 showed a high number of fishing vessel activities, indicating these two port areas are primarily fishing ports.
[0087] To identify the spatial functions of ports, this paper uses the TF-IDF algorithm to identify port area functions and evaluates the importance of port areas based on information entropy. The analysis results for Quanzhou Port are shown in Table 2.
[0088] Table 2 Comprehensive Evaluation of Quanzhou Port
[0089]
[0090] Based on the TF-IDF algorithm and information entropy calculations, it was found that most of Quanzhou Port's port areas are small fishing ports primarily used by fishing boats, while the commercial and industrial ports, mainly used by cargo ships and tankers, have a higher degree of integration. This indicates that commercial and industrial ports have higher port area classifications and are more important to the overall port, accommodating various types of vessels. Fishing ports, on the other hand, are typically designed specifically for fishing boats, and the vessels operating in fishing ports are usually only fishing boats. Their economic status is far lower than that of commercial and industrial ports, hence their lower port area classification. Meizhou Bay and Quanzhou Bay also have port areas primarily used by law enforcement vessels, suggesting that these two port areas likely house dedicated maritime law enforcement management agencies.
[0091] This invention, based on the refined spatial range of different port areas obtained according to the ship aggregation situation, can eliminate the influence of interference factors and improve the accuracy of port area spatial range identification. According to the type and frequency of ships berthed in the port area, the port area is classified from the functional level. Furthermore, the concept of information entropy is introduced. The importance of each port area is measured by the richness of ship types berthed in the port area, which is represented by information entropy. This allows for the evaluation of the importance of port areas from the perspective of port area function, thereby better demonstrating the actual operation of the port area.
[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.
Claims
1. A method for evaluating the importance of a port area, characterized in that, Includes the following steps: (1) Obtain the trajectory point data of all ship activities and the navigation trajectory point data of each ship; perform cluster analysis on the trajectory point data of all ship activities, determine the port area based on the clustering results, convert the trajectory points in the port area into a plane, and thus determine the spatial range of each port area; after obtaining the spatial range of each port area, first determine whether the spatial range of each port area intersects with the coastline. If there is no intersection, the spatial range is determined not to be a port area, and the subsequent steps are not continued; if there is an intersection, the steps (2) are continued. (2) Identify the ship entry behavior based on the ship activity trajectory point data and the spatial range of each port area obtained in step (1); The types of vessels that enter the port and the frequency of each type are statistically analyzed for each port area. The term "entry into port" refers to the act of causing the ship's navigation trajectory to intersect with the spatial scope of the port area. If a vessel's own navigation trajectory point is detected within the spatial range of a port area, it is determined that the vessel has entered the port area, and the vessel is regarded as a vessel docked in the port area, and the type of the vessel is recorded. (3) Calculate the information entropy of each port area based on the type of vessel that enters the port and the frequency of the type, and measure the importance of each port area by the value of the information entropy.
2. The port area importance evaluation method according to claim 1, characterized in that, In step (1), buffer analysis is performed on the trajectory points in each cluster result. The buffer is a circle with the trajectory point as the center and the radius set. The buffers generated by the points in the same cluster are merged to form the spatial range of each port area.
3. The method for evaluating the importance of a port area according to claim 1, characterized in that, In step (1), the density-based clustering algorithm DBSCAN is used to perform cluster analysis on the ship activity trajectory point data.
4. The port area importance evaluation method according to claim 1, characterized in that, In step (2), the method also includes identifying the functions of the port area and determining the most important functions of each port area. The most important functions of the port area are related to the types of ships docked in the port area and their corresponding entry frequencies.
5. The port area importance evaluation method according to claim 4, characterized in that, The TF-IDF algorithm is used to identify port area functions. The calculation steps for identifying port area functions are as follows: Let there be m types of ships T1, T2, T3, …, T m n port areas P1, P2, P3, …, P n So, Hong Kong P i The formula for calculating the TF value of a ship of type j is: ; In the formula, The type is T j Ships docked in port area P i The quantity in For Hong Kong area P i The total number of ships docked in China; Port Area P i The formula for calculating the IDF value of a ship of type j is: ; In the formula, n represents the total number of port areas. For ships including type T j The number of port areas, if none of the port areas contain this type of vessel, then =0; Based on the above formula, we can obtain P for the port area. i The formulas for calculating the TF-IDF values of different types of ships are as follows: ; After calculating the TF-IDF value of each type of vessel, the function corresponding to the vessel type with the highest TF-IDF value is taken as the most important function of the port area.
6. The method for evaluating the importance of a port area according to claim 1, characterized in that, The formula for calculating the information entropy of a port area is: ; Where n is the number of ship types berthed in the port area, p i The probability of vessel type i docking in this port area is calculated using the following formula: ; in n is the number of ship types berthed in the port area; m i Let M be the number of times vessel type i calls at this port area, and M be the total number of times all types of vessels call at this port area. The higher the information entropy value, the more diverse the types of ships docked in the port area, and the greater the importance of the port area to the entire port.
Citation Information
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