Adaptive time-space dimension ship frequent activity area extraction method

Abstract

The present application belongs to the technical field of ship AIS data clustering, and designs an adaptive time-space dimension ship frequent activity area extraction method, which is used to solve the problem that the current extraction method of frequent activity area only focuses on the spatial information of trajectory data and ignores the time information, resulting in the extracted frequent activity area being not accurate enough. The method comprises the following steps: S1) preprocessing the ship AIS data; S2) extracting the single time-space granularity ship frequent activity area by using the grid density peak value clustering algorithm; and S3) extracting the multi-time-space granularity ship frequent activity area. The present application adopts an adaptive time-space dimension ship frequent activity area extraction method, which can extract the ship frequent activity area by clustering analysis under the premise of ensuring that the ship AIS data information is relatively complete. Compared with the traditional ship frequent activity area extraction method, the present application can more effectively extract the ship frequent activity area under the multi-time-space granularity, realizes the purpose of extracting the ship frequent activity area under the multi-time-space granularity, and improves the accuracy of ship frequent activity area extraction.

Description

Technical Field

[0001] This invention belongs to the field of ship AIS data clustering technology, and relates to an adaptive spatiotemporal dimension method for extracting frequently active areas of ships. Background Technology

[0002] The shipping industry plays an indispensable role in global economic development. With the rapid growth of the global economy, the number of ships has also increased dramatically. Due to the frequent occurrence of ship collisions in densely populated areas, maritime safety has become a critical issue. The Automatic Identification System (AIS) has emerged to address this need. This system contains various navigational information about ships, such as ship number, latitude and longitude, speed, and data collection time. By clustering and analyzing historical AIS data, frequently active areas of ships can be extracted, and navigation patterns within these areas can be analyzed. This allows for the orderly planning of ship navigation, improves the efficiency of ship entry and exit, and effectively reduces the occurrence of collisions, thus playing a vital role in ensuring maritime safety.

[0003] Currently, research on extracting frequently active areas mainly focuses on resident trajectory and vehicle trajectory data, while there are fewer methods for extracting frequently active areas using ship trajectories. Some existing methods are implemented through clustering techniques, but they only focus on the spatial information of trajectory data during the clustering process and do not consider the temporal information. Therefore, when faced with ship AIS data that has both spatial and temporal attributes, the clustering effect is often poor and cannot reflect the distribution of frequently active areas of ships at different time granularities.

[0004] Therefore, an adaptive spatiotemporal dimension method for extracting frequent ship activity areas is designed. This method considers both spatial and temporal information when extracting frequent activity areas, employing a grid density peak clustering method. This method adaptively selects the density threshold of frequent activity areas within different time periods, obtaining frequent activity areas for different time periods. Simultaneously, it automatically merges frequent activity areas from adjacent time periods on the time axis, resulting in frequent activity areas at multiple spatiotemporal granularities. This scheme is simple to implement and can reflect the distribution of frequent ship activity areas at different spatiotemporal granularities, providing a new solution and research approach for extracting frequent ship activity areas from ship AIS data. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive spatiotemporal dimension method for extracting frequent ship activity areas. First, historical AIS data of ships is preprocessed. Then, frequent ship activity areas within different time periods are extracted through grid density peak clustering. Finally, the frequent ship activity areas are adaptively fused along the time axis to obtain frequent activity areas at multiple spatiotemporal granularities.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] An adaptive spatiotemporal dimension method for extracting frequently active areas of ships, the method comprising the following steps:

[0008] Step 1) Preprocessing of ship AIS data;

[0009] Step 2) Extraction of frequently active ship activity areas at a single spatiotemporal granularity;

[0010] Step 3) Extraction of frequently active areas of ships at multiple spatiotemporal granularities.

[0011] Furthermore, step 1) specifically includes the following steps:

[0012] Step 11) Single Trajectory Extraction. A single ship trajectory refers to the route formed by a ship from one port to another. This invention is designed for a specific sea area. Considering that ships may form multiple single trajectories within the observation period, it determines whether the ship's speed is 0 and whether the acquisition time of two adjacent data points is greater than a given time threshold to extract the single trajectory from the ship's AIS data. The i-th trajectory can be represented as:

[0013]

[0014] Where n represents the number of trajectory points contained in the trajectory, and the trajectory points , Indicates the time of trajectory point acquisition. , , Let represent the longitude, latitude, and speed of ship i at time t, respectively.

[0015] Step 12) Outlier Removal. Remove outliers from the trajectory data, such as points with negative speeds, longitudes exceeding 180°, latitudes exceeding 90°, or points that deviate from the overall trajectory.

[0016] Step 13) Trajectory Interpolation. A single ship trajectory may contain missing data, and even after deleting outliers, data gaps may still appear, leading to a decrease in trajectory data quality. This invention uses linear interpolation to fill in the missing data and improve data quality. The method is as follows:

[0017] Set time threshold ,like Calculate the number of interpolations:

[0018]

[0019] This represents the average sampling time interval for normal sampling of this trajectory, and the attribute values ​​of the inserted trajectory points are calculated:

[0020]

[0021] Indicates the inserted first A trajectory point.

[0022] Furthermore, step 2) specifically includes the following steps:

[0023] Step 21) Extraction of frequently active ship activity areas at a single spatiotemporal granularity. Assume a ship trajectory dataset... The time span is Given time granularity Spatial granularity (number of grids) ), to obtain the next moment , ;

[0024] Step 22) Extraction of areas with frequent ship activity. Time period to be obtained. Add data from within to a collection In this study, a grid density peak clustering algorithm was used to extract areas of frequent ship activity. The main idea of ​​the algorithm is to combine grid clustering and density peak clustering. First, the data point objects are transformed into grid objects, that is, the latitude and longitude of the study area are evenly divided into grids. Divide into equal parts, and obtain A grid of objects is generated, and then the density peak clustering algorithm is used to perform cluster analysis on the grid objects. The grid division principle is to ensure that the number of grids with data is greater than 1 / 5 of the total number of grids.

[0025] There are currently two methods for selecting grid objects: 1) using the center point of the grid as the representative point; 2) using the center of the data in the grid as the representative point. However, both methods may result in a virtual representative point that is far from the data points in the grid, which can affect the clustering results. To address this issue, this invention proposes that the selection of grid representative points should meet at least two conditions: 1) they should actually exist; 2) they should be closest to other data points in the grid. Therefore, based on these two conditions, this invention uses the point within the grid that is closest to other data points as the representative point of the grid object.

[0026] Density peak clustering algorithm is based on two important assumptions: (1) the density of cluster centers is higher than that of surrounding data points; (2) the distance between cluster centers and higher density points is relatively large. Current research focuses on data points as the research object. However, due to the influence of navigation status and external factors on ship AIS data acquisition, situations may arise where, within the same time period, a ship in one area has a high AIS data acquisition frequency, while a ship in another area has a low AIS data acquisition frequency. If only data points are considered, it would be assumed that the area with the high data acquisition frequency has a high density. However, in practice, we believe that the densities of these two areas should be the same. To address this issue, this invention argues that the number of data points should not be used as the density calculation standard, but rather the number of ships should be used. Therefore, this invention expresses the density of grid objects as:

[0027]

[0028] In the formula, Indicates the current grid , A function that represents the number of ships within a grid.

[0029] The relative distance representation is changed from the distance between data points to the distance between grid objects, expressed as:

[0030]

[0031] In the formula, Represented as a grid object and grid objects Euclidean distance.

[0032] To achieve automatic selection of cluster centers, this invention employs a combination of the elbow method and box plots. First, the relative density distance is calculated:

[0033]

[0034] In the formula, These represent the normalized grid density and relative distance, respectively. The normalization method used is the minimum-maximum normalization method, which can be expressed as:

[0035]

[0036] in These are the normalized data feature values. These are the feature values ​​of the data before normalization. It represents the maximum value among the features of this type of data. This is the minimum value among the data of this type.

[0037] Then Sort the values ​​in descending order, find the inflection point using the elbow method, and add the grid objects to the left of the inflection point to the candidate set of cluster centers. This section may contain mesh objects that are not cluster centers, such as those with high local density but small relative distances, or large relative distances but low local density. Since their product is also large, they may also be identified as cluster centers. Therefore, the candidate set of cluster centers needs to be further refined. Perform the screening.

[0038] In this invention, the box method is combined to evaluate the candidate set of cluster centers. Filter the results. Select all... Add value to collection Calculate the sets respectively upper quartile and lower quartiles Where n is the length of the set, and the outlier truncation threshold for the set is defined as follows:

[0039]

[0040] In this invention, it is believed that, The larger the value, the greater the probability that the grid object will be the center of a cluster. Value exceeds threshold The number of grid objects has far exceeded that of collections. Other elements in, therefore, will be included in this invention. Value exceeds threshold The grid object is added to the cluster center candidate set. In the middle, the candidate set of cluster centers will be... and cluster center candidate set intersection As preliminary candidate centers, the remaining data points are assigned to the clusters of their nearest high-density neighbors, thus obtaining clusters.

[0041] To identify areas of frequent ship activity within a given time period, this invention considers areas with a high number of ships (i.e., high grid density) and typically located at the center of clusters, making them more likely to become the nearest high-density grid to other grids. Therefore, this invention statistically analyzes the number of times each grid becomes the nearest high-density grid to other grids. It considers that grids that are not frequently active typically have lower density, with almost zero occurrences of this criterion. Based on this idea, this invention uses the maximum grid density with zero occurrences as the hotspot area selection threshold, achieving adaptive threshold selection. The number of times a grid becomes the nearest high-density grid to other grids can be expressed as:

[0042]

[0043] In the formula, The frequently active area is defined as:

[0044]

[0045] In the formula, This represents the clusters obtained from clustering. Representing a cluster The area of ​​frequent activity in the middle This is a function for maximizing the value. The frequently active regions obtained are saved to a set. Inside, and determined Minimum and maximum density values ​​within a given time period.

[0046] make The next time period for extracting frequently active regions is determined as: start time. End time Repeat step 22 to extract frequently active regions in the next time period, until the entire time span has been traversed. .

[0047] Furthermore, step 3) specifically includes the following steps:

[0048] Step 31) Extraction of Frequent Ship Activity Areas at Multiple Spatiotemporal Granularities. In Step 2 above, frequent activity areas for different time periods were obtained. These areas may be frequent activity areas within consecutive adjacent time periods. We can merge these areas to obtain frequent activity areas with a larger temporal granularity.

[0049] Step 32) Determine the fusion start time Calculate the next time step , ;

[0050] Step 33) Determine the starting time period for merging frequently active areas. Determine the next fusion time period. , ;

[0051] Step 34) If the time period and Their frequent activity areas overlap. Calculated in The minimum and maximum mesh densities within a given time period are min_density and max_density, respectively. , Add the values ​​of a, min_density, and max_density to set S to obtain the values ​​within the time interval. If a region is frequently active, then merge the frequently active regions for the next time period; otherwise, merge the regions for the next time period. (Return to step S33).

[0052] Step 35) When the frequently active areas in the two time periods in Step 34) overlap, continue extending along the time axis. Repeat steps 3 and 4 until the entire time span has been traversed. ;

[0053] Step 36) Merge frequently active areas for the next time period. (Return to step 33)

[0054] Step 37) Continue until the entire time span has been traversed. By merging the frequent activity areas, we can obtain the set S of frequent ship activity areas at multiple spatiotemporal granularities.

[0055] The beneficial effects of this invention are as follows: When extracting frequently active ship activity areas, this invention considers both temporal and spatial information of ship trajectory data. While ensuring sufficient effectiveness of the ship trajectory data, it effectively improves computational efficiency by using a gridding method. Simultaneously, it uses an adaptive method to determine the density filtering threshold, enabling the extraction of frequently active ship activities within different time periods. Through temporal fusion of frequently active areas, it can extract frequently active ship activity areas at multiple spatiotemporal granularities. Compared to traditional methods that only focus on spatial information for frequently active area extraction, this invention solves the problems of lack of temporal constraints and incomplete extraction of frequently active ship activity areas. It achieves the extraction of frequently active ship activity areas at multiple spatiotemporal granularities, improves clustering results, and can extract frequently active ship activity areas that conform to actual conditions. Attached Figure Description

[0056] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0057] Figure 1 A flowchart of the overall method provided for embodiments of the present invention.

[0058] Figure 2 A schematic diagram of mesh division provided by the present invention.

[0059] Figure 3 A schematic diagram of grid representative point selection provided by the present invention.

[0060] Figure 4 A partial ship AIS data .csv file provided for embodiments of the present invention Detailed Implementation

[0061] The following will further explain the concept, specific structure and technical effects of the present invention in conjunction with the accompanying drawings and embodiments, so as to fully understand the purpose, features and effects of the present invention.

[0062] This invention provides an adaptive spatiotemporal dimension method for extracting areas of frequent ship activity, which can be automated using computer software technology, such as... Figure 1 The diagram shown is a flowchart of the overall method of the present invention. Figure 2 This is a schematic diagram of the grid division of the present invention, in which "." represents ship trajectory data points and squares represent grid division. Figure 3 This diagram illustrates the selection of representative points within a clearly defined grid, where "." represents ship trajectory points, squares indicate grid division, and "+" represents representative points of the grid. The method includes the following steps: Step 1) Preprocessing of ship AIS data; Step 2) Extraction of frequently active ship activity areas across different time periods; Step 3) Extraction of frequently active ship activity areas at multiple spatiotemporal granularities. Each step is described in detail below:

[0063] Furthermore, step 1) specifically includes the following steps:

[0064] Step 11) Single Trajectory Extraction. A single ship trajectory refers to the route formed by a ship from one port to another. This invention is designed for a specific sea area. Considering that ships may form multiple single trajectories within the observation period, it determines whether the ship's speed is 0 and whether the acquisition time of two adjacent data points is greater than a given time threshold to extract the single trajectory from the ship's AIS data. The i-th trajectory can be represented as:

[0065]

[0066] Where n represents the number of trajectory points contained in the trajectory, and the trajectory points , Indicates the time of trajectory point acquisition. , , Let represent the longitude, latitude, and speed of ship i at time t, respectively.

[0067] Step 12) Outlier Removal. Remove outliers from the trajectory data, such as points with negative speeds, longitudes exceeding 180°, latitudes exceeding 90°, or points that deviate from the overall trajectory.

[0068] Step 13) Trajectory Interpolation. A single ship trajectory may contain missing data, and data loss may also occur after deleting outliers, leading to a decrease in trajectory data quality. This invention uses linear interpolation to fill in the missing data and improve data quality. The method is as follows:

[0069] Set time threshold ,like Calculate the number of interpolations:

[0070]

[0071] This represents the average sampling time interval for normal sampling of this trajectory, and the attribute values ​​of the inserted trajectory points are calculated:

[0072]

[0073] Indicates the inserted first A trajectory point.

[0074] Furthermore, step 2) specifically includes the following steps:

[0075] Step 21) Extraction of frequently active ship activity areas at a single spatiotemporal granularity. Assume a ship trajectory dataset... The time span is Given time granularity Spatial granularity (number of grids) ), to obtain the next moment , ;

[0076] Step 22) Extraction of areas with frequent ship activity. Time period to be obtained. Add data from within to a collection This study employs a grid density peak clustering algorithm to extract areas of frequent ship activity. The main idea of ​​the algorithm is to combine grid clustering and density peak clustering. First, the data point objects are transformed into grid objects, that is, the latitude and longitude of the study area are uniformly divided into grids. Divide into equal parts, and obtain A grid of objects is generated, and then the density peak clustering algorithm is used to perform cluster analysis on the grid objects. The grid division principle is to ensure that the number of grids with data is greater than 1 / 5 of the total number of grids.

[0077] There are currently two methods for selecting grid objects: 1) using the center point of the grid as the representative point; 2) using the center of the data in the grid as the representative point. However, both methods may result in a virtual representative point that is far from the data points in the grid, which can affect the clustering results. To address this issue, this invention proposes that the selection of grid representative points should meet at least two conditions: 1) they should actually exist; 2) they should be closest to other data points in the grid. Therefore, based on these two conditions, this invention uses the point within the grid that is closest to other data points as the representative point of the grid object.

[0078] Density peak clustering algorithm is based on two important assumptions: (1) the density of cluster centers is higher than that of surrounding data points; (2) the distance between cluster centers and higher density points is relatively large. Current research focuses on data points as the research object. However, due to the influence of navigation status and external factors on ship AIS data acquisition, situations may arise where, within the same time period, a ship in one area has a high AIS data acquisition frequency, while a ship in another area has a low AIS data acquisition frequency. If only data points are considered, it would be assumed that the area with the high data acquisition frequency has a high density. However, in practice, we believe that the densities of these two areas should be the same. To address this issue, this invention argues that the number of data points should not be used as the density calculation standard, but rather the number of ships should be used. Therefore, this invention expresses the density of grid objects as:

[0079]

[0080] In the formula, Indicates the current grid , A function that represents the number of ships within a grid.

[0081] The distance between data points is converted to the distance over time between grid objects using a relative distance representation method, as follows:

[0082]

[0083] In the formula, Represented as a grid object and grid objects Euclidean distance.

[0084] To achieve automatic selection of cluster centers, this invention employs a combination of the elbow method and box plots. First, the relative density distance is calculated:

[0085]

[0086] In the formula, These represent the normalized mesh density and relative distance, respectively. The normalization method used is the minimum-maximum normalization method, which can be expressed as:

[0087]

[0088] in These are the normalized data feature values. These are the feature values ​​of the data before normalization. It represents the maximum value among the features of this type of data. It is the minimum value among the features of this type of data.

[0089] Then Sort the values ​​in descending order, find the inflection point using the elbow method, and add the grid objects to the left of the inflection point to the candidate set of cluster centers. This section may contain data points that are not cluster centers, such as those with high local density but small relative distances, or large relative distances but low local density. Since their product is also large, they may be identified as cluster centers. Therefore, the candidate set of cluster centers needs to be further refined. Perform the screening.

[0090] In this invention, the box method is combined to evaluate the candidate set of cluster centers. Filter the results. Select all... Add value to collection Calculate the sets respectively upper quartile and lower quartiles Where n is the length of the set, and the outlier truncation threshold for the set is defined as follows:

[0091]

[0092] In this invention, it is believed that, The larger the value, the greater the probability that the grid object will be the center of a cluster. Value exceeds threshold The number of grid objects has far exceeded that of collections. Other elements in, therefore, will be included in this invention. Value exceeds threshold Data points are added to the candidate set of cluster centers. In the middle, the candidate set of cluster centers will be... and cluster center candidate set intersection As preliminary candidate centers, the remaining grid objects are assigned to the clusters of their nearest high-density neighbors, resulting in clusters.

[0093] To identify areas of frequent ship activity within a given time period, this invention considers areas with a high number of ships (i.e., high grid density) and typically located at the center of clusters, making them more likely to become the nearest high-density grid to other grids. Therefore, this invention statistically analyzes the number of times each grid becomes the nearest high-density grid to other grids. It considers that grids that are not frequently active typically have lower density, with almost zero occurrences of this criterion. Based on this idea, this invention uses the maximum grid density with zero occurrences as the hotspot area selection threshold, achieving adaptive threshold selection. The number of times a grid becomes the nearest high-density grid to other grids can be expressed as:

[0094]

[0095] In the formula, The frequently active area is defined as:

[0096]

[0097] In the formula, This represents the clusters obtained from clustering. Representing a cluster The area of ​​frequent activity in the middle This is a function for maximizing the value. The frequently active regions obtained are saved to a set. Inside, and determined Minimum and maximum density values ​​within a given time period.

[0098] make The next time period for extracting frequently active regions is determined as: start time. End time Repeat step 22 to extract frequently active regions in the next time period, until the entire time span has been traversed. .

[0099] Furthermore, step 3) specifically includes the following steps:

[0100] Step 31) Extraction of Frequent Ship Activity Areas at Multiple Spatiotemporal Granularities. In Step 2 above, frequent activity areas for different time periods were obtained. These areas may be frequent activity areas within consecutive adjacent time periods. We can merge these areas to obtain frequent activity areas with a larger temporal granularity.

[0101] Step 32) Determine the fusion start time Calculate the next time step , ;

[0102] Step 33) Determine the starting time period for merging frequently active areas. Determine the next fusion time period. , ;

[0103] Step 34) If the time period and Their frequent activity areas overlap. Calculated in The minimum and maximum mesh densities within a given time period are min_density and max_density, respectively. , Add the values ​​of a, min_density, and max_density to set S to obtain the values ​​within the time interval. If a region is frequently active, then merge the frequently active regions for the next time period; otherwise, merge the regions for the next time period. (Return to step S33).

[0104] Step 35) When the frequently active areas in the two time periods in Step 34) overlap, continue extending along the time axis. Repeat steps 3 and 4 until the entire time span has been traversed. ;

[0105] Step 36) Merge frequently active areas for the next time period. (Return to step 33);

[0106] Step 37) Continue until the entire time span has been traversed. By merging the frequent activity areas, we can obtain the set S of frequent ship activity areas at multiple spatiotemporal granularities.

[0107] By performing the above steps, clustering information can be performed on a large amount of ship AIS trajectory data, extracting frequent activity areas of ships in different time periods, and adaptively fusing these areas in time. This allows for the extraction of frequent ship activity areas at multiple spatiotemporal granularities, making the extracted frequent ship activity areas richer and more accurate.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An adaptive spatiotemporal dimension method for extracting frequently active areas of ships, comprising the following steps: Step 1: Ship AIS data preprocessing; Step S1.1: By determining whether the ship's speed is 0 and whether the acquisition time of two adjacent data points is greater than a given time threshold, a single trajectory is extracted from the ship's AIS data. The i-th trajectory is represented as: ； in, n represents the number of trajectory points contained in the trajectory. , Indicates the time of trajectory point acquisition. , , These represent the longitude, latitude, and speed of ship i at time t, respectively. Step S1.2: Outlier deletion. Traverse the trajectory data and delete outliers that do not conform to the laws of physical motion. The outliers include numerical outliers with negative velocity values, absolute longitude values ​​exceeding 180°, and absolute latitude values ​​exceeding 90°, as well as trajectory drift points where the sailing speed calculated based on the time interval and spatial distance between adjacent trajectory points exceeds a preset maximum speed threshold. Step S1.3: Trajectory interpolation. Missing data is filled using linear interpolation, as follows: Set time threshold ,like Calculate the number of interpolations: ； This represents the average sampling time interval for normal sampling of this trajectory, and the attribute values ​​of the inserted trajectory points are calculated: ； Indicates the inserted first A trajectory point; Step 2: Extraction of frequently active ship activity areas at a single spatiotemporal granularity; Step S2.1: Extraction of frequently active ship activity areas at a single spatiotemporal granularity, assuming a ship trajectory dataset. The time span is Given time granularity Spatial granularity, to obtain the next time step. , ; Step S2.2: Extract areas of frequent ship activity and obtain time periods. Add data from within to a collection In this study, a grid density peak clustering algorithm was used to extract areas of frequent ship activity, and the latitude and longitude of the study area were uniformly divided into... Divide into equal parts, and obtain For each grid object, the density statistical standard is the number of ships within the grid. The density peak clustering algorithm is used to cluster the grid objects. The grid division satisfies that the number of grids with data is not less than 1 / 5 of the total number of grids. The point that actually exists within the grid and has the smallest distance from other data points in the grid is selected as the representative point of the grid object. The density of the mesh object is expressed as: ； In the formula, Indicates the current grid , A function representing the number of ships within a statistical grid; The relative distance representation is changed from the distance between data points to the distance between grid objects, expressed as: ； In the formula, Represented as a grid object and grid objects Euclidean distance; The elbow method and box plots are used to select cluster centers. First, the relative density distance is calculated: ； In the formula, These represent the normalized mesh density and relative distance, respectively. The normalization method used is the minimum-maximum normalization method, expressed as: ； in These are the normalized data feature values. These are the feature values ​​of the data before normalization. It represents the maximum value among the features of this type of data. It is the minimum value among the features of this type of data. Then Sort the values ​​in descending order, find the inflection point using the elbow method, and add the grid objects to the left of the inflection point to the candidate set of cluster centers. Then, the box method is combined to analyze the candidate set of cluster centers. Filter and select all Add value to collection Calculate the sets respectively upper quartile and lower quartiles Where n is the length of the set, and the outlier truncation threshold for the set is defined as follows: ； Will Value exceeds threshold The grid object is added to the cluster center candidate set. In the middle, the candidate set of cluster centers will be... and cluster center candidate set intersection As preliminary candidate centers, the remaining grid objects are assigned to clusters of their nearest high-density neighbors, resulting in clusters. Statistical analysis is performed on each grid, calculating the number of times each grid is the nearest high-density grid to other grids within a preset time period; wherein, the nearest high-density grid is the grid with a greater number of ships than its adjacent grids within the preset time period; when the number of times a grid is the nearest high-density grid to other grids is equal to 0, the maximum grid density of that grid is determined as the hotspot area screening threshold; the number of times a grid is the nearest high-density grid to other grids is expressed as: ； In the formula, Frequent activity areas are defined as: ； In the formula, This represents the clusters obtained from clustering. Representing a cluster The area of ​​frequent activity in the middle The function is the maximum value, and the frequently active regions obtained are saved to a set. Inside, and determined Minimum and maximum density values ​​within a time period make The next time period for extracting frequently active regions is determined as: start time. End time Repeat step S2.2 to extract frequently active regions in the next time period, until the entire time span has been traversed. ; Step 3: Extraction of frequently active ship activity areas at multiple spatiotemporal granularities; Step S3.1: Extraction of frequent ship activity areas at multiple spatiotemporal granularities. For the frequent ship activity areas obtained in Step 2 at different time periods, merge the frequent ship activity areas in consecutive adjacent time periods to obtain frequent ship activity areas at a larger time granularity. Step S3.2: Determine the fusion start time Calculate the next time step , ; Step S3.3: Determine the starting time period for merging frequently active areas. Determine the next fusion time period. , ; Step S3.4: If the time period and Their frequent activity areas overlap. Calculated in The minimum and maximum grid densities within a given time period are min_density and max_density, respectively. , Add (a, min_density, max_density) to set S to obtain the density over time period. If a region is frequently active, then merge the frequently active regions for the next time period; otherwise, merge the regions for the next time period. Return to step S3.3; Step S3.5: When the frequently active areas in the two time periods in step S3.4 overlap, continue extending along the time axis. Repeat step S3.4 until the entire time span has been traversed. ; Step S3.6: Merge frequently active areas for the next time period. Return to step S3.3; Step S3.7: Continue until the entire time span has been traversed. The fusion of frequent activity areas is completed, resulting in a set S of frequent ship activity areas at multiple spatiotemporal granularities.

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