An adaptive physical information-guided ship trajectory probability prediction method

Abstract

This invention discloses an adaptive physical information-guided ship trajectory probability prediction method. The method includes the following steps: collecting historical time series ship trajectory data to construct a standardized dynamic feature sequence; deducing physical trajectory evolution characteristics based on the ship's three-degree-of-freedom dynamic model, extracting data-driven features using a time-series convolutional encoder, and dynamically fusing them with physical feature weights; inputting the fused features into a multi-layer nested Gaussian process module, using a deep Gaussian process to model the feature distribution layer by layer, and ultimately outputting a complete probability distribution of predicted control variables; sampling based on the predicted control variable distribution, generating a future trajectory distribution that meets physical constraints through three-degree-of-freedom dynamic integration, and defining a joint loss function to reversely optimize neural network parameters. This method balances trajectory prediction accuracy, physical rationality, and uncertainty quantification capabilities, providing reliable support for intelligent monitoring of water transportation.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent water transportation, and in particular relates to a ship trajectory probability prediction method guided by adaptive physical information. Background Art

[0002] With the rapid development of the global shipping industry, the density of waterway traffic continues to rise, and the navigation environment is becoming increasingly complex. Collisions between ships and between ships and fixed structures on the water are becoming frequent, posing a serious threat to navigation safety and the safety of port and shipping facilities. In this context, ship trajectory prediction has attracted widespread attention as a key means of ensuring navigation safety and reducing collision risks. Accurate, real-time prediction of future ship trajectories provides critical support for collision warning, intelligent waterway scheduling, maritime traffic flow management, and emergency decision-making.

[0003] Existing research on ship trajectory prediction primarily relies on data-driven approaches, employing machine learning or deep learning techniques to model historical trajectory data. Typical approaches include traditional machine learning models such as support vector machines and random forests, as well as deep time series models such as recurrent neural networks, long short-term memory networks, and temporal convolutional networks. These approaches learn from large amounts of historical trajectory data to fit ship motion patterns and achieve short-term or medium- to long-term predictions of future trajectories. These approaches have achieved some success in specific scenarios. However, purely data-driven approaches generally suffer from the following shortcomings: Firstly, they rely heavily on large-scale, high-quality annotated data, leading to significant performance degradation when trajectory data is scarce, subject to noise, or in a changing environment. Secondly, these approaches often overlook the dynamic laws and physical constraints governing ship motion. Consequently, in environments with complex currents, wind, and waves, predicted trajectories may exhibit physical implausibility, dynamic distortion, or significant deviations from the true trajectory. Furthermore, existing approaches have limited ability to model the uncertainty of future motion, making it difficult to effectively quantify prediction confidence. This poses potential risks in safety-critical applications such as ship collision warning.

[0004] In recent years, some research has attempted to incorporate physical information, such as dynamic equations and motion constraints, into trajectory prediction to overcome the limitations of purely data-driven approaches. The incorporation of physical information not only improves the model's ability to interpret real-world motion mechanisms but also enhances the physical plausibility and robustness of predictions in small sample sizes or out-of-distribution scenarios, showing promising development prospects. Summary of the Invention

[0005] Technical Problem: This invention addresses the shortcomings of existing ship trajectory prediction methods in terms of physical consistency, extrapolation capability, and uncertainty modeling by proposing an adaptive, physical-information-guided probabilistic ship trajectory prediction method. This method integrates physical features derived from a ship's three-degree-of-freedom dynamics model with temporal features extracted through data-driven analysis. The method dynamically adjusts the weights of these two features through an adaptive fusion mechanism. Furthermore, a deep Gaussian process is introduced as a control variable prediction module to achieve complete probabilistic distribution modeling of the control variable.

[0006] Technical solution: The present invention provides an adaptive physical information-guided ship trajectory probability prediction method comprising the following steps:

[0007] Step 1, data acquisition and preprocessing: collect historical time series ship trajectory data, calculate heading angle, heading angular rate, acceleration and heading angular acceleration, and perform normalization to construct a standardized dynamic feature sequence;

[0008] Step 2: Adaptive physics-data joint modeling: Based on the ship's three-degree-of-freedom dynamics model, the physical trajectory evolution characteristics are deduced. The data-driven features of the standardized dynamic feature sequence obtained in step 1 are extracted through the temporal convolutional Transformer encoder (TCT). The fusion weights are dynamically adjusted based on the physical and data features to achieve adaptive feature fusion.

[0009] Step 3: Control variable probability prediction based on deep Gaussian process (DGP): The fused features are input into a multi-layer nested Gaussian process module, which models the feature distribution layer by layer and ultimately outputs the complete probability distribution of the predicted control variable.

[0010] Step 4, physical-guided trajectory deduction and optimization: Sampling is performed based on the predicted control quantity distribution, and the future trajectory distribution that meets the physical constraints is generated through three-degree-of-freedom dynamic integral deduction. A joint loss function is defined, including trajectory reconstruction loss, deep Gaussian process negative log-likelihood loss, and physical consistency loss. Based on this joint loss function, the neural network parameters are reversely optimized to predict the future ship trajectory.

[0011] in:

[0012] In step 1, the data collection and preprocessing steps specifically include:

[0013] Use microwave radar to collect ship trajectory data to form a time series set The fixed radar reference system takes the radar installation point as the origin, the X-axis is parallel to the mainstream direction of the channel, and the Y-axis is perpendicular to the X-axis, forming a right-handed rectangular coordinate system; among them, t Corresponding sampling timestamp, x t for tThe position coordinate of the ship in the X-axis direction of the fixed radar reference system at this moment, y t for t The position coordinate of the ship in the Y-axis direction of the fixed radar reference system at this moment, v t For ships in t Radial velocity at time;

[0014] Estimate the ship's t Heading angle at the moment , heading angular rate r t , acceleration , heading angular acceleration , the calculation formula is:

[0015] ,

[0016] in is the time interval between adjacent frames, y t-1 for t The position coordinate of the ship in the Y-axis direction of the fixed radar reference system at time -1, x t-1 for t -1 moment, the position coordinate of the ship in the X-axis direction of the fixed radar reference system, The ship is t -1 heading angle at time, v t-1 The ship is t Radial velocity at time -1, r t-1 yes t -1 moment ship heading angular rate;

[0017] Combined dynamics eigenvector , and normalize it to obtain a standardized feature sequence .

[0018] In step 2, the adaptive physical-data joint modeling specifically includes a physical deduction module, a data feature modeling module, and an adaptive fusion module;

[0019] Physical deduction module: The future trajectory of the ship is deduced based on the 3-DOF dynamic model. During the deduction process, the transverse velocity component is ignored and the ship's track change is assumed to be dominated by the longitudinal navigation and heading angle changes. The 3-DOF dynamic equations are:

[0020] ,

[0021] in for tThe longitudinal velocity component of the ship at time for t The lateral velocity component of the ship at time for t The rate of change of the ship's heading angle at the moment. Extract physical deduction features, including: instantaneous track curvature and the instantaneous acceleration modulus ;

[0022] Data feature modeling module: standardize the feature sequence The multi-layer perceptron is input to perform feature dimensionality upgrade to enhance the expressive power of the original normalized dynamic features. The upgraded features are input to the temporal convolutional transformer encoder (TCT) to extract local dynamic changes and long-term evolution trends to form a data-driven feature vector. ;

[0023] Adaptive fusion module: dynamically calculates adaptive fusion weights based on physical deduction characteristics and data-driven characteristics , the value range is [0, 1], as follows:

[0024] ,

[0025] Where, is the parameter matrix; is the bias term; is the Sigmoid activation function;

[0026] Finally, the physical and data features are integrated: ,

[0027] Where, is the fusion feature vector; is the physical deduction eigenvector.

[0028] In step 3, the control variable probability prediction step based on the deep Gaussian process DGP specifically includes:

[0029] Fusion feature sequence Input DGP, each layer The conditional distribution of the model input features is:

[0030] ,

[0031] in, For the The fused feature samples output by the layer; For the -1 layer output fusion feature sample; For the Layer Gaussian process mapping, which models the nonlinear correlation between input and output based on kernel functions; It is the pre-processing function of input features, including affine transformation, feature expansion and other operations;

[0032] Gaussian process kernel function Used to measure the similarity of input points, the radial basis kernel function is selected, which is in the form of:

[0033] ,

[0034] Where, is the kernel function amplitude, i.e. the output standard deviation; d is the Euclidean distance between any two input samples; is the kernel function length scale, which controls the influence of input changes on output correlation;

[0035] The final layer outputs the acceleration of each future time step and angular acceleration The predictive distribution of is in the form of the complete probability distribution modeled by the multi-layer Gaussian process, rather than a single mean or variance prediction.

[0036] In step 4, the physical guidance trajectory deduction and optimization step specifically includes:

[0037] According to the control quantity distribution of the deep Gaussian process DGP prediction output, random sampling is performed to obtain the first n subsampled control samples ;

[0038] ,

[0039] Where, For the n subsampled acceleration; For the n subsampled heading angular acceleration; 、 are the mean and standard deviation of the predicted distribution of longitudinal acceleration; 、 is the mean and standard deviation of the predicted distribution of heading angular acceleration; 、 are independent standard normal random variables;

[0040] The control quantity sample is input into the three-degree-of-freedom dynamic model for trajectory deduction. According to the deduced trajectory and the actual trajectory data, a joint loss function is defined. , including the following three parts:

[0041] Trajectory reconstruction error loss :

[0042] ,

[0043] Where, is the predicted trajectory coordinate; T is the number of prediction time steps;

[0044] Deep Gaussian Process DGP Variational Negative Log-Likelihood Loss :

[0045] ,

[0046] Where, is the approximate posterior distribution of the deep Gaussian process DGP; is the true posterior distribution; is the observation likelihood distribution of the trajectory control quantity; is the relative entropy, which measures the difference between two distributions, Indicates that the approximate distribution The mathematical expectation under

[0047] Loss of physical consistency :

[0048] ,

[0049] Where, v max is the maximum radial velocity allowed; r max is the maximum allowed heading angular rate; ReLU(·) is the activation function;

[0050] Joint total loss function Defined as:

[0051] ,

[0052] 、 、 are weight coefficients respectively; the back propagation algorithm is used based on the total loss function Optimize deep neural network parameters and complete model training.

[0053] Beneficial effects: After adopting the above scheme, the advantages of the present invention are as follows:

[0054] (1) The present invention introduces a three-degree-of-freedom dynamics model to deduce physical characteristics, which improves the physical consistency and motion rationality of the predicted trajectory and effectively avoids the physical distortion problem commonly found in pure data-driven methods.

[0055] (2) The present invention adaptively integrates physical and data features and dynamically adjusts the feature contribution ratio, thus maintaining high prediction accuracy and stability in complex environments and changing data distribution.

[0056] (3) The present invention adopts a deep Gaussian process, which can output the probability distribution of future control quantities, realize the quantification of the credibility of the prediction results, and provide support for risk assessment and intelligent decision-making.

[0057] (4) The present invention combines physical deduction with deep feature extraction and integrates probability prediction, which has higher prediction accuracy and good engineering application prospects in complex shipping environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a flow chart of the present invention;

[0059] Figure 2 Schematic diagram of the temporal convolution Transformer encoder model, TCN-1 is the first temporal convolution layer, TCN-2 is the second temporal convolution layer, TCN- n For the n Layer temporal convolution layer;

[0060] Figure 3 Schematic diagram of the deep Gaussian process DGP model. DETAILED DESCRIPTION

[0061] The technical solutions and beneficial effects of the present invention will be described in detail below with reference to the accompanying drawings.

[0062] like Figure 1 As shown, the present invention provides a ship trajectory probability prediction method guided by adaptive physical information, comprising the following steps:

[0063] Step 1, data collection and preprocessing: collect historical time series of ship trajectory data, calculate the heading angle, heading angular rate, acceleration and heading angular acceleration, and perform normalization to construct a standardized dynamic feature sequence.

[0064] Step 2: Adaptive physical-data joint modeling: Based on the ship's three-degree-of-freedom dynamic model, the physical trajectory evolution characteristics are deduced, and data-driven features are extracted through the temporal convolutional Transformer encoder TCT (Temporal Convolutional Transformer). The fusion weights are dynamically adjusted according to the physical and data characteristics to achieve adaptive feature fusion.

[0065] Step 3: Control quantity probability prediction based on Deep Gaussian Processes (DGP): The fused features are input into a multi-layer nested Gaussian process module, which models the feature distribution layer by layer and ultimately outputs the complete probability distribution of the predicted control quantity.

[0066] Step 4, physics-guided trajectory deduction and optimization: Sampling is performed based on the predicted control quantity distribution, and the future trajectory distribution that meets the physical constraints is generated through three-degree-of-freedom dynamic integral deduction. A joint loss function is defined, including trajectory reconstruction loss, deep Gaussian process negative log-likelihood loss, and physical consistency loss. The neural network parameters are reversely optimized based on this joint loss function.

[0067] In step 1, the data collection and preprocessing steps specifically include:

[0068] Use microwave radar to collect ship trajectory data to form a time series set The fixed radar reference system takes the radar installation point as the origin, the X-axis is parallel to the mainstream direction of the channel, and the Y-axis is perpendicular to the X-axis, forming a right-handed rectangular coordinate system. t Corresponding sampling timestamp, x t is the position coordinate of the ship in the X-axis direction of the fixed radar reference system, y t is the position coordinate of the ship in the Y-axis direction of the fixed radar reference system, v t For ships in t Radial velocity at time.

[0069] Estimate the ship's t Heading angle at the moment , heading angular rate r t , acceleration , heading angular acceleration , the calculation formula is:

[0070] ,

[0071] in is the time interval between adjacent frames, y t-1 for t The position coordinate of the ship in the Y-axis direction of the fixed radar reference system at time -1, x t-1 for t -1 moment, the position coordinate of the ship in the X-axis direction of the fixed radar reference system, The ship is t -1 heading angle at time, v t-1 The ship is t Radial velocity at time -1, r t-1 yes t -1 The ship's heading angular rate at the moment.

[0072] Combined dynamics eigenvector , and normalize it to obtain the standardized feature sequence .

[0073] In step 2, the adaptive physical-data joint modeling specifically includes a physical deduction module, a data feature modeling module, and an adaptive fusion module.

[0074] Physical deduction module: The future trajectory of the ship is deduced based on the three-degree-of-freedom (3-DOF) dynamic model. During the deduction process, the transverse velocity component is ignored and it is assumed that the change in the ship's track is dominated by the change in longitudinal navigation and heading angle. The 3-DOF dynamic equations are:

[0075] ,

[0076] in for t The longitudinal velocity component of the ship at time for t The lateral velocity component of the ship at time for t The rate of change of the ship's heading angle at the moment. Extract physical deduction features, including: instantaneous track curvature and the instantaneous acceleration modulus .

[0077] Data feature modeling module: such as Figure 2 As shown, the normalized feature sequence Input the multi-layer perceptron to perform feature dimensionality upgrade to enhance the expressive power of the original normalized dynamic features. Input the upgraded features into the TCT encoder to extract local dynamic changes and long-term evolution trends to form a data-driven feature vector .

[0078] Adaptive fusion module: dynamically calculates adaptive fusion weights based on physical deduction characteristics and data-driven characteristics , the value range is [0, 1], as follows:

[0079] ,

[0080] Where, is the parameter matrix; is the bias term; is the Sigmoid activation function.

[0081] Finally, the physical and data features are integrated:

[0082] ,

[0083] Where, is the fusion feature vector; is the physical deduction eigenvector.

[0084] In step 3, the control amount probability prediction step based on DGP specifically includes:

[0085] like Figure 3 As shown, the fusion features Input deep Gaussian process DGP. Each layer Model the conditional distribution of input features, which is of the form:

[0086] ,

[0087] in, For the The fused feature samples output by the layer; For the -1 layer output fusion feature sample; For the Layer Gaussian process mapping, which models the nonlinear correlation between input and output based on kernel functions; It is a pre-processing function for input features, which may include operations such as affine transformation and feature expansion.

[0088] Gaussian process kernel function Used to measure the similarity of input points, the radial basis kernel (RBF kernel) is often used, in the form of:

[0089] ,

[0090] Where, is the kernel function amplitude (output standard deviation); d is the Euclidean distance between any two input samples; is the kernel function length scale, which controls the impact of input changes on output correlation.

[0091] The final layer outputs the acceleration of each future time step and angular acceleration The predictive distribution of is in the form of the complete probability distribution modeled by the multi-layer Gaussian process, rather than a single mean or variance prediction.

[0092] In step 4, the physical guidance trajectory deduction and optimization step specifically includes:

[0093] According to the control quantity distribution of the deep Gaussian process DGP prediction output, random sampling is performed to obtain the first n subsampled control samples :

[0094] ,

[0095] Where, For the nsubsampled acceleration; For the n Subsampled heading angular acceleration; 、 are the mean and standard deviation of the predicted distribution of longitudinal acceleration; 、 is the mean and standard deviation of the predicted distribution of heading angular acceleration; 、 are independent standard normal random variables.

[0096] The control quantity sample is input into the three-degree-of-freedom dynamic model for trajectory deduction. Based on the deduced trajectory and the actual trajectory data, a joint loss function is defined: , including the following three parts:

[0097] Trajectory reconstruction error loss :

[0098] ,

[0099] Where, is the predicted trajectory coordinate; T is the number of prediction time steps.

[0100] Deep Gaussian Process DGP Variational Negative Log-Likelihood Loss :

[0101] ,

[0102] Where, is the approximate posterior distribution of the deep Gaussian process DGP; is the true posterior distribution; is the observation likelihood distribution of the trajectory control quantity; is the relative entropy, which measures the difference between two distributions; Indicates that the approximate distribution The mathematical expectation of .

[0103] Loss of physical consistency :

[0104] ,

[0105] Where, v max is the maximum radial velocity allowed; r max is the maximum allowed heading angular rate; ReLU(·) is the activation function.

[0106] Joint total loss function Defined as: ,

[0107] 、 、 are weight coefficients respectively. The back propagation algorithm is used based on the total loss function , optimize the deep neural network parameters and complete the model training.

Claims

1. A ship trajectory probability prediction method guided by adaptive physical information, characterized by The steps include: Step 1, data acquisition and preprocessing: collect historical time series ship trajectory data, calculate heading angle, heading angular rate, acceleration and heading angular acceleration, and perform normalization to construct a standardized dynamic feature sequence; Step 2: Adaptive physics-data joint modeling: Based on the ship's three-degree-of-freedom dynamics model, the physical trajectory evolution characteristics are deduced. The data-driven features of the standardized dynamic feature sequence obtained in step 1 are extracted through the temporal convolutional Transformer encoder (TCT). The fusion weights are dynamically adjusted based on the physical and data features to achieve adaptive feature fusion. Step 3: Control variable probability prediction based on deep Gaussian process (DGP): The fused features are input into a multi-layer nested Gaussian process module, which models the feature distribution layer by layer and ultimately outputs the complete probability distribution of the predicted control variable. Step 4, physical-guided trajectory deduction and optimization: Sampling is performed based on the predicted control quantity distribution, and the future trajectory distribution that meets the physical constraints is generated through three-degree-of-freedom dynamic integral deduction. A joint loss function is defined, including trajectory reconstruction loss, deep Gaussian process negative log-likelihood loss, and physical consistency loss. Based on this joint loss function, the neural network parameters are reversely optimized to predict the future ship trajectory.

2. The method for predicting ship trajectory probability guided by adaptive physical information according to claim 1, characterized in that: In step 1, the data collection and preprocessing steps specifically include: Use microwave radar to collect ship trajectory data to form a time series set The fixed radar reference system takes the radar installation point as the origin, the X-axis is parallel to the mainstream direction of the channel, and the Y-axis is perpendicular to the X-axis, forming a right-handed rectangular coordinate system; among them, t Corresponding sampling timestamp, x t for t The position coordinates of the ship in the X-axis direction of the fixed radar reference system at this moment, y t for t The position coordinate of the ship in the Y-axis direction of the fixed radar reference system at this moment, v t For ships in t Radial velocity at time; Estimate the ship's t Heading angle at the moment , heading angular rate r t , acceleration , heading angular acceleration , the calculation formula is: ， in is the time interval between adjacent frames, y t-1 for t The position coordinate of the ship in the Y-axis direction of the fixed radar reference system at time -1, x t-1 for t -1 moment, the position coordinate of the ship in the X-axis direction of the fixed radar reference system, The ship is t -1 heading angle at time, v t-1 The ship is t Radial velocity at time -1, r t-1 yes t -1 moment ship heading angular rate; Combined dynamics eigenvector , normalize it and get the standardized feature sequence .

3. The method for ship trajectory probability prediction guided by adaptive physical information according to claim 1, characterized in that: In step 2, the adaptive physical-data joint modeling specifically includes a physical deduction module, a data feature modeling module, and an adaptive fusion module; Physical deduction module: The future trajectory of the ship is deduced based on the 3-DOF dynamic model. During the deduction process, the transverse velocity component is ignored and the ship's track change is assumed to be dominated by the longitudinal navigation and heading angle changes. The 3-DOF dynamic equations are: ， in for t The longitudinal velocity component of the ship at time for t The lateral velocity component of the ship at time for t The rate of change of the ship's heading angle at any moment; Extract physical deduction features, including instantaneous track curvature and the instantaneous acceleration modulus ; Data feature modeling module: standardize the feature sequence The multi-layer perceptron is input to perform feature dimensionality upgrade to enhance the expressive power of the original normalized dynamic features. The upgraded features are input to the temporal convolutional transformer encoder (TCT) to extract local dynamic changes and long-term evolution trends to form a data-driven feature vector. ; Adaptive fusion module: dynamically calculates adaptive fusion weights based on physical deduction characteristics and data-driven characteristics , the value range is [0, 1], as follows: ， Where, is the parameter matrix; is the bias term; is the Sigmoid activation function; Finally, the physical and data features are integrated: , Where, is the fusion feature vector; is the physical deduction eigenvector.

4. The method for ship trajectory probability prediction guided by adaptive physical information according to claim 1, characterized in that: In step 3, the control variable probability prediction step based on the deep Gaussian process DGP specifically includes: Fusion feature sequence Input deep Gaussian process DGP, each layer The conditional distribution of the model input features is: ， in, For the The fused feature samples output by the layer; For the -1 layer output fusion feature sample; For the Layer Gaussian process mapping, which models the nonlinear correlation between input and output based on kernel functions; It is the pre-processing function of input features, including affine transformation and feature expansion operations; Gaussian process kernel function Used to measure the similarity of input points, the radial basis kernel function is selected, which is in the form of: ， Where, is the kernel function amplitude, i.e. the output standard deviation; d is the Euclidean distance between any two input samples; is the kernel function length scale, which controls the influence of input changes on output correlation; The final layer outputs the acceleration of each future time step and angular acceleration The predictive distribution of is in the form of the complete probability distribution modeled by the multi-layer Gaussian process, rather than a single mean or variance prediction.

5. The method for ship trajectory probability prediction guided by adaptive physical information according to claim 1, characterized in that: In step 4, the physical guidance trajectory deduction and optimization step specifically includes: According to the control quantity distribution of the deep Gaussian process DGP prediction output, random sampling is performed to obtain the first n subsampled control samples : ， Where, For the n subsampled acceleration; For the n subsampled heading angular acceleration; 、 are the mean and standard deviation of the predicted distribution of longitudinal acceleration; 、 is the mean and standard deviation of the predicted distribution of heading angular acceleration; 、 are independent standard normal random variables; The control quantity sample is input into the three-degree-of-freedom dynamic model for trajectory deduction. According to the deduced trajectory and the actual trajectory data, a joint loss function is defined. , including the following three parts: Trajectory reconstruction error loss : ， Where, is the predicted trajectory coordinate; T is the number of prediction time steps; Deep Gaussian Process DGP Variational Negative Log-Likelihood Loss : ， Where, is the approximate posterior distribution of the deep Gaussian process DGP; is the true posterior distribution; is the observation likelihood distribution of the trajectory control quantity; is the relative entropy, which measures the difference between two distributions; Indicates that the approximate distribution The mathematical expectation under Loss of physical consistency : ， Where, v max is the maximum radial velocity allowed; r max is the maximum allowed heading angular rate; ReLU(·) is the activation function; Joint total loss function Defined as: ， 、 、 are weight coefficients respectively; the back propagation algorithm is used based on the total loss function Optimize deep neural network parameters and complete model training.

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