A method for monitoring ship re-provisioning behavior

Abstract

The application discloses a ship offshore replenishment behavior monitoring method, and belongs to the field of offshore situation awareness and data analysis. The application finds a data cleaning method suitable for the problem, and proposes a new feature extraction method for the problem. Then, a random forest model is used to train on a self-built data set to obtain a good classifier. Unlike other classification and anomaly detection methods, the application calculates the change amount of adjacent trajectory points to extract a feature sequence in the feature extraction, and calculates sequence statistical features on the basis. The application also proposes an NTD nearest track distance of a replenishment ship track, which is used as a feature related to a receiving ship of a sample, and is used as a track feature together with statistical features. The nearest track distance considers the simultaneity and directionality of two tracks when calculating the track distance. When the nearest track distance is used as one of the features, the classification effect of the model is improved. The random forest model trained by the application can effectively distinguish whether a track contains a replenishment behavior.

Description

Technical Field

[0001] This invention relates to a method for monitoring ship replenishment behavior at sea, belonging to the field of maritime situational awareness and data analysis technology. Background Technology

[0002] With the expansion of maritime deployments and the increasing complexity of the operational environment in modern naval warfare, the strategic importance of at-sea replenishment has become particularly prominent. Detecting and analyzing at-sea replenishment activities is crucial for optimizing replenishment strategies and revealing the movements and deployments of foreign militaries. Furthermore, from a maritime situational awareness perspective, understanding the replenishment activities of foreign militaries at sea is of paramount importance for discerning their strategic intentions.

[0003] AIS (Automatic Identification System) is an automated tracking system widely used by ships and maritime monitoring agencies to exchange navigation information between vessels and coastal stations. AIS equipment provides information on a vessel's identity, type, position, course, speed, and other relevant maritime information. This information helps improve maritime safety, especially in busy waterways and under conditions of limited visibility. AIS also supports maritime traffic management and environmental protection by allowing for more effective vessel monitoring and management.

[0004] Current literature on at-sea replenishment can be broadly divided into two parts: one part studies specific issues in the replenishment process, and the other part focuses on replenishment strategies and route planning. There is almost no literature on the detection of at-sea replenishment behavior based on AIS data. This paper represents a meaningful first attempt at monitoring replenishment behavior using AIS data and machine learning algorithms.

[0005] Existing literature based on AIS data and machine learning algorithms mostly focuses on tasks such as classifying the types and behaviors of maritime targets and detecting anomalies. In classification research, the main focuses include three aspects: 1) the dataset (containing sample information and corresponding categories); 2) feature extraction methods; and 3) the selection of classification algorithms and models.

[0006] Among the proposed methods, feature extraction for ship tracks is quite diverse. One method treats the track as an object, extracting static attributes and statistical information from the AIS (Air Traffic Information System). A second method directly uses data items from the original AIS, such as speed, navigation status, latitude and longitude, heading, ground heading, and timestamps, as features. A third method transforms the track into an image using the latitude, longitude, and speed values ​​of the trajectory points, and then leverages the advantages of convolutional neural networks (CNNs) in image recognition to classify ship behavior.

[0007] In addition to the Convolutional Neural Network (CNN) models used in the aforementioned literature, many other models have been applied to classification problems based on AIS data, such as Decision Tree (DT), Support Vector Machine (SVM), Hidden Markov Model, Conditional Random Field, K Nearest Neighbor (KNN), Random Forest, 1D-CNN, GRU, LSTM, and clustering algorithms in unsupervised learning.

[0008] A comprehensive analysis of existing methods reveals the following gaps in current research: 1) Classification of ship behavior largely focuses on simple maneuvering behaviors such as navigation or anchoring, neglecting operational behaviors like replenishment at sea. 2) Most current research is based on datasets from specific sea areas, which may contain implicit geographical features, leading to poor generalization results to other sea areas. Replenishment at sea, however, is global, and can occur in any sea area. 3) In the few methods that can generalize training results to any sea area, there is usually an assumption of high-frequency trajectory signal transmission without prolonged interruptions, and interpolation methods can reconstruct the navigation trajectory between two points relatively well. However, replenishment at sea often involves sharp drops in signal transmission frequency or prolonged signal interruptions, and changes in signal transmission frequency in the trajectory contain important information. Therefore, existing methods cannot be directly applied to the detection of replenishment at sea. Summary of the Invention

[0009] The purpose of this invention is to provide a method and technical approach for monitoring ship replenishment behavior at sea from raw AIS data. First, data cleaning is required. Then, a feature extraction method suitable for this problem is proposed. Finally, a model is trained based on the extracted features, thereby enabling real-time monitoring of ship replenishment behavior at sea.

[0010] like Figure 1 As shown, the technical approach of this invention mainly includes four steps: data cleaning, feature extraction, model training, and real-time monitoring. The detailed methods will be described step by step below:

[0011] (1) Data cleaning

[0012] AIS information transmission is based on shortwave communication in the VHF band, specifically on two channels: 161.975MHz and 162.025MHz. Airborne AIS equipment broadcasts its own navigation data at fixed time intervals. Therefore, signal errors are unavoidable during transmission and propagation through the medium.

[0013] The trajectory samples in the dataset used in this paper are raw AIS trajectories, the reliability of which is difficult to guarantee. If subsequent feature extraction is performed directly on trajectories without data cleaning, the impact of errors will be amplified, and they may even be incorrectly used as features of the trajectory. To avoid noise and errors in the raw AIS data severely affecting subsequent maritime replenishment detection, data cleaning is essential. The data cleaning process can be summarized in the following three steps:

[0014] 1) Clear invalid data points:

[0015] Each field in AIS data has a fixed range of values. For invalid data points in the trajectory where the field value is outside the range of the field value (such as longitude 181 degrees, latitude 91 degrees) or the field value is missing, the signal point can be directly removed.

[0016] 2) Duplicate data point removal:

[0017] The timestamps of data points in the trajectory are determined by the time the signal is received. If multiple receivers receive the same signal, two data points with different timestamps will appear in the trajectory, containing completely identical data information. In this case, this paper only needs to retain the data point that arrives first among the duplicate points.

[0018] 3) Noise point removal:

[0019] Finally, noise points with significant deviations in the trajectory need to be removed. The most common error in noise points is incorrect latitude and longitude fields in the signal, causing a significant difference between the ship's position and the trajectory's sailing trend. Based on a survey of various replenishment ships' data, the maximum speed of a replenishment ship should not exceed 25 knots. Therefore, the time interval and great circle distance between adjacent points in the trajectory can be calculated. If the speed between a point and the two points before and after it exceeds the ship's limit, this point can be considered a data point with an incorrect latitude and longitude field and should be removed as noise. After removing noise points, the sailing speeds in the trajectory are all within a reasonable range.

[0020] (2) Feature extraction

[0021] Feature extraction can be divided into three steps.

[0022] The first step is to extract feature sequences from the original AIS data sequence. Unlike other methods that directly use information from the AIS data as features, the feature sequences in this method are calculated based on the changes between two adjacent data points.

[0023] The second step is to calculate the statistical values ​​of the feature sequence. For AIS data sequences of different lengths, the length of their feature sequences also varies. Therefore, in order to unify the feature patterns of samples of different lengths, statistical values ​​are further extracted from the feature sequences extracted in the first step as features.

[0024] The third step is to calculate the nearest distance (NTD) of the trajectory. In order to take into account the information implicit in the supply receiving ship, the third step is to calculate the nearest distance (NTD) of the trajectory. This is a new method that takes into account the simultaneity of the trajectory while calculating the trajectory distance, and is used to find supply receiving ship trajectories that are close to the original trajectory.

[0025] The nearest distance (NTD) calculated in the third step will be used as a feature of the trajectory. This, along with the statistical features calculated in the second step, will form the overall feature set of a trajectory and be input into the random forest model for training or identification. The processing details for each step are as follows:

[0026] 2.1 Feature Sequence Extraction

[0027] AIS data contains a wealth of implicit geographical information, such as latitude and longitude indicating the region where a ship is located, and heading potentially containing route or port information. Many studies input data from a single region (e.g., the area around a port) into the model, which introduces geographical biases, limiting the model's applicability to the region where the training data was collected and preventing its global applicability. To avoid this, this paper focuses on trajectory variations, minimizing the introduction of geographical biases.

[0028] For the reasons mentioned above, this paper calculates the change between two adjacent data points in the trajectory. An AIS track containing n trajectory points can be represented by the following formula:

[0029] Tr={ <t i ,lon i ,lat i ,s i ,c i ,ns i >|i=1,2…n}

[0030] A navigation trajectory is a set of attribute vectors of waypoints, where t i lon represents the timestamp of the i-th track point. i Let lat represent the longitude of the i-th waypoint. i s represents the latitude of the i-th waypoint. i c represents the speed at the i-th waypoint. iLet c' represent the ground heading (COG - Course Over Ground) of the i-th trajectory point. Its original value range is [0, 3600]. The angle between c' and true north is represented by a clockwise angle. For ease of calculation, this paper converts it to radians. That is, let the original heading be c'. i c i =c′ i ×2π / 3600, c i The range becomes [0, 2π], where π represents pi. i This represents the navigation status of the i-th waypoint.

[0031] AIS data primarily contains four types of information: ship status, position, speed, and heading. When considering the detection of replenishment trajectories at sea, information should also be extracted from these factors and categorized. Assume two adjacent points P in trajectory Tr... i P i+1 By calculating the changes at two points, this paper can obtain the following four types of characteristics:

[0032] 1) State characteristics:

[0033] · NS i This represents the maximum value of the navigation state. The normal navigation state should be 0 (main engine powered navigation). Taking the maximum value of the navigation state can preserve abnormal navigation states.

[0034] ·Δt i me i =t i+1 -t i , Δt i me i For P i With P i+1 The longer the reception time interval, the lower the signal transmission frequency, and the more likely it is that the ship is deliberately concealing its whereabouts.

[0035] 2) Displacement characteristics:

[0036] ·Δlat i =d i st{(lon i ,lat i ),(lon i ,lat i+1 )},Δlat i For P i To P i+1 The component of the displacement in the latitudinal direction, if given by P i To P i+1The sign is positive when moving north and negative when moving south. The distance calculation `dist` represents the great circle distance between two points, in kilometers.

[0037] ·Δlon i =d i st{(lon i ,lat i ),(lon i+1 ,lat i )},Δlon i For P i To P i+1 The component of the displacement in the longitude direction, if given by P i To P i+1 Moving eastward results in a positive sign, while moving westward results in a negative sign.

[0038] · P represents i To P i+1 Speed ​​in the latitudinal direction.

[0039] · P represents i To P i+1 Speed ​​in the longitude direction.

[0040] 3) Angular characteristics:

[0041] · Δcog i For P i With P i+1 The change in the direction of travel. The change is the smaller angle between the directions of travel of the two points, if from P... i To P i+1 A clockwise rotation results in a positive sign, while a counter-clockwise rotation results in a negative sign.

[0042] ·rot i =Δcog i / Δt i me i rot i P represents i To P i+1 The turning rate.

[0043] 4) Velocity characteristics:

[0044] ·Δsog i =s i+1 -s i ,Δsog i This indicates the change in velocity value between two points in AIS data.

[0045] ·speed i =|d i st{(lon i ,lat i ),(lon i+1 ,lat i+1 )}| / Δt i me i speed i P represents i To P i+1 The sailing speed is calculated from the absolute value of the displacement distance and the time interval, where the displacement distance is the great circle distance between the two points, in kilometers.

[0046] ·acc i =Δsog i / Δt i me i acc i P represents i To P i+1 The acceleration is calculated from the velocity values ​​in the AIS data.

[0047] Therefore, after feature sequence extraction, a trajectory Tr of length n yields an 11-dimensional feature sequence F of length n-1. T .

[0048]

[0049] F T By calculating the changes in adjacent points in the trajectory, the regional characteristics contained in the original trajectory are eliminated, thus avoiding the problem that the model cannot generalize to other regions.

[0050] 2.2 Statistical Feature Extraction

[0051] Since this paper selects at-sea replenishment as the research object, its AIS signal transmission frequency does not meet the requirements set by the International Maritime Organization (IMO), and the AIS system frequently shuts down. Therefore, the signal transmission frequency should also be considered as a feature to aid classification. Consequently, it is impossible to standardize the trajectories to a uniform length, which poses a challenge for classification models that require fixed input dimensions. A common approach is to treat the trajectory as a whole, ignoring its temporal characteristics, and extracting various statistical measures of the sequence as features of the trajectory.

[0052] For the feature sequence F T The navigation state sequence NS i These are discrete state values; this paper only needs to take the maximum value in the sequence, while the other ten dimensions of the feature sequence are obtained by taking the mean, maximum value, and standard deviation of the sequence, respectively. Since F... TThis corresponds to the amount of change; the minimum value usually indicates no change, therefore, except for the slower sailing speed. i Aside from sequences that may represent anomalies, the minimum value is not counted for the remaining sequences. Using this method, this paper can identify the feature sequence F. T Further extract its statistical values ​​as features. For the feature sequence F T We can extract the statistical feature set A:

[0053] A={max(NS)}∪{max(S),min(S),std(S)|S∈B}

[0054] Where max represents the maximum value, min represents the minimum value, and std represents the standard deviation. Set B contains Δtime, Δlat, Δlon, and speed. lat speed lon The ten characteristic sequences are Δcog, rot, Δsog, speed, and acc. Therefore, A contains a total of 1 + 10 × 3 = 31 statistical values.

[0055] 2.3 Minimum Gauge

[0056] A typical at-sea replenishment mission lasts for several hours. During the replenishment process, the replenishment ship and the receiving ship need to sail at the same speed and with a small gap. From the trajectory, it can be seen that the tracks of the replenishment ship and the receiving ship are closely aligned. This external feature is quite indicative of at-sea replenishment behavior; therefore, adding this feature to the feature set can further assist the classifier in classification. Current methods for calculating trajectory distance do not consider the simultaneity and directionality of the two trajectories. Therefore, this paper proposes a method to calculate the nearest trajectories (NTD) of the replenishment ship at the same time as the original trajectory, where the trajectories in a similar direction are closest to it. The calculation method is as follows:

[0057] For a trajectory Tra, this paper can express it as Tra = { <T i ,P i The form of >|i=1,2…n}, where T i Let P be the point i The timestamp. The distance between adjacent trajectories of trajectory Tra is calculated as follows:

[0058] 1) Search for trajectories within the neighborhood

[0059] First, this paper needs to search for trajectories to be calculated in the neighborhood of the original trajectory. These trajectories should have a high degree of similarity to the original trajectory in both time and space.

[0060] If we denote an isolated point around the original trajectory as P θ Its timestamp is T θ Based on the timestamp T1 of the earliest data point in the original trajectory and the timestamp T of the latest data point... n This article can define a time frame, namely point P. θ T1 needs to be satisfied <T θ <T n Regarding distance, this paper sets the distance threshold to 5km. The distance between the searched data point and the nearest point in the trajectory should be less than 5km, i.e., min{distance(P θ ,P i )}<5(i=1,2…n), where n is the length of the trajectory Tra, and distance is the great circle distance between two points, in kilometers (km).

[0061] All data points that meet the time and space requirements are divided into sets according to MMSI (Marine Mobile Service Identifier), and then sorted in ascending order by timestamp within the sets to form trajectories, thus obtaining a set of trajectories that meet the conditions.

[0062] 2) Data Point Matching Using Dynamic Time Warping (DTW) Dynamic Time Warping is an effective time series analysis tool. Its core idea is to create a cost matrix to represent the distance between all point pairs in two time series, and then find a path through this matrix that minimizes the overall difference between the two series. This path-finding process involves calculating the cumulative cost of each point and selecting a path that minimizes these cumulative costs, thus achieving optimal alignment between the two series. This method allows for non-linear matching on the time axis, enabling effective comparison and alignment even when the sampling frequencies of the two series are inconsistent, and therefore has been widely used in various fields. For a trajectory that meets the conditions in the previous step, the transmission frequency and arrival time of its data points must differ from the original trajectory. DTW can find the best match for the data points in the two trajectories according to their timestamps, meaning the two trajectories are aligned on a time scale. Simultaneously, to avoid incorrect matching of two points with large time differences, the data point pairs obtained by DTW will be further filtered to remove data point pairs with a time difference exceeding 30 minutes.

[0063] 3) Calculate the average distance between the matched data points.

[0064] Using the DTW algorithm, this paper obtains several matching data point pairs between two trajectories. When calculating the spatial distance between each data point pair, considering that the difference in headings between the two trajectories is also an important factor in determining whether a ship is accompanying another vessel, this paper adds a penalty coefficient α. aWith point P b The distance can be expressed as D(P) a ,P b ) = distance(P a ,P b )×α, where D(P) a ,P b ) represents point P a ,P b The distance after adding the penalty coefficient, where distance is the great circle distance between two points in kilometers (km), and α is the penalty coefficient.

[0065] The penalty coefficient α depends on point P a With point P b heading c a With c b Difference g(c) a ,c b ),make

[0066]

[0067] Where π represents the value of a circle's pi.

[0068] The penalty coefficient α is then...

[0069]

[0070] |g(c a ,c b )| represents g(c a ,c b The absolute value of ).

[0071] In other words, when the difference in heading angle exceeds 45 degrees, or even greater than 90 degrees, the probability that the two tracks are traveling together is low, and the distance between the two points should be magnified. After calculating the distance for all matching data point pairs in the two tracks, the average distance is the distance between the two tracks, i.e.

[0072]

[0073] Where k is the number of data point pairs obtained by DTW.

[0074] 4) Record the minimum distance and adjacent trajectories

[0075] After calculating the distances between the original trajectory and all trajectories in the neighborhood, the trajectory with the smallest distance is selected as the adjacent trajectory, and this distance is called the adjacent trajectory distance. If no other trajectory is found in the neighborhood, the adjacent trajectory distance of the original trajectory is set to the maximum value of 100km.

[0076] (3) Model Training

[0077] During the model training phase, this paper uses a self-built dataset, which is structured as follows:

[0078] This paper uses replenishment activity trajectories as positive samples, labeled with 1, and normal navigation trajectories without replenishment activity as negative samples, labeled with 0. Both positive and negative samples are trajectories captured within a 24-hour time window and a single voyage. For all types of US replenishment ships (including oil replenishment ships, comprehensive replenishment ships, ammunition replenishment ships, and fast replenishment ships), based on available data (including the date of a replenishment activity, the replenishment ship's MMSI, and the receiving ship's MMSI), this paper uses replenishment trajectories with replenishment dates between January 1, 2021, and January 1, 2023 as the positive sample set. On the other hand, ships equivalent to replenishment ships are generally oil tankers with a deadweight tonnage of less than 50,000 tons corresponding to oil replenishment ships, and general cargo ships with a deadweight tonnage of less than 50,000 tons corresponding to ammunition, comprehensive, and replenishment ships. These ships are randomly selected, and navigation segments at random geographical locations are used as the negative sample set.

[0079] After the data cleaning and feature extraction steps described above, the trajectory samples in the dataset are used as the union of the obtained statistical feature set A and the nearest track distance NTD as features, which are then input into the model for training. This allows the random forest model to learn how to distinguish whether a trajectory contains replenishment behavior.

[0080] To avoid the evaluation results from depending on a specific data split due to using a single training / test data split, the experiment employed a 10-fold cross-validation method. Each experiment included ten trials, with 90% of the total dataset being randomly selected as the training set and 10% as the test set in each trial to verify the model's training performance. After ten trials, the average of the model evaluation metric scores from these ten trials was taken as the model evaluation metric score for that experiment.

[0081] To find the optimal parameters and structure for each model, grid search was used to identify the best hyperparameters before formal training. Parameter selection in random forests primarily focused on the number of trees (50, 100, 150, 200), maximum depth (4, 6, 8, 10), minimum split size (integers from 2 to 10), and minimum number of leaf nodes (integers from 1 to 10). This resulted in 1440 possible parameter combinations. Experiments were conducted on each of these 1440 combinations, comparing the classification performance under different parameter combinations. Finally, the parameter combination with the highest F1 score was selected as the optimal parameter combination for the model.

[0082] The final parameters for the random forest are selected as follows:

[0083]

[0084] (4) Real-time monitoring

[0085] During the model training phase, a random forest classifier capable of recognizing resupply activities was trained using a resupply behavior dataset. For a real-time arriving trajectory, the random forest classifier can determine whether it contains resupply activities based on the features extracted from the trajectory. If the output value of the random forest classifier is 1, it is determined that the real-time arriving trajectory contains maritime resupply activities; if the output value is 0, it is determined to be a normal trajectory without resupply activities. Therefore, for suspicious vessels to be monitored, features extracted from daily trajectory segments are input into the classifier to determine whether resupply activities occurred at that time.

[0086] The key point of this invention is:

[0087] This invention provides an effective technical approach to the problem of monitoring maritime replenishment activities. It identifies a suitable data cleaning method and proposes a novel feature extraction method. A random forest model is then trained on a self-built dataset to obtain a classifier with good performance. Unlike other classification and anomaly detection methods, this paper calculates the changes in adjacent trajectory points to extract feature sequences, and then calculates statistical features based on these sequences. This paper also proposes the NTD (Nearest Distance) orbital distance of the replenishment ship trajectory as a feature related to the receiving ship, which, along with the statistical features, constitutes the trajectory's overall feature. The nearest distance takes into account the simultaneity and directionality of two trajectories when calculating the distance. When used as one of the features, the model's classification performance is improved. Attached Figure Description

[0088] Figure 1 This is the overall technical route of the present invention. Detailed Implementation

[0089] 1. Comparison of model performance on the dataset

[0090] The average classification performance of the five models used in the experiment after ten-fold cross-validation is shown in the table below. In addition to the metrics for measuring classification ability, the average training time cost per fold was also used as a reference metric. Among the metrics for measuring classification ability, recall is more important for the problem of maritime replenishment detection because this paper aims to identify as many replenishment trajectories as possible.

[0091] In the comparison models, SVM and CatBoost use the same feature extraction method as Random Forest, while 1DCNN and LSTM models directly use the feature sequence F obtained in step one of the feature extraction stage. T It can be used directly as an input method.

[0092] Firstly, as can be seen from the first and second parts of the table, the classification effect was enhanced after adding the nearest track gauge as a feature, indicating the positive role of the nearest track gauge in this problem.

[0093] Data from Parts 2 and 3 show that Random Forest, CatBoost, and 1D CNN all possess strong classification capabilities, demonstrating good performance across the board. This indicates that the feature extraction methods used, combined with appropriate models, can effectively accomplish the task of detecting maritime replenishment activities. Among the three, Random Forest exhibits the highest recall rate, reaching 0.96. Its accuracy, precision, and F1 score are 0.962, 0.979, and 0.968, respectively.

[0094] From the perspective of average training time cost, the simpler machine learning model Random Forest has an absolute speed advantage over CatBoost, which is based on deep learning and uses 1D CNN. Furthermore, Random Forest is faster than CatBoost among machine learning models.

[0095] Considering both classification performance and time consumption, the random forest model, which uses time series statistical features as input, is significantly better than other models in the problem of maritime replenishment detection.

[0096]

[0097] 2. Real-time monitoring of the random forest model's performance

[0098] To further verify the effectiveness and practical value of the method, this paper uses a random forest model to monitor replenishment ships of known countries in real time. Between January 1, 2023 and November 30, 2023, the model detected 781 replenishment behavior records of 59 replenishment ships from 15 countries and regions.

[0099] This article presents statistics categorized by country and type of replenishment ship. A total of 59 replenishment ships were detected engaging in at-sea replenishment activities during the experiment. The United States accounted for approximately 50% (29 ships), Germany for approximately 17% (10 ships), and the remaining countries had a total of 20 ships. From the perspective of replenishment ship type, the two main types (oil replenishment ships and comprehensive replenishment ships) had roughly the same number of ships.

[0100]

[0101] The table below shows the statistics of the number of resupply operations. The United States, Germany, and Canada had the most resupply operations, accounting for 48.4%, 23.2%, and 6.8% of the total, respectively.

[0102]

[0103] This invention utilizes the proposed technical approach to train a random forest model that can effectively distinguish whether a trajectory includes replenishment activity. On the dataset established in this paper, the random forest model achieved an average accuracy of 0.962, a recall of 0.960, and a precision of 0.979 with 10-fold cross-validation, and the training speed is relatively fast. The trained random forest model was used to monitor maritime replenishment activities in real time. From January 1st to November 30th, 2023, a total of 781 replenishment activities from 59 replenishment ships of 15 countries were detected.

Claims

1. A method for monitoring ship replenishment behavior at sea, characterized in that, The process includes four steps: data cleaning, feature extraction, model training, and real-time monitoring. (I) Data Cleaning The trajectory samples in the dataset used are the original AIS trajectories. The data cleaning process consists of the following three steps: 1) Clear invalid data points: Each field in AIS data has its fixed range of values; for invalid data points in the trajectory where the field value is outside the range of values ​​or the field value is missing, the signal point is directly removed. 2) Duplicate data point removal: The timestamp of the data point in the trajectory is determined by the time the signal is received. If multiple receivers receive the same signal, two data points with different timestamps will appear in the trajectory, with completely identical data information. In this case, only the data point that arrives first among the duplicate points needs to be retained. 3) Noise point removal: Finally, noise points with large deviations in the trajectory need to be removed; the maximum speed of the supply ship should not exceed 25 knots; therefore, the time interval and great circle distance between two adjacent points in the trajectory are calculated. If the speed between a point and the two points before and after it exceeds the ship's limit, the point is considered to be a data point with an error in the latitude and longitude field and should be removed as noise. (II) Feature Extraction Feature extraction consists of three steps; The first step is to extract feature sequences from the original AIS data sequence; feature The sequence is calculated based on the change between two adjacent data points; The second step is to calculate the statistical values ​​of the feature sequence. For AIS data sequences of different lengths, the length of their feature sequences is also different. Therefore, in order to unify the feature patterns of samples of different lengths, statistical values ​​are further extracted from the feature sequences extracted in the first step as features. The third step is to calculate the nearest distance (NTD) of the trajectory. The calculated NTD will be used as a feature of the trajectory, and together with the statistical features calculated in the second step, they will be used as the features of a single trajectory, which will then be input into the random forest model for training or identification. The processing details of each step are as follows: 2.1 Feature Sequence Extraction The change between two adjacent data points in the trajectory is calculated; an AIS track containing n trajectory points is represented by the following formula: ； A navigation trajectory is a set of attribute vectors of waypoints, where This represents the timestamp of the i-th waypoint. This represents the longitude of the i-th waypoint. Represents the latitude of the i-th waypoint; This represents the speed at the i-th waypoint; Let represent the ground heading of the i-th trajectory point, and its original value range is . This represents the clockwise angle relative to true north, which is then converted to radians; that is, let the original heading be... , = , The range becomes , Represents pi; This indicates the navigation status of the i-th waypoint; AIS data contains four types of information: ship status, position, speed, and heading; assuming a trajectory Two adjacent points , ; By calculating the changes at two points, the following four types of characteristics are obtained: 1) State characteristics: , This represents the maximum value for the navigation state. , for and The receiving time interval; 2) Displacement characteristics: , for to The component of the displacement in the latitudinal direction, if from to The sign is positive when moving north and negative when moving south; the distance calculation dist is the great circle distance between two points, in kilometers; , for to The component of the displacement in the longitude direction, if from to Moving eastward results in a positive sign, while moving westward results in a negative sign. , express to Speed ​​in the latitudinal direction; , express to Speed ​​in the longitude direction; 3) Angular characteristics: , for and The change in the direction of travel; the change is the smaller angle between the directions of travel of the two points, if from... to A clockwise rotation results in a positive sign, while a counter-clockwise rotation results in a negative sign. , express to The turning rate; 4) Velocity characteristics: , This represents the change in velocity values ​​between two points in AIS data; , express to The sailing speed is calculated from the absolute value of the displacement distance and the time interval, where the displacement distance is the great circle distance between the two points, in kilometers. , express to The acceleration is calculated from the velocity values ​​in the AIS data; Therefore, a trajectory of length n After feature sequence extraction, an 11-dimensional feature sequence of length n-1 was obtained. ; ； ， ； 2.2 Statistical Feature Extraction For feature sequences Among them, the navigation state sequence These are discrete state values; only the maximum value in the sequence needs to be taken. For the other ten dimensions of the feature sequence, this paper obtains the mean, maximum value, and standard deviation of the sequence. Because... This corresponds to the change in quantity, except for the slower sailing speed. Except for sequences representing anomalies, the minimum value is not counted for other sequences. Take the set of statistical features : ； Where max represents the maximum value, min represents the minimum value, and std represents the standard deviation; set B contains These ten feature sequences; The CCP contains 1 + 10 × 3 = 31 statistical values; 2.3 Minimum Gauge The closest track distance (NTD) for the supply ship is calculated at the same time as the original trajectory, taking into account the shortest distance to its surroundings in a similar direction. The calculation method is as follows: For a trajectory In other words, to express it as In the form of, For point Timestamp; then the trajectory The distance between adjacent trajectories is calculated as follows: 1) Search for trajectories within the neighborhood If we represent an isolated point around the original trajectory as... Its timestamp is Based on the timestamp of the earliest data point in the original trajectory The timestamp of the latest data point Define the time frame, i.e., point Need to meet Set the distance threshold to 5km; the distance between the searched data point and the nearest point in the trajectory should be less than 5km, i.e. , where n is the trajectory Length, The great circle distance between two points is expressed in kilometers. All data points that meet the time and space requirements are divided into sets according to the Maritime Mobile Service Identifier (MMSI), and then sorted in ascending order by timestamp within the sets to form trajectories, thus obtaining a set of trajectories that meet the conditions. 2) Data point matching using Dynamic Time Warping (DTW) For a trajectory that meets the conditions in the previous step, the transmission frequency and arrival time of its data points must differ from the original trajectory. DTW is used to find the best match for the data points in the two trajectories according to the timestamp, that is, the two trajectories are aligned on the time scale. At the same time, in order to avoid two points with large time differences being incorrectly matched, the data point pairs obtained by DTW will be further filtered to remove data point pairs with a time difference of more than 30 minutes. 3) Calculate the average distance between the matched data points. DTW yields several matching data point pairs from two trajectories; a penalty coefficient is added when calculating the spatial distance of each data point pair. ,point With point The distance is expressed as ,in Point Distance after adding penalty coefficient, The great circle distance between two points, expressed in kilometers. This is the penalty coefficient; Penalty coefficient Depends on the point With point course and Differences ,make ； in Represents pi (π). Then the penalty coefficient for ; express The absolute value; In other words, when the difference in heading angle exceeds 45 degrees, or even greater than 90 degrees, the distance between the two points should be magnified; after calculating the distance for all matching data point pairs in the two trajectories, the average distance is the distance between the two trajectories, i.e. ； Where k is the number of data point pairs obtained by DTW; 4) Record the minimum distance and adjacent trajectories After calculating the distance between the original trajectory and all trajectories in the neighborhood, the trajectory with the smallest distance is selected as the adjacent trajectory, and its distance is the adjacent trajectory distance; if no other trajectory is found in the neighborhood, the adjacent trajectory distance of the original trajectory is set to the maximum value of 100km. (III) Model Training The dataset uses replenishment activity trajectories as positive samples, labeling them 1, and normal navigation trajectories without replenishment activity as negative samples, labeling them 0. Both positive and negative samples are trajectories captured within a 24-hour time window of a single voyage. For all types of replenishment ships, including oil replenishment ships, comprehensive replenishment ships, ammunition replenishment ships, and fast replenishment ships, based on available data including the date of replenishment activity for a particular replenishment ship, the replenishment ship's MMSI, and the receiving ship's MMSI, replenishment trajectories between replenishment dates are used as the positive sample set. On the other hand, these ships are randomly selected, and navigation segments at random geographical locations are used as the negative sample set. After the data cleaning and feature extraction steps described above, the trajectory samples in the dataset will yield a set of statistical features. The union of the nearest track distance (NTD) with the nearest track distance (NTD) is used as a feature and input into the model for training, enabling the random forest model to learn how to distinguish whether a track contains a replenishment action. The experiment uses a ten-fold cross-validation method, which means that each experiment contains ten trials. Each trial randomly selects the training set and the test set to verify the model training effect. After ten trials, the average of the model evaluation index scores of these ten trials is taken as the model evaluation index score of that experiment. Before formal training of each model, grid search was used to find the optimal hyperparameters for the model; the parameters in the random forest were selected based on the number of trees (50, 100, 150, 200), maximum depth (4, 6, 8, 10), minimum sample split, and minimum sample leaf node; therefore, there are a total of 1440 parameter combinations. Experiments were conducted on each of the 1440 parameter combinations to compare the classification performance under different parameter combinations, and finally the parameter combination with the highest F1 score was selected as the optimal parameter combination for the model. (iv) Real-time monitoring During the model training phase, a random forest classifier capable of recognizing resupply behavior was trained using a resupply behavior dataset. For a real-time arriving trajectory, the random forest classifier determines whether it contains resupply behavior based on the features extracted from the trajectory. If the output value of the random forest classifier is 1, it is determined that the real-time arriving trajectory contains maritime resupply behavior; if the output value is 0, it is determined that it is a normal trajectory that does not contain resupply behavior.

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