Machine learning identification modeling method for intelligent ship maneuvering motion based on PINN

Abstract

The present application relates to the technical field of ship motion identification modeling, and discloses an intelligent ship maneuvering motion machine learning identification modeling method based on PINN. The present application first constructs an intelligent ship maneuvering motion fusion model: a mechanism model considering the influence of hydrodynamic force, rudder angle and propeller is constructed by referring to Abkowitz's overall model, a data-driven model fitting the response of uncertain disturbance is constructed, and then the two are weighted and fused; subsequently, based on physical information neural network modeling, the input and output of PINN are determined, a total loss function coupled with the physical loss function and the data loss function is designed, and the network parameters are trained and optimized through normalization processing and cyclic iteration. The Z-shaped maneuvering test data of the Mariner ship is verified, and the model is significantly improved in accuracy, robustness and interpretability, which can meet the needs of intelligent ship autonomous navigation.

Description

Technical Field

[0001] This invention relates to the field of boat motion recognition and modeling, and more particularly to a machine learning-based method for intelligent boat handling motion recognition and modeling based on PINN. Background Technology

[0002] In recent years, with the rapid development of information technology and artificial intelligence, the intelligence level of ships has been continuously improving, and intelligent ships have become a hot topic in the shipping industry. Intelligent ships, also known as autonomous surface vessels, integrate the Internet of Things, big data, and artificial intelligence technologies, possessing advantages such as safety, reliability, and economy, and represent the future direction of ship development. Furthermore, the development of advanced technologies such as digital twins, cloud computing, and ship-shore collaboration has greatly promoted the intelligent management of shipping transportation. Undoubtedly, continuous monitoring and evaluation of ships, as well as the construction of shore-based control centers, will enable ships to develop in a more flexible and intelligent manner.

[0003] With the rapid development of intelligent vessels, they are gradually becoming excellent alternatives to traditional vessels. The autonomous navigation and collision avoidance systems of intelligent vessels require a more intelligent motion mathematical model to meet the needs of motion characteristic analysis and motion planning control during operation. Over the past few decades, vessel maneuvering modeling has played a crucial role in vessel controllers, maritime traffic simulators, and vessel design evaluation. Autonomous navigation technology is a key technology for realizing vessel motion functions, and establishing a vessel maneuvering motion mathematical model is an important foundation for the research and development of autonomous navigation systems. A high-precision vessel motion model is the basis for designing a reliable navigation controller and accurately predicting vessel maneuvering motion. Therefore, establishing a reliable and effective vessel maneuvering motion mathematical model is of great significance for improving the intelligence level of vessels. With the development of autonomous vessel technology, the safety of autonomous navigation has become particularly important. An accurate vessel maneuvering model has high practical value for providing accurate motion prediction or designing control systems. When vessels perform tasks requiring high maneuverability, such as obstacle avoidance or navigation in narrow waters, the vessel dynamics model can be used to predict the vessel's future behavior or trajectory and determine whether the current control strategy is safe or whether the planned path meets dynamic constraints. Then, the vessel takes the correct actions to avoid a collision. Furthermore, mathematical modeling of vessel maneuvering motion, as a fundamental technology for autonomous vessel digital twin systems, has been extensively studied. Establishing a reliable maneuvering model helps calibrate the performance of modified vessels, promoting digital twins and vessel automation. Currently, the number of intelligent vessels under construction is steadily increasing, clearly outlining the goal of moving towards a digital and automated era. Obviously, to achieve better maneuvering, control, and monitoring, the demand for high-precision vessel maneuvering models will increase significantly.

[0004] Currently, the identification of ship maneuvering motion models often employs methods that rely solely on fitting ship motion data. However, when ships navigate in open environments where water and air meet, they are subject to complex influences from time-varying environmental factors such as wind, waves, and currents. Their maneuvering motion also changes with their navigation conditions, such as ballast and speed, exhibiting strong nonlinear characteristics. Therefore, while this data-driven identification method can reflect the ship's maneuvering motion characteristics to some extent, it often struggles to balance modeling accuracy and physical interpretability. Research on the fusion of ship motion mechanisms and data often focuses on a simple combination of the two, typically using the data-driven model as a correction term to fit uncertainties such as environmental disturbances and measurement errors encountered during navigation. By introducing a weighting coefficient, a simple linear weighted combination of data and mechanistic models is performed, thereby improving the model's interpretability to some extent. However, this fusion approach remains relatively simplistic, treating data and physical laws as two independent factors. It fails to fully explore the potential synergistic effects between the data-driven model and the mechanistic model, lacking a deep-level fusion mechanism. Consequently, the model's adaptability and accuracy in different navigation scenarios remain limited. Summary of the Invention

[0005] To address the aforementioned problems, this invention discloses a machine learning-based modeling method for intelligent vessel maneuvering motion identification based on PINN, comprising the following steps:

[0006] S1. Construct a fusion model of intelligent vessel handling motion:

[0007] S11. Analyze the maneuvering characteristics of intelligent vessels, considering the influence of three types of mechanistic factors—hydrodynamics, rudder angle, and propeller—on the vessel's motion, describe the vessel's motion process under different maneuvering conditions, and construct a mechanistic model.

[0008] S12. Analyze the characteristics of uncertainties affecting the navigation process of the vessel. Considering the influence of the natural environment, the changes in its own load, and the errors caused by the sensors in collecting and transmitting information, construct a data-driven model. The data-driven model uses the vessel's motion state, thrust, and rudder angle as inputs to fit the dynamic change response of the vessel to the above-mentioned uncertainties.

[0009] S13. Based on the aforementioned mechanism model and data-driven model, construct a fusion model of ship handling motion that integrates mechanism and data;

[0010] S2. Intelligent vessel maneuvering motion recognition and modeling based on physical information neural networks:

[0011] S21. Determine the input and output of PINN: The input layer contains the state variables and control variables of the boat's motion, and the output layer contains the state change variables of the boat's motion and the combined external forces and torques;

[0012] S22. Design the loss function of PINN: including a physical loss function based on the physical laws of boat motion and a data loss function based on data-driven mean square error. Couple the physical loss function and the data loss function to obtain the total loss function.

[0013] S23. Training PINN: By minimizing the total loss function, the network parameters of PINN are updated using an optimizer to complete the construction of the intelligent boat handling motion recognition model.

[0014] Preferably, in step S11, the mechanism model is constructed with reference to the Abkowitz global model, and uses Taylor series expansion while retaining third-order terms to describe the hydrodynamics and torques during the boat's motion in a dimensionless manner.

[0015] The Abkowitz holistic model treats the boat, propeller, and rudder as a whole, represents the hydrodynamic forces acting on the boat as functions of motion and control inputs, and uses sway speed, roll speed, and bow angular velocity as state variables, and rudder angle as control variable.

[0016] Preferably, in step S12, the boat motion parameters generated by the uncertainty interference include four parts, namely, parameters generated by changes in the boat's navigation state and sensor influence, parameters generated by wind influence, parameters generated by wave influence, and parameters generated by current influence.

[0017] The actual motion parameters of a boat are equal to the sum of the motion parameters of the boat under undisturbed conditions and the motion parameters of the boat caused by the aforementioned uncertainties and disturbances.

[0018] Preferably, in step S13, the fusion model is a weighted fusion model, which is obtained by multiplying the mechanism model and the data-driven model by their respective weights and then adding them together, wherein the weights of the mechanism model and the data-driven model are preset weight coefficients.

[0019] The data-driven model focuses on predicting residuals, which are the differences between the actual values ​​of the vessel's motion state and the predicted values ​​of the mechanistic model. The predicted values ​​of the residuals and the predicted values ​​of the mechanistic model are connected by direct summation, thereby combining the mechanistic model and the data-driven model.

[0020] Preferably, in step S21, the state variables of the PINN input layer are velocity vectors, which include sway velocity, roll velocity, and bow angular velocity; the control variables include thrust, rudder angle, and rudder angle.

[0021] The tensor shape of the input layer is a tensor that is 6 times the number of data in each batch, where the number of data in each batch is the sample size of the input data in each batch during training.

[0022] The state change variables of the output layer are acceleration vectors, which include sway acceleration, roll acceleration, and pitch acceleration.

[0023] The combined external forces and moments include horizontal thrust, lateral force, and yaw moment; the tensor shape of the output layer is also a tensor of 6 times the number of data in each batch.

[0024] Preferably, in step S21, the PINN has at least 3 hidden layers, wherein the number of neurons in the first to fourth hidden layers is 128 each, and the number of neurons in the fifth hidden layer is 64.

[0025] The hidden layer uses the hyperbolic tangent activation function, the output layer uses the linear activation function, and the dropout coefficient of the hidden layer is set to 0.2 to prevent the model from overfitting.

[0026] Preferably, in step S22, the physical loss function is constructed based on the dynamic equations of the boat's motion, and the corresponding physical constraint residual equations include three:

[0027] The first residual equation is the mass of the boat multiplied by the sway acceleration minus the product of the sway velocity and the bow roll velocity, minus the horizontal thrust.

[0028] The second residual equation is the mass of the boat multiplied by the sway acceleration, plus the product of the pitch velocity and the yaw rate, minus the lateral force.

[0029] The third residual equation is the yaw moment of inertia on the z-axis multiplied by the yaw acceleration, minus the yaw torque; the data loss function is the mean square error between the predicted value of PINN and the actual value of the ship's motion state.

[0030] The total loss function is the sum of the calculated results of the data loss function and the physical loss function.

[0031] Preferably, in step S23, before training PINN, the input and output variables of PINN are subjected to min-max normalization. The specific processing method is as follows:

[0032] The minimum value in the original data is subtracted from the original data, and then divided by the difference between the maximum and minimum values ​​of the original data to obtain the normalized data. During training, the fourth-order Runge-Kutta method is used to calculate the state prediction value of the next time step, and the state prediction value and the action quantity are input into PINN for iterative training.

[0033] Preferably, in step S23, the optimizer is the Adam optimizer;

[0034] When it is necessary to capture the periodic features of boat motion, the Snake activation function is used. The Snake activation function is calculated by adding the input value and then dividing it by the parameter α, and the parameter α is optimized and adjusted during training.

[0035] Preferably, it also includes a model performance verification step:

[0036] Using the Mariner boat model as the object, the Z-shaped maneuvering test data of the boat model was used for verification; among them, the 20° / 20° Z-shaped maneuvering test data was used for model training, and the sampling frequency of the training data was 10Hz and the sampling duration was 600s;

[0037] The 30° / 30° Z-shaped manipulation test data was used for model generalization testing. The sampling frequency of this test data was 10Hz and the sampling duration was 700s.

[0038] The root mean square error and the coefficient of determination are used as evaluation indicators for model performance. The accuracy of the model is evaluated by calculating the numerical values ​​of these two indicators.

[0039] Compared with the prior art, the beneficial effects of the present invention are:

[0040] This invention addresses the problems of weak robustness, insufficient interpretability, and limited fusion methods of vessel maneuvering motion identification models under the influence of complex environmental factors. It analyzes the characteristics of intelligent vessel maneuvering motion, considering the influence of hydrodynamics, rudder angle, and propeller on vessel motion, describing the vessel's motion under different maneuvering conditions, determining the physical laws governing vessel motion, and constructing a mechanistic model. It also analyzes the impact of uncertainties, constructing a data model to address the uncertainties caused by natural environmental influences, changes in the vessel's own load, and errors generated by sensors in information acquisition and transmission in complex navigation environments. Finally, based on the aforementioned mechanistic model and data-driven model, a vessel maneuvering motion fusion model is constructed. Attached Figure Description

[0041] Figure 1 A flowchart of a machine learning method for identifying and modeling the physical information of intelligent boat handling motion provided by the present invention;

[0042] Figure 2 This is a diagram of the overall architecture of the PINN algorithm of this invention;

[0043] Figure 3 The PINN algorithm iteration process loss convergence graph;

[0044] Figure 4 A comparison chart of prediction results and errors for the training set;

[0045] Figure 5 A comparison chart of prediction results and errors for the test set;

[0046] Figure 6 This is a graph showing the evaluation metrics for the test set. Detailed Implementation

[0047] Please refer to Figure 1-6 The purpose of this invention is to address the limitations and shortcomings of using the Kalman filter algorithm to obtain displacement and attitude information during the autonomous berthing and unberthing process of unmanned surface vessels. This invention introduces an adaptive mechanism to optimize and improve the multi-source sensor information fusion algorithm, proposing an improved Kalman filter algorithm based on adaptive theory. The flowchart of this invention is shown below. Figure 1 As shown.

[0048] Construction of a fusion model for intelligent vessel handling motion:

[0049] This study analyzes the maneuvering characteristics of intelligent vessels, considering the influence of hydrodynamics, rudder angle, and propeller mechanisms on vessel motion. It describes the vessel's motion under different maneuvering conditions and constructs a mechanistic model. The study also analyzes the impact of uncertainties, constructing a data model to address the uncertainties caused by the natural environment, changes in the vessel's own load, and errors generated by sensors in information acquisition and transmission. Based on the aforementioned mechanistic and data models, a mechanistic-data fusion model is constructed, and the fusion method is studied to build a highly nonlinear vessel maneuvering motion model.

[0050] The goal of boat motion modeling is to establish a mathematical model that takes the boat's motion state, thrust, and rudder angle as inputs and produces an optimal fit between the boat's actual response and the model's predictions. The more accurate the mapping between input and output, the smaller the gap between the established model and the real model. Referring to Abkowitz's famous overall boat model, with the fixed coordinate system G of the hull as the origin, the hydrodynamic forces and torques acting on the boat are expressed as functions of motion variables and rudder angle, with velocity components as state variables and rudder angle as control variables. The boat dynamics model can be written as:

[0051] (1)

[0052] In the formula, m is the mass of the vessel (including additional mass). Let z be the yaw moment of inertia along the z-axis. Let be the longitudinal coordinate of the ship's center of gravity. and These represent the projections onto the sway acceleration, lateral sway acceleration, and pitch acceleration, respectively.

[0053] The Abkowitz holistic model treats the boat, propeller, and rudder as a whole, and considers the hydrodynamic force F acting on the boat as a function of the motion input and control input, i.e. Assuming the boat is traveling at a constant speed, the Taylor series expansion, retaining only the third-order terms, can be represented by the Abkowitz global mathematical model as follows:

[0054] (2)

[0055] In the formula, and It is a nonlinear function relating the vessel's velocity or angular velocity to the rudder angle, containing first to third-order hydrodynamic derivatives. and It is the derivative of the angular acceleration of a ship or the acceleration of a fluid.

[0056] This paper uses the Abkowitz global model as a reference to construct a mechanism model, and applies Equation (2). The Taylor series expansion is used to approximate the hydrodynamic forces and moments of the boat's motion. The hydrodynamic forces and moments can be described dimensionlessly as follows:

[0057] (3)

[0058] Since the influence of uncertain factors such as environmental disturbances and changes in the vessel's own load is not easy to quantify accurately, it is difficult to use them as specific inputs to the model. Therefore, it is necessary to consider the changes in the vessel's motion variables under the influence of external factors. This paper constructs an identification model to fit the dynamic change response of the vessel to uncertain disturbances within the data-driven model.

[0059] Considering that the motion variables u, v, and r of a vessel are affected by external environmental factors and the vessel's own characteristics during actual navigation, the measured motion variables such as u, v, and r will contain uncertainties. The goal of building a data-driven model for vessel maneuvering motion is to establish a mathematical model that takes the vessel's motion state, thrust, and rudder angle as inputs and produces an optimal fit between the model's predictions and the actual response. This modeling approach aims to fit the vessel's dynamic response to uncertainties and bridge the hydrodynamic gap between the actual vessel system and the mathematical model.

[0060] The parameters that affect a vessel during actual navigation can be expressed as:

[0061] (4)

[0062] In the formula, These are the actual motion parameters of the boat. These are the motion parameters of the boat under undisturbed conditions. The motion parameters of the vessel caused by uncertain disturbances can be expressed as:

[0063] (5)

[0064] In the formula, The effects of changes in the vessel's navigation status and the influence of sensors, The effects of wind, The impact of the waves, The effects of the flow.

[0065] Based on the formula following a nonlinear mapping function, we can obtain... and With u, v, r and The relationships between them are used as the model to be identified:

[0066] (6)

[0067] In the formula, Indicates and and Related nonlinear functions, and The calculation formula is:

[0068] (7)

[0069] In the formula, Sampling time.

[0070] The results obtained from actual navigation or free navigation model experiments Substituting into the above formula, we get the result reflecting the input. To output A large amount of data on mapping relationships.

[0071] (8)

[0072] In the formula, This represents the true value of the boat's motion state. These are the predicted values ​​obtained from the mechanistic model. The residual between the actual values ​​of the vessel's motion state and the predicted values ​​from the mechanistic model. This represents the predicted value of the residual. and As input to the mechanistic model, For output, and As input to the data-driven model, This is the output.

[0073] By adding a hydrodynamic correction term to the nonlinear mechanism model A mechanism- and data-driven weighted fusion model is established. This correction term can theoretically estimate the hydrodynamic error caused by the idealized approximation. The weights of the mechanism model and the data-driven model in the weighted fusion model are set as shown in equation (9):

[0074] (9)

[0075] In the formula, Represented as a weighted fusion model, Represented as a mechanistic model, This is represented as a data-driven model.

[0076] The overall structure of the weighted fusion model is represented as follows:

[0077] (10)

[0078] The data-driven part focuses on predicting residuals, establishing a direct summation connection between the predicted residual values ​​and the predicted values ​​of the mechanistic model, thereby achieving a combination of mechanistic and data-driven models.

[0079] Intelligent vessel maneuvering motion recognition modeling based on physical information neural networks:

[0080] Variables in boat motion data must obey their kinematic and dynamic equations. However, traditional machine learning algorithms lack sufficient guidance from physical knowledge, leading to low information utilization efficiency. The PINN method in deep learning integrates physical principles into neural network modeling, aiming to capture the dynamic behavior of intelligent boats and establish a horizontal three-degree-of-freedom boat maneuvering motion model with long-term predictive capabilities. By introducing a loss term based on physical information during the training phase, the network ensures that its predictions are consistent with established physical laws. PINN combines the advantages of data-driven machine learning with physical models, enabling the identification model's predictions to follow the physical laws governing boat motion.

[0081] The motion of an intelligent vessel in a complex environment is a nonlinear, time-varying dynamic system. The system state consists of the vessel's attitude angles, speed, and angular velocity; propeller speed and rudder angle are the control variables; and the state derivatives include the accelerations of the three horizontal degrees of freedom (sway, pitch, and roll). In an intelligent vessel motion system, the state is represented by S, and the motion input is represented by A. To construct an equivalent vessel motion model, a function F needs to be determined, which includes the parameter θ*, to describe the mapping relationship from the state space to the state derivative space.

[0082] (11)

[0083] The PINN function is used to fit the boat's motion state, predicting it using the current motion state and control input. Its state derivative at time step n is expressed as:

[0084] (12)

[0085] In the formula, Sn and An represent the current state and action input of the boat's motion, respectively, and θ* represents the network parameters. Therefore, the core of constructing the AUV dynamic model lies in determining the parameters θ* of the FPINN network.

[0086] The overall architecture of the PINN algorithm is as follows: Figure 2 As shown, the input layer contains the state variables and control variables of the boat's motion, i.e.

[0087] (13)

[0088] In the formula, Represents the velocity vector. Including thrust rudder angle and rudder angle Therefore, the network input is a tensor of shape 6×Nbatch (Nbatch represents the number of data in each batch). The output layer consists of state change variables and the combined external forces and torques, i.e.

[0089] (14)

[0090] In the formula, Represents the acceleration vector. Representing the forces and torques acting on the boat, the network output is a tensor of shape 6×Nbatch. The hidden layers use the hyperbolic tangent activation function, while the output layer uses the linear activation function.

[0091] PINN embeds physical constraint equations into the loss function, implementing physical constraints during training by constructing residual terms. The physical constraint loss function is defined as follows:

[0092] (15)

[0093] The physical constraint residual equation is as follows:

[0094] (16)

[0095] In the formula, m is the mass of the boat. Let X be the yaw moment of inertia, and let X, Y, and N be the horizontal thrust, lateral displacement, and yaw moment, respectively.

[0096] The data-driven mean squared error loss function is defined as:

[0097] (17)

[0098] In the formula, It is the network's predicted value, and It is the actual value.

[0099] The total loss function is:

[0100] (18)

[0101] The network parameters θ* are updated using the Adam optimizer by minimizing the total loss function:

[0102] (19)

[0103] To avoid gradient vanishing or exploding problems caused by differences in data scale, input and output variables are normalized when calculating the physical constraint loss. A fourth-order Runge-Kutta method is used to calculate the state prediction value for the next time step, and this value, along with the action value, is input into the network for iterative training to improve the model's long-term predictive ability.

[0104] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "include," "contain," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0105] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A machine learning-based modeling method for intelligent boat handling motion identification based on PINN, characterized in that, Includes the following steps: S1. Construct a fusion model of intelligent vessel handling motion: S11. Analyze the maneuvering characteristics of intelligent vessels, considering the influence of three types of mechanistic factors—hydrodynamics, rudder angle, and propeller—on the vessel's motion, describe the vessel's motion process under different maneuvering conditions, and construct a mechanistic model. The mechanism model is constructed with reference to the Abkowitz global model, and uses Taylor series expansion while retaining third-order terms to describe the hydrodynamics and torques during the boat's motion in a dimensionless manner. The Abkowitz holistic model treats the boat, propeller, and rudder as a whole, represents the hydrodynamic forces acting on the boat as functions of motion and control inputs, and uses swell velocity, roll velocity, and bow angular velocity as state variables, and rudder angle as control variable. S12. Analyze the characteristics of uncertainties affecting the navigation process of the vessel. Considering the influence of the natural environment, the changes in its own load, and the errors caused by the sensors in collecting and transmitting information, construct a data-driven model. The data-driven model uses the vessel's motion state, thrust, and rudder angle as inputs to fit the dynamic change response of the vessel to the above-mentioned uncertainties. S13. Based on the aforementioned mechanism model and data-driven model, construct a fusion model of ship handling motion that integrates mechanism and data; S2. Intelligent vessel maneuvering motion recognition and modeling based on physical information neural networks: S21. Determine the input and output of PINN: The input layer contains the state variables and control variables of the boat's motion, and the output layer contains the state change variables of the boat's motion and the combined external forces and torques; S22. Design the loss function of PINN: including a physical loss function based on the physical laws of boat motion and a data loss function based on data-driven mean square error. Couple the physical loss function and the data loss function to obtain the total loss function. S23. Training PINN: By minimizing the total loss function, the network parameters of PINN are updated using an optimizer to complete the construction of the intelligent boat handling motion recognition model.

2. The intelligent vessel maneuvering motion machine learning identification and modeling method based on PINN according to claim 1, characterized in that, The boat motion parameters caused by uncertainty disturbances include four parts: parameters caused by changes in the boat's navigation state and sensor effects, parameters caused by wind effects, parameters caused by wave effects, and parameters caused by current effects. The actual motion parameters of a boat are equal to the sum of the motion parameters of the boat under undisturbed conditions and the motion parameters of the boat caused by the aforementioned uncertainties and disturbances.

3. The intelligent vessel maneuvering motion machine learning identification and modeling method based on PINN according to claim 1, characterized in that, The fusion model is a weighted fusion model, which is obtained by multiplying the mechanism model and the data-driven model by their respective weights and then adding them together. The weights of the mechanism model and the data-driven model are preset weight coefficients. The data-driven model focuses on predicting residuals, which are the differences between the actual values ​​of the vessel's motion state and the predicted values ​​of the mechanistic model. The residual predictions and the mechanistic model predictions are connected by direct summation, thus combining the mechanistic model with the data-driven model.

4. The intelligent vessel maneuvering motion machine learning identification and modeling method based on PINN according to claim 1, characterized in that, The state variables of the PINN input layer are velocity vectors, which include sway velocity, roll velocity, and pitch velocity; the control variables include thrust, yaw angle, and rudder angle. The tensor shape of the input layer is a tensor that is 6 times the number of data in each batch, where the number of data in each batch is the sample size of the input data in each batch during training. The state change variables of the output layer are acceleration vectors, which include sway acceleration, roll acceleration, and pitch acceleration. The combined external forces and moments include horizontal thrust, lateral force, and yaw moment; the tensor shape of the output layer is also a tensor of 6 times the number of data in each batch.

5. The intelligent vessel maneuvering motion machine learning identification and modeling method based on PINN according to claim 1, characterized in that, PINN has at least 3 hidden layers, with 128 neurons in each of the 1st to 4th hidden layers and 64 neurons in the 5th hidden layer. The hidden layer uses the hyperbolic tangent activation function, the output layer uses the linear activation function, and the dropout coefficient of the hidden layer is set to 0.2 to prevent the model from overfitting.

6. The intelligent vessel maneuvering motion machine learning identification and modeling method based on PINN according to claim 1, characterized in that, The physical loss function is constructed based on the dynamic equations of the boat's motion, and the corresponding physical constraint residual equations include three: The first residual equation is the mass of the boat multiplied by the sway acceleration minus the product of the sway velocity and the bow roll velocity, minus the horizontal thrust. The second residual equation is the mass of the boat multiplied by the sway acceleration, plus the product of the pitch velocity and the yaw rate, minus the lateral force. The third residual equation is the yaw moment of inertia on the z-axis multiplied by the yaw acceleration, minus the yaw torque; the data loss function is the mean square error between the predicted value of PINN and the actual value of the ship's motion state. The total loss function is the sum of the calculated results of the data loss function and the physical loss function.

7. The intelligent vessel maneuvering motion machine learning identification and modeling method based on PINN according to claim 1, characterized in that, Before training PINN, the input and output variables of PINN are processed using min-max normalization. The specific processing method is as follows: Subtract the minimum value from the original data, and then divide by the difference between the maximum and minimum values ​​of the original data to obtain the normalized data. During training, the fourth-order Runge-Kutta method is used to calculate the state prediction value for the next time step, and this state prediction value is input into PINN along with the action quantity for iterative training.

8. The intelligent vessel maneuvering motion machine learning identification and modeling method based on PINN according to claim 1, characterized in that, The optimizer is the Adam optimizer; When it is necessary to capture the periodic features of boat motion, the Snake activation function is used. The Snake activation function is calculated by adding the input value and then dividing it by the parameter α, and the parameter α is optimized and adjusted during training.

9. The intelligent vessel maneuvering motion machine learning identification and modeling method based on PINN according to claim 1, characterized in that, It also includes a model performance verification step: Using the Mariner boat model as the object, the Z-shaped maneuver test data of the boat model were used for verification; among them, the 20° / 20° Z-shaped maneuver test data were used for model training, and the sampling frequency of the training data was 10Hz and the sampling duration was 600s; The 30° / 30° Z-shaped manipulation test data were used for model generalization testing. The sampling frequency of the test data was 10Hz and the sampling duration was 700s. The root mean square error and the coefficient of determination are used as evaluation indicators for model performance. The accuracy of the model is evaluated by calculating the numerical values ​​of these two indicators.

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