A ship track prediction method based on improved ascidian multi-output support vector

Abstract

This invention provides a ship trajectory prediction method based on improved multi-output support vectors for tunicate salps. Specifically, it involves filtering and preprocessing AIS trajectory data provided by the U.S. Coast Guard Navigation Center; optimizing the hyperparameters of the model using tunicate salps parameters; constructing and evaluating the final multivariate support vector model; and comparing it with other optimization methods and various support vector machines. The invention uses AIS data collected by the U.S. Coast Guard Navigation Center for model training and validation. Results show that this method performs well under strong latitude-longitude coupling and remains excellent even under weak latitude-longitude coupling. Furthermore, it improves the tunicate swarm (SSA) optimization method by using an algorithm to find suitable parameters, avoiding interference from subjective human factors. The algorithm has fewer control parameters and is easy to implement. Finally, it incorporates features of adaptive weighting algorithms and outlier algorithms for improvement.

Description

Technical Field

[0001] This invention belongs to the fields of ship maneuvering and artificial intelligence, specifically relating to a ship trajectory prediction method based on improved multi-output support vectors of tunicates. Background Technology

[0002] With the development of the shipbuilding industry and artificial intelligence technology, intelligent ships are gaining increasing attention from countries and institutions. Intelligent ships are technologically advanced, operate around the clock, react quickly, and do not suffer from decision fatigue, giving them significant advantages in both commercial and civilian applications. Intelligent collision avoidance systems, as a crucial component of new intelligent navigation systems, are one of the key technologies of intelligent ships. Intelligent ships achieve scientific collision avoidance functions, ensuring safe navigation in increasingly complex waterway transportation situations, thereby completing various tasks such as transportation, patrolling, and monitoring. Support vector machines (SVMs) have shown good performance in ship trajectory prediction. They can construct decision functions by increasing dimensionality through kernel functions under nonlinear conditions, simultaneously minimizing empirical errors and structural errors (model complexity), avoiding the overfitting problem of neural networks, and exhibiting good modeling capabilities even with small samples, ensuring the real-time prediction of ship trajectories. However, conventional support vector machines are single-output models. In ship trajectory prediction, multiple support vector models are often constructed and their outputs are combined to predict the future trajectory of the ship. However, the method of constructing models separately ignores the coupling relationship between multi-dimensional outputs and performs poorly when there is strong coupling between outputs. Therefore, it is necessary to find a multi-output support vector machine algorithm that takes into account the coupling relationship between outputs. Summary of the Invention

[0003] The purpose of this invention is to provide a ship trajectory prediction method based on improved multi-output support vectors of the tunicate sea squirt.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A ship trajectory prediction method based on improved multi-output support vectors of tunicate sea squirts, the specific steps of which are as follows:

[0006] Step 1: Filter and preprocess the AIS track data provided by the U.S. Coast Guard Navigation Center;

[0007] Step 2: Optimize the hyperparameters of the model by performing parameter optimization on the tunicate.

[0008] Step 3: Construct the final multivariate support vector model and evaluate it;

[0009] Step 4: Select other optimization methods and compare them with various support vector machines.

[0010] Further, step 1 specifically involves using AIS data from the past four time points as input variables. For the time information in the ship's trajectory data, the time difference Δt is used as a feature variable, and the ship's heading is represented by both sine and cosine functions. To avoid the disconnect between 360° and 0° in the heading, let the heading at time t be C. t The corresponding trigonometric function value is sin C. t and cosC t Let δ t and φ t This provides a unique expression for the bow angle.

[0011] To eliminate the differences between different attributes of AIS data and reduce model prediction error, the input data of the model is normalized. After normalization, the attribute differences between data are removed, and all dimensions of data are in the same numerical range, which is limited to [0,1].

[0012] Further, step 2 specifically involves: initializing the SSA population size to 100, setting a maximum number of iterations to 15, initializing the location of the salps population and using the individual salps location values ​​as hyperparameters of the LSSVM to construct a prediction model; employing a three-fold cross-validation LSSVM model, using the error covariance matrix as the loss function, and calculating the fitness of individual salps; updating the individual salps locations according to the salps movement rules to enable the salps population to move.

[0013] Determine if the iteration has ended. If the maximum number of iterations has not been reached, repeat this step except for initialization. Finally, use the position of the best-fit individual in the salps population as the hyperparameter of the MLSSVR prediction model.

[0014] Further, step 3 specifically involves: selecting AIS data from 100 container ships with different trajectories after data cleaning and processing to create input variables as training data; constructing a prediction model using hyperparameters optimized by the sea squirt; and adding the error covariance matrix COV to quantitatively evaluate the coupling error between the output data based on the mean square error (MSE) and correlation coefficient (R) used to evaluate the predicted longitude of the data.

[0015] Further, step 4 specifically involves: verifying the generalization ability of the model by selecting three additional ship trajectories of the same type with significant differences from the training data as validation, obtaining the fitting results of the dynamic information of the AIS data, and evaluating and comparing the improved accuracy of the proposed method in model fitting and ship trajectory prediction with the SALSSVM, Particle Swarm Optimization Support Vector Regression (PSOSVR), and Grid Search Multi-Output Least Squares Support Vector Machine (GRIMLSSVM) to verify the model's generalization ability.

[0016] Technical effect

[0017] Compared with the prior art, the beneficial effects of the present invention are:

[0018] This invention employs an improved tunicate swarm optimization algorithm combined with multi-output least squares support vector regression to construct a ship trajectory prediction model. This model can simultaneously predict changes in the latitude and longitude of the trajectory. The model considers the coupling relationship between latitude and longitude, improving prediction accuracy even with strong coupling between outputs. Furthermore, it improves the tunicate swarm algorithm by incorporating adaptive weights and outlier features, avoiding premature convergence and the tendency to get trapped in local optima in high dimensions. Finally, experiments were conducted using AIS data collected by the U.S. Coast Guard Navigation Center in 2021 for model training and validation, and comparisons were made with predictions from other models. The results show that this invention performs well under conditions of strong latitude and longitude coupling, such as ship turning. It also performs well under conditions of weak latitude and longitude coupling, such as ship straight-ahead navigation, providing decision-making and risk assessment for intelligent ship collision avoidance systems or serving as a reference for maritime personnel. Attached Figure Description

[0019] Figure 1 This is the support vector mapping model of the present invention;

[0020] Figure 2 This is a framework diagram of specific embodiments of the present invention;

[0021] Figure 3 This is a schematic diagram illustrating the change of the loss value of the tunicate seaspining vessel as a function of the number of iterations in this invention;

[0022] Figure 4 This is a flowchart of the iterative optimization process of the *Sulphurus salicifolius* of the present invention. Detailed Implementation

[0023] The present invention will now be further described with reference to the accompanying drawings.

[0024] The purpose of this invention is to address the potential coupling relationships in ship trajectory prediction outputs and construct a deep ship prediction model. It proposes a trajectory prediction method using a multivariate output support vector machine (SVM) optimized by a biomimetic algorithm. The focus is on the coupling relationships between ship outputs, demonstrating good performance even under conditions of strong coupling. Furthermore, the magnitude of hyperparameters (such as regularization factors) in the multivariate SVM affects the balance between structural and empirical risks in the model. This invention improves the Slug Group Algorithm (SSA) optimization method, using an algorithm to find suitable parameters, avoiding interference from subjective human factors. The algorithm has fewer control parameters and is easier to implement. To address the problems of premature convergence and susceptibility to local optima in high-dimensional models, this invention incorporates the characteristics of adaptive weighting and outlier algorithms. The model was trained and validated using AIS data collected by the U.S. Coast Guard Navigation Center. The results show that the proposed method performs well under conditions of strong latitude and longitude coupling and also performs excellently under conditions of weak latitude and longitude coupling.

[0025] In ship trajectory prediction methods, Support Vector Machine (SVR) models can construct decision functions by increasing dimensionality through kernel functions under nonlinear conditions, such as... Figure 1 As shown, by simultaneously minimizing empirical error and structural error (model complexity), the overfitting problem of neural networks is avoided, and good modeling ability is maintained even with small samples, ensuring the real-time performance of ship trajectory prediction. However, conventional support vector machines are single-output models, and ship trajectory prediction often employs the construction of multiple support vector models, combining the outputs of multiple models to predict the future route of the ship. However, the method of constructing models separately ignores the coupling relationship between multi-dimensional outputs, resulting in poor performance when there is strong coupling between outputs. To address these issues, this invention provides a ship trajectory prediction method based on an improved multi-output support vector model of the tunicate sea squirt.

[0026] The overall construction process framework of the model of this invention is as follows: Figure 2 As shown, the entire model framework is mainly divided into four parts: track data processing, parameter optimization, model construction and evaluation, and multi-model result evaluation and comparison. Within this framework, the track data processing part primarily functions to filter and select effective data, extract data features, and perform standardization to enhance data characteristics, such as... Figure 3 As shown, in the parameter optimization part, the salps population searches for the parameters to construct the model in three-dimensional space. After adding adaptive weights, the salps perform a fast global search at the beginning of the iteration, which is relatively slow. However, it converges quickly in the middle stage and performs a local optimum search in the later stage. Even after introducing the outlier algorithm, some salps will still leave the population to search independently, trying to escape possible local optima. The specific flowchart is as follows. Figure 4As shown in the diagram, in the evaluation model construction section, in addition to evaluating the predicted longitude of the data using mean squared error (MSE) and correlation coefficient (R), an error covariance matrix (COV) is added to quantify the coupling error between the output data. This allows the optimization of the *Symplocos salsa* model to incorporate the coupling error between outputs into the loss function, improving the model's understanding of the relationships between multiple outputs. In the multi-model result evaluation and comparison section, multiple sets of AIS data with different track characteristics are compared with other commonly used optimization methods and models, demonstrating the effectiveness and advantages of the improved *Symplocos salsa* multi-output support vector prediction. While maintaining sufficient accuracy when the multi-output coupling is weak, it achieves high accuracy and small error under strong coupling outputs, meeting the collision avoidance decision-making information needs of intelligent ships, proving its practical significance in real-world applications.

[0027] The algorithm for optimizing the parameters of the tunicate sea squirt of this invention is as follows:

[0028] During their movement, salps exhibit a leader performing global exploration while followers engage in thorough local exploration, significantly reducing the likelihood of getting trapped in local optima. This movement pattern endows salps chains with strong global exploration and local exploitation capabilities. This invention uses hyperparameters from MLSSVR, such as regularization factors, relaxation variables, and parameters in the radial basis function, as the positional information of the salps. It uses the covariance of the predicted latitude and longitude as the loss function for the search, and incorporates adaptive weighting algorithms and outlier algorithms to enhance the global and local search capabilities of salps swarms.

[0029] The algorithm first divides the population into two groups: leaders and followers. Leaders search for food and act autonomously, while followers move according to a strict hierarchy, influenced only by the preceding tunicate, in a chain-like manner towards food. Compared to other biological populations, the leader's influence on the group is relatively low; the leader only directly affects the position updates of the followers immediately following them. This influence decreases with each subsequent follower, ensuring diversity among the later-ranking followers during the update process.

[0030] Let the search space be a D×N Euclidean space, where D is the dimension and N is the population size. The position of the tunicate in the space is denoted by X. n =[X n1 ,X n2 ,…,X nD ] T The location of the food is indicated by F. n =[F n1 ,F n2 ,…,F nD ] T This indicates that the upper bound of the search space is μb and the lower bound is lb. The individual positions of the tunicate are initialized as follows:

[0031] X D×N =rand(D,N)·(μb(D,N)-lb(D,N))+lb(D,N) (1)

[0032] To enhance the global optimization ability of salps, the first half of the individuals in the salps chain are designated as leaders. The formula for updating the leader's position is as follows:

[0033]

[0034] Among them, f pos f represents the position of the food (the current global optimum). lead c2 and c3 are random numbers between [0,1], representing the position after the leader moves. Here, l is the decay function used to balance global exploration and local convergence. L is the current iteration number and L is the maximum iteration number.

[0035] The latter half of the individuals in the salver chain are all followers, and their update position movement formula is as follows:

[0036]

[0037] Where f Folli with f Folli-1 These are the updated follower positions and the original follower positions, respectively.

[0038] Calculate the updated population fitness by comparing the updated fitness value of each salps with the fitness value of the current food. If the updated salps have a better fitness value than the food, then the location of the salps with the better fitness value is taken as the new food location. Repeat the above steps until a certain number of iterations are reached or the fitness value reaches a termination threshold. Once the termination condition is met, output the current food location as the estimated location of the target.

[0039] However, the SSA algorithm suffers from problems such as low estimation accuracy, premature convergence, slow convergence speed, and easy getting trapped in local optima during the function optimization process. To address these problems, this invention improves the algorithm by incorporating adaptive inertia weights and outlier image values.

[0040] Adaptive inertia weights are used in many swarm intelligence optimization algorithms. Larger weights in the early stages of the search enhance global search capabilities, while smaller adaptive weights in the later stages enhance local optimization capabilities. The adaptive weight function is as follows:

[0041]

[0042] Among them, w min ,w maxf is the preset minimum and maximum inertia coefficient. mean f is the average fitness of all particles in the current iteration. min This represents the minimum fitness of all particles in the current iteration.

[0043] The lower the fitness, the closer the distance, and in this case, a local search is more necessary;

[0044] The greater the fitness, the farther the distance, and in this case, a global search is even more necessary;

[0045] The formula for the leader's position movement, after adding a self-inertia weight, becomes the following form:

[0046]

[0047] The follower's position movement formula has been updated as follows:

[0048]

[0049] Outcast elephants refer to male elephants in a clan that leave the clan to live independently after reaching a certain age. This invention borrows this idea, setting an outcast value in the tunic chain, so that the individual with the worst fitness no longer follows the previous individual but moves to a random position. This enhances the global optimization ability of the tunic algorithm and avoids getting trapped in local optima.

[0050] The present invention constructs a multivariate support vector model (MSVR) as follows:

[0051] Support Vector Machines (SVMs) utilize an adaptive edge-based loss function to project the learning data into a high-dimensional linear feature space, thereby reducing the complexity of the solution and finding the optimal decision function in the feature space. SVMs are known for their good generalization performance and ability to handle nonlinear models using kernel techniques.

[0052] When solving a regression problem, the problem is transformed into the form of a regression function:

[0053] f(x)=ω T x+b (7)

[0054] Where ω is the weight vector ω∈R n , b is the deviation b∈R.

[0055] Least squares support vector regression (LS–SVR) is an improvement on support vector machines. This algorithm is an improvement on the standard SVM algorithm by Suykens et al. LS–SVR rewrites the first-order loss function of SVM as a second-order loss function, changes the inequality constraints to equality constraints, and uses the sum of squared errors loss function as the empirical loss of the training set. This transforms the problem of solving a quadratic programming problem into the problem of solving a system of linear equations, thus improving the speed and convergence accuracy of the solution.

[0056] The objective function of the least squares method is as follows:

[0057]

[0058] Where, ζ i Here, c is the relaxation factor, and c is the regularization parameter.

[0059] To implement the multi-output functionality of support vector machines, we can use ω i Rewritten as ω i =ω0+v i When the vector v is similar to each other among the multiple outputs of the model i When the differences between the multiple outputs of the model are large, the vector ω0 is small. ω0 represents the commonality among the model outputs. i This indicates the heterogeneity between the model outputs. The objective function under constraints is as follows:

[0060]

[0061] Where, ψ ii =ζ T ζ, V = v T v, v = (v1, v1, ..., v) m )∈R n×m ζ=(ξ1,ξ2,…,ξ m )∈R l×m , W=(ω0+v1,ω0+v2,…,ω0+v m )∈R n×m , B = (b1, b2, ..., b m )∈R l×m λ,γ∈R + These are two regularization parameters.

[0062] The above equation can be transformed into an unconstrained Lagrange problem as follows:

[0063]

[0064] Where A = (α1, α2, ..., α) m )∈R l×m Let be the Lagrange operator matrix. Solve according to the KKT conditions.

[0065] Therefore, the above optimization problem can be equivalently represented as a constrained optimization problem involving only V and B, as shown below:

[0066]

[0067] Similar to LSSVM, eliminating V,ζ through KKT conditions yields the following linear system:

[0068]

[0069] in,

[0070] Solving for α and b using the above equation yields the nonlinear ship trajectory prediction model represented by the kernel function:

[0071]

[0072] Ship trajectory prediction uses mean squared error (MSE) and correlation coefficient (R) to evaluate the predicted longitude of the data. This paper, in addition to using these two methods, adds the error covariance matrix (COV) to quantify the coupling error between the output data. This allows the optimization of the *Symplocos salina* model to incorporate the coupling error between outputs into the loss function, improving the model's understanding of the relationships between multiple outputs. Assume the true value is y = {(y...} 11 ,y 12 ),(y 21 ,y 22 ),…,(y n1 ,y n2 The predicted value is )} The expression for the evaluation index is:

[0073]

[0074]

[0075]

[0076] in

[0077] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A ship track prediction method based on improved sea squirt multi-output support vector, characterized in that: The specific steps are as follows: Step 1: Screening and preprocessing of AIS track data provided by the US Coast Guard Navigation Center; Step 2: Parameter optimization of the model; The adaptive weight function is as follows: Among them, w min ,w max f is the preset minimum and maximum inertia coefficient. mean f is the average fitness of all particles in the current iteration. min This represents the minimum fitness of all particles in the current iteration. The smaller the fitness, the closer the distance, and the more local search is needed; The larger the fitness, the farther the distance, and the more global search is needed; The leader's position movement formula is changed to the following form after increasing the self-inertia weight: The follower's position movement formula is updated as follows: In the sea squirt chain, the out-of-range value is set, and the individual with the worst fitness is moved to a random position, so that the sea squirt algorithm enhances the global optimization ability; Step 3: Constructing the final multi-element support vector model and evaluating it; Step 4: Selecting other optimization methods and comparing them with various support vector machines.

2. The ship track prediction method based on improved Ciona intestinalis multi-output support vector of claim 1, characterized in that: Step 1 is specifically: AIS data of the past 4 time points as input variables, the time information in the ship track data adopts the time difference Δt as a characteristic variable, and the ship heading is jointly represented by the sine and cosine functions; to avoid the split problem of the ship heading from 360° to 0°, the ship heading at time t is C t , and the corresponding trigonometric function converted value is sinC t and cosC t , set as δ t and φ t , to uniquely express the ship heading angle; To eliminate the differences between different attributes of AIS data and reduce the prediction error of the model, the input data of the model is normalized. After normalization, the attribute difference between data is removed, and all dimensions of data are limited to [0, 1].

3. The ship track prediction method based on improved Ciona intestinalis multi-output support vector of claim 1, characterized in that: Step 2: Initialize the SSA population size to 100, set the maximum number of iterations to 15, initialize the sea squirt group position, and set the sea squirt individual position value as the LSSVM hyperparameter to construct the prediction model; use three-fold cross-validation LSSVM model, use error covariance matrix as loss function, calculate sea squirt individual fitness; update sea squirt individual position according to sea squirt movement rule, make sea squirt group move; If the maximum number of iterations is not reached, repeat this step except initialization; finally, the optimal fitness individual position in the sea squirt population is used as the hyperparameter of the MLSSVR prediction model.

4. The ship track prediction method based on improved Ciona intestinalis multi-output support vector of claim 1, characterized in that: Step 3: After data cleaning and processing, select 100 AIS data of different tracks of container ships to make input variables as training data, select sea squirt optimized hyperparameters to construct prediction model, use mean square error MSE and correlation coefficient R to evaluate the prediction longitude of data, and add error covariance matrix COV to quantitatively evaluate the coupling error between output data.

5. The ship track prediction method based on improved sea squirt multi-output support vector of claim 1, characterized in that: Step 4: Verify the generalization ability of the model, select 3 different ship trajectories of the same type as verification in addition to the training data, get the fitting result of AIS data dynamic information, and select sea squirt least square support vector machine SSALSSVM, particle swarm support vector regression PSOSVR, and grid search multi-output least square support vector machine GRIMLSSVM for evaluation and comparison.

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